[
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure13-1.png",
        "caption": "Fig. 13. 5\u20135\u20135 RPR-equivalent PMs in the second family. (a) 2-uRPFS/DSvPR. (b) 2-uPRFS/DSvPR. (c) 2-uRRFS/DSvRR. (d) 2-uRPRijU/DSvRR",
        "texts": [
            " However, for example, one can set i = v and j = w for a uRPRijU limb and i = w and j = u or a ijUvRRR or a ijUvRPR limb. A 2- uRPRvwU/wuUvRRR and a 2-uRPRvwU/wuUvRPR PM is, thus, obtained as shown in Fig. 11. We can readily verify that the wR pairs in vwU and wuU are idle, and the 2-uRPRvwU/wuUvRRR works like an overconstrained 2-uRPRvR/uRvRRR PM. Table VII enumerates 49 RPR-equivalent PMs in this category Fig. 12 shows four RPR-equivalent PMs belonging to the first family in 5\u20135\u20135 category. For the readers\u2019 sake, Fig. 13 shows four RPR-equivalent PMs belonging to the second family in the 5\u20135\u20135 category. B. {L1} = {X(u)}{X(v)} and {L2} = {G(u)}{S(F )} With F (B,v) and {L3} = {S(D)}{G(v)} With D \u2208 axis(O, u) When {L1} = {X(u)}{X(v)} and {L2} = {G(u)}{S (F)}, the intersection of {L1} and {L2} is given by {L1} \u2229 {L2} = {X(u)}{X(v)} \u2229 {G(u)}{S (F) } = {G(u)}{R(B, v)}{T(u)} \u2229 {G(u)}{R(B,v)} \u00d7{R(F, i)}{R(F, j)} = {G(u)}{R(B,v)}({T(u)} \u2229 {R(F, i)}{R(F, j)}) = {G(u)}{R(B,v)}. (22) Let {L3} = {S(D)}{G(v)} with D \u2208 axis(O, u)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001409_1.1698540-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001409_1.1698540-Figure12-1.png",
        "caption": "FIG. 12. Flow around a rotating sphere.",
        "texts": [
            " Considering the possible differences in size and surface condition of the balls, the agreement is reasonably good and undoubtedly better agreement would be found by substituting accepted values for the velocities. DISCUSSION OF NEGATIVE LIFT Bernoulli's theorem states that for ideal frictionless flow, along any stream line the total energy is constant, i.e., p+ p V2/2+ pgh= a constant. (14) A qualitative explanation of the Magnus effect can be given on this basis. With the sphere rotating clockwise as in Fig. 12, the velocity at a on stream line A is higher than at b on stream line B. Since the kinetic energy is higher at a than at b, the pressure is lower at a than at b and there is a resultant upward force. The wake is deflected downward. This accounts for the experience with a rough sphere such as a standard golf ball and with a smooth sphere at high rotational speeds but not for the opposite effect with a smooth sphere at low rotational speeds. At low velocities this situation is disturbed by fric tion and turbulence",
            " 826 curve but above the critical region the experimental curves approach the ideal case rather closely. To a reasonable approximation, the conditions on the opposite sides of a rotating sphere may be represented by the pressure curves for a stationary sphere, using the appropriate velocities for each side. On the side rotating against the wind stream, the effective Rey nolds' number is high and on the side rotating with the wind stream it is low. For low rotational speeds, the conditions at a in Fig. 12 might correspond roughly to the curve for Vo=35 feet per second in Fig. 13 and the conditions at b to the curve for Vo= 135 feet per second. This analogy does not hold for the whole surface but fits fairly well in the region near cp = 90\u00b0 which is of most importance in determining the lift since the effec- tive vertical component of the normal pressure is high in this region. On this basis it is evident that the pres sure at b is lower than at a and the transverse force will be downward or the lift is negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000236_s0890-6955(99)00076-0-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000236_s0890-6955(99)00076-0-Figure4-1.png",
        "caption": "Fig. 4. Waviness on the inner race.",
        "texts": [
            " (5) is a function of instantaneous movements of the shaft centre in the horizontal radial plane; x, y and the axial direction: z [14]: di5x cos qi cos a1y sin qi cos a1z sin a2 C 2 (14) The ball-to-races contact deflection is, therefore, a function of the cage rotational frequency as well as a function of the diametral clearance, itself a function of surface topography of the rolling and mating members. The diametral clearance, C, for a perfect bearing is obtained as [24]: C052(ro1ri2d)(12cos a0) (15) The surface waviness of bearing rings and balls introduces a variation in the diametral clearance C, being a function of the number of waves and the corresponding speed of the appropriate member. Thus [7]: C52Hro1ao sinS2p,o lo D1ro1ai sinS2p,i li D2d22ab sinS2p,b lb DJ(12cos a) (16) Where in general ,=Rf (see Fig. 4) and R is the radius of the rolling member (races or ball). Surface waviness occurs on the inner and outer raceway tracks, as well as on individual balls. Therefore, the wavelength, l, for each surface is given as: l5 2pR n (17) Replacing for , and l in Eq. (16) for each surface, the diametral clearance can be obtained and halved to give the radial internal clearance in the direction of each ball contact at any instant of time. The total contact deflection in any radial direction is then obtained by replacing for this radial internal clearance (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000150_j.jmatprotec.2007.10.051-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000150_j.jmatprotec.2007.10.051-Figure12-1.png",
        "caption": "Fig. 12 \u2013 Schematic sections through location A\u2032\u2013A\u2032\u2032 in Fig. 11. (a) SMD weld bead lay-up, (b) post flange machining and (c) final specimen extraction operation.",
        "texts": [],
        "surrounding_texts": [
            "The current trials have demonstrated the potential of SMD technology in the fabrication of complex engineering structures. Within the aerospace sector, the near net shape capability of additive SMD should offer obvious benefits in terms of improved materials yield and a reduction in mechanical surface removal operations\u2014both key factors controlling the cost of individual components. SMD provides a relatively rapid manufacturing process for large-scale features and can be automated through efficient multi-axis and multi-arm robotic controlled welding systems. n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 439\u2013448 446 j o u r n a l o f m a t e r i a l s p r o c e s s i However, detailed consideration must be given to the ultimate metallurgical and microstructural condition evolved during SMD manufacture. In particular, the present study has highlighted the presence of deleterious phases within the Alloy 718 MIG weld deposition structures (i.e. relatively brittle laves and phase segregation encouraged by extended time at high temperature during either deposition, through the cumulative exposure to transient deposition, or subsequent post-deposition heat treatment (PDHT)). The present study has confirmed previous reports (Cieslak et al., 1986; Jones et al., 1989), noting that these phases evolve in preferred orientations, potentially inducing an anisotropic mechanical response under subsequent loading. Volumetric changes associated with phase transformation may also have a local shearing effect across interfaces. In addition, associated discontinuities in the form of cracks and shrinkage porosity have been identified. In DS/ML weld deposition structures, the degree of reheating introduced during overlay operations appears to be critical for controlling the introduction of these defects (Metallographic Characterisation of IN718, 2003; Bowers et al., 1997; Qian and Lippold, 2003a,b). However, despite systematic optimization of the major weld control parameters such features persist. This may prove to be a significant limitation in considering MIG for aerospace applications. Added to this, the adverse effects of residual stress have also been demonstrated (affected during either machining or PDHT operations) through the introduction of macroscopic cracking in this feature of the demonstrator casing component. For high integrity components in aero gas turbines subjected to relatively demanding loading regimes, such phases as laves and delta must either be eliminated through precise thermo-mechanical processing or otherwise demonstrated to be \u201cbenign\u201d under typical service conditions (i.e. the component demonstrates sufficient \u201cphase tolerance\u201d and resists the formation of a critically sized crack from a pre-existing flaw over a specified period of operation). Given this philosophy, the major engine manufacturers appear to be adopting consistent strategies for additive manufacture (AM), restricting the techniques\u2019 potential use to non-critical component locations at this stage of process maturity (Kinsella, 2006). Even in the present example of the developmental combustor casing, the SMD flange was designed as an additive feature upon an internal wall pedestal, ensuring the flange itself would not experience design limiting hoop stresses. However, casing structures routinely experience at least one major fatigue cycle per flight; the thermal\u2013mechanical cycle imposed during normal engine use and shut down. High cycle fatigue may also be superimposed as a result of vibration. Therefore, improvements in additive technologies to avoid the introduction of crack initiating defects would clearly be advantageous. It is unlikely that MIG-based SMD used for hybrid near net shape components without a homogenisation treatment can eliminate the laves phase formation, due to the restrictions on pool size and hence the influence on freezing rate and segregation. To this end, methods of metal deposition, having smaller volumetric build unit sizes, may prove more suitable for the manufacture of higher integrity components. By controlling the build up of material on the microscopic scale (for example individual molten \u201cpools\u201d may be less than a millimetre diam- deposition) structure in Alloy 718. eter with some AM techniques) any incipient porosity, the evolving grain size and the internal microstructure are all fundamentally smaller. The resultant volume of material should also demonstrate more homogeneous mechanical properties and any long range residual stresses minimized. Macro-scale demonstration components are currently under manufacture for future detailed characterization (Fig. 14)."
        ]
    },
    {
        "image_filename": "designv10_1_0000426_9781118680469-Figure13.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000426_9781118680469-Figure13.9-1.png",
        "caption": "FIGURE 13.9 Bilayer model of artificial muscle.",
        "texts": [
            " This electrochemically controllable volume change is reminiscent of the actuation in natural muscle tissue and is currently the most promising component of artificial muscles. The simplest version of artificial muscles is composed of a bilayer of the CP film and the passive layer [96]. In this system, the dimensions of the CP layer are electrochemically controlled to produce a stress gradient across the two film interfaces and results in macroscopic bending. A typical artificial muscle constructed from the CP/passive layer model is shown in Figure 13.9. The oxidation of the CP film promotes the inclusion of electrolyte into the film which causes swelling and anticlockwise bending. The reduction of the film induces the expulsion of electrolyte and therefore the device bends in the clockwise direction. In these systems, a conductive counter electrode is required to allow the current flow and generate electrochemical reaction that causes the volume change of the CPs. Valero et al. describe a PPy\u2013dodecylbenzenesulfonate\u2013perchlorate/tape bilayer artificial muscle with reversible movements through subsequent oxidation and reduction of the PPy layer [97]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000927_0094-114x(82)90042-8-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000927_0094-114x(82)90042-8-Figure4-1.png",
        "caption": "Figure 4. Uncertainty configuration.",
        "texts": [
            ") Figure 3(a-f) illustrate the displacement functions of a spatial 5-1ink RCRCR mechanism with dimensions au = lO/~(3)m 0/12 = 150 o S l ! = lOm a23 = 10.0 a23 = 315 \u00b0 $33 = 5/V'(2) a34 = 5/X/(2) 0/34 = 2700 $55 = 20 a45 = 0.0 0/45 = 90 \u00b0 aSl = 20/~/(3) 0/51 = 300 \u00b0 All the 6 \u00d7 6 determinants were zero at 05 = 90% and the determinant of the screws of the C2 - R3 - C4 - R5 pairs plotted against 0s is superimposed on the input-output function 01 VS 05 in Fig. 3(a). The mechanism has an uncertainty configuration as illustrated by Fig. 4, and all the, displacement functions Figs. 3(a-f) exhibit a double root at 05 = 90 \u00b0. Consider now that a 6 x 6 determinant Di = 0 (i denotes the 6 \u00d76 determinant which excludes the ith screw) of the 7 x 6 matrix of the Pliicker coordinates. It follows that all the screws except the ith screw are linearly dependent and, therefore, the ith joint cannot move instantaneously. Figure 5 illustrates the input--output function 01 vs 05 of an RCRCR mechanism with the following dimensions al2 = 25 m 0~12 = 60 \u00b0 S "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001958_tie.2016.2595481-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001958_tie.2016.2595481-Figure3-1.png",
        "caption": "Fig. 3. One-link manipulator.",
        "texts": [
            " In this section, two practical examples are given to illustrate to application of Theorem 1 and the corresponding controller. 0278-0046 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. First, a popular benchmark of application example, i.e., the tracking control of a one-link manipulator actuated by a brush dc (BDC) motor is presented. A one-link manipulator is shown in Fig. 3, whose dynamics is described by [37]{ Dq\u0308 + Bq\u0307 + N sin(q) = I + \u2206I MI\u0307 = \u2212HI \u2212Kmq\u0307 + V, (28) where q, q\u0307 and q\u0308 stand for the link angular position, velocity, and acceleration, respectively; I denotes the motor current; V represents the input voltage; and \u2206I is the current disturbance. Notice that the first subsystem in (28) stands for the dynamics of the one-link robot, and the second subsystem represents the dynamics of the BDC motor. Usually, the motor dynamics are neglected in the servo control design [37], since the electrical dynamics are inherently faster than the mechanical dynamics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001961_978-3-319-68792-6_51-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001961_978-3-319-68792-6_51-Figure3-1.png",
        "caption": "Fig. 3. Team Delft gripper.",
        "texts": [
            " We also learned that suction was the better performing grasp option, which we confirmed in early tests. The solution designed is based on an industrial robot arm, a custom made gripper and 3D cameras, as shown in Fig. 2. For the robot arm we chose a 7 degrees of freedom SIA20F Motoman mounted on an horizontal rail perpendicular to the shelf. The resulting 8 degrees of freedom allowed the system to reach all the bins with enough manoeuvrability to pick the target objects. We customized our own gripper to handle all the products in the competition (see Fig. 3). It has a lean footprint to manoeuvre inside the bins, and a 40 cm length to reach objects at the back. It includes a high flow suction cup at the end, with a 90\u25e6 rotation allowing two orientations, and a pinch mechanism for the products difficult to suck. Both the suction cup rotation and the pinch mechanism are pneumatically actuated. A vacuum sensor provides boolean feedback whether the suction cup holds anything. For object detection a 3D camera is mounted in the gripper to scan the bins, while another one is fixed on a pole above the tote"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001502_j.steroids.2018.12.003-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001502_j.steroids.2018.12.003-Figure6-1.png",
        "caption": "Fig. 6. Mechanisms involved in detection of cholesterol using Hb as mediator of electrons for detection of H2O2 [44].",
        "texts": [
            "0 phosphate buffer solution when ChOx was further immobilized on the PANI/Au modified electrode. This result showed that the PANI/Au nanocomposite was a good candidate for the development of the cholesterol biosensor. The biosensor displayed a response time of 3 s. Some common interferents like glucose and ascorbic acid did not cause interference due to the use of a low operating potential [44]. Sophisticated molecular architectures can be produced with the layer-by-layer (LbL) method, which may combine distinct materials on the same film (Fig. 6). In this study, cholesterol amperometric biosensor was designed from LbL films containing hemoglobin (Hb) and cholesterol oxidase in addition to the polyelectrolytes poly(allylamine hydrochloride) (PAH) and poly(ethylene imine) (PEI). Following an optimization procedure, an LbL film deposited onto ITO substrates, with the architecture ITO(PEI/Hb)5(PEI/COx)10, yielded a sensitivity of 93.4 \u03bcA \u03bcmol L\u22121 cm\u22122 for cholesterol incorporated into phospholipid liposomes, comparable to state-of-the-art biosensors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.32-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.32-1.png",
        "caption": "Fig. 3.32 Empennage layout",
        "texts": [
            " In steady forward flight, the horizontal tailplane generates a trim load that reduces the main rotor fore\u2013aft flapping; similarly, the vertical fin generates a sideforce and yawing moment serving to reduce the tail rotor thrust requirement. In manoeuvres, the tail surfaces provide pitch and yaw damping and stiffness and enhance the pitch and directional stability. As with the fuselage, the force and moments can be expressed in terms of coefficients that are functions of incidence and sideslip angles. Referring to the physical layout in Figure 3.32, we note that the principal components are the tailplane normal force, denoted Ztp, and given by Ztp = 1 2 \ud835\udf0cV2 tpStpCztp (\ud835\udefctp, \ud835\udefdtp) (3.252) which gives rise to a pitching moment at the centre of gravity, i.e. Mtp = (ltp + xcg)Ztp (3.253) and the fin sideforce, denoted by Yfn, i.e. Yfn = 1 2 \ud835\udf0cV2 fnSfnCyfn(\ud835\udefcfn, \ud835\udefdfn) (3.254) 126 Helicopter and Tiltrotor Flight Dynamics which gives rise to a yawing moment at the centre of gravity, i.e. Nfn = \u2212(lfn + xcg)Yfn (3.255) where Stp and Sfn are the tailplane and fin areas, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure23.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure23.5-1.png",
        "caption": "Fig. 23.5 Example structures and profile customization",
        "texts": [
            " The most important findings during the investigation of requirements was that designers could easily create parts in NX that neither obey the yard standards nor were supported by manufacturing. As a result this requires performing the appropriate customization of NX and some kind of validation functionality as part of the link between two CAD systems. The customization of the CAD system serves two purposes: it should support designers with ready-made building blocks like profile cross sections and it should ensure successful data export. As with all kinds of customizations it is important to find the right granularity of building blocks (Fig. 23.5). There should be a balance between patronizing the designer by providing only a few canned solutions and leaving too much freedom. 23 Shipbuilding 681 The second and more involving step in the project was the design and implementation of a solution for the link between the two CAD systems. This link had to transfer the information created in NX containing the manufacturing geometry, validate it against rules defined by the yard and import it into TRIBON for manufacturing purposes. The fundament for all involved activities is the data model of the link solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001409_1.1698540-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001409_1.1698540-Figure1-1.png",
        "caption": "FIG. 1. Forces on a golf ball in flight.",
        "texts": [
            "22 On: Sat, 22 Nov 2014 12:57:39 Tait15 calculated the forces on a golf ball in flight by observing the trajectory and the time of flight and then attempted to explain the trajectory in terms of these forces. However, he had no convenient way of determin ing the ball velocities and, in general, the values he assumed were too high and the air forces correspond- ingly high but he was able to show that the transverse force had a significant effect on the trajectory. A typical golf ball trajectory is shown in Fig. 1, with a convenient way of defining the aerodynamic forces. The total force, R, is resolved into two com ponents, a drag, D, in the line of and opposite to the motion, and a lift, L, perpendicular to the motion. The lift is upward for the usual case of under spin and down ward for over spin. Frequently the axis of rotation is not exactly horizontal and then these forces have hori zontal components which cause \"hooking\" and \"slicing.\" In play velocities vary over a wide range; translational velocities of more than 225 feet per second and rota tional velocities up to 8000 r",
            " CALCULATED TRAJECTORlES Trajectories for given typical conditions would be interesting but without additional information the calculations cannot be made with any certainty. Neither the manner in which Land D vary with trans lational speed nor the time rate of change of rotational speed are known. Consequently, only a few calculations have been made, for the conditions assumed in Table I, and the results are shown in Fig. 14. The equations of motion are: tPx/dt2=(gD/W) cosO-(gL/W.) sinO (16) tPy/dt2=-g-(gD/W) sinO+(gL/W) cosO, (17) where the various terms have the meaning indicated in Fig. 1. The values of L, D and O[tanO= (dy/dt)/(dx/dt)] for the various cases were substituted in these equations and the values of x and y obtained by Moulton's method of successive approximations.25 \u2022\u2022 Moulton, N I'!W Methods in Exterior Ballistics (University of Chicago Press, Chicago, 1926). VOLUME 20, SEPTEMBER, 1949 Data for a direct check on these trajectories are not available but the results are reasonable. For all the cases, air resistance reduces the maximum theoretical carry by at least one-third"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001080_s00170-016-9429-z-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001080_s00170-016-9429-z-Figure10-1.png",
        "caption": "Fig. 10 Positive and negative angles and line coloring",
        "texts": [
            " In the case of L-PBF, the temperature gradient is largest in the build direction as the cooling occurs towards the base plate via conduction and towards the environment at the top layer. Analyzing the orientation of the dendrites may reveal the effect of different heating/cooling cycles resulting from process parameters on the microstructure of the IN625. The growth directions in the different microstructures resulting from different process conditions are identified with image analysis using MATLAB. By looking at the XZ cross section of the test coupons, boundaries of columnar grains are identified and their directions with respect to the Z axis are obtained (Fig.10). Looking at YZ cross sections would also yield similar results due to the rotational scan strategies. After the image processing algorithm detects growth directions in the SEM images, growth angles are calculated. These angles are positive in the counterclockwise direction from the Z axis, as shown in Fig. 9. Lines with positive inclination are shown in blue whereas lines with positive inclination are shown in red. Lines with angles close to 0\u00b0 appear white and coloring gets stronger with increasing angle magnitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000024_s0022112072001612-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000024_s0022112072001612-Figure5-1.png",
        "caption": "FIGURE 5. Measurements recorded in on0 cycle of a cilium\u2019s beat. Lagrangian point sk along cilium. (X, , Y,, Z,, T,) specifies the point during cycle, while the dashed line indicates its path through one cycle.",
        "texts": [
            " The general movement of a cilium a t a point (zl, xz) on the XIOXz plane was defined in (9), although in the numerical models we take gz = 0 because the available data is only in a two-dimensional form. The movement of a cilium is periodic, so we can represent & (i = 1,2 ,3) by a Fourier series expansion in 7. The following measurements are records of the cilium\u2019s movement. We take K stations along the length of a cilium, denoted by sk ( k = 1, . . ., K ) , and at each station sk we record the periodic movement of the cilium (X,, Y,, Z,, T,), p = I, . . ., 2N + 1. (Xp, Y 2,) denotes the path the point skon the cilium traces out in one cycle (see figure 5 ) . The Fourier series representation for gc (i = I, 2,3) is as follows: N n= 1 N n=l 1 = Bu,(s) + [u,(s) cos n7 + b,(s) sin n ~ ] , g2 = +co(s) + x [c,(s) cos n7 + d,(s) s inn~] , J N n=l g3 = ijo(s) + c [ f , ~ COB n7 + g,w sin n71, where a,(s), b,(s), c,(s), d,(s), fn(s) and g,(s) are polynomial functions of s, determined by a least-squares fit. The Fourier series coefficients a;, b t , . . . are obtained at each point s, and the polynomials a&), b,(s), . . . are then obtained by a least-squares fit to the coefficients",
            " Further inaccuracy occurs for the case of Paramecium, where the cilium\u2019s beat is plainly three-dimensional, but no reliable data are available on its three-dimensional movement. Pleurobrachia probably contravenes the low Reynolds number assumption, but on the other hand the best available data that we have are on this organism. The Fourier-series-least-squares process was used with N = 3 for Paramecium, N = 4 for Opalina and N = 5 for Pleurobrachia with M = 3 in all cases. The data were collected at 10 points along the cilium (excluding the origin). In figure 5 we see the approximate analytic representation for the movement of the cilia. It appears to be reasonably accurate except in regions of high curvature. It may be argued that it is pointless t o obtain the least-squares fit to the cilium\u2019s movement where a direct numerical approach would be more appropriate. We prefer the present approach because of the inadequacies of the data, so that in the following calculations the gradients used will be analytic values obtained from the Fourier-least-squares fit described in (31)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure5.14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure5.14-1.png",
        "caption": "Figure 5.14.3. Geometry of the steering axis of a wheel.",
        "texts": [
            " On the other hand, a low reverse efficiency helps to reduce the transmission of road roughness disturbances back to the driver, at the cost of some loss of the important feel that helps a driver to sense the frictional state of the road. Hence, there is a conflict in steering design which must be resolved according to the particular application. For independent suspension there are two principal steering systems in use, one based on a steering box, the other on a rack-and-pinion. In the typical steer- Suspension Characteristics 285 ing box system (Figure 5.14.1), known as the parallelogram linkage, the steering wheel operates the Pitman arm A via the steering box. The box itself is nowadays usually a cam and roller or a recirculating ball worm-and-nut system. The gear ratio of the box alone is usually somewhat less than that of the overall ratio because of the effect of the links. Symmetrical with the Pitman arm is an idler arm B, connected by the relay rod C, so that the whole linkage is geometrically symmetrical, although the forces are introduced on one side",
            " Precision is of great importance in the steering system, and the rack system has a superior reputation, although it is quite difficult to observe any substantial 286 Tires, Suspension and Handling difference between a rack and a good box system in comparative driving tests. To prevent play in the various inter-link ball-joints, they are spring-loaded. Where the suspension is mounted on a subframe which has some compliance relative to the body, in the interests of steering precision it is desirable to also mount the steering rack or box on the subframe. On trucks it is still common to use a rigid axle at the front, mounted on two longitudinal leaf-springs. Usually the wheel steering arms are connected together by a single tie-rod (Figure 5.14.2). Steering is effected by operating a second steering arm A on one of the wheels by the horizontal drag link B from a vertical Pitman arm C. This acts from the side of the steering box which is mounted on the sprung mass. For all systems, the wheels and hubs are pivoted about the kingpin axis (Figure 5.14.3). Nowadays, on cars at least, kingpins are no longer used; the steering axis is now defined by a pair of ball-joints. In front view the axis is at the kingpin inclination \u03b8k, usually from 0 to 20\u00b0, giving a reduced kingpin offset b at the ground. The inclination angle helps to give space for the brakes. Where the steering arms are forward (rack in front of the wheel centers) it also gives room to angle the steering arms for Ackermann geometry. Sometimes a negative offset is used, this giving straighter braking when surface friction varies between tracks",
            "065 kg m2, averaging 0.040 kg m2. However, they are connected by the overall gear ratio of typically 20, and inertias are factored by the gear ratio squared, so the steering wheel angular inertia referred to the road wheel motion is about 16 kg m2, which is much greater than that of the road wheels. The dominant compliance is the torsional compliance of the steering column, typically 25 Nm/rad. Depending on the design, sometimes other compliances should be included such as the long tie-rod D on a rigid axle (Figure 5.14.2). 5.14.2 Static Steering Torque The torque required to steer the road wheels is greatest for static vehicle con- ditions. Provided that the kingpin axis is not too far from the center of tire contact, for example if it is in the footprint, as it usually is, the following empirical equation gives a fair estimate of the static steering torque at the road wheel: where pi is the inflation pressure. The corresponding mean friction radius is 290 Tires, Suspension and Handling where is the equivalent inflation area",
            " These ideally balance from side-to-side, but will not do so when the driveshafts are at different angles for any reason, for example because they are of different lengths or because of body roll, or engine torque rock, or when the shaft torques are different as may occur when a limited-slip differential is fitted. The consequences of the tire forces may be found by considering the three forces and moments at the center of tire contact. The rolling resistance moment and the overturning moment are negligible in this context. The aligning torque, acting about the vertical axis, may easily be resolved into its component about the kingpin axis (Figure 5.14.3). The sum for the two wheels is This moment attempts to rotate the steering in such a way as to restore straight running. The tire lateral force acts at a distance c cos\u03b8 from the axis, so the steering moment for the pair of wheels for small \u03b8 is For positive caster offset c this acts in the same sense as the aligning torque moment, and therefore also has a stabilizing effect. The tractive force acts at a moment arm of d cos\u03a6 giving a wheel pair moment for small \u03a6 of Suspension Characteristics 291 The two tractive forces balance each other in the symmetrical condition but, as for the driveshaft torques, may be unbalanced with a limited-slip differential, especially on variable surfaces, this leading to the characteristic steering fight of limited-slip front-drive vehicles",
            " Also, the outer tire has greater vertical force, hence needing a greater slip angle than the inner tire for 294 Tires, Suspension and Handling maximum cornering force. Finally, roll steer effects may give a significant steer angle difference. Even anti-Ackermann (negative fA) has been used on occasion, and various steering geometries are used in practice. If the steering is not perfect Ackermann, then at low speed each wheel pair must adopt equal and opposite slip angles to give zero net force. The most convenient way to obtain the different steer angles of the Ackermann layout is to angle the steering arms inward (for a rack behind the kingpins), as in Figure 5.14.1, so that as steer is applied there is a progressive difference in the effective moment arms. This slanting of the arms also helps with wheel and brake clearance. It is widely believed that aligning the steering arms so that their lines intersect at the rear axle will give true Ackermann steering (the Jeantaud diagram). However, this is far from true; the actual Ackermann factor varies in a complex way with the arm angle, rack length, rack offset forward or rearward of the arm ends, whether the rack is forward or rearward of the kingpins, and with the actual mean steer angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000113_70.105387-Figure19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000113_70.105387-Figure19-1.png",
        "caption": "Fig. 19. Two antisymmetrical optimal paths.",
        "texts": [
            " The computation time for the branch and bound search was about 3 min of CPU time, and for the local optimizations about 20 min. Using a larger Omax would retain only one path, reducing computation time to about 5 min. The low computation time of the local optimization is attributed to the closeness of the initial guess to the optimal solution. The time spent to obtain a good initial guess with the branch and bound search was, therefore, well worth it. SHILLER AND DUBOWSKY: COMPUTING GLOBAL TIME-OPTIMAL MOTIONS 793 Fig. 19 shows a case where the optimization converged to two optimal paths. In this case, the end points are antisymmetric relative to the center, and as expected, there are two antisymmetrical optimal solutions with similar traveling times. The times are not identical for both paths because of the inaccuracies associated with the numerical optimization. B. Two-Link Manipulator with Obstacles The task for the manipulator is to move between the same end points as in Fig. 14 in minimum time while avoiding the obstacles shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.33-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.33-1.png",
        "caption": "Fig. 3.33 Influence of rotor downwash on tail surfaces",
        "texts": [
            " The local incidence at the tailplane, assumed constant across its span, may be written as \ud835\udefctp = \ud835\udefctp0 + tan\u22121 [ w + q(ltp + xcg) \u2212 k\ud835\udf06tp \u03a9R\ud835\udf060 u ] , u \u2265 0 (3.256) (\ud835\udefctp)reverse = (\ud835\udefctp)forward + \ud835\udf0b, u < 0 (3.257) The local flow velocity at the tail can be written in the form \ud835\udf072 tp = [ u2 + (w + q(ltp + xcg) \u2212 k\ud835\udf06tp \u03a9R\ud835\udf060)2 (\u03a9R)2 ] (3.258) where \ud835\udf07tp = Vtp \u03a9R (3.259) The parameter k\ud835\udf06tp defines the amplification of the main rotor wake uniform velocity from the rotor disc to the tail. The tailplane incidence setting is denoted by \ud835\udefctp0. The main rotor wake will impinge on the horizontal tail surface only when the wake angle falls between \ud835\udf121 and \ud835\udf122 (see Figure 3.33), given by \ud835\udf121 = tan\u22121 ( ltp \u2212 R hr \u2212 htp ) and \ud835\udf122 = tan\u22121 ( ltp hr \u2212 htp ) (3.260) otherwise, k\ud835\udf06tp can be set to zero. In Ref. 3.49, Loftin gives wind tunnel measurements for a National Advisory Committee for Aeronautics (NACA) 0012 aerofoil section for the complete range of incidence, \u2212180\u2218 <\ud835\udefc < 180\u2218. From these data, an approximation to the normal force coefficient can be derived in the form |Cztp | \u2264 Cztpl Cztp (\ud835\udefctp) = \u2212a0tp sin \ud835\udefctp (3.261) |Cztp | > Cztpl Cztp (\ud835\udefctp) = \u2212Cztpl sin \ud835\udefctp \u2223 sin \ud835\udefctp \u2223 (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000279_jsvi.2001.3848-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000279_jsvi.2001.3848-Figure1-1.png",
        "caption": "Figure 1. Rotational degree-of-freedom model of planetary gears.",
        "texts": [
            " For multi-stage gear systems, there are surprisingly few studies on parametric instabilities from multiple meshes. Tordion and Gauvin [7] and Benton and Seireg [8] analyzed the instabilities of two-stage gear systems with a mesh phasing between the two mesh sti!nesses. However, their instability conclusions are contradictory. This was recently clari\"ed by Lin and Parker [9] using perturbation and numerical analyses. Lin and Parker also derived simple formulae that allow designers to suppress particular instabilities by properly selecting contact ratios and mesh phasing. For planetary gears (Figure 1), which have multiple time-varying mesh sti!nesses, no systematic study on their parametric instability has been found in the literature. August and Kasuba [10] and Velex and Flamand [11] numerically computed dynamic responses to mesh sti!ness variations for planetary gears with three sequentially 0022-460X/02/010129#17 $35.00/0 ( 2002 Academic Press phased planets. Their results showed the dramatic impact of mesh sti!ness variation on dynamic response, tooth loads, and load sharing among planets",
            " In this same spirit, this study shows that particular parametric instabilities can be eliminated under certain phasing conditions that can be achieved by proper selection of design parameters. Tooth separation non-linearity induced by parametric instability is numerically simulated and shown to have great impact on the unstable system responses. 2. SYSTEM MODEL AND MODAL PROPERTIES The planetary gear dynamic model used is based on the one developed by Lin and Parker [12]. Translational degrees of freedom in that model are eliminated, and only rotational motions of the gear bodies are considered (Figure 1). Rotational motions of the carrier, ring, sun, and planets are denoted by h h , h\"c, r, s, 1,2 , N, where N indicates the number of planets. The gear bodies are assumed rigid with moments of inertia I c , I r , I s , I p . The sun}planet and ring}planet tooth meshes are modelled as linear springs with time-varying sti!nesses k sn (t), k rn (t), n\"1,2 , N. Damping and clearance non-linearity are not considered in the determination of instability boundaries, though they are added later in a numerical example for response calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001608_tie.2017.2772153-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001608_tie.2017.2772153-Figure1-1.png",
        "caption": "Fig. 1. Configuration of the modified octorotor helicopter.",
        "texts": [
            " All the rotors\u2019 axes of rotation are fixed and parallel. The only thing that can vary is the speed of the rotor. Each pair of the opposite rotors turns the same way. In fact, in order to keep the compact structure of the modified octorotor helicopter, the extra four rotors should be added just under the original ones, respectively. The rotation direction of each added rotor is set opposite to the original one inspired by a coaxial helicopter, which can counteract the yaw torque mutually, as depicted in Fig. 1. 1) Kinematic Equations: In order to model the octorotor helicopter, two coordinate systems are employed: the local navigation frame and the body-fixed frame [4]. The axes of the body-fixed frame are denoted as (ob , xb , yb , zb), and the axes of the local navigation frame are denoted as (oe , xe , ye , ze). The position XI = [xe, ye , ze ]T and attitude \u0398I = [\u03c6, \u03b8, \u03c8]T of the octorotor helicopter are defined in the local navigation frame that is regarded as the inertial reference frame. The translational velocity V B = [u, v, w]T and rotational velocity \u03c9B = [p, q, r]T are defined in the body-fixed frame",
            " The relationship between the generated thrust Tj and the jth motor input is given as Tj = Ku \u03c9 s+ \u03c9 uj , j = 1, 2, . . . , 8, where Ku is a positive gain, \u03c9 is the actuator bandwidth, and uj is pulse width modulation input of the jth motor. In order to make it easy to model the actuator dynamics, a new variable u\u2217j is defined to represent the dynamics of the jth motor as u\u2217j = \u03c9 s+ \u03c9 uj . The corresponding torque \u03c4j generated by the jth rotor is modeled as \u03c4j = Kyu \u2217 j , where Ky is a positive gain. According to the configuration of the octorotor helicopter, as shown in Fig. 1, the total thrust Uz along the z-direction is given by the sum of the thrusts from the eight rotors Uz = T1 + T2 + T3 + T4 + T5 + T6 + T7 + T8 . The positive roll moment is generated by increasing the thrusts in the left rotors (T3 and T7) and decreasing the thrusts in the right rotors (T4 and T8) simultaneouslyU\u03c6 = Ld(T3 \u2212 T4 + T7 \u2212 T8). Similarly, the positive pitch moment is generated by increasing the thrusts in the rear rotors (T1 and T5) and decreasing the thrusts in the front rotors (T2 and T6) simultaneously U\u03b8 = Ld(T1 \u2212 T2 + T5 \u2212 T6), and the yaw moment is caused by the difference between the torques exerted by the four clockwise and another four counter-clockwise rotating rotors U\u03c8 = (\u03c41 + \u03c42 \u2212 \u03c43 \u2212 \u03c44 \u2212 \u03c45 \u2212 \u03c46 + \u03c47 + \u03c48)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001434_0094-114x(80)90021-x-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001434_0094-114x(80)90021-x-Figure2-1.png",
        "caption": "Figure 2.",
        "texts": [
            " I do so because it will be relevant in places to point out his apparent lack of rigour or knowledge, and it is conceivable that Bricard's own minor failings were in part responsible for the confusion which abounds concerning his linkages. In a summary[9] of \"m6canismes paradoxaux\" containing only turning pairs, Bricard lists three distinct 6-bar loops as well as his octahedral linkages. He has previously pointed out that, for mobility, all six joint axes must belong to a linear complex, but gives a reason for mobility of each of the first three linkages separately. 1. The general line-symmetric case The 6-R line-symmetric loop in its greatest generality is illustrated by the model shown in Fig. 2. It is to be noted, in particular, that offsets are non-zero and skew angles between adjacent joints are not necessarily rightangles. It is more common to observe special forms of this linkage, such as the model shown in Fig. 3. I believe that Bricard's explanation of this loop's mobility is facile, and the reader is referred to Waldron's [8, 10] screw system analysis of the 6-H line-symmetric chain for a satisfactory treatment. It is the easiest of the Bricard loops to analyse algebraically. One has immediately the parametric constraints a12 = a45 a23 = a56 a34 = a61 0/12 ~ 0/45 0/23 ~ 0/56 0/34 ~ 0/61 R1 = R 4 R2 = R5 R3 = R 6 and the independent closure equations OI ~ 04 (1",
            " Bian qua dtautres chercheurs [2,7,11-133 aient con~ent~ ces r~canismes et/ou aient ar~plifi~ lea aspects g~om~triques de ces octa~dres d~formables, aucune publication n'a analys~ le mouvement relatif entre lea membres. L'obJet de cat article eat d'utiliser la ~thode des 6quations de clSture [3,6,8] pour d~crire pleinement 1as cinq m~canismes distincts. Cette analyse compl~ta le travail sur les m~canisnms surcontraints connus qui ne contiennent qua lea couples tournants [5,6]. 286 La premiere cha~ne de Bricard est la boucle g~n~rale ~ ligne de sym~trie (Fig. 2), con- ditionn~e par les ~quations (1.1-5). La deuxi~me est le m~canisme g~n~ral ~ plan de sym~trie (Fig. 4), qui eat sujet aux ~quations (2.1-5). Le troisi~me type distinct est le m~canisme tri~dre unique (Figs. 7,8), conditionn~ par les ~quations (3.1-5). On peut d~river tout droit le restant des trois octa~dres d~formables de Bricard [i~, mais l'un d'eux est un cas special de la cha~ne A ligne de sym~trie susmentionn~e. La quatri~me boucle (Figs. 16,17) est d~riv~e d'un octa~dre ~ plan de sym~trie, ~ais n'a pas elle-m~me un plan de sym~trie"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure12.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure12.2-1.png",
        "caption": "Figure 12.2 Mechanical scanning of ultrasound probes for image acquisition of 2D B scans to obtain 3D ultrasound images through volume rendering.",
        "texts": [
            " At this point, however, it is considered appropriate to briefly review the current state of the art in 3D ultrasound technology. 12.1.1.2 Current Technology Concept of 3D Visualization Methods for Ultrasound Systems Current 3D ultrasound imaging systems have three components: image acquisition, reconstruction of the 3D image, and display [1, 4, 5, 8\u201314]. The first component is crucial in ensuring that optimal image quality is achieved. In producing a 3D image, the conventional line array transducer is moved over the anatomy while 2D images are digitized and stored in a microcomputer, as shown in Figure 12.2. To reconstruct the 3D geometry without geometric distortion, the relative position and angulation of the acquired 2D images must be known accurately. Over the years there are numerous developments and evaluating techniques for obtaining 3D ultrasound images using the following two approaches: mechanical scanning and freehand scanning [1, 4, 5, 8\u201314]. Mechanical Scanning Based on earlier work, Fraunhofer has developed systems [1] in which the ultrasound transducer is mounted in a special assembly, which can be driven by a motor to move in a linear fashion over the skin or tilted in equal angular 372 DIGITAL 3D/4D ULTRASOUND IMAGING ARRAY steps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001149_j.mechmachtheory.2016.08.005-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001149_j.mechmachtheory.2016.08.005-Figure12-1.png",
        "caption": "Fig. 12. Pitting damage modeling (slight to severe \u2013 from left to right).",
        "texts": [
            " Linear analysis means [40] \u201cThe displacement response U of a structure is a linear function of the applied load vector R; i.e., if the loads are \u03b1R instead of R, where \u03b1 is a constant, the corresponding displacements are \u03b1U.\u201d To perform linear analysis, mesh nodes of the pinion and the gear are coupled. In this way, we do not need to use contact elements in our finite element model [41]. The same pitting levels are modeled in the driving gear using the FEM as did in the case study. The three pitting levels modeled using FEM are given in Fig. 12. The driven gear is assumed to be perfect regardless of the pitting level of the driving gear. Each pitting level is modeled in the same way as we did in Section 3. Circular pits with diameter of 2mm and depth of 1mm are used to mimic the pits. The exact location of the circular pits is given in Fig. 7. The driven gear bore is fixed while a torque is applied on the driving gear bore. The gear mesh stiffness is calculated as follows [42]: \u03b8 = ( ) k T R , 4.1 t T b 2 where T is torque applied on the driving gear bore, Rb is the base circle radius of the gear and \u03b8T is the angular displacement of the gear base circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002133_j.msea.2010.08.034-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002133_j.msea.2010.08.034-Figure1-1.png",
        "caption": "Fig. 1. Schematic of experimental set-up.",
        "texts": [
            " A recent study performed in authors\u2019 labratory has demonstrated that, defect free components of IN-625 an be fabricated by LRM. The study focused on the optimization of rocesses parameters and characterization of microstructure and echanical properties (like hardness, tensile strength and impact oughness) of the resultant part [20]. .1. Experimental The LRM setup consisted of an indigenously developed 3.5 kW O2 laser system [21], integrated with a beam delivery system, o-axial powder-feeding nozzle and a 3-axis CNC work station, s shown schematically in Fig. 1. Raw laser beam, emanating ut of the laser system, was folded with a 45\u25e6 water-cooled old-coated plane copper mirror and the folded laser beam was ubsequently focused with a 127 mm focal length ZnSe lens, housed n a water-cooled co-axial copper nozzle. LRM process involved canning the substrate with a defocused laser beam of about mm diameter along with simultaneous injection of Inconel 625 lloy powder (particle size range: 45\u2013106 m) into the resulant melt pool through the co-axial copper nozzle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000214_robot.1993.291970-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000214_robot.1993.291970-Figure4-1.png",
        "caption": "Figure 4: Join-Link train.",
        "texts": [
            " In modeling a joint-link train, additional manufacturing errors must be considered: 1) Dimensional errors of the base (or position errors of the U joints); 2) Dimensional errors of the moving plate (or position errors of the ball joints); 3) Offset errors in the length readings of the prismatic actuator; and 4) Installation errors that occur when connecting the joints to the actuators. By treating each joint-link train as a serial kinematic chain, the above manufacturing and assembly errors can be accurately modeled. Kinematically, a joint-link train can be modeled by a set of consecutive transformations from frame {B} to frame {P} as illustrated in Figure 4. In this figure frames were assigned as follows: frames {0} and { l } to the U joint; frame (2) to the prismatic joint; and frames ( 3 ) to ( 5 ) to the ball joint. For convenience, an additional frame {6}, the origin of u,hich coincides with that of frame ( 5 ) and with its orientation the same as of frame {P}, is introduced. Eight transformations are needed to model each jointlink train in order to express the pose of the end-effector (tool) with respect to base: ( 5 ) B T, = 'To T, T, T, T, T, T, T, where BTo and T, are fixed homogeneous transformations from {B} to (0) and from (6) to {P} rcspcctively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure3.23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure3.23-1.png",
        "caption": "Fig. 3.23 Rectangular layer winding for a cylinder-type reactor",
        "texts": [
            " The active part is behind the metallic middle part of the cylinder (grey on Fig. 3.22a) that is on half potential as the magnetic core itself. The metal cylinder controls the electric field inside for the active part in oil and outside for the surface of the reactor in air. The (blue) insulating cylinders overtake the role of the bushings of the reactor. The outer field strength distribution is controlled by the toroid electrodes. For a good utilization of the limited space inside the cylinder, the windings have a rectangular cross section (Fig. 3.23). Care is taken for the high mechanic stability of the wire layers by a special compact insulation. Reactor cascades: Cylinder-type reactors can easily be connected in series for higher voltages by stacking one above the other. In opposite to a transformer cascade such a reactor cascade (Fig. 3.24) increases the test power by each additional reactor. Reactor cascades are applied when higher test voltages are required, with not too high test currents for GIS testing and for applied voltage tests on transformers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000024_s0022112072001612-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000024_s0022112072001612-Figure2-1.png",
        "caption": "FIGURE 2. (a) The Stokeslet near field during the effective stroke of a cilium; ( b ) Stokeslet field during recovery stroke; and (a ) the relative near fields in a wave of beating cilia. In region 0 the fluid is influenced mainly by the effective stroke while in @ it is influenced equally by both movements.",
        "texts": [
            " ( z 2 - $2)2 + 4 1 4 where the components r: are defined in (7). To include the influence of all the cilia we need to sum the velocities over an array of similar slender bodies. A physical interpretation of the movement of a cilium in terms of near- and far-field influences can be given. We can approximate the region around the force singularity, which has a Stokeslet (O(l/r)) velocity field, by a sphere of radius it3. This means that during the effective stroke the cilium influences a relatively large volume of fluid with its Stokeslet field (see figure 2 (a ) ) in comparison with its movement in the recovery stroke, when only the region in the close proximity of the cilium is influenced by the near field (figure 2 ( b ) ) . Furthermore, one can extend this to a row of cilia in different stages of their beat. The Stokeslet region influenced by the effective beat consists of the upper half of the ciliary sublayer, while only the lower part feels the recovery stroke. Thus one might anticipate the oscillatory component of the velocity to be small in relation to the mean flow in the upper half of the cilia sublayer. Conversely, the oscillatory component can be quite large in comparison with the mean flow in the lower part of the sublayer (figure 2 (c)). A further feature contributing to the large effective stroke Stokeslet region is that the force is larger during the effective stroke in antiplectic metachronism. This is due to two factors, one being the larger relative velocities of the effective stroke, the other being the fact that a slender body exerts nearly twice the force (for a given velocity) if it moves normally instead of tangentialIy, Thus, we have two reasons why a cilium moves in a near rigid-body motion in its effective stroke, and close to the wall during the recovery movement, these being the near-field influences on the fluid and the force exerted in each phase of the beat",
            " This does not allow us to say anything about the local flow properties of the cilium (e.g. the flat combplates of the Ctenophores tend to \u2018capture\u2019 some particles, especially near their base). The velocity field of most interest to us is the mean field, so we define u = U+U\u2019, where U = 5, (11) with the bar over the velocity symbol implying the time mean. Because of the path of movement of a cilium we would expect 111\u20181 to be considerably less than I Ul in a region x3 > 6, where 6 < %L, L being the length of the cilium (see figure 2). The micro-structure in ciliated organisms 9 Equation (10) is difficult to evaluate, but it may be simplified if we take both a time and a spatial average in the xl, x2 plane. To improve the convergence of the double sum we apply the Poisson summation formula, which employs the Pourier-transformed double sum (see, for example, Lighthill 1958, p. 67; Jones 1966, p. 276). The transformed sum now becomes a decreasing exponential infinite series, so for an approximation we consider only the zeroth term, an estimation being obtained for the error"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000024_s0022112072001612-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000024_s0022112072001612-Figure11-1.png",
        "caption": "FIGURE 11. Diagram illustrating variations in sign of forces (PI and Fa) during beating cycle of a cilium.",
        "texts": [
            " One would intuitively expect little flow and low shear rates in this region of the cilia sublayer. In Opalina, which exhibits symplectic metachronism and which does not have the same distinction between the effective and recovery strokes, it is found that the force distribution is different. It appears that F3 is large, relatively speaking, during the period when the bending wave is being propagated up the cilium immediately before its effective stroke (i.e. 3-5 in figure 6). To give us some understanding of the oscillation of sign experienced by F3, figure 11 has been used to help explain this. During the effective stroke, F3 changes sign as the cilium moves past the x3 axis. It again changes sign during the propagation of the bending wave along the cilium, and may alter again before the beginning of the effective stroke. The bending moment follows a similar pattern to Fl in that it is large and positive during the effective stroke and small and negative during the recovery stroke for antiplectic metachronism. 6.4. Rate of working Another physical quantity which is of interest to both the zoologist and the fluid dynamicist is the rate of working P of a cilium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003265_tpel.2019.2900559-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003265_tpel.2019.2900559-Figure5-1.png",
        "caption": "Fig. 5. Movement state of the PMSM during the inductance identification.",
        "texts": [
            " The instantaneous torque of the machine during the inductance identification process can be obtained from the torque equation, which is given as       em f q d q d qT p i L L i i (11) where p is the number of pole-pairs. Since the injected voltages are the parameters directly controlled in the inductance identification as presented in (6), it is necessary to clarify the relation among the injection voltages, the feedback current and the rotation angle. Furthermore, because only the q-axis current produces torque, the movement state of PMSMs is investigated under a certain current setting Iqset. The movement of PMSMs is illustrated by the machine model shown in Fig. 5. In Fig. 5, \u0394\u03b8e is the rotation angle of the rotor with the q-axis current varying from 0 to Iqset in the hysteresis control based ASI method. J is the inertia of the machine, and Tem is the electromagnetic torque. The motion equation of PMSMs is defined as 0885-8993 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 2 2 d d   e emT J t (12) where d d   em e T t t J "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003937_j.engfailanal.2017.08.028-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003937_j.engfailanal.2017.08.028-Figure4-1.png",
        "caption": "Fig. 4. Finite element models of the gear with tooth root crack.",
        "texts": [
            " 3) for the crack propagation path in order to reveal their effects on gear tooth fillet-foundation stiffness, which are also introduced as follows: Case 1: A straight line which is symmetrical about the symmetrical line of the tooth; Case 2: An arc curve with the radius of 16 mm, and the center of the corresponding circle lies at the symmetrical central line of the tooth; Case 3: An arc curve with the radius of 8 mm, and the center of the corresponding circle lies at the symmetrical central line of the tooth. Then, the finite element models of the gear are established. In order to get higher calculation accuracy and acceptable computation cost, the concentrated tooth with tooth root crack is discretized with smaller grids while the rest part has relatively coarse grids. Most of the elements in the model are hexahedron. The total number of the elements is about 222,000 and the total number of nodes is about 244,000. The complete finite element model is shown in Fig. 4. The applied boundary conditions are explained as follows. In order to avoid the effect from the tooth flexible deformation, the material of the tooth segment above the tooth root crack is set as a rigid body (see the tooth part above the crack in Fig. 4), and the material of other parts is steel with the parameters in Table 1. The displacement of the nodes on the surface of the gear inner hole are constrained to be zero. And a force distributed uniformly along the tooth width is applied to the gear tooth involute profile along the line of action, which is shown in Fig. 4. Then, the displacement of the nodes in the direction of acting force can be extracted after calculation. Finally, the stiffness of the gear fillet-foundation can be obtained by, = K \u03b4 F 1 fFEM FEM (21) where, KfFEM is the stiffness of the gear fillet-foundation by FEM, \u03b4FEM is the displacement of the node. F is the applied force. In this paper, on the basis of the three crack paths introduced in Section 3, the stiffness of the gear fillet-foundation is calculated by using the two improved methods proposed in Section 2, where the crack length is extended from 0% to 70% of the total length of the fictitious crack path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000238_iros.2005.1545143-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000238_iros.2005.1545143-Figure3-1.png",
        "caption": "Fig. 3 Presentation of singularities",
        "texts": [
            " They can be parted into three categories: under-mobilities [14], over-mobilities [14], and internal singularities [15]. These notions can be partly explained using linear kinematic equation [16]: JxX = Jq4 (1) where x is the vector of operational velocities and q is the vector of actuated joints velocities. In order to explain these categories of singularities, a simple two-dofparallel mechanism is proposed: - On one hand, under-mobilities occur when Jq is singular. In that case, a velocity q can be applied without producing any motion on the traveling plate (Fig. 3a), - On the other hand, over-mobilities occur when JX is singular. In that case, it is possible to have x X 0 without moving the actuators (Fig. 3b). At last, \"internal\" singularities can occur for some mechanisms. They cannot be enlightened thanks to JX or Jq, and a more complete study has to be done. On Fig. 4, an internal singularity occurs when the parallelogram becomes flat. In that case, orientation of traveling plate cannot be guaranteed (this orientation does not belong to operaltional velocities). Placing actuators of H4 with a homogeneous repartition, i.e. placed at 90\u00b0 one relatively to each other, leads to internal singularities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003546_tmag.2015.2446951-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003546_tmag.2015.2446951-Figure4-1.png",
        "caption": "Fig. 4. Open-circuit flux line distributions with DC currents at the d- and qaxis rotor positions. (a) Rotor at d-axis (Idc = 0A) (b) Rotor at q-axis (Idc = 0A). (c) Rotor at d-axis (Idc = 8A) (d) Rotor at q-axis (Idc = 8A)",
        "texts": [
            "1 diiiiqqiiiidNT dcdqdcdqr \u03c8\u03c8 \u2212= (3) 2 )],,([ 2 )],,([ dcdqqdcdqqd iiidriiiiriV \u03c9\u03c8\u03c9\u03c8 ++\u2212= (4) mfrNef = (5) where T, d, q, id, iq, idc, V, r, \u03c9, fe, and fm are the torque, daxis flux-linkage, q-axis flux-linkage, d-axis current, q-axis current, DC current, phase voltage, phase resistance, angular frequency, electrical excitation frequency, and the corresponding mechanical frequency, respectively. III. ELECTROMAGNETIC PERFORMANCE In this section, the electromagnetic performance, i.e. the airgap flux density, open-circuit flux-linkage, back-EMF, cogging torque and electromagnetic torque of the HSSPM machine is investigated. The flux line distribution is shown in Fig. 4 with the rotor at d-axis (rotor pole and stator pole aligned and q-axis (rotor pole rotated by 9o mech.) on open- circuit for different DC currents of 0A and 8A. It is worth mentioning that with DC current excitation of 8A, the stator is much less saturated compared to the case 0A. In addition, magnetic flux now links both the rotor and stator. The main advantage of the hybrid-excited machine is its ability to regulate the air-gap flux density using the DC current. This flux regulation capability is demonstrated by investigating the radial component of the air-gap flux density shown over 180 (\u00b0mech) due to machine symmetry, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003443_bf02120338-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003443_bf02120338-Figure4-1.png",
        "caption": "Fig. 4. The general state of loading of each flat spring.",
        "texts": [
            " (1) -- L sin a ' This means t ha t for small angles q0 the pivot point coincides with th6 initial point of intersection of the two springs, and tha t the distort ion at the ends is bound by the same condit ion (1) for each flat spring separately. In the extreme case where the angle 2a is zero, the angle ~0 according to the first eq. (1) is undetermined and the condit ion [ = } L 9 no longer holds. No fixed pivot point can then be indicated, so t h a t for our fur ther considerations we must make the reservation tha t the intersection angle 2a is not very small. The general s tate of loading for each of the two springs is represented in fig. 4, The bending moment at point x is M x = Mo + D X - Ny. (2) When E denotes Young's modulus of elasticity and I the (smallest) linear moment of inertia of the flat spring, the curvature 1/p is given by 1 1 0 E[ (M~ + Dx Ny). (3) S ince the deflection is considered to be small, we m a y put the curvature 1/0 equal to d2y/dx 2, so tha t eq. (3) leads to the differential equat ion V dx ---fd2y + q2y = ~1 (M o + Dx); where q . = ~ - . (4) By adapt ing the general solution of (4) to the boundary conditions y = 0 and dy/dx = 0 at x = 0, we find for the de f l ec t i on /o f the end x ~ L 1 D M o / - q N ( q L - - s i n q L ) + N ( 1 - - c o s q L ) , (5) and for the corresponding angle of deflection D M o q, = ~ - (I - - cos qL) 4- ~\\f q sin qL",
            " From this it follows at the same time that the paths described by points of the members during the relative movement deviate somewhat from the arcs of a circle, so that the momentary pivot point is slightly shifted with respect to the initial intersection of the springs. Taking into account the conditions of equilibrium of each spr~ng Appl. Sci. Res. A I 21\" separately, we may deduce b y reason of symmet ry that the forces present at the spring ends can only run parallel to the line of symme t ry and that the bending moments must be equal two b y two. This is i l lustrated in fig. 8. If the spring A D is fixed at A we obtain the same state of loading as given in fig. 4, except tha t now 9 N = Q s i n ( a + ~9), D --- - - Q cos (a + .~-9). (11) Since we are no longer confined to small angles of deflection, in eq. (3) the curvature 1/e must now be replaced b y d g ' / d s where s is the arc length measured along the spring from its fixed end and 9' the slope of the tangent at the point (x, y). With dx /ds ~ cos 9' and d y / d s ~- sin 9', differentiation of eq. (3) with respect to s gives 2 D L 2 D s , ~ : '=- -x ,___ Y (13) a - - E 1 ' t a n f l - - - - ~ , a ' = ~ L ' ~l -~ , we can write this equation as d29 ' a da '2 + 2 sin-----fl sin (9' -- /3) = 0. (14) Further , on account of (2), (3) and 1 t0 = dg'/ds = dg'lLda', d 9' M~L da' E I (15) Multiplication of equation (14) b y d9'/da' and subsequent integration gives (dg'/2 a -g~Ta' / - - s i n ~ cos (9' - - fl) = sin~--fi Y, (16) where y represents a constant of integration. As we shall find conf irmed later on, the central line of the deflected spring shows no points of inflection, and therefore the bending moment M.~ is a lways positive (see fig. 4). Owing to eq. (15) the differential quot ient dg'/d~' is then also positive, so tha t the solution of eq. (16) is V dg' - _ a X/y + cos ( 9 ' - - f l ) . (17) da' Sinfl \" Along the spring from its fixed end to i& free end, the reduced arc length a' = s/L increases from 0 to the value 1, whilst the angle 9' increases from 0 to 9. Thus the integration of eq. (17) leads to the relati6n ~0 = 1 - - ~ j - a , @ + cos (9, __ fl ) . (18) o Fur the r , since dx/ds -= d ( / d a ' = cos 9' and dy/ds = & l ' /de ' = sin 9' , the dimensionless coordinates of the end of the spring are found to be ~0 t - Z - V r + cos ( 9 ' - - f l ) ' o / i / s i n f l / \" sin 9' dg ' I / / (20) n - Z ~ - - 7 - "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000673_bf00375605-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000673_bf00375605-Figure1-1.png",
        "caption": "Fig. 1. Kinematic configuration",
        "texts": [
            " Finally Section 6 contains a complete geometric analysis of the solutions based on the formulas derived previously. We begin by deriving the kinematic equations of motion for the ball. Let q = (ql, q2, q3) denote the coordinates of a point in fR 3 relative to a fixed right-handed orthonormal frame el, e2, e3 centered at a point O in the stationary plane, with e3 perpendicular to this plane and pointing upward. a l , a2, and a3 denote a right-handed orthonormal frame fixed to the ball at its center. This setting is shown in Fig. 1. The frame al, a2, a3 is called the moving frame. The coordinates of any point of N3 relative to this moving frame are denoted by Q = (Q1, Q2, Q3), qlel + q2e2 + q3e3 = Qlal + Q2a2 + Qsa3 if and onlY if q = (ql, q2, qs) = (Q1, Q2, Q3)R = OR. Each motion of the ball is described by the motion of its center and the motion of the moving frame. We need extra notations in order to be more specific. For any point A in fR 3, O-~ denotes the vector defined by the line segment OA. If we denote by C the center of the ball, then OA = OC + CA"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001657_tfuzz.2014.2310491-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001657_tfuzz.2014.2310491-Figure1-1.png",
        "caption": "Fig. 1: Conventional deterministic dead zone models.",
        "texts": [
            " Note that all the aforementioned dead zone output \u0393(u) of the actuator is deterministic and precise in character, i.e., for a given input u in the actuator, the actuator output \u0393(u) is a certain value. Generally, there are two conventional deterministic 1063-6706 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. dead zone models, which are displayed in Fig.1. However, in practical applications, parameters of the dead zone, due to the influence of the physical characteristics of the actuators and environment, are often uncertain and imprecise. Therefore, it is very important to study the dead zone problem with uncertain features. In this paper, a fuzzy dead zone model is proposed to describe the uncertainty and imprecision existing in the dead zone. The main advantages of this paper are that \u2022 This is the first attempt to deal with the control problem of nonlinear strict-feedback systems with fuzzy dead zone input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000069_ip-epa:19981982-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000069_ip-epa:19981982-Figure14-1.png",
        "caption": "Fig. 14 Relations between the different angles",
        "texts": [
            "2 Principle of regulation The regulation is based on a two-stage control, the first stage acts on rotor cunents d and q as a current supply. The second regulates the stator voltages. Each axis d and q is regulated independently of the other. In 8 Double-fed running: mode 111 8.1 Control strategies Several strategies for the control of the double-fed induction machine are possible. In one of then the reference frame is aligned with the stator voltage. It is supposed that the stator voltage of d axis is equal to zero (Fig. 14). This frame is used by references as [4, 71. Moreover the stator voltage is quasi constant, imposed by the network. R, and therefore derivative terms can be also neglected: Stator voltage in a synchronous reference frame: 0 = &.Ids - ws.$qs vs = Rs, Iqs + ws.$ds $qs = Rs.Ids Z 0 vs (20) (21) (22) (23 ) Therefore $ds 73 - 4 s WS With these simplifications all the stator flux is on the d axis. Rotodrive brings a supplementary advantage as demonstrated in [8, 91, the stator reactive power can also be controlled"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003234_10426914.2015.1026351-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003234_10426914.2015.1026351-Figure8-1.png",
        "caption": "FIGURE 8.\u2014The injection mold insert with conformal cooling channel. (a) CAD model, (b) SLM parts.",
        "texts": [
            " Considering the fact that the hardness of CrFe7C0.45 is higher than that of Fe\u2013Cr, with increasing laser power, the hardness of part increased. In addition, it can be found that the average values of the hardness yielded from 46.6 0.62 to 50.7 0.99 HRC, which is close to that of the AISI 420 processed by austenitizing heat treatment [20] and meets the requirements in the injection mold application. The injection mold insert (40 45 15 mm3) with conformal cooling channel was successfully fabricated as shown in Fig. 8, and it was well applied for the company of mold manufacturing in China. In this work, the fully dense AISI 420 tool steel was successfully manufactured directly from powders using the SLM. The microstructure, phase, and the hardness indicated that the SLM is potential for the application of plastic injection mold. The main conclusions can be drawn as follows: 1. The melt characteristic was concluded and processing window was established for the AISI 420 powder processed by SLM. 2. The Fe\u2013Cr and CrFe7C0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003984_j.snb.2016.10.059-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003984_j.snb.2016.10.059-Figure1-1.png",
        "caption": "Fig. 1 (a) Schematic illustration and (b) photographic image of the rGO/\u03b1-Fe2O3 hybrid nanocomposite-based sensor.",
        "texts": [
            " X-ray photoelectron spectroscopy (XPS) analysis was measured on an ESCALAB MK II X-ray photoelectron spectrometer using Mg as the exciting source. Raman spectra were obtained on J-YT64000 Raman spectrometer with 514.5 nm wavelength incident laser light. The structure and morphology of the samples were obtained by the transmission electron microscopy (TEM, JEOL JEM-3010). Field emission scanning electron microscope (FESEM: HITACHI, Japan, SU8010) images of rGO/\u03b1-Fe2O3 were also taken. 2.5. Fabrication and gas sensing measurements The prepared rGO/\u03b1-Fe2O3 nanocomposites were mixed with deionized water to obtain solution in a mortar. Fig. 1 shows a schematic image and a photograph of this sensor substrate. The droplet has covered a ceramic plate (6mm\u00d73mm, 0.5mm in thickness) in which a pair of interdigitated gold electrodes (electrodes width and distance: 0.15mm) was printed by photolithographing. The sensor was heated at 70 \u00b0C for 5 h before testing. The measurement was carried out by placing the sensor in a glass vessel with a given concentration of target gas. The response of the gas sensor is defined as the ratio of the resistance of the sensor tested in air (Ra) to that tested in the detection gases (Rg)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000917_c3cp50929j-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000917_c3cp50929j-Figure1-1.png",
        "caption": "Fig. 1 Sketch of the biofuel flow cell.",
        "texts": [
            " The biocatalytic cathodes were prepared by immobilization of laccase: the PBSE-functionalized electrodes were incubated for 1 hour in the solution of laccase (1.5 mg mL 1) in potassium phosphate buffer (10 mM, pH 7.0). The immobilization reactions proceeded at room temperature with moderate shaking. The enzyme-modified electrodes were stored (4 1C) in the same buffer until used in the biofuel cell. Characterization of the enzymemodified electrodes (cyclic voltammetry, enzyme content, etc.) was described in detail elsewhere.23,24 The flow cell with the dimensions shown in the sketch, Fig. 1, included the buckypaper electrodes modified with PQQ-GDH and laccase in the anode and the cathode, respectively, and the inlet/outlet of the cell were connected to plastic tubes of 0.5 mm internal diameter. A human serum solution with the glucose concentration of 6.4 mM was pumped (MINIPULS 3, Gilson) at the volumetric rate of 58.9 mL min 1, mimicking blood flow in a human capillary of 0.008 mm at the linear rate of 1 mm s 1 characteristic of a resting person.40 Note that the volumetric flow rate was scaled up to generate the same linear rate in the tube of a bigger diameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003751_j.jmatprotec.2018.04.013-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003751_j.jmatprotec.2018.04.013-Figure1-1.png",
        "caption": "Fig. 1. DMLS produced cubes from gas atomized AlSi10Mg_200C powder.",
        "texts": [
            " This work aims to focus on this gap to investigate corrosion behavior of the DMLS-AlSi10Mg_200C alloy in compared with its cast counterpart (Die cast A360.1 A l alloy) with the particular focus on the microstructure and the formed micro-constituents after each manufacturing process. This study can be used as a roadmap to substitute different conventional alloys with their additively manufactured equivalents. For this study, several AlSi10Mg_200C cube specimens (10\u00d7 10\u00d710mm) were additively manufactured (shown in Fig. 1) from gas atomized commercial AlSi10Mg_200C powder from EOS using an EOS M290 metal 3D printer machine through DMLS technique (Additive Metal Manufacturing, Inc. (AMM), Concord, ON, Canada). The machine was equipped with a 250\u00d7 250\u00d7325mm size platform and a 400W Yb-fibre laser with 100 \u03bcm spot size. The average particle size of the alloy powder with a regular spherical shape was 8.8 \u00b1 7 \u03bcm (Asgari et al., 2017). The nominal composition of the alloy is reported in Table 1. To minimize the internal stresses in the printed samples, the DMLS was processed at elevated building platform temperature of 200 \u00b0C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.9-1.png",
        "caption": "FIGURE 5.9. Illustration of a 2R planar manipulator robot and DH frames of each link.",
        "texts": [
            "24) 246 5. Forward Kinematics Rzi,\u2212\u03b8i = \u23a1\u23a2\u23a2\u23a3 cos \u03b8i \u2212 sin \u03b8i 0 0 sin \u03b8i cos \u03b8i 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.25) Dxi,\u2212ai = \u23a1\u23a2\u23a2\u23a3 1 0 0 \u2212ai 0 1 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.26) Rxi,\u2212\u03b1i = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 cos\u03b1i \u2212 sin\u03b1i 0 0 sin\u03b1i cos\u03b1i 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (5.27) Using i\u22121Ti = iT\u22121i\u22121 we find i\u22121Ti = iT\u22121i\u22121 (5.28) = \u23a1\u23a2\u23a2\u23a3 cos \u03b8i \u2212 sin \u03b8i cos\u03b1i sin \u03b8i sin\u03b1i ai cos \u03b8i sin \u03b8i cos \u03b8i cos\u03b1i \u2212 cos \u03b8i sin\u03b1i ai sin \u03b8i 0 sin\u03b1i cos\u03b1i di 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . Example 141 DH transformation matrices for a 2R planar manipulator. Figure 5.9 illustrates an RkR planar manipulator and its DH link coordinate frames. 5. Forward Kinematics 247 Based on the DH Table 5.5 we can find the transformation matrices from frame Bi to frame Bi\u22121 by direct substitution of DH parameters in Equation 5.11. Therefore, 1T2 = \u23a1\u23a2\u23a2\u23a3 cos \u03b82 \u2212 sin \u03b82 0 l2 cos \u03b82 sin \u03b82 cos \u03b82 0 l2 sin \u03b82 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.29) 0T1 = \u23a1\u23a2\u23a2\u23a3 cos \u03b81 \u2212 sin \u03b81 0 l1 cos \u03b81 sin \u03b81 cos \u03b81 0 l1 sin \u03b81 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.30) and consequently 0T2 = 0T1 1T2 = \u23a1\u23a2\u23a2\u23a3 c (\u03b81 + \u03b82) \u2212s (\u03b81 + \u03b82) 0 l1c\u03b81 + l2c (\u03b81 + \u03b82) s (\u03b81 + \u03b82) c (\u03b81 + \u03b82) 0 l1s\u03b81 + l2s (\u03b81 + \u03b82) 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 ",
            "30) We find two values for \u03b82 for c = \u22123.232 \u03b82 = 0.7555416816 rad \u2248 43.28934959 deg (6.31) \u03b82 = \u22120.4880785028 rad \u2248 \u221227.96483827 deg (6.32) and we get no real answer for c = \u22125.232. \u03b83 comes from (6.23). If \u03b82 = 0.755 rad then we have \u03b83 = atan2 \u00b5 dx cos \u03b81 + dy sin \u03b81 \u2212 l2 cos \u03b82 l1 + l2 sin \u03b82 \u2212 dz \u00b6 \u2212 \u03b82 = .1913201914 rad \u2248 11 deg (6.33) and if \u03b82 = \u22120.488 rad then we have: \u03b83 = \u2212.1913201910 rad \u2248 \u221211 deg (6.34) 6. Inverse Kinematics 331 Example 184 Inverse kinematics for a 2R planar manipulator. Figure 5.9 illustrates a 2R planar manipulator with two RkR links according to the coordinate frames setup shown in the figure. The forward kinematics of the manipulator was found to be 0T2 = 0T1 1T2 (6.35) = \u23a1\u23a2\u23a2\u23a3 c (\u03b81 + \u03b82) \u2212s (\u03b81 + \u03b82) 0 l1c\u03b81 + l2c (\u03b81 + \u03b82) s (\u03b81 + \u03b82) c (\u03b81 + \u03b82) 0 l1s\u03b81 + l2s (\u03b81 + \u03b82) 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . The inverse kinematics of planar robots are generally easier to find analytically. The global position of the tip point of the manipulator is at\u2219 X Y \u00b8 = \u2219 l1 cos \u03b81 + l2 cos (\u03b81 + \u03b82) l1 sin \u03b81 + l2 sin (\u03b81 + \u03b82) \u00b8 (6",
            "81) which shows that JD= \u23a1\u23a2\u23a3 \u2202X \u2202r \u2202X \u2202\u03b8 \u2202Y \u2202r \u2202Y \u2202\u03b8 \u23a4\u23a5\u23a6 = \u2219 cos \u03b8 \u2212r sin \u03b8 sin \u03b8 r cos \u03b8 \u00b8 . (8.82) There is only one rotational joint coordinate, \u03b8. The rotation matrix 0R2 indicates that: 0\u03c9\u03032 = 0R\u03072 0RT 2 = \u03b8\u0307k\u0303 (8.83) So, 0\u03c92 = \u23a1\u23a3 \u03c91 \u03c92 \u03c93 \u23a4\u23a6 = \u23a1\u23a3 0 0 \u03b8\u0307 \u23a4\u23a6 (8.84) and therefore, \u03c93 = JR \u03b8\u0307 (8.85) JR = 1 (8.86)\u23a1\u23a3 X\u0307 Y\u0307 \u03c93 \u23a4\u23a6 = \u23a1\u23a3 cos \u03b8 \u2212r sin \u03b8 sin \u03b8 r cos \u03b8 0 1 \u23a4\u23a6\u2219 r\u0307 \u03b8\u0307 \u00b8 (8.87) Example 243 Jacobian matrix for the 2R planar manipulator. A 2R planar manipulator with two RkR links was illustrated in Figure 5.9 and is shown in Figure 8.3 again. The manipulator has been analyzed in Example 141 for forward kinematics, and in Example 184 for inverse kinematics. The angular velocity of links (1) and (2) are 0\u03c91 = \u03b8\u03071 0k\u03020 (8.88) 0 1\u03c92 = \u03b8\u03072 0k\u03021 (8.89) and 0\u03c92 = 0\u03c91 + 0 1\u03c92 = \u00b3 \u03b8\u03071 + \u03b8\u03072 \u00b4 0k\u03020 (8.90) and the global velocity of the tip position of the manipulator is 0d\u03072 = 0d\u03071 + 0 1d\u03072 = 0\u03c91 \u00d7 0d1 + 0\u03c92 \u00d7 0 1d2 = \u03b8\u03071 0k\u03020 \u00d7 l1 0 \u0131\u03021 + \u00b3 \u03b8\u03071 + \u03b8\u03072 \u00b4 0k\u03020 \u00d7 l2 0\u0131\u03022 = l1\u03b8\u03071 0j\u03021 \u00d7 l2 \u00b3 \u03b8\u03071 + \u03b8\u03072 \u00b4 0j\u03022. (8.91) The unit vectors 0j\u03021 and 0j\u03022 can be found by using the coordinate transformation method, 0j\u03021 = RZ,\u03b81 1j\u03021 = \u23a1\u23a3 cos \u03b81 \u2212 sin \u03b81 0 sin \u03b81 cos \u03b81 0 0 0 1 \u23a4\u23a6\u23a1\u23a3 0 1 0 \u23a4\u23a6 = \u23a1\u23a3 \u2212 sin \u03b81cos \u03b81 0 \u23a4\u23a6 (8",
            "77) shows that \u00b7 G\u03c9\u0303B = Gd dt G\u03c9\u0303B = GR\u0308B GRT B + GR\u0307B GR\u0307T B = GR\u0308B GRT B + G\u03c9\u0303B G\u03c9\u0303 T B (10.78) and therefore, GR\u0308B GRT B = \u00b7 G\u03c9\u0303B \u2212 G\u03c9\u0303B G\u03c9\u0303 T B. (10.79) Hence, the acceleration vector of the body point becomes Gr\u0308P = \u00b5 \u00b7 G\u03c9\u0303B \u2212 G\u03c9\u0303B G\u03c9\u0303 T B \u00b6\u00a1 GrP \u2212 GdB \u00a2 + Gd\u0308B (10.80) where \u00b7 G\u03c9\u0303B = G\u03b1\u0303B = \u23a1\u23a3 0 \u2212\u03c9\u03073 \u03c9\u03072 \u03c9\u03073 0 \u2212\u03c9\u03071 \u2212\u03c9\u03072 \u03c9\u03071 0 \u23a4\u23a6 (10.81) and G\u03c9\u0303B G\u03c9\u0303 T B = \u23a1\u23a3 \u03c922 + \u03c923 \u2212\u03c91\u03c92 \u2212\u03c91\u03c93 \u2212\u03c91\u03c92 \u03c921 + \u03c923 \u2212\u03c92\u03c93 \u2212\u03c91\u03c93 \u2212\u03c92\u03c93 \u03c921 + \u03c922 \u23a4\u23a6 . (10.82) Example 278 Acceleration of joint 2 of a 2R planar manipulator. A 2R planar manipulator is illustrated in Figure 5.9. The elbow joint has a circular motion about the base joint. Knowing that 0\u03c91 = \u03b8\u03071 0k\u03020 (10.83) we can write 0\u03b11 = 0\u03c9\u03071 = \u03b8\u03081 0k\u03020 (10.84) 0\u03c9\u03071 \u00d7 0r1 = \u03b8\u03081 0k\u03020 \u00d7 0r1 = \u03b8\u03081RZ,\u03b8+90 0r1 (10.85) 0\u03c91 \u00d7 \u00a1 0\u03c91 \u00d7 0r1 \u00a2 = \u2212\u03b8\u030721 0r1 (10.86) and calculate the acceleration of the elbow joint 0r\u03081 = \u03b8\u03081RZ,\u03b8+90 0r1 \u2212 \u03b8\u0307 2 1 0r1. (10.87) 10. Acceleration Kinematics 541 Example 279 Acceleration of a moving point in a moving body frame. Assume the point P in Figure 10.4 is indicated by a time varying local position vector BrP (t)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure6.31-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure6.31-1.png",
        "caption": "Fig. 6.31 Effects of rear steering on the achievable region: rear wheels turning opposite of the front wheels (left), rear wheels turning like the front wheels (right)",
        "texts": [
            "30 Vehicle with too much understeer: \u03b2\u2013\u03c1 MAP with lines at constant u, a\u0303y and \u03b4 168 6 Handling of Road Cars shapes also because an oversteer vehicle becomes unstable for certain combinations of speed and steer angle, as already pointed out when discussing Fig. 6.24. These critical combinations form a sort of stability boundary which collects all points where the u-curves and \u03b4-lines are tangent to each other, as shown in both Figs. 6.24 and 6.29. On the opposite side, a vehicle with too much understeer has an achievable region like in Fig. 6.30, which comes with Fig. 6.21. The effects of rear steering (in addition to front steering, of course) are shown in Fig. 6.31. The picture on the left is for the case of rear wheels turning opposite of the front wheels, with \u03c7\u0302 = \u22120.1 in (6.74), whereas the picture on the right is for rear wheels turning like the front wheels, with \u03c7\u0302 = 0.1. The vehicle slip angle \u03b2 is pretty much affected (cf. Fig. 6.28). Basically, a negative \u03c7\u0302 moves the achievable region 6.11 Vehicle in Transient Conditions (Stability and Control Derivatives) 169 upwards, and vice versa. On the other hand, \u03c7\u0302 does not impinge on the available region in the plane (\u03b4, \u03c1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure1.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure1.4-1.png",
        "caption": "FIGURE 1.4. Symbolic illustration of revolute joints in robotic modeles.",
        "texts": [
            " Relative rotation of connected links by a revolute joint occurs about a line called axis of joint . Also, translation of two connected links by a prismatic joint occurs along a line also called axis of joint. The value of the single coordinate describing the relative position of two connected links at a joint is called joint coordinate or joint variable. It is an angle for a revolute joint, and a distance for a prismatic joint. A symbolic illustration of revolute and prismatic joints in robotics are shown in Figure 1.4(a)-(c), and 1.5(a)-(c) respectively. The coordinate of an active joint is controlled by an actuator. A passive joint does not have any actuator. The coordinate of a passive joint is a function of the coordinates of active joints and the geometry of the robot arms. Passive joints are also called inactive or free joints. Active joints are usually prismatic or revolute, however, passive joints may be any of the lower pair joints that provide surface contact. There are six different lower pair joints: revolute, prismatic, cylindrical, screw, spherical, and planar"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002117_j.mechmachtheory.2019.103597-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002117_j.mechmachtheory.2019.103597-Figure2-1.png",
        "caption": "Fig. 2. The displacement of the inner ring with the combined loads.",
        "texts": [
            " [32] , whose value is depended on the total curvature B ( B = f i + f o \u22121), in which f i and f o are the groove curvature of the inner and outer rings, respectively. The axial displacement of the bearing with the preload F p is expressed as \u03b4ap = BD sin ( \u03b1p \u2212 \u03b10 ) cos \u03b1p (2) 2.2. Load distribution from the SAM According to the discussions in Refs. [18] and [27] , The inner and outer rings are assumed to be parallel in the SAM according to the load distribution model of the ACBB with the combined loads. As shown in Fig. 2 , an axial displacement \u03b4a and radial displacement \u03b4r of the inner ring can be produced by the central axial load F a and radial load F r . The normal displacement of the inner ring relative to the outer ring is given as \u03b4\u03c8 = \u03b4max [ 1 \u2212 1 1 + \u03b4a tan \u03b1 \u03b4r (1 \u2212 cos \u03c8) ] (3) where \u03b4\u03c8 , \u03b4a , and \u03b4r are the normal displacement, axial displacement and radial displacement, respectively; and \u03b4max is the maximum normal displacement when the corresponding azimuth \u03c8 is equals to 0 \u00b0, in which \u03b4max = \u03b4a sin \u03b1+ \u03b4r cos \u03b1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure14-1.png",
        "caption": "Fig. 14. Sketch of a DSvPR-uRPFS-uRRvRRR PM.",
        "texts": [
            " The intersection of three limb bonds is given by {L1} \u2229 {L2} \u2229 {L3} = {G(u)}{R(B, v)} \u2229 {S(D)}{G(v)} = {R(O, u)}{T2(\u22a5u)}{R(B, v)} \u2229{R(O,u)}{R(D, i)}{R(D, j)}{T2(\u22a5v)}{R(B, v)} = {R(O, u)}({T2(\u22a5u)} \u2229 {R(D, i)}{R(D, j)} {T2(\u22a5v)}{R(B, v)}. (23) Note that {T2 (\u22a5u)} \u2229 {R (D, i)} {R (D, j)} {T2 (\u22a5v)} = {T(w)}. Therefore, we have {L1} \u2229 {L2} \u2229 {L3} = {R(O, u)}{T(w)}{R(B, v)}. (24) The above analysis shows that the end-effector motion is RPR equivalent with limb 1 generating {X(u)}{X(v)}, limb 2 generating {G(u)}{S(F)} with F (B, v), and limb 3 generating {S(D)}{G(v)} with D (O, u). Fig. 14 shows the sketch of a DSvPR-uRPFS-uRRvRRR PM in this subcategory. There are 863 RPR-equivalent PMs in this subcategory totally, which are not enumerated here for simplicity. Moreover, their potential in practice is limited due to three different limb chains. A new family of RPR-equivalent PMs is disclosed using the Lie group algebraic properties of the set of rigid-body displacements. The motions generated by the limb chains of the PMs are products of Lie subgroups that contain the RPR motion. Numerous novel RPR-equivalent PMs are enumerated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure2.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure2.18-1.png",
        "caption": "Fig. 2.18",
        "texts": [],
        "surrounding_texts": [
            "E2.6 Example 2.6 A thin-walled tube is subjected to bending and torsion such that the following stresses act at points A and B: \u03c3A,B x = \u00b125 MPa, \u03c3A,B s = 50 MPa, \u03c4A,B xs = 50 MPa . Determine the principal stresses and their directions at A and B. Results: see (A) Point A \u03c31 = 89.0 MPa, \u03c32 = \u221214.0 MPa, \u03d5\u2217 1 = 52.0\u25e6, \u03d5\u2217 2 = \u221238.0\u25e6. Point B \u03c31 = 75.0 MPa, \u03c32 = \u221250.0 MPa, \u03d5\u2217 1 = 63.4\u25e6, \u03d5\u2217 2 = \u221226.6\u25e6. E2.7 Example 2.7 A thin-walled bathysphere (radius r = 500 mm, wallthickness t = 12.5 mm) is lowered to a depth of 500 m under the water surface (pressure p = 5 MPa). Determine the stresses in the wall. Result: see (A) \u03c3t = \u2212100 MPa (in any section). E2.8 Example 2.8 A thin-walled cylindrical vessel has the radius r = 1 m and wall-thickness t = 10 mm. Determine the maximum internal pressure pmax so that the maximum stress in the wall does not exceed the allowable stress \u03c3allow = 150 MPa. r t p Fig. 2.19 Result: see (A) pmax = 1.5 MPa. 2.5 Summary 75"
        ]
    },
    {
        "image_filename": "designv10_1_0001530_978-3-642-81857-8-Figure3.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001530_978-3-642-81857-8-Figure3.7-1.png",
        "caption": "Fig. 3.7~. Simulation of tracking of nominal trajectory: .observer errors (UMS-3B)",
        "texts": [
            " the motion is shown in three quarter projection in space (the gripper is assumed to be fixed with respect to the third member). In Fig. 3.5. the minimal tra jectories are presented for all three manipulator angles and in Fig. ~.6. the corresponding driving torques are presented. As the second example of nominal trajectory synthesis we shall consid er the synthesis of nominal trajectories for the manipulator UMS-2 [8J. Let the basic configuration of the manipulator change proportionally during the functibna1 movement from the initial position qO(O) = {O, 0, O} to qO(,) = {l,57[rad], O,20[m], O,30[m]}, ,= 2 sec (Fig. 3.7). Such a prescription is possible due to the relatively simple kinematic structure of the basic manipulator configuration. The actuators are modelled by second-order systems (3.2.1). A velocity profile has been adopted such that; in the interval t\u00a3(O, ,/2), the accelerations of the internal manipulator coordinates are constant and positive: q1 1 5 d l 2 .. 2 0 3 1 2 .. 3 0 2 1 2 d i th , ra sec , q = , m sec , q = , m sec , an n e interval t~(,/2, ,): q1 = -1,5 rad/sec2 q2 = -0,3 m/sec2 , q3 = -0,2 m/sec2 \u2022 The nominal trajectories, the torques (forces) and control inputs of the 181 basic system configuration are presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002042_adem.201900617-Figure27-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002042_adem.201900617-Figure27-1.png",
        "caption": "Figure 27. Examples of parts produced by powder bed processes: a) a Co-29Cr-6Mo part fabricated by EBM;[165] b) EOS IN718 combustor part;[39] and c) Renishaw AM250 fuel system component.[166] All images reproduced with permission. a) Copyright 2017, Elsevier; b) Copyright 2019, Material Solutions; c) Copyright 2019, Renishaw.",
        "texts": [
            "[47] The powder bed AM process is best known for its ability to manufacture intricate structures, not feasible with conventional methods or DED. Comparing the powder bed with the DED process, the powder bed process requires a greater amount of raw material, the changeover to different material is lengthy, and also there are problems in maintaining level powder beds.[18] In addition, voids, microcracks, and lack of fusion are often observed in laser sintering/melting AM parts[164]; post-process HIP is often required. Some examples of parts produced with powder bed processes are shown in Figure 27. Realizing the limitation of powder bed processes with preplaced alloy powder, directly fed alloy powder or wire into the laser beam (or arc) through a side feeding mechanism came into Adv. Eng. Mater. 2019, 1900617 1900617 (16 of 35) \u00a9 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim use, as shown in Figure 28. The DED process closely resembles conventional laser welding or arc welding. The direct feeding of powder gives rise to the opportunity of shielding the powder during melting, improving material usage, and increasing deposition rate",
            "[39] The fiber laser melts fine metal powder and builds up parts layer by layer. The EOS system can be used to produce AM parts made of a large variety of metals, including Al-Si-10Mg, Co\u2013Cr alloys, maraging steel MS1, HX, IN625, and 17-4 PH, stainless steels CX, GPI, and 316L, and Ti-6Al-4V. It was also estimated that the mean cost to manufacture parts, using EOS model EOSINT M270, is about \u00a36.18 cm 3, with a productivity rate of 37.58 g h 1, compared with the CM process rate of 100 g h 1.[168] An IN718 combustor manufactured using an EOS system is shown in Figure 27b. Concept Laser GmbH (Germany) manufactures 3D printing systems based on a fiber laser for metal components. Their largest model, the X LINE 200R, utilizes two 1 kW lasers and claims to have the world\u2019s largest build envelop (for PBF processes) of 800 400 500mm3.[40] Similar to other systems, parts are directly created from 3D CAD files and sliced into 2D laser scanning patterns. Each representative 2D section of the part is laser sintered in the solid phase with or without instantaneous consolidation at melting point, depending on the material being used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000426_9781118680469-Figure6.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000426_9781118680469-Figure6.12-1.png",
        "caption": "FIGURE 6.12 Organization of the bent-core molecules in circular domains for different structures such as (+)-SmCsPF (a), (\u2212)-SmCsPF (b), (+)-( )-[SmCsPF]aPS (c), and (\u2212)- ( )-[SmCsPF]aPS (d), development of the dark extinction brushes in circular domains, and assignment of these structures to different circular domains observed in the texture (e) for a compound [99]. The optical tilt angle can be calculated from the uniform SmCsPF circular domains, and the enantiomeric excess (ee) in ( )- [SmCsPF]aPS can be estimated by the ratio between the angles of extinction brushes with respect to crossed polarizers and the maximum optical tilt angle provided by circular domains with uniform SmCsPF structures. The ee (50%) in (c) and (d) is not exactly equal to those in circular domains observed in (e), and the assignment is only to indicate the existence of (+)- and (\u2212)-( )-[SmCsPF]aPS structures. To be consistent with [99], the dipole is directed from the positive to the negative as defined in chemistry. Reproduced from [99] with permission from the American Chemical Society.",
        "texts": [
            " It was proposed that oligo(siloxane) or oligo(carbosilane) sublayers formed via the microsegregation of these silane segments suppress interlayer fluctuations which are favorable for the AF organization of molecules, therefore stabilizing the FE state. These segregated siloxane [134] and carbosilane [99] layers have been identified by the X-ray ODSs corresponding to a width of SiMe2O (\u223c0.7 nm) or SiMe2CH2 (\u223c0.6 nm) units. Although the textures of DC phases have very low birefringence, colorful circular domains (Fig. 6.12e) can be yielded from the isotropic liquid under an E-field. In these circular domains, extinction brushes have different angles (i.e., optical tilt angle) with respect to crossed polarizers. If the circular domains with the maximum optical tilt angle have uniformly synclinic (+)- or (\u2212)-SmCsPF layer organizations (Fig. 6.12a and b), those with smaller angles were proposed to have a nonequal distribution of oppositely tilted (+)- and (\u2212)-SmCsPF layer stacks (Fig. 6.12c and d), assigned as ( )-[SmCsPF]aPS. The enantiomeric excess (ee) value, an indication of the configurational inhomogeneity of this system, can be estimated by comparing 206 ELECTRIC- AND LIGHT-RESPONSIVE BENT-CORE LIQUID CRYSTALS the optical tilt angle of a uniform SmCsPF stack with that of a nonequally distributed SmCsPF stack. The frequency was found to influence the formation of different SmCP structures in DC phases. For instance, a low frequency E-field or dc favors an SmCsPF structure with extinction brushes inclined to crossed polarizers in a circular domain, while a high frequency E-field or ac favors an SmCaPF structure with extinction brushes coinciding with crossed polarizers in a circular domain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001697_j.proeng.2013.08.227-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001697_j.proeng.2013.08.227-Figure3-1.png",
        "caption": "Fig. 3. Scanning strategy used on SLM experiments Based from (Kruth et al. 2005, Delgado et al., 2011b)",
        "texts": [
            " The system consisted on a vertical milling centre equipped with an Ytterbium-fiber laser type (FL x50s, Rofin) which operates at a maximum power of 500W in continues wave at a 1080 nm of wavelength. The welding head was equipped with a focal length and collimator of 125mm producing a minimum spot size of 150 m. The powder layers were deposited on a building platform plate of Steel AISI 1045 with a built inclined plane which permitted the evaluation of the process at different layer thicknesses. 2.3 Single track forming process To simplify the interpretation, samples were built using a straight laser scan, as shown in Fig. 3. Each experiment consisted on a single track of 230 mm in length, where the powder layer thickness was varied continuously from 40 to 500 mm. The building process was specified under four families or groups of experiments. Each family corresponded to a different scan speed value, and within each family the straight tracks were produced under different laser power values. The summary of the factorial design of experiments (DOE) used on the deposition are listed on Table 2. The SLM process was performed without a controlled atmosphere"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003807_j.triboint.2017.12.027-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003807_j.triboint.2017.12.027-Figure7-1.png",
        "caption": "Figure 7: Mesh created on Gmsh with 55539 nodes and 254118 elements.",
        "texts": [
            " The model will be applied and compared with three different operating conditions: oil jet lubricated steel gears, oil dip lubricated FZG type A gears and unlubricated polymer gears. A steel spur gear [27] was considered, whose geometric characteristics and material properties are presented in AppendixB (see Table B.9 and Table B.10). The gear is lubricated with a Mobil Jet II oil, whose physical properties are enumerated also in AppendixB (see Table B.11). The operating conditions considered can be found in Table 1. The mesh was created on Gmsh with 55539 nodes and 254118 tetrahedron elements as presented in Figure 7. 3.1.1. Determining oil/air phase mixture The parameter that takes into account the volume ratio between air and oil in the mixture is \u03b1mix. A situation of dry contact corresponds to \u03b1mix=1 and a situation of oil sump lubrication corresponds to \u03b1mix=0. This phenomenon of oil\u2019s aeration 5 M ANUSCRIP T ACCEPTE D Table 2: The \u03b1mix parameter as function of rotational speed. Rotational Speed [rpm] Long et al. [27] Current FEM 2000 0.3 0.1 4000 0.4 0.3 6000 0.5 0.4 which is a major cause of gear no-load power losses, mainly at very high speeds, was studied in detail by Le Prince et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure6.17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure6.17-1.png",
        "caption": "Figure 6.17.2. Free-body diagram for a car on a super-elevated corner.",
        "texts": [
            "17 Banking Road slopes can be divided into two main types: longitudinal and lateral. Lateral slopes are commonly known as banking, or just as camber in the case of modest slopes used for water drainage. On the straight, banking results in a side force component mg sin\u03b8 where \u03b8 is the road angle. The tire vertical reaction becomes mg cos\u03b8 which can be approximated as mg for practical camber cases up to 8\u00b0. For a primary neutral vehicle, the lateral force at G can be opposed by equal slip angles at the two ends, so the vehicle will drift sideways without rotation, Figure 6.17.1(a). With no control steer change, an understeering vehicle will tend to generate less lateral acceleration at the front, and so will rotate away from the side force, turning down the slope, Figure 6.17.1(b). An oversteer vehicle will initially drift away but will ultimately turn up the slope, Figure 6.17.1(c), because less lateral acceleration is generated at the rear. 408 Tires, Suspension and Handling To maintain a straight path in the steady state, the side force acting at G calls for slip angles, but no kinematic steer angle: Allowing for suspension effects using cornering compliance, the attitude angle is and the steer angle required is where k is the primary understeer gradient. Thus a neutral steer vehicle will be in equilibrium at an attitude angle but zero steer angle. A primary understeer vehicle will need to be steered up the slope, and an oversteer vehicle down it",
            " At Steady-State Handling 409 the fairly large value of kU = 0.5 deg/m s 2 (5 deg/g) and a side slope of 5\u00b0, then \u03b4 = 0.44\u00b0, or about 8\u00b0 at the steering wheel, and \u03b2 0.5\u00b0. A straight road of banking \u03b8 will require a lateral friction coefficient of tan\u03b8 merely to maintain a straight path. This may be difficult to achieve in icy conditions. A small amount of banking is also common on corners, and this may be favorable or unfavorable. More extreme banking, sometimes called super-elevation and with angles as great as 40\u00b0 (Figure 6.17.2), is found on some racing circuits and on high-speed test circuits. In such cases the road cross-section is usually curved with greater angles high up, so that the driver can choose the desired banking angle. In Figure 6.17.2, a vehicle is cornering with lateral acceleration A = V2/R at constant height on a banked road. The tire forces required are The mean required tire cornering coefficient is Setting F to zero, no tire lateral force will be required if the slope angle is and this condition may actually be achieved on super-elevated circuits. In this case the normal reaction is greatly increased to mg/cos\u03b8. This is liable to bring a conventional vehicle down onto its bump stops. Vehicles designed for such conditions generally have very stiff or rising-rate suspensions, and appropriately uprated tires"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000443_tmag.2010.2093872-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000443_tmag.2010.2093872-Figure2-1.png",
        "caption": "Fig. 2. Flux distribution of the study models in the load condition: (a) 8-pole and 12-slot model; (b) 8-pole and 9-slot model.",
        "texts": [
            "00 \u00a9 2011 IEEE As the component of total force, the radial force of PMSM can be well calculated in the Maxwell stress tensor method [5]. The force density of the radial component can be obtained as (1) where is the permeability of air, and and are the flux densities of the radial and tangential components, respectively. In order to obtain the flux density in (1), the magneto-static field FEA is processed. The governing equation is described as (2) where is the magnetic potential vector, is the current density vector, is the magnetization vector, and is the reluctivity of the permanent magnet. Fig. 2 shows the flux distribution of the study models in the load condition . It can be seen that the flux distribution in the 8-pole/9-slot model is obviously asymmetrical. In the same load condition (3.5 Nm), the tangential and radial components of flux density in the air gap of these two models are calculated and shown in the Fig. 3. It is observed that both the tangential and radial components of the flux density of 8-pole/12-slot model are spatially periodic, while the flux densities of 8-pole/9-slot model are nonperiodic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002624_j.promfg.2017.07.163-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002624_j.promfg.2017.07.163-Figure1-1.png",
        "caption": "Figure 1 Schematic of Wire and Arc Additive Manufacturing with integrated rolling [5]",
        "texts": [
            " The process uses an electrical arc as a heat-source to melt feedstock metal wire, which is deposited onto a base plate [4]. The WAAM process comprises successive cycles of melting, depositing and cooling to result in a near-net shape deposit. Cold-work through rolling may be subsequently employed to improve microstructural properties and relieve residual stresses induced by thermal cycles incurred through the deposition process [5][6]. WAAM with an integrated roller consists of an arc torch is shown in Figure 1 [5]. To achieve end-product status, heat treatment for residual stress relief and/or to develop mechanical properties and finish machining is required [8]. Compared to powder based AM methods, WAAM offers several distinct benefits. In certain materials, directed deposition and cheaper wire feedstock mean that cost be reduced significantly compared to PBF. Further, processing issues such as powder agglomeration, recycling are overcome. Concerns with development of full density and microstructure of non-heat treatable materials in PBF and Binder Jetting may be overcome by the inter-pass rolling which is easily implemented in WAAM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003887_j.ijmecsci.2019.05.012-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003887_j.ijmecsci.2019.05.012-Figure1-1.png",
        "caption": "Fig. 1. Sketch map of the spur gear tooth with a uniform crack on the tooth root.",
        "texts": [
            " Thus, a tooth crack model proosed by Chen and Shao [15] is employed in which both the crack length nd depth are considered in order to model the tooth crack propagation t different stages. Firstly, the determination of mesh stiffness with a niform crack depth along the tooth width is presented as a basis. Next, or the tooth crack with a non-uniform depth along the tooth width, y dividing the gear tooth into multiple thin slices, the crack depth for ach slice could be regarded as a constant, and then the total gear mesh tiffness could be obtained by integrating the stiffness of all slices. Fig. 1 depicts the sketch map of a spur gear tooth with an effecive length d . The tooth crack here has a constant depth q through the hole tooth width with a crack angle \ud835\udefd and an initial angle position \ud835\udefe. andya and Parey [11] utilized a single tooth two-dimensional finite elment model (FEM) to simulate the crack propagation. The crack path as predicted and the crack angle \ud835\udefd was obtained based on the FEM esults. The crack angle \ud835\udefd varied from 62\u00b0 to 84\u00b0 for different crack levls in a low contact ratio gear pair, and it varied from 68\u00b0 to 77\u00b0 in a igh contact ratio gear pair. Mohammed et al. [16,19,30] considered he crack angle to be 70\u00b0 in their cracked tooth model. Based on these revious studies, the crack angle \ud835\udefd is chosen to be 70\u00b0 in this study. Ma t al. [13,14,31] proposed an improved mesh stiffness model for cracked pur gears, in which the crack initial position \ud835\udefe was considered to be 35\u00b0 \ud835\udefe is the angle between the tangent of the crack point and the horizonal axis, as shown in Fig. 1 ). Their proposed model was validated by the EM and found to be of high precision. Therefore, in this study the crack s also estimated to occur at 35\u00b0 tangent point, i.e., \ud835\udefe = 35\u00b0. The gear mesh stiffness in this research is calculated by using the otential energy method. The potential energy of a gear tooth is esti- ated to contain four components, namely, bending energy, axial com- ressive energy, shear energy and Hertzian energy [9,10] . Besides, the llet-foundation deflection should also be taken into consideration [32] . For the gear tooth with a uniform root crack in Fig. 1 , the bendng and shear stiffness will be influenced by the tooth crack, while he axial compressive stiffness will remain the same as that for perect tooth because the crack part can still bear the axial compresive force [10,13,18] . Therefore, the formulations of bending stiffness b,crack , shear stiffness k s,crack , axial compressive stiffness k a and Hertzian Table 1 Coefficients of the polynomial function. A i B i C i D i E i F i L \u2217 ( h fi, \ud835\udf03f ) \u2212 5 .574 \u00d710 \u2212 5 \u2212 1 .9986 \u00d710 \u2212 3 \u2212 2 .3015 \u00d710 \u2212 4 4 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003949_j.jmapro.2018.09.011-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003949_j.jmapro.2018.09.011-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration and pictures of the experimental setup. (a, d) Schematic representation of the experimental conditions for in-situ observation and single-track formation on powder bed/substrate, the high-speed camera is focused onto the processing area at an angle of 15\u00b0. (b) A high-speed camera is mounted outside the protective window to imaging the processes and (c) the plate half-covered by the powder bed with laser tracks, the scan direction is indicated by the red arrow (from powder bed to bare plate). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)",
        "texts": [
            " However, with the study focused on the mechanisms of material redistribution during LPBF, the resulting melt track and the relationship between process stability and spatter generation, were not presented. By using high speed observation, this study aims to provide a better understanding of the vapor plume behavior evolution and spatter generation during single track experiments under different laser speeds, with an attempt to link the in-situ observation results to the process stability and the resulting melt tracks. Experiments were carried out in a self-developed LPBF system as presented in Fig. 1. This system is equipped with an CW ytterbium-fiber laser (IPG YLR-500-WC-SM, USA) in combination with a scan head (SCANLAB hurry SCAN\u00ae 30, Germany). The laser system provides a maximum power of 500W in continuous mode with a wavelength \u03bb=1.07 \u03bcm. The laser spot diameter is 100 \u03bcm (1/e2, Gaussian mode) at the processing platform. 304-stainless steel powders of spherical shape and substrate were used to generate single tracks in this study. The powder size is ranging from 30 to 46 \u03bcm, with a d(0.5)= 36.8 \u03bcm. A series of experiments were designed and carried out to investigate the vapor plume behavior during single track formation with or without the powder layer. A \u223c60 \u03bcm -thick layer of powder was manually spread onto half of the substrate using a stainless-steel razor edge (Fig. 1c). A 400W laser beam scanned across the powder bed and then onto the bare substrate (from left to right) at 5 different scan speeds ranging from 200mm/s to 2000mm/s to generate single melt tracks. The length of the melt tracks was kept constant at L=30mm for all the experiments with a fixed scan interval of 5mm. In this way, each laser track in this study is a combination of 15mm-long laser powder bed fusion track (left half) and 15mm-long laser fusion track without powder (right half) melted and observed under exact identical experimental conditions, as illustrated in Fig. 1c. By comparing the phenomena of both sides, the effects of powder layer on the melting process can be better identified, as will be shown in the following section. The LPBF chamber is filled with argon to provide a protective atmosphere for all the experiments, but no shielding gas flow was applied above the powder bed. The volumetric energy density (VED) delivered to the laser-metal interaction zone can be defined using the equation [24,26]: = P \u03c0\u03c3 vVED 4 / 2 where VED means the volumetric energy density (J/mm3), P is the laser power (W), \u03c3 is laser spot diameter (mm) and v is laser scan speed (mm/ s) (Table 1). Off-axis monitoring technique was utilized to investigate the plume behavior and spatter generation during single track formation in LPBF. An i-SPEED 716 high-speed CMOS camera (ix-cameras, the UK) is mounted outside the protective chamber window of the LPBF system (Fig. 1a) and focused at an observation angle of 15\u00b0 above the processing platform. Images were acquired at a fixed rate of 20,000 frames per second (fps), with a constant exposure time of 50 \u03bcs and a special resolution of 106\u00d7762 pixels, to reduce blur due to the rapid motion of the laser beam. No external illumination was applied for the observation. As a result, only objects above a certain temperature, such as the vapor plume, melt pool and spatters, can be bright enough to be observable to the CMOS sensor within the extremely short exposure time (50 \u03bcs) according to Planck's law"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003443_bf02120338-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003443_bf02120338-Figure8-1.png",
        "caption": "Fig. 8. The state of loading of the springs when the cross-spring pivot is not subjected to external forces while being deflected through a large angle ~.",
        "texts": [
            " From this it follows at the same time that the paths described by points of the members during the relative movement deviate somewhat from the arcs of a circle, so that the momentary pivot point is slightly shifted with respect to the initial intersection of the springs. Taking into account the conditions of equilibrium of each spr~ng Appl. Sci. Res. A I 21\" separately, we may deduce b y reason of symmet ry that the forces present at the spring ends can only run parallel to the line of symme t ry and that the bending moments must be equal two b y two. This is i l lustrated in fig. 8. If the spring A D is fixed at A we obtain the same state of loading as given in fig. 4, except tha t now 9 N = Q s i n ( a + ~9), D --- - - Q cos (a + .~-9). (11) Since we are no longer confined to small angles of deflection, in eq. (3) the curvature 1/e must now be replaced b y d g ' / d s where s is the arc length measured along the spring from its fixed end and 9' the slope of the tangent at the point (x, y). With dx /ds ~ cos 9' and d y / d s ~- sin 9', differentiation of eq. (3) with respect to s gives 2 D L 2 D s , ~ : '=- -x ,___ Y (13) a - - E 1 ' t a n f l - - - - ~ , a ' = ~ L ' ~l -~ , we can write this equation as d29 ' a da '2 + 2 sin-----fl sin (9' -- /3) = 0",
            " cos 89 With the aid of (23), (25), (26) and (31), this equation can also be written as Z = - - - a - - V 2 ( y + cos 2~Oo) - - V 2 ( r + cos 2~o~) - - ~/ a 9} (35) - - ~ cos ~ cos ~- As to the state of stress in the springs, it is to be remarked that the bending moments have an extreme value at the two spring ends x = 0 (9' = Y'o) arid x ---- l (~v' = %). For these bending moments Mo and M l we find, by means of the eqs (15), (17) and (21), the relations M~ / a E 1 2sin/5 \" V'2(y+c~176176 I M~L_]//aE_I 2 sin/3 \" ~/2(7 + c~ 27't)\" ] (36) As is evident from fig. 8, the moment M that has to be exerted on the cross-spring pivot in order to bring about an angle of deflection amounts to M = M o + M I + QL sin a sin ~ ~0. Owing to (11), (13) and (23), QL2/EI = a/2.sin/3. Thus for the moment M we find the relation ML I V a /V2< + cos + cos [ E1 2 sin/3 % ] / a s inas in 89 ~o}. (37) + 2 sin t~ In accordance with (21) and (27) the constant of integrat ion 7 appears to be 7 = 2 / k 2 - I = 2k . 2 - 1, (38) whilst, owing to the first equat ion (25), (26) and (28), the quan t i t y Va/2 sin fl amounts to # - - - = sin fl In these equat ions k or k* = 1/k and the limits of integrat ion ~0 and * and ~* are to be regarded as known functions of a and 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure4.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure4.16-1.png",
        "caption": "Fig. 4.16 Sketch showing pitching moments at the aircraft centre of mass",
        "texts": [
            " In forward flight, a positive perturbation in normal velocity, w, causes a greater increase in lift on the advancing than on the retreating side of the disc. The disc flaps back giving rise to a positive, nose-up, destabilizing, pitching moment. This effect does not change in character between an articulated rotor (Puma) and a hingeless rotor (Lynx), but the magnitude is scaled by the hub stiffness. The pitching moments arise from three major sources \u2013 the main rotor, the tailplane, and the fuselage (Figure 4.16), written as shown in Eq. (4.60). M = MR + Mtp + Mf (4.60) 190 Helicopter and Tiltrotor Flight Dynamics M \u2248 \u2212 ( Nb 2 K\ud835\udefd + hRT ) \ud835\udefd1c \u2212 (xcg + hR\ud835\udefes)T + (ltp + xcg)Ztp + Mf (4.61) The pitching moments from the rotor, tailplane, and fuselage are shown in Figure 4.16. The contribution of the tail to Mw is always stabilizing \u2013 with a positive incidence change, the tail lift increases (Ztp reduces), resulting in a nose-down pitch moment. The importance of the horizontal tail to the derivative Mw and helicopter pitch stability is outlined in Ref. 4.7, where the sizing of the tail for the YUH-61A is discussed. The contribution from the fuselage is nearly always destabilizing; typically, the aerodynamic centre of the fuselage is forward of the centre of mass. The overall contribution from the main rotor depends on the balance between the first two terms in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000030_j.engstruct.2004.07.007-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000030_j.engstruct.2004.07.007-Figure1-1.png",
        "caption": "Fig. 1. Gear pair geometry.",
        "texts": [
            " The modeling of the dynamic behavior of gear pairs is a problem that has been studied extensively; see [18] for a review of bibliography. A number of models ranging from simple models of one-degree of freedom to complex models with many variables have been proposed. In this work, a mass-spring model is used because of its simplicity. The one-degree of freedom model is sufficient for at least a qualitative description of the problem, while a time-varying stiffness affected by the crack magnitude can be introduced. The basic geometry of the gear pair is presented in Fig. 1. Following the analysis in the original work of Harris [19] and subsequent work by Blankenship and Singh [20], it can be shown that the normalized equation of the gear pair is \u20acn\u00f0s\u00de \u00fe 2f _n\u00f0s\u00de \u00fe K\u00f0h\u00den\u00f0s\u00de \u00bc fo \u00fe K\u00f0h\u00ded\u00f0h\u00de \u00f015\u00de where s the normalized time; n(s) the normalized displacement; f the system damping coefficient; K(h) the normalized stiffness; fo the normalized excitation force; d(h) the normalized geometrical error; h\u00f0s\u00de \u00bc Xs the angular displacement. This equation can be solved numerically provided that an expression for the stiffness K(h) is given"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002770_acc.2014.6859328-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002770_acc.2014.6859328-Figure3-1.png",
        "caption": "Fig. 3: Hovering with tilted arms",
        "texts": [
            " The proportional- derivative control laws are used to control \u2206\u03c9\u03c6,\u2206\u03c9\u03b8,\u2206\u03c9\u03c8 and \u2206\u03c9f which are deviations that result into forces/moments causing roll, pitch, yaw, and a net force along the zB axis, respectively, and are calculated as: \u2206\u03c9\u03c6 = kp,\u03c6(\u03c6des \u2212 \u03c6) + kd,\u03c6(pdes \u2212 p) \u2206\u03c9\u03b8 = kp,\u03b8(\u03b8 des \u2212 \u03b8) + kd,\u03b8(q des \u2212 q) \u2206\u03c9\u03c8 = kp,\u03c8(\u03c8des \u2212 \u03c8) + kd,\u03c8(rdes \u2212 t) (20) where p, q and t are the component of angular velocities of the vehicle in the body frame. The relationship between these components and the pitch, roll, and yaw are provided in [14]. The relationship between the tilt angles of individual rotors, given by \u03b8desi , i = 1, 2..4, and the reference pitch and roll angles is given by : \u03b8des1 \u03b8des2 \u03b8des3 \u03b8des4  =  1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1   2\u03c6desh 2\u03b8desh \u2206\u03c6h \u2206\u03b8h  (21) where \u03c6desh and \u03b8desh are reference roll and pitch angles and \u2206\u03c6h and \u2206\u03b8h orientation deviations. Fig. 3 shows the orientation of the vehicle with respect to the tilted propellers. A proportional-derivative controller is used to control the orientation deviation using the reference orientation values as: \u2206\u03c6h = kp,\u03c6h (\u03c6desh \u2212 \u03c6) \u2212 kd,\u03c6h p \u2206\u03b8h = kp,\u03b8h(\u03b8desh \u2212 \u03b8) \u2212 kd,\u03b8hq (22) In order to have the quad-rotor track a desired trajectory ri,T , the command acceleration, r\u0308desi is calculated from proportional-derivative controller based on position error, as [13]: (r\u0308i,T \u2212 r\u0308desi ) + kd,i(r\u0307i,T \u2212 r\u0307i) + kp,i(ri,T \u2212 ri) = 0 (23) where ri and ri,T (i = 1, 2, 3) are the 3-dimensional position of the quad-rotor and desired trajectory respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000443_tmag.2010.2093872-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000443_tmag.2010.2093872-Figure8-1.png",
        "caption": "Fig. 8. Vector of the calculated local forces: (a) 8-pole/12-slot model; (b) 8-pole/9-slot model.",
        "texts": [],
        "surrounding_texts": [
            "The mechanical characteristic of a motor can be described as (6) where is the vector of the displacement, is the mass matrix, is the damping matrix, is the stiffness matrix, and is the applied force vector [1], [7]. In this study, the vector only consists of the harmonic components of the calculated local force, because the dc component has no effect on the vibration and noise. Fig. 11(a) and (b) show the calculated vibrations of these two motors at 2500 rpm and 3.5 Nm output torque, respectively."
        ]
    },
    {
        "image_filename": "designv10_1_0003403_1.4031071-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003403_1.4031071-Figure2-1.png",
        "caption": "Fig. 2 Coupon orientation and support structures (shown in red/darker gray) for the (a) vertical, (b) horizontal, and (c) diagonal build directions",
        "texts": [
            " 137, NOVEMBER 2015 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use have had supports; however, it would be difficult to remove these supports after the build was completed. The horizontal surfaces of the channels were intentionally unsupported to replicate situations, where internal features require supports but cannot be accessed for support removal. The support structures used to build the coupons are shown in Fig. 2. In addition to using supports for surfaces angled at 40 deg or less, supports were placed on other features, such as the coupon flanges, to prevent distortion by anchoring the part to the build plate. For this study, the support structures were generated using a commercial stereolithography (STL) file editing and build preparation software. A state of the art DMLS machine was used to manufacture the test coupons using the machine parameters given in Table 1. Prior to building the coupons, a qualification block was built out of Inconel 718 to calculate the material scaling parameters and beam offset",
            " When building the upper surface of the channel in the diagonal build direction, the heat from the laser penetrated deeper than the current layer, melting some of the powder inside the channel. This overmelting generated the globular features shown in Fig. 7. In addition, these defects compounded the distortion seen in the upper channel surface by hindering the creation of subsequent layers [29]. Conduction differences during the build could have exacerbated the deformations and inconsistencies seen with the different build directions. Given the support structures shown in Fig. 2, the heat from the melt pool must conduct to the build plate through different paths in each build direction. In the diagonal build direction, there are no supports on the downward facing exterior surface. Therefore, all of the heat must conduct to the plate through the small amount of support structure at the bottom of the flange. This small connection to the build plate could have slowed the rate of solidification each layer, and thus impeded the ability to hold a tight tolerance on the overhanging upper surface of the channel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002359_j.isatra.2019.01.017-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002359_j.isatra.2019.01.017-Figure1-1.png",
        "caption": "Fig. 1. The robot manipulator with two DOF.",
        "texts": [
            "5 \u03c7T\u03c7 \u2212 \u221a Li\u03bbmin (R2) \u03c7T\u03c7 \u2264 \u2212\u03b52 \u221a Li ( V4 \u03bbmin (P2) ) 1 2 V4 \u03bbmax (P2) \u2212 \u221a Li\u03bbmin (R2) V4 \u03bbmax (P2) = \u2212\u03b341V \u2212 1 2 4 \u2212 \u03b342V4 (64) where \u03b341 = \u03b52 \u221a Li\u03bbmin(P2) \u03bbmax(P2) and \u03b342 = \u221a Li\u03bbmin(R2) \u03bbmax(P2) . It follows from the lemma that the dynamic system (52) is finite-time stable. That is, the sliding mode variable s and the estimate error f\u0303d will converge to zero in finite time. The proof is completed. In this section, to verify the performance of the presented controller, simulations of a two degree-of-freedom (DOF) robot manipulator (shown in Fig. 1) are performed. The dynamic model of the robot manipulator with two DOF in Fig. 1 is expressed as[ M11 M12 M12 M22 ][ q\u03081 q\u03082 ] + [ \u22122C11q\u03072 \u2212C11q\u03072 0 C11q\u03072 ][ q\u03071 q\u03072 ] + [ G1g G2g ] = [ \u03c41 \u03c42 ] + [ \u03c41d \u03c42d ] (65) where M11 = (m1 + m2) r21 + m2r22 + 2m2r1r2 cos (q2), M12 = m2r22 + m2r1r2 cos (q2), M22 = m2r22 , C11 = m2r1r2 sin (q2), G1 = (m1 + m2) r1 cos (q2) + m2r2 cos (q1 + q2), and G2 = m2r2 cos (q1 + q2). The parameter values in the robot system (64) are assigned as m1 = 1 kg, m2 = 1 kg, r1 = 1 m, and r2 = 1 m. To demonstrate the convergence properties of the proposed TSMS, the TSMSs s\u2032 = z\u0307 + sig\u03b1 (z) and s = z\u0307 + \u00b5 (z) sig\u03b1 (z) are used for comparison"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure3-6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure3-6-1.png",
        "caption": "Fig. 3-6 Rotor \u03b1\u03b2 and dq equivalent windings.",
        "texts": [
            " Equation (3-28) and Equation (3-29) can be written as follows in a vector form, where each vector contains a pair of variables\u2014the first entry corresponds to the d-winding and the second to the q-winding: v v R i i d dt sd sq s sd sq sd sq d         =         +         + \u2212\u03bb \u03bb \u03c9 0 1 1 0               [ ] . Mrotate \u03bb \u03bb sd sq (3-30) Note that the 2\u00a0\u00d7\u00a02 matrix [Mrotate] in Eq. (3-30) in the vector form corresponds to the operator (j) in Eq. (3-27), where j(=\u00a0ej\u03c0/2) has the role of rotating the space vector \u03bbs dq_ by an angle of \u03c0/2. Rotor Windings An analysis similar to the stator case is carried out for the rotor, where the \u03b1\u03b2 windings affixed to the rotor are shown in Fig. 3-6 with the \u03b1-axis aligned with rotor A-axis. The d-axis (same as the d-axis for the stator) in this case is at an angle \u03b8dA with respect to the A-axis. Following the procedure for the stator case by replacing \u03b8da by \u03b8dA results in the following equations for the rotor winding voltages v R i d dt rd r rd rd dA rq= + \u2212\u03bb \u03c9 \u03bb (3-31) and v R i d dt rq r rq rq dA rd= + +\u03bb \u03c9 \u03bb , (3-32) where d dt dA dA\u03b8 \u03c9= is the instantaneous speed (in electrical radians per second) of the dq winding set in the air gap with respect to the rotor A-axis speed (rotor speed), that is, MATHEMATICAL RELATIONSHIPS OF THE dq WINDINGS 39 40 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS \u03c9 \u03c9 \u03c9dA d m= \u2212 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000892_tcyb.2015.2447153-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000892_tcyb.2015.2447153-Figure4-1.png",
        "caption": "Fig. 4. Single-link flexible joint manipulator.",
        "texts": [
            " (40) According to Theorem 2, the adaptive law \u03b8\u0302 (k) and the control law u(k) are chosen, respectively, as \u03b8\u0302 (k + 1) = \u03b8\u0302 (k) + T \u239b \u239d 2\u2211 i=1 r 2\u03b72 i z2 i (k) \u2212 \u03b2\u03b8\u0302(k) \u239e \u23a0 (41) u(k) = \u2212 z2(k) g 2 ( \u03b8\u0302 (k) 2\u03b72 2 + k2 + 1 + g\u03042 + g\u03041 2 ) (42) where z1(k) = x1(k) \u2212 yd(k) and z2(k) = x2(k) \u2212 \u03b11(k). The stabilizing function \u03b11 is given by \u03b11(k) = \u2212 z1(k) g 1 ( \u03b8\u0302 (k) 2\u03b72 1 + k1 + 1 + g\u03041 2 ) . The simulation results are shown in Fig. 3. It can be seen that the tracking performance can be achieved when the controller (42) is applied to discrete system (40). Example 2: Consider a single-link manipulator with flexible joint shown in Fig. 4. The mathematical model describing the motion of the system is given by Iq\u03081 + Mgl sin q1 + k(q1 \u2212 q2) = 0, Jq\u03082 \u2212 k(q1 \u2212 q2) = u (43) where q1 and q2 denote the link joint position and the rotation angle of motor, respectively; I is the rotary inertia of the joint, and J is the rotary inertia of the motor; M and l denote the mass and centroid length of the link; g represents the gravitational acceleration, and k is the stiffness coefficient of the joint; u is the control input representing the motor input torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003950_j.ymssp.2018.09.027-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003950_j.ymssp.2018.09.027-Figure3-1.png",
        "caption": "Fig. 3. Mating process of a spur gear pair with friction forces.",
        "texts": [
            " As defined in [10,20], micro-pitting is usually in very small size, therefore, its effect can be modeled as the increase of the tooth surface roughness. The tooth spalling (or macro-pitting) is often in large size which is capable of blocking the formation of a lubricant film and reducing the effective tooth contact length, see Fig. 2. The reduced tooth contact length directly decreases the strength of the contacting teeth on supporting the dynamic loads, which is generally modeled by decreased gear TVMS within the spalling area [23]. The mating process of a spur gear pair with tooth contact friction forces is shown in Fig. 3. The line of action B1B2 is tangent to the base circles of the pinion and gear at points B1 and B2. Line segment P1P2 is the actual effective contact locus, where point P1 is the starting contact point (approach point), and P2 corresponds to the separation point. a0 is the pressure angle,x1 andx2 are rotational speeds. Fpg is the total dynamic mesh force of the mating process (along the action line B1B2). Fg1 and Fp1, Fg2 and Fp2, represent the tooth contact friction forces of each mating tooth pair. The mating tooth can be simplified as equivalent cylinders in contact with time-varying radii of the tooth curvatures r1 and r2 (Fig. 2) or rp1, rp2, rg1, rg2 (Fig. 3) and forming a lubrication filmwith width of 2b.up1 \u00bc x1 rp1, ug1 \u00bc x2 rg1 are the moving speeds of the contact point of each surface along the off-line of action [24]. For ordinary spur gear pairs with contact ratio less than 2, the length of the time-varying radii (rpi, rgi) can be determined from rpi \u00bc rbp hpi \u00fe tan\u00f0\\B1OPP1\u00de rgi \u00bc \u00f0rpp \u00fe rpg\u00desina0 rpi ( i \u00bc 1; 2; \u00f01\u00de in which i denotes the ith gear tooth, hpi is the contact angle of the ith tooth pair. For a spur gear pair, the contact angle of the followed second gear tooth lags with respect to the first gear tooth pair by hp1 2p=N where N is the number of gear teeth",
            " The \\B1OpP1 \u00bc arccos Rbp=OpP1 with OpP1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 ag \u00fe OpOg 2 2Rag OpOgcos \\OpOgP1 q and \\OpOgP1 \u00bc arccos Rbg=Rag a0 [25], rbp and rbg , rpp and rpg , rap and rag are the radii of the base circle, pitch circle, and addendum circle of pinion and gear, respectively (see Fig. 3). The evaluation of the dynamical friction forces and damping ratios of the contacting tooth surfaces with lubrication effects involves the analysis of the lubrication film thickness, contact pressure, oil viscosity, surface roughness, moving velocity, effective contact area, and film shear stress etc. The mixed elastohydrodynamic lubrication (mixed-EHL) theories are widely applied to analyze the contact properties of a mating gear tooth pair with gear tooth pitting and spalling. The gear tooth in the healthy surface area is assumed smooth, in which the asperity has limited effects on film thickness and pressure distribution. Therefore, the two surfaces in contact are assumed supported by a lubrication film [26]. For an arbitary gear mesh point, the line contact mixed-EHL equations under isothermal conditions can be expressed as [27] d dx qh3 g dp dx \u00bc 12us d\u00f0qh\u00de dx h \u00bc hc \u00fe x2 2R \u00fe t\u00f0x\u00de \u00fe r\u00f0x\u00de t\u00f0x\u00de \u00bc 2 pE R xe x0 p\u00f0s\u00deln\u00f0s x\u00de2ds\u00fe ck w R xe x0 p\u00f0x\u00dedx \u00bc 0 8>>>>< >>>: \u00f02\u00de where x corresponds to the x-axis of the coodinate system, as shown in the zoomed area of Fig. 3. x0 and xe are the coordinates of inlet and outlet positions, respectively. R is the equivalent raduis, us is the equivalent speed, p is the contact pressure, hc is the central film thickness, h is the film thickness, t(x) is the surface elastic deformation, s is the integration variable on the x axis, r(x) is surface roughness function, ck is a constant,w is the load per unit contact length. q is the oil density which is a function of contact pressure and can be approximated as q = q0(1 + 0.6p/(1 + 1",
            " should be utilized to validate the results. Fig. 5 shows the effects of tooth pitting and spalling on the tooth contact load sharing ratio (LSR), EHL central pressure and film thickness evaluated by Eq. (5) under constant load and speed conditions of Fpg = 1000 N and x = 1500 rpm. The number of teeth of pinion and gear are N1 = 16 and N2 = 48 respectively, more details of the gear properties are presented in Table 1 in the appendix. The horizontal-axis in Fig. 5 is the distance of the mesh point relative to the pitch point (point P in Fig. 3) along the line of action, where a negative distance value indicates the mesh point is on the left side of point P (within line segment P1P), and vice versa for positive distance values. Due to the considerable high gear ratio (3:1) and small base radius of the driving pinion, the contact equivalent radius and speed are in small values at the approach point (P1 in Fig. 3). As the mating process progresses from P1 to P2, the equivalent contact radius and speed increase, see Fig. 5(a), and the lubricant condition improves as a result of increased lubricant film thickness and decreased central pressure, Fig. 5(b). The high central pressure at the starting contact point is mainly due to the low equivalent radius at the beginning. Lower equivalent radius R indicates higher dimensionless load (W \u00bc w=\u00f0E0R\u00de) and smaller Hertzia contact width (b \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8wR=\u00f0pE0\u00de p ), both increasing the contact pressure, as explained in [32]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.49-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.49-1.png",
        "caption": "FIGURE 5.49. Hayati-Roberts (HR) notation to avoid the singularity in the DH method.",
        "texts": [
            " In this condition, the DH notation has a singularity, because a small change in the spatial positions of the parallel joint axes can cause a large change in the DH coordinate representation of their relative position. The Hayati-Roberts (HR) notation is another convention to represent subsequent links. HR avoids the coordinate singularity in the DH method for the case of parallel lines. In the HR method, the direction of the ziaxis is defined in the Bi\u22121 frame using roll and pitch angles \u03b1i and \u03b2i as shown in Figure 5.49. The origin of the Bi frame is chosen to lie in the xi\u22121yi\u22121-plane where the distance di is measured between oi\u22121 and oi. Similar to DH convention, there is no unique HR convention concerning the freedom in choosing the angle of rotations. Furthermore, although the HR method can eliminate the parallel joint axes\u2019 singularity, it has its own singularities when the zi-axis is parallel to either the xi\u22121 or yi\u22121 axes, or when zi intersects the origin of the Bi\u22121 frame. Example 181 F Parametrically Continuous Convention method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure8.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure8.18-1.png",
        "caption": "Fig. 8.18 Schematic for interconnected suspensions",
        "texts": [
            " But in the system of Fig. 8.13 we have only two parameters, namely k1 and k2. Therefore the following equations k1 + k2 = kzz k1a1 \u2212 k2a2 = kz\u03b8 k1a 2 1 + k2a 2 2 = k\u03b8\u03b8 (8.103) may not all be fulfilled. As anticipated, the scheme of Fig. 8.13 is not as general as it may seem at first. We need a suspension layout with three springs, although we still have only two axles. Interconnected suspensions are the solution to this apparent paradox. A very basic scheme of interconnected suspensions is shown in Fig. 8.18. Its goal is to explain the concept, not to be a solution to be adopted in real cars (although, it was actually employed many years ago). To understand how it works, first suppose the car bounces, as in Fig. 8.19. The springs contained in the floating device F get compressed, thus stiffening both axles. On the other hand, if the car pitches, as in Fig. 8.20, the floating device F just translates longitudinally, without affecting the suspension stiffnesses. This way we have introduced the third independent spring k3 in our vehicle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003978_tie.2016.2565442-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003978_tie.2016.2565442-Figure2-1.png",
        "caption": "Fig. 2. A 3-D SLIM model with the solid back iron secondary",
        "texts": [
            " The primary, which is supplied by an inverter to change the voltage and frequency, consists of iron cores and coppery coils. The secondary side is a combination of a magnetically conductive part, such as an iron plate, and an electrically conductive part, such as an aluminum or copper plate. The solid and laminated back iron secondary are usually applied in engineering practice for the simple structure and low cost. In Fig.1, the entry and exit end causes end effects along the direction of travel. The coordinates shown in Fig.2 are defined as: x is the traveling direction of the magnetic field and this direction is called the longitudinal, y is the direction of lamination of the primary core and y is also called the transverse, and z is the normal direction of the pole face and the vertical. In Fig. 2, a 3-D SLIM model with solid back iron secondary is shown. When the primary is supplied by an inverter, the air-gap flux is produced between the primary and secondary. Through the reaction between the air-gap flux and the eddy current in the secondary, two types of forces, i.e. thrust (Fx) and vertical forces (Fz), are produced. Thrust is a tractive force and it is used to drive the train. Vertical force usually is the attractive force which increases the running resistance and the pressure of the rails",
            " In the solving region, fundamental equations of the magnetic field with eddy currents of the secondary taken into account can be written as follows , , 1 1 1 - -ix ix ix px i sx i i i i A A A J J x x y y z z                                , , 1 1 1 - - iy iy iy py i sy i i i i A A A J J x x y y z z                                , , 1 1 1 - -iz iz iz pz i sz i i i i A A A J J x x y y z z                                  , ix i ix sx i A v A J t           (1)   , iy i iy sy i A v A J t              , iz i iz sz i A v A J t           where v, A, \u03bc, \u03c3, Jp, Js are the velocity, the vector magnetic potential, the permeability, the conductivity, the current density of the primary and eddy current in secondary, respectively. Subscripts x, y, z, i, denote x-, y-, z- components and the region number in Fig.2, respectively. In each region, we get 0278-0046 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Region 1: , 0p iJ  , , 0s iJ  , 0i  , i Core  Region 2: , 0s iJ  , i Cu  , 0i  Region 3: , 0p iJ  , , 0s iJ  , 0i  , 0i  (2) Region 4: , 0p iJ  , i Al  , i Al  Region 5: , 0p iJ  , i Iron  , i Fe  where Core , Iron and 0 are the permeability of the primary core, iron plate and vacuum, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003657_j.measurement.2020.108855-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003657_j.measurement.2020.108855-Figure1-1.png",
        "caption": "Fig. 1. Megawatt-scale Wind turbine.",
        "texts": [
            " E-mail address: jinxin191@hotmail.com (X. Jin). Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement https://doi.org/10.1016/j.measurement.2020.108855 Received 15 September 2020; Received in revised form 18 November 2020; Accepted 7 December 2020 Measurement 172 (2021) 108855 X. Jin et al. Measurement 172 (2021) 108855 Modern WTGS bearings can be divided into two types: drivetrain bearings and adjustment slewing bearings [91011], as shown in Fig. 1. Drivetrain bearings can be spherical-, cylindrical- or tapered roller types [121314], and generator bearings use coated bearing (ceramic and conductive microfibers) and hybrid bearings [15].Structures of slewing bearings in wind power industry are more complicated than drivetrain bearings, including outer/inner raceway, rollers, bolts connection and gear teeth [16]. According to number of rows and location of gears, WTGS slewing bearings can be classified into four types, as shown in Fig. 2. WTGS Slewing bearings mainly include pitch- and yaw bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003546_tmag.2015.2446951-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003546_tmag.2015.2446951-Figure17-1.png",
        "caption": "Fig. 17. Flux density distributions for different copper loss at rotor d-axis position. (a) HSSPM - 50W (Idc = 3.64A, Iq = 5.14A). (b) VFM - 50W (Idc = 3.74A, Iq = 5.28A). (c) HSSPM - 400W (Idc = 10.28, Iq = 14.54A). (d) VFM - 400W (Idc = 10.59A, Iq = 14.98A).",
        "texts": [
            " A comparison of their iron losses and the PM eddy current loss of the HSSPM machine at 4000rpm rotor speed is shown in Fig. 16, for the same values of total copper loss. Both machines have similar total losses at low copper loss but the total iron loss increases faster in the HSSPM machine with increasing copper loss. It is approximately 20-25% higher at the highest copper loss considered. The PM eddy current loss remains comparatively very low with increasing copper loss. The flux density distributions for all machines at 50W and 400W copper loss is shown in Fig. 17. Magnetic saturation is reduced in the HSSPM machine compared to the variable flux machine, especially at high electric loading. (a) (a) (b) 0 60 120 180 240 300 360 0 0.5 1 1.5 2 2.5 Rotor position (\u00b0elec.) E le ct ro m ag ne ti c to rq ue ( N m ) HSSPM (100W) HSSPM (500W) VFM (100W) VFM (500W) 0018-9464 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000847_j.msea.2010.12.010-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000847_j.msea.2010.12.010-Figure3-1.png",
        "caption": "Fig. 3. Schematic of the gauge volume position for neutron diffraction measurements.",
        "texts": [
            "9 mm vertical slits in the incident eam and 2 mm horizontal slits in the diffracted beam resulting n an effective diffracting gauge volume of 2 mm \u00d7 2 mm \u00d7 1.8 mm. his takes the vertical beam divergence and slit to diffracting gauge olume distance into account. Lattice spacing measurements were made in three orthogonal irections in the form of line scans along the x-axis. Two line scans, entred in the y-direction were carried out for each sample at two eight positions, namely 2 mm (z = 2) from the substrate and 2 mm rom the top of the walls (distance from substrate varies depending n sample height, see Table 2). As indicated in Fig. 3 sample TW2 as also scanned along two further lines (z = 4.3 and 6.6 mm). Elasic strains were calculated using Eq. (1) where d0 is the stress-free d-spacing: \u03b5h k l = dh k l \u2212 d0 h k l d0 h k l (1) Once the strain is determined at a given location in three orthogonal directions, it is possible to calculate the corresponding stresses: x = Eh k l((1 \u2212 h k l)\u03b5x + h k l(\u03b5y + \u03b5z)) (1 + vh k l) (1 \u2212 2 h k l) . . . (2) where Eh k l and vh k l are the diffraction elastic constants for a specific h k l reflection and \u03b5x, \u03b5y and \u03b5z are the strains measured in the three orthogonal directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.24-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.24-1.png",
        "caption": "Fig. 3.24 Rotor blade pitch motion",
        "texts": [
            " 116 Helicopter and Tiltrotor Flight Dynamics Of course, one of the key driving mechanisms in the coupling process is the development of in-plane aerodynamic loads caused by blade pitch; any additional dynamic blade twist and pitch effects will also contribute to the overall coupled motion, but blade pitch effects have such a profound first-order effect on flapping itself that it is in this context that they are now discussed. Rotor Blade Pitch In previous analysis in this chapter the blade pitch angle was assumed to be prescribed at the pitch bearing in terms of the cyclic and collective applied through the swash plate. Later, in Section 3.4, the effects of blade elastic torsion are referred to, but there are aspects of rigid blade pitch motion that can be addressed prior to this. Consider a centrally hinged blade with a torsional spring to simulate control system stiffness, K\ud835\udf03 , as shown in Figure 3.24. For simplicity, we assume coincident hinges and centre of mass and elastic axis so that pitch\u2013flap coupling is absent. The equation of motion for rigid blade pitch takes the form \ud835\udf03\u2032\u2032 + \ud835\udf062 \ud835\udf03 \ud835\udf03 = Mp + \ud835\udf142 \ud835\udf03 \ud835\udf03i (3.213) where the pitch natural frequency is given by \ud835\udf062 \ud835\udf03 = 1 + \ud835\udf142 \ud835\udf03 (3.214) where MP is the normalised applied moment and \ud835\udf03i is the applied blade pitch. The natural frequency for free pitch motion (i.e. with zero control system stiffness) is one-per-rev; because the so-called propeller moment contribution to the restoring moment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure6-1.png",
        "caption": "Fig. 6. Six-axis hybrid PKM based on a 2-UPR/RPU PM.",
        "texts": [
            " For example, compared with the 2-UPR-SPR PM in Exechon robot, the 2-UPR/RPU PM has a simpler structure because the one spherical joint is replaced by a universal joint. Another advantage is the two specified axes of rotation that will simplify the control and calibration of the PKM. However, the workspace of the 2-UPR/RPU PM is smaller than that of the 2-UPR-SPR PM in Exechon robot because one rotation in the 2-UPR/RPU PM is near the moving platform and is not amplified by link length. This disadvantage can be Fig. 6 shows a six-axis hybrid PKM that is being built in Zhejiang Sci-Tech University. The PKM consists of a 2-UPR/RPU PM and an articulated RR serial mechanism. A linear guide is used to move the working table along the short side of the workspace of the 2-UPR/RPU PM. RPR-equivalent PMs in subcategory 4\u20134\u20135 can be constructed with two 4-DOF limbs in Table II and one 5-DOF limbs in Table III. We neglect the architectures with limbs generating {X(u)}{X(v)} because it would be very lengthy to enumerate RPR-equivalent PMs with limbs generating {X(u)}{X(v)}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000901_1.1830045-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000901_1.1830045-Figure11-1.png",
        "caption": "Fig. 11 Cable-1,3,5 quadratic curves \u201ef\u00c40 deg, static case\u2026",
        "texts": [
            " for which the end-effector is a 10 kg 2 m rigid bar with its center of mass at the mid point and with two connecting points at its ends. The connecting points of the base are, respectively, at ~1,0!, ~9,0!, ~5,10!, ~9,10!, ~1,10!, and ~0,5!. Dotted and continuous lines refer, respectively, to singularity and twocable equilibrium. Figure 10 shows the first step of the procedure: the creation of all the quadratic curves for every combination of cables; they are the potential boundaries of the workspace. We can easily notice the great number of sections that will be generated at the next step. Figure 11 shows the four curves for one particular threecable set, and Fig. 12 shows the corresponding subworkspace. Transactions of the ASME 13 Terms of Use: http://asme.org/terms Downloaded F Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 09/04/20 Finally, Fig. 13 shows the resulting workspace. Figures 14 and 15 show the x2y workspace for other orientations and dynamic states. A fundamental and systematic analysis of cable-driven planar parallel mechanisms has been performed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000252_taes.1984.310452-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000252_taes.1984.310452-Figure1-1.png",
        "caption": "Fig. 1. Link coordinate system and its parameters.",
        "texts": [
            " With appropriate P= (X,, yj, z,, 1)T modification and adjustment, the user can generalize and extend the method to most present day industrial robots Ai1 = with rotary joints and obtain the arm solution easily. cos Oi -cos cx; sin O0 sin cx; sin 0, ai cos O0 Ai-_ sin0i cos (x cos 0, -sin (x, cos 0 a, sin 0i 11. LINKS, JOINTS, AND COORDINATE = 0 sin x; cos (; di TRANSFORMATION L0 0 0 1 To describe the translational and rotational for a rotary joint. (2) relationship between adjacent links, a Denavit- With the basic rules for establishing an orthonormal Hartenberg matrix representation [9] for each link is used coordinate system for each link and the geometric and shown in Fig. 1. From Fig. 1 an orthonormal interpretation of the joint and link parameters, a coordinate frame system (xi, yi, zi) is assigned to link i, procedure for establishing consistent orthonormal where the zi axis passes through the axis of motion of coordinate systems for a robot is outlined in [5]. An joint i + 1, and the xi axis is normal to the zi- 1 axis example of applying this algorithm to a six-joint PUMA pointing away from it, while the y, axis completes the robot arm is given in Fig. 2. The six A> homogeneous right hand rule",
            " These indicators can also be set from the P' + knowledge of the joint angles of the robot arm using the -ARM * p 5p2 + p2 - d2 + pvd2 corresponding decision equations. We shall later give the cos 01 =2 2(4 decision equations that determine these indicator values. Px \u00b1 (24 The decision equations can be used as a verification of where positive square root is taken in these equations and the inverse kinematics solution. ARM is defined as in (9). In order to evaluate 01 for -r LEE & ZIEGLER: ROBOT INVERSE KINEMATICS SOLUTION USING GEOMETRIC APPROACH 699 xo-yo plane t~~~~~~~-0.\u00b0 o x ad- .Fo Fig 1,w aefu ifrn r 01 . -cr, an arc tangent function, atanc2(-) which 0c1 =atan2sin 0 retums tan d() adjusted to the proper quadrant will be dcos0ow used. It is defined as EF = p,, A atan2 -ARM pi,- pd2-2d-p.d2y -I R .p l p2-d2+pd0 =atan2y L-AR Pr X + r 00.0.900, for +x and + -.01. (26) 900 .0 1800, for -x and +Fy (25) Joint Two Solution. To find joint 2, we project the 1800 I0 - A90, for -Oxand-Ay position vector p onto the xL -Ay2plane as shown in Fig. -900 .0 00, for +x and -y 6. From Fig. 6, we have four different arm configurations",
            " These joint angles are also used to compute the decision equations to obtain the three arm configuration indicators. These indicators together with the arm matrix T are fed into the inverse solution routine The authors would like to thank R. Horner who wrote to obtain the joint angle solution which should agree with a \"C\" program to verify the above direct and inverse the joint angles fed into the direct kinematics routine kinematics equations together with their corresponding previously. A computer simulation block diagram is decision equations. shown in Fig. 1 1. LEE & ZIEGLER: ROBOT INVERSE KINEMATICS SOLUTION USING GEOMETRIC APPROACH 705 REFERENCES [5] Lee, C.S.G. (1982) [I] Pieper, DL. (1968) Robot arm kinematics, dynamics, and control.: * . , ~~~~~~~~~~~~IEEEComputer, 15. 12 (Dec. 1982), 62-80.The kinematics of manipulators under computer control. [] Pl Coput(1981) Computer Science Department, Stanford University, [6 Paul, R.P. (1981) Artificial Intelligence Project Memo 72, Oct. 24, 1968. Robot Manipulators: Mathematics, Programming and Control [2] Paul, R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000927_0094-114x(82)90042-8-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000927_0094-114x(82)90042-8-Figure6-1.png",
        "caption": "Figure 6. Stationary configuration.",
        "texts": [
            " Figure 5 illustrates the input--output function 01 vs 05 of an RCRCR mechanism with the following dimensions al2 = 25 m 0~12 = 60 \u00b0 S . = 30 m a23 = 30 a23 = 45 \u00b0 $33 = 25 a34 = 40 o~34 = 35 \u00b0 $55 = 0 a45 = 10 a45 = 300 as] = 32 asl = 10 \u00b0 MMT Vol. 17, No. 2-43 124 125 Superimposed on the input-output function are the graphs of the determinants Di and /)5 plotted against 05. It is clear that Dl = 0 when (d0Jd05)= 0, and link a,2 has a limit position. Also, D5 = 0 when (d05/d01) = 0, and the link a45 has a limit position. An interesting stationary configuration of the RCRCR mechanism occurs (Fig. 6) when the two screws representing the slider displacement of the cylindric pairs become linearly dependent. All the remaining five rotational motions must be instantaneously zero. This type of stationary configuration is difficult'to explain without a numerical example. The input--output function 0, vs 05 together with the slider-displacement functions $2 vs 0s and $4 vs 05 are illustrated by Figs. 7(a-c) of an RCRCR mechanism with the following dimensions a12 = 5%/(3) m a 1 2 = 90 \u00b0 $1, = 30m a23 = 15 a23 = 270 $33 = 20 a34"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002089_tia.2010.2103915-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002089_tia.2010.2103915-Figure2-1.png",
        "caption": "Fig. 2. Types of motors with concentrated windings.",
        "texts": [
            " Table I shows the specification of an experimental IPM motor to confirm the validity of the 3-D FEM. The motor has one interior magnet per pole. It is a sintered magnet of which remnant flux density is 1.2 T. Each magnet is segmented into ten pieces along the axial length. The stator has 24 slots with concentrated windings. Both the stator and rotor cores are laminated. The inverter is an insulated-gate-bipolar-transistortype PWM inverter of which carrier frequency is 10 kHz. The amplitude and phase of the armature current is set at Ia = 300 A and \u03b2 = 60\u25e6, respectively. Fig. 2 shows the cross sections of the analyzed motors. In the calculation, not only the experimental IPM motor but also the SPM motor are investigated. An identical stator is employed for each motor. The volumes of the magnets are also identical. Fig. 3 shows the methods of magnet segmentation. Although the axial segmentation is applied to the experimental IPM motor, the effect of the circumferential segmentation is also investigated in the calculation. B. Verification of 3-D FEM First, the measured and calculated results of the experimental IPM motor are compared in order to confirm the validity of the 3-D FEM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003873_j.jmatprotec.2018.04.040-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003873_j.jmatprotec.2018.04.040-Figure3-1.png",
        "caption": "Fig. 3. Dimensions of tensile samples.",
        "texts": [
            " These process parameters are listed in Table 2. Metallographic samples were prepared by a super computerized numerical control (CNC) wire electrical discharge machine. An OLYMPUS (GX71) optical microscope was used to observe the microstructure of the deposited walls. Three groups each of horizontal and vertical tensile specimens were prepared for each deposited wall. The extract position and sequence for the specimen manufacturing procedure are presented in Fig. 2. The dimensions of the tensile samples are shown in Fig. 3. These samples were exanimated at room temperature using an electronic universal testing machine (model AGS-X10KN) at a strain rate of 2mm/min. The fracture morphology was observed using a FEI Quanta 260 F scanning electron microscope. As seen in the photographs of the deposited wall in Fig. 4, the surfaces of six groups of deposited walls are well formed, with no apparent cracks, pores, or inclusions. For the same deposition current of 130 A with a deposition speed ranging from 30 cm/min to 60 cm/min, the height of the deposited walls visibly decreases, while its surface- forming and waviness characteristics improve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002255_978-3-319-09287-4-Figure12.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002255_978-3-319-09287-4-Figure12.5-1.png",
        "caption": "Fig. 12.5 Simulation of a double Flectofin , B position of the planar fins, B real position of the fins pushing against each other, E opened fins due to bending of the backbone (Lienhard et al. 2011)",
        "texts": [
            " Engineering principles Natural principles Light materials Anisotropy Light structures Heterogeneity Hierarchy Light systems Multifunctionality Adaptability Further optimisation of the basic Flectofin principle was aimed at folding two fins outward from one common element and thereby doubling the shaded area per element while hardly affecting the view. In contrast to the S. reginae the elastic 12 Bio-inspired, Flexible Structures and Materials 287 kinetics of the double Flectofin would need to be actuated from a common backbone. This system is shown in Fig. 12.5, with a configuration of two fins that theoretically interpenetrate (A). Therefore, they rest in position (B) where they push against each other and share a large contact area which highly increases their stability. As shown in Fig. 12.5, due to their concave curvature in their inactive state the fins bend outwards when the backbone is actuated (C\u2013F). The leaning against each other of the fins in their \u2018rest position\u2019 also serves to stiffen the fins against wind deformation. As a positive side effect of the symmetrical deformation, the eccentric forces in the backbone that are induced by the bending of the fin counteract each other. This limits the torsion in the backbone and results in a more filigree profile. It was found that the elastic kinetic system relies on perfect symmetry which is difficult to produce on a larger scale"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure4-1.png",
        "caption": "Fig. 4. Kinematic description of a belt element on the pulley wrap.",
        "texts": [],
        "surrounding_texts": [
            "Many papers have been published over the last two decades to describe dynamic interactions in a belt CVT system. The most commonly used power-transmitting device in a belt-type CVT is either a steel V-belt or a rubber V-belt. A lot of relevant work on metal and rubber V-belts is subsequently cited as such CVTs are extensively researched by today\u2019s automobile manufacturers and scientists. Most existing models of belt CVTs, with a few exceptions, are steady-state models that are based on the principles of quasi-static equilibrium. Gerbert [17,18] extensively work on understanding the mechanics of traction belts, especially metal pushing V-belts and rubber V-belts. The author used quasi-static equilibrium analysis to develop a set of equations that capture the dynamic interactions between the belt and the pulley. Since the belt is capable of moving both radially and tangentially, variable sliding angle approach was implemented to describe friction between the belt and the pulley. Previously, many researchers like Kimmich [19], Gutyar [20], Amijima [21], etc., assumed constant sliding angle over the pulley wrap to derive the equations of motion of belt. The variable sliding angle approach required that the equilibrium, compatibility, and constitutive equations be solved simultaneously for predicting the dynamics of a belt\u2013pulley system. Only centripetal effects were modeled to account for the influence of belt inertia on system dynamics. Figs. 3 and 4 illustrate the geometric configuration, sliding plane, and simplified kinematics of a V-belt CVT drive with negligible belt flexural effects. Only the sliding or active arcs, represented in Fig. 3 as (1,10), contribute actively to torque transmission. (a,a0) represent the wrap angles of the belt\u2013pulley contacting arcs, whereas (sin,sl) represent the input and load torques on the driver and driven pulleys, respectively. Gerbert [22] also analyzed the slip behavior of a rubber belt CVT. Slip was classified on the basis of creep, compliance, shear deflection, and flexural rigidity of the belt. The author also discussed slip during wedging due to poor fit between the belt and the pulley. Finite element analysis was used to calculate shear deflections in the belt and to determine stick\u2013slip conditions for the belt. However, the work did not account for the influence of belt inertia, loading conditions, and belt radial variations (due to pulley axial forces) on the slip behavior. Gerbert [17] also studied the influence of flexural rigidity and inertia on the dynamics of a rubber V-belt pulley system. Again, only centripetal effects were modeled to account for belt inertia. Owing to flexure, the belt no longer follows a straight-line motion after exiting the pulleys. As a result of the flexural effects, the contact arc becomes smaller than the nominal one and the traction capacity of the belt drive increases. The author used ordinary beam theory to predict the entrance and exit slopes of the belt. The flexural rigidity has tremendous influence on the seating and unseating behavior of the belt. Rapid variation of curvature may change the direction of frictional forces, which consequently affects the torque capacity of the belt\u2013CVT drive. Gerbert [23] also studied the influence of pulley skewness and flexure on the mechanics of V-belt drives. Deflection of pulley sheaves in the axial direction widens or shortens the groove width, thereby influencing the motion of belt in the pulley groove. The displacement of pulley sheaves can be attributed to the phenomena of local deflection, plate deflection, and pulley skewness. Fig. 5 [44] illustrates the variation in pulley groove width due to elastic deformation in the axial direction and due to skewness of the pulley halves. The local deflection depends on the local axial pressure. Plate theory was used to obtain the global deflection of pulley halves. Later, the plate equations and the belt equations were solved simultaneously to obtain the dynamic performance indicators of the belt\u2013pulley system. Skewness of the pulley may be caused by clearances in the guides of the movable pulley half. The author reported the existence of singular solutions (also known as orthogonal points, \u2018\u2018orthogonalpunkts\u201d) where the frictional forces are radially directed and all the derivatives in the differential equations vanish. The character of a solution at an orthogonal point to a great extent determines the character of the solution at other locations and conditions. The work concluded that the axial forces for pulleys with small to medium skewness did not differ much from the ones in ideal case (i.e. with parallel pulley halves). On the other hand, large skewness considerably increased the pulley axial forces for low to medium torque applications. Worley and Dolan [24] extended Gerbert\u2019s work [17] to formulate closed-form solutions using approximate mathematical functions to describe the numerical results of both driver and driven pulleys. Hyperbolic and trigonometric forms were developed to describe the tension distribution over the main active arc of contact (excluding the seating and unseating regions). The authors were able to get results in close agreement to Gerbert\u2019s numerical results; however, conformity to the driver pulley system dynamics was not obtained. Sorge [25] studied transient mechanics of rubber V-belt variators in order to understand CVT behavior during speed ratio shift. The results obtained differed significantly from those at steady state. For moderate shift speed and high angular speed, partial adhesive regions appeared where the belt wound along the spirals of Archimedes. Simple closed-form approximations were proposed to facilitate the calculation of variator operative characteristics. Sorge and Gerbert [26] developed a third order rubber V-belt model considering no inertial and flexural effects. They introduced the concept of \u2018\u2018adhesive-like\u201d contact in V-belt mechanics. They proposed that V-belts do not stick to pulley walls along the entire contact arc, but pass through an idle-like region where sliding occurs at extremely low relative velocity. The trajectory is nearly circular in this region and the tension is almost constant. Sorge [27] also analyzed the mechanics of a metal V-belt CVT under the influence of pulley bending. The belt was considered rigid for the purpose of model development. The author used the concepts of virtual displacement to obtain approximations to belt trajectories, tension distributions, axial thrusts, and slip. The author reported that the influence of pulley deflection is important when belt trajectory is closer to the outer radius. The influence decreases near the middle radius and becomes negligible near the inner clamped radius. Therefore, the use of a mixed model was suggested at smaller radii in order to aptly capture the dynamics due to elastic deformations of both belt and pulley. Sorge [28] also used the concepts of deformation and elastic wedging to analyze rubber V-belt mechanics. The author\u2019s primary objective was to analyze belt trajectory. The study involved the theoretical problem of determining tension distribution and radial penetration of a rubber V-belt. Flexural and inertial effects were neglected. The belt deformation was correlated only to the axial forces, and Poisson effects were neglected. The author incorporated transverse elasticity of the belt and used force-deformation equations to obtain sliding conditions and approximate closed-form solutions to the belt\u2013pulley system. Micklem et al. [15] incorporated elastohydrodynamic lubrication theory to model friction between a metal V-belt and the pulley sheaves, and studied transmission losses due to wedging action of the belt. The authors also discussed the influence of elemental gaps on the slip behavior of a belt CVT system. However, certain unrealistic assumptions, such as uniform band tension, uniform loading and unloading arcs over the pulley wraps, negligible inertial effects, etc., were incorporated during the course of model development. Speed variation in the belt due to deformation and compressive loads was also neglected. Karam and Play [29] did a discrete analysis of a metal V-belt drive. They used quasi-static equilibrium analysis and numerical techniques to derive global equilibrium equations from elemental part equations. The belt elements were always assumed to be in compression, while the bands were always in tension. The bands and pulleys were also assumed to be rigid. They also observed that only part of the contact arc (i.e. the active or sliding arc) contributed effectively to torque transmission. The steel bands aided power transmission at low transmission ratios, but acted against it at high ratios. They later included an approximate model of pulley deformations in their CVT model and observed an increase in pulley axial forces for the same torque loading conditions. Asayama et al. [30] developed a theoretical model-based on quasi-static equilibrium analysis to describe variations in band tension and segment compression force and to predict clamping pressures necessary to prevent gross belt slip. They also included relative motion between bands and segments (since they have different radii of rotation) in their model to predict changes in band tension. The bands were treated as rigid. However, microslip behavior of the CVT system was predicted using the elastic deformations of belt segments. Later, the authors also incorporated an approximate pulley deformation model to study the influence of pulley flexibility on the dynamic performance of the CVT system. Although the results from the numerical model were able to conform to the experimental observations for band tensile force, conformity with measured compressive force was not attained. Kim and co-workers [31,32] investigated the metal belt behavior analytically and experimentally. They proposed a speed ratio\u2013torque load\u2013axial force relationship to calculate belt slip. They obtained the equations of motion using quasi-static equilibrium conditions and reported that the gross slip points depend on the torque transmitting capacity of the driven side. Numerical results showed that the belt radial displacement increased in the radial inward direction for the driven pulley, while that of the driver increased slightly and decreased with the increasing torque load. The effects of inertia and flexure were neglected and the band tension was assumed to be constant. Massouros [33] investigated elastic creep velocity of a rubber V-belt analytically and experimentally. The belt creep velocity depends not only on the structural characteristics of the belt, but also on the operational characteristics of the CVT. It also affects the torque transmitting capacity of a belt drive. During power transmission with a belt\u2013pulley system, the velocity of the driving side of the belt is larger than the driven side. The gradual change in velocity from the larger value to the lower value, and inversely, occurs due to the elastic creep of the belt on the pulley wrap arcs. The belt creep occurs in the direction of motion on the driven pulley and opposite to the moving direction on the driving pulley. It was reported that the belt creep velocity at each point of the arc of creep is a linear function of transmitted power and varies exponentially along the arc of creep. The belt dynamics was again modeled using quasi-static equilibrium concepts. Kobayashi et al. [34] investigated the torque transmitting capacity of a metal pushing V-belt CVT under no driven-load condition. A simulation procedure was outlined to predict the slip ratio and slip-limit torque of a metal V-belt CVT system under steady-state quasi-static equilibrium conditions. Their research focused on the microslip characteristic of a V-belt CVT, which is due to the redistribution of elemental gaps in the belt. The slip hypothesis was based on the assumption that slip only occurred on the pulley where the gaps were present and those gaps were distributed evenly in an idle sector at the entrance of the loading pulley. The authors observed the existence of active and idle arcs during different phases of transmission, as depicted in Fig. 6 [34]. The active arcs are those regions of belt\u2013pulley wrap that contribute effectively to torque transmission, whereas the idle arcs do not participate in torque transmission. The band tension remains nearly constant in these idle arcs. Since the compressive force in belt elements decreases in the idle arc region, there is redistribution of elemental gaps, which consequently causes microslip phenomenon in a metal belt CVT system. Sun [35] did performance-based analysis of a metal V-belt drive, using quasi-static equilibrium concepts, to obtain a set of equations to describe belt behavior at steady state. Friction between individual bands in a band pack was also taken into consideration during the course of model development. Bonsen et al. [36] analyzed slip and efficiency in a metal pushing V-belt CVT. High clamping force levels reduce the efficiency of a CVT. However, high clamping forces are necessary to avoid excess slip between the belt and the pulley. If a small amount of slip is allowed, the clamping force level can be reduced. The authors investigated the variation of transmitted torque with slip. Radial slip was attributed to CVT shifting and spiral running of the belt. It was proposed that the amount of radial slip depends on the pulley deformation effects, shifting speed, and driver pulley angular speed. Tangential slip was defined based on the redistribution of elemental gaps (as in [34]). It was reported that the traction coefficient, a measure of the torque capacity of a CVT, increases with slip in the microslip regime. However, once the maximum torque capacity of a CVT is attained, the slip rises dramatically and the traction coefficient begins to decrease. The friction between the belt and the pulley was modeled according to Stribeck\u2019s friction law. The force distributions were obtained using Asayama\u2019s [30] model. The authors also concluded that the traction coefficient is largely dependent on CVT ratio and is not much affected by pulley speed and clamping pressure. However, the efficiency of a CVT depends not only on the clamping pressure but also on the CVT ratio. Amijima et al. [37] analyzed the axial force distribution on a block-type CVT analytically as well as experimentally. The authors proposed a unique relation to relate the angular position of a belt element on the pulley wrap to its sliding angle. The equations of motion were derived using quasi-static equilibrium concepts and a relationship was developed to relate the axial forces to belt tension, belt material properties and groove angle. The experiments indicate that the thrust force profile varies over the pulley wrap; it is the maximum at the exit point and increases as the transmitted load increases. The authors reported that even when only initial tension is applied, the thrust pressure is not constant through the contact arc in spite of there being no power transmission. The thrust force increases as the transmitted load increases in any speed ratio. It was also reported that the thrust force on the smaller pulley is usually higher than that on the larger pulley. Sferra et al. [38] developed a unique model of a metal V-belt CVT in order to simulate its transient behavior. The model included inertial and pulley deformation effects. Discrete and continuous shifting behaviors were simulated in order to analyze efficiency and power losses due to friction between the belt and the pulley halves. The results showed high loss of effi- ciency during shifting transients. Power losses due to other parasitic effects were not included in the model. Ide and Tanaka [39] experimentally measured the contact forces between a metal pushing V-belt and the pulley sheaves using ultrasonic waves. The relative change in the shape of belt wrapping arc due to variations in the clamping force and transmitted torque was detected. The results showed that the shape of belt wrapping arc was not co-axial with the pulley axis, and this was attributed to asymmetrical pulley deformation. In driven condition and driving with a small torque, the contact force distribution exhibited peaks at the inlet and outlet of the pulleys, as depicted by a representative example plot in Fig. 7 [39]. The peak on the outlet was higher, especially on the pulley with larger pitch radius. It was proposed that asymmetrical pulley deformation and self-locking of the belt on the pulley were responsible for the high peak at the outlet. The authors also observed that the high peak of the contact force at the outlet decreases as the driving torque increases. This was attributed to the increase in belt compressive force and the elimination of self-locking phenomenon of the belt. Ide et al. [40] also used simplified dynamic models of a metal V-belt CVT to analyze the response of a CVT-equipped vehicle to a rapid speed ratio change. They also experimentally investigated [41] the shift speed characteristics of a metal belt CVT. They observed that there were two different phases during ratio change. One was the creep mode when the belt clamping force was not small, and the other was slip mode when the belt clamping force was small. They also noted that the shift speed in creep mode increased in proportion to the pulley rotating speed, whereas it was independent of the pulley speed under slip mode. Also, a large radial slip occurred over the entire contacting arc of the belt on the pulley under slip mode conditions. Bullinger and Pfeiffer [42,43] developed a detailed elastic model of metal V-belt CVT system to determine its power transmission characteristics at steady state. Pulley, shaft, and belt deformations were taken into account. The frictional constraints were modeled using the theory of unilateral constraints. The belt dynamics was specified by separate longitudinal and transverse approaches. The transversal dynamics was modeled using the Ritz-approach based on B-splines. The longitudinal dynamics was described by using the Lagrange coordinate formulation. Sattler [44] analyzed the mechanics of a metal chain and V-belt considering longitudinal and transverse stiffness of the chain/belt, and pulley misalignment and deformations. The pulley deformation was modeled using a standard finite element analysis. The pulley was assumed to deform in two ways, pure axial deformation and a skew deformation. The model was primarily used to study efficiency aspects of belt and chain CVTs. Ye and Yi [45] also developed a multibody dynamic model of a metal V-belt CVT to find the metal block trajectories and to calculate the forces acting on the block and the ring/band by changing the speed and torque ratios. The ring/band was modeled using spring-damper elements. However, in their study, the simulation was conducted under steady-state conditions and the effects due to transient conditions were not considered. Carbone et al. [46] developed a theoretical model of a metal pushing V-belt to understand the transient dynamics of a belt CVT drive during rapid speed ratio variations. The belt was modeled as a one-dimensional continuous body with zero radial thickness and infinite axial stiffness. Non-dimensional equations were defined to encompass different loading scenarios; however, the inertial coupling between the belt and the pulley was not modeled in detail. Carbone et al. [47] also studied the influence of clearance between belt elements on the rapid shifting dynamics of a metal pushing V-belt CVT. The effects of band tension and belt inertia were neglected in the analysis. The clearance between belt elements was modeled as a kinematic strain. The authors reported that power transmission is assured only if an active arc exists where the elements are pressed against each other and where compressive forces among the steel elements grow. The idle arc, where the steel elements are separated and no compression exists, does not contribute to torque transmission. On the driver pulley, a \u2018\u2018shock\u201d section was observed which separated the idle arc from the active arc. On the driven pulley, there was no shock section, but an \u2018\u2018expansion wave\u201d kind of phenomenon occurred as the clearances among belt elements grew on the idle arc. Carbone et al. [48] used two friction models, namely a Coulomb friction model and a visco-plastic friction model, to model friction between the belt and the pulley for accurately predicting CVT shifting dynamics during slow and fast maneuvers. The authors reported that the Coulomb friction model is unable to correctly predict the shift dynamics of a CVT during slow maneuvers (i.e. creep-mode phases), but it could well predict the limiting traction capacity and dynamic behavior of a CVT in slip-mode (rapid shifting) phases. However, a visco-plastic model is not only able to accurately predict CVT behavior in creep-mode phases, but also able to detect the transition from creep mode to slip mode. The authors also proposed simple relations to correlate shift speed to clamping force ratio, driver pulley speed, and torque load. Later, Carbone et al. [49,50] extended their previous work [46] to investigate the influence of pulley deformation on the shifting mechanism of a metal V-belt CVT. Coulomb friction hypothesis was used to model friction between different surfaces. Flexural effects of the belt were neglected; however, pulley bending was considered based on Sattler\u2019s model [44]. The authors assumed equal pulley deformations and also that the belt\u2013pulley wrap angles did not deviate considerably from 180 . The only inertial effects taken into account were due to the centripetal acceleration of the belt. Moreover, the free span dynamics of the belt were not modeled. The authors predicted that the Coulomb friction model was able to accurately describe shifting behavior of a CVT in creep and slip modes if pulley bending effects were taken into account. The authors suggested that in steady state, the pressure and tension distributions were unaffected by pulley bending and depended only on the thrust ratio. However, pulley bending played a significant role in determining the transient response of the variator. It was shown that in creep mode, the rate of change of speed ratio continuously increases as the stiffness of pulley decreases. The model was also able to predict the influence of pulley angular speeds on the rate of change of speed ratio. The authors reported that during creep-mode phases, the shift speed is almost linearly related to the logarithm of pulley clamping force ratio. Experiments done by a number of researchers, especially those done by Fujii and Kanehara, have shown that both tensile force in the band pack and compressive force in the belt elements aid in torque transmission. Their work suggests that these forces vary non-uniformly over the pulley wrap, which invalidates the assumption of constant band tension made by other researchers. Fujii et al. [51] experimentally investigated the tensile force in bands and the compressive force in belt elements. The authors observed the existence of active and idle arcs on the driving pulley and suggested that under some operating conditions, it is plausible for the bands to contribute up to 40\u201345% of the total transmitted torque. The authors also reported that the band tension distributions exist due to relative slip velocities between the bands and the segments. The band pack tensile force was observed to decrease around the smaller of the two pulleys in the direction of belt travel. Consequently, the band tension impeded torque transfer in high ratio and facilitated the transfer of torque in low ratio. This could happen to such an extent that in low ratio, for a range of lower torque levels, the entire torque load was observed to be transferred by the band tension alone. Fujii and co-workers [52] used a number of strain gauged belt elements to measure the forces acting in various directions on the belt element. The experiments were conducted on a constant transmission ratio CVT at low belt speeds and clamping pressures. Time histories of pulley normal force, belt compressive force, transmitting force (i.e. the tangential friction force between a belt element and the pulley), radial friction force, element shoulder force, etc. were recorded during the experiment. Since it was difficult to measure compression in the free span of the belt CVT system, a straight-line fit between the entry and exit conditions on each pulley was assumed. The pulley normal force was reported to be unevenly distributed on the contact arcs. The element normal force exhibited peaks at the entry and exit of the pulleys (similar to the observations of Ide and Tanaka [39]). Also, it was observed that the normal force per element was lower on the pulley with the larger wrap angle. The authors also reported the existence of idle and active arcs at higher transmission ratios. The radial friction force restricted the penetration of a belt element into the pulley, except at the pulley exits where it acted to retain the belt element in the pulley wedge. Fushimi et al. [53] developed a numerical model to calculate the steady-state force distributions and compared them to the previously published experimental results. The metal V-belt is modeled using a lumped-parameter approach with three kinds of springs and two kinds of interfacial elements for the block and the ring, as shown in Fig. 8 [53]. The interfacial elements were used to capture friction effects between the block and the pulley, and between the ring and the block. Fujii and co-workers [54] later extended their previous experimental setup to record the forces in a metal belt CVT system under the conditions of varying transmission ratio. Time histories of various forces acting in a belt\u2013pulley system were recorded. However, none of the above-mentioned papers of Fujii et al. included any kind of theoretical modeling of the metal V-belt CVT system. Moreover, since the experiments were conducted at low speeds and low pressures, inertial and deformation effects could not be captured in detail. Later, Fujii and Kanehara co-authored a paper with Kuwabara [55] where they proposed an advanced numerical model to analyze power-transmitting mechanism in a metal pushing V-belt CVT. The forces acting in the system were estimated not only at steady states but also during transitional states where the speed ratio was changing. The band tension is not assumed to be constant. The model takes into account the various dynamic interactions occurring among bands, elements and pulleys. It was observed that bands transmitted negative power under over-drive conditions (i.e. when the pitch radius on driven pulley is smaller than the driver pulley radius). So, in order to meet load, the blocks transmitted more power than the nominal. Much greater thrust was needed to shift the speed ratio during transitional state than in steady state. The authors also observed that the thrust ratio (ratio of the driver axial force to the driven axial force) slightly increased with increasing the coefficient of friction between the belt and the pulley. Coulomb friction was used to model friction between all the surfaces. The influence of flexure and belt inertia was neglected during the course of model development. Fig. 9 [55] depicts some steady-state results from Fujii and co-workers [55] that highlight the combined role of band pack and element forces in successful torque transmission. Here, the authors (i.e. Fujii et al.) defined speed ratio as the ratio of belt pitch radius on the driven pulley to that on the driver pulley. Fujii and Kanehara also co-authored a paper with Fujimura [56,57] where they used mean coefficients of friction and shifting gradients to reveal the shifting mechanism of a metal V-belt CVT. Shifting gradient is a non-dimensional parameter which is defined as the radial increment of a block sitting on a pulley in radial direction per unit block path. The experimental results showed that thrust force and sliding speed influenced the mean coefficients of friction. The authors also observed that the shifting gradient was influenced neither by pulley speed nor by torque ratio. Torque ratio is defined as the ratio of transmitted torque to the maximum transmittable torque. An increase in shifting gradient was observed with increasing the thrust of a pulley in which the belt pitch radius was increasing, whereas it decreased with increasing the thrust of a pulley in which the belt pitch radius was decreasing. However, the authors did not include the influence of belt tensile and compressive forces on the shifting gradient of the variator. Fujii and Kanehara later co-authored a paper with Kataoka [58] where they analyzed shift mechanisms of the variator and characterized friction between the blocks and the pulleys. The authors concluded that the shifting gradient is governed not only by block elastic deformations (due to the pulley thrusts), but also by ring tension and block compression. The authors developed quasi-static equilibrium equations to estimate target pulley thrusts at steady and transitional states. Both driving and driven pulley thrusts were calculated by considering the forces on the blocks at pulley entrance. Experimental conformity was also reported for not only steady state, but also transitional state conditions. The frictional performance of CVT fluids and the frictional characteristics of block\u2013pulley contact interfaces were evaluated by applying the mean coefficient of friction as a friction parameter. It was found from experiments that the estimated coefficient of friction of CVT fluids was not constant with respect to the operating conditions. It varied with the relative sliding speed of the blocks with respect to the pulleys, sliding direction, and normal pressure acting on the V-surface of the block. Srivastava and Haque [59\u201361] developed a detailed transient dynamic model of a metal pushing V-belt block-type CVT. The goal was to understand the transient dynamic behavior of a belt element as it traveled from the inlet to the exit of driver and driven pulleys. The inertial coupling due to radial and tangential motions of the belt was modeled in detail. The interaction between the band pack and the belt element (which has been neglected in a lot of previous models) was also taken into account during the course of model development. Flexural effects due to belt motion were neglected; however, pulley flexibility was taken into account using Sferra\u2019s correlations [38]. Also, the contact between the belt and the pulleys was modeled not only by classical continuous Coulomb friction law, but also by certain mathematical/analytical models of friction that capture different loading/operating conditions (e.g. stiction, lubrication, etc.). It is evident from their work that not only the configuration and loading conditions, but also the inertial forces, influence the dynamic performance of a CVT, especially the slip behavior and torque capacity. The authors also reported that the inactive arc region of a band pack is different from that of a belt element. This consequently led to the formation of shock sections at the element\u2013band interface separating the inactive region of pulley wrap from the active region. However, the results reported were valid for one cycle i.e. till the belt moved past the exit of either of the two pulleys. Fig. 10 [61] depicts the free-body diagrams of the metal V-belt CVT drive reported by the authors to capture the various transient dynamic performance indices of the CVT system. Srivastava et al. [59,62] also highlighted the significance of a feasible set of initial operating conditions required to initiate torque transmission in a CVT system. The authors proposed that a CVT, being a highly nonlinear system, needs a specific set of operating conditions, which can be found using an efficient search mechanism, in order to successfully meet the load requirements. The authors used genetic algorithms (GA) to capture this feasible set and also highlighted its efficiency in capturing this set by comparing it to the results generated from the design of experiments (DOE). The optimization objective function was aptly chosen to maximize the torque transmission capacity of the CVT system. Srivastava and Haque [63] developed a metal pushing V-belt CVT model at steady state to study its microslip behavior and to define its operating regime. They discussed the influence of torques and axial forces on belt slip. Slip was based on the redistribution of elemental gaps and formation of inactive arcs (as proposed by Kobayashi et al. [34]). The model is able to predict the maximum transmittable torque before the belt undergoes gross slip. The authors again observed that the CVT operated in a definite regime of axial forces and torques for successfully meeting the load requirements on driven pulley. They predicted the minimum axial force necessary to initiate torque transmission and the maximum axial force that the CVT could sustain (based on slip behavior and not on stress, wear, or fatigue effects). The operating regimes for axial forces and torques were obtained by running numerous simulations with varying transmission ratios. Fig. 11 [61] illustrates representative time histories from the authors\u2019 belt CVT model for an operating condition of 200 N m input torque and 100 N m load torque at a constant driver pulley speed of 2000 rpm under stiction and lubricated contact conditions. The results emphasize the influence of inertial effects on the dynamic performance and torque capacity of the CVT system (refer to [61] for details). Akehurst [64] theoretically and experimentally investigated the loss mechanisms associated with an automotive metal Vbelt CVT. The author developed mathematical models to describe torque loss mechanisms in a belt CVT drive. Radial friction effects were neglected in the analysis except in the entry and exit regions of the pulleys. The author also assumed that all the bands shared the tension load evenly. The main torque loss event is proposed to occur due to bands sliding relative to each other and the segment, and the segments sliding relative to the pulley. Two further loss models were developed to describe losses as the segments traversed the pulley wrap arcs. These losses were due to pulley deflections causing the segments to contact the pulley past ideal exit and entry points (wedge loss) and to penetrate further into the pulley than the ideal belt pitch radius (penetration loss). The wedge loss proposed was similar to the previously developed empirical model of Micklem et al. [65] and was based on the radial deflection of belt elements at the entry and exit regions of the pulleys. Tangential belt slip was again investigated on the basis of redistribution of gaps between the belt elements (as in [34]). In addition to the torque loss associated with the belt, the author studied other parasitic losses in the transmission system, like seal and bearing drag losses, pump losses, clutch drag losses, meshing losses, churning and windage losses. In steady state, it was observed that the losses in high ratio at low speeds were lower than low ratio losses, due in part to the reduced pump losses. However, as speeds increased, the high ratio losses exceeded those in low ratio. This was attributed to increased belt torque losses and final drive losses. Also, it was noted that in both ratios the torque loss increased with output torque loading. However, in low ratio conditions, the torque loss under no load conditions was higher than when the transmission was lightly loaded. Kluger and Long [66] presented an overview of current manual, automatic, and continuously variable transmission efficiencies. The authors qualitatively discussed loss mechanisms in these transmissions and suggested design improvements to enhance transmission efficiency. As the belt-type CVTs require pressures of up to 3 MPa, the pumping power requirements represent a very large portion of the overall CVT power loss. The authors suggested the use of a radial ball pump or a radial piston pump to reduce the pumping losses during sheave actuation. The authors reported that the manual transmission is the most efficient transmission among all three transmission technologies. However, since their technology is quite mature, there is very little room for improvement in terms of efficiency and fuel economy. Kluger and Fussner [67] also discussed the mechanisms, forces, and efficiencies of different types of CVT, especially push belt CVT, elastomer belt-type CVT, toroidal CVT, nutating type CVT, and epicyclic CVT. The amount of power which can be transmitted by a push belt-type CVT is dependent on either the tensile strength of the bands or the transverse buckling strength of the belt elements. The dynamics within the steel bands play a crucial role in determining the maximum torque that can be transmitted. The authors suggested that the torque transmission in a metal belt CVT system is due to both pushing forces in the belt elements and the friction forces between the elements and the bands. Singh and Nair [68] developed mathematical models of different CVT designs by using existing literature and later normalized the information to allow comparison of different CVT concepts (i.e. toroidal, chain, belt, hydrostatic types) on an equitable basis. The models were used to compute efficiencies of individual CVTs at selected points of the entire operating envelope. The authors reported that the rubber belt CVT, in general, is the most efficient among all. The PIV chain CVT is inefficient for low torques and the traction CVT is less efficient than the chain and belt CVTs for under-drive ratios. Chung and Sung [69] analytically and experimentally studied vibration of a rubber V-belt CVT during speed ratio change. On the basis of motion characteristics of the CVT, the major components were modeled as an instantaneous flexible four-bar linkage for studying the belt vibration behavior. The free span of the axially moving belt was modeled as a flexible coupler link, while the variable diameter driving and driven sheaves were modeled as the crank and rocker links, respectively. The authors used the mixed-variational principle to derive the equations of motion of the vibratory CVT system. The boundary and initial conditions were determined from the physical configuration of a practical CVT system. The free span length of the belt was obtained from contact analysis. A parametric study on natural frequencies of the belt was performed using assumed-modes method. The authors observed that the natural frequencies of both tight- and slack-sides of the belt decreased as the CVT accelerated. Moreover, in steady state, higher belt tensions led to higher natural frequencies. Also, the natural frequency of the belt was observed to decrease with increasing transport velocity. Pfeiffer and co-workers [70] analyzed self-induced vibrations in a pushing V-belt CVT using highly simplified dynamic models. The free span length of the belt was assumed to be constant in the analysis. It was shown that certain friction characteristics, especially those having negative gradient with respect to relative velocity, could induce self-excited vibrations in the belt. The friction characteristic and the elasticity of the pulley sheaves determined the working area where vibrations occurred. The authors also observed that increasing pulley stiffness decreased belt vibration, but failed to eliminate them completely. Fig. 12 [70] depicts the excitation mechanism proposed by the authors."
        ]
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.30-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.30-1.png",
        "caption": "Fig. 3.30 Sketch of tail rotor subsystem",
        "texts": [
            " Initially, we shall ignore the nonuniform effects described above and derive the tail rotor forces and moments from simple considerations. The interactional effects will be discussed in more detail in Section 3.4.2. The relatively small thrust developed by the tail rotor, compared with the main rotor (between 500 and 1000 lb (2220 and 4440 N) for a Lynx-class helicopter), means that the X and Z components of force are also relatively small and, as a first approximation, we shall ignore these. Referring to the tail rotor subsystem in Figure 3.30, we note that the tail rotor sideforce can be written in the form YT = \ud835\udf0c(\u03a9T RT )2sT a0T (\ud835\udf0bR2 T ) ( CTT a0T sT ) FT (3.219) where \u03a9T and RT are the tail rotor speed and radius, sT, and a0T the solidity and mean lift curve slope, and CTT the thrust coefficient given by Eq. 3.220: Modelling Helicopter Flight Dynamics: Building a Simulation Model 121 The scaling factor FT is introduced here as an empirical fin blockage factor, related to the ratio of fin area Sfn to tail rotor area (Ref. 3.46): FT = 1 \u2212 3 4 Sfn \ud835\udf0bR2 T (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003221_j.mechmachtheory.2019.103670-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003221_j.mechmachtheory.2019.103670-Figure6-1.png",
        "caption": "Fig. 6. Flexible support structure of these herringbone gears.",
        "texts": [
            " These herringbone gears are coupled by 2 totally similar helical gears but the 2 helical gears have an opposite helical angle. 2. All the components are considered as units with 4 degrees of freedom. That is 3 translational degrees of freedom and one degree of freedom of rotation. 3. All the flexible support components are simulated by low-stiffness spring and damper. The support condition is treated as flexible support when the support stiffness is lower than 1% of normal support stiffness. The schematic view of the flexible support of each gear is shown in Figure 6 , which fully demonstrates the theory of flexible support structure. In Figure 6 , (a) shows the flexible support structure of sun gear. (b) shows the flexible support structure of planet gears. And (c) shows the flexible support structure of ring gear. Based on these assumptions, the dynamic behaviors of flexible support system are calculated by the dynamic model established in the second part. 4.2. Time-varying meshing stiffness excitation System parameters are input into the Kisssoft software and the average meshing stiffnesses ( K m ) of the gear train are obtained by evaluation module"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001528_00207170802342818-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001528_00207170802342818-Figure1-1.png",
        "caption": "Figure 1. The sketch maps of principal angle response in the form of polar coordinates (a) conventional stabilisation method, (b) set stabilisation method.",
        "texts": [
            " (1995), Lizarralde and Wen (1996) and Park (2005), the desired quaternion is designed to be (1, 0, 0, 0)T while ( 1, 0, 0, 0)T is designed to be an unstable equilibrium, or a repeller. Then it is said that since in physical space both of the equilibria are the same, global asymptotical stability can be obtained. However, this is not true. According to the stability theory, if ( 1, 0, 0, 0)T is definitely unstable it cannot be considered the same as the stable equilibrium (1, 0, 0, 0)T. One can observe clearly from Figure 1(a) that all the states near it just escape from it. Moreover, under those controllers, all the states have to be driven to (1, 0, 0, 0)T even if they are located very close to ( 1, 0, 0, 0)T. This phenomenon is called \u2018unwinding\u2019 in Bhat and Bernstein (2000b). Our purpose in this article is to design a set stabilisation law to make both of the equilibria stable D ow nl oa de d by [ C as e W es te rn R es er ve U ni ve rs ity ] at 0 9: 57 3 0 O ct ob er 2 01 4 so that the states can converge to the equilibrium which is closer to them (Figure 1b). Remark 1: Since the initial values of the principal angle usually can be restricted or transformed to be in [ , ], it seems that the unwinding phenomenon can be avoided. However, it is not a global description and is not suitable for large angle manoeuvre, especially those tasks with frequent and continuous rotation. Furthermore, as pointed out in Bhat and Bernstein (2000b) the resulting feedback law will be discontinuous. In this section, a global control law is presented for stabilising the attitude of a rigid spacecraft described by (2)\u2013(3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002035_j.optlaseng.2016.08.005-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002035_j.optlaseng.2016.08.005-Figure3-1.png",
        "caption": "Fig. 3. A schematic of experimental set-up.",
        "texts": [
            " Laser cladding was carried out on these specimens by varying different process parameters as shown in Table 2, and thermo-cycles were recorded during the process. Argon gas was used as a shielding as well as shrouding gas to protect the optical components of the laser processing head from fumes and the molten pool from oxidation respectively. Shrouding gas was directed towards the processing zone at 5 l/min flow rate through a 6 mm diameter copper pipe inclined at 45\u00b0 and 5 cm away from the molten pool. The laser beam spot diameter was maintained 3 mm throughout the experiment. Three replicates were taken for each experiment. Fig. 3 shows the schematic of the experimental setup. The pyrometer was sighted on the specimen at 45\u00b0 to the axis of laser beam. The laser deposited specimens were cross sectioned, mirror polished and etched with a solution of 50 ml HCl, 25 ml HNO3, 0.2 g CuCl2 and 100 ml deionised water. Clad geometry and microstructures were characterised by optical and scanning electron microscopy. EDS analysis was utilised to determine the chemical composition. Phase identification was performed using X-ray diffractometer with Cu K\u03b1 radiation at 40 kV and 40 mA using a continuous scan mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000176_10402004.2010.551804-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000176_10402004.2010.551804-Figure8-1.png",
        "caption": "Fig. 8\u2014Loaded ball rolling on a curved track. Below, the contact area showing two lines of pure rolling and zones of sliding.",
        "texts": [],
        "surrounding_texts": [
            "Again, following (156), a simple two-dimensional thermal model can be obtained by assuming oil conduction only along the normal direction (e.g., Crook (59)). In this way, the integration of temperature-dependent viscosity in the contact area will be now possible. The domain is then discretized in nx \u00d7 ny points, and for each grid point (i, j ) a normal heat source can be calculated, q\u0307i,j = u\u0304Si,j \u03c4i,j [30] Using the rheological model for an Eyring fluid, the shear stress matrix is \u03c4i,j = \u03c4o sinh\u22121 ( \u03b7i,j \u03b3\u0307i,j \u03c4o ) [31] and for a limiting shear stress fluid, \u03c4i,j = \u03c4Li,j [ 1 + ( \u03c4Li,j \u03b7i,j \u03b3\u0307i,j )n]\u22121/n [32] Notice that the limiting shear stress \u03c4L is considered in the reference as a variable quantity. The shear rate \u03b3\u0307i,j can also be a variable quantity if the slip profile is not constant in the contact (e.g., rolling bearings). The viscosity is function of pressure and temperature as given by Eq. [33]. \u03b7(p,T) = \u03b7of (p)g(T) [33] D ow nl oa de d by [ U ni ve rs ity o f H ai fa L ib ra ry ] at 0 0: 58 2 4 Se pt em be r 20 13 To calculate the temperature rise distribution in the oil film, it is assumed that the heat vector is conducted only in the z direction, disregarding convection from the oil. The wall temperature rise (( Ts)i,j ) is calculated following an FFT procedure described in the reference (156). This temperature is used as a boundary condition in a heat conduction analysis of a plate with internal heat generation (film) to calculate the lubricant temperature distribution. The following equation is obtained: Ti,j = ( Ts)i,j + hq\u0307i,j 12koil [34] An application example is included in the reference, where the sliding speed is allowed to vary in the contact area (156). Consider the case of a loaded ball rolling on a curved track (ball bearing geometry) as shown in Fig. 10b. Macro-sliding will be induced due to the conformity of the contact. This configuration is similar to a ball-bearing ball running on its raceway. For the described problem, in general the sliding velocity varies along the axis y, transverse to the rolling direction (along the longest semi-width b) following Eq. [35], us(y) = Sou\u0304 [ 1 \u2212 ( y \u2212 c 0.34b \u2212 c )2 ] [35] where So is the sliding/roll ratio at the center of the contact, at y = 0, and c is an offset value of the center along y. The same example of the ball bearing 6309, described in Houpert and Leenders (130), is reproduced here, taking c = 0. The present 2D model was used to solve the described problem for increasing sliding velocity in the center of the contact. Figure 9a shows the sliding velocity distribution in the contact, as obtained from Eq. [35] for the case in which So = 0.0162 (1.62 %) and c = 0. Figure 9b shows the corresponding distribution of surface temperature rise in the contact area for the fastest moving body with a mesh of 35\u00d735 points, and low values of temperature rise are reached around the lines of pure rolling, where the heat input is relatively low. Figure 9c depicts the obtained temperature rise in the lubricant. The maximum value reached is 65\u25e6C and in the center of the contact the maximum is 32\u25e6C. The results from the literature (130), included in Fig. 9d show a maximum oil temperature of about 58\u25e6C and in the center (y = 0) the maximum value is about 26\u25e6C, read from the graph. The present calculations show the corresponding values of 60\u25e6C and 35\u25e6C, respectively. For the wall temperature, the reference (156) shows the two maxima at 8 and 4\u25e6C (from the graph), whereas with the present method the calculated values are 10.5 and 6.5\u25e6C; see Fig. 9b."
        ]
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure4-11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure4-11-1.png",
        "caption": "Fig. 4-11 Current and fluxes at some time t\u00a0>\u00a00, with the rotor blocked.",
        "texts": [
            " This torque will be proportional to B\u0302r and isq (slightly less than isq by a factor of Lm/Lr due to the rotor leakage flux, where Lr equals L Lm r+ \u2032 in the per-phase equivalent circuit of an induction machine): T k B L L iem r m r sq=      1 \u02c6 , (4-20) where k1 is a constant. If no action is taken beyond t\u00a0=\u00a00+, the rotor currents will decay and so will the force on the rotor bars. This current decay would be like in a transformer of Fig. 4-6 with a short-circuited secondary and with the primary excited with a step of current source. In the transformer case of Fig. 4-6, decay of i2 could be prevented by injecting a voltage equal to R2i2(0+) beyond t\u00a0 =\u00a0 0+ to overcome the voltage drop across R2. In the case of an induction machine, beyond t\u00a0=\u00a00+, as shown in Fig. 4-11, we will equivalently rotate both the d-axis and the q-axis stator windings at an appropriate slip speed \u03c9slip in order to maintain B tr( ) completely along the d-axis with a constant amplitude of B\u0302r, and to maintain the same rotor-bar current distribution along the q-axis. This corresponds to the beginning of a new steady state. Therefore, the steady-state analysis of induction machine applies. As the d-axis and the q-axis windings rotate at the appropriate value of \u03c9slip (notice that the rotor is still blocked from turning in Fig. 4-11), there is no net rotor flux linkage along the q-axis. The flux linkage along the d-axis remains constant with a flux density B\u0302r \u201ccutting\u201d the rotor bars and inducing the bar voltages to cancel the iRbar voltage drops. Therefore, the entire distribution rotates with time, as shown in Fig. 4-11 at any arbitrary time t\u00a0>\u00a00. For the relative distribution and hence the torque produced to remain the same as at t\u00a0=\u00a00+, the two windings must rotate at an exact \u03c9slip, which depends linearly on both the rotor resistance \u2032Rr and isq (slightly less by the factor Lm/Lr due to the rotor leakage flux), and inversely on B\u0302r \u03c9slip ( / ) ,= \u2032 k R L L i B r m r sq r 2 \u02c6 (4-21) where k2 is a constant. Now we can remove the restriction of \u03c9mech\u00a0=\u00a00. If we need to produce a step change in torque while the rotor is turning at some speed \u03c9mech, then the d-axis and the q-axis windings should be equivalently rotated at the appropriate slip speed \u03c9slip relative to the rotor speed \u03c9 \u03c9m p=( )( / )2 mech in electrical rad/s, that is, at the synchronous speed \u03c9yn\u00a0=\u00a0\u03c9m\u00a0+\u00a0\u03c9slip, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001388_tro.2013.2289019-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001388_tro.2013.2289019-Figure2-1.png",
        "caption": "Fig. 2. (a) Configurations that cause (12) to become degenerate, for \u2016p\u2016 = 125 mm. (b) An example set of actuator-magnet position solutions that achieve a desired field rotation axis \u03c9\u0302h = [0,\u22121, 0]T when the actuator magnet\u2019s rotation axis is constrained to \u03c9\u0302a = [0, 0,\u22121]T and \u2016p\u2016 = 125 mm. The positions p1 and p2 are the +p\u0302 and \u2212p\u0302 solutions, respectively, given by (13). If the actuator magnet\u2019s spin direction can be reversed such that \u03c9\u0302a = [0, 0, 1]T, then p3 and p4 are the corresponding +p\u0302 and \u2212p\u0302 solutions.",
        "texts": [
            " After selecting the first basis vector to be \u03c9\u0302h , a second basis vector \u03c9\u0302\u22a5 h is \u03c9\u0302\u22a5 h = (I \u2212 \u03c9\u0302h\u03c9\u0302T h)\u03c9\u0302a \u2016(I \u2212 \u03c9\u0302h\u03c9\u0302T h)\u03c9\u0302a\u2016 . (12) Since \u03b3 is the projection of p\u0302 onto \u03c9\u0302h , the vector +p\u0302 can be formed from the orthonormal basis as +p\u0302 = |\u03b3|\u03c9\u0302h + \u221a 1 \u2212 |\u03b3|2\u03c9\u0302\u22a5 h (13) where |\u03b3| is obtained from (11), and the solution for \u2212p\u0302 is given by \u22121(+p\u0302). After \u00b1p\u0302 is determined, \u2016p\u2016 can be selected without changing the result of (13). There are two cases when (12) becomes degenerate and the aforementioned approach for constructing \u00b1p\u0302 breaks down, both are illustrated in Fig. 2(a). The first case occurs when \u03c9\u0302h = \u03c9\u0302a . In this case, it can be verified using (11) that \u03b32 = 1 implying that \u00b1p\u0302 are parallel to \u03c9\u0302h and \u03c9\u0302a . These positions correspond to axial positions (see Fig. 1). The second degenerate case occurs when \u03c9\u0302h = \u2212\u03c9\u0302a . In this case, \u03b32 = 0 implying that \u00b1p\u0302 must be perpendicular to \u03c9\u0302h and \u03c9\u0302a . There are an infinite number of solutions in this case, and all correspond to radial positions (see Fig. 1). Reversing the actuator magnet\u2019s spin direction turns one degenerate case into the other. In every other nondegenerate case, spinning the actuator magnet about \u03c9\u0302a in one direction admits two unique solutions for p\u0302, and spinning in the opposite direction changes the sign of \u03c1, produces another value of \u03b32 from (11), and admits two additional unique solutions for p\u0302 making, in total, four unique solutions that produce a desired field rotation axis \u03c9\u0302h given a reversible actuator-magnet rotation axis \u03c9\u0302a . Fig. 2(b) shows an example set of actuator-magnet positions that achieve a desired field rotation axis when the actuator magnet\u2019s rotation axis is constrained but is permitted to reverse direction. For rotating UMDs, a common failure mode that results in the loss of control authority occurs when the UMD steps out of synchronization with the rotating field as the field rotates. The rotation frequency above which the applied magnetic torque is too weak in magnitude to keep the UMD synchronized with the rotating field is referred to as the \u201cstep-out\u201d frequency and is denoted by \u2016\u03c9so\u2016",
            " Although they were originally obtained by setting the actuator magnet\u2019s position and solving for the required actuator-magnet axis of rotation, Fig. 6(b) and (c) can also be used to demonstrate the actuation of the capsule UMD while maintaining a constrained actuator-magnet rotation axis. In this example, the desired field rotation axis at the UMD\u2019s position is \u03c9\u0302h = [0,\u22121, 0]T, and the actuator magnet\u2019s rotation axis is constrained to lie parallel to the z-axis, with the ability to reverse the actuator magnet\u2019s direction of spin. The four position solutions, given by (13), that achieve the desired field rotation axis are shown in Fig. 2(a). Two of the four solutions, p2 and p3 , place the actuator magnet below the experimental setup\u2019s floor and are not physically achievable. The other two solutions, p1 and p4 , correspond to the actuatormagnet rotation axes \u03c9\u0302a = [0, 0,\u22121]T and \u03c9\u0302a = [0, 0, 1]T, and are shown in Fig. 6(b) and (c), respectively. When multiple feasible solutions exist, the position can be chosen to maximize the contribution of magnetic force to actuation, improve the robustness of actuation to uncertainty in the UMD\u2019s location [32], or maximize the configuration-space distance of the robot manipulator from singularities or joint limits"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001307_ecc.2009.7074482-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001307_ecc.2009.7074482-Figure1-1.png",
        "caption": "Fig. 1. Notations in the body frame.",
        "texts": [
            " Analytic formulas for the generated forces and torques are determined and incorporate the motion of the quadrotor. In Section III, with these torques and forces, we obtain a 6 D.O.F. model with four inputs being the rotation speeds of the four propellers. By successively accounting for the coupling of the propellers dynamics, the rigid body dynamics, and the flexibility of the propellers, the study proposes three models of increasing complexity. In Section IV, we expose analysis results which permit to stress the merits and limitations of the developed models. We consider a quadrotor UAV as depicted in Fig. 1. We note u,v,w its translational speed and p,q,r its angular rates in body axes (xb,yb,zb). The body frame is obtained by a rotation of an inertial frame by the Euler angles (\u03c8 ,\u03b8 ,\u03c6 ). Considering a general wind speed which coordinates in the body frame are uw, vw, ww, and the induced velocity vi being a consequence of the rotation of the rotor blades, we use the following notations : u\u0304 = uw\u2212u, v\u0304 = vw\u2212v, w\u0304 = vi + ww \u2212 w. Each motor acts on the body depending on its rotation speed and the lever-arm L which is the length between the rotation axis and the center of gravity (Fig. 1). The mass of the quadrotor is around 1 kilogram. Our modeling is widely inspired by works on largesize helicopter rotors [9], [10], [11], and models proposed specifically for quadrotors [6], [7]. We transpose the largesize rotors modeling techniques to small-size rotors, taking into account angular rates, which are negligible at larger scales. By contrast with [12], [13], we do not neglect the forward flight speed (u,v). The aerodynamic effects applied to the rotor are evaluated by integrating, along each rotor blade, the aerodynamic resultant force per surface increment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure12.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure12.11-1.png",
        "caption": "FIGURE 12.11. A 2R planar manipulator carrying a load at the endpoint.",
        "texts": [
            " The forward Newton-Euler equations of motion allows us to start from a known action force system (1F0, 1M0), that the base link applies to the link (1), and calculate the action force of the next link. Therefore, analyzing the links of a robot, one by one, we end up with the force system that the end-effector applies to the environment. Using the forward or backward recursive Newton-Euler equations of motion depends on the measurement and sensory system of the robot. 664 12. Robot Dynamics Example 332 F Recursive dynamics of a 2R planar manipulator. Consider the 2R planar manipulator shown in Figure 12.11. The manipulator is carrying a force system at the endpoint. We use this manipulator to show how we can, step by step, develop the dynamic equations for a robot. The backward recursive Newton-Euler equations of motion for the first link are 1F0 = 1F1 \u2212 X 1Fe1 +m1 1 0a1 = 1F1 \u2212m1 1g+m1 1 0a1 (12.182) 1M0 = 1M1 \u2212 X 1Me1 \u2212 \u00a1 1d0 \u2212 1r1 \u00a2 \u00d7 1F0 + \u00a1 1d1 \u2212 1r1 \u00a2 \u00d7 1F1 + 1I1 1 0\u03b11 + 1 0\u03c91 \u00d7 1I1 1 0\u03c91 = 1M1 \u2212 1n1 \u00d7 1F0 + 1m1 \u00d7 1F1 + 1I1 1 0\u03b11 + 1 0\u03c91 \u00d7 1I1 1 0\u03c91 (12.183) and the backward recursive equations of motion for the second link are: 2F1 = 2F2 \u2212 X 2Fe2 +m2 2 0a2 = \u2212m2 2g\u2212 2Fe +m2 2 0a2 (12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003677_rob.21651-Figure18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003677_rob.21651-Figure18-1.png",
        "caption": "Figure 18. ICARUS UGV SAR Hardware.",
        "texts": [
            " Currently, the robot tracks are powered by two electromotors, allowing the UGV robot system a top speed of 3 km/h and to climb stairs and ramps up to 45\u25e6. The platform is able to operate up to 3 h in mixed operation conditions. More information about this platform can be found in Balta, De Cubber, Doroftei, Baudoin, & Sahli (2013) and Conduraru et al. (2012). For the experiments shown in this paper, we have also used two other platforms: A Dr-Robot Jaguar 4 \u00d7 4 equipped with laser 3D scanner based on rotary SICK LMS 100, as shown in Figure 18(a). A Husky platform equipped with geodetic laser system Z+F IMAGER 5010, as shown in Figure 18(b). Data from Z+F IMAGER were used to create a virtual environment for training tools. The main goal of these platforms is to help in exploring the area and to gather data necessary for building the 3D maps. The Dr-Robot platform is dedicated for fast scanning of buildings from the outside and the inside. The Husky platform is part of the training and support system and carries a high-accuracy laser scanner for gathering precise data. Gathered maps can be used later to create realistic training environments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001134_154770206x99343-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001134_154770206x99343-Figure1-1.png",
        "caption": "Fig. 1 Sun-planet and planet-ring gear mesh modeling",
        "texts": [
            " The planetary set and the defects are modeled. The time-frequency method of Wigner-Ville, widely used in conditionmonitoring operations, is used to characterize the signature of each fault. This method is suitable for such diagnosis and gives valuable information about the presence and effects of gear tooth defects. The problem addressed in this analysis is the plane vibration of a one-stage spur planetary gear train with N planets (p) and one sun (s), ring (r), and carrier (c), as presented in Fig. 1. Bearings are modeled by linear springs. The gear mesh is modeled by linear springs acting on the lines of action. Each component has three degrees of freedom: two translations, uj and vj, and one rotation, wl, with wj = rj \u03b8 j (j = c,r,s,l,\u2026N) as the base radius. Damping is not considered, but it could be introduced in parallel with gear mesh and bearing stiffness. F. Chaari, T. Fakhfakh, and M. Haddar, Dynamics of Mechanical Systems Research Unit, Mechanical Engineering Department, National School of Engineers, BP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002666_j.cirpj.2017.04.001-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002666_j.cirpj.2017.04.001-Figure1-1.png",
        "caption": "Fig. 1. Turbofan engine with six stages in civil airplanes [5].",
        "texts": [
            " This study showed that the combination of cladding and remelting can be used to deposit single-crystal structures and was able to establish a reproducible laser process to this effect. The results obtained indicate that the process is a promising candidate for the repair of turbine blade tips and warrants further research into the microstructure and thermomechanical properties of the repaired areas. \u00a9 2017 CIRP. Contents lists available at ScienceDirect CIRP Journal of Manufacturing Science and Technology journa l home page : www.e l sev ier .com/ loca te /c i rp j High pressure turbine blades are located in the hot section of aircraft engines (Fig. 1) and convert gaseous energy exiting the combustion chamber into mechanical energy. These blades are subject to high temperatures, high stress, vibration effects, centrifugal and fluid forces that can result in creep, fracture or yielding fractures [1] and threaten the mechanical integrity of the parts. To meet the rising requirements of the aerospace industry, turbine entry temperatures are raised in order to increase the power output and the thermodynamic efficiency of such engines, thereby creating a high stress environment for the blades [2]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003967_09506608.2020.1868889-Figure23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003967_09506608.2020.1868889-Figure23-1.png",
        "caption": "Figure 23. Image of the envisioned integrated PSPP modelling and simulation approach and associated length scales.",
        "texts": [
            " The microstructure of materials that results from the solidification process dictates thematerial properties (such as its response to deformation). The process\u2013microstructure\u2013property\u2013performance correlation in this process will be increasingly better understood through multi-scale modelling [270]. Due to the complexity of the design environment, the most optimal design can only be tracked computationally, thus reducing the time and number of experiments and discovering new design paths [279]. Figure 23 illustrates the integration, which is required to connect performance and process through knowledge of the microstructure and properties of the material. The needs for and benefits of the processmodelling and simulation capability are reported in several roadmaps for AM [6,21,199,280\u2013282]. Data mining and data-driven based models using PSPP relationships in AM Implementation of ICME requires full PSPP linkages, challenging for metal AM due to the limits and assumptions of currentlyknown physics-based models"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003826_j.jmapro.2020.07.035-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003826_j.jmapro.2020.07.035-Figure5-1.png",
        "caption": "Fig. 5. Sample cross-section of the location where microstructure and hardness were evaluated.",
        "texts": [
            " An optical microscope (Zeiss Axio Imager M2m) and a field emission scanning electron microscope (ZEISS SUPRA 55 V P) were employed. Vickers hardness measurements for the three material conditions were carried out under a load of 0.5 kgf for a dwell time of 10 s, using a Wilson Instruments hardness tester (402MVD Knoop-Vickers tester). For each material condition, a hardness profile was constructed out of 9 measurements from the top to the bottom of the sample, keeping a distance of 0.2 mm from the surface to the center of the first indentation and a distance of 0.5 mm between the other indentations. Section A-A in Fig. 5 indicates the region of the specimen in which the microstructure and hardness were analyzed. Residual stresses and phases within the microstructure were evaluated for each material condition by X-ray diffraction (XRD) using a PANalytical Empyrean Pro multipurpose diffractometer equipped with a Cu K\u03b1-source. The preparation of the samples for these tests consisted of removing a surface layer of 0.1 mm by milling and then stripping a 100 mm\u00b2 region located in the center of the sample (approximately 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000236_s0890-6955(99)00076-0-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000236_s0890-6955(99)00076-0-Figure3-1.png",
        "caption": "Fig. 3. Loaded region in a bearing.",
        "texts": [
            " Expressions for well known bearing contributions have been obtained and are listed below [3] (all symbols are defined in the nomenclature): (i) Cage frequency: fc5 fs 2S12 d cos a D D (1) (ii) Ball passage frequency (ball to outer race relative motion): fbo5Nfc (2) (iii) Ball to inner race frequency: fbi5 fs 2S11 d cos a D D (3) (iv) Ball frequency: fb5 Dfs 2d (4) These principal speed-dependent frequencies of ball bearings appear in the spectra of any shaft and bearing system under dynamic conditions. Their amplitude contribution depends upon the variation in the dynamic stiffness of the assembly, governed by a host of factors that determine the spread of the loaded region in bearings (see Fig. 3). With increased radial interference and the applied axial preload the loaded region spreads circumferentially, thus increasing the static and dynamic stiffness of the support bearings, whilst reducing the chance of emerging contact clearances under running conditions. This means that variations in the dynamic stiffness of the supports is less likely under operating conditions, hence reducing the effect of bearing induced vibrations. There are, however, many other sources of bearing vibration such as waviness of rolling elements; balls and races, as well as the existence of off-sized balls in the ball complement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.35-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.35-1.png",
        "caption": "Fig. 4.35",
        "texts": [
            " Therefore the hypothesis of Bernoulli that the cross sections remain plane is only a first approximation and the shear strain w \u2032 + \u03c8 (see (4.25)) is an average shear strain \u03b3\u0303. It should be noted again that in addition to the vertical shear stresses in the cross sections there are horizontal shear stresses 4.6 Influence of Shear 155 Fig. 4.34 V V x z w\u2032 \u03c8 dx that act between horizontal layers of the beam (complementary stresses). This fact can easily be demonstrated with the aid of two smooth beams and lying on top of each other (Fig. 4.35). During bending, the beams move relative to each other in the area of contact (smooth surfaces!). This relative sliding may be prevented if the beams are bonded together by welding, gluing or riveting. This will generate shear stresses in the contact area which have to be supported by the bonding (e.g. the weld seam). F We will now determine the shear stresses in beams with thinwalled cross sections, restricting ourselves to open cross sections. We assume that the shear stresses \u03c4 at a position s of the cross section are constant across the thickness t and that they are parallel to the boundary (Fig",
            " Integration over the cross section yields the strain energy per unit length Ui \u2217 \u03c4 = 1 2 \u222b \u03c42 G dA. (6.19) We now equate (6.18) and (6.19): 1 2 V 2 GAS = 1 2 \u222b \u03c42 G dA. (6.20) If the distribution of the shear stress \u03c4 in the cross section is known, the integral in (6.20) can be evaluated and thus the shear area AS and the shear correction factor \u03ba can be calculated. To illustrate the method we consider a rectangular cross section. According to (4.39) the distribution of the shear stress is given by \u03c4 = 3 2 V A ( 1\u2212 4 z2 h2 ) (see Fig. 4.35b). Inserting \u03c4 into (6.20) and using dA = b dz and A = b h yields 1 AS = 9 4 1 A2 h/2\u222b \u2212h/2 ( 1\u2212 4 z2 h2 )2 b dz = 6 5 1 b h . Hence, we obtain AS = 5 6 b h, \u03ba = AS A = 5 6 (6.21) for a rectangular cross section. The average shear strain \u03b3\u0303 = w\u2032 + \u03c8 = V GAS = 1.2 V GA is therefore 20% larger than the shear strain that would be caused by a uniform distribution \u03c4 = V/A of the shear stress. Similar considerations lead to values between 0.8 and 0.9 of the shear correction factor \u03ba for solid cross sections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000736_0278364904047392-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000736_0278364904047392-Figure5-1.png",
        "caption": "Fig. 5. Wheel\u2013terrain contact angle \u03b3 for rigid wheel on deformable terrain.",
        "texts": [
            " Consider a planar two-wheeled system on uneven terrain (see Figure 4). In this analysis the terrain is assumed to be rigid, and the wheels are assumed to make point contact with the terrain. For rigid wheels on deformable terrain, the singlepoint assumption no longer holds. However, an \u201ceffective\u201d wheel\u2013terrain contact angle is defined as the angular direction at Universitats-Landesbibliothek on December 12, 2013ijr.sagepub.comDownloaded from of travel imposed on the wheel by the terrain during motion (see Figure 5). In Figure 4, the rear and front wheels make contact with the terrain at angles \u03b31 and \u03b32 from the horizontal, respectively. The vehicle pitch, \u03b1, is also defined with respect to the horizontal. The wheel centers have speeds \u03bd1 and \u03bd2. These speeds are in a direction parallel to the local wheel\u2013terrain tangent due to the rigid terrain assumption. The distance between the wheel centers is defined as l. For this system, the following kinematic equations can be written: \u03bd1 cos (\u03b31 \u2212 \u03b1) = \u03bd2 cos (\u03b32 \u2212 \u03b1) (13) \u03bd2 sin (\u03b32 \u2212 \u03b1) \u2212 \u03bd1 sin (\u03b31 \u2212 \u03b1) = l\u03b1\u0307"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure8.13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure8.13-1.png",
        "caption": "Figure 8.13. The lift forces created on spinning spheres is called the Magnus Effect. An overly simplified application of Bernoulli's Principle is often incorrectly used to explain the cause of this fluid force. Spin on the tennis ball drags the boundary layer of fluid in the direction of the spin. Fluid flow past the ball is slowed where the boundary layer opposes the free stream flow, increasing the fluid pressure. The topspin on this ball (like the ball in figure 8.6) creates a downward lift force that combines with gravity to make a steep downward curve in the trajectory.",
        "texts": [
            " Activity: Bernoulli's Principle An easy way to demonstrate Bernoulli's Principle is to use a small (5 10 cm) piece of regular weight paper to simulate an airplane wing. If you hold the sides of the narrow end of the paper and softly blow air over the top of the sagging paper, the decrease in pressure above the paper (higher pressure below) will lift the paper. Recall that it was noted that Bernoulli's Principle is often overgeneralized to explain the lift force from the Magnus Effect. This oversimplification of a complex phenomenon essentially begins by noting that a rotating sphere affects motion in the boundary layer of air (Figure 8.13) because of the very small irregularities in the surface of the ball and the viscosity of the fluid molecules. Fluid flow past the ball is slowed where the boundary layer rotation opposes the flow, but the free stream fluid flow will be faster when moving in the same direction as the boundary layer. For the tennis ball with topspin illustrated in Figure 8.13, Bernoulli's Principle would say that there is greater pressure above the ball than below it, creating a resultant downward lift force. As direct and appealing as this explanation is, it is incorrect because Bernoulli's Principle does not apply to the kinds of fluid flow past sport balls since the fluid flow has viscous properties that create a separation of the boundary layer (Figure 8.6). Bernoulli's Principle may only apply to pressure differences away from or outside the boundary layer of a spinning ball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002086_j.engfailanal.2014.12.020-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002086_j.engfailanal.2014.12.020-Figure5-1.png",
        "caption": "Fig. 5. Direction of forces acting on gear tooth.",
        "texts": [
            " 4(a) F is a force acting on gear tooth surface along line of action (LOA), Fv and Fh are vertical and horizontal components of acting force F respectively. Similarly in Fig. 4(b) and (c) f is friction force which acts perpendicular to force F, fv and fh are vertical and horizontal components of friction force f respectively. Pressure angle is represented by a1 in Fig. 4. In Fig. 4(b) and (c) it has been shown that friction force f always acts perpendicular to the force F, and its value is equal to the product of coefficient of friction l and force F, i.e. f \u00bc lF \u00f021\u00de Using (21) and resolving force F and friction force f as shown in Fig. 5 modified value of tangential and radial forces acting on gear tooth can be calculated. Table 2 shows the expression for radial and tangential forces acting on gear tooth. Friction force changes the value of tangential force and radial force, due to which bending stiffness and axial compressive stiffness will change. Hertzian stiffness will remain unchanged. Putting values of radial and tangential component in (6)\u2013(8), expression for bending mesh stiffness, shear mesh stiffness and axial compressive stiffness can be given as follows: Bending stiffness; 1 kb \u00bc R a2 a1 3 f1\u00fecos a1f\u00f0a2 a\u00de sin a cos agg lfa1\u00fea2\u00fesin a1f\u00f0a2 a\u00de sin a cos agg\u00bd 2\u00f0a2 a\u00de cos a 2EL sin a\u00fe\u00f0a2 a\u00de cos a\u00bd 3 da; \u00f022\u00deR a2 a1 3 f1\u00fecos a1f\u00f0a2 a\u00de sin a cos agg\u00felfa1\u00fea2\u00fesin a1f\u00f0a2 a\u00de sin a cos agg\u00bd 2\u00f0a2 a\u00de cos a 2EL sin a\u00fe\u00f0a2 a\u00de cos a\u00bd 3 da; \u00f023\u00de 8>< >: Shear stiffness; Axial compressive stiffness; 1 ka \u00bc R a2 a1 \u00f0a2 a\u00de cos a\u00f0sin a1\u00fel cos a1\u00de2 2EL\u00bdsin a\u00fe\u00f0a2 a\u00de cos a da; \u00f026\u00deR a2 a1 \u00f0a2 a\u00de cos a\u00f0sin a1 l cos a1\u00de2 2EL\u00bdsin a\u00fe\u00f0a2 a\u00de cos a da \u00f027\u00de 8< : In the above expressions Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.13-1.png",
        "caption": "Fig. 3.13 Example of MacPherson strut [3]",
        "texts": [
            " More precisely, in a first-order analysis, it suffices to consider the roll centers and the roll axis, as discussed in the next section. Let us start having a closer look at the suspension linkages. In case of purely transversal independent suspensions, like those shown, e.g., in Fig. 3.11, it is easy to obtain the instantaneous center of rotation Bi of each wheel hub with respect to the vehicle body. Another useful point is the center Ai of each contact patch. The same procedure can be applied also to the MacPherson strut. The kinematic scheme is shown in Fig. 3.12, while a possible practical design is shown in Fig. 3.13. The MacPherson strut is the most widely used front suspension system, especially in cars of European origin. It is the only suspension to employ a slider, marked by number 2 in Fig. 3.12. Usually, the slider is the damper, which is then part of the suspension linkage. To obtain the instantaneous center of rotation Bi of each wheel hub with respect to the vehicle body it suffices to draw two lines, one along joints 3 and 4, and the other through joint 1 and perpendicular to the slider (not to the steering axis, which goes from joint 1 and 3, as also shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000088_027836499101000106-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000088_027836499101000106-Figure12-1.png",
        "caption": "Fig. 12. Coordinate systems of PUMA robots.",
        "texts": [
            " , KN are distinct integers and must lie in between 1 and Nf - 1. If the first measurement configuration eel, 182, ... , 18N) is selected, then a sequence of optimal measurements configurations can be found from equation (24). It can be seen that a set of preferential measurement configurations for planar mechanisms should be well spaced in the joint space as well as in the Cartesian space. 5.2. PUMA Type Robots Many of the current industrial robots have a somewhat similar regional structure, as shown in Figure 12. Kumar et al. (1986) have shown that this structure with L2 = L3 is one of the optimal structures for working volume. For this mechanism, only the geometric parameters are modeled; their nominal values are shown in Table 4. Among the 21 parameters in the kinematic model, 15 error parameters are shown to be observable. The position error model with nominal values of the geometric parameters becomes at MICHIGAN STATE UNIV LIBRARIES on February 22, 2015ijr.sagepub.comDownloaded from 60 where and Because the dimension of observable error parameter space is 15 and each measurement provides three position data, at least five measurements are needed to fully identify the 15 error parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003617_iet-epa.2016.0044-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003617_iet-epa.2016.0044-Figure7-1.png",
        "caption": "Fig. 7 Vibration and noise distribution at peak frequency",
        "texts": [
            " Similarly, the equations are solved and the solutions include: (i) n = 1, v = 12\u03bc\u20137; (ii) n = 3, v = 12\u03bc\u201317; (iii) n = 3, v = 17 \u00b1 12\u03bc; (iv) n = 1, v = 7 \u00b1 12\u03bc. It is noted that the 0th spatial order force is not considered here to explain the vibration and noise peaks in spite of their large amplitude in low and medium frequency band. The motor investigated in the paper has small size and the 0th modal frequency is higher than 10,000 Hz. Those 0th order force components are far away from the modal frequency and thus are not able to induce significant vibration and noise. This is confirmed by the spatial pattern of vibration and noise peaks shown in Fig. 7 which illustrates that the spatial pattern at peak frequency depends on the lowest spatial force order except the 0th order. However, when discussing the vibration and noise in motors with large size or in high frequency band around the 0th modal frequency, the 0th order force should be considered because the corresponding force frequency could be close to the modal frequency. Fig. 8a shows the relationship between current amplitude and overall SWL in PMSM with different slot-pole combinations. The noise of P2S12C2 and P8S12C1 is higher than that of other motors due to the IET Electr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003722_j.ymssp.2021.108319-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003722_j.ymssp.2021.108319-Figure17-1.png",
        "caption": "Fig. 17. Gear teeth from the dry test: (a) new pinion before the test, (b) worn pinion after the test, (c) new driven gear,(d) worn driven gear after the test.",
        "texts": [
            " This is a two-way relationship between surface pitting propagation and tooth profile change. The comparison analysis between measurements and simulations can guarantee accurate tooth profile change prediction and surface pitting propagation prediction results, as shown in Fig. 12 and Fig. 16. Compared with the lubricated test, the dry test represents an extreme case, with severe abrasive wear and a correspondingly large change in the tooth profile, but very little surface pitting propagation (see Fig. 17 and Fig. 18). The proposed approach is however still effective under dry conditions, as will be demonstrated in this section. During the dry test, the gear surface becomes rougher and rougher with a high wear rate (in terms of wear depth); see Fig. 19. However, surface roughness Sa only indicates the surface morphology change. To intuitively represent the tooth profile change during the dry test, the mass of wear particles collected on adhesive paper was weighed to calculate the mean wear depth of the worn gears, which can be used to verify the effectiveness of the proposed method in tooth profile change monitoring and prediction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure3-8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure3-8-1.png",
        "caption": "Fig. 3-8 Torque on the rotor d-axis.",
        "texts": [
            " In contrast, choosing \u03c9d\u00a0=\u00a00, that is, a stationary d-axis (often chosen to be aligned with the a-axis of the stator with \u03b8da\u00a0=\u00a0 0), leads to the rotor and the stator dq winding voltages and currents oscillating at the synchronous frequency in a balanced sinusoidal steady state. The choice of \u03c9d\u00a0=\u00a0\u03c9m results in dq winding voltages and currents in the stator and the rotor varying at the slip frequency; this choice is made for analyzing synchronous machines, as we will discuss in Chapter 9. 3-5 ELECTROMAGNETIC TORQUE 3-5-1 Torque on the Rotor d-Axis Winding On the rotor d-axis winding, the torque produced is due to the flux density produced by the q-axis windings in Fig. 3-8. The peak of the flux density distribution \u201ccutting\u201d the rotor d winding due to isq and irq, each flowing through 3 2/ Ns turns of the q-axis windings (using Eq. 2-3), is: \u02c6 / B N p i L L irq g s sq r m rq=       +       \u00b50 3 2 mmf , (3-40) ELECTROMAGNETIC TORqUE 43 where the factor Lr/Lm allows us to include both the magnetizing and the leakage flux produced by irq. Using the torque expression in chapter 10 of Reference [1] used in the previous course, and noting that the current ird in the rotor d-axis winding flows through 3 2/ Ns turns, the instantaneous torque on the d-axis rotor winding is (see problem 10-1 in chapter 10 of Reference [1]) T p N p r B id s rq rd,rotor / =      2 3 2 \u03c0 \u02c6 . (3-41) As shown in Fig. 3-8, this torque on the rotor is counter-clockwise (CCW), hence we will consider it as positive. Substituting for B\u0302rq from Eq. (3-40) into Eq. (3-41), T p r N p i L L id g s sq r m r, / rotor =             + 2 3 20 2 \u03c0 \u00b5 q rdi       . (3-42) Rewriting Eq. (3-42) below, we can recognize Lm from Eq. (2-13) T p r N p d g s Lm ,rotor =            2 3 2 0 2 \u03c0 \u00b5 i L L i isq r m rq rd+       . Hence, T p L i L i i p id m sq r rq rd rq rd rq , ( ) .rotor = + = 2 2 \u03bb \u03bb (3-43) 3-5-2 Torque on the Rotor q-Axis Winding On the rotor q-axis winding, the torque produced is due to the flux density produced by the d-axis windings in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure12.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure12.12-1.png",
        "caption": "Fig. 12.12 Schematic diagram of four-beam moir\u00e9 interferometry [20]",
        "texts": [
            " Moir\u00e9 interferometry is used to measure tiny deformations of solid bodies, caused by mechanical forces, temperature changes, or other environmental changes [20]. It has been applied for studies of composite materials, polycrystalline materials, layered materials, piezoelectric materials, fracture mechanics, biomechanics, structural elements and structural joints. It is practiced extensively in the microelectronics industry to measure thermally induced deformation of electronic packages. Moir\u00e9 interferometry combines the simplicity of geometrical moir\u00e9 with the high sensitivity of optical interferometry, measuring in-plane displacements (Fig. 12.12). It is characterised by a list of excellent qualities. Moir\u00e9 interferometry has a proven record of applications in engineering and science. 12 Reverse Engineering 333 Computer Tomography (CT) allows three-dimensional visualization of the internals of an object. It provides a large series of 2D X-ray cross-sectional images taken around a single rotational axis [3]. By projecting a thin X-ray or Y-ray beam through one plane of an object from many different angles and measuring the amount of radiation that passes through the object along various lines of sight, a cross-sectional image for the scanned surface is reconstructed (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001708_tia.2009.2023393-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001708_tia.2009.2023393-Figure1-1.png",
        "caption": "Fig. 1. Three-dimensional finite-element mesh for IPM motor with concentrated windings (126 198 tetrahedral edge finite elements).",
        "texts": [
            " The formulations [5] are \u2207\u00d7 ( 1 \u03bc \u2207\u00d7 A ) = Ja \u2212 \u03c3 ( \u2202A \u2202t + \u2207\u03c6 ) + 1 \u03bc0 \u2207\u00d7 M (2) \u2207 \u00b7 { \u03c3 ( \u2202A \u2202t + \u2207\u03c6 )} = 0 (3) va = voa + Raia = d\u03a6 dt + Raia (4) where A and \u03c6 are the magnetic vector and electric scalar potentials, respectively, and \u03bc and \u03c3 are the permeability and the conductivity, respectively. Ja is the armature current density, M is the magnetization of the permanent magnet, va and ia are the armature voltage and current, respectively, Ra is the armature coil resistance, and \u03a6 is the flux linkage of the armature coil. va is given due to the PWM voltage waveform [4]. Fig. 1 shows the finite-element mesh. The first-order tetrahedral edge finite elements are employed in the discretization. The analyzed region is reduced to 1/20 of the core length, which corresponds to half the thickness of the magnet, by imposing different boundary conditions on each side [5]. The number of time steps per time period is set at 1024 for correct consideration of the carrier harmonics of the PWM inverter. The rotor region is shifted at each time step due to the rotational speed of the rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000109_s0007-8506(07)63450-7-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000109_s0007-8506(07)63450-7-Figure8-1.png",
        "caption": "Figure 8 : Piezoelectric microgripper [34].",
        "texts": [
            " The deformation of the spring was made through a force applied exactly in the centre of the \"U\" stripe in order to obtain a symmetrical opening of the jaws. The force is obtained either byTg piezoelectric disk translator or a piezoelectric Picomotor (New Focus) (see figure 7). A - non-magnetic - CuBez alloy was chosen for the jaws. Carrozza et al. [32] and Ando et al. [33] built parallel jaw grippers driven by a piezoelectric element of which the motion is amplified through lever mechanisms with flexible hinges. Breguet et al. [34] cut the whole gripper out of a piezoceramic plate as shown in figure 8. The electrodes are designed to render active only the parts of the piezo which are underneath them. A piezoelectric force sensor can be easily integrated in one of the jaws. The gripper is about 3 cm long and opens f 18 pm at the tip for a voltage of 150 V. A similar approach is followed by Bellouard et al. [35] for the design of a SMA gripper. The whole gripper structure is cut out of a single SMA plate. One prototype uses twoway shape memory effect, the other, which is shown in figure 9, uses the elasticity of the structure itself as bias spring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure7-1.png",
        "caption": "Fig. 7. Contact model of a pair of elastic bodies: (a) three-dimensional view and (b) section view.",
        "texts": [
            " Pairs of contact points in the case that there are no AE, ME and TM can be used. It is only needed to take effects of ME and TM on gap calculations into account when to calculate gaps of the pairs of contact points with the Eq. (6). Since a face contact model as shown in Fig. 5 is used in LTCA, effects of ME and TM on tooth engagement at a arbitrary engagement position, such as outer and inner limit positions of loads, can be considered automatically if the Width in Fig. 5 is made large enough. In Fig. 7, and are one pair of elastic bodies which will contact each other when an external force P is applied. Contact of this pair of elastic bodies is handled as contact of many pairs of points on both supposed contact surfaces of and like gear\u2019s contact as shown in Fig. 5. These pairs of contact points are expressed as (1 1 0), (2 2 0), . . . ,(m m 0), (a a 0), (k k 0), (j j 0), (b b 0),. . . and (n n 0). n is the total number of contact point pairs. Fig. 7(b) is a section view of Fig. 7(a) in the normal plane of the contact bodies. In Fig. 7, ek is a clearance (or backlash) between a optional contact point pair (k k 0) before contact. Fk is contact force between the pair of contact points (k k 0) in the direction of its common normal line when k contacts with k 0 under the load P (It is assumed that all the common normal lines of the contact point pairs are approximately along the same direction of the load P in this paper because a contact area is usually very narrow. This assumption is reasonable in engineering.). xk, xk0 are deformations of the points k and k 0 in the direction of the force Fk after contact. d0 is the initial minimum clearance between and and d is the relative displacement of the points O1 and O2 (the loading points in Fig. 7(b)). For the optional contact point pair (k k 0), if (k k 0) contacts, \u00f0xk \u00fe xk0 \u00fe ek\u00de, the amount of the deformations and clearance on the point pair (k k 0), shall be equal to the relative displacement quantity d, and if (k k 0) does not contact, \u00f0xk \u00fe xk0 \u00fe ek\u00de shall be greater than d. Eqs. (7) and (8) are used to express these relationships in the following. Eqs. (7) and (8) can be also summed with Eq. (9): xk \u00fe xk0 \u00fe ek d > 0 \u00f0Not contact\u00de \u00f07\u00de xk \u00fe xk0 \u00fe ek d \u00bc 0 \u00f0Contact\u00de \u00f08\u00de Then xk \u00fe xk0 \u00fe ek d P 0 \u00f0k \u00bc 1; 2; ",
            " Step 9: Input loaded torque Torque is inputted here for LTCA using in the equations of mathematical programming method. Step 10: Set up mathematical model of LTCA and perform mathematical programming calculations Set up mathematical model of Eqs. (17)\u2013(19) and solve these equations with Modified Simplex Method of mathematical programming method. Tooth loads (contact forces between the pairs of contact points) and relative deformation of the pair of gears along the line of action (d as shown in Fig. 7(b)) are obtained here. Step 11: Output tooth load distribution of the pair of gears with AE, ME and TM Tooth contact pattern and tooth load distribution of the pair of gears with AE, ME and TM can be obtained. Step 12: Calculate contact stresses on tooth surfaces and calculate tooth root stresses with 3D-FEM Tooth contact stresses are calculated by the method stated in Section 3.6 when load distribution on each tooth is known. Tooth root stresses are calculated by 3D-FEM with the model as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001001_1.3453357-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001001_1.3453357-Figure7-1.png",
        "caption": "Fig. 7 Hydrodynamic interaction between the cage and a roller",
        "texts": [
            " Once such an assumption is made the local load deflection relationship is obtained by either equation (18) or (20), presented earlier for a line contact. The important step is to calculate the actual deflection or clearance from the prescribed position of the rollers, cage, and the races. This is done by manipulating the matrix equations similar to the ones described earlier for roller/race interactions. The algebraic details have been omitted here for brevity. Roller/Cage Hydrodynamics. As shown schematically in Fig. 7, JULY 1979, VOL. 101 /299 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 05/02/2015 Terms of Use: http://asme.org/terms the dominant velocity component for the roller/cage hydrodynamics will be the roller angular velocity about its polar x axis. It will be as sumed that all the hydrodynamic action takes place on the cylindrical surface only, and the end faces are free of any forces, although a lu bricant churning torque on the ends will be considered in the next section. With such a geometry of interaction the conventional \"long bear ing\" approximation will be valid and in terms of the (x, y) coordinate frame shown in Fig. 7. op op -\u00ab oy ox and the Reynolds equation is written as ~ (h3 OP) = 6 UJi. oh ox ox ox (45) where p is the local pressure, h is the film thickness, U (= Wi d/2) is the relative sliding velocity and /1 is the viscosity of the lubricant. In accordance with the coordinate system shown in Fig. 7, let the exit be donated by x = Xo where the pressure gradient will be zero and let the corresponding film thickness be ho. Also let the pressure be zero at the entrance edge ofthe cage located at x = -I'. Then the in tegrated form of equation (45) may be written as ('X h(x') - ho p(x) = 6/1U Jl' h(x')3 The equivalent radii Rx along the x direction is just the radius of the roller and the radius is infinite along the y direction and it will be further assumed that op/oy = O. Thus, it will only be necessary to determine the pressure profile at y = o"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002117_j.mechmachtheory.2019.103597-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002117_j.mechmachtheory.2019.103597-Figure5-1.png",
        "caption": "Fig. 5. The loads applied on the q th ball.",
        "texts": [
            " 3 , \u03b8 x and \u03b8 y are the angular position coordinates of the inner ring respected to the x and y axises, respectively; the balls are numbered by 1\u2013q; \u03d5 is the angular difference between two adjacent balls; \u03d5q is the azimuth of the q th ball; and the ball distribution and coordinate system definition of the bearing are given in Fig. 3 . When the ACBB is subjected to the combined loads, the inner ring will produce the axial displacement \u03b4a and radial displacement \u03b4rq . The positions of the shifted ball center and groove curvature centers for the q th ball are depicted in Fig. 4 . Here, the ball center will be moved to O b from O b \u2019 ; the curvature center of the groove of the inner ring will be moved to O i from O i \u2019 . The loads applied on the q th ball are depicted in Fig. 5 . The geometry and compatibility equations for the ACBB are represented as ( A 1 q \u2212 X 1 q ) 2 + ( A 2 q \u2212 X 2 q ) 2 \u2212 [ ( f i \u2212 0 . 5) D + \u03b4iq ]2 = 0 (6) X 2 1 q + X 2 2 q \u2212 [ ( f o \u2212 0 . 5) D + \u03b4oq ] 2 = 0 (7) where \u03b4i q and \u03b4o q are the contact deformations of the inner and outer rings, respectively. The equations of the load distribution are represented as Q iq sin \u03b1iq \u2212 Q oq sin \u03b1oq \u2212 M gq ( \u03bbiq cos \u03b1iq \u2212 \u03bboq cos \u03b1oq ) = 0 (8) D Q iq cos \u03b1iq \u2212 Q oq cos \u03b1iq + M gq D ( \u03bbiq cos \u03b1iq \u2212 \u03bboq sin \u03b1oq ) + F cq = 0 (9) where \u03bbi q and \u03bbo q are the distribution coefficients of the friction moments between the rings and the q th ball, respectively; moreover, \u03bbi q + \u03bbo q is equal to 2; F c q is the centrifugal force of the q th ball; M g q is the friction moment of the q th ball; and Q i q and Q o q are the contact forces applied on the inner and outer rings, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.5-1.png",
        "caption": "FIGURE 2.5. Corner P of the slab at first position.",
        "texts": [
            " Similarly, rotation \u03b2 about the Y -axis and rotation \u03b3 about the X-axis are described by the Y -rotation matrix QY,\u03b2 and the X-rotation matrix QX,\u03b3 respectively. QY,\u03b2 = \u23a1\u23a3 cos\u03b2 0 sin\u03b2 0 1 0 \u2212 sin\u03b2 0 cos\u03b2 \u23a4\u23a6 (2.21) 2. Rotation Kinematics 37 QX,\u03b3 = \u23a1\u23a3 1 0 0 0 cos \u03b3 \u2212 sin \u03b3 0 sin \u03b3 cos \u03b3 \u23a4\u23a6 (2.22) The rotation matrices QZ,\u03b1, QY,\u03b2, and QX,\u03b3 are called basic global rotation matrices. We usually refer to the first, second and third rotations about the axes of the global coordinate frame by \u03b1, \u03b2, and \u03b3 respectively. Example 3 Successive rotation about global axes. The final position of the corner P (5, 30, 10) of the slab shown in Figure 2.5 after 30 deg rotation about the Z-axis, followed by 30 deg about the Xaxis, and then 90 deg about the Y -axis can be found by first multiplying QZ,30 by [5, 30, 10]T to get the new global position after first rotation\u23a1\u23a3 X2 Y2 Z2 \u23a4\u23a6 = \u23a1\u23a3 cos 30 \u2212 sin 30 0 sin 30 cos 30 0 0 0 1 \u23a4\u23a6\u23a1\u23a3 5 30 10 \u23a4\u23a6 = \u23a1\u23a3 \u221210.6828.48 10.0 \u23a4\u23a6 (2.23) and then multiplying QX,30 and [\u221210.68, 28.48, 10.0]T to get the position of P after the second rotation\u23a1\u23a3 X3 Y3 Z3 \u23a4\u23a6 = \u23a1\u23a3 1 0 0 0 cos 30 \u2212 sin 30 0 sin 30 cos 30 \u23a4\u23a6\u23a1\u23a3 \u221210.6828",
            "24) B G\u03c9\u0303B = \u2212B B\u03c9\u0303G. (7.25) G\u03c9B and can always be expressed in the form G\u03c9B = \u03c9u\u0302 (7.26) where u\u0302 is a unit vector parallel to G\u03c9B and indicates the instantaneous axis of rotation. Using the Rodriguez rotation formula (3.4) we can show that R\u0307u\u0302,\u03c6 = \u03c6\u0307 u\u0303 Ru\u0302,\u03c6 (7.27) and therefore \u03c9\u0303 = \u03c6\u0307 u\u0303 (7.28) or equivalently G\u03c9\u0303B = lim \u03c6\u21920 Gd dt Ru\u0302,\u03c6 = lim \u03c6\u21920 Gd dt \u00a1 \u2212u\u03032 cos\u03c6+ u\u0303 sin\u03c6+ u\u03032 + I \u00a2 = \u03c6\u0307 u\u0303 (7.29) and therefore \u03c9 = \u03c6\u0307 u\u0302. (7.30) Example 198 Rotation of a body point about a global axis. The slab shown in Figure 2.5 is turning about the Z-axis with \u03b1\u0307 = 10deg /s. The global velocity of the corner point P (5, 30, 10), when the slab is at \u03b1 = 30deg, is: GvP = GR\u0307B(t) BrP (7.31) = Gd dt \u239b\u239d\u23a1\u23a3 cos\u03b1 \u2212 sin\u03b1 0 sin\u03b1 cos\u03b1 0 0 0 1 \u23a4\u23a6\u239e\u23a0\u23a1\u23a3 5 30 10 \u23a4\u23a6 = \u03b1\u0307 \u23a1\u23a3 \u2212 sin\u03b1 \u2212 cos\u03b1 0 cos\u03b1 \u2212 sin\u03b1 0 0 0 0 \u23a4\u23a6\u23a1\u23a3 5 30 10 \u23a4\u23a6 = 10\u03c0 180 \u23a1\u23a3 \u2212 sin \u03c0 6 \u2212 cos \u03c06 0 cos \u03c06 \u2212 sin \u03c0 6 0 0 0 0 \u23a4\u23a6\u23a1\u23a3 5 30 10 \u23a4\u23a6 = \u23a1\u23a3 \u22124.97\u22121.86 0 \u23a4\u23a6 7. Angular Velocity 385 at this moment, the point P is at: GrP = GRB BrP (7.32) = \u23a1\u23a3 cos \u03c06 \u2212 sin \u03c0 6 0 sin \u03c0 6 cos \u03c06 0 0 0 1 \u23a4\u23a6\u23a1\u23a3 5 30 10 \u23a4\u23a6 = \u23a1\u23a3 \u221210.6728.48 10 \u23a4\u23a6 Example 199 Rotation of a global point about a global axis. The corner P of the slab shown in Figure 2.5, is at BrP = \u00a3 5 30 10 \u00a4T . When it is turned \u03b1 = 30deg about the Z-axis, the global position of P is: GrP = GRB BrP (7.33) = \u23a1\u23a3 cos \u03c06 \u2212 sin \u03c0 6 0 sin \u03c0 6 cos \u03c06 0 0 0 1 \u23a4\u23a6\u23a1\u23a3 5 30 10 \u23a4\u23a6 = \u23a1\u23a3 \u221210.6728.48 10 \u23a4\u23a6 If the slab is turning with \u03b1\u0307 = 10deg / s, the global velocity of the point P would be GvP = GR\u0307B GRT B GrP (7.34) = 10\u03c0 180 \u23a1\u23a3 \u2212s\u03c06 \u2212c\u03c06 0 c\u03c06 \u2212s\u03c06 0 0 0 0 \u23a4\u23a6\u23a1\u23a3 c\u03c06 \u2212s\u03c06 0 s\u03c06 c\u03c06 0 0 0 1 \u23a4\u23a6T \u23a1\u23a3 \u221210.6728.48 10 \u23a4\u23a6 = \u23a1\u23a3 \u22124.97\u22121.86 0 \u23a4\u23a6 . Example 200 Principal angular velocities. The principal rotational matrices about the axes X, Y , and Z are: RX,\u03b3 = \u23a1\u23a3 1 0 0 0 cos \u03b3 \u2212 sin \u03b3 0 sin \u03b3 cos \u03b3 \u23a4\u23a6 (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure5.8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure5.8-1.png",
        "caption": "Fig. 5.8",
        "texts": [
            " For this type of geometries, we can derive useful formulas for approximate solutions based on a few suitable assumptions for the stress distributions. Now we will focus on this type of cross sections, since they are of major importance in practical applications (box girder in bridge constructions, wing constructions in aeronautics, etc.). We assume that the dimensions of the thin-walled tubes with closed cross sections (= hollow cylinders) do not vary along x, i.e. we consider tubes with constant yet arbitrary thin-walled cross sections. Furthermore, we assume that the cross sections are subjected to a constant torque MT (Fig. 5.8a). As a coordinate along the center line (also called median line) of the profile (Fig. 5.8c) we introduce the arc length s. The wall thickness of the tube may vary with the arc length: t = t(s). The applied torque causes shear stresses in the cross sections. No loads are applied at the outer and inner boundaries of the cross section. Therefore we conclude that the shear stresses must be tangential to the boundaries. Since the wall thickness is small, we assume that the shear stresses are uniformly distributed across the thickness of the tube (= average shear stress). Hence, we can express them by a resulting force quantity, namely the shear flow T = \u03c4 t . (5.15) The shear flow T has the dimension force/length and is acting tangential to the median line of the profile (Fig. 5.8c). Let us now consider a rectangular element of the tube having the infinitesimal length dx and height ds as depicted in Fig. 5.8b. The left face (at x) is subjected to the shear flow T and the right face (at x + dx) is subjected to the shear flow T + (\u2202T/\u2202x)dx. There are no normal stresses in the s-direction. Therefore the equilibrium condition in this direction yields \u2193: ( T + \u2202T \u2202x dx ) ds\u2212 T ds = 0 \u2192 \u2202T \u2202x = 0 . Hence, the shear flow is constant in the x-direction. If we further assume that there are also no normal stresses in the x-direction (free warping of the cross section), then we obtain from the equilibrium condition in x-direction: \u2192: ( T + \u2202T \u2202s ds ) dx\u2212 T dx = 0 \u2192 \u2202T \u2202s = 0 . Thus, the shear flow has the same value at every point s of the cross section, i.e. T = \u03c4 t = const . (5.16) We will now derive a relation between the torque MT and the shear flow T . According to Fig. 5.8c the shear flow generates a 5.3 Thin-Walled Tubes with Closed Cross Sections 205 force Tds acting on the centerline of the tube\u2019s wall. The infinitesimal moment with respect to an arbitrarily chosen point 0 is given by dMT = r\u22a5 T ds . Here, r\u22a5 is the moment arm of the force with respect to point 0. The total moment generated by the shear flow is identical to the applied torque MT : MT = \u222e dMT = T \u222e r\u22a5ds . (5.17) The line integral (circle at the integral sign) means that, starting from an arbitrary point s = 0, we have to perform the integration along the arc length s of the whole boundary of the cross section. It can be seen from Fig. 5.8c that r\u22a5ds (= height \u00d7 base line) is twice the area of the green triangle: r\u22a5ds = 2 dAm. Thus the line integral yields \u222e r\u22a5 ds = 2Am . (5.18) Here, Am is the area enclosed within the boundary of the median line of the profile. One must be careful not to confuse this geometrical quantity with the area A = \u222e t ds of the cross section. Inserting (5.18) into (5.17) yields MT = 2Am T . (5.19) Using (5.16) the shear stresses follow as \u03c4 = T t = MT 2Am t . (5.20) This relation is known as Bredt\u2019s first formula (Rudolf Bredt, 1842\u2013 1900) or as torsion formula for thin-walled tubes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002342_j.jsv.2011.03.031-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002342_j.jsv.2011.03.031-Figure5-1.png",
        "caption": "Fig. 5. Dent on the inner race.",
        "texts": [
            " (24) it is clear that the contact stiffness is a continuous function of the angle f. Fig. 3 shows that the contact force does not act in the direction of rj under the angle yj but under the angle yC , and thus the contact force in the radial direction is FD,Co \u00bc kd,od 3=2 Do\u00fe cos\u00f0yj yC\u00de: (26) The tangential component of the contact force in the dent is neglected because the cage ensures the angular position of the rolling elements, but is taken into account as the loading on the outer race. Let there be a defect on the surface of the inner race as shown in Fig. 5. This defect will rotate with the angular speed of the shaft oS. If the defect angle \u00bdj,j\u00fejd coincides with one of the balls the deflection on that ball will be dDi\u00fe \u00bc \u00f0r Dd\u00f0jC\u00de\u00de Jwj\u00ferBCJ if \u00f0r Dd\u00f0jC\u00de\u00de Jwj\u00ferBCJ40, 0 otherwise: ( (27) Due to the different geometry in the contact, because the radius of curvature rII2 changes from r to RD, given by Eq. (24), there is a change in the contact stiffness. It should be noted that not only does the radius of curvature change but so does the sign of curvature from positive to negative, because the dent on the inner race is a concave surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002111_j.msea.2017.06.069-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002111_j.msea.2017.06.069-Figure1-1.png",
        "caption": "Fig. 1. (a) Build orientations used in the fabrication of the cylindrical test coupons, demonstrating the three different angles (0\u00b0, 45\u00b0, and 90\u00b0) to the build platform; (b) Dimensions (in mm) used in the fabrication of the monotonic tension and strain-controlled test coupons.",
        "texts": [
            " Nine strain-controlled (fatigue) test cylindrical rods and three monotonic tensile cylindrical rods were manufactured using spherical gas atomized Ti-6Al-4V powder (25\u201345 \u00b5m, ELI, 0.1% O, 0.009% N, 0.008% C, 0.17% Fe, ,0.002% H, TLS Technik GmbH&Co.), at a height of 113.6 and 114.28 mm and diameter of 14.7 and 14 mm respectively. The strain-controlled coupons were machined from the cylindrical rods according to ASTM E606/E606M [20] and the monotonic tensile coupons manufactured according to ASTM E8/E8M [21], using the dimensions in Fig. 1(b). The cylindrical rods were manufactured at three orientations with respect to the build direction: horizontal (0\u00b0), diagonal (45\u00b0), and vertical (90\u00b0) as shown in Fig. 1(a). For manufacture, the powder bed was preheated to 200 \u00b0C and the chamber was filled with argon gas until the oxygen level was reduced to 0.1%. The processing variables used in the manufacture of the cylindrical rods were laser power = 100 W; laser scanning velocity = 375 mm/s; hatch spacing = 130 \u00b5m; layer thickness = 30 \u00b5m; focal offset distance = 0 mm, similarly to a previous study work by Kourousis et al. [17]. All coupons were fabricated by employing a stripe pattern scanning strategy, which practically divides the layers into parallel stripes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000962_rob.4620070607-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000962_rob.4620070607-Figure2-1.png",
        "caption": "Figure 2. Planar four-link robot.",
        "texts": [
            " The performance of the improved configuration control scheme presented in this article is now illustrated by two computer simulation examples. The first example is chosen to demonstrate the capability of the proposed scheme to balance task errors and joint velocities, while the second example illustrates how various alternatives for redundancy utilization can be formulated within the same unified framework of improved configuration control. Consider the planar four-link robot in a horizontal plane shown in Figure 2, where the link lengths are 11 = l2 = 13 = 14 = 1 .O meter and all joint offsets and link twists are zero. The forward kinematics Y =f(@ and end-effector Jacobian matrix J, for the robot are 91 2 Journal of Robotic Systems-1990 where ct = cos(81), s 1 2 = sin(& + e2), and so on. The robot dynamic model which relates the joint torques T E 914 to the joint angles 8 E B4 is given by = M(e)e + N ( e , i) + v i (28) Expressions for the inertia matrix M E %4x4, the Conolis and centrifugal torque vector N E and the viscous friction coefficient matrix V E %4x4 can be found in the appendix",
            " The objective of this simulation example is to illustrate the capability of the improved configuration control scheme to balance task errors and joint velocities. This capability is demonstrated by considering three cases. In order to facilitate comparison between the cases, in each case the robot is assigned the same initial configuration, desired basic task, and desired additional task. These are specified as Y d t ) = [3.1 - 1.lcost OJT for t C [0, r] (31) Seraji and Colbaugh: Improved Configuration Control 91 3 where defines the Cartesian position of the distal end of the second link (see Fig. 2). Thus the robot is commanded to have its end-effector follow a straight-line path of length 2.2 meters in 7r seconds, while simultaneously maintaining the distal end of link 2 at its initial position. Observe that it is impossible to successfully perform both the basic task and the additional task simultaneously. Indeed, it is not possible for the robot to perform the basic task alone, since the desired final position of the end-effector is outside the robot workspace. These task requirements are therefore chosen specifically to represent a challenging test for the control scheme proposed earlier",
            " The three cases are now considered separately: Case One As described in an earlier section, using the improved configuration control approach, it is possible to specify r\u2019 > r additional tasks to be achieved in a Seraji and Colbaugh: Improved Configuration Control 91 9 \u201cleast-squares\u201d sense, where r = n - m is the degree-of-redundancy of the robot. The first case considered in this simulation example illustrates this approach to redundancy resolution. Consider the planar four-link robot shown in Figure 2 and defined in (26)-(28). Define the basic task coordinates to be the Cartesian position of the end-effector (y1 , y2) and the terminal link angle 4, thus Y = [yl y 2 4IT, and since 8 E !R4 we have r = 1. Let the additional task coordinates be the Cartesian position of the distal end of link 2, then 2 = [zl time (aecond) Figure S(d). Variation of the joint velocity norm. 920 Journal of Robotic Systems-1 990 Fngure 6(s). Evolution of the robot configuration. zZIT E !XZ and r\u2018 = 2 > r. The improved configuration control scheme (29) is now used for the kinematic control of the robot for the case in which the additional task is \u201cover-specified",
            " The singularity-robustness and task-prioritization features are obtained only at a slight extra computational cost. Current research is aimed at extending the approach to dynamic configuration control, where inverse kinematic transformation is not required. Development of systematic methods for selection and automatic adjustment of the basic task, additional task, and joint velocity weighting factors is also a subject of current investigations. This appendix presents the dynamic model for the planar four-link robot used in the simulation study and shown in Figure 2. The robot dynamic parameters are link masses ml = m2 = m3 = rn4 = lO.Okg, joint viscous friction coefficients u1 = u2 = u3 = u4 = 40.0 Nt.m./rad.s-l; the link inertias are modeled by thin uniform rods. The dynamic model relating the joint torques 7 to the joint angles 8 is given by where M = [mu], N = [nil, and V = diag(ui) have the following representations: 32 s m14 = m41 = 3.33 + 5c4 + 5c34 + 5~2% m23 = m32 = 16.67 + lOc4 + 5 c ~ + 15C3 m24 = m42 = 3.33 + 5c4 + 5~~~ m33 = 16.67 + 10c4 m g = 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure4-9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure4-9-1.png",
        "caption": "Fig. 4-9 Currents at t\u00a0=\u00a00+.",
        "texts": [
            " Therefore, Br( )0\u2212 , equal to Bms( )0\u2212 , is horizontally oriented along the d-axis (same as the a-axis at t\u00a0=\u00a00\u2212). 4-5-2 Step Change in Torque at t\u00a0=\u00a00+ Next, we will see how this induction machine can produce a step change in torque. Initially, we will assume that the rotor is blocked from turning (\u03c9mech\u00a0=\u00a00), a restriction that will soon be removed. At t\u00a0=\u00a00+, the three stator currents are changed as a step in order to produce a step change in the q-axis current isq, without changing isd, as shown in Fig. 4-9a. The current isq in the stator q winding produces the flux lines \u03c6m isq, that cross the air gap and link the rotor. The leakage flux produced by isq can be safely neglected from the discussion here (because it does not link the shorted rotor cage), similar to neglecting the leakage flux produced by the primary winding of the transformer in the previous analogy. Turning our attention to the rotor at t\u00a0=\u00a00+, we note that the rotor is a short-circuited cage, so its flux linkage cannot change instantaneously. To oppose the flux lines produced by isq, currents are instantaneously induced in the rotor bars by the transformer action, as shown in Fig. 4-9a. This current distribution in the rotor bars is sinusoidal, as justified below using Fig. 4-9b: To justify the sinusoidal distribution of current in the rotor bars, assume that the bars x \u2212 x\u2032 constitute one short-circuited coil, and the bars y \u2212 y\u2032 the other coil. The density of flux lines produced by isq is sinusoidally distributed in the air gap. The coil x \u2212 x\u2032 links most of the flux lines produced by isq. But the coil y \u2212 y\u2032 links far fewer flux lines. Therefore, the current in this coil will be relatively smaller than the current in x \u2212 x\u2032. These rotor currents in Fig. 4-9a produce two flux components with peak densities along the q-axis and of the direction shown: 1. The magnetizing flux \u03c6m ir, that crosses the air gap and links the stator. 2. The leakage flux \u03c6\u2113r that does not cross the air gap and links only the rotor. By the theorem of constant flux linkage, at t\u00a0=\u00a00+, the net flux linking the short-circuited rotor in the q-axis must remain zero. Therefore, at t\u00a0 =\u00a0 0+, for the condition that \u03c6rq,net\u00a0 =\u00a0 0 (taking flux directions into account): VECTOR CONTROL WITH d-AXIS ALIGNED WITH ROTOR FLUX 69 70 VECTOR CONTROL OF INDUCTION-MOTOR DRIVES \u03c6 \u03c6 \u03c6m i m i rsq ro o o, ,( ) ( ) ( ).+ + += + (4-19) Since isd and the d-axis rotor flux linkage have not changed, the net flux, Br , linking the rotor remains the same at t\u00a0=\u00a00+ as it was at t\u00a0=\u00a00\u2212. The space vectors at t\u00a0=\u00a00+ are shown in Fig. 4-10. No change in the net flux linking the rotor implies that Br has not changed; its peak is still horizontal along the a-axis and of the same magnitude as before. The rotor currents produced instantaneously by the transformer action at t\u00a0=\u00a00+, as shown in Fig. 4-9a, result in a torque Tem(0+). This torque will be proportional to B\u0302r and isq (slightly less than isq by a factor of Lm/Lr due to the rotor leakage flux, where Lr equals L Lm r+ \u2032 in the per-phase equivalent circuit of an induction machine): T k B L L iem r m r sq=      1 \u02c6 , (4-20) where k1 is a constant. If no action is taken beyond t\u00a0=\u00a00+, the rotor currents will decay and so will the force on the rotor bars. This current decay would be like in a transformer of Fig. 4-6 with a short-circuited secondary and with the primary excited with a step of current source"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.16-1.png",
        "caption": "FIGURE 2.16. Euler angles frame e\u0302\u03d5, e\u0302\u03b8, e\u0302\u03c8.",
        "texts": [
            " Hence, the Euler set of angles in rotation matrix (2.106) is not unique when \u03b8 = 0. Example 23 Euler angles application in motion of rigid bodies. The zxz Euler angles are good parameters to describe the configuration of a rigid body with a fixed point. The Euler angles to show the configuration of a top are shown in Figure 2.15 as an example. Example 24 F Angular velocity vector in terms of Euler frequencies. A Eulerian local frame E (o, e\u0302\u03d5, e\u0302\u03b8, e\u0302\u03c8) can be introduced by defining unit vectors e\u0302\u03d5, e\u0302\u03b8, and e\u0302\u03c8 as shown in Figure 2.16. Although the Eulerian frame is not necessarily orthogonal, it is very useful in rigid body kinematic analysis. 2. Rotation Kinematics 57 The angular velocity vector G\u03c9B of the body frame B(Oxyz) with respect to the global frame G(OXY Z) can be written in Euler angles frame E as the sum of three Euler angle rate vectors. E G\u03c9B = \u03d5\u0307e\u0302\u03d5 + \u03b8\u0307e\u0302\u03b8 + \u03c8\u0307e\u0302\u03c8 (2.122) where, the rate of Euler angles, \u03d5\u0307, \u03b8\u0307, and \u03c8\u0307 are called Euler frequencies. To find G\u03c9B in body frame we must express the unit vectors e\u0302\u03d5, e\u0302\u03b8, and e\u0302\u03c8 shown in Figure 2.16, in the body frame. The unit vector e\u0302\u03d5 =\u00a3 0 0 1 \u00a4T = K\u0302 is in the global frame and can be transformed to the body frame after three rotations. B e\u0302\u03d5 = BAG K\u0302 = Az,\u03c8Ax,\u03b8Az,\u03d5K\u0302 = \u23a1\u23a3 sin \u03b8 sin\u03c8 sin \u03b8 cos\u03c8 cos \u03b8 \u23a4\u23a6 (2.123) The unit vector e\u0302\u03b8 = \u00a3 1 0 0 \u00a4T = \u0131\u03020 is in the intermediate frame Ox0y0z0 and needs to get two rotations Ax,\u03b8 and Az,\u03c8 to be transformed to the body frame. B e\u0302\u03b8 = BAOx0y0z0 \u0131\u0302 0 = Az,\u03c8 Ax,\u03b8 \u0131\u0302 0 = \u23a1\u23a3 cos\u03c8 \u2212 sin\u03c8 0 \u23a4\u23a6 (2.124) The unit vector e\u0302\u03c8 is already in the body frame, e\u0302\u03c8 = \u00a3 0 0 1 \u00a4T = k\u0302"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003272_tvt.2020.2993725-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003272_tvt.2020.2993725-Figure4-1.png",
        "caption": "Fig. 4. Typical flux distribution, and mechanical and electrical angles in a 3-phase 12/8 SRM.",
        "texts": [
            " The relative position of the rotor pole with respect to the mechanical angle of a stator pole defines the electrical angle of that stator pole. The torque production is dependent on this electrical angle. Therefore, if the coils around the stator poles, which have the same electrical angle, are excited with the same current, these poles generate the same torque, and those coils make up a phase. Hence, there is a relationship between the number of stator poles, number of rotor poles, and number of phases, which will be quantified in this section. A. Electrical Angle of Stator Poles Fig. 4, shows the mechanical and electrical angles of a 3- phase 12/8 SRM. The angles inside the stator and rotor poles are mechanical angles representing the center axis location of the poles. The electrical angle of a certain stator pole is related to its relative position with respect to the rotor pole and the direction of rotation. The SRM characteristics such as the flux linkage and torque are functions of the electrical angle of the stator poles and, hence, the rotor position [21]. Besides, radial force density characteristics, which is the source of stator vibrations, also changes with the rotor position [22]. For the counter clockwise (CCW) rotation, the electrical angle of a stator pole can be calculated as [23]: \ud835\udf03\ud835\udc60!\"!#$_&&' = \ud835\udc5a\ud835\udc5c\ud835\udc51'(\ud835\udf03\ud835\udc5f(!#) \u2212 \ud835\udf03\ud835\udc60(!#)) \ud835\udc41* + 180+, 3605 (1) where \u03b8rmech and \u03b8smech are the mechanical angles of a rotor and stator pole, respectively. The constant 180\u00b0 comes from the assumption in Fig. 4, that Nr#1 is aligned with Ns#1 at the initial position. Similar to mechanical position, electrical angle also has a 360\u00b0 cycle, which is incorporated in (1) with the mod function. Authorized licensed use limited to: Newcastle University. Downloaded on May 17,2020 at 23:19:28 UTC from IEEE Xplore. Restrictions apply. 0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. For the 12/8 SRM in Fig. 4, the stator poles sharing the same electrical angle are symmetrically distributed around the stator circumference. The coils of these poles are connected to form a phase. When they are excited with current, they generate the same torque in the same direction which maintains a balanced operation. Each phase has Ns/m stator poles. Besides, the difference between the mechanical angles of the stator poles in one phase is related to Ns/m. These Ns/m stator poles having the same electrical angle is dependent on the mechanical position of the rotor poles and, hence, the number of rotor poles, Nr. Therefore, there is a relationship between the number of rotor poles and the number of stator poles per phase, which can be expressed as the configuration index [24]: \ud835\udc58 = !! !\" \"\u2044 . (2) For the 3-phase 12/8 SRM, k = 2. In order to achieve a balanced operation, the configuration index should have a positive integer value. For example, if the 12/8 configuration is operated as a 4-phase motor, k would be 2.667, and Ns#1, Ns#5, and Ns#9 would belong to the same phase. It can be observed from Fig. 4 that these poles have different electrical angles. They would generate torque in different directions and the rotor would be locked. Besides, for Ns/m = 3, the flux distribution in Fig. 4 could not be achieved. However, not every integer value of k provides a working SRM configuration. For example, for Ns = 12, m = 3, and Nr = 12, k = 3. In this case, all phases will have the same electrical angle, which cannot maintain multiphase operation. If Ns = 8 and Nr =12, then k = 6 for m = 4. In this case, all phases will be either at 180\u00b0 or 0\u00b0 electrical degrees, which also creates a locked rotor condition. This happens because the configuration index, k is an integer multiple of a prime factor of the number of phases",
            " Most of the conventional SRM configurations have an even number of stator poles per phase; for example, for a 3-phase 12/8 SRM, Ns/m = 4 and for a 4-phase 24/18 SRM, Ns/m = 6. As shown in Table 1, pole configurations calculated by (3) include SRMs with an odd number of stator poles per phase, such as 3-phase 9/12, 4-phase 12/9, and 3-phase 15/10 SRMs. Fig. 6 shows the mechanical and electrical angles in a 3- phase 9/12 SRM, which has 3 stator poles per phase. It can be seen that the 9/12 SRM has similar electrical angles as the 12/8 SRM in Fig. 4 and the 6/14 SRM in Fig. 5. As shown in Fig. 4, when the coils of a phase of the 12/8 SRM are energized, four magnetic poles are created, which is equivalent to the number of stator poles per phase. Only the stator poles belonging to the excited phase generate the magnetic flux lines; making the mutual coupling between phases negligible, which is an important feature of SRMs. In the 12/8 SRM, the coils of the consecutive stator poles of a phase have opposite directions. This enables the flux pattern shown in Fig. 4. If the same coil pattern is applied to a 9/12 SRM, it would not be possible to have the number of magnetic poles equal to the number of stator poles per phase (Ns/m = 3). As circled in Fig. 6, the opposing flux direction cannot be maintained, since one of the flux loops opposes the coil direction. As a result, the dotted flux line in Fig. 6 would not be generated and a 9/12 SRM would have an unbalanced operation. In SRMs with an odd number of stator poles per phase, balanced magnetic poles can be generated by using a mutually coupled coil configuration as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001967_s11071-018-4314-y-Figure23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001967_s11071-018-4314-y-Figure23-1.png",
        "caption": "Fig. 23 Schematic of a dent profile [157,158]",
        "texts": [
            " Therefore, it was very necessary to clearly understand the vibration and noise generation mechanisms in REBs, which was very useful for detecting and diagnosing the bearing dents. Venner and Lubrecht [154,155] presented a numerical dent model based on the simulation results, whose profile is shown in Fig. 22. This dent profile model was validated by the experimental results conducted by N\u00e9lias and Ville [156]. Ashtekar et al. [157,158] introduced a new dynamic method to predict the influences of race dents on the dynamic motions of a REB. The dent profile was assumed to be a circular one, and its cross-section was defined as a sinusoidal one, as shown in Fig. 23. In this model, a load\u2013deflection relationship was used to replace the Hertzian load\u2013deflection relationship based on a dry contact elastic model and the superposition principle, whichwas a function of ellipticity ratio, load, dent diameter, and dent depth. This relationship could be applied to formulate interactions between the rolling element and dents. Antaluca andN\u00e9lias [159] conducted amethodology including a FE method and a semi-analytical elastic\u2013 plastic code to predict the rolling damage produced by the dents vicinity in a dry circular point contact for a REB"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure22.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure22.3-1.png",
        "caption": "Figure 22.3 Incremental network with N active nodes accessing space\u2013time data.",
        "texts": [
            " In the process, we motivate and introduce the incremental LMS algorithm and two versions of the diffusion LMS algorithm: combine-then-adapt (CTA) and adapt-then-combine (ATC) diffusion LMS. We also comment on the performance of the algorithms via analysis and computer simulations. Consider a network with N nodes and assume initially that at least one cyclic path can be established across the network. The cyclic path should enable information to be moved from one node to a neighboring node around the network and back to the initial node (see Fig. 22.3). Obviously, some topologies may permit several possibilities for selecting such cyclic trajectories. Assume further that each node k has access to time realizations {dk(i), uk,i} of zero-mean data {dk, uk}, k = 1, . . . , N , where each dk is a scalar and each uk is a 1 \u00d7 M (row) regression vector. We denote the M \u00d7 M covariance matrices of the regression data by Ru,k = Eu\u2217 kuk (at node k), (22.3) and the M \u00d7 1 cross-covariance vectors by Rdu,k = Edku \u2217 k (at node k) (22.4) where E is the expectation operator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000524_0956-5663(94)80127-4-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000524_0956-5663(94)80127-4-Figure17-1.png",
        "caption": "Fig. 17. Optical biosensing by monitoring surface plasmon resonance .",
        "texts": [],
        "surrounding_texts": [
            "Biosensors & Bioelectronics\naI\nbI\nPOLISHED FIBRE CORE REVEALED\nd\nREFLECTED LIGH i\nFig. 16. Optical waveguide detection of antibody - antigen reaction: (a) planar waveguide, (b) surface relief grating, and (c) polished fibre .\nFLUID SAMPLE\nCURVED GROOVE\nTransducer aspects of biosensors\nEvanescent field detection in an optical waveguide .\nusing flat prisms has been demonstrated (11)\ngio for amino acids, present in most proteins, at DETECTOR ultraviolet and visible wavelengths. The concept\nhas also been tested (11) for the immunoassay of insulin using polished optical fibres .\nVarious other types of optical biosensor, based on optical absorbance or fluorescence characteristics of the analyte to be detected, have also been reported in the literature (11) . A recent example is a fluorescence capillary fill device (FCFD) (51-53) for immunoassays, which measures the intensity of fluorescent light (evanescent wave component) emitted by the fluorescencelabelled antigen reagent competing with sample antigen for the limited number of antibody binding sites present on its waveguide .\n6.3 Surface plasmon resonance (SPR)\nAnother optical phenomenon which has recently received considerable attention as a transducer in biosensors is surface plasmon resonance . A surface plasmon wave is a particular kind of electromagnetic wave which propagates along the surface of a metal . Optical excitation of a surface plasmon is caused by evanescent waves and can be achieved if an incident light beam is reflected at the surface of a glass substrate coated with a thin metal film . With proper choice of the metal and its thickness, surface plasmon resonance occurs, resulting in absorption of the light at a certain angle of incidence of the light beam. This effect is observed as a sharp minimum in the intensity of the reflected light . The resonance angle is very sensitive to variations of the refractive index of the medium bonding the",
            "R. S. Sethi\nmetallized surface. Antibody-antigen reaction or absorption of gases on the surface can therefore be detected as a change in the resonance angle .\nIn its basic configuration, a prism (Fig . 17) or a diffraction grating is metallized with a thin gold film . A very thin layer of antibody (5 to 10 nm) is then deposited on top of the gold layer . The refractive index of this system is known . The introduction of test species, for example blood containing antigen, results in the formation of an antibody-antigen complex. This changes the refractive index and hence the surface plasmon resonance angle . For example, a change of 0. 1 nm in the layer thickness can result in a 0 .01 degree change in the resonance angle, which can be measured accurately . A laser is used to excite the surface plasmons in the conductive metal film, and the angle of incidence at which the plasmon resonance occurs is measured by a photodetector .\nThis technique is very sensitive and its feasibility has been demonstrated in a model immunoassay system (11) human immunoglobulin (hIgG)/antiIgG, in which it was shown that less than 2 \u00b5g/ ml could readily be detected . The main limitation of this technique for immunosensing is that the sensitivity depends upon the molecular weight of the adsorbed layer which controls its optical thickness, so that low concentrations of small molecules (Mol. Wt . <250) such as haptens are unlikely to be measurable .\nSince this article was written, a resonant mirror biosensor system developed jointly by GECMarconi Materials Technology, Northants, and Fisons Applied Sensor Technology, Cambridge, has been marketed by Fisons . The details of basic principle of its operation and associated\nBiosensors & Bioelectronics\ninstrumentation are described by R . Cush et al., in Biosensor & Bioelectronics, vol 8, 1993, pp . 347-353 . It is a novel design based on optical evanescent wave technology which combines the simplicity of surface plasmon resonance (SPR) with the enhanced sensitivity of waveguiding techniques. It utilizes a dielectric resonant structure to probe reactions occurring in a sensing layer and is aimed at the real-time monitoring of biological assays, without use of label molecules .\nThe non-electrical nature of optical systems confers important safety advantages on a biosensor for medical, industrial and military applications . Remote sensing of explosives and toxins, for example, would be enormously advantageous . Optical fibre probes are also mechanically flexible, small, inexpensive and disposable .\n7. CHROMATOGRAPHIC MICROSEPARATION AND DETECTION ON A SILICON WAFER\nMicro-analysis of mixtures of analytes by biosensing does not generally require any separation of the various components prior to detection . However, there are likely to be certain complex mixtures where separation may be necessary . Traditionally, chromatography and electrophoresis are used in molecular biology to separate components from a mixture and to aid analysis . Microcircuit fabrication technology has enabled miniaturization of this process, essentially by producing microcolumns in silicon . This separation technology has been combined with one of the sensor technologies discussed earlier to produce a miniaturized chromatographic separation and conductimetric detection device in silicon . A US patent (54) has been granted to us . This approach offers two advantages :\n(i) the separation of analyte molecules relaxes the specificity demands on the sensor at the exit end of the `chromatographic column', and (ii) the relative transit times of molecules through the `column' can be used as an identification technique in itself, once the system has been calibrated .\nThis device, with certain accessories, can be used in a similar fashion to conventional chromatography and is capable of micro-separation and detection of bio-chemical and chemical species .",
            "producing microscopic chromatographic channels on a thermally-oxidized silicon substrate and\nmetallizing at one end with a pair of titanium/\ngold contacts . The channels may be cut by a variety of techniques, such as diamond or laser\nsawing, crystallographic etching, ion-beam mill-\ning, etc . The silicon substrate is mounted using\nan epoxy adhesive onto an alumina strip, which\nin turn is epoxy-bonded to a gold-plated package\nwith several insulated pins for electrical connec-\ntions. The metal electrode contacts at the exit\nend are wire-bonded to the pins and are employed\nfor conductimetric sensing of the eluted species .\nAnother pair of contact metal electrodes, when\ninstalled at the other end of the channels, will\nmake the device suitable for electrophoretic\nwork .\nThe channels were filled with 1 .5% agarose\nsolution which formed a gel. Test experiments\nwere conducted with a number of enzymes in\nbuffer solutions and their movement in the\nchannels was examined fluoroscopically under\nultraviolet light . Next several electrolytes were\nexamined and the species near the `exit' end of\nthe channels were detected conductimetrically .\nFigure 19 shows a typical plot of conductance\nversus various concentrations of a sodium phos-\nphate buffer solution, commonly employed for enzymic solutions . The results of these conduc-\ntance tests were as expected .\nVery recently, an integrated multichannel chro-\nmatographic separation and detection device on\nTransducer aspects of biosensors\n600- 0 25 50 75\nCONCENTRATION/mm"
        ]
    },
    {
        "image_filename": "designv10_1_0001011_tmech.2016.2614672-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001011_tmech.2016.2614672-Figure6-1.png",
        "caption": "Fig. 6. The quadrotor used throughout the experiments in the Motion Capture Laboratory at Nanyang Technological University, Singapore",
        "texts": [
            " 5 was equipped with external optical motion capture system which provides real-time position and attitude measurement of a rigid body in a three dimensional space with an update rate of 100 Hz and accuracy level of 1 mm [32]. Retro-reflective markers were affixed to the quadrotor in a unique pattern to provide visual feedback of its predefined body frame for recognition. Three markers would be sufficient to compute all six DOFs of the vehicle. However, for redundancy reasons and to compensate individual shifts, five markers are used as shown in Fig. 6. Image data from 20 MX-VICON infrared cameras were sent to the ground computer via Ethernet connection. Then, VICON tracking software processes these flight data into six DOFs information as an input to our control system in MATLAB/Simulink. This platform provides accurate and high sample rates for state estimation. Therefore, the precision of this localization and pose recognition setup is sufficient and eliminates the need of data fusing with other on-board navigation sensors, such as LIDAR or GPS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002152_j.addma.2017.12.009-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002152_j.addma.2017.12.009-Figure1-1.png",
        "caption": "Fig. 1. (a) Image of samples fabricated in this study on the SLM 2800HL building platform. Each sample has different manufacturing process parameters as listed in Table 1. (b) Schematic representation of one of the samples shown in (a) with the red arrows to demonstrate where parts are sectioned for microscopic analysis. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " The pre-alloyed Al-Si10-Mg powder which has been gas atomized is used as printing powder. The average particle size is ranging between 30 m and 50 m. Rectangular e to capture the manufacturing process. The building chamber is bright enough to M. Taheri Andani et al. / Additive Ma s u t E W ( t o f s i f t 3.1. Recoil pressure and spatter particles formation mechanism F d esults in the ejection of a portion of molten material (droplet spatter) and powder ear the melting pool (powder spatter). amples (10 mm \u00d7 6 mm \u00d7 10 mm) as shown in Fig. 1(a), are made sing different process parameters listed in Table 1. In this table, he energy input is calculated using the following relation: = P v.h.t (1) here P,v, h, and t are laser power (W), laser scanning speed mm/s), hatch spacing (mm), and layer thickness (mm), respecively. Process parameters used in processing sample No.1 is the ptimized set of parameters recommended by SLM machine Manuacturer Company. Two sets of parameters with different laser scan peed (one higher and one lower than the optimized scan velocty) are chosen to investigate the role of laser scan speed on spatter ormation",
            " 5 show ots show the borders of the sample. (For interpretation of the references to colour in thi nufacturing 20 (2018) 33\u201343 35 process. Design of experiment methods should be considered in the future work. It may worth noting that sample 1, 2, and 3 are made with the first laser beam and samples 4 and 5 made the second laser beam. However, since the operation conditions of both laser beams are similar, it would not make any difference if all samples made by one laser beam. All samples are shown in Fig. 1(a) are sectioned in different directions (see Fig. 1(b)) using a diamond cutoff wheel and are mounted in epoxy resin. The metallographic mounted specimens are ground in abrasive sandpaper down to 1200 grit and then polished with the diamond suspension of 9 m, 6 m, 3 m, and 1 m. Final polishing is done with 0.25 m particle size alumina suspension and 0.05 m particle size colloidal silica. Post polishing, the samples were etched using Keller\u2019s etchant, Optical microscopy (Leica DM4000 M) and Scanning Electron Microscopy (SEM) (LEO1530VP) are used for microscopic analysis",
            " In this study, 6000 frames per second (fps) is utilized which is selected based on the provided external light source. To capture the high-speed videos for different process parameters listed in Table 1, a part which its manufacturing process parameters change in every 10 layers is used. Consequently, the first data set relates to process parameters is utilized in the fabrication of sample No.1 (See Table 1). 3. Results and discussion The high power density of the heat source during the SLM process, rapidly melt and evaporate the material surface. Conse- n in Fig. 1(a) (laser power = 350 W and laser scan velocity = 2000 mm/s). The green s figure legend, the reader is referred to the web version of this article.) q t s P W t r i a t r d M f t s eported. (a) The number of segmented spatter particles in the various range of spa reated spatter particles decreases. (b) The total induced spatter area in three diffe onditions. uently, there exists a high vapor pressure as shown in Fig. 3 on he molten surface known as recoil pressure. This induced recoil is ummarized as follow [11]: = 0",
            " However, the trend is not linear because as the laser scan velocity increases, the induced e p r 1 ( ( t l ( t by only about 13%. It is worth mentioning that the reported spatter nergy input (Eq. (1)) is reduced and depending on the boiling temerature of the material, the amount of reduction in the produced ecoil pressure will be different. Fig. 7(a) illustrates the spatter particle distribution within 16 ms of laser processing operation for three different laser power see samples No. 1, No. 2, and No. 3 in Fig. 1(a)). Also, Fig. 7(b) and c) show the total detected area and the number of the created spater particles in these three conditions, subsequently. Increasing the aser power during the SLM process causes the energy input (Eq. 1)) and consequently the recoil pressure to increase and result in he creation of a higher number of spatter particles. Comparing Figs. 6 and 7, it can be concluded that the effects of the laser scan velocity on the number of produced spatter particles are more pronounced than those of laser power",
            " 9(b)) on the build surface and the laser melts the next layer (Fig. 9(c)), spatter particle A is melted completely. However, spatter particle B is much larger than layer thickness and the laser just melts a portion of it. As the next layer is formed, the spatter particle B creates an inclusion in the part (Fig. 9(d)). Fig. 10 shows the optical micrographs of the surface of SLM samples made by three different laser power inputs, in three view s d t a b a a p i S S F t 4 i t d a d p a e s t F t i v ection as illustrated in Fig. 1(b). Fig. 11 shows the distribution of efects observed in each image of Fig. 10. Fig. 12(a)\u2013(c) compare he defect percentage observed in each image with the amount of ssessed total produced spatter particles area and the total numer of induced spatter particles, respectively. It can be found that lthough by decreasing the laser power input the amount of creted spatter particles decreases, the defect percentage on SLM arts is increased. It can be legitimized by the fact that decreasng the power input, result in reducing the energy input during LM process and subsequently, the laser beam couldn\u2019t melt the Ali10-Mg powder and as well as large spatter particles completely"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002307_2.1481707jes-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002307_2.1481707jes-Figure1-1.png",
        "caption": "Figure 1. An image of a SLM-produced Ti-6Al-4V alloy sample.",
        "texts": [
            " Both the hatch spacing (distance between scan lines) and the layer thickness were 100 \u03bcm. The layers were scanned using continuous laser mode according to a zigzag pattern, which was alternated by 90\u25e6 between each successive layer. This parameter setup guarantees nearfull density (i.e. greater than 99%) and good surface quality of the SLM-produced Ti-6Al-4V samples. The chemical composition of the SLM-produced Ti-6Al-4V alloy in wt% was 0.01 C, 0.002 H, 0.14 O, 0.02 N, 0.22 Fe, 6.25 Al, 4.04 V and Ti balance. Fig. 1 schematically presents the picture of a Ti-6Al-4V alloy sample fabricated through SLM technique. Heat treatment.\u2014Prior to heat-treatment, the side view of the SLM-produced Ti-6Al-4V alloy (i.e. the XZ plane31) was chosen as the studied plane, and its surface was abraded with SiC paper down to 2000 grit, cleaned with double-distilled water, ultrasonically cleaned in ethanol, and then dried in air. The SLM-produced Ti-6Al-4V alloy samples were heat treated at 500, 850 or 1000\u25e6C for 2 hours in a tube furnace"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003263_asjc.1946-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003263_asjc.1946-Figure1-1.png",
        "caption": "Fig. 1. Structure of Quadrotor UAV. [Color figure can be viewed at wileyonlinelibrary.com]",
        "texts": [
            " The main contribution of this paper is that it proposes a novel control method in accordance \u00a9 2018 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd with fractional-order theory, which can increase the speed of response and convergence. This novel method is employed to quadrotor UAV effectively. The quadrotor UAV model contains external disturbances, which becomes more useful than the ideal model. II. THE ANALYSIS OF QUADROTOR UAV MODEL 2.1 Dynamic model The typical quadrotor UAV consists of four rotors. The structure of a typical quadrotor UAV is shown in Fig. 1. For a more precise description of the space motion state of the quadrotor UAV, two types of common coordinate system, the earth coordinate system \ud835\udf43 = [x, y, z] and the body coordinate system \ud835\udf3c = [\ud835\udf53,\ud835\udf3d,\ud835\udf4d] are defined. The \ud835\udf43 = [x, y, z] denotes the position of the quadrotor UAV. The attitude of the quadrotor UAV is controlled by roll angle, pitch angle and yaw angle (i.e. \ud835\udf53,\ud835\udf3d,\ud835\udf4d). The translational dynamic and rotational dynamic of the quadrotor UAV are: mV\u0307 = RE BTB + GE , (1) JW\u0307 = \u2212W \u00d7 JW + MB, (2) where m is the quality of the quadrotor UAV, V = [u, v,w] denotes a vector and (u, v,w) represents the translational speed of X,Y,Z directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000008_tec.2005.853765-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000008_tec.2005.853765-Figure11-1.png",
        "caption": "Fig. 11. Stators and rotor of 12-slot/10-pole motors. (a) Stator with coils on all teeth, (b) stator with coils on alternate teeth, and (c) rotor.",
        "texts": [
            " Since the fifth- and seventh-harmonic winding factors are much smaller, the line back-EMF waveform of the 12- slot/10-pole motors is significantly more sinusoidal than that of the 15-slot/10-pole motor. In addition, Figs. 7 and 8 show finite element predicted phase back-EMF and line back-EMF waveforms, respectively, when the influence of magnetic saturation in the stator iron is neglected. As will be seen, the results are in good agreement with the analytical predictions. Figs. 9 and 10 compare finite element predicted EMF waveforms when saturation is accounted for with measured EMF waveforms for the motors shown in Fig. 11, when they are driven at constant speed. The most significant difference between motors in which all the teeth are wound and those in which only alternate teeth are wound is in their winding inductances. The finite element predicted self inductances per phase and the mutual inductance between phases for the two 12-slot/10-pole motors are, respectively, 3.03 and \u22120.34 mH when all the teeth are wound, and 4.64 and 0.0023 mH when alternate teeth are wound, which are in good agreement with the analytical predictions [14], [15] and with measured results obtained by using an inductance bridge, as shown in Table IV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003514_j.optlastec.2018.01.005-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003514_j.optlastec.2018.01.005-Figure6-1.png",
        "caption": "Fig. 6. Variation of relative density with different processing parameters of the bulk materials fabricated using the four nanocomposite systems (a) pure 316L, (b) 316L with 2 wt% 40 nm TiC, (c) 316L with 4 wt% 40 nm TiC, and (d) 316L with 2 wt% 800 nm TiC.",
        "texts": [
            " 5a\u2013c shows that the FWHM increased when TiC content was increased, demonstrating that the grain refinement effect became stronger with increasing TiC content. The FWHM of the bulk material with 2 wt% 40 nm TiC was larger than that of the 2 wt% 800 nm TiC sample for all of the diffraction peaks. Thus, this demonstrates that the 40 nm TiC particles were superior to the 800 nm TiC particles in relation to the grain refinement effect. The drainage method was used to measure the density of the fabricated blocks. Fig. 6 shows that the relative densities of the bulk material fabricated using the four nanocomposite systems varied with laser power and exposure time. The relative density is defined as follows: qrelative \u00bc qreality=\u00f0q316L wt1%\u00fe qTiC wt2%\u00de 100% \u00f01\u00de where qreality represents the actual measured value, q316L is the standard density of 316L (7.98 kg/cm3), qTiC is the standard density of TiC (4.93 kg/cm3), and wt1% and wt2% represent the mass fraction percentages of 316L and TiC, respectively. The relative densities ranged from 84.49% to 99.05% in Fig. 6a, 78.08% to 98.34% in Fig. 6b, 72.50% to 96.19% in Fig. 6c, and 83.75% to 98.05% in Fig. 6d, and decreased with increased TiC content. In Fig. 6a\u2013d, the same pattern is observed, in which the relative densities tended to increase with increasing exposure time and laser power. Fig. 7a shows that the relative densities increased with increasing laser power, and that the rate of this increase gradually become slower. When the laser power was increased from 120 W to 200 W, the relative densities increased from 94.07% to 99.01% for pure 316L, from 89.1% to 98.34% for 316L with 2 wt% 40 nm TiC, from 89.22% to 96.19% for 316L with 4 wt% 40 nm TiC, and from 91"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.1-1.png",
        "caption": "FIGURE 2.1. A rotated body frame B in a fixed global frame G, about a fixed point at O.",
        "texts": [
            " This problem is equivalent to having the position of the end-effector and asking for a set of joint variables that make the robot reach the point P . In this part, we develop the transformation formula to move the kinematic information back and forth from a coordinate frame to another coordinate frame. KinematicsPart I : 2 Rotation Kinematics Consider a rigid body with a fixed point. Rotation about the fixed point is the only possible motion of the body. We represent the rigid body by a body coordinate frame B, that rotates in another coordinate frame G, as is shown in Figure 2.1. We develop a rotation calculus based on transformation matrices to determine the orientation of B in G, and relate the coordinates of a body point P in both frames. 2.1 Rotation About Global Cartesian Axes Consider a rigid body B with a local coordinate frame Oxyz that is originally coincident with a global coordinate frame OXY Z. PointO of the body B is fixed to the ground G and is the origin of both coordinate frames. If the rigid body B rotates \u03b1 degrees about the Z-axis of the global coordinate frame, then coordinates of any point P of the rigid body in the local and global coordinate frames are related by the following equation Gr = QZ,\u03b1 Br (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001967_s11071-018-4314-y-Figure22-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001967_s11071-018-4314-y-Figure22-1.png",
        "caption": "Fig. 22 Dent profile based on real dents [154]",
        "texts": [
            " The differences between the spalls and dents were the surrounding material pile-up at the fault zone, which was named as shoulders. The surrounding shoulder plays an important role in producing the vibrations and noises in REBs [153]. Therefore, it was very necessary to clearly understand the vibration and noise generation mechanisms in REBs, which was very useful for detecting and diagnosing the bearing dents. Venner and Lubrecht [154,155] presented a numerical dent model based on the simulation results, whose profile is shown in Fig. 22. This dent profile model was validated by the experimental results conducted by N\u00e9lias and Ville [156]. Ashtekar et al. [157,158] introduced a new dynamic method to predict the influences of race dents on the dynamic motions of a REB. The dent profile was assumed to be a circular one, and its cross-section was defined as a sinusoidal one, as shown in Fig. 23. In this model, a load\u2013deflection relationship was used to replace the Hertzian load\u2013deflection relationship based on a dry contact elastic model and the superposition principle, whichwas a function of ellipticity ratio, load, dent diameter, and dent depth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure4.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure4.10-1.png",
        "caption": "FIGURE 4.10. An RPR manipulator robot.",
        "texts": [
            " Motion Kinematics transformation of this motion is: GTB = Dd\u0302,dRu\u0302,\u03c6Dd\u0302,\u2212d = \u2219 I d 0 1 \u00b8\" RK\u0302, \u03c0 2 0 0 1 # \u2219 I \u2212d 0 1 \u00b8 = \u23a1\u23a2\u23a2\u23a3 1 0 0 2 0 1 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u23a1\u23a2\u23a2\u23a3 c\u03c02 \u2212s\u03c02 0 0 s\u03c02 c\u03c02 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u23a1\u23a2\u23a2\u23a3 1 0 0 \u22122 0 1 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a3 0 \u22121 0 2 1 0 0 \u22122 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (4.122) Consider a point on the cylinder that was on the origin. After the rotation, the point would be seen at: Gr = GTB Gr = \u23a1\u23a2\u23a2\u23a3 0 \u22121 0 2 1 0 0 \u22122 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u23a1\u23a2\u23a2\u23a3 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a3 2 \u22122 0 1 \u23a4\u23a5\u23a5\u23a6 (4.123) Example 95 End-effector of an RPR robot in a global frame. Point P indicates the tip point of the last arm of the robot shown in Figure 4.10. Position vector of P in frame B2 (x2y2z2) is 2rP . Frame B2 (x2y2z2) can rotate about z2 and slide along y1. Frame B1 (x1y1z1) can rotate about the Z-axis of the global frame G(OXY Z) while its origin is at Gd1. The position of P in G(OXY Z) would then be at Gr = GR1 1R2 2rP + GR1 1d2 + Gd1 = GT1 1T2 2rP = GT2 2rP (4.124) where 1T2 = \u2219 1R2 1d2 0 1 \u00b8 (4.125) GT1 = \u2219 GR1 Gd1 0 1 \u00b8 (4.126) and GT2 = \u2219 GR1 1R2 GR1 1d2 + Gd1 0 1 \u00b8 . (4.127) Example 96 End-effector of a SCARA robot in a global frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000832_icems.2009.5382812-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000832_icems.2009.5382812-Figure10-1.png",
        "caption": "Fig. 10. Magnetic flux distribution at minimum linkage magnetic flux.",
        "texts": [
            " 8 shows that magnetic flux increases by addition of the magnetic flux of the variable magnetized magnet and the constant magnetized magnet. Fig. 9 shows the air gap magnetic flux density distribution. The air-gap magnetic flux density is about 0.55 T at the average in the state of the maximum linkage magnetic flux. If the polarity of the variable magnetized magnet is reversed, the linkage magnetic flux by the permanent magnets will become the minimum. The analysis results at this state are shown in Fig. 10 and Fig. 11. The magnetic flux distribution of Fig. 10 shows that the magnetic flux of the variable magnetized magnet and the constant magnetized magnet cancels each other and the flux adds in the rotor. Thus, the magnetic flux of the permanent magnet closes in the rotor. Fig. 11 shows distribution of the air gap magnetic flux density. The air-gap magnetic flux density has become about 0 in the state of the minimum linkage flux. As mentioned above, the results confirmed that the principle model can change the linkage magnetic flux by permanent magnets from the maximum of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001315_978-1-4419-1117-9-Figure5.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001315_978-1-4419-1117-9-Figure5.7-1.png",
        "caption": "Fig. 5.7 Schematic representation of the spatial 5-dof parallel mechanism with prismatic actuators",
        "texts": [
            "6, the independent coordinates have been chosen for convenience as .x; y; z; i ; j /, where x; y; z are the position coordinates of a reference point on the platform and . i ; j / are the joint angles of the Hooke joint attached to the platform. Other coordinates may be chosen. Assume that the centers of the joints located on the base and on the platform are located on circles with radii Rb and Rp, respectively. A fixed reference frame O xyz is attached to the base of the mechanism and a moving coordinate frame P x0y0z0 is attached to the platform. In Fig. 5.7, the points of attachment of the actuated legs to the base are represented with Bi and the points of attachment of all legs to the platform are represented by Pi , with i D 1; : : : ; n. Point P is the reference point on the platform and its position coordinates are P.x; y; z/. The Cartesian coordinates of the platform are given by the position of point P with respect to the fixed frame, and the orientation of the platform (orientation of frame P x0y0z0 with respect to the fixed frame), represented by matrix Q"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000487_0278364912469821-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000487_0278364912469821-Figure1-1.png",
        "caption": "Fig. 1. Sketch of the modifications of reaction forces when walking on stairs as opposed to on a slope. We see that the friction cones (dashed lines) depend on the orientation of the surface. A controller that does not take into account the surface orientation will generate the same reaction forces (plain arrows) independently of the orientation of the surfaces as long as the state of the robot is the same \u2013 such a scenario is typically the case if one minimizes only command costs. Minimization of the reaction forces tangential to the surface will, in contrast, optimize reaction forces in a direction that takes into account the orientation of the surface.",
        "texts": [
            " The friction cone is a purely geometric constraint that is defined by a friction constant and the orientation of the contact surface with the contacting foot. In the case of locomotion, to avoid slipping, one would like to have the reaction forces as orthogonal to the constraint surface as possible. In other words, the tangential forces should be minimized. Moreover in the case of a flat foot on the ground, the resulting moment around the foot should be as small as possible. The cost to optimize should therefore take into account the orientation of the ground in order to redirect contact forces in a more desirable direction (Figure 1). In order to minimize the tangential forces and the moments around the foot, we propose the following cost W\u03bb = \u23a1 \u23a2\u23a3 TT leg1Wleg1Tleg1 0 . . . 0 TT legnWlegnTlegn \u23a4 \u23a5\u23a6 (26) with Wlegi = diag( Ktx, Kty, 1, Kmx, Kmy, Kmz) (27) at St Petersburg State University on January 13, 2014ijr.sagepub.comDownloaded from where Tlegn is a rotation matrix that corresponds to the orientation of the surface with respect to the inertial frame (i.e. it aligns the reaction forces and moments of a foot taken in the inertial frame with the orientation of the surface)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.75-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.75-1.png",
        "caption": "Fig. 10.75 Three tiltrotor configurations; top to bottom \u2212 The Bell/NASA/Army XV-15 (CTR-S), Eurocopter\u2019s EUROTILT (CTR-M) and EUROFAR (CTR-L) concepts",
        "texts": [
            " One of the questions posed was, \u2018Is it feasible to confer equivalent flying qualities on different members of a family of civil tiltrotor (CTR) aircraft of different sizes, with all-up-mass varying between 5 and 15 tonnes?\u2019 Such \u2018equivalence\u2019 would provide a common architecture for the flight control system design and implementation as well as facilitating pilot conversion training. How the question was tackled was reported in Refs. 10.77 and 10.78, with an overview of the results given in Ref. 10.63, from which this piece is taken. The study was based on the three configurations shown in Figure 10.75, designated as CTR-S (small, FXV-15), CTR-M 680 Helicopter and Tiltrotor Flight Dynamics (medium, Ref. 10.5), (EUROTILT) CTR-L (large, Ref. 10.79) (EUROFAR). The specific question related to the low-speed manoeuvring capability in helicopter mode. Could all three tiltrotors meet the ADS-33 Level 1 requirements sufficiently well that they could be considered to have \u2018unified\u2019 handling, enabling pilots to convert from one type to another with minimal training? Configuration data for the three aircraft are given in Table 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000232_j.trac.2012.06.004-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000232_j.trac.2012.06.004-Figure5-1.png",
        "caption": "Figure 5. Left: Inhibition of edge-plane-like sites caused by the addition of Nafion to a graphite-modified electrode. Right: Re-orientation of gra ene layer caused by the addition of Nafion to a graphene-modified electrode (Reproduced from [106], by permission of the Royal Society of Chemistry).",
        "texts": [
            " [106] reported that graphite-based amperometric electrodes (sensitivity: 49.0 lA/mM) exhibited greatly enhanced electro-catalytic activity over graphene (32.8 lA/mM) at 400 mV. This was attributed to an increased percentage of edgeplane sites. However, after the introduction of Nafion, sensitivities were reversed due to the potential discrimination effect from interferents. Graphene and Nafion (42.2 lA/mM) were superior to graphite and Nafion (32.0 lA/mM) due to substantial re-orientation and disorder of graphene (Fig. 5). This was an indication that: (1) composite materials are essential for graphenebased amperometric biosensors; and, (2) the orientation of the graphene sheets in these com- posite materials is crucial. Nafion is not the only or the best material to improve the amperometric characteristics of graphene {e.g., ZnO nanospheres [107], for example, lead to similar results with respect to LOD and sensitivity [108] but provide a wider linear range for hydrogen-peroxide detection (1.8 lM to 2.3 mM) at an almost identical potential (about -0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure18-1.png",
        "caption": "Fig. 18. CAD model of fault in (a) outer race, (b) inner race and (c) ball.",
        "texts": [
            " A number of models of rolling element bearing are available in literature where the localised faults are modelled as small notches of triangular or rectangular shape. In reality, however, the imperfections that occur in industrial applications are not of regular geometry. However, the shape of the fault does not change the fault diagnosis schemes in frequency domain analysis, e.g. vibration analysis. Faults can be modelled in CAD geometry of inner race, outer race and ball by cutting of different types of slots or sections. In the present analysis, the regular faults in the outer race, inner race and ball are modelled as shown in Fig. 18(a), (b) and (c), respectively. These are exactly the same faults in the faulty bearings supplied with MFS system, which has been used in the experiments. The 3-D multi-body deep groove ball bearing model has the same geometric parameters of Rexnord MB-ER-16K ball bearing used in the MFS system. ADAMS models implementing different types of faults were simulated and the acceleration signals along vertical direction of pedestal (load zone direction) were collected as fault signatures. The data are collected for 10 s time window with a preferred step size of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002473_amr.633.135-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002473_amr.633.135-Figure8-1.png",
        "caption": "Fig. 8. Manufacturability optimisation of high-value aerospace component in isometric (upper) and side-elevation (lower) views. Inset identifies staircase effects",
        "texts": [
            " Despite these opportunities for innovative manufacture, there are many design constraints that must be accommodated in order to achieve the repeatability required of high-value aerospace applications while minimising the associated production costs. These design constraints may be included in the final design following topographic optimization or implicitly defined in the parametric optimization. Design Constraints of the SLM Process. Of the design considerations of relevance to SLM manufacture, the most pertinent is the inclination angle between the build platen and the product, \u03c6 (Fig. 8). In particular, the inclination angle provides a correlation to: \u2022 Surface finish \u2013 the inclination angle, in combination with the associated layer thickness [24], results in staircase effects (Fig. 8). Staircase effects increase with reducing inclination angle (but do not occur when \u03c6 = 0), and result in surface roughness that can compromise fatigue resistance. \u2022 Manufacturability \u2013 highly acute inclination angles are not manufacturable without the use of support material. It is desirable to minimise the use of support material as it represents a cost that does not directly contribute to the as-used component; however, a compromise is usually required between the use of support material and other design considerations",
            " Based on this simulation, a preferred manufacture orientation can be identified, and regions with undesirable inclination angle can either be redesigned, or supported with appropriate support structures. Case Study: Manufacturability Optimisation of High-Value Aerospace Bracket. The highvalue aerospace component designed in this work has been subject to manufacturability optimisation. In particular, regions with undesirable inclination angle have been identified and overcome by geometry modification or the use of support material (Fig. 8): \u2022 Geometry modification \u2013 the inclination angle of the upper truss element is highly acute. To avoid the necessity of support material, the horizontal element was inclined slightly. Note that this inclination introduces staircase effects (Fig. 8, inset). Advanced Materials Research Vol. 633 143 \u2022 Internal gussets \u2013 Fig. 6 showed the example of added internal gussets to allow for the manufacture of the optimized overhang features, thereby minimizing the use of support material. \u2022 Minor support \u2013 the annular reinforcement rings initially required support material to allow manufacture. The detail design was modified to reduce the necessity for support material, however, minor use of support structures was still required. \u2022 Large scale support \u2013 the annular feature geometry is set by the mating components, and cannot be modified"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001214_j.rcim.2017.02.002-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001214_j.rcim.2017.02.002-Figure11-1.png",
        "caption": "Fig. 11. Experimental setup. (a) Practical experimental platform. (b) 3D illustration for the platform.",
        "texts": [
            " 10(c\u2013 d) can not only derive the optimal value of \u03b86, but also describe the distributing characteristics of the deformation on \u03b86. Therefore, \u03b86 can be properly adjusted according to this map to satisfy the tool motion better. From the above, the optimized values as well as the performance maps of \u03b82, \u03b8 real3 and \u03b8 \u03b8~4 6 have been derived. Thus, the robot machining posture can be optimized and the initial placement of the workpiece with respect to the robot can also be determined. The workpiece placement will be discussed in details in Section 6.3. The layout of the system architecture for experiments is illustrated in Fig. 11. The experimental system contains four components: a Comau Smart5 NJ 220-2.7 robot, a mass (43.3 kg) which is connected to the EE, a laser tracker and its retroreflector, and a fixture which is used to transfer the vertical mass gravity to the force applied on the xaxis of J6 by using a pulley wheel shown in Fig. 11(b). The vertical and horizontal positions of the pulley wheel can be adjusted for different experimental configurations. The laser tracker has been calibrated to measure the EE with respect to the robot base frame. To minimize the measurement noise, 10 results are acquired for the same configuration and their average is adopted as the result. For every configuration, the Cartesian positions of the EE with and without payload are recorded, respectively, and then the deviation between them is evaluated as the EE deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure14-1.png",
        "caption": "Fig. 14. FEM models.",
        "texts": [
            " It was also found that the calculated results were agreement with the measured ones well. Gears used as research objects are given in Table 1. In Table 1, the wheel is cut by a hob under accuracy requirement of JIS 5th grade. Fig. 2 is the measured 3D machining errors distributed on entire the tooth surface of the wheel. The pinion is ground under accuracy requirement of JIS 0 grade. So machining errors of the pinion are ignored in the calculations. Torque conditions are also given in Table 1. These torques are used for all the calculations in the following. Fig. 14 is FEM models of the pair of gears used in LTCA. Fig. 14(a) is FEM mesh-dividing pattern of the wheel. The pinion is also divided similarly. Fig. 14(b) is FEM model in the part of tooth-contact. Four pairs of teeth are shown. The reference face as shown in Fig. 6(a) is fine divided with 48 meshes within the contact width \u2018\u2018Width\u2019\u2019 and 20 meshes within the face width. Nodes on inner hole surface (hub of the gears) as shown in Fig. 14(a) are fixed as the boundary conditions of FEM when deformation influence coefficients and TRBS are calculated. As it has been stated that the outer limit of the single pair tooth-contact is used as the \u2018\u2018worst load position\u2019\u2019 to do LTCA and TSCS calculations of the pair of gears as shown in Table 1. Fig. 15 is contour lines of calculated TSCS when there are no ME, AE and TM. This TSCS is distributed on the reference face as shown in Fig. 6(a). In Fig. 15, the horizontal axis (X-axis) is face width of the gears and the vertical axis (Y-axis) is contact width Width as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000506_0954405981515590-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000506_0954405981515590-Figure2-1.png",
        "caption": "Fig. 2 (Left to right) Vertical, hollow box and horizontal test part geometries",
        "texts": [
            " These geometries were previously produced on the three-dimensional welding system and were shown to be influenced by temperature. The hollow box part was composed of 82 layers of weld to form a structure 100mm \u00d7 100mm \u00d7 100mm high; each layer consisted of a single, continuous weld, 3.5mm wide. The vertical wall consisted of a solid structure of weld 100mm long \u00d7 100mm high \u00d7 10mm wide. The horizontal slab measurements were the same as the vertical slab, but rather than standing the part lay flat on the base plate. Figure 2 shows the three part geometries. The material used to build the test parts was NOVOFIL 70 SG2, a 1mm diameter, copper-coated mild steel wire (C \u00bc 0:08, Mn \u00bc 1:5, Si \u00bc 0:90, P \u00bc 0:01, S \u00bc 0:01, Cu \u00bc 0:20). This material conformed to the following standards: BS 2901 A18, AWS E70 S-6 and DIN 8559 B00897 IMechE 1998Proc Instn Mech Engrs Vol 212 Part B SG2. The manufacturer claimed a tensile strength of over 540N/mm2 and a yield strength of over 450N/mm2. Because the strength of the material was high and its weldability good, it was deemed as being suitable for building three-dimensional welded parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003989_j.fusengdes.2017.01.032-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003989_j.fusengdes.2017.01.032-Figure11-1.png",
        "caption": "Fig. 11. Support structure analysis of ITER FW Panel part.",
        "texts": [
            " f no support structure is present at a location with an angle smaller han 45\u25e6, there is a risk of deformation. The support structures in ig. 10a and c are normally not dense and easy to be removed as een in Fig. 10b. However, the support structures become a probem when they are buried in complex internal pipe systems and 32 Y. Zhong et al. / Fusion Engineering a a T F a m 4 f a S d 1 2 3 4 5 6 [ [ [ [ [ [ [ [ [18] Eaton, R.B., V, Technical Specification \u2212316L(N)-IG forging for Blanket, in re difficult to reach manually or be blown away by shot-peening. he CATIA model in Fig. 11 shows there are two places in the ITER W Panel part that need support structures, which are not removble afterwards. Slightly tilting or re-arrangement of the inner pipes aking the angle larger than 45\u25e6 may solve this problem. . Conclusions It is the first time that AM is applied to fabricate nuclear usion related components with complex design. The physical nd mechanical properties, the microstructures of SLM and EBM S316L, and the ITER FW Part manufacturing were compared and iscussed. The results show: Almost fully dense SS316L were prepared both by SLM and EBM with optimized laser/electron beam parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure48-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure48-1.png",
        "caption": "Fig. 48 a Model of a skull prototyped; b simulated model of the skull developed with deposited filaments in CLFDM; c skull dome made by FDM process with 0.33-mm-thick layers [68]",
        "texts": [
            " Somemodels have complex structures or suspended structure. In order to reduce the need for the support structure and the number of layers, and to improve the deposition accuracy, it is necessary to select the surface slicing algorithm. At present, there is no surface slicing algorithm applied to WAAM, but the surface slicing algorithm has been widely used in the field of non-metal rapid prototyping. Chakraborty developed a new rapid prototyping method for the formation of curved layer fused deposition modeling (CLFDM, shown in Fig. 48) in the field of fused deposition of ABS, which reduces the step effect compared with the planar slicing algorithm [68]. Especially the manufacture of thinwalled curved parts has great advantages. Close to the WAAM system is the work of Zhao and Ma; they used the KUKA robot\u2019s wire feed (ABS) system and proposed two non-p lana r s l i c ing me thods : the decomposition-based surface slicing strategy and the transformation-based cylindrical surface slicing algorithm. The former is based on the STEP model, which is capable to cut the mesh model and verifying the feasibility of the proposed method by printing two components with the robot [69]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.45-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.45-1.png",
        "caption": "Fig. 4.45",
        "texts": [
            "47) As in case 1, we assume that the deflections v and w are independent of y and z: v = v(x), w = w(x). In addition, we apply the hypotheses of Bernoulli (see Section 4.5.1): the cross sections remain plane and stay perpendicular to the deformed axis of the beam. Now we introduce the angles of rotation \u03c8y and \u03c8z of the cross section about the y-axis and the z-axis, respectively (positive sense of rotation according to the cork-screw rule). In the following, we first determine the displacement u in axial direction of an arbitrary point P of the cross section with the coordinates y, z (Fig. 4.45). Due to a small rotation \u03c8y only, this point is displaced by an amount z \u03c8y in the positive x-direction. Similarly, a small rotation \u03c8z leads to the displacement \u2212y \u03c8z. Therefore, the 4.7 Unsymmetric Bending 165 total displacement is obtained as u = z \u03c8y \u2212 y \u03c8z. With the relations \u03c8y = \u2212 w\u2032, \u03c8z = + v\u2032 (see Fig. 4.45 and note that the cross section is perpendicular to the deformed axis of the beam) we get u = \u2212 (w\u2032 z + v\u2032 y). The strain \u03b5 = \u2202u/\u2202x is therefore given by \u03b5 = \u2212 (w\u2032\u2032 z + v\u2032\u2032 y), (4.48) and Hooke\u2019s law \u03c3 = E \u03b5 finally yields \u03c3 = \u2212 E(w\u2032\u2032 z + v\u2032\u2032 y). (4.49) The bending moments My and Mz are the resultant moments of the normal stresses \u03c3 in the cross section (note the senses of rotation): My = \u222b z \u03c3 dA, Mz = \u2212 \u222b y \u03c3 dA. (4.50) With (4.49) we obtain My = \u2212 E [w\u2032\u2032 \u222b z2 dA+ v\u2032\u2032 \u222b y z dA ] , Mz = E [ w\u2032\u2032 \u222b y z dA+ v\u2032\u2032 \u222b y2 dA ] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000436_j.jmmm.2009.07.030-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000436_j.jmmm.2009.07.030-Figure1-1.png",
        "caption": "Fig. 1. A scheme of the two interacting cylindrical permanent magnets: (a) with a common axis and (b) with parallel but displaced axes. R is the magnets radius, ti their aspect ratios, Z the distance between their centers, Mi their magnetizations, r their lateral displacement, and x the gap between the poles.",
        "texts": [
            " As for the geometry, the cylindrical magnets are of equal radius R and are magnetized uniformly along the cylinder axis of symmetry. In our derivations, we do not allow any magnetization vector rotation during the interaction, which may be thought as the effect of a strong intrinsic axial anisotropy induced by the manufacturer, nor do we consider sets of magnets with rotated axes of symmetry. In this case, either set consists of just one cylindrical magnet. The interacting cylinders are sketched in Fig. 1a. If we choose the coordinate system with the z-axis along the cylinders axis, then the attraction force acts only along z and can be expressed according to (1) as follows: Fz \u00bc @E @Z \u00bc 2pm0M2R3 @Jd @Z ; \u00f02\u00de where m0 is the permeability of vacuum and Jd the dipolar coupling integral defined in [5]. Following the computational method described in [1] the dipolar coupling integral Jd can be expressed as Jd\u00f0t1; t2; B\u00de \u00bc 2 Z \u00fe1 0 J2 1\u00f0q\u00de q2 sinh\u00f0qt1\u00desinh\u00f0qt2\u00dee qz dq; \u00f03\u00de where ti \u00bc ti/(2R), i \u00bc 1, 2, are the aspect ratios of the two cylinders, z \u00bc Z/R is the reduced distance between the centers of the two cylinders (see Fig. 1a) and J1(q) is a modified Bessel function of the first kind. On the assumption that the integral in (3) converges uniformly, we may exchange the order of integration and derivation arriving at Fz \u00bc 8pKdR2 Z \u00fe1 0 J2 1\u00f0q\u00de q sinh\u00f0qt1\u00desinh\u00f0qt2\u00dee qz dq; \u00f04\u00de where we have introduced the magnetostatic energy constant Kd \u00bc m0M2/2 for convenience of notation. Eq. (4) is the attraction force acting in the axial direction, while no attraction forces exist in x and y. As for numerical evaluation of the integral in (4) it is convenient to convert the integral to a more manageable form",
            " It is worth noting that the integral in (3) can be also expressed as combination of complete elliptic integrals using the following relations: Jd \u00bc 2 X1 i;j\u00bc 1 i j A 1 11 \u00f0B\u00fe it1 \u00fe jt2;1;1\u00de; \u00f08\u00de A 1 11 \u00f02o;1;1\u00de \u00bc 4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00feo2 p 3p \u00bd\u00f01 o2\u00deE\u00f0k2\u00de \u00feo2K\u00f0k2\u00de o; \u00f09\u00de where k2 2 \u00bc 1/(1+o2). Using (6) and (7) we may calculate the contact force of two identical cylindrical magnets. The contact force (F0) between two magnets is defined as the attraction force with zero axial and lateral gaps between the magnets. From Fig. 1, we can see that zero gap corresponds to z \u00bc 2t and t \u00bc t1 \u00bc t2. Substituting z \u00bc 2t in (6) and using (7) and the fact that A11 0 (0,1,1) \u00bc 0.5 we arrive at F0 \u00bc 8KdR2t 1 l1 \u00bdE\u00f0l21\u00de K\u00f0l21\u00de 1 l2 \u00bdE\u00f0l22\u00de K\u00f0l22\u00de ; \u00f010\u00de where l1 \u00bc 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe 4t2 p and l2 \u00bc 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe t2 p . Eq. (10) can be also transformed into a series in powers of l1 and l2 F0 \u00bc 4pKdR2t X1 n\u00bc1 2n 2n 1 \u00f02n 1\u00de!! \u00f02n\u00de!! 2 \u00f0l2n 1 2 l2n 1 1 \u00de: \u00f011\u00de The sum in (11) converges quickly for large aspect ratios t, giving fast and reasonably accurate estimates of contact forces between two long cylinders",
            " However, (12) was derived within a somewhat different approximation than (10), and this becomes particularly evident when t is small: in the limit t-0, the contact force per unit volume predicted by (12), that is 3/4 Kd/R, is just about 85% of the value predicted by (10), that is 4 log(2)/p Kd/R. At this stage, it is difficult to assess which of the two formulas is closer to reality. To ascertain which of the two may be deemed \u2018\u2018more correct\u2019\u2019, we will compare both with experimental results in Section 3. The arrangement of magnets is shown in Fig. 1b. The distance between axes (lateral displacement) is denoted as r. In this case, the magnetostatic energy is E\u00f0r; B\u00de \u00bc 8pKdR3 Z \u00fe1 0 J0 rq R J2 1\u00f0q\u00de q2 sinh\u00f0qt1\u00desinh\u00f0qt2\u00dee qB dq: \u00f013\u00de The energy gradient, i.e. the force, is then Fz \u00bc 8pKdR2 Z \u00fe1 0 J0 rq R J2 1\u00f0q\u00de q sinh\u00f0qt1\u00desinh\u00f0qt2\u00dee qB dq; \u00f014\u00de or in an equivalent form Fz \u00bc 2pKdR2 Z \u00fe1 0 J0 rq R J2 1\u00f0q\u00de q X1 i;j\u00bc 1 i j e q\u00f0B\u00feit1\u00fejt2\u00de dq: \u00f015\u00de For r \u00bc 0 (the common axis case), Eq. (15) transforms into Eq. (4). In summary, for deriving (14) or (15) we assume uniform magnetization that does not rotate in the presence of other magnets",
            " Only in some special cases it is worthwhile estimating the integral in (14) with further approximations. A special case of interest is when the axial distance between magnets in question is several times larger than the magnet radius. If the cylindrical magnets are far from each other, we may find an approximation of the integral in (15) by expanding the Bessel functions around q \u00bc 0 according to their definitory power series [12]. Then, by using z \u00bc (t1+t1)/(2R)+x/R, where x is the gap between the magnets (see Fig. 1), we obtain Fz 1 2 pKdR4 X1 i;j\u00bc0 \u00f0 1\u00dei\u00fej \u00f0x\u00fe it1 \u00fe jt2\u00de 2 1 3 2 r2 \u00f0x\u00fe it1 \u00fe jt2\u00de 2 \" # : \u00f016\u00de If, additionally, t1 \u00bc t2 \u00bc t and r \u00bc 0 then (16) turns into Fz 1 2 pKdR4 1 x2 \u00fe 1 \u00f0x\u00fe 2t\u00de2 2 \u00f0x\u00fe t\u00de2 \" # : \u00f017a\u00de Eq. (17a) gives the approximate force between two distant identical cylindrical magnets with the vectors of magnetization lying on their common axis. Fig. 2 shows a comparison between the force approximation (17a) and the exact force (4) for various magnet distances, while we used permanent magnets with the following parameters: R \u00bc 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003330_j.isatra.2019.08.045-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003330_j.isatra.2019.08.045-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of a quadrotor UAV vehicle. The inertial reference frame is represented by {I}, and the body reference frame is denoted by {B}.",
        "texts": [
            " Also, it is proven that the power demanded by any controller is reduced when using the power reduction methodology. \u00a9 2019 ISA. Published by Elsevier Ltd. All rights reserved. 1. Introduction Recently, the interest on Unmanned Aerial Vehicles (UAV), also called drones, has increased. They are flying platforms comprising airships, fixed wing, or Vertical Take-off and Landing (VTOL) vehicles. Quadrotors are a type of UAV with four rotors attached to a rigid cross airframe and placed equidistant from its center of mass, as depicted in Fig. 1. These systems have three degrees of freedom (DOF) for their rotational motion, three DOF for their translational motion, and only four actuators available as control inputs. Hence, quadrotors are underactuated systems, with the coordinates x, y being the underactuated translational coordinates [1]. 1.1. Overview Quadrotors are essential research systems due to their appealing features. For instance, they have the ability for hovering and operating in places with reduced space [2]; high thrust-weight ratio and outstanding maneuverability [2]; utilization of small propellers for thrust generation, which diminishes its complexity [2]; and their ability to react and continue in flight even after actuator or sensor faults [3,4]",
            " A matrix of the form A = diag{a1, . . . , an} \u2208 Rn\u00d7n represents a diagonal matrix with elements a1, . . . , an on the main diagonal. For a given square matrix, \u03bbmin(\u00b7), \u03bbmax(\u00b7) represent its minimum and maximum eigenvalues, respectively. When required, the square brackets [\u00b7] are used to indicate the units of a given quantity. Finally, if no confusion is present, the arguments of functions will be omitted. 2. Quadrotor dynamics A diagram representing the structure of a quadrotor vehicle is shown in Fig. 1. This system possesses four identical rotors and propellers. Rotors 1 and 3 rotate in the counter-clockwise direction (around vector \u2212b3), while the others rotate in the opposite direction. The quadrotor position is described by the inertial frame {I} = {i1, i2, i3}; the body frame {B} = {b1, b1, b3}, attached to its center of mass, describes the quadrotor orientation. Parameter m \u2208 R denotes the quadrotor mass, L the arm length, and I \u2208 R3\u00d73 the inertia tensor. By assuming a symmetric mass distribution, I = diag{Ixx, Iyy, Izz} in {B}, where each diagonal element refers to the corresponding principal inertia moment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure7.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure7.6-1.png",
        "caption": "Figure 7.6. The shoulder flexion torques of anterior deltoid and long head of the biceps can be summed to obtain the resultant flexion torque acting to oppose the gravitational torque from the weight of the arm.",
        "texts": [
            " 172 FUNDAMENTALS OF BIOMECHANICS The state of an object's rotation depends on the balance of torques created by the forces acting on the object. Remember that summing or adding torques acting on an object must take into account the vector nature of torques. All the muscles of a muscle group sum together to create a joint torque in a particular direction. These muscle group torques must also be summed with torques from antagonist muscles, ligaments, and external forces to determine the net torque at a joint. Figure 7.6 illustrates the forces of the anterior deltoid and long head of the biceps in flexing the shoulder in the sagittal plane. If ccw torques are positive, the torques created by these muscles would be positive. The net torque of these two muscles is the sum of their individual torques, or 6.3 N\u2022m (60 \u2022 0.06 + 90 \u2022 0.03 = 6.3 N\u2022m). If the weight of this person's arm multiplied by its moment arm created a gravitational torque of \u201316 N\u2022m, what is the net torque acting at the shoulder? Assuming there are no other shoulder flexors or exten- CHAPTER 7:ANGULAR KINETICS 173 Application: Muscle-Balance and Strength Curves Recall that testing with an isokinetic dynamometer documents the strength curves (joint torque\u2013angle graphs) of muscle groups"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000013_978-3-540-30301-5_35-Figure34.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000013_978-3-540-30301-5_35-Figure34.4-1.png",
        "caption": "Fig. 34.4 Representation in a Fr\u00e9net frame",
        "texts": [
            "3) used from now on is \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 x\u0307 = u1 cos \u03b8 , y\u0307 = u1 sin \u03b8 , \u03b8\u0307 = u1 L tan \u03c6 , \u03c6\u0307 = u2 , (34.5) where \u03c6 represents the vehicle\u2019s steering wheel angle, and L is the distance between the rear and front wheels\u2019 axles. In all forthcoming simulations, L is set equal to 1.2 m. The object of this subsection is to generalize the previous kinematic equations when the reference frame is a Fr\u00e9net frame. This generalization will be used later on when addressing the path following problem. Let us consider a curve C in the plane of motion, as illustrated on Fig. 34.4, and let us define three frames F0, Fm, and Fs, as follows. F0 = {0, i, j} is a fixed frame, Fm = {Pm, im, jm} is a frame attached to the mobile robot with its origin \u2013 the point Pm \u2013 located on the rear wheels axle, at the mid-distance of the wheels, and Fs = {Ps, is, js}, which is indexed by the curve\u2019s curvilinear abscissa s, is such that the unit vector is tangents C. Consider now a point P attached to the robot chassis, and let (l1, l2) denote the coordinates of P expressed in the basis of Fm",
            " Besides, it is preferable in practice that the robot\u2019s longitudinal velocity u1 remains positive all the time in order to prevent the relative orientations between all vehicles (i. e., the non-actively controlled variables involved in the system\u2019s zero dynamics) to take overly large values (the jackknife effect). This issue will be discussed further in Sect. 34.4. Car This technique also extends to car-like vehicles by choosing a point P attached to the steering wheel frame and not located on the steering wheel axle. Unicycle Let us adopt the notation of Fig. 34.4 to address the problem of following a path associated with a curve C in the plane. The control objective is to stabilize the distance d at zero. From (34.9), one has d\u0307 = u1 sin \u03b8e +u2(\u2212l2 sin \u03b8e + l1 cos \u03b8e) . (34.14) Recall that in this case the vehicle\u2019s longitudinal velocity u1 is either imposed or prespecified. We will assume that the product l1u1 is positive, i. e., the position of the point P with respect to the actuated wheels axle is chosen in relation to the sign of u1. This assumption will be removed in Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003314_j.ymssp.2018.01.005-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003314_j.ymssp.2018.01.005-Figure1-1.png",
        "caption": "Fig. 1. Pitting tooth model: (a) a single pit [3,4,15\u201317,22] and (b) multiple pits distributed evenly [14].",
        "texts": [
            " [23] introduced a finite element model to assess the consequences of pitting on the meshing stiffness, where a single pit was modeled in an elliptical shape. Jia et al. [24] and Cooley et al. [25] also employed finite element models for mesh stiffness calculation of pitting gears. Tan et al. [26] experimentally created natural pitting under different levels of load and exhibited pitting progression with acoustic emission (AE) techniques. The aforementioned studies mainly focus on a single pit [3,4,15\u201317,22], shown in Fig. 1(a) or multiple pits distributed evenly [14], shown in Fig. 1(b), which are far different from the real conditions of tooth pitting in Fig. 2. According to the American Society for Metals (ASM) handbook, pitting initiates due to a fatigue crack either at the surface of the gear tooth or at a small depth below the surface [1]. Apparently, the occurrence of surface cracks largely depends on the material defect and surface treatment of the gear tooth, which means that pits should emerge randomly, instead of a single pit or multiple pits distributed evenly. In other words, as one kind of surface faults, once the pitting occurs, no matter slight or severe, it would emerge with a series of pits on the gear tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002582_soro.2016.0051-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002582_soro.2016.0051-Figure3-1.png",
        "caption": "FIG. 3. (a) The six DoF continuum manipulator. (b) CAD model of the design. DoF, degree of freedom.",
        "texts": [
            " For tracking the position and orientation of the manipulator, the Aurora tracking system (Northern Digital, Inc.) is used with a six DoF electromagnetic probe. The probe is attached at the end of the manipulator. If the environment is free of electromagnetic disturbances, the system specifies an accuracy of 0.70 mm and 0.30 (RMS). The Aurora system also specifies the uncertainty of each measurement, which is useful during the learning step for removing outliers in the data. The manipulator setup for the experiments is shown in Figure 3. In this section, a brief analysis of the manipulator characteristics is summarized. A representation of the manipulator workspace is shown in Figure 4, which is obtained by motor babbling (The range of orientation is 52 , 135 , 128 ). The un-actuated home position is marked with a larger circle. Two thousand sample points were measured for this purpose. The same data will be used for the learning process, which is described in the next section. From a direct observation of the workspace, we can notice that the workspace is skewed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003291_jfm.2014.50-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003291_jfm.2014.50-Figure4-1.png",
        "caption": "FIGURE 4. (Colour online) Schematic (top view) of the wave force acting on the walker in the low-memory regime. The walker orbits in a circle of radius r0 with angular speed u0= |r0\u03c9| while bouncing with period TF on a fluid bath rotating with angular frequency \u2126 . The force F acting on the drop at x= xp(t) is primarily due to the wave created by the prior bounce at x = xp(t \u2212 TF), whose form is suggested by the circular wave crest. The radial component of the force is |F| sin \u03b8 . The wave force thus causes the observed orbital radius r0 = au0/2\u2126 to be larger than the inertial orbital radius rc = u0/2\u2126 .",
        "texts": [
            " Plots of the drop\u2019s orbital radius and orbital frequency as a function of \u2126 in the lowmemory regime are shown in figure 1(a,b), and adequately collapse the data presented in Harris & Bush (2014). In figure 1(c,d), we begin to see some deviation from the low-memory result (4.6) for the orbits of smallest radius, as these orbits have the longest orbital memory. The a-factor, and the associated increase of the orbital radius relative to inertial orbits, may be understood in terms of the geometry of the wave force. Figure 4 shows that the force F on the drop due to the wave generated during its prior impact has a component |F| sin \u03b8 = |F| u0TF/2r0 that points radially outwards. In the low-orbitalmemory regime, the drop\u2019s trajectory is primarily influenced by the waves generated by a few prior impacts, all of which make contributions pointing radially outwards. The prefactor a can thus be understood as originating from the dynamic influence of the walker\u2019s guiding wavefield. Alternatively, the anomalously large radius of the walker\u2019s orbit may be understood as resulting from an increased effective mass m\u0303 associated with its wave field, as (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure5-1.png",
        "caption": "Fig. 5. Pulley deformation model: (a) axial deformation; (b) pulley skewness [44].",
        "texts": [
            " Rapid variation of curvature may change the direction of frictional forces, which consequently affects the torque capacity of the belt\u2013CVT drive. Gerbert [23] also studied the influence of pulley skewness and flexure on the mechanics of V-belt drives. Deflection of pulley sheaves in the axial direction widens or shortens the groove width, thereby influencing the motion of belt in the pulley groove. The displacement of pulley sheaves can be attributed to the phenomena of local deflection, plate deflection, and pulley skewness. Fig. 5 [44] illustrates the variation in pulley groove width due to elastic deformation in the axial direction and due to skewness of the pulley halves. The local deflection depends on the local axial pressure. Plate theory was used to obtain the global deflection of pulley halves. Later, the plate equations and the belt equations were solved simultaneously to obtain the dynamic performance indicators of the belt\u2013pulley system. Skewness of the pulley may be caused by clearances in the guides of the movable pulley half"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002086_j.engfailanal.2014.12.020-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002086_j.engfailanal.2014.12.020-Figure2-1.png",
        "caption": "Fig. 2. Force resolution on spur gear tooth (a) when shaft is aligned, and (b) when shaft is misaligned.",
        "texts": [
            " 1 shows the difference between aligned shaft and misaligned shaft with h of misalignment angle. According to the properties of involute profile, the line of action is the common normal to the tooth profile. Correspondingly, the acting force F of the contact teeth should be always along the line of action. But when there is shaft misalignment in gear shaft the force F will act making an angle h with normal. This effect will change the value of forces acting on gear tooth. This concept is explained in Fig. 2, where due to misalignment, value of radial and tangential forces change. Pressure angle (a1) will remain same in both the cases. On resolving the forces as shown in Fig. 2 for aligned shaft and misaligned shaft the values of forces Ft, Fr and Fa can be obtained, where Ft, Fr and Fa are tangential, radial and axial components of force F respectively on the gear tooth. Expressions for various forces acting on gear tooth are mentioned in Table 1. The Hertzian stiffness and the axial compressive stiffness do not change due to misalignment, and can be given as [3], kh \u00bc pEL 4\u00f01 m2\u00de \u00f05\u00de 1 ka \u00bc Z a2 a1 \u00f0a2 a\u00de cos a sin2 a1 2EL\u00bdsina\u00fe \u00f0a2 a\u00de cos a da \u00f06\u00de The bending mesh stiffness and the shear mesh stiffness vary due to shaft misalignment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001967_s11071-018-4314-y-Figure16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001967_s11071-018-4314-y-Figure16-1.png",
        "caption": "Fig. 16 Schematic of a outer race fault [102]",
        "texts": [
            " This model considered the masses of the rolling elements, races, and shaft. The rectangular displacement excitation model was also used to formulate the localized fault. Nakhaeinejad and Bryant [102] established a multibody dynamic model for a REB with a localized fault on the races and rolling elements based on vector bond graphs. The centrifugal and gyroscopic influences, contact separations, and contact slip were formulated. The fault was described according to the surface profile changes, as shown in Fig. 16, where w is the fault width, h is the fault depth, and \u03b2 f is the fault angular position in body coordinate. This model considered the fault shape, width and depth on the displacement excitation.Also, itwas a rectangular displacement excitation model since the surface profile was assumed to be a rectangular one. Kankar et al. [103] described a mathematical model to predict the vibrations of a REBwith a localized fault on the races and balls under the radial load. This model also used a rectangular displacement excitation model to formulate the fault, whose shape was similar as that listed in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure12.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure12.18-1.png",
        "caption": "Fig. 12.18 Example of a measurement report. The deviations from the CAD data are displayed and evaluated (e.g. passed, failed, colour markings) [24]",
        "texts": [
            " 12.17) are used in many European trains. Each swiveltruck needs to be measured and delivered with a measuring protocol. The measurement of these swivel-trucks, a task that a few years ago could have only been performed using tactile 3D CMMs or measuring arms, can be carried out easily and efficiently with a portable TRITROP photogrammetry system. With TRITOP and an automated evaluation routine, one person is able to perform the measurement of such a swivel-truck and create a measurement report (Fig. 12.18) within forty minutes. 12 Reverse Engineering 341 According to [24], this time is required to apply the reference points, mark the characteristic features, place the scale bars, record about fifty images and transfer them to a laptop, carry out an automatic evaluation (the definition of the marker lines, the alignment of the measurement data with the nominal data, the calculation of the deviations) and to prepare and print out a measurement report. The case presented in [25] covers the measurement of a large iron casting for a wind turbine gearbox with an optical LED-based triangulation system (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002645_1.4032168-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002645_1.4032168-Figure8-1.png",
        "caption": "Fig. 8 CAD image of rig used to measure pressure drop and heat transfer in additively manufactured test coupons",
        "texts": [
            " This fusing effectively smoothed some of the roughness features that would have been present on the each individual surface. A test rig was built to collect pressure drop and heat transfer measurements of each of the test coupons using a similar design to that already presented by Weaver et al. [20] and Stimpson et al. 051006-4 / Vol. 138, MAY 2016 Transactions of the ASME Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jotuei/934863/ on 03/21/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use [18]. The rig, shown in Fig. 8, was built with a smooth contraction chamber that supplied uniform velocity air to the coupon inlet. The exit expansion chamber was made identical to the inlet for simplicity of fabrication. The coupon was mounted between the inlet and exit pieces and sealed with rubber gaskets between the mating surfaces. Pressure taps were installed upstream of the inlet contraction and downstream of the exit expansion to measure the pressure drop across the coupon. This pressure drop was modified to account for expansion losses associated with a sharp exit into a large reservoir"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001525_tia.2009.2036507-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001525_tia.2009.2036507-Figure1-1.png",
        "caption": "Fig. 1. Proposed magnetic harmonic gear topology. (a) Magnetic harmonic gear with pw = 1. (b) Magnetic harmonic gear with pw = 2. (c) Magnetic harmonic gear with pw = 3.",
        "texts": [
            " As a result of the variable air-gap length, the magnetic fields, which are produced by both sets of permanent magnets, are modulated such that asynchronous space harmonics are generated by one set of magnets which have the same number of poles as the other set of permanent magnets, and vice versa. Due to the sinusoidal profile of both the high-speed and lowspeed rotors, the air-gap length between the stator and the lowspeed rotor can be expressed as g = gmax + gmin 2 + ( gmax \u2212 gmin 2 ) cos (pw(\u03b8 \u2212 \u03c9ht)) (1) where gmax and gmin are the maximum and minimum air-gap lengths, respectively, \u03c9h is the angular velocity of the highspeed rotor, and pw is the number of sinusoidal cycles which result in the air gap between the low-speed rotor and the stator. Fig. 1 shows magnetic harmonic gears with pw = 1, pw = 2, and pw = 3. The radial component of the flux density distribution due to the low-speed rotor magnets, at a radial distance r, can be written in the following form: Br(r, \u03b8) = ( \u2211 m=1,3,5,... brm(r) cos (mp(\u03b8 \u2212 \u03c9rt) + mp \u03b80) ) \u00d7 [\u03bb0 + \u03bb1 cos (pw(\u03b8 \u2212 \u03c9ht))] = \u2211 m=1,3,5,... (brm(r) cos (mp(\u03b8 \u2212 \u03c9rt) + mp \u03b80) \u03bb0) + (brm(r) cos (mp(\u03b8 \u2212 \u03c9rt) + mp \u03b80) \u00d7 \u03bb1 cos (pw(\u03b8 \u2212 \u03c9ht))) 0093-9994/$26.00 \u00a9 2010 IEEE = \u2211 m=1,3,5,... (brm(r) cos (mp(\u03b8 \u2212 \u03c9rt) + mp \u03b80) \u03bb0) + ( brm(r)\u03bb1 2 \u00d7 cos ((mp \u2212 pw)\u03b8 + (pw\u03c9h \u2212 mp\u03c9r)t + mp \u03b80) ) + ( brm(r)\u03bb1 2 \u00d7 cos ((mp + pw)\u03b8 \u2212 (pw\u03c9h+ mp\u03c9r)t + mp \u03b80) ) (2) where \u03c9r and p are the angular velocity and number of pole pairs of the low-speed rotor, respectively, and \u03bb0 and \u03bb1 are the first two Fourier coefficients for the modulating function which is associated with the radial component of flux density as a result of the sinusoidal variation of the air-gap length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.66-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.66-1.png",
        "caption": "FIGURE 5.66. A 2R manipulator, acting in a horizontal plane.",
        "texts": [
            " Attach the spherical wrist of Exercise 22 to the cylindrical manipulator of Exercise 20 and make a 6 DOF cylindrical robot. Change your DH coordinate frames in the exercises accordingly and solve the forward kinematics problem of the robot. 27. An RkP manipulator. Figure 5.65 shows a 2 DOF RkP manipulator. The end-effector of the manipulator can slide on a line and rotate about the same line. Label the coordinate frames installed on the links of the manipulator and determine the transformation matrix of the end-effector to the base link. 5. Forward Kinematics 321 z0 28. Horizontal 2R manipulator Figure 5.66 illustrates a 2R planar manipulator that acts in a horizontal plane. Label the coordinate frames and determine the transformation matrix of the end-effector in the base frame. 29. SCARA manipulator. A SCARA robot can be made by attaching a 2 DOF RkP manipulator to a 2R planar manipulator. Attach the 2 DOF RkP manipulator of Exercise 27 to the 2R horizontal manipulator of Exercise 28 and make a SCARA manipulator. Solve the forward kinematics problem for the manipulator. 30. F Roll-Pitch-Yaw spherical wrist kinematics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000060_s11661-008-9557-7-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000060_s11661-008-9557-7-Figure3-1.png",
        "caption": "Fig. 3\u2014Model for stacking of individual deposited metal disks.",
        "texts": [
            " During laser deposition, a liquid pool of molten material is formed, and the shape of this pool is affected by the laser beam intensity profile and the presence of thermocapillary convection. In order to render the problem tractable, it is assumed that laser beam intensity has a uniform distribution, and the melt pool geometry is approximately cylindrical. The deposited cylinder materials in the melt pool are assumed uniform in size. The present formulation is equivalent to assuming that deposition is formed by the stacking of melt disks, as shown in Figure 3, with a thickness equivalent to the average thickness of a deposited layer. An assumption of no interfacial thermal contact resistance between any two metal disks is made, given the presence of remolten metal. In summary, the simplifying assumptions made in the present article are listed as follows: (1) each deposited material in the melt pool is approximated as a thin metal disk, (2) the initial temperature of the metal disk prior to heat transfer into the preceding layer is uniform, and (3) the heat conduction in the deposited metal disks and substrate are one-dimensional"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001701_014003-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001701_014003-Figure5-1.png",
        "caption": "Figure 5.Temperature distribution duringmelting in the case of a 5 mm spacing distance between thin plates.",
        "texts": [
            " For simplicity, all of these steps are regarded as one single step and are merged into the melting. The cooling step is defined as the time interval between the two consecutive melting steps. Due to the very small width of the thin plates (1 mm), the heat loss by radiation on the top surface was assumed to be negligible. The AM process in EBM\u00ae occurs under a very high level of vacuum in the chamber (below 9\u00d7 10\u22124 mbar). Therefore, the heat transfer by convection on the top surface of the powder can be neglected. 4.1.Numerical results Figure 5 shows the temperature distribution in the domain with a spacing distance of 5 mm. According to the results of the numerical model, the spacing distance has no considerable influence on the temperature distribution during the melting step. Almost the same temperature profiles were achieved at different spacing distances. Therefore, only the results of one of the spacing distances (i.e., 5 mm) is illustrated in figure 5. The similarity of temperature distribution could be explained by the fact that according to the electron beam scanning speed of 100 mm s\u22121 and the trace length of 3 mm, the melting step occurred quickly (0.03 s). It is notable that the powder bed around the solidified zone has a low Figure 4.The influence of the number of elements on themaximum temperature in themelt pool at the domainwith a 5 mmspacing distance. A very high absorption coefficient was used. thermal conductivity. In such a short interaction time, the heat transfer through the powder bed has minimal influence on the temperature distribution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001967_s11071-018-4314-y-Figure29-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001967_s11071-018-4314-y-Figure29-1.png",
        "caption": "Fig. 29 Schematic of a off-sized raceway [227] and b off-sized rolling elements",
        "texts": [
            " [225] conducted an analytical model to predict the vibrations of SRBs with the surface waviness. The external axial load and self-aligning contact angle were formulated in their model. Also, the cosinoidal function was applied to describe the timevarying displacement excitation generated by the surface waviness. They denoted that the direction and magnitude of the self-aligning contact angle have significant effects on the vibrations for SRBs. 3.2 Off-sized components Geometric imperfection of the bearing componentswas a common manufacturing issue for REBs as shown in Fig. 29. In the bearing assembly process, geometric errors of the rolling elements often occurred since a large amount of rolling element with relatively small size were loaded in a REB [195]. On the other hand, off-sized raceway may be produced during the manufacturing process or structural deformations produced by unsuited large loads [226]. In particular, the offsized components in REBs have significant effects on the rotational accuracy and vibration levels of REBs. Consequently, the accurate prediction of the vibration characteristics of REBs could be very important for their condition monitoring and diagnosis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure5-1.png",
        "caption": "Fig. 5. Face-contact model for loaded tooth contact analysis.",
        "texts": [
            " Lead crowning and end relief are usually used for tooth modifications of a gear. In Fig. 4, one kind of lead crowning curve and two kinds of end relief curves are given. An arc is used for lead crowning. One arc with two straight lines and three straight lines are used for end relief. \u2018\u2018Q\u2019\u2019 is used to express the maximum quantity of lead crowning and end relief. Tip and root relieves are also used to modify tooth profile. Since the same methods presented in this paper can be used to treat tip and root relieves, detailed descriptions are omitted here. Fig. 5 is a face-contact model used for LTCA of a pair of spur gears in this paper. Engagement of a pair of spur gears (Gear 1 and Gear 2) on the geometric contact line is shown in Fig. 5(b). Fig. 5(a) is a 3-D view of the engaged tooth surface of Gear 1. In Fig. 5(a), loaded tooth contact is assumed to be on a reference face with a contact width. Of course, this reference face is a part of the tooth surface of Gear 1 and the geometric contact line is located at the center of this reference face. In Fig. 5(a), many lines parallel to the geometric contact line are made artificially. These lines (including the geometric contact line) are called reference lines and many points on the reference lines are made artificially. These points are called contact reference points, or simply say reference points. These reference points shall be used as contact points in LTCA. That is to say, tooth contact on the reference face of Gear 1 shall be replaced by the contacts on the reference points when FEM is used to perform LTCA",
            " The responsive contact points on tooth surface of Gear 2 are found geometrically according to the positions of the reference points on Gear 1. It is introduced in the following how to find the positions of the responsive contact points on tooth surface of Gear 2, especially in the case that there are AE, ME and TM. In the case that there are no AE, ME and TM, positions of the responsive contact points on tooth surface of Gear 2 can be found easily according to the positions of the reference points on tooth surface of Gear 1. For example, in Fig. 5(a), k is an arbitrary reference point on the reference face of Gear 1, in order to find the responsive contact point on tooth surface of Gear 2, a section plane that passes through the point k and is parallel to the end face of Gear 2 is made. Fig. 5(b) is this section plane. In Fig. 5(b), tooth engagement state of Gear 1 and Gear 2 is shown. Since there are no AE, ME and TM, tooth profiles of Gear 1 and Gear 2 are involute curves in this section plane. Then, a 2-D coordinate system (O0 X0Y0) is made in the section plane. Where, O0 is the geometrical contact point on the tooth profile of Gear 2, X0 axis is the line of action of the pair of gears and Y0 axis is the vertical line to the line of action. In the 2-D coordinate system (O0 X0Y0), a line that passes through the point k and is parallel to the X0 axis is made",
            " In the case that there are ME and TM for a pair of gears, since ME and TM do not affect gear positions, only affect tooth profile, so it is not necessary to make additional calculations to find position of Gear 1 and positions of the responsive contact points on tooth surface of Gear 2. Pairs of contact points in the case that there are no AE, ME and TM can be used. It is only needed to take effects of ME and TM on gap calculations into account when to calculate gaps of the pairs of contact points with the Eq. (6). Since a face contact model as shown in Fig. 5 is used in LTCA, effects of ME and TM on tooth engagement at a arbitrary engagement position, such as outer and inner limit positions of loads, can be considered automatically if the Width in Fig. 5 is made large enough. In Fig. 7, and are one pair of elastic bodies which will contact each other when an external force P is applied. Contact of this pair of elastic bodies is handled as contact of many pairs of points on both supposed contact surfaces of and like gear\u2019s contact as shown in Fig. 5. These pairs of contact points are expressed as (1 1 0), (2 2 0), . . . ,(m m 0), (a a 0), (k k 0), (j j 0), (b b 0),. . . and (n n 0). n is the total number of contact point pairs. Fig. 7(b) is a section view of Fig. 7(a) in the normal plane of the contact bodies. In Fig. 7, ek is a clearance (or backlash) between a optional contact point pair (k k 0) before contact. Fk is contact force between the pair of contact points (k k 0) in the direction of its common normal line when k contacts with k 0 under the load P (It is assumed that all the common normal lines of the contact point pairs are approximately along the same direction of the load P in this paper because a contact area is usually very narrow",
            " Objective Function Z \u00bc X n\u00fe1 \u00fe X n\u00fe2 \u00fe \u00fe X n\u00fen \u00fe X n\u00fen\u00fe1 \u00f017\u00de Constraint conditions \u00bdS fF \u00fe dfeg \u00fe \u00bdI fY g \u00fe \u00bdI fZ 0g \u00bc feg \u00f018\u00de fegTfF g \u00fe X n\u00fen\u00fe1 \u00bc P \u00f019\u00de where \u00bdS \u00bc \u00bdSkj \u00bc \u00bdakj \u00fe ak0j0 ; k \u00bc 1; 2; . . . ; n; j \u00bc 1; 2; . . . ; n fZ 0g \u00bc fX n\u00fe1;X n\u00fe2; . . . ;X n\u00fengT fF g \u00bc fF 1; F 2; . . . ; F k; . . . ; F ngT fY g \u00bc fY 1; Y 2; . . . ; Y k; . . . ; Y ngT feg \u00bc fe1; e2; . . . ; ek; . . . ; engT F k P 0; Y k P 0; ek P 0; d P 0; k \u00bc 1; 2; . . . ; n X n\u00fem P 0; m \u00bc 1; 2; . . . ; n\u00fe 1 When to do LTCA of a pair of teeth with AE, ME and TM, akj and ak0j0 can be regarded as deformation influence coefficients of the pairs of contact points on reference faces of Gear 1 and Gear 2 as shown in Fig. 5 separately. They can be calculated with 3-D FEM. P can be regarded as the total load of the pair of gears along the line of action. P can be calculated with Eq. (20). In Eq. (20), rb is radius of gear base circle. {e} is gap array that consists of all pairs of contact points on the reference face as shown in Fig. 5(a). {e} can be calculated geometrically. {F} is a array of tooth loads between the pairs of contact points. d is relative deformation of the pair of gears along the line of action. When akj, ak0j0 , {e} and P are known, {F} and d can be calculated by solving the Eqs. (17)\u2013(19) with the Modified Simplex Method of mathematical programming principle. Then tooth contact pattern can be obtained by drawing contour lines of {F}. Since gear transmission has a very high efficiency (about 95\u201398%), friction between the contact tooth surfaces is ignored in LTCA",
            " Modification curve and modification quantity can be changed simply by two parameters, one is used to stand for type of the modification curve and the other is used to stand for the modification quantity. Step 5: Divide FEM meshes of the pinion and the wheel automatically Programs are developed to be able to divide FEM meshes of the pinion and the wheel automatically when structure dimensions, gearing parameters, tooth engagement position parameter and FEM mesh-dividing parameters are given. Of course ME, AE and TM have been given before FEM mesh dividing. Step 6: Form pairs of contact points on contact reference faces Pairs of contact points on the contact reference faces as shown in Fig. 5 are made according to the methods stated in Sections 3.1 and 3.2. Step 7: Calculate backlash ek of every pair of contact points Backlash ek of every pair of contact points is calculated geometrically and automatically when the pair of spur gears with ME, AE and TM is positioned in 3-D coordinate system (A0 XYZ) as shown in Fig. 1 and pairs of contact points are made. Step 8: Calculate deformation influence coefficients of the contact points on the contact reference faces by 3-D, FEM When the pairs of contact points on Gear 1 and Gear 2 as shown in Fig. 5 are made, deformation influence coefficients of all the assumed contact points are calculated by 3-D, FEM. For an example, when to calculate deflection influence coefficients of a contact point on the reference face of Gear 1 as shown in Fig. 5(a), FEM model as shown in Fig. 20(a) is used and a unit force is applied on the contact point along the line of action, then deformations of the contact point and other contact points on the reference face along the lines of action are calculated with a 3-D, FEM. This calculation is repeated for all the remained contact points on the reference face as shown in Fig. 5(a). Then deformation influence coefficient matrix of Gear 1 is formed by these calculated deformations. The same calculations are made for Gear 2. Step 9: Input loaded torque Torque is inputted here for LTCA using in the equations of mathematical programming method. Step 10: Set up mathematical model of LTCA and perform mathematical programming calculations Set up mathematical model of Eqs. (17)\u2013(19) and solve these equations with Modified Simplex Method of mathematical programming method. Tooth loads (contact forces between the pairs of contact points) and relative deformation of the pair of gears along the line of action (d as shown in Fig",
            " N 1\u00f0n; g; f\u00de \u00bc \u00f01 n\u00de\u00f01 g\u00de\u00f01\u00fe f\u00de=8 N 2\u00f0n; g; f\u00de \u00bc \u00f01\u00fe n\u00de\u00f01 g\u00de\u00f01\u00fe f\u00de=8 N 3\u00f0n; g; f\u00de \u00bc \u00f01\u00fe n\u00de\u00f01\u00fe g\u00de\u00f01\u00fe f\u00de=8 N 4\u00f0n; g; f\u00de \u00bc \u00f01 n\u00de\u00f01\u00fe g\u00de\u00f01\u00fe f\u00de=8 N 5\u00f0n; g; f\u00de \u00bc \u00f01 n\u00de\u00f01 g\u00de\u00f01 f\u00de=8 N 6\u00f0n; g; f\u00de \u00bc \u00f01\u00fe n\u00de\u00f01 g\u00de\u00f01 f\u00de=8 N 7\u00f0n; g; f\u00de \u00bc \u00f01\u00fe n\u00de\u00f01\u00fe g\u00de\u00f01 f\u00de=8 N 8\u00f0n; g; f\u00de \u00bc \u00f01 n\u00de\u00f01\u00fe g\u00de\u00f01 f\u00de=8 N 9\u00f0n; g; f\u00de \u00bc 1 n2 N 10\u00f0n; g; f\u00de \u00bc 1 g2 N 11\u00f0n; g; f\u00de \u00bc 1 f2 \u00f021\u00de Fig. 20 is FEM models of the pair of gears. Fig. 20(a) is FEM mesh-dividing pattern of the wheel. The pinion is also divided similarly. Fig. 20(b) is FEM model in the part of tooth contact. Four pairs of teeth are shown. The reference face as shown in Fig. 5(a) is fine divided with 48 meshes within the contact width \u2018\u2018width\u2019\u2019 and 20 meshes within the face width. Nodes on inner hole surface (hub of the gears) as shown in Fig. 20(a) are fixed as the boundary conditions when deformation influence coefficients and RBS calculations are performed. Calculations are conducted at six cases. Case 1 is the case that no ME, AE and TM are considered in the calculations. Case 2 is the case that only 0.04 misalignment error of the gear shafts on the plane of action of the gears is given"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure9.13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure9.13-1.png",
        "caption": "Fig. 9.13 Main components of HST [74]",
        "texts": [
            " Therefore, an alternative system was necessary, that should be located in space, outside the atmosphere. The HST has been deployed 1990 in low-Earth orbit (600 km). It has been designed to observe the space permanently and to be maintainable, therefore adjustments can be performed during regular servicing missions. For this purpose, it has been equipped with necessary components such as grapples and handholds for control [74], but also with diverse components that enable the communication as well as an external control. Figure 9.13 depicts the major components of HST. 9.6.2.1 Requirement Definition and System Specification The main requirement to the HST has been to provide relevant data to astronomers in order to help them conducting research in their scientific domain. Astronomerscientists who took the role of a customer defined the requirements regarding the capability of HST. Among others, they described the observations that the HST should enable, when and by whom observing operations were to be performed [74]. Requirements also regarded the external controlling of the HST, design, development, in-orbit operations, maintenance and so on",
            " Finally, the implementation of the system architecture has been more impacted by technical requirements rather than the cost projections [74]. This phase was characterized among others by the following activities: \u2022 Risk, cost, schedule and configuration management \u2022 Independent review and payload specification groups \u2022 Case-dependent simulation, laboratory and ground testing prior to initial flight and on-orbit repair \u2022 Definition of relative roles and contributions of involved stake holders. The high requirements (e.g. tolerance requirements) to the mirror that contains the primary mirror (Fig. 9.13) have been important factors to be considered in this phase. Innovative solution approaches were introduced in order to counter the weight of the mirror and therefore achieve the goal of zero gravity of the mirror for testing purposes [74]. Further critical points have been among others, the engineering and assembly of main sub-systems and components as well as guidance sensors. Reducing the mirror size from 3 m to 2.4 revealed itself to be a substantial modification, since other main components were impacted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000477_0079-6425(63)90037-9-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000477_0079-6425(63)90037-9-Figure13-1.png",
        "caption": "Fig. 13. Section through solid-liquid interface according to Jackson and Chalmers' analysis.",
        "texts": [
            " It is realized that the simplified treatment developed below applies only to the ideal case where the widths of the two phases are equal and where the radii of curvature of the solid-liquid interfaces of the lamellae of both phases are equal and constant over the whole lamellar width. The symmetry of the interphase boundary groove implies that the solid-liquid surface energies of the ~ and ~ phases are equal. The more general case of unequal phases and an unsymmetrical interphase boundary groove has not been worked out. Consider a cross section taken through the lamellar part of the structure normal to the interphase boundaries as drawn in Fig. 13. Resolving the surface energies vertically, 0 2~xt \" cos ~ = ax~ We have also from the geometry X 0 = ,\" c o s and therefore cos 2 -- ~ - 4~ axL 2a:(r~ o r - - - - r 3. EUTECT1C ALLOY S O L I D I F I C A T I O N 119 The diffusion equation of the solute ahead of one of the lameUae was given previously in Tiller's analysis and is z ( c f - c~) z (1 --k~)CER~= D Z ? (1 - - k~) C~: RX (C~ -- CE) = 8 D (1 - - k~,) C e RXm~, and therefore A T c = 8D (9) The undercooling at the centre of a lamella due to a curvature of r is, f rom the Gibbs-Thomson formula ~ TE Lt~ Now"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure5.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure5.9-1.png",
        "caption": "Fig. 5.9 How the lateral flapping \ud835\udefd1s changes as the feedback gain is increased; all aircraft are rolling to starboard at the point of zero roll angle",
        "texts": [
            "5, shown in Figure 5.7, ensures this rapid response. The hub moment rolls the fuselage to port but, as soon as the roll rate builds up, the powerful damping (Lp) slows the motion down. At the critical condition, the initial flap angle leads to an undamped oscillation with the rotor and fuselage in antiphase; when the disc is tilted to port (\ud835\udefd1s positive), the fuselage is tilted to starboard (\ud835\udf19 positive). The feedback control effectively cancels out the flapping due to the roll rate damping, as illustrated in Figure 5.9. As the gain increases further, the system goes unstable with negative \ud835\udefd1s providing a destabilizing moment as the fuselage rolls through zero attitude (Figure 5.9). With roll attitude and lateral flapping equal and opposite at the critical condition, we can see what is at the heart of this coupling problem. The unintended consequence of strong roll attitude control is that, beyond Modelling Helicopter Flight Dynamics: Stability Under Constraint and Response Analysis 273 the critical condition, as the disc flaps to port (+\ud835\udefd1s), the controller is applying +\ud835\udf031c to increase the port flapping further. To gain further insight into the rotor parameters that affect the changes in damping around the critical condition, we need to find an approximation for this oscillatory roll-flap mode, isolating it from the subsidence heading \u2018west\u2019 along the real axis in Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002277_j.jmapro.2020.08.060-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002277_j.jmapro.2020.08.060-Figure12-1.png",
        "caption": "Fig. 12. (left) Microstructure of the center parts of the oscillated wall in YZ and XY planes; (right) Microstructure of the overlapped wall in YZ and XY planes.",
        "texts": [
            " 4 shows the theoretical waveform of the current signal of both manufactured walls. It is obtained by interpolating from the database designed by EWM for steel material, 80 % Ar\u201320 % CO2 shielding gas, 1.2 mm wire diameter and 8 m/min wire feed rate. The drop formation frequency in this case is 138.2 Hz. This figure also shows the process of drop formation and its correlation with the current signal. For metallographic analysis, samples were transversely crosssectioned (XZ), longitudinally cross-sectioned (YZ) and sectioned between layers (XY) (axes referenced in Fig. 12) with a metallic saw, mechanically polished and etched with 2% Nital solution (Nitric and Ethanol acid), successively. Once the samples were metallographically prepared, microstructures and macrostructures were observed with the Eclipse MA200 (Nikon) microscope. For macro-examination and Vickers hardness testing, samples were taken, transversally, in the central part of the walls at three heights: the top, the middle and in the bottom. Vickers hardness testing was performed at room temperature, utilizing the Duramin A-300 (Struers) hardness testing machine, according to standard ISO 6507-1 [22]",
            " In our case, due to different thermal cycles created because of the different deposition sequences and paths, it is expected that the microstructure in the oscillated wall and the overlapped wall will be different. In previous studies, Choi and Hill [26] analyzed the microstructure on ER70S-6 welds, which is helpful to analyze the microstructure of our walls. In Fig. 10a,b the macrographs of the upper and lower part of the overlapped wall are observed in the transversal direction of the wall (plane XZ) (axes referenced in Fig. 12). In these images, each contributed bead and HAZ are clearly visible. In this heterogeneous microstructure, areas with polygonal ferrite and acicular ferrite can be differentiated. The creation method of acicular ferrite in weld beads was reviewed by Babu [28]. In the upper part of the wall (Fig. 10 a.1) a mixture of acicular ferrite, allotriomorphic ferrite and bainite is seen since this part has not experienced the thermal effect of the following layer. A similar microstructure was obtained by Shassere et al",
            " In Fig. 10 b.2, this variation can be seen, with the grain size being bigger in the top part compared to the lower part. This variation is also a consequence of the different thermal history that the areas have undergone. For example, the grain coarsening in the HAZ zone was reported widely in the literature [26,28,30]. On the other hand, Fig. 11c,d present the macrographs of the upper and lower part of the oscillated wall in the transversal direction of the wall (plane XZ) (axes referenced in Fig. 12). In this case, the microstructure is totally different. The heat input layer by layer, reported in the previous section, produces the formation of layer bands. These bands are easily differentiated in Fig. 11c,d and the distances between the bands are equal to the layer height. In the upper part of the wall, as in the case of the overlapped wall, a mixture of acicular ferrite, allotriomorphic ferrite and bainite microstructures (Fig. 11 c.1) is observed because this part has not undergone the thermal effect of the successive deposited beads",
            " Since only one oscillatory bead is deposited in each layer, the thermal input is uniform throughout all the layers and, therefore, this homogeneity in the microstructure is observed. Even so, small grain size variations are noticed at different heights of the wall but, in general, the grain size is 10 ASTM, larger than the overlapped one. This larger grain size is due to the heat accumulation effect and the consequent low cooling rate. The same behavior was obtained by Oliveira et al. [17] and Dirasu et al. [3] in their research. Fig. 12 presents the axes referenced, taken for the microstructural analysis, and the microstructures of the center parts of the oscillated and overlapped walls in planes YZ and XY. In these planes, the polygonal ferrite microstructure can also be observed and, as in the XZ plane, slightly larger grain sizes can be observed in the oscillated wall than in the overlapped wall. With regard to the hardness analysis, the hardness and the microstructure are closely related, and hardness mapping can illustrate the E"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001214_j.rcim.2017.02.002-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001214_j.rcim.2017.02.002-Figure15-1.png",
        "caption": "Fig. 15. The placements of workpiece with respect to the robot. (a\u2013b) The fixture with workpiece. (c) Un-optimized placement. (d) Optimized placement.",
        "texts": [
            " 14, it can be seen that the actual deformations have the same distribution characteristics with that of DEI\u22121, which further verifies the correctness of the proposed deformation evaluation index and its map. To verify that the workpiece placement optimization can be achieved according to the above maps plotted by using the performance evaluation indexes, a drilling operation is adopted in the following. The placement of the workpiece with respect to the robot is scheduled before machining. As shown in Fig. 15(a) and (b), the flat workpiece is fixed on a fixture, whose position with respect to the robot is undefined and the angle of pitch can be adjusted. The aim of the machining is to drill out a hole on the workpiece. Fig. 15(c) and (d) illustrate an unoptimized placement and the optimized placement, respectively. The un-optimized placement is selected arbitrarily, and the optimized placement is determined by the optimized posture of the Comau NJ 220-2.7 robot. The simulation configurations and results are summarized in Table 3. It can be seen that DEI are 795.25 (1/Nmm) and 1966.3 (1/ Nmm) for the un-optimized and optimized placements. Thus, it is predicable that the machining accuracy for the optimized placement will be better because the deformation is smaller during the drilling process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002342_j.jsv.2011.03.031-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002342_j.jsv.2011.03.031-Figure7-1.png",
        "caption": "Fig. 7. Analysed bearing during run-up. (a) Geometrical properties of the bearing. (b) Analysed bearing-pedestal structure.",
        "texts": [
            " The radii of curvature for the rolling element that are taken into account to calculate the contact stiffness are rI1 \u00bc rb, rI2 \u00bc rb: (31) The contact deformation between the dent and the outer race is given by dD,bo \u00bc Jrj\u00fer12J\u00feR2 R\u00f0y\u00de if Jrj\u00fer12J\u00feR2 R\u00f0y\u00de40, 0 else ( (32) and the contact force in the radial direction of the ball position is given by FD,Co \u00bc kD,Cod 3=2 D,bo r\u00fe\u00f0xo xi\u00decosyj\u00fe\u00f0yo yi\u00desinyj wj cos\u00f0yj fC\u00de: (33) In this section the presented model was used to simulate the vibration response of a bearing with different faults during run-up. Whenever the fault is in contact with its mating surface, one of the equations (26)\u2013(33) is used to replace the appropriate equations for the contact force in Eqs. (13)\u2013(16). The bearing under investigation is NMB R-1240KK1, shown in Fig. 7(a), whose parameters are given in Table 1. The outer ring is assumed to be closely fitted into another aluminium ring, which represents the housing of the bearing and the under half of the aluminium ring is connected with springs to the fixed pedestal, as shown in Fig. 7(b). The aluminium ring is 3 mm thick, and is connected with 36 linear springs to the fixed pedestal. The stiffness of the connecting spring is ks\u00bc100 000 N/m. In the analysed case a simple support structure was chosen to avoid confusing the bearing vibration with the structural vibration, since the transfer path of the housing could change the vibration signal. The outer ring of the bearing and the aluminium ring is modelled with 72 finite elements. The bearing loads are assumed to be the gravitational load and the unbalanced force",
            " The unbalance of the rotor is meu\u00bc2 10 5 kg m. From the radius of the inner and outer races it is clear that the radial clearance in the bearing is c\u00bc 5 mm. The contact angle of the bearing is calculated from an equation in Ref. [18] as a0 \u00bc cos 1 1 c 2A , (34) where A is given by A\u00bc rII1i\u00ferII10 rb: (35) The initial contact angle for the analysed bearing is a\u00bc 12:23. The outer ring, the inner ring and the shaft are made from steel. The dynamic response of the bearing will be taken from point P1, which is on the top of the aluminium ring, Fig. 7(b). The geometrical properties of the local faults are shown in Fig. 8. The faults on the inner race and the ball will rotate and their position will move in and out of the loading zone in the bearing. The fault on the outer race is stationary, and the position of the dent on outer race is very important. Analyses will be made for the dent in the middle of the loading zone, at the bottom of the outer race. For the numerical solution the initial conditions and the step size are very important for a successful and economical computational solution",
            " According to the signal decomposition paradigm, the WT can be classified as the continuous WT (CWT), the discrete WT (DWT) and wavelet packet analysis. For the detection of the present bearing fault the CWT transform will be used. The damaged bearing will produce small amplitudes of vibration in the high-frequency band as the response of the bearing and the housing to the impact that is caused by the fault. This highfrequency band has to be known prior to the wavelet analysis. In the analysed case, Fig. 7(b), the high-frequency response will be at the eigenfrequency of the bearing/housing-pedestal system, which is around 8.2 kHz; the eigenfrequency of the shaft is around 11.3 kHz, although this frequency varies due to the changing position of the balls, and the first eigenfrequency of the outer ring with the aluminium ring is around 36 kHz. The existence of vibrations in these frequency bands will be used to identify the bearing faults. The classification of the bearing faults will be made based on the time interval between the repetitive vibrations in the high-frequency band"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003530_tie.2019.2905808-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003530_tie.2019.2905808-Figure1-1.png",
        "caption": "Fig. 1. A basic model of quadrotor UAVs.",
        "texts": [
            " Section II sets up the whole control system and states the control problem. Section III and IV gives details of the proposed NN-based dynamic inversion control system. Section V provides both simulation and experimental results, and gives discussions. Section VI concludes the paper and suggests future work. In this section, the dynamics of quadrotor UAV is explained first, and then the structure of conventional PID control is described in detail, finally the problem statement is presented. As shown in Fig. 1, a quadrotor UAV is an underactuated system with six degrees of freedom (DOF) [27], where E = {xe, ye, ze} and B = {xb, yb, zb} indicate inertial and body frames, respectively. x = (x, y, z)T represents the position 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. and V = (u, v, w)T represents the velocity of the quadrotor. Similarly, \u0398 = (\u03c6, \u03b8, \u03c8)T and \u03c9 = (p, q, r)T indicate the attitude and rotational velocity of the quadrotor, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000030_j.engstruct.2004.07.007-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000030_j.engstruct.2004.07.007-Figure10-1.png",
        "caption": "Fig. 10. Experimental test rig.",
        "texts": [
            " In a broad sense, the method might be considered as a filter bank structure similar to the wavelet method. The main difference is that the number of bands and the actual scaling is determined by the data. Each IMF presents a differing amount of sensitivity to the existence of damage and this is to be exploited in the analysis of the experimental results carried out in a subsequent paragraph. The experimental rig consists of two electrical machines, a pair of spur gears, a power supply unit with the necessary speed control electronics and the data acquisition system. Referring to Fig. 10, a DC machine of 1.5 kW rotates the pinion. The load is provided by an AC asynchronous machine, which is configured as a brake. The transmission ratio is 35=19 \u00bc 1:842, which means that an increase in rotational speed is achieved. The characteristics of the spur gear pair are given in Table 1. The vibration signal generated by the gearbox was picked up by an accelerometer bolted to the pinion body and the electrical signal was transferred to an external charge amplifier through slip rings. No form of signal averaging was used as the signal to noise ratio has been considered high enough"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure50-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure50-1.png",
        "caption": "Fig. 50 a CAD model; b boundary model; c simplified model; e partition region; e volume decomposition; f sub-volume regrouping; g slicing along multiple directions [70]",
        "texts": [
            " Therefore, the application of multi-directional slice algorithm in WAAM has been studied a lot. Ding studied multi-directional slicing algorithms: for complex model structures, contour boundaries were searched for and then the model was decomposed into simple 3D models [70]. These models maintain the parent-child relationship in a tree structure. Then each sub-3D model is sliced along the normal direction of the respective decomposed boundary surfaces, and finally a three-dimensional sub-component is reconstructed according to the tree structure; its effect is shown in Fig. 50. As long as the indexing machine is added to the substrate, the algorithm can allow the WAAM system to deposit materials in multiple directions, completely eliminating the support structure. The proposed algorithm has important engineering significance for the development of mature WAAM technology. Nguyen also studied the slice-based algorithm based on the direction change. The algorithm also first decomposes the complex 3D model [71]. Each sub-component obtains the centroid axis by analyzing the geometric information of two adjacent layers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure8.17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure8.17-1.png",
        "caption": "Figure 8.17. The principle of spin is used on a golf ball to create lift forces (FL) that affect ball trajectory, while spin on a basketball is primarily used to modify ball rebound to increase the chance of a made basket.",
        "texts": [
            " As the ball gradually rotates, air flow can be diverted by a seam or valve stem, making the ball take several small and unpredictable \u201cbreaks\u201d during its trajectory. So spin, and the lack of it, on a sport ball has a major effect on trajectory. spin on a projectile. The Principle of Spin is related to using the spin on a projectile to obtain an advantageous trajectory or bounce. Kinesiology professionals can use the principle of spin to understand the most successful techniques in many activities. The upward lift force created by backspin in a golf shot increases the distance of a drive (Figure 8.17a), while the backspin on a basketball jump shot is primarily used to keep the ball close to the hoop when impacting the rim or backboard (Figure 8.17b). The bottom of a basketball with backspin is moving faster than the center of the ball be- cause the ball is rotating. This increases the friction force between the ball and the rim, decreasing the horizontal velocity of the ball, which makes the ball bounce higher. In applying the spin principle, professionals should weigh the trajectory and bounce effects of spin changes. Applying spin to projectiles by throwing or striking have a key element in common that can be used to teach clients. The body or implement applies force to the ball off-center, creating a torque that produces spin on the projectile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001670_j.jallcom.2018.09.200-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001670_j.jallcom.2018.09.200-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the laser scanning pattern for all SLM built samples.",
        "texts": [
            " However, there is still a lack of research on the effect of heat treatment on the microstructure and corrosion properties of the IN718 superalloy fabricated by SLM. This work mainly focuses on the effect of solid solution and double aging heat treatment on the microstructures and corrosion properties of the IN718 superalloy. The IN718 powder was used with a size distribution of 40e60 mm. The chemical composition of the IN718 powders was given in Table 1, and IN718 samples were fabricated by the SLM machine (Renishaw AM 250, Renishaw, England) equipped with a YLR-400 fiber laser. The schematic diagram of the forming process was shown in Fig.1. The parameters of the SLM process were shown in Table 2. The specimens prepared by SLM were heat treated, and the parameters were shown in Table 3. The corrosion test was performed at room temperature, and the exposed surface area of the sample was 0.5 cm 0.1 cm. A standard saturated calomel electrode was used as a reference electrode, a platinum electrode as an auxiliary electrode, and the sample as a working electrode. The test solution was 5wt% NaNO3, and the Tafel curve was used to quantitatively analyze the corrosion resistance of IN718 superalloy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003657_j.measurement.2020.108855-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003657_j.measurement.2020.108855-Figure8-1.png",
        "caption": "Fig. 8. Geometrical interference model [31].",
        "texts": [
            " In this part, relevant researches for slewing bearings are reviewed and summarized. Related researches mainly focus on the static capacity and load distribution. Wang [30] built static models for pitch bearing considering clearances and can accurately analyze the static capacity influenced by clearance, initial contact angle and raceway curvature radius. Based on geometric interaction model, Aguirrebeitia [3132] established the theoretical model to predict the static load capacity of pitch-and yaw bearings by considering the influence of preloading, as shown in Fig. 8. Based on Hertz Formula, Yu [33] investigated the load distribution of yaw bearing. Compared with theoretical prediction, Finite element analysis can X. Jin et al. Measurement 172 (2021) 108855 carry out further researches on fatigue life analysis. Through finite element analysis, HERAS [34] obtained the stiffness curves of WTGS slewing bearings, shown in Fig. 9. Herewith, an effective tool was developed to estimating the stiffness. Plaza [35] introduced super elements into finite element model to significantly reduce the calculation cost when the accuracy can be guaranteed meantime"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002403_tmag.2017.2658634-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002403_tmag.2017.2658634-Figure1-1.png",
        "caption": "Fig. 1. The structure of machines. (a)Proposed PMV machine. (b)Regular surface PMV machine.",
        "texts": [
            " Given that double salient structure is preferred in the proposed machine, the airgap permeance function can be calculated as [10] 0 1 0 1 r 0 ( , ) [ cos( )] [ cos(P )] s s s s r r s g t Z t               (6) Only taking the working flux harmonics into account, the flux density can be expressed as 1 r 2 r 3 r ( , ) cos(P ) cos(( P ) ) cos(( P ) ) C Cs C Cs C Cs C Cs B t B t B Z t B Z t                (7) 1 r 2 r ( , ) cos(( P ) ) cos(( P ) ) H Hs H Hs H Hs B t B Z t B Z t             (8) The flux density components excited by stator and rotor magnets are given in Table I, while \u03a9 (\u03c9=Pr\u03a9) means the mechanical speed of the rotor. As observed, pole pairs and speed of the flux density due to magnets in stator and rotor separately are exactly the same, and magnetization directions of the two sets of PMs should be selected to satisfy that \u03b8Cs=\u03b8Hs=\u03b8s to maximize the working harmonic as shown in Fig. 1. TABLE I AIR-GAP FLUX DENSITY EXCITED BY STATOR AND ROTOR MAGNETS Consequent pole Halbach array Pole pairs Speed Pole pairs Speed Z-Pr -Pr\u03a9/(Z-Pr) Z-Pr -Pr\u03a9/(Z-Pr) Z+Pr Pr\u03a9/(Z+Pr) Z+Pr Pr\u03a9/(Z+Pr) Pr \u03a9 \u2013 In order to expediently analyze the EMF harmonics, winding function theory is employed as shown below: 1,3,5, ( ) cos( )s j s s j N N jP      (9) where Nj is the peak value of the jth harmonics of one phase armature winding function. The back-EMF expression can be obtained as, r r r r r 2 0 1 2 3 P P P 2 3 P P ( , ) ( ) [ sin( ) sin( ) sin( )] [ sin( ) sin( )] s s s s s g stk P s s s g stk j C j C j C Z Z j j j P P P g stk j H j H Z Z j j P P C H d e r L B t N d dt r L N B t N B t N B t r L N B t N B t e e                                          It\u2019s interesting that the proposed PMV machine can be regarded as the integration of one consequent pole PMV machine and one large slot opening, Halbach magnet array flux reversal PM machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure4.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure4.11-1.png",
        "caption": "FIGURE 4.11. The SCARA robot of Example 96.",
        "texts": [
            " Position vector of P in frame B2 (x2y2z2) is 2rP . Frame B2 (x2y2z2) can rotate about z2 and slide along y1. Frame B1 (x1y1z1) can rotate about the Z-axis of the global frame G(OXY Z) while its origin is at Gd1. The position of P in G(OXY Z) would then be at Gr = GR1 1R2 2rP + GR1 1d2 + Gd1 = GT1 1T2 2rP = GT2 2rP (4.124) where 1T2 = \u2219 1R2 1d2 0 1 \u00b8 (4.125) GT1 = \u2219 GR1 Gd1 0 1 \u00b8 (4.126) and GT2 = \u2219 GR1 1R2 GR1 1d2 + Gd1 0 1 \u00b8 . (4.127) Example 96 End-effector of a SCARA robot in a global frame. Figure 4.11 depicts an RkRkP (SCARA) robot with a global coordinate frame G(OXY Z) attached to the base link along with the coordinate frames 4. Motion Kinematics 173 B1(o1x1y1z1) and B2(o2x2y2z2) attached to link (1) and the tip of link (3). The transformation matrix, which is utilized to map points in frame B1 to the base frame G is GTB1 = \u23a1\u23a2\u23a2\u23a3 cos \u03b81 \u2212 sin \u03b81 0 l1 cos \u03b81 sin \u03b81 cos \u03b81 0 l1 sin \u03b81 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (4.128) and the transformation matrix that is utilized to map points in frame B2 to the frame B1 is B1TB2 = \u23a1\u23a2\u23a2\u23a3 cos \u03b82 \u2212 sin \u03b82 0 l2 cos \u03b82 sin \u03b82 cos \u03b82 0 l2 sin \u03b82 0 0 1 \u2212h 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure56-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure56-1.png",
        "caption": "Fig. 56 aDecompose the complex contour into some convex hulls; b one of the sub-convex hull forms its own ZIGZAG path; c the sub-ZIGZAG paths are connected to form a continuous path [75]",
        "texts": [
            " Although ZIGZAG is the most widely used filling method, when the contour is complicated, this filling method will be inefficient; especially when manufacturing the wall structure or the inner cavity structure, the generated ZIGZAG path is often inefficient and inaccurate, in order to fill complex contours. Ding proposed a method of decomposing complex contours [75]. The basic principle is to decompose complex contours into several convex hulls, and then generate corresponding sub-ZIGZAG paths for each sub-convex. Based on the geometric information of the contour decomposition, these sub-paths are connected into a continuous and complete path with only one arc extinction point, as shown in Fig. 56. The algorithm of sub-ZIGZAG works well for complex contours, but this algorithm requires the decomposition of the complex contours. The whole process requires more computation time. The algorithm does not meet the requirements of real-time manufacturing and monitoring feedback. In order to meet the requirements of real-time, the efficiency of the filling algorithm is required. Wang proposed an innovative filling algorithm, which does not require the decomposition of complex contours, and obtains a continuous ZIGZAG path [76]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002411_tsmc.2018.2866519-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002411_tsmc.2018.2866519-Figure2-1.png",
        "caption": "Fig. 2. Two inverted pendulums connected by a spring.",
        "texts": [
            " (71) Let \u03b50 (b0/a0) and E[V] = a0, then [(d(E[V]))/dt] 0. Consequently, if E[V] a0, then E[V(t)] a0\u2200t 0. In addition, one has 0 E[V] b0 \u03b50 + ( V(0)\u2212 b0 \u03b50 ) \u03c3\u2212\u03b50t. (72) Based on the results in [50] and [51], we can conclude that all the signals in the closed-loop systems are SGUUB in probability. IV. APPLICATION EXAMPLES Two examples will be presented to illustrate the effectiveness and practicability of the proposed control scheme in this section. Example 1: We consider the control of two inverted pendulum connected by a spring as depicted in Fig. 2 [47]. The equations of motion for the pendulums are described by d\u03be1,1 = ( \u03be1,2 ) dt + \u03be2 1,1d\u03c9 d\u03be1,2 = ( 1 J1 u1 + f1,2 + d1,2 ) dt + sin ( \u03be1,1 ) d\u03c9 \u03b71 = \u03be1,1 d\u03be2,1 = ( \u03be2,2 ) dt + \u03be2 2,1d\u03c9 d\u03be2,2 = ( 1 J1 u2 + f2,2 + d2,2 ) dt + cos ( \u03be2,1 ) d\u03c9 \u03b72 = \u03be2,1 (73) where (\u03be1,1, \u03be1,2) = (q1, q2) T and (\u03be1,1, \u03be2,2) T = (q\u03071, q\u03072) T with q1 and q2 are the angular displacements of the pendulums from vertical and angular rates, respectively. f1,2 = ((m1gr/J1) \u2212 (hr2/4J1)) sin \u03b71 + (hr2/4J1) sin \u03b72, d1,2 = (hr/2J1)(l \u2212 b), f2,2 = ((m2gr/J2) \u2212 (hr2/4J2)) sin \u03b72 + (hr2/4J2) sin \u03b71, and d2,2 = \u2212(hr/2J2)(l \u2212 b)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001616_j.optlastec.2018.11.014-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001616_j.optlastec.2018.11.014-Figure2-1.png",
        "caption": "Fig. 2. Laser scanning strategy.",
        "texts": [
            " Furthermore, the relationship between the processing parameters, microstructure and mechanical properties is established to provide a theoretical reference for titanium alloys fabricated by SLM. The material used in this study was a gas-atomized spherical Ti6Al4V powder with an average particle size of 38 \u03bcm, as shown in Fig. 1. The SLM process was carried out using an SLM Solution 280 HL SLM system, which employs double Yb:YAG lasers with a spot size of 90 \u03bcm and a maximum laser output power of 400W (Fig. 2a). Cubic samples with dimensions of 60\u00d710\u00d710mm were fabricated with a powder layer thickness of 30 \u03bcm, hatch spacing of 100 \u03bcm and different ranges of laser power and scan speed. The specific process parameters are presented in Table 1. The layers were scanned in separate stripes using a continuous laser mode and a zigzag pattern, which was alternated by 60\u00b0 between each successive layer as shown in Fig. 2b. Before experiment, the building chamber was evacuated to an O2 content below 50 ppm, and then filled with an inert argon atmosphere. The platform was heated to 200 \u00b0C and the temperature was maintained by conductively controlled heating elements at a set level throughout the process. Following the SLM process, the samples were cut from the substrate with spark erosion wire cutting for performance testing. Forged Ti6Al4V samples were selected, and their tensile properties were compared with those of SLM samples prepared in the optimal parameter intervals"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000472_tsmc.1981.4308713-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000472_tsmc.1981.4308713-Figure3-1.png",
        "caption": "Fig. 3. Link parameters d, a for prismatic joint.",
        "texts": [
            " In the case of intersecting joints, the direction of the x axis is parallel or antiparallel to the vector cross product Zn-I X Zn. Notice this condition is also satisfied for the x axis directed along the normal between joints n and n + 1. For the nth revolute joint when xn,, and xn are parallel and have the same direction, 0,n is at its zero position. In the case of a prismatic joint the distance dn is the joint variable. The direction of the joint axis is the direction in which the joint moves. Although the direction of the axis is defined, unlike a revolute joint, its position in space is not defined (see Fig. 3). In the case of a prismatic joint the length an has no meaning and is set to zero. The origin of the coordinate frame for a prismatic joint is coincident with the next defined link origin. The z axis of the prismatic link is aligned with the axis of joint n + 1. The xn axis is parallel or antiparallel to the vector cross product of the direction of the prismatic joint and Zn. For a prismatic joint, we will define its zero position, with di = 0, to be when xn,, and xn intersect. With the manipulator in its zero position, the positive sense of rotation for revolute joints or displacement for prismatic joints can be decided and the sense of the direction of the z axes determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003389_j.oceaneng.2020.107884-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003389_j.oceaneng.2020.107884-Figure1-1.png",
        "caption": "Fig. 1. AUV coordinate system.",
        "texts": [
            " To study the motion model of underwater robot, the motion of underwater robot is approximated to the general motion of rigid body in fluid. According to the origin of the coordinate system, the coordinate system is divided into fixed coordinate system E \u2212 \u03be\u03b7\u03b6 and motion coordinate system O \u2212 xyz. The former is defined as a fixed point on the earth, while the latter is defined as AUV. The coordinate system satisfies the right-hand Cartesian rectangular coordinate system. The positive direction is north, east and down, as shown in Fig. 1. The fixed coordinate system E \u2212 \u03be\u03b7\u03b6 describes the AUV\u2019s spatial position and attitude. \u03b7 = [\u03be \u03b7 \u03b6 \u03d5 \u03b8 \u03c8 ] is defined in a fixed coordinate system, where heading angle \u03c8 , trim angle \u03b8, heel angle \u03d5 all represent the angle of AUV motion coordinate system relative to fixed coordinate Z. Yan et al. Ocean Engineering 217 (2020) 107884 system. \u03bd = [u v w p q r] is defined in a motion coordinate system, where u, v, w are the longitudinal, transverse vertical, speeds respectively. p, q, r respectively represent the roll angle speed, pitch angle speed and heading angular speed",
            " In general, the roll motion is regarded as self-stable and the roll amplitude is very small, which can be regarded as the heel angle \u03d5 = 0 and heel angular velocity p = 0. The relationship between \u03b7 and \u03bd are expressed by the following formula: \u03b7\u0307= J(\u03b7)\u03bd (1) where J(\u03b7)= [ J1(\u03b7) 03\u22172 02\u22173 J2(\u03b7) ] (2) J1(\u03b7)= \u23a1 \u23a3 cos \u03c8 cos \u03b8 \u2212 sin \u03c8 sin \u03b8 cos \u03c8 sin \u03c8 cos \u03b8cos \u03c8sin \u03b8 sin \u03c8 \u2212 sin \u03b8 0 cos \u03b8 \u23a4 \u23a6 (3) J2(\u03b7)= [ 1 0 0 1/cos \u03b8 ] (4) J(\u03b7) is transition matrix, 03\u22172 is a 3 \u00d7 2 zero matrix, 02\u22173 is a 2\u00d7 3 zero matrix, J1(\u03b7) is linear velocity transformation matrix, J2(\u03b7) is angular velocity transformation matrix. \u03b8 and \u03c8 are Euler Angle in Fig. 1. According to the AUV model proposed by Fossen, its vector representation is M\u03bd\u0307+C(\u03bd)\u03bd + D(\u03bd) + g(\u03b7) = \u03c4 (5) M is inertial matrix, M = MRB + MA. MRB is rigid body mass matrix, MRB = diag(m,m,m,Iy,Iz). MA is additional inertia matrix, MA = diag( \u2212 Xu\u0307, \u2212 Yv\u0307, \u2212 Zw\u0307, \u2212 Mq\u0307, \u2212 Nr\u0307). m is the mass of AUV, Iy and Iz are inertial tensors, Xu\u0307, Yv\u0307, Zw\u0307, Mq\u0307 and Nr\u0307 are measurable hydrodynamic coefficients. C(\u03bd) is Coriolis and centripetal matrix, C(\u03bd) = CRB(\u03bd)+ CA(\u03bd). CRB(\u03bd) is rigid body Coriolis force and centripetal force matrix, CA(\u03bd) is hydrodynamic Coriolis force and centripetal force matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.101-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.101-1.png",
        "caption": "Fig. 17.101 Wind generator (Enercon)",
        "texts": [
            " Disadvantages of using solar energy: \u2022 It is weather dependent.\u2022 It is expensive.\u2022 Due to its efficiency it requires a lot of space. Wind Energy Wind is moving air that results from different temperature zones created by solar energy. By using wind turbines, kinetic wind energy can be used to generate electrical energy [17.29, 30]. Wind turbines consist of numerous components, including the blades, a shaft, a generator, and a tower. The shaft is connected to the blades, and rotates as the blades are turned by the wind (Fig. 17.101). It can either be connected directly or via a gear box to the generator, which converts the kinetic energy into electrical energy. The power P of a wind energy converter is proportional to the coating area of the rotor blades A and the cube of the wind speed v3. The maximal theoretic aerodynamic efficiency of an ideal wind turbine is Part C 1 7 .6 59.3% [17.31]. Today efficiencies are 38\u201350% depending on the technology used. The nominal power of a wind turbine ranges from a few watts up to 7 MW (2008)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure10.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure10.6-1.png",
        "caption": "Fig. 10.6 Adhesion and sliding zones in the case \u03b5 = \u03c3 = const",
        "texts": [
            " To distinguish between the solutions in the adhesion and in the sliding regions, we will use the symbols ea and es , respectively. Each bristle, which behaves independently of the others, is undeformed when it enters the contact patch through the leading edge x\u03020(y\u0302). Its tip sticks to the ground and, due to the skating velocity Vt between the bristle root and the road, a deflection e immediately starts to build up, along with a tangential stress t = ke. To better understand the roles played by adhesion and sliding, we refer to Fig. 10.6, where a fairly unusual pressure pattern has been depicted. 6More convenient governing equations for the sliding state are given in (10.52) and (10.53). 304 10 Tire Models At first there is adhesion, and Eq. (10.46) applies with initial condition ea = 0 at x\u03020 (point A in Fig. 10.6). A simple integration provides the behavior of the bristle deflection ea in the adhesion zone ea(x\u0302, y\u0302) = \u222b x\u0302 x\u03020 e\u2032dx\u0302 = \u222b x\u0302 x\u03020 \u03b5dx\u0302 = \u222b x\u0302 x\u03020 [ \u03c3 \u2212 \u03d5(x\u0302j \u2212 y\u0302i) ] dx\u0302 = \u2212\u03c3 (x\u03020 \u2212 x\u0302) + \u03d5 [ (x\u03020 \u2212 x\u0302)(x\u03020 + x\u0302) 2 j \u2212 y\u0302(x\u03020 \u2212 x\u0302)i ] (10.48) It is worth noting that this expression is linear with respect to \u03c3 and \u03d5. Moreover, it is not affected by the pressure distribution. The magnitude of ea is given by |ea| = \u221a ea \u00b7 ea = (x\u03020 \u2212 x\u0302) \u221a (\u03c3x + \u03d5y\u0302)2 + ( \u03c3y \u2212 \u03d5 x\u03020 + x\u0302 2 )2 (10.49) Expressions (10.48) and (10.49) simplify considerably if \u03d5 = 0, that is \u03b5 = \u03c3 = const. Line A\u2013B in Fig. 10.6 shows an example of linear growth (\u03b5 = \u03c3 ). According to (10.46), the adhesion state is maintained as far as k|ea| < \u03bc0p, that is up to x\u0302s = x\u0302s(\u03c3 , \u03d5, y\u0302) (point B in Fig. 10.6) where |t| = k \u2223\u2223ea(x\u0302s , y\u0302) \u2223\u2223= \u03bc0p(x\u0302s, y\u0302) (10.50) 10.3 Brush Model Steady-State Behavior 305 In the proposed model, as soon as the static friction limit is reached at point x\u0302 = x\u0302s , the following sudden change in the deflection (massless bristle) occurs es(x\u0302s , y\u0302) = \u03bc1 \u03bc0 ea(x\u0302s , y\u0302) (10.51) Therefore, at the transition from adhesion to sliding the deflection preserves its direction, but with a sudden reduction in magnitude (line B\u2013C in Fig. 10.6). The sliding state starts with es(x\u0302s , y\u0302) as initial condition and evolves according to (10.47). Apparently, (10.47) is a system of two nonlinear first-order ordinary differential equations. However, it can be recast in a simpler, more convenient form es \u00b7 es = ( \u03bc1p k )2 ( es \u00d7 (\u03b5 \u2212 e\u2032 s )) \u00b7 k = 0 (10.52) that is, using components e2 x + e2 y = ( \u03bc1p k )2 ex ( \u03b5y \u2212 e\u2032 y )= ey ( \u03b5x \u2212 e\u2032 x ) (10.53) which is a differential-algebraic system. Indeed, the sliding state requires \u2022 the magnitude of the tangential stress t to be equal to the kinetic coefficient of friction times the pressure (curved line C\u2013D in Fig. 10.6); \u2022 the direction of t (and hence of e) to be the same as that of the sliding velocity V\u03bc = Vr(\u03b5 \u2212 e\u2032 s). These are precisely the two conditions stated by (10.52) or (10.53). Although, in general, the exact solution cannot be obtained by analytical methods, some features of the solution are readily available. Let s be a unit vector directed like the sliding velocity V\u03bc, that is such that V\u03bc = |V\u03bc|s (10.54) or, equivalently, t = \u2212|t|s and e = \u2212|e|s. As well known, for any unit vector we have s \u00b7 s\u2032 = 0, where s\u2032 = \u2202s/\u2202x\u0302",
            "47) es = \u2212\u03bc1p k s =\u21d2 e\u2032 s = \u2212\u03bc1p \u2032 k s \u2212 \u03bc1p k s\u2032 (10.56) Combining (10.54), (10.55) and (10.56) we get V\u03bc Vr = |V\u03bc|s Vr = \u03b5 \u2212 e\u2032 s = (\u03b5 \u00b7 s)s + (\u03b5 \u00b7 m)m + \u03bc1p \u2032 k s + \u03bc1p k \u2223\u2223s\u2032\u2223\u2223m = ( \u03b5 \u00b7 s + \u03bc1p \u2032 k ) s (10.57) which shows which terms actually contribute to the sliding velocity. In most cases, the sliding regime is preserved up to the trailing edge, that is till the end of the contact patch. However, it is interesting to find the conditions that can lead the bristle to switch back to adhesion (point D in Fig. 10.6). From (10.57) it immediately arises that |V\u03bc| = 0 \u21d0\u21d2 \u03b5 \u00b7 s + \u03bc1p \u2032 k = 0 (10.58) Since s depends on the solution es of the algebraic-differential system of equations (10.53), this condition has to be checked at each numerical integration step. The governing equation (10.47) of the sliding state deserves some further discussion. The \u201cannoying\u201d term (\u03b5 \u2212 e\u2032 s)/|\u03b5 \u2212 e\u2032 s | is simply equal to \u03b5/|\u03b5| if es and \u03b5 are parallel vectors. This observation may suggest the following approximate approach to (10",
            "86) provide the complete solution for this case. Therefore, the tangential stress t at each point of the contact patch P is given by t(x\u0302, y\u0302) = { ta = \u2212tas = \u2212\u03c3k(x\u03020(y\u0302) \u2212 x\u0302)s, (adhesion) ts = \u2212tss = \u2212\u03bc1p(x\u0302, y\u0302)s, (sliding) (10.87) where s = \u03c3/\u03c3 , ta = |ta | and ts = |ts |. Actually, as in Fig. 10.10, we have assumed that, for any y, a single adhesion region (x\u0302s(\u03c3, y\u0302) \u2264 x\u0302 \u2264 x\u03020(y\u0302)) is followed by a single sliding region (\u2212x\u03020(y\u0302) \u2264 x\u0302 < x\u0302s(\u03c3, y\u0302)), as it is normally the case. However, as shown in Fig. 10.6 for a fairly unrealistic pressure distribution, it is possible, at least in principle, to have multiple regions. Summing up, we have the following features (Fig. 10.10): \u2022 the tangential stress t is directed like \u03c3 , with opposite sign; \u2022 ta grows linearly in the adhesion region; \u2022 ts follows the \u03bc1p pattern in the sliding region; \u2022 both ta and ts are not affected by the direction of \u03c3 ; \u2022 the higher \u03c3 , the steeper the growth of ta and hence the closer the transition point x\u0302s to the leading edge x\u03020"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.33-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.33-1.png",
        "caption": "FIGURE 5.33. An articulator manipulator with three DOF .",
        "texts": [
            "32 illustrates a practical Eulerian spherical wrist. The three rotations of Roll-Pitch-Roll are controlled by three coaxes shafts. The first rotation is a Roll of B4 about z4. The second rotation is a Pitch of B5 about z5. The third rotations is a roll of B6 about z6. 280 5. Forward Kinematics 5.5 Assembling Kinematics Most modern industrial robots have a main manipulator and a series of interchangeable wrists. The manipulator is multibody so that it holds the main power units and provides a powerful motion for the wrist point. Figure 5.33 illustrates an example of an articulated manipulator with three DOF . This manipulator can rotate relative to the global frame by a base motor at M1, and caries the other motors at M2 and M3. Changeable wrists are complex multibodies that are made to provide three rotational DOF about the wrist point. The base of the wrist will be attached to the tip point of the manipulator. The wrist, the actual operator of the robot may also be called the end-effector, gripper, hand, or tool. Figure 5.34 illustrates a sample of a spherical wrist that is supposed to be attached to the manipulator in Figure 5.33. To solve the kinematics of a modular robot, we consider the manipulator and the wrist as individual multibodies. However, we attach a temporary coordinate frame at the tip point of the manipulator, and another temporary frame at the base point of the wrist. The coordinate frame at the temporary\u2019s tip point is called the takht, and the coordinate frame at the base of the wrist is called the neshin frame. Mating the neshin and takht frames assembles the robot kinematically. The kinematic mating of the wrist and arm is called assembling. The coordinate frame B8 in Figure 5.33 is the takht frame of the manipulator, and the coordinate frame B9 in Figure 5.34 is the neshin frame of the wrist. In the assembling process, the neshin coordinate frame B9 sits on the takht coordinate frame B8 such that z8 be coincident with z9, and 5. Forward Kinematics 281 x8 be coincident with x9. The articulated robot that is made by assembling the spherical wrist and articulated manipulator is shown in Figure 5.35. The assembled multibody will always have some additional coordinate frames"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001713_j.mechmachtheory.2016.11.014-Figure18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001713_j.mechmachtheory.2016.11.014-Figure18-1.png",
        "caption": "Fig. 18. Finite element model for the analysis.",
        "texts": [
            " Since the values of the stresses computed by the MEPE model and computed by the model accounting the contact stiffness presented here (TCMS, Teeth and Contact Mesh Stiffness model), are very similar, the agreement of the new model with the FEM results should be as good as the agreement of the FEM results with the MEPE model. In this section, these previous studies will be complemented with the comparison of both FEM and MEPE results with those of the new TCMS calculation method based on the meshing stiffness accounting the contact deflections. The results of the same analyses expressed in terms of load sharing ratio and meshing stiffness are also compared. For this study, the ANSYS\u00a9 general purpose program has been used. Fig. 18 shows the FE model used including the pinion and the wheel in contact. The rotation of the wheel is prevented and the pinion can rotate around its axis. A torque is applied to the pinion axis, inducing a relative rotation between the pinion and the wheel, due to the tooth deflection. Elements SOLID 45 have been used to form the FE mesh, combined with elements CONTA 173 and TARGET 170 for pinion and wheel contact zones, respectively. The total number of elements and nodes is slightly different for each studied transmission, but is around 340,000 elements and 350,000 nodes, providing high enough resolution for the analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001792_j.trac.2019.05.031-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001792_j.trac.2019.05.031-Figure1-1.png",
        "caption": "Fig. 1. The amperometric enzyme biosensors response mechanisms. The first-generation biosensors consist of primarily co-substrate/co-product redox indicator. (B) The secondgeneration biosensors necessitate an artificial redox mediator. (C) The third-generation biosensors require the direct electron transfer between enzyme [1]. \u00a92016, reproduced with permission from Elsevier.",
        "texts": [
            " The difficulties of transmitting electrical signals between biological recognition elements and t, Faculty of Sciences, Ege signal transducers are the main barriers in electrochemical systems. Some unwanted phenomena such as deep suppressed electroactive prosthetic groups in the protein structures, protein denaturation and/or disapproving protein direction on the electrodes obstruct the simple electron transfer between large redox proteins and transducers. Depending on the utilized transducers, biosensors could be divided into threemain generations (Fig.1) [1]. The first-generation biosensors revolve around the electrical responses occurring through the diffusion of reaction products to the transducers. These biosensors have seen many drawbacks such as high-applied potential, which causes some changes and brings possible interference, fluctuant concentrations of the product, which brings systematic complexity and decrease in electrical currents, and finally causes detection limitations [2]. The use of mediators between the reaction products and transducers had improved the system response and caused the introduction of the second generation [3]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure8.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure8.11-1.png",
        "caption": "Figure 8.11. The kinetics of the lift and drag forces can be explained by Newton's laws and the interaction of the fluid and the object. The air molecules (\u00b7) deflecting off the bottom of the discus creates the lift (FL) and drag (FD) acting on the discus.",
        "texts": [
            " It is unknown if this improves performance from increased surface area for the hand, or that the flow through the fingers acts like a slotted airplane wing in modifying the lift created at lower speeds of fluid flow. Coaches should base their instruction on the kinematics of elite swimmers and allow scholars to sort out whether lift, drag, or a vortex (swirling eddies) modifying the flow of fluid is the primary propulsive mechanism for specific swimming strokes. There are two common ways of explaining the cause of lift: Newton's Laws and Bernoulli's Principle. Figure 8.11 shows a side view of the air flow past a discus in flight. The lift force can be understood using Newton's second and third laws. The air molecules striking the undersurface of the discus are accelerated or deflected off its surface. Since the fluid is accelerated in the direction indicated, there must have been a resultant force (FA) acting in that direction on the fluid. The reaction force (FR) acting on the discus creates the lift and drag forces on the discus. The other explanation for lift forces is based on pressure differences in fluids with different velocities discovered by the Swiss mathematician Daniel Bernoulli"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000024_s0022112072001612-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000024_s0022112072001612-Figure4-1.png",
        "caption": "FIGURE 4. The shaded region indicates the altered averaging area in the effective beat for (a) symplectic and (b ) antiplectic metachronism.",
        "texts": [
            " To gain some idea of the magnitude of this ratio we define two angular frequencies which correspond to the effective and recovery strokes. Thus, we define 0- = 2~e0-?./(0-e+0-?.), (19) where CT is equal to the average angular frequency and ce and crr are equal to the effective and recovery angular frequencies respectively. In figures 4 (a) and ( b ) we illustrate the averaging areas for the \u2018basic element \u2019 ab during the effective strokes for both symplectic and antiplectic metachronism. It is obvious from The micro-structure in ciliated organisms 11 figure 4 (a) that during the effective stroke in symplectic metachronism the cilia are close together, whereas in antiplectic metachronism the cilia are spread out. In the recovery stroke the opposite occurs, but in this case the cilia are moving much more slowly, especially in antiplectic metachronism (for symplectic metachronism CJr,. N l, for antiplectic metachronism 2 5 uJar 5 3) and in a region z3 < BL, so the weight functions w(s, t ) will be near 1. We can make some general observations about the stresslet strength S, (a = 1,2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.4-1.png",
        "caption": "Fig. 3.4 Instantaneous velocity center C and definition of its coordinates S and R",
        "texts": [
            "7) can be inverted to get u(t) = cos\u03c8(t)x\u03070(t) + sin\u03c8(t)y\u03070(t) v(t) = \u2212 sin\u03c8(t)x\u03070(t) + cos\u03c8(t)y\u03070(t) r(t) = \u03c8\u0307(t) (3.10) 3.2 Vehicle Congruence (Kinematic) Equations 51 These equations show that u(t) and v(t), despite being velocities, cannot be expressed as derivatives of other functions.1 In other words, a formula like v = y\u0307 is totally meaningless. As well known, if r = 0 any rigid body in planar motion has an instantaneous center of zero velocity C, that is a point such that VC = 0. With the aid of Fig. 3.4 it is easy to obtain the position of C of a vehicle in the body-fixed frame GC = Si + Rj (3.11) where R = u r (3.12) is the distance of C from the vehicle axis, and S = \u2212v r (3.13) is the longitudinal position of C. Quite surprisingly, R is very popular, whereas S is hardly mentioned anywhere else. The instantaneous center of zero velocity C, or velocity center, is often misunderstood. Indeed, it is correct to say that the velocity field of the rigid body is like a 1The reason is that df = cos\u03c8dx0 + sin\u03c8dy0 is not an exact differential since there does not exist a differentiable function f (x0, y0,\u03c8)",
            " However, vehicle engineers are also interested in the kinematics of the wheels, since it strongly affects the forces exerted by the tires. According to (3.3), the velocity of the center P11 of the left front wheel is given by V11 = VG + rk \u00d7 GP11 = (ui + vj) + rk \u00d7 ( a1i + t1 2 j ) (3.41) Performing the same calculation for the centers of all wheels yields V11 = ( u \u2212 rt1 2 ) i + (v + ra1)j V12 = ( u + rt1 2 ) i + (v + ra1)j V21 = ( u \u2212 rt2 2 ) i + (v \u2212 ra2)j V22 = ( u + rt2 2 ) i + (v \u2212 ra2)j (3.42) Therefore, the angles \u03b2\u0302ij between the vehicle longitudinal axis i and Vij can be obtained as (Fig. 3.4) tan(\u03b2\u030211) = v + ra1 u \u2212 rt1/2 = \u03b211 = tan(\u03b411 \u2212 \u03b111) tan(\u03b2\u030212) = v + ra1 u + rt1/2 = \u03b212 = tan(\u03b412 \u2212 \u03b112) tan(\u03b2\u030221) = v \u2212 ra2 u \u2212 rt2/2 = \u03b221 = tan(\u03b421 \u2212 \u03b121) tan(\u03b2\u030222) = v \u2212 ra2 u + rt2/2 = \u03b222 = tan(\u03b422 \u2212 \u03b122) (3.43) The tire slip angles \u03b1ij of each wheel (positive if clockwise) are given by (Fig. 3.4) \u03b1ij = \u03b4ij \u2212 \u03b2\u0302ij (3.44) It is very important to realize that even small steering angles \u03b4ij may significantly affect \u03b1ij and hence the tire friction forces. As thoroughly discussed in Sect. 2.7.2, tire kinematics can, in most cases, be conveniently described by means of the translational slips \u03c3x and \u03c3y and the spin slip \u03d5, defined in (2.55), (2.56) and (2.57), respectively. 3.2 Vehicle Congruence (Kinematic) Equations 57 According to (2.43), the rolling velocity of each wheel is equal to \u03c9ij ri , where \u03c9ij is the angular velocity of the rim and ri is the rolling radius"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001410_physreve.88.062702-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001410_physreve.88.062702-Figure4-1.png",
        "caption": "FIG. 4. Schematic picture of the swimmer configuration\u2014its surface and axis of symmetry are respectively given by S and e, with the latter\u2019s direction dictated by the swimming direction in the absence of a wall. A laboratory reference frame has Cartesian coordinates x,y,z and the position vector of the swimmer\u2019s center, a point on its surface and an external field point, relative to this frame, are respectively denoted by X , x\u2032, and x. Analogously, a point on the swimmer\u2019s surface relative to a body fixed frame with origin at the swimmer center, is denoted \u03be \u2032.",
        "texts": [
            " For the integral kernel in the case of the free-slip wall, only the image singularity is required (see, for example, Appendix B of [29]), and the Green function is given by Gslip ij (x\u2032,x) = Gij (x\u2032,x) \u00b1 Gij (x\u2032,x\u2217), (10) where x\u2217 is the mirror image of x with respect to the infinite wall, x\u2217 = x \u2212 2h z\u0302, and z is an unit vector along the z axis. The sign in (10) is taken to be positive when i = x,y and negative otherwise. The boundary condition on the surface of the swimmer, S, is a continuity of velocity, so that the fluid velocity matches the local surface velocity of the swimmer. The position of the swimmer surface \u03be in the laboratory frame can be written as \u03be = X + B \u00b7 \u03be \u2032 (Fig. 4), where X is the origin of the body frame in the laboratory frame, corresponding to the center of the swimmer, \u03be \u2032 = x\u2032 \u2212 X is the surface position in the body frame, and, following [25], B is a set of column basis vectors of the body frame. Let U and be the translational and rotational velocity of the origin of the laboratory frame X . Then the surface velocity of the swimmer in the laboratory frame is v(\u03be ) = U + \u00d7 \u03be \u2032 + B \u00b7 \u03be\u0307 \u2032. (11) The boundary condition that the velocity vector field does not slip relative to the swimmer surface deformation, 062702-4 v(x\u2032) = u(x\u2032), thus becomes uj = Ui + \u03b5ijk j\u03be \u2032 k + Bij \u03be\u0307 \u2032 j = \u2212 1 8\u03c0\u03bc \u222b S Gij (x\u2032,x\u2032\u2032)qj (x\u2032\u2032)dSx\u2032\u2032 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.14-1.png",
        "caption": "Fig. 10.14 Flapping of a gimbal rotor model showing the longitudinal and lateral gimbal rotation angles \ud835\udefd1c and \ud835\udefd1s",
        "texts": [
            " To explain this behaviour, it is convenient to express the gimbal dynamics in terms of angular motion in the non-rotating frame. The degrees of freedom then become \ud835\udefd1c and \ud835\udefd1s as in Eq. (10.10), or in the nomenclature of the FLIGHTLAB modelling, a and b (see Appendix 10A). The case is hover with input drive shaft fixed with constant rotorspeed \u03a9. The equations of motion will be formulated by deriving the relationship between the aerodynamic loading and the acceleration of a blade element, in the same way as in Chapter 3. The angular velocity of the gimbal can be written in the gimbal coordinate frame (Figure 10.14) as \ud835\udf4eg = \u2212?\u0307?1c jg + ?\u0307?1sig + \u03a9kg (10.11) The rotorspeed \u03a9 is now in the gimbal frame, compared with the articulated rotor where \u03a9 was in the hub frame, i.e. \ud835\udf4eg(art) = \u2212?\u0307?1c jg + ?\u0307?1sig + \u03a9kh (10.12) This seemingly innocuous difference has powerful consequences. Using the axes systems described in Appendix 10A, we can transform the angular velocity into blade coordinates, using the transformation for 612 Helicopter and Tiltrotor Flight Dynamics unit vectors \u23a1\u23a2\u23a2\u23a3 ig jg kg \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a3 cos\ud835\udf13 \u2212 sin\ud835\udf13 0 sin\ud835\udf13 cos\ud835\udf13 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u23a1\u23a2\u23a2\u23a3 ib jb kb \u23a4\u23a5\u23a5\u23a6 (10.13) the angular velocity of the gimbal in blade axes is then given by the expression \ud835\udf4eb = \ud835\udf14xbib + \ud835\udf14yb jb + \ud835\udf14zbkb (10.14) where \ud835\udf14xb = ?\u0307?1s cos\ud835\udf13 \u2212 ?\u0307?1c sin\ud835\udf13 \ud835\udf14yb = \u2212?\u0307?1s sin\ud835\udf13 \u2212 ?\u0307?1c cos\ud835\udf13 \ud835\udf14zb = \u03a9 (10.15) The difference with the articulated rotor can be shown to be the absence of the \u03a9 component in \ud835\udf14xb, i.e. \ud835\udf14xb(art) = ?\u0307?1s cos\ud835\udf13 \u2212 ?\u0307?1c sin\ud835\udf13 + \u03a9(\ud835\udefd1c cos\ud835\udf13 + \ud835\udefd1s sin\ud835\udf13) (10.16) Figure 10.14 illustrates the gimbal rotating in two directions, and the relevant axes systems. Note that the angular velocity in the blade axis, Eq. (10.15), contains components in the direction of blade flap (the jb axis) and normal to this (about the ib axis). This is a difference with the articulated (individual) blade modelling, where only the first effect was included. The gimbal flaps about two axes and rotates with \u03a9 as a rigid body so we did not see these effects in the single blade dynamics. These effects mean that an individual blade approach to modelling a gimbal requires that the dynamics of all blades and their couplings are included",
            " To understand the development of loads during manoeuvres, it will be useful to refer to the velocity components at a rotor-blade section; derivations are included in Appendix 10D, with descriptions of the axis systems used in the FLIGHTLAB tiltrotor models contained in Appendix 10A. Tiltrotor Aircraft: Modelling and Flying Qualities 689 Modelling for SLA \u2013 Oscillatory Yoke (Chordwise) Bending Moments These loads develop during pitch and yaw manoeuvres in airplane and conversion modes, due primarily to the significant lift forces acting in the plane of the rotor disc, on the highly twisted tiltrotor blades. For a gimbal proprotor (Figure 10.14), the three contributions to an individual blade moment (Mb) (positive up as with flapping \ud835\udefd) arise from the spherical spring (S), aerodynamics (A) and inertia (I), MbS + MbA + MbI = 0 (10.61) where, MbS = \u2212K\ud835\udefd\ud835\udefd (10.62) MbA = R \u222b 0 \ud835\udcc1(rb)rbdrb (10.63) MbI = R \u222b 0 rbm(rb)azdrb (10.64) The inertial moment can be expanded using Eq. (10.19). For the case of a proprotor oriented for airplane mode, we replace the roll rate (p) with yaw rate (r). Following the analysis of gimbal rotors earlier in this chapter, but including the spring effect, the expanded inertial moment (neglecting rate of change of gimbal tilt rate) is given by the expression MbI = 2\u03a9I\ud835\udefd[(r \u2212 ",
            "5) points out along the blade, while ybl points in the direction of rotor rotation. On the left rotor (right side viewing Figure 10A.5), ybl also points in the direction of rotation so the xbl axis points towards the rotor hub. For both right and left rotors, the zbl axes point forward. 10A.2 Gimbal Flapping Dynamics In the main body of this chapter the gimbal dynamics were represented by a rigid body rotating about three axes; \u03a9t about the output drive shaft and tilt angles \ud835\udefd1c and \ud835\udefd1s about non-rotating gimbal axes (Figure 10.14). The expression for the acceleration of a blade element was shown to have cyclic components, each with two contributions; one from the acceleration of the gimbal tilt angle, the other due to the gyroscopic effect from the tilt rate (Eq. (10.19)). Integrating the combination of the inertial and aerodynamic forces along a blade radius then gave us the dynamic equations for the tilt angles (Eq. (10.21)) from which the response to cyclic pitch could be derived (Figure 10.15). In this appendix, the blade element angular velocity and translational acceleration are derived from an individual-blade perspective, for comparison with the analysis of articulated blade flapping in Chapter 3 and Appendix 3A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000010_robot.1998.680611-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000010_robot.1998.680611-Figure1-1.png",
        "caption": "Figure 1: Single leg implementation. Reaction frame {A} is assumed to be in the same orientation as reference frame {0} so that ZR = 1.",
        "texts": [
            " We used the first strategy in the control of Spring Flamingo. 3 Virtual Actuator Implementation for a Planar Biped With Feet and Ankles We use Virtual Actuators [13] and Virtual Model Control [12], two techniques based on intuition, to implement some of the strategies of the previous section. In this section we .present the mathematics to implement virtual compssnents on Spring Flamiingo for the support leg in single support or both legs in double support, following the procedure described in [13]. 3.1 Single Leg Implementation Figure 1 shows a. simple planar, five link, four joint, serial robot model that we use to represent a single leg of our walking robot. The toe joint and link do not exist on the real robot (Figure 2). They are used to represent the point on the foot in which no torque is applied. We refer to this as the \u201cvirtual toe point\u201d. It is similar to the center of pressure on the foot or the zero moment point [16] except that it is a commanded quantity, not a measured one, and is based1 on static, not dynamic, considerations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001001_1.3453357-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001001_1.3453357-Figure6-1.png",
        "caption": "Fig. 6 Exaggerated view of roller corner and race flange interaction",
        "texts": [
            " Thus, an additional transfor\u00b7 mation from the race azimuth to flange frame is introduced. Transformation from race azimuth to race flange frame: (Trl (0, 'Y, 0)] where the angle 'Y will depend on the particular flange under consideration as shown, in an exaggerated fashion, in Fig. 5. It should also be noted that the race azimuth angle will now be defined by the relevant center of curvature of the roller corner and not by the center of roller. Let us consider a point, 0, on the locus of the center of curvatures of the roller corner, as shown in Fig. 6. For cylindrical rollers this locus will be a circle and the position vector locating 0, with respect to the roller geometric center in roller frame, is given as It will be necessary to write re in the race frame, and ultimately in the flange frame, and, hence, we recall the transformation from the roller to race frame from the preceding section. (30) Also, a vector rbrg locating the roller geometric center with respect to the race geometric center can be written in terms of the various vectors introduced in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000513_s11661-008-9566-6-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000513_s11661-008-9566-6-Figure3-1.png",
        "caption": "Fig. 3\u2014(a) Upper surface microstructure of laser deposition track and (b) an illustration of columnar crystal growth.",
        "texts": [
            " The LENS processing is essentially a dynamic process **PHILIPS is a trademark of Philips Electronic Instruments Corp., Mahwah, NJ. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, SEPTEMBER 2008\u20142239 because the heat source is continuously moving. As the laser beam moves away, the maximum temperature gradients are constantly changing direction. The growing columnar crystals are thus trying to follow the maximum temperature gradients while still maintaining their preferred 100h i direction, as shown in Figure 3, the upper surface microstructure of laser scanning track and crystal growth. This can result in changes to the crystal growth direction. The change in crystal growth direction at the melt pool center is due to the solidification front trying to keep pace with the moving laser beam. Because the crystal growth velocity attempts to keep pace with laser travel velocity, the velocity of the solidification front can be given by R \u00bc v cos h \u00bd2 where h is the angle between the scan direction and the growth direction, and v is the laser travel speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003657_j.measurement.2020.108855-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003657_j.measurement.2020.108855-Figure2-1.png",
        "caption": "Fig. 2. WTGS slewing bearings.",
        "texts": [
            " Measurement 172 (2021) 108855 Modern WTGS bearings can be divided into two types: drivetrain bearings and adjustment slewing bearings [91011], as shown in Fig. 1. Drivetrain bearings can be spherical-, cylindrical- or tapered roller types [121314], and generator bearings use coated bearing (ceramic and conductive microfibers) and hybrid bearings [15].Structures of slewing bearings in wind power industry are more complicated than drivetrain bearings, including outer/inner raceway, rollers, bolts connection and gear teeth [16]. According to number of rows and location of gears, WTGS slewing bearings can be classified into four types, as shown in Fig. 2. WTGS Slewing bearings mainly include pitch- and yaw bearing. The similarities and differences between them are as follows: (1). Similarities Slew bearings support thrust and radial loads of several thousand kilo-Newton and have large diameters of several meters, which rotational speeds are only a few R.P.M. to optimize the power, pitch/yaw motors need to be started frequently, requiring low friction and high sensitivity. Due to incomplete rotation of yaw and pitch bearings, inner and outer raceways of bearings swing in a small range of angle",
            " (2) Few relative research For Slewing bearings in wind power industry, there are limited literatures and standard methods available for failure prediction, monitoring and diagnosis, as summarized in Table 6. Under harsh operating environment, pitch- and yaw bearings usually bears large alternating loads, resulting in serious uneven distribution of contact forces. Serious failures, such as bolt breakage and raceway damage, can be observed frequently. It is urgent to establish health indicators and forecasting models to assess risk level of slewing bearings for a reasonable management, monitoring and maintenance solution. (3) Measurement As shown in Fig. 2, slewing bearings include gear and bearing. Any signal measured is a mixture from both parts. An important issue is hence to separate one from the other. But from Table 2 and Table 5, objects condition monitoring methods focus on are the raceway and rolling elements. Gear Signal is missing. Moreover, for failure analysis of slewing bearings, most of measurements were carried out in the idealized laboratory environment by implanting artificial defects. However, in operating conditions, the low frequency fault vibration signal is composed of weak nonlinear components, making great difficulties in the assessment of risk level"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003791_j.jsv.2016.01.016-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003791_j.jsv.2016.01.016-Figure10-1.png",
        "caption": "Fig. 10. A schematic model of the gearbox epicyclic test rig.",
        "texts": [
            " 9(b) are very abundant, and amplitudes at some orders turn to be smaller than the amplitudes in Fig. 8(b). For example, the amplitude at order of 99 in Fig. 9(b) is smaller than that at the same order in Fig. 8(b). Moreover, many additional components, such as the components at orders of 100 and 101, appear in Fig. 9(b) while they are totally suppressed in Fig. 8(b). In this section, in order to verify the effectiveness of the established phenomenological models, three experiments are conducted on an epicyclic gearbox test rig. A schematic model of the test rig is shown in Fig. 10. The test rig contains a two-stage epicyclic gearbox, a 3 hp motor for driving and a magnetic brake for loading. The magnetic brake is connected to the output shaft and the load can be controlled by a brake controller. The test rig also has a speed controller to control the motor rotating speed. The sun gear rotates with the input shaft connected to the rotor, the ring gear is fixed with the housing of the gearbox, three or four planet gears center on the sun gear, and the planet carrier can rotate to transmit torque to the output shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000008_tec.2005.853765-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000008_tec.2005.853765-Figure2-1.png",
        "caption": "Fig. 2. 12-slot/10-pole machine with concentrated coils. (i) Coils wound on all teeth. (a) Typical winding arrangement, (b) coil MMF vectors, and (c) phase vectors. (ii) Coils wound on alternate teeth. (a) Typical winding arrangement, (b) coil MMF detectors, and (c) phase vectors.",
        "texts": [
            " The air-gap flux-density distribution for a slotted motor is obtained by introducing a relative permeance function \u03bbrel(\u03b8) [13], such that Bairgap(r, \u03b8) = Bslotless(r, \u03b8)\u03bbrel(\u03b8). (2) Typical open-circuit field and air-gap flux-density distributions for the 12-slot and 15-slot, 10-pole motors are shown in 0885-8969/$20.00 \u00a9 2005 IEEE Fig. 1. As will be seen, analytically predicted results, from (2), are in good agreement with finite-element predictions. When each stator tooth carries a coil, the Magnetomotive force (MMF) vectors are as shown in Fig. 2 for a 12-slot/10-pole motor, the winding arrangement being AA\u2019B\u2019BCC\u2019A\u2019ABB\u2019C\u2019C (coils A and A\u2019 being of opposite priority). If only alternate teeth carry a coil, the winding arrangement is AB\u2019CA\u2019BC\u2019, the number of coils being halved while the number of turns per coil is doubled so as to maintain the same number of total series turns per phase. Consequently, the end-winding will usually be slightly longer. However, the distribution factor is unity, so that the winding factor for a motor in which only alternate teeth carry a coil is higher than that for a motor in which all the teeth are wound. From Fig. 2, the winding factors Kdpn (the product of the coil pitch factor Kpn and coil disposition factor Kdn) for the 12-slot/10-pole motors can be derived as Kdpn = sin2(np\u03c0/Ns), when all teeth are wound (3) Kdpn = sin(np\u03c0/Ns), when alternate teeth are wound. (4) For other combinations of slots and poles, winding factors can be similarly derived, and are summarized in Table II. Typical values are given in Table III, which also includes the winding factor for a 15-slot/10-pole machine. It can be seen that the winding factor for the fundamental is close to 1 for all the slot and pole number combinations, while that for the harmonics whose order is close to the number of stator slots and multiples thereof is also relatively high"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002326_j.actamat.2014.12.046-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002326_j.actamat.2014.12.046-Figure14-1.png",
        "caption": "Fig. 14. The variation of magnitudes of Ghkl and Vhkl ahead of the solidification interface in the transverse section of the molten pool with a = 0 and b = +45 .",
        "texts": [
            " With the increase in angle b from 0 to +45 , the epitaxial columnar dendrite along the (010)/[100] crystallographic orientation appears at the right toe edge and expands toward the center line of the molten pool. As shown in Fig. 13(f), when b = +45 , the epitaxial columnar dendrite along the (010)/[100] crystallographic orientation ((010)/[100] crystal) meets the epitaxial columnar dendrite along the (001)/[100] crystallographic orientation ((001)/ [100] crystal) at the center line of the molten pool. Fig. 14 shows the geometrical relationship of magnitudes of Ghkl and Vhkl along the preferred growth directions relative to those normal to the solidification interface with b = +45 . Comparing Figs. 14 and 5(b), it is obvious that the magnitude of G0 0 1 increases while V0 0 1 decreases at the left side of the molten pool. The (001)/[100] crystallographic orientation is therefore more competitive than the (0 10)/[100] crystallographic orientation at the left toe edge of the transverse section of the molten pool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.7-1.png",
        "caption": "FIGURE 2.7. Positions of point P in Example 5 before and after rotation.",
        "texts": [
            " Rotation Kinematics Example 5 Global rotation, local position. If a point P is moved to Gr2 = [4, 3, 2] T after a 60 deg rotation about the Z-axis, its position in the local coordinate is: Br2 = Q\u22121Z,60 Gr2 (2.34)\u23a1\u23a3 x2 y2 z2 \u23a4\u23a6 = \u23a1\u23a3 cos 60 \u2212 sin 60 0 sin 60 cos 60 0 0 0 1 \u23a4\u23a6\u22121 \u23a1\u23a3 4 3 2 \u23a4\u23a6 = \u23a1\u23a3 4.60 \u22121.95 2.0 \u23a4\u23a6 The local coordinate frame was coincident with the global coordinate frame before rotation, thus the global coordinates of P before rotation was also Gr1 = [4.60,\u22121.95, 2.0]T . Positions of P before and after rotation are shown in Figure 2.7. 2.2 Successive Rotation About Global Cartesian Axes The final global position of a point P in a rigid body B with position vector r, after a sequence of rotations Q1, Q2, Q3, ..., Qn about the global axes can be found by Gr = GQB Br (2.35) where, GQB = Qn \u00b7 \u00b7 \u00b7Q3Q2Q1 (2.36) 2. Rotation Kinematics 41 and, Gr and Br indicate the position vector r in the global and local coordinate frames. GQB is called the global rotation matrix. It maps the local coordinates to their corresponding global coordinates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002581_j.jmatprotec.2016.11.013-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002581_j.jmatprotec.2016.11.013-Figure15-1.png",
        "caption": "Fig. 15. Bucket prototype (a), colored maps",
        "texts": [
            " Case study A Pelton wheel bucket has been chosen for the application of the odel because of its complex geometry characterized by several urvatures. This wheel is an impulse hydraulic turbine commonly sed as high and medium heads and, recently, more attention is aid to small and mini hydro power plants (Williamson et al., 014). Hence great effort is addressed to the design of efficient mall turbines aiming to satisfy environmental issues, reliability nd cheapness. This way AM can meet the need for customization nd the reduction of material wastage in waterwheel fabrication. The bucket prototype, shown in Fig. 15a, has been fabricated ith the same system and process parameters described in the e predicted (b) and measured (c) Ra values. Section 3. For the validation of the prediction model, the half of the bucket has been divided in 34 zones and the roughness measurements have been performed by using the same measure procedure described in the Section 3 except for the form compensation of the curved surfaces: in this case an elliptical compensation has been applied in accordance with the bucket shape. The obtained measures have been graphed in the map of Fig. 15c and compared to the predicted values reported in Fig. 15b. This plot has been constructed by coloring each triangle constituting the original STL model according to the calculated Ra value. In particular the normal to the STL facet has been considered with the stratification direction to obtain the local stratification angle. The resulting Ra has been correlated to an indexed color palette. The same palette has been used to color each measurement zone. The wide range of the local stratification angle, owned by the considered geometry, allows evaluating the model responsiveness. From the comparison a good agreement emerges. The zones from F to K and O are fabricated with a local stratification angle equal to 0\u25e6. The model, for those surfaces, predicts 6 m Ra as indicated by the violet color in Fig. 15b. The experimental outcomes provided accordant values ranging from 6 m to 8 m Ra within the assessed model variability. Slightly higher local stratification angles (3\u25e6 and 5\u25e6) can be found in the bottom of the bucket (zone A): the predicted average roughness is about 11 m and the measures lie in the range 12\u201313 m. This is a little overestimation for a roughness measurement highlighting the effectiveness of the model. The zones B1 and B3 are inclined in the range 10\u25e6\u221214\u25e6 and a full correspondence between experimental and modeled values is observed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure3-1.png",
        "caption": "Fig. 3. Helical gears tooth model.",
        "texts": [
            " However, the tooth surfaces of two engaging helical gears contact on a straight line inclined to the axes of the gears. The length of the contact line changes gradually from zero to maximum and then changes from maximum to zero (see in Fig. 2). This makes the vibration characteristics of helical gears different from those of spur gears. Obviously, the mesh stiffness of helical gears cannot be calculated as same as spur gears due to the existence of helix angle. However, if helical gears are divided into some independent thin pieces whose thickness is dy (see in Fig. 3), the helical gears can be considered as a series of staggered spur gears with no elastic coupling since they are usually negligible for narrow-faced gears with low helix angles. Then the stiffness of the whole tooth can be obtained by integration along face width. That is why this method is named accumulated integral potential energy method. According to the idea mentioned above, the bending energy of any thin piece can be expressed as dUb \u00bc F2 2dkb \u00bc Z d y\u00f0 \u00de 0 Fb d y\u00f0 \u00de\u2212x\u00f0 \u00de\u2212Fah y\u00f0 \u00de\u00bd 2 2EdIx dx \u00f011\u00de where dIx \u00bc 1 12 \u00f02hx\u00de3d y represents the area moment of inertia of the section where the distance from the dedendum circle is x, the other parameters are shown in Fig. 3. Through proper simplification, the bending mesh stiffness of the thin piece is dkb \u00bc 1Z d y\u00f0 \u00de 0 3 d y\u00f0 \u00de\u2212x\u00f0 \u00de cos\u03b11 y\u00f0 \u00de\u2212h y\u00f0 \u00de sin \u03b11 y\u00f0 \u00de\u00bd 2 2Eh3xdy dx : \u00f012\u00de Then integrating the function over y, the total bending mesh stiffness can be obtained, which can be expressed as kb \u00bc Z l 0 1Z d y\u00f0 \u00de 0 3 d y\u00f0 \u00de\u2212x\u00f0 \u00de cos\u03b11 y\u00f0 \u00de\u2212h y\u00f0 \u00de sin \u03b11 y\u00f0 \u00de\u00bd 2 2Eh3x dx dy \u00f013\u00de where a1(y) is assumed as the linear change, which can be expressed as a1(y) = \u03b11 + (\u03c6 \u2212 \u03b11)y/l. l in Eq. (13) is defined as the effective contact face width of gear meshing",
            " l can be calculated as l \u00bc \u03bc cot \u03b2b\u00f0 \u00de \u03bc \u2264 L2 L L2 b \u03bc b L1 \u00fe L2 L\u2212 \u03bc\u2212L1\u2212L2\u00f0 \u00de cot \u03b2b\u00f0 \u00de L1 \u00fe L2 b \u03bc 8< : \u00f014\u00de where L2 \u00bc L tan \u03b2b \u00f015\u00de L1 \u00bc \u03b5\u03b1Pbt\u2212L2 \u00f016\u00de tan \u03b1n \u00bc tan\u03b1t cos\u03b2 \u00f017\u00de tan \u03b2b \u00bc tan \u03b2 cos \u03b1t \u00f018\u00de Pbt \u00bc pt cos \u03b1t \u00bc \u03c0mn cos \u03b2 cos \u03b1t \u00f019\u00de where Pbt is the transverse base pitch, \u03b5\u03b1 is the transverse contact ratio, \u03b2 is the helix angle, \u03b1t is the transverse pressure angle,mn is the normal module, L is the face width, and \u03b2b is helix angle on the base cylinder. According to the geometry of involute profile, d(y), h(y), x, hx can be expressed as d y\u00f0 \u00de \u00bc Rb cos \u03b11 y\u00f0 \u00de \u00fe \u03b11 y\u00f0 \u00de\u2212\u03b12\u00f0 \u00de cos\u03b11 y\u00f0 \u00de\u2212 cos\u03b12\u00bd h y\u00f0 \u00de \u00bc Rb \u03b11 y\u00f0 \u00de \u00fe \u03b12\u00f0 \u00de cos \u03b11 y\u00f0 \u00de\u2212 sin \u03b11 y\u00f0 \u00de\u00bd x \u00bc Rb cos \u03b1 \u00fe \u03b1\u2212\u03b12\u00f0 \u00de cos\u03b1\u2212 cos\u03b12\u00bd hx \u00bc Rb \u03b1 \u00fe \u03b12\u00f0 \u00de cos \u03b1\u2212 sin \u03b1\u00bd 8>< >: \u00f020\u00de where Rb is the radius of base circle, the other parameters are defined in Fig. 3. After simplifying the formula (13), the bending mesh stiffness Kb can be expressed as kb \u00bc Z l 0 1Z \u03b12 \u2212\u03b11 y\u00f0 \u00de 3 1\u00fe cos\u03b11 y\u00f0 \u00de \u03b12\u2212\u03b11 y\u00f0 \u00de\u00f0 \u00de sin\u03b1\u2212 cos\u03b1\u00bd f g2 \u03b12\u2212a\u00f0 \u00de cos\u03b1 2E sin\u03b1 \u00fe \u03b12\u2212\u03b1\u00f0 \u00de cos\u03b1\u00bd 3 d\u03b1 dy: \u00f021\u00de However, the denominator of formula (21) is indefinite integral and non-integrable, that means the precise result cannot be obtained. So in order to solve this problem, the summation method instead of integral is required. The formula (21) can be rewritten as follows kb \u00bc XN i\u00bc1 1 Z \u03b12 \u2212\u03b11 0 3 1\u00fe cos \u03b11 0 \u03b12\u2212\u03b11 0 sin \u03b1\u2212 cos\u03b1 h in o2 \u03b12\u2212a\u00f0 \u00de cos\u03b1 2E sin \u03b1 \u00fe \u03b12\u2212\u03b1\u00f0 \u00de cos\u03b1\u00bd 3 d\u03b1 \u0394y \u00f022\u00de where a1 0 \u00bc \u03b11 \u00fe \u00f0\u03c6\u2212\u03b11\u00de\u00f0i=N\u00de, \u0394(y) = l/N, and N is the number of the thin piece which the helical gears is divided into"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000434_13552541311323281-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000434_13552541311323281-Figure1-1.png",
        "caption": "Figure 1 (a) Specimen orientations; specimen geometry used for (b) tensile and relaxation and (c) creep tests",
        "texts": [
            "011 per cent B, Ni (balance). A Concept Laser \u201cLaserCusingw M1\u201d machine of inspire AG irpd was used to manufacture the test specimens. The substrates were 1.4301 steel plates. These plates were milled and cleaned with ethanol before use. Pure Argon was chosen as shielding gas, since welding of nickel-base alloys under nitrogen atmosphere is prone to increased pore formation (Schuster, 2009). To evaluate potential anisotropic material behaviour, all specimens were built in two directions, as shown in Figure 1. The z-axis is parallel to the build direction, whereas each layer is parallel to the xy-plane. Note that the angle between x-axis and xy-specimens\u2019 axis is random. The specimens used for tensile and stress relaxation tests were built as cylinders of 71mm height and 11.7mm in diameter. The cylindrical specimens used for creep tests had a diameter of 15.5mm and a height of 76.5mm. After building up the specimens by SLM, they were all cut off from the substrate plate by electrodischarge machining. As shown in Figure 1, the specimens were machined to their end contour after hot isostatic pressing (HIP), standard solution (SHT) and precipitation hardening (PHT) heat treatment at 1,1208C/2 h and 8508C/ 24 h, respectively. HIP needs to be applied to remove the remaining microcracks and voids, which would have a strong adverse effect on the mechanical integrity. Tensile tests at ambient and elevated temperature (8508C) of M10 specimens were carried out according to ISO 6892 with a 50 kN load cell at a strain rate of ,4 per cent/min",
            "The temperature was controlled and monitored directly on the sample by means of two R type thermocouples. After achieving the required temperature of 8508C, the samples were held for 3 h before commencing the test. Selective laser melting (SLM) technology L. Rickenbacher, T. Etter, S. Ho\u0308vel and K. Wegener Volume 19 \u00b7 Number 4 \u00b7 2013 \u00b7 282\u2013290 Metallurgical analysis of specimens was done on longitudinal cuts along the specimen axis.The cuttingplanewas in the centre of the specimen but random with respect to rotation along the z- resp. x-axis, as shown in Figure 1, respectively. Grinding of the specimens was started with 150 grit disk (corundum) followed by polishing with 15, 9, 6, 3, and 1mm diamond suspension. The porosity was measured optically using digital image processing. At 50x magnification areas with optically highest porosity were chosen. The porosity was measured within a reference area of 1.5 \u00a3 1.5mm2. The given values correspond to the average of three measurements. In order to reveal the grain size and morphology, the specimens were etched in Adler reagent (50ml H2O, 100ml HCl, 30 g FeCl3, 6 g (NH4)2[CuCl4]2) for few seconds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000842_robot.2006.1641979-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000842_robot.2006.1641979-Figure1-1.png",
        "caption": "Fig. 1. Motion planning for a 7-DOF manipulator: Taking a plate out of a dishwasher. (Experiment Dishwasher)",
        "texts": [
            " The third workspace, shown in Figure 9, consists of the kitchen environment; the task is to grasp a spherical object in a drawer. The average computation time was 0.7 seconds. The second workspace shown in Figure 9 shows a difficult grasping problem: An object is to be grasped in the confined space of a cabinet. Note that the initial configuration has the end-effector of the robot\u2019s arm placed under the cabinet, so that the arm has to fold to get around the cabinet. The average computation time for 100 trials in this experiment was approximately 17.6 seconds. Another difficult workspace is shown in Figure 1. Here the task is to take a plate out of the dishwasher. The dishwasher basket has highly complex geometry, consisting of about 30, 000 triangles, which makes distance computation expensive. This task was solved in an average of 4.3 seconds. Table I summarizes the results of all of our experiments. The examples presented and the fact that all test runs converged demonstrate that our new algorithm is already capable of solving typical planning problems with high reliability. When comparing the performance to other planning systems, it is important to keep in mind that our approach solves the problem of grasp selection in addition to path planning"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001737_j.addma.2016.03.006-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001737_j.addma.2016.03.006-Figure2-1.png",
        "caption": "Figure 2: EDM cut specimen model",
        "texts": [
            " Figure 1: Inconel 718 specimen orientation After the specimens were removed from the build plate, they were cut into six cross sections using a gold wire Electrical Discharge Machining (EDM) process. Wire EDM is the preferred cutting method when minimal material removal is desired. Furthermore, it aids in keeping heat affected zones from forming during machining. In order to distinguish between the beginning and end of the scan line, six different colored markers were used to mark the back sides of each specimen. Figure 2 depicts the cross sections and dimensions of each specimen after the EDM process. The specimen number, which corresponds to a certain beam power and speed, was marked numerically and graphically, with a series of white dots, to ensure proper sample identification after cutting. Table 1 lists the process parameters used for the fabrication of the Inconel 718 specimens. Once the specimens were cut, there were two orientations utilized for measuring melt pool geometries; top view and cross section views"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000827_j.engfailanal.2014.04.005-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000827_j.engfailanal.2014.04.005-Figure3-1.png",
        "caption": "Fig. 3. Schematic of spur gear when z < 42 (a) and z > 42 (b).",
        "texts": [
            " According to the knowledge of prin- ciple of mechanics, the radius of gear base circle rb and root circle rf can be calculated as: rb \u00bc mz 2 cos\u00f0h\u00de; rf \u00bc mz 2 h a \u00fe c m \u00f011\u00de where m, z, h represent module, number of teeth and pressure angle, respectively. h a, c are addendum and tip clearance coefficients. If h a \u00bc 1, c \u00bc 0:25, h \u00bc 20 , when rb is equal to rf, the number of teeth z 42 can be obtained by using formula (11). The potential energy method assumes the gear tooth as a variable cross-section cantilever beam which is fixed on the gear base circle. In this way, the potential energy stored in the part between base circle and root circle (the grid line portions as shown in Fig. 3) will be ignored. This defect must be corrected for further accurate calculation of time varying mesh stiffness. of the coefficients of Eq. (9). If the number of teeth is less than 42 (see in Fig. 3(a)), rb > rf the energy stored in the part between base and root circles must be added on the original foundation. If the number of teeth is more than 42 (see in Fig. 3(b)), the energy stored in the part between base circle and root circle must be subtracted on the original foundation. Therefore, when the number of teeth is less than 42, the formula of bending potential energy Ub (see in formula (2)) can be corrected as Ub \u00bc Z d 0 \u00bdFb\u00f0d x\u00de Fah 2 2EIx dx\u00fe1 Z rb rf 0 \u00bdFb\u00f0d\u00fe x1\u00de Fah 2 2EIx1 dx1 \u00f012\u00de where Ix1 represents the area moment of inertia of the section where the distance from the tooth root is x1. Form the geometry of involute profile, d, x, hx can be expressed as d \u00bc rb\u00bdcos a1 \u00fe \u00f0a1 \u00fe a2\u00de sina1 cos a2 x \u00bc rb\u00bdcos a \u00f0a2 a\u00de sina cos a2 hx \u00bc rb\u00bd\u00f0a2 \u00fe a\u00de cos a sina 8>< >: \u00f013\u00de After simplify the formula (12), the bending mesh stiffness Kb can be expressed as kb \u00bc 1 Z a2 a1 3f1\u00fe cos a1\u00bd\u00f0a2 a1\u00de sin a cos a g2\u00f0a2 a\u00de cos a 2EL\u00bdsina\u00fe \u00f0a2 a\u00de cos a 3 da\u00fe Z rb rf 0 \u00bd\u00f0d\u00fe x1\u00de cos a1 h sina1 2 EIx1 dx1 ",
            " Modeling of rotor-bearing system The typical flexible rotor-bearing system to be analyzed consists of a rotor composed of discrete disks, rotor segments with distributed mass and elasticity, and discrete bearings. Such a system is illustrated in Fig. 8. 3.1.1. The dynamic model of elastic axis According to the principle of finite element method, dividing the rotor into a number of beam elements (see in Fig. 9(a)). The stiffness matrix, mass matrix and the gyroscopic matrix of two-node beam elements is shown in Fig. 3(b) are deduced [22]. Each node of the beam elements has six degrees of freedom x, y, z are displacements in X\u2013Y\u2013Z, and hx, hy, hz are rotation angles of the three directions, respectively. The node displacements of the rotor element can be expressed as qe \u00bc \u00bdxA yA zA hAx hAy hAz xB yB zB hBx hBy hBz T \u00f027\u00de The energy of the complete element is obtained by summing the elastic bending and kinetic energy expressions together. E \u00bc 1 2 _qeT Me T \u00feMe R _qe \u00fe 1 2 Jpx2 \u00fex _qeT Geqe \u00fe 1 2 qeT Keqe \u00f028\u00de The Lagrange equation of motion for the finite rotor element using Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003992_1350650117711595-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003992_1350650117711595-Figure9-1.png",
        "caption": "Figure 9. Normal and modified gear tooth models: (a) standard tooth; (b) modified tooth (Source: Imrek54).",
        "texts": [
            "51 Modifying the width of plastic gear tooth Tooth width modification in plastic gears is another technique employed by some researchers.53\u201355 It was found that the maximum Hertzian surface stress occurred in the region where single tooth pair was in contact. The high surface stresses caused thermal damage in single tooth pair contact region due to the accumulation of heat on the tooth surface. To overcome this thermal damage, the surface stress was decreased by increasing the width of the gear tooth in the single tooth contact region as shown in Figure 9. The increasing width of the gear tooth resulted in the reduction of the tooth load by an amount of F/b (i.e. the normal tooth load per unit face width) (N/mm) in the single tooth contact region. Thus a homogeneous load distribution was achieved throughout the gear tooth profile. The modified gears were tested at different torques and a constant rotational speed and their performance was compared with the unmodified gears. Results showed that the thermal damage was delayed for the gears with modified tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000088_027836499101000106-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000088_027836499101000106-Figure1-1.png",
        "caption": "Fig. 1. Coordinate systems of RM 501 robot.",
        "texts": [
            " The robot has five de- grees of freedom, and its maximum repeatability is specified as \u00b1 0. 5 mm. The coordinate measuring machine (CMM) is a computer-controlled machine equipped with an MP-30/35 processor and HP 9000 series 300 computer with a 9153 disk drive. The accuracy of this CMM is about 0.006 mm. Therefore the measurement device is adequately accurate for this study. For simplicity, joints 4 and 5 of the robot are locked (fixed) in this experiment. Its coordinate systems along with kinematic parameters are shown in Figure 1, and their corresponding nominal values are given in the third column of Table 1. Because it is difficult to precisely locate the probe tip of the CMM to the center of the end effector, as shown in Figure 2, four measurements are taken on plane A and the other four on the surface of cylinder, then the center point C of the end effector is calculated. This procedure is repeatedly used to obtain well-spaced 102 center positions of the end effector over the work volume of the robot. The resulting raw data are then used to estimate parameter values of the robot kinematic model and to study the implications of the defined observability measure in robot calibration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000765_626837-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000765_626837-Figure1-1.png",
        "caption": "FIG. 1.-Interference structure type 1, consisting of interlocking domes and basins.",
        "texts": [
            " (v) The orientation of the outcrop surface. The basic geometry of the compound structure appears to be controlled by features (i) and (ii), and there seem to be three fundamental types of complex structure. The geometry of these three main types may be modified in various ways by features (iii) and (iv), and the nature of the shape of the surface outcrop pattern also depends on factor (v). TYPE 1. WHERE THE G DIRECTION OF SECOND FOLDS LIES CLOSE TO AXIAL PLANE OF FIRST FOLDS The first fundamental type of combined structure is shown in figure 1. In figure 1, A, simple cylindroidal anticlines and synclines trend east-west across the block, and in figure 1, B, a second set of shear folds (structures developed by differential move- ment along closely spaced shearing planes; see Becker, 1882) have been superimposed on them. The main features of the resulting structure have been simply analyzed in figure 2, where the traces of two sets of folds have been superimposed. It will be seen that there are various possible combinations of the two sets of structures: anticlines intersect anticlines at position (i), synclines in- This content downloaded from 128",
            " In a similar way, where the two synclines cross the resulting mutual depression in both folds develops a basin, and where anticlines cross synclines the result is a depression in the anticlinal axis and a culmination in the synclinal axis. The resulting combination, if well developed, consists of a series of interlocking domes and basins (Weiss, 1959), each basin surrounded by four domes and each dome surrounded by four basins. The shapes of the domes and basins depend on the relative intensites of the two foldings and on the relation of the limbs of the first folds to the movement direction that produced the second. Figure 1, B, illustrates the effect on the dome-basin pattern of a change in the intensity of the shear component of the second folds across the model. On the east side of the block the first structures are more intense than the second structures, and the domes and basins tend to be elongated in a direction parallel to the first-fold traces, whereas on the west side of the block where the second structures are most well developed, folds and the domes and basins are elongated in a north-south direction. The shape of the domes and basins is, however, also controlled by the angle between the second-fold movement direction and the limbs of the first folds. Where this angle is small (e.g., on the southern limbs of first-fold synclines shown in fig. 1, B), the amplitude of the second fold on this limb is small, while if it should happen that the second-fold a direction lies on the firstfold limb, no folds can develop (Ramsay, 1960). If this angle is large, then second folds of large amplitude are developed (e.g., on the northern limbs of the first-fold synclines shown in fig. 1, B). The linear structures in such models are somewhat complex, those of first-fold generation are deformed by the second-shear movements, and although variable in orientation they are always contained in a plane controlled by the initial orientation of the lineation and the a direction of the second folds. The second-fold axes and parallel lineations are strictly controlled by the orientation of the limbs of the first folds. For example, where there are two principal directions of bedding planes (fig. 1, A, the first-fold limbs), two main directions of second-fold axes are developed, initially located at the intersection of the first-fold limbs with the shear plane (ab) of the second folds (Weiss and McIntyre, 1957; Ramsay, 1958, 1960; Weiss, 1960). The flattening component of the second deformation modifies the geometry considerably (fig. 1, C). It produces a decrease in wavelength in the second-shear folds and an increase in their amplitude together with a change in shape of the first folds. Both sets of folds become tighter, and therefore the domes and basins are seen to be more acute. The first-fold axes are more strongly deformed and the plane in which they lie is positioned closer to the axial planes of the second folds. The change in orientation is related to the amount of compression, and it might be possible to make quantitive estimates of any variation in flattening across the second folds (Ramsay, 1961, fig",
            " However, I think it can be shown that, although the ment of the local principal compression direction. At any one point, however, since there can never be more than one direction of maximum principal stress (Nadai, 1950), there can never be more than one set of folds with axial planes arranged normal to this direction. CONCLUSIONS 1. The complex surface shape produced by the interference of one fold system on another depends on the relationship between the second-phase movement direction and TABLE 1 Type Type 1 (fig. 1) Type 2 (fig. 8) Type 3 (fig. 11) Relationship of Second-Fold Movement Direction to First Folds Lies between or on first-fold limbs Does not lie between first-fold limbs Does not lie between first-fold limbs Angular Relation of FirstFold Axes to Second- Fold Axial Plane Any angle Moderate to high angle Low angle Type Type 1: (i) (ii) (iii) Type 2 Type 3 TABLE 2 Relationship of SecondFold Movement Direction to First Folds Interference Patterns Figure 15, A Regular closed interlocking forms or \"eyes\" (fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure5.15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure5.15-1.png",
        "caption": "Figure 5.15.1. Turning geometry at very low speed (negligible lateral acceleration).",
        "texts": [
            "15 Turning Geometry When a vehicle moves in a curved path at a very low speed the lateral acceleration is very small, so the body roll and the axle lateral forces are negligible. Thus the wheel angles are those arising geometrically, not from the need to produce lateral force. There may, however, be opposing slip angles on the two ends of an axle, giving zero net force. For a normal vehicle with front steering, to turn with zero slip angles means that the turning center C must be in line with the rear axle (Figure 5.15.1). The Suspension Characteristics 293 front wheels must be steered by different amounts, the inner wheel more, in order for both of them to have zero slip angle. The difference between the steer angles for both wheels to have zero or equal slip angles equals the Langensperger angle \u03bb subtended at the turning center by the axle. This is known as the Ackermann steering concept, although actually invented by Langensperger, which we would expect to be desirable for low-speed maneuvering to avoid tire scrub, squeal and wear",
            " Moving the rack forward or backward to change the tie-rod angles can be a useful way to adjust the Ackermann factor, the most important single variable being the angle between the tie-rod and the steering arm in plan view, the Ackermann factor being proportional to the deviation of this angle from 90\u00b0. With straight tie-rods, to obtain an Ackermann factor close to 1.0 may require the projected steering arm intersection point to be at about 60% of the distance to the rear axle. Suspension Characteristics 295 The attitude angle \u03b2 is the angle between the vehicle centerline and the velocity vector, which is perpendicular to the radial lines shown in Figure 5.15.1, in which it may be seen that at low speed (negligible lateral acceleration) the attitude angle \u03b2r is zero, and at the center of mass Hence the attitude angle is negative; however, it is positive-going as lateral acceleration develops. The two ends of the vehicle corner at different radii (Figure 5.15.1). This is one reason why four-wheel-drive vehicles need a center differential or front overrun clutch. At low speed, with zero slip angles, The difference of radii is known as the offtracking: where R is the turn radius of the center of mass. The offtracking can be about 0.4 m for cars, leading to occasional curbing of the rear wheels, or worse. It is more problematic for long trucks, and especially for trailers. It can be obviated by fourwheel steering as is now available for some cars. The low-speed mean steer angle will here be called the kinematic steer angle: from the axle line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.56-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.56-1.png",
        "caption": "Fig. 17.56a,b Construction of (a) commutator small power motor ferromagnetic DC motor for 12 V: 1 \u2013 magnet part, 2 \u2013 iron interference, 3 \u2013 armature, 4 \u2013 commutator with brushes; (b) universal motor with movement of the brush axis: 1 \u2013 commutation axis",
        "texts": [
            "004 K\u22121) has to be considered as well as the deviation of the demagnetization characteristic in a high negative field strength; it has to be assured that at low ambient air temperature (\u221220 \u25e6C) the start-up short-circuit current does not result in permanent demagnetization. Universal Motors These are motors which can work in both DC and AC systems. Nowadays they mostly use onephase alternating current, especially in household appliances. The major advantage of these machines is that the rotating speed is not bound to the network frequency. For example, a vacuum cleaner that works at a rotating speed of up to 25 000 min\u22121 can achieve a very high power-to-weight ratio. The universal motor is setup as shown in Fig. 17.56b. The unloaded speed is limited by windage and friction. Because of their capability to operate at high speeds, universal motors of a given horsepower rating are significantly smaller than other kinds of AC motors operating at the same frequency. Universal motors are ideal for home devices such as hand drills, hand grinders, food mixers, routers, and vacuum cleaners. Unfortunately the lifetime of such motors is limited by the lifetime of the brushes, which is about 2500 h. Power Electronics is basically used to transform one electrical system into another"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002625_tii.2018.2792002-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002625_tii.2018.2792002-Figure1-1.png",
        "caption": "Figure 1. 6 DOF Sta\u0308ubli TX90L industrial robot mounted on linear axis [8].",
        "texts": [
            " Time optimal motion planning for robotic systems and time optimal path following have been topics of intensive research [2]\u2013[6]. Two of the earliest works on path following are [1], [7]. None of these approaches proposed so far have taken into account the continuity required to respect technological limits, which is the vital prerequisite that allows the time optimal motions to be actually carried out by a real robot. This is addressed in the present paper. As an example consider the redundant 7 DOF manipulator in Fig. 1, which will be used in this paper as a use case. It consists of a 6 DOF industrial robot (Sta\u0308ubli TX90L) mounted on a linear axis. The EE is required to move along an ellipse as A. Reiter, A. Mu\u0308ller and H. Gattringer are with the Institute of Robotics, Johannes Kepler University Linz, Altenbergerstra\u00dfe 69, 4040 Linz, Austria. E-mail: {alexander.reiter,a.mueller,hubert.gattringer}@jku.at shown in Fig. 1. The tool axis is required to stay perpendicular to the ellipse, but the EE can freely rotate about the tool axis. This corresponds to a five axis manipulation task, such as grinding, milling, spray painting, or gluing. The robot is operated with a model-based control scheme consisting of a nonlinear feed-forward and linear feedback control. A time optimal solution was computed (with the method presented later in this paper), where the joint trajectories are required to be C2 continuous, i.e. twice continuously differentiable",
            " Joint space decomposition was originally introduced in [21]. Therein, the joint space C is considered as the product C = Cr \u00d7Cnr of two subspaces with dim Cr = r and dim Cnr = m. Coordinates qr \u2208 Cr are the redundant (or primary), and qnr \u2208 Cnr are the non-redundant (or secondary) coordinates. In particular, for redundant manipulators comprising a nonredundant serial robot for which a closed-form IK solution is known, the coordinates separation is straightforward. For example the 6 DOF industrial robot as part of the redundant 7 DOF manipulator in Fig. 1 possesses a closed form IK solution. In this case, the forward kinematic mapping (1) splits into the part f1 (q1) due to the linear axis, with joint space Cr, and the forward kinematics f2 (q2)\u25e6 \u00b7 \u00b7 \u00b7 \u25e6f7 (q7) of the 6R manipulator, with joint space Cnr. In general, the mappings fi can be arbitrarily associated to the redundant and nonredundant part. Then, however, the IK problem for the nonredundant kinematic chain will have to be solved numerically. Accordingly, the Jacobian J in the velocity forward kinematics mapping (2) is decomposed as Jr \u2208 Rl,r and 1551-3203 (c) 2017 IEEE",
            " For the decomposition with q>r = (q2, q4) the Jacobian Jnr is singular in the initial configuration. JSD switching algorithms that choose a suitable separation and thus avoid algorithmic singularities may be considered. The optimization problem with q>r = (q3, q4) does not converge within 1000 iterations. 1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Fig. 1 shows a Sta\u0308ubli TX90L industrial robot that is mounted on a linear axis. This example has been discussed in the introduction section. The goal is to determine joint trajectories such that a prescribed elliptic EE path is tracked in a minimum time rest-to-rest motion while the last axis of the spherical wrist (tool axis) is required to stay perpendicular to the ellipse (the EE is free to rotate about this axis). The path is defined in closed-form in terms of a path parameter s \u2208 [0, 1]. The joint trajectories are required to be continuously differentiable up to four times. The manipulator depicted in Fig. 1 consists of a serial chain with one prismatic joint and six revolute joints, i.e. C = R\u00d7T6. The corresponding joint coordinate vector is q> = (q1, . . . , q7), and n = dim C = 7. The EE pose is described by coordinates zE = (RIE, rE) \u2208 SE(3), and the workspace is W \u2282SE(3), m = dimW = 6. Thus, according to [29], the manipulator is considered kinematically redundant with degree (n\u2212m) = 1. The taskspace T is of dimension l = dim T = 5 as the EE position and only the rotation about two axes are considered",
            " 8 to 10 show the optimal C4 time evolutions of the path parameter s, the joint angles q and the motor torques \u03c4 , respectively, that were obtained with JSD. Note that the axes of all joint quantities are normalized w.r.t. their respective limits as are the time axes w.r.t. tf. The visible steps in the motor torques in Fig. 10 are again due to Coulomb friction effects, i.e. they occur at sign changes of the corresponding joint velocities, c.f. Fig. 9. The C4 trajectory obtained using JSD was experimentally verified using the robot depicted in Fig. 1 that uses PD joint control with feed-forward torques. The recorded lag error shown in Fig. 11 is deemed negligible for most applications, therefore the trajectory planning result is admissible. Note that these results heavily depend on the accuracy of the model used to compute the feed-forward torques by means of inverse dynamics. Therein, knowledge of accurate model parameters is crucial. Details about the identification process for the robot considered in this example are found in [41]. In this paper, the time-optimal path tracking problem for kinematically redundant manipulators was formulated as an NLP problem that is solved with a multiple shooting method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure13-1.png",
        "caption": "Fig. 13. Tooth contact areas and limits.",
        "texts": [
            " When akj, ak0j0 , {e} and P are known, {F} and d can be calculated by solving the Eqs. (17)\u2013(19) with the Modified Simplex Method of mathematical programming principle. Then tooth contact pattern can be obtained by drawing contour lines of {F}. Since gear transmission has a very high efficiency (about 95\u201398%), friction between the contact tooth surfaces is ignored in LTCA. P \u00bc Transmitted Torque=rb \u00f020\u00de A tooth usually has one tooth engagement position (single pair tooth-contact area as shown in Fig. 13) and two teeth engagement position (double pair tooth-contact area as shown in Fig. 13) when it rotates in one meshing period. This engagement position is given by a parameter in the program developed for LTCA. Fig. 8(a) is an image of two pairs of teeth engagement. When to perform LTCA of two pairs of teeth with AE, ME and TM, akj, ak0j0 and {e} are built at the two places of the two pairs of teeth as shown in Fig. 8(a) with s at the same time. Then they are submitted into Eqs. (17)\u2013(19) to calculate {F} and d. In this time, {F} includes loads shared by tooth 1 and tooth 2. Tooth load-sharing rate can be calculated when loads at all the contact points on the reference face of tooth 1 are summed and loads at all the contact points on the reference face of tooth 2 are summed according to the results of {F}",
            " 14 and gearing parameters such as tooth number, module, pressure angle, profile-shifting coefficients. This software is also suitable for a pair of high contact ratio gears when addendum coefficient is inputted. Step 2: Input position parameter of teeth engagement Engagement position of a tooth from engaging-in to engaging-out is expressed as \u2018\u2018a position parameter\u2019\u2019. When value of this position parameter is given continually, engagement position of the tooth from engaging-in to engaging-out can be determined continually. Of course, the inner limit and outer limit positions as shown in Fig. 13 can also be determined by this parameter with special values. Before LTCA and strength calculations are performed, tooth engagement position must be determined by giving value to this parameter. Step 3: Input FEM mesh-dividing parameters for the gears Some parameters are used to control FEM mesh-dividing pattern of the gears. That is to say, to determine where should be fine divided and where should be roughly divided. Usually, tooth contact areas and tooth root are fine divided. FEM mesh-dividing pattern of the gears can be changed simply through changing values of these FEM mesh-dividing parameters",
            " Rademacher [15] investigated the relationship among tooth contact length, quantity \u2018\u2018Q\u2019\u2019 of lead crowning and loaded torque by a lot of experimental measurements and some theoretical calculations. Rademacher\u2019s experimental results are used here to compare with the results calculated by the FEM presented in this paper. Figs. 10 and 11 are relationships between tooth contact length and the loaded torque. Rademacher measured these relationships using one spur gear with lead crowning Q = 20 lm and the mating gear without crowning. Parameters of this pair of spur gears are given in Fig. 10. Fig. 10 is the tooth contact length measured in single pair tooth contact area as shown in Fig. 13. It is expressed as 2a. 2a is also calculated by FEM in this paper when the gears engage at the pitch point. Calculated results are compared with Rademacher\u2019s experimental results in Fig. 10. Fig. 11 is the tooth contact length measured in double pair tooth contact area as shown in Fig. 13. It is expressed as 2a 0. Since there are two \u2018\u2018double pair tooth contact area\u2019\u2019 (one area is near the tip and the other is near the root) on tooth surface as shown in Fig. 13 for gears having contact ratio in the range 1 < e < 2, tooth contact length 2a 0 in the two areas are calculated by FEM when the gears engage at the middle of the double pair tooth contact areas. Fig. 11 is the comparison of 2a 0 between FEM results and Rademacher\u2019s experimental results. Rademacher\u2019s calculation results are also given in Figs. 10 and 11. From Figs. 10 and 11, it is found that FEM results are well agreement with Rademacher\u2019s experimental results. Fig. 12 is FEM results of the maximum surface contact stresses obtained at the same time when FEM calculations are performed",
            "04 misalignment error on the plane of action, machining error as shown in Figs. 2 and 15 microns lead crowning are considered together in the calculations. Calculation results of the six cases are given in the following. For gears having contact ratio in the range 1 < e < 2, ISO standards calculate the nominal contact stress at the pitch point at the first, then converts contact stress at the pitch point to the contact stress at the inner limit of single pair tooth contact on the pinion or wheel as shown in Fig. 13 by using the single pair tooth contact factors ZB (Pinion) or and ZD (Wheel), finally use the converted contact stress for surface contact strength calculation. JGMA standards use tooth contact stress at the pitch point for surface contact strength calculation. For the pair of gears as shown in Table 1, LTCA and SCS calculations are performed at outer limit and inner limit of the single pair tooth contact area when no ME, AE and TM are considered. Figs. 21 and 22 are contour lines of calculated SCS distributed on the reference face as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001104_tmag.2012.2201493-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001104_tmag.2012.2201493-Figure2-1.png",
        "caption": "Fig. 2. Cross-section lamination of prototype machine.",
        "texts": [
            " During the machine analysis, the utilizing of this technique can be summarized as follows: the machine is firstly solved in the finite element (FE) model under full load conditions, then the permeability of each element is fixed and used to resolve the model linearly without electric loading, similar to the conventional open-circuit. In this case, 0018-9464/$31.00 \u00a9 2012 IEEE the \u201copen-circuit\u201d characteristics can be calculated accounting for the influence of electric loading, i.e., magnetic saturation on load. The analysis method and results are validated by the experimental results of the prototype machine, which is illustrated in Table I and Fig. 2. The analyzed prototype machine, which is designed to be used in a power steering system, has relatively small cogging torque (Fig. 3) because it has a ten pole-12 slot combination (fractional-slot), optimal pole-arc to pole-pitch ratio and a shaped rotor [24]\u2013[27], [35]. However, its rotor is still step skewed by four steps of 1.5 mechanical degrees, i.e., one slot pitch, to guarantee that the output torque smoothness requirements are still satisfied even with the influence of manufacturing tolerances"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000987_j.engfailanal.2014.11.018-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000987_j.engfailanal.2014.11.018-Figure8-1.png",
        "caption": "Fig. 8. Dynamic model of a spur gear pair.",
        "texts": [
            "2 Hz, which are denoted by f1 and f2, respectively, and gear meshing frequency fe is equal to 916.7 Hz, meshing frequency of the belt wheel with 32 teeth fb is 533.3 Hz. In order to investigate the fault features of a cracked gear pair, it is necessary to consider the dynamic characteristics of the geared rotor system. Based on Ref. [2], a FE model of a geared rotor system is established according to the size of the test rig (see Fig. 7). Dynamic model of a spur gear pair formed by gears 1 and 2 is shown in Fig. 8 where the typical spur gear meshing is represented by a pair of rigid disks connected by a spring-damper set along the plane of action, which is tangent to the base circles of the gears. O1 and O2 are their geometrical centers, X1 and X2 the rotating speeds, rb1 and rb2 the radii of the gear base circles, respectively. e12(t) denotes non-loaded static transmission error which is formed solely by the geometric deviation component. Assuming that the spur gear pair studied in the paper is perfect, non-loaded static transmission error e12(t) will be zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure24.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure24.11-1.png",
        "caption": "Fig. 24.11 The third design: \u2018Desire\u2019",
        "texts": [
            " This container comprises a tissue paper chamber and six compartments for users to contain and sort various cookies. The transparent biscuit container lid allows users to see the cookies inside the container without opening it. As the white arrow shows, users can rotate the compartment around the tissue paper chamber to search for cookies they desire. Each of the individual compartments can be taken out easily by simply lifting it upward. Both biscuit container lid and tissue paper chamber lid are snap-fit. The tissue paper chamber lid is further customized with fruit scent. The third design, \u2018Desire\u2019 (see Fig. 24.11), is a snap-fit container with chocolate shape and is made of brown matte plastics. There is a stickman, which is a tissue paper container, lain on the top of \u2018Desire\u2019. The happy and bright smile on the stickman may cheer users with some positive emotions. Users can play with the stickman and have more interactions with their companion. The tissue paper 24 Consumer Goods 717 container has two choices of scents, which are chocolate and milk. A temporary waste storage, hidden at the bottom of the container, is designed for users to throw their waste easily and conveniently"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002352_1077546317716315-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002352_1077546317716315-Figure2-1.png",
        "caption": "Figure 2. An analytical model of a RB with a LOD on its races.",
        "texts": [
            " Comparisons of the simulation results from the presented model and previous models considering sharp edges show the superiority for the presented model. The results show that the proposed model can be used to establish the relationship between the vibration characteristics and LOD edge shapes, which can provide some guidance for the incipient LOD detection and diagnosis for the RBs. Some examples for the LOD on the bearing race are given in Figure 1. To investigate vibration characteristics of a lubricated RB with a LOD on its races, the roller\u2013race contact deformation is lumped to a springdamping element, as shown in Figure 2, which is partially based on the assumptions presented by Sunnersjo\u0308 (1978). Here, the outer race is fixed in a rigid support, and the inner race is fixed rigidly with the shaft. The proposed model could describe the time-varying impact force (TVIF) caused by the LODs with different edge shapes. Based on the experimental results in Branch et al. (2013), the LOD sharp edges will be changed to some cylindrical-likely surfaces due to rollers\u2019 impacts, as shown in Figure 3, where the dash and solid lines represent the sharp and cylindrical edges, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure7-3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure7-3-1.png",
        "caption": "Fig. 7-3 d-axis aligned with the rotor flux; stator and rotor current vectors are shown for definition purposes only.",
        "texts": [
            " 7-1 UNDERSTANDING DFIG OPERATION Prior to writing dynamic equations, we will describe the DFIG operation by first assuming steady state and neglecting all parasitic, such as UNDERSTANDING DFIG OPERATION 111 stator and rotor leakage inductances and resistances. We will assume the number of turns on the stator and the rotor windings to be the same. This operation is described in terms of dq-axis, as compared with the steady-state analysis in Reference [1], which was described without the help of dq-axis analysis. In this analysis, we will assume that the d-axis is aligned with the rotor flux-linkage space vector such that the rotor flux linkage in the q-axis is zero. This is shown in Fig. 7-3. It should be noted that having neglected the leakage fluxes, the fluxlinkage in the rotor d-axis is the same as the stator flux in the d-axis (refer to Eq. 3-19, Eq. 3-20, Eq. 3-22). We will write all the necessary equations in steady state under the assumptions indicated earlier and where P and Q inputs are defined into the stator and the rotor. Using the equations in Chapter, the following equations can be written. Stator Voltages vsd d sq sq= \u2212 = =\u03c9 \u03bb \u03bb0 0( )since (7-1) vsq d sd= \u03c9 \u03bb (7-2) v V vsq d sd s sd= = \u2261 =\u03c9 \u03bb 2 3 0\u02c6 ( ),constant since (7-3) where V\u0302s is the amplitude of the stator voltage space vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure2-6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure2-6-1.png",
        "caption": "Fig. 2-6 Space vector representation of mmf. (a) (b)",
        "texts": [
            " (2-19) shows that the mutual inductance and hence the flux linkages between the stator and the rotor phases vary with position \u03b8m as the rotor turns. 2-6 REVIEW OF SPACE VECTORS at any instant of time, each phase winding produces a sinusoidal fluxdensity distribution (or mmf) in the air gap, which can be represented by a space vector (of the appropriate length) along the magnetic axis of that phase (or opposite to, if the phase current at that instant is negative). These mmf space vectors are F ta a( ), F tb a( ), and F tc a( ), as shown in Fig. 2-6a, with an arrow (\u201c\u2192\u201d) on top of an instantaneous quantity 16 INduCTIoN MaCHINE EQuaTIoNS IN PHaSE QuaNTITIES where the superscript \u201ca\u201d indicates that the space vectors are expressed as complex numbers, with the stator a-axis chosen as the reference axis with an angle of 0\u00b0. assuming that there is no magnetic saturation, the resultant mmf distribution in the air gap due to all three phases at that instant can simply be represented, using vector addition, by the resultant space vector shown in Fig. 2-6b, where the subscript \u201cs\u201d represents the combined stator quantities: F t F t F t F ts a a a b a c a( ) ( ) ( ) ( ).= + + (2-20) The earlier explanation provides a physical basis for understanding space vectors. We should note that unlike phasors, space vectors are also applicable under dynamic conditions. It is easy to visualize the use of space vectors to represent field distributions (F, B, H), which are distributed sinusoidally in the air gap at any instant of time. However, unlike the field quantities, the currents, the voltages, and the flux linkages of phase windings are treated as terminal quantities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001915_tac.2011.2173424-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001915_tac.2011.2173424-Figure2-1.png",
        "caption": "Fig. 2. Convergence of the differentiator and performance of the pitch control.",
        "texts": [
            " As follows from (8), , where is the fifth row of and is the fifth entry of . Let the upper bound of be known a priori, and . Then get (9) where is a design parameter. Define as the right-hand side of inequality (9) with . The command signal is chosen for simulation. The initial tracking errors are and , , , 2, 3 at . The initial values of the differentiator are , ,2,3. The Mach number , altitude , and are sampled with the noise magnitudes 0.05 [m/sec], 5 [m], 0.02 [rad] and 0.01 [rad/s] respectively. The performance of the whole system is demonstrated in Fig. 2. The accuracies and are obtained with . VI. CONCLUSION Performance of the th-order differentiator [10] based on high-order sliding modes is studied when the available bound of the th-order derivative is a continuous function of time. The differentiator is proved to preserve exactness and local convergence. It is also robust, if the logarithmic derivative is bounded. In that case the convergence is semi-global in some specific sense. Once the differentiator outputs converge to the corresponding input derivatives, they remain equal to the derivatives also in the future, if is continuous"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure6.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure6.10-1.png",
        "caption": "Figure 6.10.1. Bicycle model with suspension steer effects.",
        "texts": [
            " If the differential is not a simple open type, there can be power steer effects because of lateral differences in tractive force acting on the rigid-body vehicle, and from compliance power steer, whether front or rear. If the steering wheel angle or the 366 Tires, Suspension and Handling reference steer angle is being considered, then the steering compliance is also of significance. Aerodynamics may play a part, but this is considered separately in Sections 6.14 and 6.15. An extremely simple vehicle without suspension was analyzed in Sections 6.4 and 6.5, for which the following simple results were found: A more complex vehicle will now be considered, but remaining in the linear range. Figure 6.10.1 illustrates a \"bicycle model\" vehicle with simple suspension, incorporating suspension understeer effects of \u03b4 S U f and \u03b4S U r. With these suspension effects, Positive \u03b4SUf and \u03b4 S U r are defined to call for an increased \u03b4, i.e., an understeer effect. Hence \u03b4 S U r is positive when the rear wheel attempts to increase its cornering force, and \u03b4SUf is positive when the front wheel tries to decrease its cornering force. The corresponding steer angle gradient is where the suspension understeer gradient kSU is the sum of geometric steer and compliance steer parts: Steady-State Handling 367 368 Tires, Suspension and Handling acceleration, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002251_s11071-013-1104-4-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002251_s11071-013-1104-4-Figure1-1.png",
        "caption": "Fig. 1 A spur gear pair model",
        "texts": [
            " The theoretical predictions are verified with direct numerical simulations by construction of the bifurcation diagrams and computation of the plane phase portraits, time histories, power spectra, and Poincare section. Finally, Sect. 5 presents some brief conclusions. For the purpose of illustration, a generalized model of a spur gear pair system is considered. It is assumed that the transmission shafts and the bearing of the gear system are inflexible, so that the parametric and nonlinear effects in the meshing are accentuated. Figure 1 shows a generalized model for a single mesh gear system, which the gear mesh is modeled as a pair of rigid disks connected by a spring damper set along the line of action. The gears are represented by their base circles with radius ra and rb , respectively. Ia and Ib are the mass moments of inertia of the gears. K and c represent the time varying mesh stiffness and a constant mesh damping. The backlash function fh, is usually used to represent gear clearances and an internal displacement excitation e(t), is also applied to the gear mesh interface to represent manufacturing errors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000148_s0890-6955(03)00091-9-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000148_s0890-6955(03)00091-9-Figure3-1.png",
        "caption": "Fig. 3. Components of thermally induced preload bearing system.",
        "texts": [
            " The heat generation and heat transfer in a motorized spindle system are much more complicated than those associated with the conventional spindle-bearing system addressed in Stein and Tu [17]. Bossmanns [34] and Bossmanns and Tu [4,5] developed a comprehensive thermal model to quantify all heat sources, heat sinks, and transfer paths in the housing, spindle shafts, motor, cooling air or water, and bearings. Based on the temperature field predicted by this thermal model for the entire motorized spindle, a more general preload model is proposed in this paper. The rear bearing pairs of the tested spindle is rigidly preloaded with a rigid spacer as in Fig. 3. The initial temperatures of the outer ring/the housing sleeve, inner ring/shaft, and balls are T0 o, T0 i and T0 b, respectively. When these temperatures increase due to heat generated in the built-in motor and the bearings, the sleeve, rings, balls and shaft expand in both axial and radial directions, resulting in thermal preload. From Fig. 3, it is observed that the axial thermal expansion difference is mostly caused by the shaft and the spacer. Their difference ( l) in expansion can be expressed as 1 asxi(T1 i T0 i ) asxo(T1 o T0 o) (7) where as is the linear expansion coefficient of steel which is the material of the shaft and sleeve; xi and xo are the distances of the contact points between the paired bearings of inner and outer rings; T1 i and T1 o are the new temperatures of the shaft and housing/spacer respect- ively. The relationship of xi, xo and the distance of the centers of the bearing pair (xb) are xi xb 1 2 Dbsin\u03b8 (8) xo xb 1 2 Dbsin\u03b8 (9) In the radial direction, if the diameters of the bearing are specified as Fig. 3, the expansion difference of the inner ring and outer ring would be 2 1 2 as[Dio(T1 ir T0 ir) Doi(T1 or T0 or)] (10) where Dio is the inner diameter of the outer ring, Doi is the outer diameter of inner ring, Tir, is the temperature of the inner ring, and Tor, is the temperature of the outer ring. The rolling elements would expand according to the following equation 3 1 2 abDb(T1 b T0 b) (11) Finally, the total deformation of the bearing in the direction of line of contact can be expressed as the following equations based on the assumption that the contact angle remains constant after thermal deformation 1 rcos\u03b8 asin\u03b8 (12) Then, the thermally induced preload could be obtained as Pa,t kt 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.61-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.61-1.png",
        "caption": "FIGURE 5.61. A set of non-industrial connected links.",
        "texts": [
            " Forward Kinematics x0 y0 x1 a l z0 P Spherical manipulators are made by attaching a polar manipulator shown in Figure 5.56, to a one-link R`R(\u221290) manipulator shown in Figure 5.51 (b). Attach the polar manipulator to the one-link R`R(\u221290) arm and make a spherical manipulator. Make the required changes to the coordinate frames Exercises 3 and 9 to find the link\u2019s transformation matrices of the spherical manipulator. Examine the rest position of the manipulator. 19. F Non-industrial links and DH parameters. Figure 5.61 illustrates a set of non-industrial connected links. Complete the DH coordinate frames and assign the DH parameters. 5. Forward Kinematics 317 z0 zi 318 5. Forward Kinematics 20. Modular cylindrical manipulators. Cylindrical manipulators are made by attaching a 2 DOF Cartesian manipulator shown in Figure 5.57, to a one-link R`R(\u221290) manipulator shown in Figure 5.51 (a). Attach the 2 DOF Cartesian manipulator to the one-link R`R(\u221290) arm and make a cylindrical manipulator. Make the required changes into the coordinate frames of Exercises 3 and 11 to find the link\u2019s transformation matrices of the cylindrical manipulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002398_0142331215608427-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002398_0142331215608427-Figure1-1.png",
        "caption": "Figure 1. The structure of the quadrotor unmanned aerial vehicle.",
        "texts": [
            " The dynamic model has an important role in understanding the behaviour of the quadrotor UAV. Since the functional details embodying the plant dynamics are inputs to the controller design procedure, it is essential to obtain an accurate dynamic model of the vehicle (Bouabdallah 2007; Bouabdallah et al., 2004a; Elsamanty et al., 2013; Kim et al., 2010; Pounds, 2008; Zhang et al., 2014). The quadrotor system consists of two pairs of counterrotating rotors, which eliminate anti-torque occurring due to the undesired yaw motion produced by the rotors (Mahony et al., 2012). Referring to Figure 1, the propeller pair 1 and 3 rotates in the counter direction with respect to propeller pair 2 and 4. Roll motion around the x-axis can be obtained by inversely and proportionally changing the angular velocities of rotors 2 and 4, and similarly pitch motion can be made possible by inversely and proportionally changing the angular velocities of rotors 1 and 3 where the difference of the four propellers\u2019 velocities yields yaw motion about the z-axis. The coordinates and structure of the quadrotor are depicted in Figure 1. In order to obtain the model parameters of the quadrotor, a number of assumptions are made. In the derivation of the model, Euler\u2013Lagrange formalism or Newton\u2013Euler formalism are considered frequently (Bouabdullah et al., 2004a; Castillo et al., 2005; Hamel et al., 2002; Mian and Daobo, 2008; Zhang et al., 2014). It should be pointed out that the Newton\u2013Euler method is straightforward and is applied in this paper. Nevertheless, the results of both methods capture the same physical reality. The developed model is dependent upon the known constants, any uncertainty on which can subsequently be handled via system identification methods (Bergamasco and Lovera, 2014; Gremillion, 2010; Zhang et al",
            " thrust and drag forces are proportional to squares of the propellers\u2019 angular velocities; 5. the centre of mass and the origin of the body fixed frame are coinciding. at UNIV OF CONNECTICUT on October 13, 2015tim.sagepub.comDownloaded from The dynamics that emerge due to the extraction of the external force to body of the quadrotor can be depicted on the body fixed coordinate frame and the following representation is obtained to model translational and rotational motions: mI3 3 3 0 0 I _v _v + v 3 mv v 3 Iv = F t \u00f01\u00de In Figure 1, frame E denotes the earth fixed frame, B denotes the body fixed frame and R is a transformation matrix from B to E. In (1), I 2 R3x3, v is the body angular velocity and v is the body linear velocity vector. The dynamics in (1) can explicitly be written as below: _z= v \u00f02\u00de and _v = gez + 1 m TRez \u00f03\u00de I _v= v 3 Iv+ tf tg \u00f04\u00de sk(v)=RT _R \u00f05\u00de where z = (x, y, z)T represents the position of the body fixed coordinate frame with respect to the earth fixed coordinate frame, v represents the linear velocities in the earth fixed frame, T is the thrust force produced by propellers, g is the gravitational acceleration and ez stands for the z component of the unit vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002630_s00604-018-2809-3-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002630_s00604-018-2809-3-Figure4-1.png",
        "caption": "Fig. 4 The illustration of the fabrication procedure of the graphene\u2013PANI hollow spheres (RGO-PANI HS). In the first step, the PANI wrapped PS sphere was formed by mixing negatively charged PS sphered with positively charged PANI. In the second step, the negatively charged RGO sheets selfassembled on PANI@PS by dipping PANI@PS into RGO dispersion. The first and second steps are multiple times repeated to produce (RGO\u2013PANI)n@PS. In the final step, the PS core was removed by dipping in tetrahydrofuran (THF) to generate RGOPANI HS [83]. Copyright (2015) Elsevier Ltd.",
        "texts": [
            " GO was reduced in the presence of polystyrene sulfonate. The sulfonated group imparts the negative charge to the rGO and provides a stable dispersion of negatively charged rGO. The positive charge PANI dispersion was also produced. A rGO-PANI multilayer encapsulated PS sphere was fabricated using a layer by layer assembly method by the interaction of the negative charge rGO and positively charged PANI. The PS core was removed with the help of tetrahydrofuran to get 3D rGO-PANI hollow spheres (Fig. 4) [83]. The fabrication of the 3D graphene by the chemical deposition looks simple and cost-effective. The 3D network is obtained from the GO. GO synthesis and handling are convenient. Due to the hydrophilic nature of GO, it is easily dispersed in the aqueous medium [84]. GO is reduced using various reducing agents. The reduction of GO can introduce more defects into the rGO. Furthermore, the reduction of the GO not able to restore the pristine graphene network and some oxygen functional group still retained by the surface which substantially affects the performance of the material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000600_s0022112004009759-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000600_s0022112004009759-Figure2-1.png",
        "caption": "Figure 2. Three steps in generating a mesh for the initial filament shape: (a) the domain is subdivided into three quadrilateral regions or subdomains, (b) an algebraic mesh is constructed as an initial guess for the solution of the mesh equations, and (c) the mesh equations are solved to give the elliptic mesh solution.",
        "texts": [
            " For the sake of computational efficiency, the coordinates r and z are mapped onto the unit square in the computational domain with coordinates {(\u03be, \u03b7) : 0 \u03be, \u03b7 1} using subparametric mapping, as described by Christodoulou & Scriven (1992) (see, also, Bathe 1982). Specifically, r and z are everywhere expanded using bilinear basis functions except along the free surface where 5-node basis functions with an extra node along the boundary are used to increase the accuracy of representing the curved shape of the filament. A prerequisite for using the elliptic mesh generation technique is that the domain be divided into a number of quadrilateral subdomains, as illustrated in figure 2(a), with local coordinates (\u03bej , \u03b7j ), where j = 1, 2, . . . , is the index of the subdomain. Since all integrations are performed upon mapping each element onto the computational domain with coordinates \u03be and \u03b7, the mesh equations are written in what follows with respect to the (\u03be, \u03b7) domain. The Galerkin weighted residuals of the pair of partial differential equations used to determine the unknown mesh coordinates (ri, zi) are (Christodoulou & Scriven 1992; Notz et al. 2001) Ri \u03be = \u222b A [\u221a r2 \u03be + z2 \u03be r2 \u03b7 + z2 \u03b7 + \u03b5s ] \u2207\u03be \u00b7 \u2207\u03c6i |J | d\u03be d\u03b7 \u2212 \u03b5\u03be \u222b A f (\u03be ) ln ( r2 \u03be + z2 \u03be ) \u03c6i \u03be d\u03be d\u03b7 \u2212 M\u03be \u222b \u2202A f (\u03be ) ln ( r2 \u03be + z2 \u03be ) \u03c6i \u03be d\u03be = 0, i = 1, ",
            " While these functions are beneficial for concentrating the mesh where desired, a poor choice of either f (\u03be ) or g(\u03b7) may lead to acute angles where the mesh coordinate curves intersect each other and the boundaries. Setting M\u03be or M\u03b7 to zero, however, can result in an undesirable mesh concentration along a boundary. Hence, the optimal choice for the mesh parameters and the functions f (\u03be ) and g(\u03b7) must be determined through experimentation. In this paper, the mesh is concentrated axially where the filament necks and it is distributed nearly uniformly in the radial direction. Once the domain has been subdivided into quadrilateral subdomains, as shown in figure 2(a), an algebraic mesh as shown in figure 2(b) is generated as an initial guess for the solution of the mesh equations. In order to solve the mesh equations over the entire domain, the subdomains are patched together through the boundary conditions on (3.1) (see Christodoulou & Scriven 1992; Notz et al. 2001). Along the external boundaries of the domain, physical conditions replace one of the mesh equations in order to determine the location of that boundary in physical space. The condition r = 0 is used in place of (3.1a) in subdomains 1 and 2 along the symmetry axis. The condition z = 0 is used in place of (3.1b) in subdomain 1 and (3.1a) in subdomain 3 along the mid-plane of symmetry. The kinematic boundary condition (2.3b) is used in lieu of (3.1b) in subdomains 2 and 3 along the free surface except when determining the initial mesh. At time t = 0, the analytic description of the initial filament shape is used for this purpose. The mesh equations are then solved to determine the locations of the mesh points, as shown in figure 2(c). An example mesh when Oh = 10\u22122 and Lo = 15 at time t = 10.990 is shown in figure 3 (cf. figure 10 below). As shown in figure 2, the number of elements deployed in meshes used in this work can be characterized by three independent parameters. Here NZ denotes the number of elements used in the \u03b71- and \u03be3-directions, NR1 denotes the number of elements used in the \u03be1- and \u03be2-directions, and NR2 denotes the number of elements used in the \u03b72- and \u03b73-directions. Moreover, NR1 \u2248 NR2 and their sum is defined as NR = NR1 + NR2. While NZ NR, determination of appropriate values of these parameters requires systematic mesh refinement studies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.8-1.png",
        "caption": "Fig. 3.8 Suspensions in their reference configuration: swing axle (left) and double wishbone suspension (right)",
        "texts": [
            "79) where \u0394Zi will be obtained after the suspension analysis (see Sect. 3.8.11). Consistently with the hypotheses listed at p. 47, the suspension mechanics will be analyzed assuming very small suspension deflections and tire deformations. This is what a first order analysis is all about. Of course, it is not the whole story, but it is a good starting point.3 More precisely, the following aspects will be addressed: \u2022 suspension internal coordinates; \u2022 suspension and tire stiffnesses; \u2022 suspension internal equilibrium. Figure 3.8 shows two possible suspensions in their reference configuration (vehicle going straight at constant speed). It also serves the purpose of defining some relevant quantities. First of all, the reference configuration is supposed to be perfectly symmetric. More precisely, the left and right sides are exactly alike (including springs). Points Ai mark the centers of the tire contact patches. Points Bi are the instantaneous centers of rotation of the wheel hub with respect to the vehicle body. Here, for simplicity, the suspension linkage is supposed to be rigid and planar",
            " Just take the most classical cantilever beam, of length l with a concentrated load F at its end. Strictly speaking, the bending moment at the fixed end is not exactly equal to F l, since the beam deflection takes the force a little closer to the wall. But this effect is usually neglected. 68 3 Vehicle Model for Handling and Performance axle suspension, point B2 is indeed the center of a joint, whereas in a double wishbone suspension (right) point B1 has to be found by a well known method. In both cases, the distances ci and bi set the position of Bi with respect to Ai (Fig. 3.8). As usual, t1 and t2 are the front and rear track lengths. Also shown in Fig. 3.8 are points Q1 and Q2. They are given by the intersection of the straight lines connecting Ai and Bi on both sides. Because of symmetry, they lay on the centerline at heights q1 and q2. Points Q1 and Q2 are the so-called roll centers and their role in vehicle dynamics will be addressed shortly. For each axle, four \u201cinternal\u201d coordinates are necessary to monitor the suspension conditions with respect to a reference configuration. A possible selection of coordinates may be as follows (Fig. 3.9) \u2022 body roll angle \u03c6s i due to suspension deflections only; \u2022 body vertical displacement zs i due to suspension deflections only (which results in track variation \u0394ti ); \u2022 body roll angle \u03c6 p i due to tire deformations only; \u2022 body vertical displacement z p i due to tire deformations only",
            " Any other kinematic quantity is, by definition, a function of the selected set of coordinates (\u03c6s i ,\u0394ti, \u03c6 p i , z p i ). It is quite important to monitor the variation of the wheel camber angle \u03b3ij as a function of the selected coordinates (\u03c6s i ,\u0394ti, \u03c6 p i , z p i ). In a first order analysis, the investigation is limited to the series expansion \u0394\u03b3ij \u2248 \u2202\u03b3ij \u2202\u03c6s i \u03c6s i + \u2202\u03b3ij \u2202\u0394ti \u0394ti + \u2202\u03b3ij \u2202\u03c6 p i \u03c6 p i + \u2202\u03b3ij \u2202z p i z p i (3.81) where all derivatives are evaluated at the reference configuration. From Fig. 3.8 and also with the aid of Fig. 3.9, we obtain the following general results for any 70 3 Vehicle Model for Handling and Performance symmetric planar suspension (cf. Fig. 9.5) \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u2202\u03b3i1 \u2202\u03c6s i = \u2202\u03b3i2 \u2202\u03c6s i = \u2212 ti/2 \u2212 ci ci = \u2212qi \u2212 bi bi \u2202\u03b3i1 \u2202\u0394ti = \u2212 \u2202\u03b3i2 \u2202\u0394ti = 1 2bi \u2202\u03b3i1 \u2202\u03c6 p i = \u2202\u03b3i2 \u2202\u03c6 p i = 1 \u2202\u03b3ij \u2202z p i = 0 (3.82) The sign convention for the camber variations \u0394\u03b3ij is like in Fig. 2.2. Therefore, in Fig. 3.9(b) we have \u0394\u03b3i1 < 0 and \u0394\u03b3i2 > 0. Equations (3.81) and (3.82) yield \u0394\u03b3i1 \u2248 \u2212 ( qi \u2212 bi bi ) \u03c6s i + \u03c6 p i + 1 2bi \u0394ti \u0394\u03b3i2 \u2248 \u2212 ( qi \u2212 bi bi ) \u03c6s i + \u03c6 p i \u2212 1 2bi \u0394ti (3.83) This is quite a remarkable formula. It is simple, yet profound. For instance, the two suspension schemes of Fig. 3.8, which look so different, do have indeed very different values of the first two partial derivatives in (3.82). On the other hand, it should not be forgotten that (3.81) is merely a kinematic relationship. There is no dynamics in it. Therefore, we must be careful not to attempt to extract from it information it cannot provide at all. Another common mistake is to state, e.g., that a suspension scheme has a typical value of the partial derivative \u2202\u03b3ij /\u2202\u03c6s i , without specifying which are the other three internal coordinates",
            " However, a more accurate analysis is not much more difficult. The load distribution due to the inertial effects of mu is schematically shown in Fig. 3.20. Basically, a centrifugal force Yu i acts on each wheel. The equilibrium of the whole system and of each suspension requires 2Yu i rr = \u0394Zu i ti Y u i rr \u2212 \u0394Zu i ci = Lu i (3.120) which yield Yu i rr ( 1 \u2212 ci ti ) = Lu i (3.121) The net effect is a small load transfer \u0394Zu i and a very small suspension roll angle, particularly if ci ti like in a double wishbone suspension, as shown in Fig. 3.8. 86 3 Vehicle Model for Handling and Performance In practical terms, in (3.113) it suffices to set Y = msay , to modify Yi accordingly, and to include an additional term mui ayrr for each axle, where mui is the corresponding unsprung mass. After quite a bit of work, we are now (almost) ready to set up our first-order vehicle model for handling and performance analyses. Essentially, setting up a model means collecting all relevant equations, their order being not important. Of course, a twoaxle vehicle is considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001441_0040-9383(67)90034-1-Figure4.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001441_0040-9383(67)90034-1-Figure4.3-1.png",
        "caption": "FIG. 4.3.",
        "texts": [
            " I t is easy to check tha t the two definitions o f P~,q agree, that each ]~t,q is a submersion, tha t Po,q -- Fq, and tha t ~ is a cont inuous m a p covering f . \\ '4' \" v , ~ o v:-',: ovo,qox<, off,,L \u00b0 % (u) FtG. 4.2. I I . When V is U with a handle of index 2 _-< n -- 1 attached N o t e . The restriction 2 ~ n is necessary, as the following example will show. Let V - - - { ( x , y ) ~ R 2 ,x 2 + y 2 = 4 } , U = { ( x , y ) ~ R 2,1 =<x 2 + y 2 < 4 } . Then V i s U with a handle of index 2 attached. Let F : I / ~ R be given by F(x, y) = x. Then f = F I U is regularly homotopic to the map f~ \u2022 U--, R obtained by submerging U in R 2 as shown in Fig. 4.3 and projecting on the x-axis. Observe the level linef~-l(0). Suppose f l extended to a submersion F1 of V in R. By regularity this level line would extend into 1 / - U as an embedded circle (Fig. 4.4). The disc bounded by this circle would then contain a maximum or a minimum for Ft, impossible if Note. The case 2 = 0 is trivial, and it will be assumed in what follows that ~ > 1. The rest of this proof imitates that given by Poenaru [20] for immersions, and requires the following definitions. Definition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure6.43-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure6.43-1.png",
        "caption": "Fig. 6.43 Lateral force applied at a point behind the neutral point (x < e)",
        "texts": [
            " If \u03b4v = 0, the steady-state distance Rp is Rp = u rp = C1C2l 2 \u2212 mu2(C1a1 \u2212 C2a2) \u2212y(C1 + C2)Fl (6.193) The numerator is always positive if u < ucr. Therefore, Rp > 0 if y < 0 and vice versa. If the point of application of the lateral force is located ahead of the neutral point, the vehicle behaves like in Fig. 6.42, turning in the same direction as the lateral force. This is commonly considered good behavior. If the point of application of the lateral force is behind the neutral point, the vehicle behaves like in Fig. 6.43. This is commonly considered bad behavior. Of course, since an oversteer vehicle has a neutral point ahead of G, the likelihood that a wind gust applies a force behind the neutral point is stronger, much stronger, than in an understeer vehicle. To understand why the first case is considered good, while the second is considered bad, we have to look at the lateral forces that the tire have to exert. In the first case, the inertial effects counteract the wind gust, thus alleviating the tire job. In the second case, the inertial effects add to the lateral force, making the tire job harder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003710_j.jmst.2020.06.036-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003710_j.jmst.2020.06.036-Figure14-1.png",
        "caption": "Fig. 14. The corrosion mechanism of AP an",
        "texts": [
            " Electrochemical experiments including potentiodynamic polarization and ESI were performed to evaluate the corrosion resistance of SLM-printed AlMgSiScZr alloy at AP and HT conditions. As presented in Tables 2 and 3, the AP sample have smaller corrosion current density (icorr, 0.148 A cm\u22122), higher pitting potential (Epit, \u2212.753 V) and oxide film resistance (Rf, 51.33 k cm2) than those of the HT sample (icorr, 2.536 A cm\u22122; Epit, \u22120.888 V; Rf, 37.56 k cm2), revealing a better corrosion resistance was obtained for the AP AlMgSiScZr alloy. The corrosion resistance of Al alloy is related to the grain size and precipitated phase, as stated in previous studies [80\u201382]. Fig. 14 shows the corrosion mechanism of AP and HT AlMgSiScZr alloys in 3.5 wt% NaCl solution. During the electrochemical tests, the precipitate of Al3(Sc, Zr) or Mg2Si acted as the cathode, and a tiny galvanic cell was formed at this position [54,83]. The Al matrix near the precipitate acted as the anode was preferentially corroded. In addition, the increase of precipitate degraded the stability of oxide layer and and promoted the pitting process. Thus, the oxide layer of HT sample was easily destroyed and the accelerated pitting corrosion process was induced by the precipitates in Al alloy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002300_j.automatica.2016.04.010-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002300_j.automatica.2016.04.010-Figure1-1.png",
        "caption": "Fig. 1. Single-link robotic manipulator system.",
        "texts": [
            ", 2014) use traditional adaptive method to design output tracking controller, that is, the bounds of unknown time-varying parameters are compensated by a series of on-line estimators whose numbers are greater than 1. In contrast, this paper combines homogeneous domination approach with the construction of a time-varying function L(t) to realize adaptive stabilization, and the adaptive scheme only requires one on-line estimator, which ensures that the dynamic order of the adaptive controller is reduced to be minimum. (1) The practical example. Consider the single-link robotic manipulator system shown in Fig. 1, where the robotic manipulator m revolves around the pivot O under the action of force. Let l be the distance between the centroid of robotic manipulator and the pivot O, \u03b8(t) \u2208 (\u2212\u03c0 2 , \u03c0 2 ) be rotational angular displacement and u(t) be an external force acting on the robotic manipulator named control input. Newton\u2019s law gives the equation of motion ml\u03b8\u0308 (t) = u(t) \u2212 mg sin(\u03b8(t)) \u2212 fl\u03b8\u0307 (t), where f is the unknown viscous friction coefficient, andmg sin(\u03b8(t)) is a component of the gravity along the tangent direction of the moving direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure3.41-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure3.41-1.png",
        "caption": "Fig. 3.41 AC test system for GIS testing with test bus",
        "texts": [
            " Typical test objects in the range up to few 10 nF are components or complete bays of gas-insulated substations (GIS), power and instrument transformers, bushings and cable samples. In an HVAC routine test, a complete cable drum may have a capacitance of some 100 nF. In case of GIS testing, the load of the test object can easily be estimated from the length of the GIS tubes and the specific capacitance Ct & 60 pF/m for a single-phase bus bar. Often, the HVAC test system is connected to a test bus, which can be arranged in the production hall (Fig. 3.41). The bus has several connection points for the GIS to be tested. Only one of the connection points is connected to the HVAC test system for a test. The others are separated and grounded, e.g. at a second, a GIS tested before is disassembled and at a third, a GIS is prepared for the next test. This solution does not require any separate test field, because the test bus and the test object have metal enclosures and are grounded. But the test bus increases the total load capacitance and the required test current",
            " If the floor grounding is considered to be necessary, one had to put an insulation foil over the area grounder, followed by a suited metal mesh or metal panels forming the floor shielding and a protection layer, usually of concrete with an upper layer of epoxy resin for air cushion transportation. In some cases, it should be considered whether the shielding of the whole test field is necessary or the application of a shielded cabin (Fig. 9.32) is sufficient. Inside such a self-carrying cabin the lowest PD noise levels can be reached. If the 9.4 Updating of Existing HV Test Fields 415 space of such a commercially available cabin is sufficient, no expensive shielding of the whole test area is required. A similar effect can be reached with a metalenclosed test system (Fig. 3.41). A perfect shielding must be completed with a perfect filtering of all voltages penetrating into the shielded area (Sect. 9.2.3). 416 9 High-Voltage Test Laboratories Chapter 10 High-Voltage Testing on Site Abstract High-voltage (HV) tests and measurements are applied for two different reasons on site: When new equipment or systems are finally assembled on site, a quality acceptance test, usually a HV withstand test (more and more completed by PD or dielectric measurements), is required to demonstrate the necessary quality and reliability for commissioning"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000426_9781118680469-Figure6.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000426_9781118680469-Figure6.2-1.png",
        "caption": "FIGURE 6.2 The general molecular structure of a bent-core molecule illustrating different constituents and bend angle . Note that RW1 and RW2, T1 and T2 can be the same or different. Modifying these constituents will generate numerous bent-core molecules.",
        "texts": [
            " For readers outside the LC community, gaining some introductory knowledge by reading some LC books [33, 34] will facilitate the understanding and enjoyment of the science described in this chapter. Bent-core mesogens are a very special type of mesogen and possess quite distinct properties from the known rod-shaped mesogens. Compared to a rod-shaped LC molecule including one rigid aromatic core and twoflexible tails, a bent-coremolecule consists of one central bent unit (BU), two rod-like aromatic wings (RWs), and two flexible tails (Fig. 6.2). Hence, bent-core molecules are also called banana or bow-shaped molecules due to their distinct bent shape (Fig. 6.1c). It is known that rod-shaped molecules can rotate freely around their long molecular axes. In contrast, FUNDAMENTALS 193 bent-core molecules have restricted rotation around their long axes owing to their bent shape, which leads to that achiral molecules produce macroscopic polar structures. Since central BUs play a determining role in the formation of polar bent-core mesophases, the central BUs are first discussed for bent-core molecules (Fig",
            " Many other BUs such as 1,3-disubstituted pyridinyl unit [35], 1,3\u2032-disubstituted biphenyl unit (Tschierske\u2019s BU) [36], m-terphenyl unit [37], and m-terpyridinyl unit [38] can be regarded as derived from 1,3-disubstituted benzene ring. The most commonly used chemicals to build BUs are resorcinol, (1,1\u2032- biphenyl)-3,4\u2032-diol, naphthalene-2,7-diol, 3-hydroxybenzoic acid, and isophthalic acid and their derivatives, which give rise to about 90% of bent-core compounds. In a bent-core molecule, the bend angle (Fig. 6.2) that is the opening angle between the two RWs primarily determined by the central angle between the two bonds which link a central BU and two linking groups X and X\u2032. Since the bend angle is generally close to the central angle, the central angle is often used to represent the bend angle. 1,3-disubstituted benzene and 2,7-disubstituted naphthalene ring have the central angle of 120\u25e6 owing to sp2 hybridization, and therefore most bent-core molecules including the two basic BUs possess the bend angle of roughly 120\u25e6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000897_j.mechmachtheory.2011.12.006-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000897_j.mechmachtheory.2011.12.006-Figure1-1.png",
        "caption": "Fig. 1. Cut-away finite element mesh of a radial ball bearing (dimensions detailed in Table 1) and a double-row cylindrical bearing (from a helicopter application).",
        "texts": [
            " Brandlein found that EHL prevails at high speed rolling conditions [4] or with heavy bearing loads [16]. Consequently, the influence of lubrication on the bearing stiffness is expected to not be significant considering the moderate rolling speed and thin fluid film (about 0.1 micrometer, 0.002% of bearing outer diameter). Bearing cages are assumed to maintain a constant angular position of each rolling element relative to each other. The finite element/contact mechanics models of rolling element bearings (Fig. 1) include important design details such as accurate roller and race crownings, internal radial and axial clearances, contact angle, roller length, bearing width, length and diameter of raceway for ball bearings, and so on. These parameters affect bearing stiffnesses significantly. They are, however, not included in many theoretical bearing models [1-4]. In addition, the finite element/contact mechanics model applies to most bearing types, including cylindrical, tapered, and spherical roller bearings, radial and angular contact ball bearings, thrust bearings, and needle bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000008_tec.2005.853765-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000008_tec.2005.853765-Figure12-1.png",
        "caption": "Fig. 12. Field distributions with phase A excited. (a) All teeth wound. (b) Alternate teeth wound.",
        "texts": [
            " The most significant difference between motors in which all the teeth are wound and those in which only alternate teeth are wound is in their winding inductances. The finite element predicted self inductances per phase and the mutual inductance between phases for the two 12-slot/10-pole motors are, respectively, 3.03 and \u22120.34 mH when all the teeth are wound, and 4.64 and 0.0023 mH when alternate teeth are wound, which are in good agreement with the analytical predictions [14], [15] and with measured results obtained by using an inductance bridge, as shown in Table IV. As will be evident from Fig. 12, the When 2p = Ns \u00b1 2, the ratio of the slot number to the pole number is fractional, and their smallest common multiple, Nscm, is generally high, which, in turn, results in a small cogging torque [16]. For example, Nscm = 30 for the 15-slot/10-pole motor, while Nscm = 60 for the 12-slot/10-pole motors. Hence, very low cogging can be achieved when 2p = Ns \u00b1 2, as evidenced by the analytically [17] and finite element predicted and the measured cogging torque waveforms shown in Figs. 13 and 14, the cogging torque waveform being measured from the reaction torque acting on the stator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000827_j.engfailanal.2014.04.005-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000827_j.engfailanal.2014.04.005-Figure8-1.png",
        "caption": "Fig. 8. Typical rotor-bearing system configuration.",
        "texts": [
            " Thus the vibration differential equation of gear-rotor system is deduced, it can be shown as follows. Mtotal \u20acq\u00fe \u00f0Gtotal \u00fe Ctotal\u00de _q\u00fe Ktotalq \u00bc Q total \u00f026\u00de The displacement vector q in formula (26) is generalized displacements of each node and the force vector Qtotal is generalized force. 3.1. Modeling of rotor-bearing system The typical flexible rotor-bearing system to be analyzed consists of a rotor composed of discrete disks, rotor segments with distributed mass and elasticity, and discrete bearings. Such a system is illustrated in Fig. 8. 3.1.1. The dynamic model of elastic axis According to the principle of finite element method, dividing the rotor into a number of beam elements (see in Fig. 9(a)). The stiffness matrix, mass matrix and the gyroscopic matrix of two-node beam elements is shown in Fig. 3(b) are deduced [22]. Each node of the beam elements has six degrees of freedom x, y, z are displacements in X\u2013Y\u2013Z, and hx, hy, hz are rotation angles of the three directions, respectively. The node displacements of the rotor element can be expressed as qe \u00bc \u00bdxA yA zA hAx hAy hAz xB yB zB hBx hBy hBz T \u00f027\u00de The energy of the complete element is obtained by summing the elastic bending and kinetic energy expressions together"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003089_978-3-319-04867-3-Figure10.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003089_978-3-319-04867-3-Figure10.4-1.png",
        "caption": "Fig. 10.4 Scheme of the preparation process of a CLCP nanocomposite film with mesogens oriented parallel to CNTs and b CLCP nanocomposite film with mesogens oriented perpendicularly to CNTs and their distinctive photomechanical behaviors. Reproduced with permission from [39, 40]. Copyright 2013",
        "texts": [
            " For practical applications, the photoinduced deformation of LCPs should be accurately controlled in a designed way. As the photomechanical behavior of LCPs is closely related to the alignment direction of mesogens, multiple 10 Nanotechnology and Nanomaterials 305 orientation directions are most desired, which can be induced by the self-assembled nanostructures. Recently, the CLCP, fabricated by utilization of ordered carbon nanotubes (CNTs) as a template to induce the LC alignment nanocomposites, were reported to exhibit excellent photodeformable behavior [39, 40]. In Fig. 10.4a, the CLCP nanocomposites showed distinctive photodeformable behaviors when they were fabricated with different preparation processes. Molten mixtures of the liquid crystalline monomer, initiator and crosslinker were injected into a LC cell that was made of two CNTs-sheet-covered glass slides with CNTs sheet inside. The freestanding CLCP nanocomposite film was obtained by photopolymerization at the liquid crystalline phase. A rapid and reversible photoinduced deformation was achieved by alternating UV and visible light irradiation, and the CLCP nanocomposite film curled along the aligned direction of CNTs indicating mesogens oriented parallel to the align direction of CNTs. This phenomenon might result from the structure of CNTs\u2019 sheet performing the same function as the surface of a rubbed polyimide film. In Fig. 10.4b, the CLCP nanocomposite film was fabricated via a different process. The LC monomer, initiator and crosslinker were all dissolved in the solvent and doped onto the CNT strip. The CLCP nanocomposite film was achieved by the photopolymerization of CNT strip in the LC cell without CNT sheets. Interestingly, a unique photomechanical behavior of the CLCP 306 L. Yu et al. nanocomposite film bending away from the light source was observed, indicating that mesogens would be oriented perpendicular to the alignment direction of CNTs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002681_j.addma.2019.04.019-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002681_j.addma.2019.04.019-Figure2-1.png",
        "caption": "Fig. 2. Reduced packing density of powder in a single layer in SLM.",
        "texts": [
            " This \u201csteady state\u201d is reached when the amount of melted powder is equal to the leveling height of the build platform. When one neglects the deposition of powder (e.g., due to spatter and denudation) and vaporization, this theoretical \u201csteady state\u201d powder layer height is equal to the leveling height of the build platform divided by the packing density of powder as given by Eq. (1) [3,9,10]. When using this equation, it has to be noted that the packing density in a single layer is lower than that determined by common powder characterization methods such as ASTM B 527-06 as shown in Fig. 2. Mindt et al. [9] numerically determined a packing density of 20% and 38% in layer heights of 30 \u03bcm and 50 \u03bcm, respectively, for a powder with a particle size distribution between 15 \u03bcm and 75 \u03bcm and a tap density of over 50%. Additionally, spatter, denudation and vaporization will lower the amount of molten material and further increase the actual powder layer height in \u201csteady state.\u201d Because the influence of spatter, denudation and vaporization on the powder layer height is unknown, it is the goal of this study to experimentally determine the actual powder layer height as well as the packing density in a single layer in the \u201csteady state\u201d (after several layers)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002101_tr.2013.2241216-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002101_tr.2013.2241216-Figure3-1.png",
        "caption": "Fig. 3. Cracked tooth model.",
        "texts": [
            " Thus, the single tooth contact and double tooth contact will alternate continuously as the pinion rotates. For these two types of contact duration, the total effective mesh stiffness can be expressed respectively, for single tooth contact, and double tooth contact, as [25], see (25)\u2013(26) at the bottom of the page. Besides, represents the first pair of meshing teeth, and represents the second pair. One crack is inserted at the pinion tooth root with initial length of . The procedure to calculate the tooth stiffness with a curved crack path is given as follows. As shown in Fig. 3, the crack increment at each crack extension step is set to . The crack tip is denoted by , where the index represents the crack propagation step. The crack length grows by in the direction determined by (24). Because the (25) (26) associated formulas to compute cracked tooth stiffness are related to four different cases, depending on the teeth meshing contact point and the crack tip position as well, in Fig. 3, the index of only symbolizes the four mentioned typical cases, and it does not mean that there are only these four crack tips. According to [25], the Hertzian and axial compressive stiffness are not affected by crack occurrence, while the bending stiffness and shear stiffness will change after the crack is introduced. The base circle of pinion centers at with the radius of The contact point is traveling along the tooth profile , and the angle of is determined by the tangential line passing . Because the force is applied at the contact point , perpendicular to the tangential line, the angle also serves as the force decomposition angle to the horizontal direction and vertical direction "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure84-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure84-1.png",
        "caption": "Fig. 84 a Schematic architecture of the ANN; b performance of an example: tool path pattern without correction and with correction; c metallic parts after face milling: (1) standard tool path; (2) proposed tool path [122]",
        "texts": [
            " One of the revelations of the previous path planning summary is as described by Occam\u2019s razor, \u201cIf no need, then no entity is added\u201d; the next step of the path planning algorithm should be to pursue low algorithm complexity and real-time, but simple path planning is usually the best. Overly complicated path planning basically loses engineering value. With the further development of artificial intelligence technology, its application inWAAM is also increasing. LamNguyen applied machine learning to solve a meaningful problem [122]. The rib web structure shown in Fig. 83 is very common in various lightweight designs. When using WAAM for path planning and processing, there will be insufficient filling at the nodes, as shown in the Fig. 84 b. The method used by Lam was to compensate for a certain path, but the amount of offset is difficult to determine, so a method based on data-driven artificial neural network (ANN) was used. The input layer is the number of turning points and four angle values, and the output layer is the offset value, as shown in the Fig. 84 a. After the model was trained, it could output the corresponding offset according to the specific geometric characteristics, so that the Fig. 79 a Ten-directional pipe joint. b Ten-directional pipe joint manufactured by WAAM [114] node area would be filled. Lam\u2019s research is very clever and enlightening, because the WAAM molding process has many similar complicated details, and it is difficult or impossible to establish an accurate mathematical model, so machine learning will be a good method. However, although machine learning is widely used in computer vision, natural language processing, automatic control, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000202_0007-1285-34-405-539-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000202_0007-1285-34-405-539-Figure2-1.png",
        "caption": "FIG. 2. Ultrasonic beam must be perpendicular to interface (as at A) for echo to return to probe.",
        "texts": [
            " The probe is applied directly to the abdominal skin through a film of olive oil which acts as a coupling medium. The patient does not have to be moved from her bed, she experiences no discomfort and each scan takes between one and two minutes. A camera placed in front of the screen records all the echoes from each scan on a single photographic display on the right shows the same echo blips now represented as intensity modulated dots of light whose position geometrically corresponds to the station of each of these interfaces along the path of the ultrasonic beam. It will be seen (Fig. 2) that the reception of these echoes depends upon the beam being as at A and not as at B where the incidence is not perpendicular and the echo is therefore lost. A method of circumventing this difficulty is shown in Fig. 3 where a hypothetical transverse section of the abdomen is scanned by a probe which is made to rock throughout a multiplicity of scanning angles. In this way there is a far better statistical chance plate as the probe, rocking slowly about 30 deg. on either side of the normal to the skin surface, slowly traverses the body, either in longitudinal or in transverse direction as required"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002706_tmag.2014.2364988-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002706_tmag.2014.2364988-Figure6-1.png",
        "caption": "Fig. 6. Winding arrangement of a 20-slot/18-pole geometry. (a) Five-phase winding. (b) Dual Five-phase winding.",
        "texts": [
            " However, using the same connection concept introduced in the previous section will be a possible new alternative. A five-phase machine model is used to validate the proposed concept and then the concept is generalized for nphases. Among the different slot-pole combinations of a five-phase PM machine with an FSCW, the 20-slot/18-pole combination has been proven to be a practical selection to concurrently maximize torque density and minimize torque ripple [21]. A 20-slot/18-pole machine with conventional double layer windings is shown in Fig. 6a. Each phase comprises four coils with a total of twenty coils for a five-phase winding. Each two nonadjacent series coils are represented using one coil in the winding connection shown in Fig 7a. For a five-phase machine with 20 slots, the angle between different phases is \u2044 . However, for a dual five-phase winding, the split-phase angle will be \u2044 . For this slot number, the angle between any two successive slots in electrical degrees will also be \u2044 , as the fundamental MMF component has a 2-pole configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000968_bf02656592-FigureI-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000968_bf02656592-FigureI-1.png",
        "caption": "Fig. IO--A discs. schematic outline of the 30 and 80 deg ferr i te",
        "texts": [],
        "surrounding_texts": [
            "in Fig. l l ( c ) . The i n t e r n a l s t r u c t u r e of an 80 deg band apparen t ly cons is t s of a heavi ly deformed f e r r i t e , having a cel l s ize of about 0.2 pm (Fig. 11). At the edge of the band, the cel ls a r e often elongated in the 80 deg d i rec t ion (at B, Fig . l l ( a ) .\nThe bands cut through the en t i re previous s t r u c t u r e , and no carb ides can be found. Microprobe ana ly s i s was pe r fo rmed is on the bands , and the carbon content was found to be e s sen t i a l l y ze ro .\nBetween closely spaced 80 deg bands the dens i ty of\n30 deg bands i n c r e a s e s subs tan t ia l ly so that a l ame l l a r s t r uc t u r e is formed. This is i l l u s t r a t e d in TEM in Figs . 9 and 12. Some of the light 30 deg r ibbons join the 80 deg bands , as shown at A in F i g s . l l ( c ) and 12.\nOr ien ta t ion Dis t r ibu t ion . The o r ien ta t ion of the two kinds of bands was studied in p a r a l l e l sec t ions as a function of s t r e s s by choosing d i f fe ren t deviat ions f rom the cen t r a l p lane of the r ing . The r e su l t is r e - produced in Fig. 13, where each point r e p r e s e n t s the mean angle of the phase in ques t ion for the whole r ing.\nThe s t r e s s d e c r e a s e s with d i s tance from the cen t ra l plane. It is evident f rom the d iagram, however, that this does not affect the or ien ta t ion of the bands. They a re well ga thered around 30 and 80 deg in a l l cases .\nDISCUSSION\nM a c r o s t r e s s e s\nFig. 4 shows the t r a n s f o r m e d layer extending from 100 to 500 ~m below the contact su r f ace . Fig. 3 shows that ma x i mum softening occurs at somewhat more than 200 ~m depth, which agrees ve ry wel l with the level of max imum shea r s t r e s s accord ing to Tab le II. (The sl ight va r i a t i on with load is not de tec table in s t ruc - tu re images ) . Thus, on a macro sca le , the r o l l i ng fatigue causes s t r u c t u r a l changes in the region of ma x i mum shear s t r e s s . This suppor t s the idea of s t r e s s induced t r a n s f o r m a t i o n s .\nThe sof tening curves indicate an in i t i a l s l ight s t r a in hardening of the m a r t e n s i t e af ter a round l0 s cycles , followed by the o c c u r r e n c e s of succes s ive ly sof ter s t r u c t u r e s .\nMETALLURGICAL TRANSACTIONS A VOLUME 7A, AUGUST 1976-1105",
            "T r a n s f o r m a t i o n M e c h a n i s m s\nOn a m i c r o s c a l e the s t r u c t u r a l changes r e s u l t in t h r e e d i s t i ngu i shab l e p roduc ts ; in ch rono log i ca l o r d e r , and as named in the p r e s e n t work, DER, 30 and 80 deg bands .\nI t is ev ident that the decay of m a r t e n s i t e i s involved in the f o r m a t i o n of the new p h a s e s . Obvious ly , the r e - sul t ing so f t e r s t r u c t u r e i s composed of m o r e o r l e s s t yp i ca l f e r r i t i c r e g i o n s , i n t e r m i x e d with ca rbon r i c h ( c a r b i d e - l i k e ) r eg ions and r e s i d u a l m a r t e n s i t e .\nBy combin ing the r e s u l t s of a l l the d i f f e r en t i n v e s t i - gat ion me thods r e p o r t e d above, a t r a n s f o r m a t i o n m e - chanism has been worked out. I t i s b a s e d on the fo l lowing p r e s u m p t i o n s :\ni) The t e m p e r a t u r e in the t r a n s f o r m i n g r eg ion i s of the o r d e r of 50~ (the m e a s u r e d t e m p e r a t u r e of the lubr ican t ) .\ni i) The h y d r o s t a t i c p r e s s u r e c o r r e s p o n d i n g to each s t r e s s cyc le l o w e r s the ac t iva t ion e n e r g y for t h e r m a l l y ac t iva t ed p r o c e s s e s .\ni i i ) Even p r o c e s s e s which a r e t h e r m o d y n a m i c a l l y i m p r o b a b l e under the p r e v a i l i n g s t a t i c condi t ions can be expec ted a f t e r a s much as 10 ~ c y c l e s of a high pu l sa t ing s t r e s s .\niv) On a m a c r o s ca l e , the c h e m i c a l compos i t i on of the p a r e n t m a r t e n s i t e i s p r e s e r v e d . In p a r t i c u l a r , th is m e a n s that the ca rbon content m u s t be ma in t a ined .\nD a r k Etching Reg ion\nThe p a r e n t m a r t e n s i t e i s t h e r m o d y n a m i c a l l y uns t a - b le under the t e s t i ng condi t ions . The t e m p e r a t u r e i s , however , not high enough to ac t i va t e the d i f fus ion dependent p r e c i p i t a t i o n of E - c a r b i d e s , t y p i c a l of t e m p e r - ing. S t r e s s induced ca rbon d i f fus ion i s neg l ig ib le d u r - ing each cyc le , but may be of i m p o r t a n c e over v e r y l a rge n u m b e r s of cyc l e s . Le t us a s s u m e that the c a r - bon in E - c a r b i d e s and in so lu t ion in the m a r t e n s i t e , about 2.7 a t . pct , g r adua l ly s e g r e g a t e s on d i s l oca t i ons , p r e s e n t at a dens i ty , p = 1013 cm -e, (The n e c e s s a r y b r e a k - u p of E - c a r b i d e s i s t r e a t e d in Ref . 15).\nThe a v e r a g e d i s l oca t i on spac ing then i s about 13b (b = s h o r t e s t i n t e r a t o m i c d i s t ance) , which i m p l i e s a m a x i m u m di f fus ion pa th of 6b and an a v e r a g e dif fus ion path of 3b for a ca rbon i n t e r s t i t i a l to r e a c h a d i s l o c a - t ion. Dur ing, say , 108 s t r e s s cyc l e s , th is r e q u i r e s only one s u c c e s s f u l l y d i rec te t t jump p e r 3 \u2022 107 s t r e s s in-\nII06-VOLUME 7A, AUGUST 1976 METALLURGICAL TRANSACTIONS A",
            "duced a t tempts . Fur ther , a complete carbon denudation of the lat t ice would r e su l t in a dis locat ion decora - t ion of no more than 6 carbon atoms per a tomic plane, threaded by a dis locat ion.\nThis view of carbon migra t ion is also supported by the observat ion of an in i t ia l increase in mic roha rdness ( s t ra in hardening, F ig . 3). According to Savitski i and Skakov a7 and Chernyak 18 a slight plas t ic deformat ion is assoc ia ted with an X - r a y line sharpening, also obse rved in fatigued bal l bear ing r ings and cold ro l l s 19 and in terpre ted by them as a t rans i t ion of carbon from the mar tens i t e la t t ice into defects .\nQuantitatively, it thus s eems poss ible to obtain a mar tens i te decay during the presen t test ing conditions. The resul t ing phase then is f e r r i t i c . It is the rmodynamical ly strongly supersa tu ra ted in carbon, though not in ord inary solution.\nHereaf te r , this phase will be r e f e r r e d to as DERf e r r i t e . It is exper imenta l ly observed to grow in groups of pa ra l l e l d iscs of a r b i t r a r y orientat ion, separa ted by res idua l mar tens i t e (see Fig. 5). Qualita t ively, the TEM images indicate some dis locat ion red is t r ibu t ion towards the faces o f thed i scs , eventually creat ing grain boundary-type in terfaces , which a r e poss ib le s i tes for excess carbon.\nThe fine mixture consti tutes the dark etching prope r t i e s of the DER, probably because of p re fe ren t ia l etching of the closely spaced phase boundaries , or different etching ra tes of the two phases .\n30 Dee Bands\nDuring continued cycling, the high s t r e s s e s can be re laxed to some extent by local p las t i c deformation.\nThe sub- su r face s t r e s s tensor , typical of the rol l ing contact, though not yet calculated, must be a symmet r i c with r e spec t to the r ing radius .lo,21 Consequently, it is probable that the plane of maximum shear s t r e s s is no longer inclined by 45 dee as in the well-known static case. (Exper imenta l work is going on at p resen t to vary the s t r e s s tensor by varying the bear ing geomet ry, together with finite e lements calculat ions of two dimensional s t r e s s cases) . The hardness curves indicate that the DER- fe r r i t e is more ducti le than the mar tens i t e . Let us assume that local flow can be nucleated and dis locat ions can escape thei r carbon decorat ion in the DER-fe r r i t e .\nDislocat ion glide then gives r i s e to shear along a well defined direct ion, given by the s t r e s s tensor , and not re la ted to the crys ta l lographic d i rec t ions . Each s t ra in nucleation si te thereby in i t ia tes a thin d iscshaped deformat ion zone, in the p resen t case inclined by 30 dee with r e spec t to the ro l l ing d i rec t ion .\nThe carbon is forced into solution, and the c o r r e s - ponding energy increase provides a dr iving force for diffusion towards the surrounding mat r ix . Because the la t ter does not deform appreciably, there wil l be a tendency of void formation along the in terface favoring the nucleation of carbides .\nCarbon t rapping at the interface wil l cause slight concentration gradients with a resu l t ing drif t velocity normal to the plane of the disc . This impl ies very short diffusion dis tances before the carbon atoms are captured for instance by s e s s i l e d is locat ions . Hereby, the carbon concentration in the in ter face will inc rease beyond what is poss ible to c lass i fy as dis locat ion decora t ion or a tmospheres . Very finely d i spe r sed carbide prec ip i ta t ion then occurs , forming two fine grained, not n e c e s s a r i l y compact d iscs of carb ides , often d is - playing a rung- l ike contras t in TEM (Fig. 14). These carbides surround the p las t ica l ly deformed disc, con-\nangte to raceway (degrees)\nI n\n100\nx XoxXX\n60 ~\nX Xexx~\n9 % X e x\nX 9 9 x\n-2 -,1\nMETALLURGICAL TRANSACTIONS A\nI innerring\nId Fig . 1 3 - - O r i e n t a t i o n of 30 and 80 deg b a n d s in p a r a l l e l s e c t i o n for con t ac t s t r e s s e s of 3280 N / r a m 2 ( \u2022 and 3720 N / r a m 2 (e).\nVOLUME 7A, AUGUST 1976-1107"
        ]
    },
    {
        "image_filename": "designv10_1_0000443_tmag.2010.2093872-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000443_tmag.2010.2093872-Figure1-1.png",
        "caption": "Fig. 1. Cross-sections of study PMSM models and winding pattern of one phase: (a) 8-pole/12-slot model; (b) 8-pole/9-slot model.",
        "texts": [
            " However, the essential influence on the vibration and noise by the different structures is not mentioned in this paper. Based on these previous works, this paper uses the numerical methods to study the effect of the combination of pole and slot on the vibration and noise of PMSM. In order to directly show the effect of the magnetic force on the vibration, a series of analysis process and prediction methods are proposed, and the validation of this process is verified by the experiment test. The cross-sections and the winding patterns of two analysis models are shown in Fig. 1. They have the identical rotor structure but different stators. The combination of pole and slot of one model is 8/12, i.e., the number of coils per phase per pole is 0.5 . The other has the 8/9 combination of pole and slot, i.e., the structure that slot number and pole number differ by one . The specifications of these two models are listed in Table I. 0018-9464/$26.00 \u00a9 2011 IEEE As the component of total force, the radial force of PMSM can be well calculated in the Maxwell stress tensor method [5]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000927_0094-114x(82)90042-8-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000927_0094-114x(82)90042-8-Figure9-1.png",
        "caption": "Figure 9. Displacement functions.",
        "texts": [],
        "surrounding_texts": [
            "Figure 1 illustrates an uncertainty configuration of a spatial 5-1ink RCRCR mechanism. (A planar representation of the RCRCR mechanism labeled with dual angle sides &ii =aii + ~ aij and dual exterior angles #j = 0~ + \u00a2 Sj (~2 = 0) is illustrated by Fig. 2). For this case all the seven screws are reciprocal to the single screw ~ as illustrated. The rank of the matrix of the screws expressed in Pliicker coordinates is 5, and, therefore, all the 6 \u00d7 6 determinants of the 7 \u00d7 6 matrix of the Pliicker coordinates are instantaneously zero. The mechanism has mobility two instantaneously. Also (see[l]) since the pitches of the screws representing revolute joints are zero ~ef i r~ tan A~ = r3 tan A3 = r5 tan ,~5 = h (8) where h is the pitch of ~ (Note, the Pliicker coordinates of a C pair are expressed in terms of the Plucker coordinates of co-axial R and P pairs[I,3]. It follows that the C pair axes and the ~ axis are mutually perpendicular.) Figure 3(a-f) illustrate the displacement functions of a spatial 5-1ink RCRCR mechanism with dimensions au = lO/~(3)m 0/12 = 150 o S l ! = lOm a23 = 10.0 a23 = 315 \u00b0 $33 = 5/V'(2) a34 = 5/X/(2) 0/34 = 2700 $55 = 20 a45 = 0.0 0/45 = 90 \u00b0 aSl = 20/~/(3) 0/51 = 300 \u00b0 All the 6 \u00d7 6 determinants were zero at 05 = 90% and the determinant of the screws of the C2 - R3 - C4 - R5 pairs plotted against 0s is superimposed on the input-output function 01 VS 05 in Fig. 3(a). The mechanism has an uncertainty configuration as illustrated by Fig. 4, and all the, displacement functions Figs. 3(a-f) exhibit a double root at 05 = 90 \u00b0. Consider now that a 6 x 6 determinant Di = 0 (i denotes the 6 \u00d76 determinant which excludes the ith screw) of the 7 x 6 matrix of the Pliicker coordinates. It follows that all the screws except the ith screw are linearly dependent and, therefore, the ith joint cannot move instantaneously. Figure 5 illustrates the input--output function 01 vs 05 of an RCRCR mechanism with the following dimensions al2 = 25 m 0~12 = 60 \u00b0 S . = 30 m a23 = 30 a23 = 45 \u00b0 $33 = 25 a34 = 40 o~34 = 35 \u00b0 $55 = 0 a45 = 10 a45 = 300 as] = 32 asl = 10 \u00b0 MMT Vol. 17, No. 2-43 124 125 Superimposed on the input-output function are the graphs of the determinants Di and /)5 plotted against 05. It is clear that Dl = 0 when (d0Jd05)= 0, and link a,2 has a limit position. Also, D5 = 0 when (d05/d01) = 0, and the link a45 has a limit position. An interesting stationary configuration of the RCRCR mechanism occurs (Fig. 6) when the two screws representing the slider displacement of the cylindric pairs become linearly dependent. All the remaining five rotational motions must be instantaneously zero. This type of stationary configuration is difficult'to explain without a numerical example. The input--output function 0, vs 05 together with the slider-displacement functions $2 vs 0s and $4 vs 05 are illustrated by Figs. 7(a-c) of an RCRCR mechanism with the following dimensions a12 = 5%/(3) m a 1 2 = 90 \u00b0 $1, = 30m a23 = 15 a23 = 270 $33 = 20 a34. = (20%/(3) - 15) a34 = 270 $55 = 10 a45 = 10 a45 = 60 a51 = 5 asi = 270 Only one branch of the input-output function is shown. When the mechanism is in the configurations labeled by points 1, 2 and 3, the two cylindric pairs are parallel, and the slider displacements can assume values between + ~ and -oo. All five rotational motions are zero for finite values of the slider displacements. However, when (i) $2 = -+ ~ and $4 = -+ ~ the mechanism can be driven through point 1. (ii) $2 = $4 = -+ oo the mechanism can be driven through points 2 and 3, and all three points are uncertainty configurations. Such configurations which Dimentberg[6] termed as points of indeterminate slipping are better explained by considering the limit positions of the input crank of the spatial 4-1ink RCCC mechanism. More recently Gilmartin and Hunt[l, 6] discussed this type of configuration. Here a more complete explanation is given for the RCCC mechanism with the aid of screw theory. An RCCC mechanism with the following dimensions has an stationary and uncertainty 126 (260l, ~1 deg 180 120 60 0 - 6 0 (-Ioo) \u00b0 I00 - S4 m 5 0 - 0 50 5 0 - 100 150 to ; (a) 85 deg i 390 ~s deg ! 390 L ~ ~- deg Figure 7. Displacement functions. configuration illustrated by Figs. 8(a-b) a12 = 1.Om a12 = 60 \u00b0 a23 = 1.5 az3 = 60 \u00b0 a34 = 2.0 0'34 = 90 \u00b0 a41 = 3.0 a41 = 90 \u00b0 $44 = 2.5m Figure 8(a) illustrates a stationary configuration of the input crank a34 Links a~2 and a23 are parallel, and the axes of _S,, _$2 and _$3 are normal to the plane defined by al2 and a23. The screws representing the slider displacements of the three cylindric joints are linearly dependent. The four 6 x 6 determinants of the 7 \u00d7 6 matrix which include the Pliicker coordinates of the slider displacements are thus simulataneously zero. The remaining three 6 \u00d7 6 determinants are not zero, and, therefore, alLfour rotational displacements are simultaneously inactive. The links a j2 and a23 are, however, free to slide. A stationary configuration of the input crank a34 occurs when 04 = 300 \u00b0, and the slider displacements $1, $2 and 5'3 have values in the range _+ ~, as illustrated by Figs. 9(a-f). However when the slider displacement $2= 0 then aj2 and a23 become coaxial, see Fig. 8(b), and the axes $1, _$2 and _$3 have a common perpendicular line. The screws representing the motions of the three cylindric pairs now belong to a system with 127 -aa4 order four, and the mechanism has an uncertainty configuration. The axis of the screw which is reciprocal to all the seven screws representing the joint motions is along the (_a12, _a23) line as illustrated by Fig. 8(h). The mechanism can now be moved out of this position by rotating the input crank back out of its limit position. Theoretically when 04 = 60 \u00b0, the input crank is stationary. A further uncertainty configuration occurs when 04 = 180 \u00b0. The slider displacements have infinite values. Clearly such configurations can never be reached in practice. The use of the Gramian for determining special configurations of overconstrained singleloop mechanism is illustrated using as an example the 4R planar mechanism (Fig. 10) with the following dimensions a12 = 5 a23 = 3 a34 = 1 a4~ = 3m. Figure 11 illustrates the input-output function O~ vs 04 together with the Gramian, G1 vs 04 which excludes the screw _M1 which represents the instantaneous motion of joint I 6 1 = ~ * ~ * ~ ~ * ~ ~ * ~ * ~ ~ * ~ ~ * ~ * ~ ~ * ~ (9) It is clear from Fig. 11 that GI = 0 for 04 = 90, and 270 \u00b0, and the screw _M1 is inactive, or the link a12 is at a limit position. Also when 04 = 180 \u00b0, all of the four 3\u00d73 Gramians are zero simultaneously and the mechanism is an uncertainty position. This is the flattened or crossover position, see Fig. 12(a). Finally, consider that the input--output function Oj vs05 of the RCRCR mechanism Fig. 5 129 R2 07\u00b0- . . o / o., -~T /._.t 04"
        ]
    },
    {
        "image_filename": "designv10_1_0001149_j.mechmachtheory.2016.08.005-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001149_j.mechmachtheory.2016.08.005-Figure11-1.png",
        "caption": "Fig. 11. A 3D finite element model built in Ansys.",
        "texts": [
            " The method proposed in this paper will generate the same mesh stiffness for these two cases. The effect of pitting distribution along tooth width direction on the mesh stiffness is not covered in this study. This will be our future work. To validate the mesh stiffness equations derived in this paper, the mesh stiffness of the same gear pair used in Section 3 is evaluated in this section using the finite element method (FEM) for comparison. The parameters of the gears are listed in Table 1. A 3D finite element model is built and shown in Fig. 11. The gear is modeled using the element type SOLID185. The element shape of the gear body and the perfect gear teeth is mapped hexahedral while that of the pitted tooth is tetrahedral. The tetrahedral shape is chosen for the pitted tooth as it can model complicated pitting profile. Six teeth are refined when the middle one or two teeth are in meshing. The gear body is modeled a rigid body to be consistent with the proposed model in Section 2. In order to model a rigid gear body in ANSYS, Young's modulus for gear body is set to be 1000 times larger than that for gear teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001398_jestpe.2018.2811538-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001398_jestpe.2018.2811538-Figure3-1.png",
        "caption": "Fig. 3. Relative position of two coils a) 24-slot/14-pole b) 24-slot/22-pole [8]",
        "texts": [
            " It has the highest d-axis current as shown in Fig. 2, which may cause PM demagnetization. Lower mutual inductance in fractional slot machines is an advantage in case of an ITSC fault. Therefore, fault characteristics of 6-phase fractional slot machines with three different pole combinations are compared in terms of magnetic couplings between coils of a phase in [8]. The response of 24-slot/22-pole and 24-slot/14-pole designs are compared when faulty phase terminals are short-circuited to suppress the short circuit faults as shown in Fig. 3. It is shown that the short circuit currents can go up to 18 p.u in 24-slot/14pole configuration, where in 24-slot/22-pole, it does not exceed 2 p.u showing that this slot pole combination is less vulnerable to ITSC fault. Series and parallel winding configurations were charcteretized and modelled in [26] and [36], and compared the ITSC fault monitoring tecniques for both winding configuraions. In brief, detecting ITSC in parallel configuration is harder due to lower local leakage flux in shorted coils under equal fault conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003080_j.phpro.2014.08.099-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003080_j.phpro.2014.08.099-Figure7-1.png",
        "caption": "Fig. 7. Web supports generated with 3Data Expert.",
        "texts": [
            " The typical applications include for example functional prototypes, small series products, individualized products or spare parts. 3.3. Test pieces in this study Two different support structures were generated in the experiments for the test piece: web supports and tube supports. Support structures were designed with 3Data Expert software created by the company DeskArtes (Finland). The support structures were crated to be easily removed without damaging the test part surface so the supports needed to be as low volume as possible. The web supports (see Fig. 7) are designed to support overhanging down-facing surfaces of bars of the test piece. The webs of the supports are used to reduce the contact area of the part surface and let the unexposed powder to be easily removed. Dimensions of web supports are 1.30 mm (sample 1) and 1.45 mm (sample 2). The design principle of tube supports (see Fig. 8) was to lower the support volume. As the tubes are hollow the contact surface is smaller which reduces the surface damage after the removal of the supports. The diameters of the tube supports are 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001971_tie.2018.2870355-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001971_tie.2018.2870355-Figure1-1.png",
        "caption": "Fig. 1. Positions of stator flux and rotor.",
        "texts": [
            " Due to the excitation characteristic of three-phase SRMs, only one phase is mainly to provide the output torque at any time. Therefore, this phase can be considered as the main phase to form the combined flux vector. The combined flux vector generally locates around the axis of the main phase, which corresponds the stator pole of the main phase in the mechanical structure. At the same time, the rotor pole is approaching the stator pole of the excited phase because of the minimum reluctance principle, as shown in Fig. 1. Flux vector\u2019s angle \ud835\udf03\ud835\udf11 is much close to the real rotor position \ud835\udf03\ud835\udc5f and the error between them becomes smaller. Thus they can be considered with no difference when indicating the rotor position. When the commutation occurs, the flux vector rotates quickly from the axis of the former phase to that of the next phase. After that, the corresponding rotor pole will rotate at the mechanical speed whereas the flux vector almost stands still. The difference between the two axes will decrease until next phase\u2019s aligned position arrives"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001948_c2sm06844c-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001948_c2sm06844c-Figure1-1.png",
        "caption": "Fig. 1 (a) A schematic of the experiment by which an elastomeric film of initia of a much thicker and stiffer elastomeric substrate. (b) Reflectance optical H \u00bc 63 mm. At 3 \u00bc 0.475, short folds formed in the vicinity of defects but did bottom left) eventually led to formation of a parallel array of folds (bottom",
        "texts": [
            " Creases formed on swelling gel surfaces have received slightly more quantitative study,4,5,9,20\u201322 but the challenges inherent to modeling swelling have made quantitative comparisons with theory difficult. Here we study both the initiation and development of creases in homogeneously compressed elastomer films through a combination of simple experimental and numerical methods. This allows for detailed quantitative comparisons between experimental measurements and numerical predictions. We find that the onset, shape, and spacing of creases are very well described by calculations of the equilibrium elastic state for a neo-Hookean material with no adjustable parameters. Fig. 1a illustrates the experimental approach, modified from a previous study of the snap-through instability of supported elastic membranes.23We apply a uniaxial tension to stretch a thick substrate from the original length L0 to a length L, and then attach to the stretched substrate a stress-free film of thicknessH that is much softer than the substrate.When the substrate is partially released to a length l, the film is subjected to a compressive strain 3\u00bc 1 (l/L). The film is in a state of uniaxial stress, because both the substrate and film are incompressible",
            " While these materials display viscoelastic behavior, compression was performed slowly across the range of 3 of interest ( 30 min between each incremental application of a strain of 0.01), and structures were measured only after allowing samples to equilibrate for at least 48 h, to ensure that the effects of viscous stresses were minimal. 1302 | Soft Matter, 2012, 8, 1301\u20131304 Films with undeformed thicknesses of H \u00bc 23\u2013147 mm were compressed by partially releasing the substrate, and observed in situ using an upright optical microscope. Beyond a certain level of strain, short creases formed in the vicinity of defects or scratches on the film surface, as shown in Fig. 1b, top left. At a higher level of strain, the creases extended laterally across the surface of the films, leading ultimately to an array of creases with fairly regular spacing (Fig. 1b, bottom right). This behavior complicates unambiguous identification of a critical strain. However, the smallest strain at which creases were found to propagate across the surface for any sample was 3 \u00bc 0.46, providing an upper bound for the experimental value of the critical strain. The creasing instability may also be affected by the PDMS/air surface energy g, which, together with Young\u2019s modulus of the film E, yields amaterial-specific length22 g/E estimated as 0.4 mmbased on a value of g \u00bc 20 mN m 1",
            " The magnitudes of the predicted and observed wavelengths are in good agreement, though the scatter in the experimental data precludes a more detailed comparison of the dependence on strain.While it has long been appreciated that the characteristic spacing between creases must scale as the film thickness,1 as this is the only relevant length scale in the problem, our results represent the first prediction of the pre-factor in this scaling relationship, as well as the first measurement of crease spacings for elastomers. Notably, experiments revealed a well-defined characteristic spacing of creases, but not perfectly regular packing (Fig. 1b), and once a parallel array had formed, This journal is \u00aa The Royal Society of Chemistry 2012 further compression led to only \u2018\u2018affine\u2019\u2019 changes, never to annihilation or appearance of new creases. These observations are consistent with the relatively weak dependence of elastic energy on aspect ratio shown in Fig. 2, and also indicate that creases are not able to fully equilibrate, thus yielding sensitivity of the observed spacing to sample history. Fig. 3b shows the calculated distance from the uppermost point on the surface to the bottom of the crease tip d1 and the depth of the selfcontacting region d2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000655_1.4002333-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000655_1.4002333-Figure4-1.png",
        "caption": "Fig. 4 Defect and deflection details: \u201ea\u2026 schematic position of t",
        "texts": [
            " The value of stiffness of housing is 1.2 107 N /mm for he present operating conditions. 2.2.2 Damping. In the proposed model, shaft and housing ampings are assumed to be hysteretic and the equivalent viscous amping coefficient is calculated using the equation as follows 19 : Cs,h = s,hKs,h ext 11 here ext is excitation frequency. 2.3 Simulation of Local Defects. In this section, mathematial simulation of local defects in the model is described. Defects n races have been shown schematically in Fig. 4. Moreover, the hotographic view of the defects is also provided in Fig. 5 for etter illustration. 2.3.1 Defect on the Inner Race. The location of defects on the nner race does not remain stationary since the inner race rotates ith the speed of the shaft s . Thus, the defect angle for the nner race in is defined as st width of defect /di . The rollng ball approaches the defect either in the loaded zone or the nloaded zone; thus, the deflection i of the ith ball varies. Addiional deflection at the jth defect j of the ball when it passes hrough the jth defect is defined by the width of the defect as ollows: j = d/2 \u2212 0",
            "0057 mm Single defect on outer race BPFO=76.67 Hz Amplitude=0.00094 m Two defects on outer race BPFO=77.14 Hz Amplitude=0.0015 mm ig. 7 Vibration response of defect free \u201ehealthy\u2026 bearing in adial direction \u201eX\u2026 at shaft speed of 1500 rpm: \u201ea\u2026 vibration of all 8 and \u201eb\u2026 vibration spectrum for housing ig. 8 Experimental vibration spectrum of housing for defect ree \u201ehealthy\u2026 bearing \u201eNs=1500 rpm\u2026 ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 03/09/2015 Terms as explained in Fig. 4. The defect\u2019s size at both inner race and outer race for single and two defects cases are kept as: length Ldefect =1.0 mm, width Wdefect =0.5 mm, and depth Ddefect =0.25 mm. The defect angle with respect to the X axis is kept at 0 deg for a single defect and two defects. However, another defect in the case of two defects is introduced at an angle of =30 deg. The defects are created on races of the test bearings by electric discharge machining EDM . 4.2.1 Defect on Inner Race 4.2.1.1 Single defect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001915_tac.2011.2173424-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001915_tac.2011.2173424-Figure1-1.png",
        "caption": "Fig. 1. Differentiator performance (a) Signal and its derivatives (b) Differentiator convergence (c) Normalized coordinates.",
        "texts": [
            " Obviously it also attracts trajectories in finite time. Using the homogeneity transformation (6) with arbitrary , , obtain the needed asymptotics. Demonstrate differentiation of signals with exponentially growing highest derivative. Consider a differential equation ! ! ! ! ! ! ! with initial values ! , ! , ! , ! . The differentiator (1) with , , , , , ! and ! ! ! ! is taken, with ! being the sampled output. The initial values of the differentiator are , . The graphs of !, !, !, ! are shown in Fig. 1(a) for . The functions rapidly tend to infinity. In particular, they are \u201cmeasured\u201d in millions, and ! is about at . The accuracies ! , ! , ! , ! are obtained with . In the graph scale of Fig. 1(a) the estimations , , , cannot be distinguished respectively from !, !, !, ! . Convergence of the differentiator outputs during the first 2 time units is demonstrated in Fig. 1(b). The convergence of the normalized errors ! , ! , ! , ! to zero during the first 2 time units is shown in Fig. 1(c). The accuracies , , , were obtained with . With the accuracies change to , , , which corresponds to Theorem 3. The accuracies change to , , , , when a measurement noise of the normalized magnitude is introduced. Note that , and respectively the real noise magnitude is at . Taking obtain , , , with the real noise magnitude at . It also corresponds to Theorem 3. V. FEEDBACK APPLICATION EXAMPLE Dynamics of an aircraft are mostly determined by its velocity (the Mach number) and the altitude (calculated via the dynamic pressure), and are studied experimentally in wind tunnel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000628_j.automatica.2011.01.024-FigureA.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000628_j.automatica.2011.01.024-FigureA.1-1.png",
        "caption": "Fig. A.1. (a) The moving coordinate frame; (b) Limit as \u03f5\u2217 \u2192 0.",
        "texts": [
            "1) where \u27e8\u00b7, \u00b7\u27e9 is the standard inner product and the inequalitymeans that the matrix of the second derivatives is nonnegative definite. It follows from the first equation in (A.1) that for any twominimumdistance points r\u2217, r\u22c6, the vectors r\u2212r\u2217 and r\u2212r\u22c6 are perpendicular to a common nonzero vector r\u0307(\u03c4 ). So the points r, r\u2217, r\u22c6 are colinear. Now suppose that r is a focal point, i.e., there is a minimumdistance point r\u2217 \u2208 D such that d0 = \u2016r \u2212 r\u2217\u2016 = R\u03ba(r\u2217) and \u03ba(r\u2217) < 0. Let T = \u03c1\u2032 be the unit tangent vector and N be the unit normal vector directed inwards D (see Fig. A.1(a)). By the second equation in (A.1), r\u2217 \u2212 r = d0N(s\u2217), and due to the Frenet-Serret formulas (Sternberg, 1999), T \u2032 = \u03baN, N \u2032 = \u2212\u03baT . (A.2) Hence \u03a6 \u2032\u2032 ss(\u03c4 , s\u2217) = \u2016T (s\u2217)\u20162 +  T \u2032(s\u2217); r\u2217 \u2212 r  = 1 + \u03ba(r\u2217)d0 \u27e8N(s\u2217);N(s\u2217)\u27e9 = 1 + \u03ba(r\u2217)R\u03ba(r\u2217) = 0; \u03a6 \u2032\u2032 ts(\u03c4 , s\u2217) = \u2212\u27e8r\u0307(\u03c4 ); \u03c1\u2032(s\u2217)\u27e9 = \u00b1v =\u0338 0, where the last equation results from the equations in (A.1) since\u2016r\u0307(\u03c4 )\u2016 = v. It follows that the determinant det\u03a6 \u2032\u2032(\u03c4 , s\u2217) = \u2212v2 < 0, whereas the inequality from (A.1) implies that this determinant is non-negative",
            "2) yields that r \u2032 = (1 + \u03bad0)T , r \u2032\u2032 = \u03ba \u2032d0T + \u03ba(1 + \u03bad0)N. Let J :=  0 1 \u22121 0  and \u2217 stand for the transposition. Then the curvature radius R of the trajectory is given by R = \u2016r \u2032 \u2016 3 |(r \u2032)\u2217Jr \u2032\u2032| = |1 + \u03bad0|3 |\u03ba||1 + \u03bad0|2 = |d0 + R\u03basgn\u03ba|. It remains to note thatR should exceed theminimal turning radius of the vehicle R. Proof of Theorem 3. We introduce the normally oriented moving Cartesian coordinate frame centered at the point r\u2217(t) \u2208 D nearest to the vehicle current position r(t), with the axis of abscissa directed towards the vehicle (see Fig. A.1(a)). Let \u03b1 denote the algebraic angle between the velocity vector of the vehicle and the axis of the abscissa. Lemma 5. Let d \u2208 [d\u2212, d+], where [d\u2212, d+] is the interval from Assumption 4. Then the following relations hold d\u0307 = v cos\u03b1, \u03b1\u0307 = u \u2212 \u03ba(r\u2217) 1 + \u03ba(r\u2217)d v sin\u03b1. (A.3) Proof. We employ the parametric representation \u03c1(s) of \u2202D and the vectors T and N from the proof of Lemma 1. Let s(t) denote the natural parameter corresponding to r\u2217(t). Then the vehicle position r(t) = \u03c1[s(t)] \u2212 d(t)N[s(t)]",
            "3), \u03b1(t) \u2192 2\u03c0m \u00b1 \u03c0/2 as t \u2192 \u221e, where m is an integer. So (A.4) yields that \u00b1s\u0307 \u2212 v 1+d0\u03ba  \u2192 0 as t \u2192 \u221e, where s is the curvilinear abscissa of the boundary point r\u2217 \u2208 \u2202Di nearest to the vehicle\u2019s position r and \u03ba is the curvature of \u2202Di at r\u2217. Due to Assumption 5, 0 \u2264 \u03ba \u2264 \u03ba+ < \u221e, where \u03ba+ does not depend on r\u2217. Hence limt\u2192\u221e \u00b1s\u0307 \u2265 v 1+d0\u03ba+ > 0, \u21d2 \u00b1s(t) \u2192 \u221e as t \u2192 \u221e, i.e., r\u2217 monotonically and repeatedly circulates around the entire boundary \u2202Di since some time instant. Whence the tangential vector \u00b1T from Fig. A.1(a) monotonically rotates about the origin by repetition of full rotations. Since \u03b1(t) \u2192 2\u03c0m \u00b1 \u03c0/2, the angular deviation between \u00b1T and the vehicle velocity v\u20d7 annihilates as time progresses (see Fig. A.1(a)). Hence \u03b8(t) \u2192 \u00b1\u221e as t \u2192 \u221e, where \u03b8(t) is the continuous orientation angle of the velocity (i.e., the vehicle itself). On the other hand, di(t) t\u2192\u221e \u2212\u2212\u2212\u2192 d0 \u21d2 di \u2264 d0 + \u03f5/2 since some time t\u2217 \u2265 tav, whereas the target T lies outside the  d0 + \u03f5  -neighborhood of Di by Assumption 8. Hence the continuous angular direction \u03b7(t) from the vehicle to the target evolves within some intervalwhose length< \u03c0 . Due to the continuity of both \u03b8(t) and \u03b7(t), there necessarily exists a time \u03c4 \u2265 t\u2217 when the vehicle is oriented towards the target: \u03b8(\u03c4 ) = \u03b7(\u03c4) + 2\u03c0 l, where l is an integer",
            " There exists \u03f5\u2217 > 0 such that whenever the vehicle undergoes a sliding motion within the maneuver of avoidance an obstacle Di, is at the distance dsafe \u2264 di \u2264 d0 + \u03f5\u2217 from Di, and is directed towards the target, the safety requirement di \u2265 dsafe associated with this obstacle is fulfilled for all points from the straight line segment L = [r; T ] connecting the vehicle\u2019s position r with the target T . Proof. We examine separately two cases. (1) di \u2264 d0, where di = distDi(r) and distDi(\u00b7) is given by (3). From the slidingmotion equation d\u0307i = \u2212\u03c7 [di\u2212d0] and (5), we see that d\u0307i \u2265 0 (A.3) =\u21d2 cos\u03b1 \u2265 0. Thus L forms an obtuse angle with the inner normal N to \u2202Di at the point r\u2217 \u2208 \u2202Di closest to r; see Fig. A.1(a). Since \u2212N = \u2207distDi(r) (Sternberg, 1999), we have  \u2207distDi(r); T \u2212 r  \u2265 0, where the distance function is convex since so is the body Di itself (Rockafellar, 1970). For such functions, the obtained inequality implies (Rockafellar, 1970) that the function non-strictly increases as the argument goes along the straight line from r to T . Hence r\u22c6 \u2208 L \u21d2 distDi(r\u22c6) \u2265 distDi(r) \u2265 dsafe, where the last inequality is assumed in the lemma. (2) d0 \u2264 di \u2264 d0 + \u03f5\u2217. Let \u03f5\u2217 < \u03b4, where \u03b4 is the controller parameter from Fig. 1(b). The slidingmotion equation and (5) yield that \u2212 \u03b3 \u03f5\u2217 \u2264 d\u0307i \u2264 0 (A.3) =\u21d2 \u2212\u03b3 \u03f5\u2217v \u22121 \u2264 cos\u03b1 \u2264 0 \u21d2 \u03c0 2 \u2264 |\u03b1| \u2264 \u03c0 2 + arcsin \u03b3 \u03f5\u2217 v . (A.11) Now we introduce the perpendicular M to the line segment S = [r, r\u2217] that intersects S at the distance d0 from the obstacle, see Fig. A.1(b). Let \u03f5\u2217 \u2192 0. Then |\u03b1| \u2192 \u03c0/2, di \u2192 d0, and L is asymptotically laid on M . Owing to Assumption 5, these convergences are uniform over all r from the stripe d0 \u2264 distDi(r) \u2264 d0 + \u03f5\u2217 and \u03b1 from the range given after the last \u21d2 in (A.11), as well as over all obstacles. Since M is separated from the forbidden area Di,forb := {r \u2032 : distDi(r \u2032) \u2264 dsafe} by positive both spatial and angular distances independent of r, \u03b1, and i, the segment L does not intersect Di,forb if \u03f5\u2217 is small enough. Now we take \u03f5\u2217 > 0 from Lemma 10, suppose that \u03f5 \u2208 (0, \u03f5\u2217), and put g := C + 2R \u2212 (d0 + \u03f5) > 0, where the inequality holds owing to (10)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001214_j.rcim.2017.02.002-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001214_j.rcim.2017.02.002-Figure9-1.png",
        "caption": "Fig. 9. Different clamping ways of the spindle. (a) Pointing configuration. (b) Hanging configuration.",
        "texts": [
            "5 rad and \u22121.2 rad to optimize the stiffness of the robot. Thus, the EE position can be roughly determined. The orientation optimization methodology aims at optimizing the force direction. Since the force direction varies in different machining applications, thus the force direction optimization needs a taskdependent evaluation index. Here, DEI proposed in Section 4 is adopted. Since \u03b82 and \u03b8 real3 have been determined in Section 5.2.1, thus only \u03b8 \u03b8~4 6 need to be optimized in the following. As shown in Fig. 9, different clamping ways will yield different expressions of DEI. However, considering the mechanical structure of the robot wrist, only the hanging configuration way shown in Fig. 9(b) is feasible for Smart5 NJ 220-2.7 robot. Under such configuration, the expression of DEI will be derived to reflect the influences of J4-J6 on the EE deformation. First, the matrix Ctt, which is a function of \u03b8 \u03b8~1 5, can be written as: \u23a1 \u23a3 \u23a2\u23a2\u23a2 \u23a4 \u23a6 \u23a5\u23a5\u23a5 C C C C C C C C C C =tt 11 12 13 21 22 23 31 32 33 (15) As mentioned in Ref. [9], when the robots are used in machining for drilling or finishing operations, the force direction is actually the axial direction of the spindle which rotates along with the orientation of the robot EE, as shown in Fig. 9(b). The force in the plane perpendicular to the axial direction of the spindle is relatively small. And it belongs to the dynamical cutting forces which can cause vibration. And vibration belongs to the category of machining dynamics Therefore, it is not considered in this paper which analyzes the static deformation. Then, the force direction with respect to the world frame can be derived by using DHm parameters, which can be written as: \u23a1 \u23a3 \u23a2\u23a2\u23a2 \u23a4 \u23a6 \u23a5\u23a5\u23a5 \u23a1 \u23a3 \u23a2\u23a2\u23a2 \u23a4 \u23a6 \u23a5\u23a5\u23a5 e S S C C S S C C C C C S C C C S S S S S C S C S C C C C C C S C S S S C C C S C S S S aC bS cC dS eC fS = ( + + ) + ( \u2212 + ) ( \u2212 + ) + ( + ) ( \u2212 ) \u2212 = + + + f 1 4 5 1 3 5 1 3 4 5 6 1 4 1 3 4 6 1 3 5 1 4 5 1 3 4 5 6 1 4 1 3 4 6 3 4 5 3 5 6 3 4 6 6 6 6 6 6 6 (16) where S \u03b8= sini i, C \u03b8= cosi i (i = 1, 2, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure14-1.png",
        "caption": "Fig. 14. A pair of spur gears.",
        "texts": [
            " Since there is no commercial FEM software available that can do this analysis, FEM software used for contact analysis and strength calculations of a pair of spur gears with AE, ME and TM are developed in a personal computer through many years\u2019 efforts based on the theory and methods presented in this paper. The following is the flowchart used for FEM software development. Every step in the flowchart is explained in the following: Step 1 : Input gearing parameters and structure dimensions of a pair of gears The FEM software is built to be able to conduct contact analysis and strength calculations of a pair of spur gears with arbitrary structure dimensions as shown in Fig. 14 and gearing parameters such as tooth number, module, pressure angle, profile-shifting coefficients. This software is also suitable for a pair of high contact ratio gears when addendum coefficient is inputted. Step 2: Input position parameter of teeth engagement Engagement position of a tooth from engaging-in to engaging-out is expressed as \u2018\u2018a position parameter\u2019\u2019. When value of this position parameter is given continually, engagement position of the tooth from engaging-in to engaging-out can be determined continually",
            " 13 for gears having contact ratio in the range 1 < e < 2, tooth contact length 2a 0 in the two areas are calculated by FEM when the gears engage at the middle of the double pair tooth contact areas. Fig. 11 is the comparison of 2a 0 between FEM results and Rademacher\u2019s experimental results. Rademacher\u2019s calculation results are also given in Figs. 10 and 11. From Figs. 10 and 11, it is found that FEM results are well agreement with Rademacher\u2019s experimental results. Fig. 12 is FEM results of the maximum surface contact stresses obtained at the same time when FEM calculations are performed. Tooth contact pattern and root strains of a pair of spur gears as shown in Fig. 14 are measured when assembly errors h = 0.42 , / = 0.04 , XE = 2.1 mm and ZE = 0.2 mm are given to the gear shaft A0B0 in Fig. 1. These gears are ground under the accuracy requirement of JIS 1st grade. A so-called power-circulating form gear test rig is used to do the tests at a very low speed (1.65 rpm) under torque T = 294 N m. Fig. 15 is the test gearbox used in the test rig. In Fig. 15, a removable support is used to give AE to the shaft of Gear 1 by changing the position of this support. Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001439_j.cirp.2010.03.021-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001439_j.cirp.2010.03.021-Figure6-1.png",
        "caption": "Fig. 6. Top: Weiss spindle with 2-3 \u2018back-to-back\u2019 bearing configuration; FE model temperatures at t = 1000 s, n = 10,000 rpm; bottom: time-history of bearing preload (Fa) and radial stiffness at spindle nose (Kr), two types of preload, n = 10,000 rpm; numbering from the spindle nose.",
        "texts": [
            " This effect can potentially lead to thermomechanical instability if the temperature\u2013preload feedback is excessively positive, which may occur when the spindle speed is too high. The experimentally validated simulation model has been used to predict contact forces, angles, internal relative displacements and contact status of inner/outer rings of the bearings, as well as the temperature distribution and thermal deformation in the spindle assembly. Example 1: An experimental belt driven spindle reported in [2] has been modeled as shown in Fig. 6. The spindle has GMN HYKH61914 and HYKH61911 bearings which are the only heat sources in the model. The spindle is modeled considering both main types of preload: constant and rigid, with equivalent initial value Fa0 = 1500 N. The resultant time-history of bearing preload (Fa) and radial stiffness at spindle nose (Kr) for both types of preload is shown in Fig. 6. Example 2: A spindle with three SKF 7010CD bearings and rigid preload has also been simulated for detailed tracking of the effects of mounting preload, centrifugal forces and temperatures during n = 15,000 rpm operation. Bearing stiffness in Fig. 7-bottom right shows the sequence of these effects. Discussion of results: In spindles with bearings preloaded with a constant force, changing temperatures alter the preload distribution among bearing groups and affect the structural dynamic properties (Fig. 6-bottom left). In case of rigid preload, changing temperatures produce extra thermal preload which has positive or negative sign depending on particular spindle design, operational conditions and time after the spindle start-up (Fig. 6-bottom right; Fig. 7). The proposed model can simulate both types of preload and also spindles with more than one preloading system. The paper presents a simulation model for predicting the effects of temperature distribution in the spindle system. The transient changes of temperatures may alter the stiffness and contact forces in the bearings which can lead to seizure and damage of the spindles. The presented model can be used to simulate transient interaction between internal bearing behavior on the one hand, and heat transfer and structural deformations in spindle parts on the other hand"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000233_robot.2004.1307414-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000233_robot.2004.1307414-Figure1-1.png",
        "caption": "Fig. 1. The miniature four rotom helicopter.",
        "texts": [
            " The reasons behind the complexity of control design for underactuated systems is that they are not fully feedback linearizable. Moreover, many recent and traditional methods of nonlinear control design including backstepping [8] [ll], forwarding [lo] [13] [14] [15], high-gainnowgain designs [ I 4 [13], and sliding mode control [9] are not directly applicable to underactuated systems with the exception of a few special cases. A. UAV Dynamics The dynamic model describing the UAV position and attitude is obtained using Newton equations. The considered UAV is a miniature four rotors helicopter (Figure 1). Each rotor consists of an electric DC motor, a drive gear and a rotor blade. Forward motion is accomplished by increasing the speed of the rear rotor while simultaneously reducing the forward rotor by the same amount. Back, left and right motion work in the same way. Yaw command is accomplished by accelerating the two clockwise turning rotors while decelerating the counterclockwise tuming rotors. The equations describing the attitude and position of an UAV are basically those of a rotating rigid body with six degrees of freedom [I61 [17]",
            " 5 9 + 0 . 7 ~ +0.125 the constant parameters of the quadrotor are: m = 2Kg, I, = I., = I , = 1.2416N/rad/s2, d = O.lm, g=9 .81m/s2 The control parameters are: A, = 16; A, = 64 Simulation results for desired and observed positions and trajectories are presented: A. Flight without perturbation Results without perturbation are shown in Fig4 to Fig-9 B. Flight with parametric Uncertainties For a uncertainly of -20% on m , Ix, Iy , Iz and d, parameters robustness of the quadrotor is shown bellow (FiglOFig1 I): C. Compewation of wind disturbances: Parameters Ap, Aq, and Ar have been introduced in control law to analyze the behavior of the system when taking into account perturbation in the controller. For Ap = 0.02, Aq = 0.03,Ar = 0.04 the following results are obtained (Fig-I2 to Figl4) : D. Discussion of results It is seen from reference trajectories tracking without perturbation (Fig4) that feedback linearization control on Euler angles is acceptable since the tracking of angles and positions was perfect (Fig5,6)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.18-1.png",
        "caption": "Fig. 3.18 Different approximate models for a hingeless rotor blade",
        "texts": [
            " Rotor Flapping\u2013Further Considerations of the Centre-Spring Approximation The centre-spring equivalent rotor (CSER), a rigid blade analogue for modelling all types of blade flap retention systems, was originally proposed by Sissingh (Ref. 3.32) and has considerable appeal because of the relatively simple expressions, particularly for hub moments, that result. However, even for moderately stiff hingeless rotors like those on the Lynx and Bo105, the blade shape is rather a gross approximation to the elastic deformation, and a more common approximation used to model such blades is the offset-hinge and spring analogue originally introduced by Young (Ref. 3.33). Figure 3.18 illustrates the comparison between the centre-spring, offset-hinge and spring and a typical first elastic mode shape. Young proposed a method for determining the values of offset-hinge and spring strength, the latter from the nonrotating natural flap frequency, which is then made up with the offset to match the rotating frequency. The ratio of offset to spring strength is not unique and other methods for establishing the mix have been proposed; for example, Bramwell 1Readers can also refer to David Peters review paper \u2019How Dynamic Inflow Survives in the Competitive World of Rotorcraft Aerodynamics, JOURNAL OF THE AMERICAN HELICOPTER SOCIETY 54, 011001 (2009) Modelling Helicopter Flight Dynamics: Building a Simulation Model 109 (Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001151_09544054jem1008-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001151_09544054jem1008-Figure1-1.png",
        "caption": "Fig. 1 Laser deposition with slotted base blocks (schematic)",
        "texts": [
            " The laser beam in that plane was rectangular with a size equal to 3.5mm (slow axis) \u00b7 2.5mm (fast axis). During the experiment, the diode laser beam was kept stationary and the workpiece was moved with a CNC x\u2013y table parallel to both the slow axis of the beam and the groove. Prior to each experiment and between tracks, the height of a sample was adjusted in the z direction using a manual adjustment mechanism on the worktable. The experimental apparatus and base samples used are illustrated in Fig. 1. After an experiment, the repair quality was initially evaluated by visual observation. The samples were then sectioned in a transverse plane, and ground and polished using standard metallographic techniques. The polished specimen surfaces were etched with 3% Nital (10 mL nitric acid, 90 mL methanol), Proc. IMechE Vol. 222 Part B: J. Engineering Manufacture JEM1008 IMechE 2008 at UNIV OF WINNIPEG on September 2, 2014pib.sagepub.comDownloaded from and the morphology and microstructures were examined using optical microscopy and a Philips XL32 ESEM-FG"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure3-2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure3-2-1.png",
        "caption": "Fig. 3-2 Representation of rotor mmf by equivalent dq winding currents.",
        "texts": [
            " In fact, if a three-phase machine were to be converted to a two-phase machine using the same stator shell (but the windings could be different) to deliver the same power output and speed, we will choose the number of turns in the each of the two-phase windings to be 3 2/ Ns. 3-2-2 Rotor dq Windings (Along the Same dq-Axes as in the Stator) The rotor mmf space vector F tr ( ) is produced by the combined effect of the rotor bar currents, or by the three equivalent phase windings, each with Ns turns, as shown in Fig. 3-2 (short-circuited in a squirrelcage rotor). The phase currents in these equivalent rotor phase windings can be represented by a rotor current space vector, where 32 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS i t i t i t e i t er A A B j C j( ) ( ) ( ) ( ) ,/ /= + +2 3 4 3\u03c0 \u03c0 (3-8) where i t F t N p r A r A s ( ) ( ) / .= (3-9) The mmf F tr ( ) and the rotor current i tr ( ) in Fig. 3-2 can also be produced by the components ird (t) and irq (t) flowing through their respective windings as shown. (Note that the d- and the q-axis are the same as those chosen for the stator in Fig. 3-1. Otherwise, all benefits of the dq-analysis will be lost.) Similar to the stator case, each of the dq windings on the rotor has 3 2/ Ns turns, and a magnetizing inductance of Lm, which is the same as that for the stator dq windings because of the same number of turns (by choice) and the same magnetic path for flux lines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003768_j.optlastec.2019.105926-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003768_j.optlastec.2019.105926-Figure3-1.png",
        "caption": "Fig. 3. Model geometry and mesh: (a) general view, (b) cross-sectional view, (c) top view showing the property change of elements.",
        "texts": [
            " For the simulation of stress field, the elasticity modulus, linear expansion coefficient, yield strength and Poisson ratio change during the temperature cycle. These parameters in the molten state are set as nearly to 0 for the simulation of the molten pool. Laser reflection occurs multiple times between powder particles, which increases the laser absorptivity of powders. Table 1 shows the absorption rate of the aluminum alloy with different laser wavelength and states [25]. The three-dimensional finite element model simplified from the experiment geometry is shown in Fig. 3. Considering the symmetry characteristic along the laser scanning direction, only half of the model was built to reduce the amount of computation. The mesh of the model was divided into three parts. The element type of AlSi10Mg powder, AlSi10Mg alloy and 5025 aluminum plate was Solid70. The whole model was divided into 414,324 elements. 32,000 elements of them were used for AlSi10Mg powder and the rest were used as 5025 aluminum plate. The AlSi10Mg powder is meshed in hexahedron elements with 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003334_s00170-020-04972-0-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003334_s00170-020-04972-0-Figure1-1.png",
        "caption": "Fig. 1 Schematic representation of the wear test",
        "texts": [
            " The wear tests were conducted for 40 min under a contact load of 15 N and a stroke length of 6 mm at room temperature in an air atmosphere without any cooling or lubricant. A tungsten carbide ball (WC 94%, CO 6%) with a diameter of 6 mm was used as a counterface material during the reciprocating wear test. As the hardness of the ball was much higher than the hardness of the specimens, no wear of the carbide ball was observed during the test and therefore, it had no effect on the wear behavior of the specimen. A schematic representation of the wear test is shown in Fig. 1. The tests were repeated to make sure that data presented is repeatable. The microstructure, porosity, and wear morphology images were obtained using a 3D Keyence VHX-6000 optical microscope. Metallographic characterization of the specimens is described elsewhere [29]. Furthermore, scanning electron microscopy (SEM) was used to characterize the microstructure. Figure 2 shows the microstructure of wrought and SLM as-built specimen. While the grains and grain boundaries are visible in the microstructure of the wrought specimen, cellular dendritic structures and columnar grain structures are visible in the microstructure of SLM as-built specimen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003115_j.mechmachtheory.2019.03.014-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003115_j.mechmachtheory.2019.03.014-Figure9-1.png",
        "caption": "Fig. 9. Meshing process for the meshing point: (a) beginning of contact, (b) distance between the meshing point is equal to s p 1 and (c) distance between the meshing point is equal to s p 2 .",
        "texts": [
            " Based on the single point observation method, the wear depth equation of the mating point P after a meshing cycle can be discretely written as: h P ,n = h P ,n \u22121 + k p P , n \u22121 s P (35) where the wear coefficient k is constant, h P, n is the wear depth of the mating point P (after n times of meshing cycles), h P ,n \u22121 is the wear depth after the previous meshing cycle, p P ,n \u22121 represents the contact pressure of the mating point P in the previous meshing cycle, and s P is the relative sliding distance of the mating point P. In order to reveal vividly the wear process of gear meshing, we sketch the meshing process for the meshing point, shown in Fig. 9 . In a certain meshing state of gear meshing, the meshing point P 1 in the driving gear and the meshing point P 2 in the driven gear are contacted, and there is a contact process shown in Fig. 9 (a, b, c). According to the Hertzian contact theory, the contact width of the meshing point P 1 and P 2 is 2 a H ( a H represents the semi-hertzian contact width). Therefore, the meshing point P 1 and P 2 need to move the distance of 2 a H to disengage, where U 1 and U 2 represent the circumferential velocity of the two meshing point. When P 1 moves the distance of 2 a H along the contact line, P 2 will move 2 a H ( U 2 / U 1 ). Similarly, when P 2 moves 2 a H along the contact line, 2 a H ( U 1 / U 2 ) will be the distance of P 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure8.42-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure8.42-1.png",
        "caption": "Fig. 8.42 Sequence of events following a tail rotor drive failure in cruise",
        "texts": [
            " The trial was conducted within the broad framework of the flying qualities methodology with task performance judged by the pilot\u2019s ability to land within the airframe limits, i.e. touchdown velocities and drift angle. Unlike a control failure, where the tail rotor continues to provide directional stability in forward flight, in a drive failure this stability augmentation reduces to zero as the tail rotor runs down. For failures from both hover and forward flight, survival is critically dependent on the pilot recognizing the failure and reducing the power to zero as quickly as possible. Figure 8.42 shows the sequence of events following a drive failure from a cruise condition. The aircraft will yaw violently to the right as tail rotor thrust reduces. The study showed that a short pilot intervention time is critical here to avoid sideslip excursions beyond the structural limits of the aircraft. The pilot should reduce power to zero as quickly as possible by lowering the collective lever. Once the yaw transients have been successfully contained, and the aircraft is in a stable condition, the engines can be shut down and the aircraft retrimmed at an airspeed of about 80 knots"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000660_icra.2011.5980244-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000660_icra.2011.5980244-Figure2-1.png",
        "caption": "Fig. 2. The control inputs of the quadrotor: The rotational rates \u03c9x, \u03c9y , and \u03c9z are tracked by an on-board controller, using gyroscope feedback.",
        "texts": [
            " (4) The translational acceleration of the vehicle is dictated by the attitude of the vehicle and the total thrust produced by the four propellers. With a representing the mass-normalized collective thrust, the translational acceleration in the inertial frame is   x\u0308 y\u0308 z\u0308   = O V R(\u03b1, \u03b2, \u03b3)   0 0 a  +   0 0 \u2212g   . (5) The vehicle attitude is not directly controllable, but it is subject to dynamics. The control inputs are the desired rotational rates about the vehicle body axes, (\u03c9x, \u03c9y , \u03c9z), and the mass-normalized collective thrust, a, as shown in Figure 2. High-bandwidth controllers on the vehicle track the desired rates using feedback from gyroscopes. The quadrotor has very low rotational inertia, and can produce high torques due to the outward mounting of the propellers, resulting in very high achievable rotational accelerations on the order of 200 rad/s2. The vehicle has a fast response time to changes in the desired rotational rate (experimental results have shown time constants on the order of 20ms). We will therefore assume that we can directly control the vehicle body rates and ignore rotational acceleration dynamics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001798_j.automatica.2015.02.004-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001798_j.automatica.2015.02.004-Figure2-1.png",
        "caption": "Fig. 2. Two inverted pendulums connected by a spring.",
        "texts": [
            " In fact, the adaptive stabilization result in Lin and Qian (2002a) is a special case of Theorem 2. In this section, we show the applicability and effectiveness of our approach on two examples illustrating the main results of the paper. Example 1. Let us illustrate the proposed switched adaptive control technique by means of a mechanical system as that has been dealt with in Spooner and Passino (1999). That is, we consider the control of two inverted pendulums connected by a spring as depicted in Fig. 2. Each pendulum may be positioned by a torque input ui applied by a servomotor at its base. The equations of motion for the pendulums are described by x\u03071 = x2, (36a) x\u03072 = m1gr J1 \u2212 hr2 4J1  sin x1 + hr 2J1 (l \u2212 b)+ u1 J1 + hr2 4J1 sin x3, (36b) x\u03073 = x4, (36c) x\u03074 = m2gr J2 \u2212 hr2 4J2  sin x3 \u2212 hr 2J2 (l \u2212 b)+ u2 J2 + hr2 4J2 sin x2, (36d) where (x1, x3)T = (q1, q2)T and (x2, x4)T = (q\u03071, q\u03072)T are the angular displacements of the pendulums from vertical and angular rates, respectively.m1 andm2 are the pendulum endmasses, J1 and J2 are the moments of inertia, h is the spring constant of the connecting spring, r is the pendulum height, l is the natural length of the spring, b is the distance between the pendulum hinges, and g is gravitational acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.35-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.35-1.png",
        "caption": "FIGURE 5.35. An articulated robot that is made by assembling a spherical wrist to an articulated manipulator.",
        "texts": [
            " The kinematic mating of the wrist and arm is called assembling. The coordinate frame B8 in Figure 5.33 is the takht frame of the manipulator, and the coordinate frame B9 in Figure 5.34 is the neshin frame of the wrist. In the assembling process, the neshin coordinate frame B9 sits on the takht coordinate frame B8 such that z8 be coincident with z9, and 5. Forward Kinematics 281 x8 be coincident with x9. The articulated robot that is made by assembling the spherical wrist and articulated manipulator is shown in Figure 5.35. The assembled multibody will always have some additional coordinate frames. The extra frames require extra transformation matrices that can increase the number of required mathematical calculations. It is possible to make a recommendation to eliminate the neshin coordinate frame and keep the takht frame at the connection point. However, as long as the transformation matrices between the frames are known, having extra coordinate frames is not a significant disadvantage. In Figure 5.35, we may ignore B8 and directly go from B3 to B4 and substitute l8 and l9 with l3 = l8 + l9. The word \"takht\" means \"chair,\" and the word \"neshin\" means \"sit\", both from Persian. Example 165 A planar 2R manipulator assembling. Figure 5.36 illustrates an example of a single DOF arm as the base for an RkR planar manipulator. This arm can rotate relative to the global frame by a motor at M1, and caries another motor at M2. Figure 5.37 illustrates a sample of a planar wrist that is supposed to be attached to the arm in Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000537_1.2803837-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000537_1.2803837-Figure3-1.png",
        "caption": "FIG. 3. The rotation rate of the doublet about its center of mass normalized by the torque on the particles about their line of centers 8 a3 /T . The normalized rate of rotation is maximum near r=2.1a, h=1.01a.",
        "texts": [
            " Since these particles might be connected by a wire, the separation between the particles remains the same and the doublet spins about its center of mass. We can measure the tensile force on the wire as the doublet rotates, but one can show that because the grand mobility tensor is symmetric, this tensile force is exactly zero regardless of separation and height above the wall. In a model lacking symmetry, some nonzero force along the line of centers is necessary to maintain the separation between the particles. Interestingly, as indicated in Fig. 3, the rate of rotation of the doublet about its center of mass, , normalized by the torque on the particles, T /8 a3, is a nonmonotonic function of both the separation between the particles, r, and the height of the doublet above the wall, h. When the particles are far apart, the rate of rotation of the doublet is decreasing as r increases because the translational speed of a particle in the doublet r /2 is set only by the coupling of a single particle to the wall. When the particles are far from the wall, the rate of rotation of the doublet is also decreasing as h increases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002323_17452759.2020.1830346-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002323_17452759.2020.1830346-Figure12-1.png",
        "caption": "Figure 12. Hydrodynamic cavitation abrasive finishing test chamber for surface finishing (Nagalingam et al. 2020b).",
        "texts": [
            " The technique showed 90 % surface texture improvements in 150 min with final Ra \u223c 3 \u00b5m and Rz \u223c 30 \u00b5m (Nagalingam, Yuvaraj, and Yeo 2020). The final profile surface textures of conventionally machined internal channels postHCAF were Ra < 1 \u00b5m (Nagalingam, Thiruchelvam, and Yeo 2019b; Nagalingam and Yeo 2020a). Due to hydrodynamic flow principles and low abrasive usage, this technique can reach highly intricate corners of a component. Excellent corner surface finish quality was also reported \u2013 preserving the dimensional integrity. Figure 12 shows the HCAF chamber with multiphase flow characteristics. The component to be surface finished is placed behind a cavitation inducer. Cavitation bubbles nucleated from the inducer travel through the internal channels. Upon contact with the solid surface, the cavitation bubble implodes \u2013 generating high-velocity micro-jets. The micro-jet travels up to \u223c 1500 m/s Figure 11. (a and b) Ultrasonic cavitation abrasive finishing apparatus (Tan and Yeo 2020; Wang, Zhu, and Liew 2019) (c) SLM IN625 surface (Wang, Zhu, and Liew 2019) (d) DMLS IN625 external and internal channels used for UCAF (Tan and Yeo 2020), (e) material removal mechanism, (f) surface topography and (g) surface morphology of additive manufactured and UCAF processed components (Tan and Yeo 2017)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001308_j.jbiomech.2010.01.031-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001308_j.jbiomech.2010.01.031-Figure2-1.png",
        "caption": "Fig. 2. During the inverted pendulum-like stance phase (A), the body vaults up and over the stance leg with measured shank angular velocity (B) negative and slowing down as kinetic energy is exchanged for potential energy (Cavagna et al., 1977). At the shank vertical event, the body COM reaches its highest point, potential energy reaches a maximum, and velocity reaches a minimum. Consequently, the IMU horizontal and vertical velocities (vx and vy) are approximately zero at mid-stance. The angular velocity of the shank (o) is slowest at this point but then accelerates as the inverted pendulum accelerates downward, exchanging potential energy for kinetic energy. The angular velocity of the shank switches from negative to positive during swing in order to progress the shank forward and return it to the correct orientation at the beginning of the next stance phase. Stride length, ST, and stride time, T are defined as the distance and time between two mid-stance shank vertical events. The characteristic feature for defining mid-stance vertical events was the local maximum during the lengthy period of negative shank angular velocity.",
        "texts": [
            " 1) according to ax\u00f0t\u00de ay\u00f0t\u00de \" # \u00bc cosy\u00f0t\u00de siny\u00f0t\u00de siny\u00f0t\u00de cosy\u00f0t\u00de \" # at \u00f0t\u00de an\u00f0t\u00de \" # 0 g \" # ; \u00f01\u00de where g is the acceleration due to the gravity and y\u00f0t\u00de is the shank angle which was computed by integrating the measured angular velocity o\u00f0t\u00de, y\u00f0t\u00de \u00bc Z t 0 o\u00f0t\u00dedt\u00fey\u00f00\u00de; \u00f02\u00de where y\u00f00\u00de is the initial shank angle before integration. We segmented the continuous walking motion into a series of stride cycles before computing the displacements. Mid-stance shank vertical events\u2014the time in the stance phase when the shank is parallel to the direction of gravity\u2014defined each new stride cycle (Fig. 2). The inverted pendulum-like behavior of the stance leg during walking allowed us to identify each mid-stance vertical event from a characteristic feature in the gyroscope signal (Fig. 2). By definition, y\u00f00\u00de \u00bc 0 at midstance vertical providing the initial condition for integrating Eq. (2). Moreover, the initial horizontal velocity vx\u00f00\u00de and vertical velocity vy\u00f00\u00de are approximately zero because of the inverted-pendulum behavior. These initial conditions allowed to compute the displacements over each stride cycle duration, T. Within each stride cycle [0 T], we computed the associated velocities vx\u00f0t\u00de and vy\u00f0t\u00de, vx\u00f0t\u00de \u00bc Z t 0 ax\u00f0t\u00dedt\u00fevx\u00f00\u00de; vy\u00f0t\u00de \u00bc Z t 0 ay\u00f0t\u00dedt\u00fevy\u00f00\u00de; \u00f03\u00de where vx\u00f00\u00de \u00bc 0 and vy\u00f00\u00de \u00bc 0",
            " The measured errors in estimating speed is most likely due to the zero velocity assumption at mid-stance shank vertical (Eq. (3)). Any deviation of the actual initial horizontal velocity from zero would result in the same amount of offset in the estimated speed. Because the shank rotates about the ankle joint at the mid-stance shank vertical event, the absolute value of the initial horizontal velocity vx\u00f00\u00de is approximately equal to the product of the angular velocity o of the shank and the distance of the sensor to the ankle joint (Fig. 2). At the mid-stance shank vertical event, the shank angular velocity reached a non-zero local maximum resulting in a positive non-zero initial horizontal velocity (Fig. 2). The speed estimation algorithm underestimated walking speed, and the underestimation became larger at faster walking speeds, because the shank retained a greater angular velocity, and therefore a larger initial horizontal velocity, at the peak of the inverted pendulum arc. One possible remedy is to estimate the initial velocity based on the angular velocity, and therefore achieve a higher accuracy. The present method yields speed estimate accuracies roughly comparable to that achieved by Sabatini and colleagues who used a sensor mounted to the foot (Sabatini et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001357_acc.2010.5531424-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001357_acc.2010.5531424-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor UAV.",
        "texts": [
            " Section 2 presents the kinematic and dynamic model of quadrotor UAV system, and coordinate transfer. Problem statement together with adaptive control design are provided in Section 3. In Section 4, Lyapunov based analysis is utilized to prove the stability of closed loop system, and the convergence of tracking errors. Numerical simulation results are presented in Section 5 to testify the proposed controller. Finally, conclusion remarks were given in Section 6. The schematic of a quadrotor UAV is shown in Figure 1. It contains four rotors which can generate four identical thrust forces denoted by fi(t), i = 1, 2, 3, 4, respectively. More details about flight properties of a quadrotor UAV can be found in [8], [6], and [9]. Let B denotes the body fixed frame attached to the quadrotor UAV, and I denotes the inertial frame. The Euclidean position of the UAV with respect to I is represented by P (t) = [ x(t) y(t) z(t) ]T \u2208 R 3, the Euler angle of the UAV with respect to I is represented by \u0398(t) = [ \u03c6(t) \u03b8(t) \u03c8(t) ]T \u2208 R 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000736_0278364904047392-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000736_0278364904047392-Figure1-1.png",
        "caption": "Fig. 1. The n\u2212wheeled vehicle on uneven terrain.",
        "texts": [
            " It is shown that the rough-terrain control method leads to increased traction and improved power consumption as compared to traditional individual-wheel velocity control. It is also shown that the wheel\u2013terrain contact angle estimation method can accurately estimate contact angles in the presence of sensor noise and wheel slip. Experimental results for a six-wheeled microrover traversing a ditch show that the proposed control method increases the net forward wheel thrust, and improves rover mobility. Consider an n-wheeled vehicle on uneven terrain, as shown in Figure 1. The vehicle is assumed to be skid-steered, so only forces in the xo \u2212 yo plane of the vehicle are considered. It is also assumed that each wheel makes contact with the terrain at a single point, denotedPi , i = {1, . . . , n}. This is a reasonable assumption for vehicles with rigid wheels (such as currently planned Mars rovers) moving on firm terrain. For vehicles moving on deformable terrain, distributed wheel\u2013terrain contact stresses can be resolved to forces at a single point. Vectors from the points Pi to the vehicle center of mass are denoted Vi = [V x i V y i ]T , i = {1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000339_tie.2011.2157278-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000339_tie.2011.2157278-Figure1-1.png",
        "caption": "Fig. 1. Phase plane division for the control of torque and stator flux (TPC).",
        "texts": [
            " The value of \u0394Te and \u0394\u03c8s are acquired from torque and flux hysteresis controllers. The calculation error of \u0394\u03c8s due to the approximation will introduce disturbance to the decision of the voltage vector control angle and, consequently, brings ripple to the control of motor electromagnetic torque. The TPC strategy in [22] also uses the stator flux vector \u03c8s as a positioning reference, and the phase plane is divided into four parts to satisfy the control of the motor torque and the stator flux (see Fig. 1). The problem is that the calculation error of vector\u03c8s will make the positioning become less accurate. In order to overcome these problems, a new TPC strategy is proposed in this paper. As is known, the position angle of vector \u03c8r is proportional to the value of rotor position angle, and this value can be acquired through a rotor position sensor. Taking vector \u03c8r as a position reference, the control voltage can be more accurately oriented. To achieve this target, the relationship between us and \u03c8r should be analyzed first"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001525_tia.2009.2036507-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001525_tia.2009.2036507-Figure2-1.png",
        "caption": "Fig. 2. Harmonic gear (pw = 1, p = 18) with high-speed rotor rotation of (a) 0\u25e6 and (b) 120\u25e6, which result in low-speed rotor rotations of 0\u25e6 and \u22126.67\u25e6, respectively (one magnet on low-speed rotor is highlighted to illustrate its rotation).",
        "texts": [
            " Furthermore, since the asynchronous space harmonic, which transmits the torque, couples with the static field produced by the stator, its velocity is zero (\u03a91,k = 0), and the gear ratio Gr can be deduced from (4) as Gr = (\u22121)k+1 pw p . (5) Finally, it should be noted that \u03c9r represents the average angular velocity of the low-speed rotor, since the individual magnets rotate at different instantaneous speeds as a result of their different relative radial positions around the sinusoidally shaped outer surface of the low-speed rotor. Fig. 2 shows the rotation of both the high-speed and low-speed rotors. Fig. 3 shows schematics of four magnetic harmonic gears, which differ from each other by the number of pole pairs on the low-speed rotor and the number of cycles in the air gap. The gears have been analyzed using 2-D magnetostatic finiteelement analysis. For all four gears, the outer radius is 85 mm, the radial thicknesses of the magnets and the back iron on both the stator and low-speed rotor are 5 mm, the minimum air-gap length gmin is 1 mm, and the maximum air-gap length gmax is 6 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003657_j.measurement.2020.108855-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003657_j.measurement.2020.108855-Figure11-1.png",
        "caption": "Fig. 11. Pitch bearing test rig and fault diagnose [39].",
        "texts": [
            " Based on the distribution of contact loads, effect of hardened depths on fatigue strength was investigated. Weak fault signals masked by strong interferences are the obstacles in detecting low-speed WTGS slewing bearings based on cyclic domain resampling. Pan [38] mapped time series signals to angle domain. The frequency change of vibration signals can be detected when the initial fault occurs, verified by life-cycle test. Liu [39] extracted weak fault signals to monitor and diagnose damaged pitch bearings based on thresholding of empirical wavelet coefficients, shown in Fig. 11. Jannie [40] proposed that measurements of pitch motor torque and current give indirect information about the condition of the pitch system. Wanye [41] used the principle of similarity, applying the historical data of the SCADA system, the health model of the pitch system is established based on the modeling method of nonlinear state assessment. Han [4243] investigated the performance and reliability of pitch bearings based on a test rig, which can simulate the operating load cases in the harsh environment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000151_ja111517e-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000151_ja111517e-Figure2-1.png",
        "caption": "Figure 2. (a and b) Illustrations of as-grown CNTF whose void volume is fully occupied by 7 nm diameter globular enzyme molecules. (c) Illustration of the linear arrangement of the enzymes trapped between the shrunk CNTF.",
        "texts": [
            "5 h of incubation, the fluorescent intensity was measured by a luminescent image analyzer system (Fuji Photo Film, LAS-3000 mini), and the amount of enzyme was determined by referencing a calibration curve. Theoretical Prospect of FDH Content inside CNTF. The previous structural analysis of the as-grown CNTF revealed a mean tube diameter of 2.8 nm by transmission electron microscopy (TEM) and an intertube pitch of 16 nm by X-ray diffraction (XRD).16,17 If we assume that FDH is a 7 nm diameter globe, four FDHs can enter the void space surrounded by 16 nm pitched CNTs (Figure 2a and b). The number of enzymes (Nenz) entrapped in a 12 \u03bcm thick CNTF is estimated by the following equation: Nenz = 4 (H/r) (S/U), where H = 1.0 mm (CNT length), r = 7.0 10-6 mm (FDH diameter), S = 12 10-3 mm2 (cross-sectional area of CNTF sheet), and U = 2.6 10-10 mm2 (the area of the void space surrounded by 16 nm pitched CNTs). The entrapped mass (6.2 \u03bcg) is derived by multiplyingNenz by the molecular weight (140 kD)/Avogadro's constant. On the other hand, as we explain later in the Results and Discussion Section, the best performance of FDH-CNTF ensemble was obtained by the film containing ca. 1.5 \u03bcg FDH (one-quarter of the limiting value, 6.2 \u03bcg) (Figure 2c). Note these arguments are based on the assumption that FDH is a 7 nm diameter globe. Electrochemical Measurements. The enzyme-CNTF ensemble film, anchored at the edge with SUS316L fine tweezers, was analyzed by a three-electrode system (BSA, 730C electrochemical analyzer) in stirred solutions using a Ag/AgCl reference and a platinum counter electrode. The catalytic currents of enzyme-CNTF ensemble films did not significantly decrease when the film was attached to a planner electrode (Supporting Information, Figure S2)",
            " The results obtained from the random CNT electrode demonstrate the general difficulty in postmodification of enzymes to the prestructured nanocarbon electrodes, which will be addressed by the present \u201cin-situ regulation\u201d approach. The content of FDH inside a CNTF film was controllable by the concentration of FDH solution in which the as-grown CNTF films were soaked for 1 h (Figure 3b). The FDH content increased toward the theoretical limiting value (6.2 \u03bcg), at which the void volume of as-grown CNTF is fully occupied by FDH (Figure 2). Such controlled entrapment of enzymes can be also examined via the degree of CNTF shrinkage (Figure 3c). Typically, the CNTF film without enzymes shrank to one-quarter of its original area; the CNTF film treated with 3 mg mL-1 FDH solution shrank to one-half of the original. The degree of shrinkage also depended on the size of enzyme. For example, a smaller enzyme, laccase, led to shrinkage to one-third of the original area. These results support our methodology, which induces in situ regulation of intrananospace of CNTF by the amount and size of entrapped enzymes",
            "4 mA cm-2 (not shown), in agreement with previous reports of conventional CNT aggregate-based enzyme electrodes.22,23 The electrode performance depended on the concentration of FDH solution used for preparing e2CNTFs, as shown in Figure 4b. Among the conditions we studied, the best performance was reproducibly obtained from the e2CNTF electrode prepared from 3 mg mL-1 FDH solution, which contains ca. 1.5 \u03bcg FDH (see Figure 3b). This value of FDH content represents one-quarter of the limiting value (6.2 \u03bcg) and can be modeled as a linear arrangement of FDH molecules trapped between the CNTs (Figure 2c). At higher contents of FDH, the current values decreased, probably because the overloaded enzymes failed to interface effectively with the CNTs. To investigate enzyme activity within the e2CNTF films, the apparent MichaelisMenten constant (Km,app) was estimated from the currents at various fructose concentrations using the Lineweaver-Burke equation24,25 (Figure 5). The derived Km,app was around 10 mM, which is in agreement with the Km value for the reaction in the bulk solution,26 indicating that the nanospace formed by CNTF shrinkage could maintain the nature of the FDH enzyme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002352_1077546317716315-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002352_1077546317716315-Figure5-1.png",
        "caption": "Figure 5. Schematic of the contact relationship for (a) case 1, (b) case 2, and (c) case 3.",
        "texts": [
            " Schematics illustrating the contact patterns between the roller and LOD are given in Figures 3 to 5. The contact pattern between the roller and LOD edge is determined by the following three parameters: (1) the ratio of LOD length to its width, which is calculated by d \u00bc L=B, in which L and B are the LOD length and width, respectively; (2) the ratio of roller size to LOD minimum size, which is calculated by rd \u00bc d=min\u00f0L,B\u00de, in which d is the roller diameter; and (3) the radius rd of cylindrical surface. Figure 5 gives the influences of LOD edge shapes on the contact patterns for different LOD cases. rd, d, and rd are applied to determine the contact patterns. The edge sizes are assumed to be larger than Hertzian contact radius in this study. Moreover, the roller length is assumed to be less than LOD width. For case 1, rd 4 1 and rd \u00bc 0, as shown in Figures 3(a) and 4(a), the roller is only in contact with the sharp edges without plastic deformations when formulating an early LOD stage case. Its contact pattern is a roller-line one. For case 2, rd 4 1 and rd 5H, shown in Figure 5(a), the contact patterns are roller\u2013roller ones when the roller is located at points A and D. This case denotes an early stage of plastic deformations at the propagated LOD edges for a small LOD. For case 3, rd 4 1 and rd H, shown in Figure 5(b), the contact patterns are also roller\u2013roller ones when the roller is located at points A and D. This case describes a middle or late stage of plastic deformations at the propagated LOD edges for a small LOD. For case 4, rd 1, as plotted in Figure 5(c), when the roller is located at points A and B, and between points C and D, the contact patterns are also the roller-roller ones. Furthermore, when the roller is in contact with the LOD bottom surface, it is a roller\u2013 plane one. This case is utilized to formulate plastic deformations at the propagated LOD edges with relatively larger dimensions. For case 1, when the roller passes over the LOD zone, the numbers of contact edges are depended on rd; when rd 5 1, they are 1, 2, and 1; and when rd 1, during the entire contact process, only one contact edge is produced",
            " For an unlubricated healthy RB, the contact deformation ih between the inner race and roller can be given by (Chen, 2007) ih \u00bc 2Q le 1 2 E0 ln 4RihRrh b2ih \u00fe 0:814 \u00f01\u00de where Q is the external force, le is the equivalent contact length, Rrh is the radius of the healthy roller, is the Poisson\u2019s ratio, E0 is the equivalent elastic modulus, and bih is the semi-width of the contact surface between the unlubricated healthy inner race and roller, which is given by bih \u00bc 1:59 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q le RihRrh Rih \u00fe Rrh 1 2 E0 s \u00f02\u00de Then, the contact stiffness coefficient between the unlubricated healthy inner race and roller Kih is calculated by Kih \u00bc Q ih \u00f03\u00de Moreover, the contact deformation oh between the unlubricated healthy outer race and roller can be given by (Chen, 2007) oh \u00bc 2Q le 1 2 E0 1 ln boh\u00f0 \u00de \u00f04\u00de where boh is the semi-width of the contact surface between the unlubricated healthy outer race and roller, which is given by boh \u00bc 1:59 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q le RohRrh Roh Rrh 1 2 E0 s \u00f05\u00de Then, the contact stiffness coefficient between the unlubricated healthy outer race and roller Koh can be calculated by Koh \u00bc Q oh \u00f06\u00de The total contact stiffness coefficient Keh between two unlubricated healthy races and one roller can be given by Keh \u00bc KihKoh Kih \u00fe Koh \u00f07\u00de For an unlubricated defective RB, the contact deformation rd between one roller and one cylindrical surface at the LOD edge can be given by rd \u00bc 2Q le 1 2 E0 ln 4RrdRrh b2id \u00fe 0:814 \u00f08\u00de where Rid is the radius of the cylindrical surface, bid is the semi-width of the contact surface, which is given by bid \u00bc 1:59 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q le RrdRrh Rrd \u00fe Rrh 1 2 E0 s \u00f09\u00de Then, the contact stiffness coefficient Krd1 between the roller and cylindrical surface on the inner race can be calculated by Krd1 \u00bc dQ d rd \u00f010\u00de When one roller is in contact with more than one cylindrical surface edges, as shown in Figure 5(a) and (b), the total radial contact stiffness coefficient Krd2 between one roller and two cylindrical surface edges can be obtained by Krd2 \u00bc nsKrd1 \u00f011\u00de where ns is the numbers of contact cylindrical surfaces between one roller and LOD edges. As depicted in Figure 5(c), when the roller is in contact with the LOD bottom surface, the contact pattern is the roller-plane one. According to Hertzian contact theory (Harris and Kotzalas, 2007), the contact stiffness coefficient Krp between the roller and bottom plane can be given by Krp \u00bc 4R0:5 rh 3 1 2r Er \u00fe 1 2o Eo \u00f012\u00de where r and o are the Poisson\u2019s ratio of the roller and outer race, respectively; Er and Eo are the elastic modulus of the roller and outer race, respectively. If the roller is in contact with the LOD edges, the total contact stiffness coefficient Keds between one roller and two races including one defective race and one healthy race for the unlubricated RB can be given by Keds \u00bc nsKrdKrh nsKrd \u00fe Krh \u00f013\u00de where Krh is the contact stiffness coefficient between the unlubricated healthy race and roller, which can be calculated by equations (1) to (6); Krd is the contact stiffness coefficient between the unlubricated defective race and roller, which can be calculated by equations (8) to (12); and the subscript s representing the numbers for cylindrical surfaces in contact is equal to 1 or 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001868_s00158-010-0496-8-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001868_s00158-010-0496-8-Figure7-1.png",
        "caption": "Fig. 7 Balanced and unbalanced states: a balanced state, b unbalanced state",
        "texts": [
            " The terminologies in gait simulation were accurately defined, and the general concepts were clarified (Vukobratovic\u0301 et al. 2006, 2007). Zero moment point is generally defined as a point on the ground where the resultant tangential moments of the active forces are zero (Vukobratovic\u0301 and Borovac 2004). Here, the forces are distinguished into two categories: active forces and passive forces. Active forces include inertia, Coriolis, gravity, and external forces. Passive forces are the ground reaction forces (GRF). The balanced and unbalanced states of the human system are illustrated in Fig. 7, where point A denotes ankle, point C is the center of mass of foot, G is foot gravity force, FA and MA are resultant force and moment of body parts excluding the contacting foot, F and M are the resultant ground reaction forces, and FI and MI are inertia forces of foot due to rotation. FZMP represents fictitious zero moment point, and FRI is foot rotation indicator. To make the ZMP concept more precise, the following explanations are given: (1) In the balanced state, the contacting foot resets fully on the floor with zero velocity and acceleration. The sign of losing dynamic balance is the rotation of the contacting foot. (2) Zero moment point is calculated from active forces under the assumption that the contacting foot is stationary. However, COP is the point where the resultant GRF acts. (3) For a balanced system, ZMP and COP coincide at an equilibrium point in the support polygon, i.e., the active and passive forces are balanced at the same point as shown in Fig. 7a. (4) For an unbalanced system, COP acts at a point P on the support polygon boundary, while the resultant active force with zero tangential moments (excluding the inertia force of the rotating foot based on assumption 2) acts at a point P\u2032 outside the support polygon as shown in Fig. 7b. Thus the contacting foot starts to rotate. The point P\u2032 is suggested as a fictitious zero moment point (FZMP) (Vukobratovic\u0301 and Borovac 2004) or foot rotation indicator (FRI) (Goswami 1999). It is noted that the inertia force of the rotating foot must be excluded while computing ZMP, otherwise point P and P\u2032 always coincide because of the equilibrium conditions of the mechanical system between active and passive forces. Based on the foregoing analysis, we can see that the key point of the ZMP concept is the inertia force of the contacting foot",
            " Since the sign of losing dynamic balance is the rotation of the supporting foot, a more generalized ZMP definition that excludes the inertia force of the supporting foot is summarized here so that both FZMP and FRI concepts can be unified into a generalized ZMP definition. Zero moment point is defined as a point on the ground where the resultant tangential moments of the active forces excluding the inertia force of the contacting foot are equal to zero. By using this generalized definition, ZMP may be outside of the support polygon, as seen in Fig. 7b. Therefore, one can claim that if the computed ZMP is in the support polygon, the system is in a stable state; otherwise, it is unstable. Mathematically, ZMP is a geometrical concept calculated from forces. It has some limitations in practical applications such as walking on uneven terrain, stair climbing, and walking while grasping a handrail. Recently, Hirukawa et al. (2006, 2007) proposed the contact wrench sum (CWS) and contact wrench cone (CWC) concepts, which extended the ZMP application to an arbitrary terrain and the case of hands contacting the environment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001474_ar300347d-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001474_ar300347d-Figure10-1.png",
        "caption": "FIGURE 10. Biotin streptavidin binding is detected by changes in device characteristics. The polymer layer avoids nonspecific protein binding. Reprinted with permission from ref 70. Copyright 2003 American Chemical Society.",
        "texts": [
            "13 The conductivity changeswere assigned to charge injection from the amine groups of the protein.13 Cytochrome c adsorption onto an individual CNTFET was detected by monitoring the decrease of transport in the CNTFET device.69 The negative shift in conductivity allowed estimating the number of adsorbed proteins.69 CNTFETs detected biotin streptavidin binding.70 The source drain current dependence on gate voltage of the CNTFET showed a significant change upon streptavidin binding to the biotin-functionalized carbonnanotube, Figure 10.70 The use of functionalized CNTFETs can be extended also to antigen antibody68 or virus recognition.71 These devices can detect, with high specificity, clinically important biomolecules associated with human diseases.67 The same approach can be used in the synthesis and fabrication of CNT microarrays for proteomics applications aimed at detecting large numbers of different proteins. These arrays are attractive because no labeling is required and all aspects of the assay can be carried out in solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001530_978-3-642-81857-8-Figure3.85-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001530_978-3-642-81857-8-Figure3.85-1.png",
        "caption": "Fig. 3.85. Case of one contact in assembly process-con",
        "texts": [
            " Case 1, when there is no contact between the hole and peg, represents free manipulator movement without reaction forces from the hole, so this situation does not differ dynamically from the task of transfer ring the working object in free space along desired trajectory and with a desired orientation. The manipulator dynamics is described by the mathematical model of open kinematic chain dynamics. Case 2 introduces the problem of the unknown reaction force acting on the manipulator via the object and influencing its dynamics. The prob lem of determining the reaction force in object-hole contact points arises. Fig. 3.84 illustrates the case of contact between the hole edge and the cylindrical surface of the peg, while Fig. 3.85 shows another possibility of single contact, namely, contact between the edge of the cylindrical base of the peg and the cylindrical surface of the hole. Both figures show the hole and peg section along the plane determined by the contact point and the symmetry axis of the hole cyl inder. Reaction forces at contact points are marked in figures. Three components of the reaction force at the point Kl or K2 are to be deter mined in the direction of the absolute coordinate system axes from Fig. (perpendicular to, the peg cylinder generatrix on which the point Kl is situated, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure4-1.png",
        "caption": "Fig. 4. 4\u20134\u20134 RPR-equivalent PMs with two uvUvRR limbs. (a) 2-uvUvRR/uRPRvR. (b) 2-uvUvRR/uPRuvU. (c) 2-uvUvRR/uPRRvR. (d) 2-uvUvRR/uRPuvU. (e) 2- U uvUvRR/uRRRvR. (f) 2-uvUvRR/uRRuvU.",
        "texts": [],
        "surrounding_texts": [
            "Fig. 6 shows a six-axis hybrid PKM that is being built in Zhejiang Sci-Tech University. The PKM consists of a 2-UPR/RPU PM and an articulated RR serial mechanism. A linear guide is used to move the working table along the short side of the workspace of the 2-UPR/RPU PM."
        ]
    },
    {
        "image_filename": "designv10_1_0001467_s10514-012-9294-z-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001467_s10514-012-9294-z-Figure4-1.png",
        "caption": "Fig. 4 When the desired GRF, f d and the desired CoP, pd computed from the desired momentum rate change are not simultaneously admissible, as indicated by pd being outside the support base, momenta objectives need to be compromised for control law formulation. Two extreme cases are illustrated. Left: linear momentum is respected while angular momentum is compromised. Right: angular momentum is respected while linear momentum is compromised",
        "texts": [
            "3 Prioritization between linear and angular momenta Given the desired momentum rate change, we determine admissible foot GRF and foot CoP such that the resulting momentum rate change is as close as possible to the desired value. If the desired GRF and CoP computed from k\u0307d and l\u0307d violate physical constraints (e.g., GRF being outside friction cone, normal component of GRF being negative, or CoP being outside support base), it is not possible to generate those k\u0307d and l\u0307d . In this case we must strike a compromise and decide which quantity out of k\u0307d and l\u0307d is more important to preserve. Figure 4 illustrates one case where the desired CoP, pd , computed from the desired momentum rate change is outside the support base, indicating that it is not admissible. Two different solutions are possible. The first solution, shown in Fig. 4, left, is to translate the CoP to the closest point of the support base while keeping the magnitude and line of action of the desired GRF f d unchanged. In this case the desired linear momentum is attained but the desired angular momentum is compromised. The behavior emerging from this choice is characterized by a trunk rotation. This strategy can be observed in the human when the trunk yields in the direction of the push to maintain balance. Alternatively, in addition to translating the CoP to the support base, as before, we can rotate the direction of the GRF, as shown in Fig. 4, right. In this case the desired angular momentum is attained while the desired linear momentum is compromised. With this strategy the robot must move linearly along the direction of the applied force due to the residual linear momentum, making it necessary to step forward to prevent falling. In this paper, we give higher priority to preserving linear momentum over angular momentum because it increases the capability of postural balance without involving a stepping. Ideally, a smart controller should be able to choose optimal strategies depending on the environment conditions and the status of the robot",
            " Since a large modeling error may negatively influence the performance of the controller, it is an important future work to improve the balance controller to be more robust against modeling errors. Due to the unilateral nature of the robot-ground contact, all postural balance controllers have intrinsic limitations. Therefore, another important venue of future work is to develop a different type of balance controller that will deal with the larger external disturbance than the postural balance controller can handle. For example, balance maintenance through stepping (Fig. 4) can cope with larger perturbations and will increase the push-robustness of the robot significantly (Pratt et al. 2006). Acknowledgements This work was mainly done while S.H.L. was with HRI. S.H.L. was also supported in part by the Global Frontier R&D Program on \u201cHuman-Centered Interaction for Coexistence\u201d funded by the National Research Foundation of Korea (NRFM1AXA003-2011-0028374). Abdallah, M., & Goswami, A. (2005). A biomechanically motivated two-phase strategy for biped robot upright balance control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure13.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure13.5-1.png",
        "caption": "Fig. 13.5 Variants of the same product",
        "texts": [
            " This relationship is saved within the CAD system as a relationship between geometrical attributes of the CAD parts; the axis of the bolt goes through the center of the hole\u2019s bottom that at the same time touches the face end of the bolt. Several problems emerge in this approach if the bolt and the hole do not belong to the same design team. The team responsible for the hole may change the hole\u2019s deepness, the bolt would lie deeper into the hole and thus all other geometrical dependencies to the bolt would move, probably deforming appearance of the DMU as a whole. This may also be the case when a part within the assembly is replaced 13 Digital Mock-up 363 by a variant of itself (Fig. 13.5). While these relationships are useful, for the DMU it is better if the geometry is placed relative in space to the origin of the parent node, avoiding changes that occur in the dynamical nature of CE [8]. In order to perform further analysis based in the DMU like completeness and maturity of the product a differentiation between external parts and assemblies has to be done in the DMU. Analogous to the dilemma between make and buy, where made parts are repaired and bought parts are replaced, in the DMU parts or assemblies that are made are versioned and those that are bought are replaced (mostly with a data exchange procedure depending on the level of integration of the supplier in the PDM system)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure7.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure7.5-1.png",
        "caption": "Figure 7.5. Isokinetic dynamometers usually measure torque because torque does not vary with variation in pad placement. Positioning the pad distally decreases the force the leg applies to the pad for a given torque because the moment arm for the leg is larger.",
        "texts": [
            " The angle of the joints affects the torque that the muscle group is capable of produc- ing because of variations in moment arm, muscle angle of pull, and the force\u2013length relationship of the muscle. There are several shapes of torque-angle diagrams, but they most often look like an inverted \u201cU\u201d because of the combined effect of changes in muscle moment arm and force\u2013length relationship (Figure 7.4). Torque is a good variable to use for expressing muscular strength because it is not dependent on the point of application of force on the limb. The torque an isokinetic machine (T) measures will be the same for either of the two resistance pad locations illustrated in Figure 7.5 if the subject's effort is the same. Sliding the pad toward the subject's knee will decrease the moment arm for the force applied by the subject, increasing the force on the leg (F2) at that point to create the same torque. Using torque instead of force created by the subject allows for easier comparison of measurements between different dynamometers. 172 FUNDAMENTALS OF BIOMECHANICS The state of an object's rotation depends on the balance of torques created by the forces acting on the object. Remember that summing or adding torques acting on an object must take into account the vector nature of torques"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001867_j.measurement.2012.08.012-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001867_j.measurement.2012.08.012-Figure2-1.png",
        "caption": "Fig. 2. Photograph of a taper roller bearing.",
        "texts": [
            " A personal computer based data acquisition system (Make: National Instrument, Model: SCXI-1000 having 4 channel input) is used to acquire the vibration data obtained from accelerometer. A program has been developed in Labview environment to acquire and display the signal along with its Fourier Transform. There is provision to record/store the signal in the hard disk of computer for further processing and analysis. The defect width has been analyzed using wavelet decomposition approach in Matlab environment. In the present study investigations have been made on four sets of the said bearing (NBC 30205 as shown in Fig. 2) each having different defect width 0.5776 mm,1.1820 mm, 1.7266 mm and 1.9614 mm on the outer race (OR). The defects have been generated using laser engraving technique. A typical defect of size 0.5776 mm is shown in Fig. 3. In this paper, results at the shaft speed of 2050 rpm are presented. When tested with the defect free bearing, the amplitude of the raw signal is obtained in the range of 1 to +1 mV as shown in Fig. 4. While dealing with the defective bearing it has been observed that amplitude of the burst in the raw signal has increased and is appearing in the range of 7 to +10 mV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000060_s11661-008-9557-7-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000060_s11661-008-9557-7-Figure1-1.png",
        "caption": "Fig. 1\u2014Schematic diagram of laser deposition with LENS.",
        "texts": [
            "1007/s11661-008-9557-7 The Minerals, Metals & Materials Society and ASM International 2008 I. INTRODUCTION AS one of a number of competing direct laser deposition processes, laser-engineered net shaping (LENS)* was developed with the goal of automatically fabricating complex-shaped or featured metallic components based on three-dimensional computer-aided design solid models of components.[1,2] LENS materials processing uses the high power density provided by the laser beam, which is focused on the deposited components, as shown in Figure 1. As a result, the built material experiences heating, melting, possible vaporization, and resolidification, so that it is considered as a thermal process. Understanding the temporal evolution of the temperature field during laser material interaction is one of the most significant factors in achieving the desired quality of processing. In the LENS process, components are deposited onto a large metal substrate, which conducts heat away from the component and acts to support the component during deposition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure3.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure3.7-1.png",
        "caption": "Figure 3.7.2. Basic body shape of Irving's Golden Arrow. (Reproduced by permission of the Council of the Institution of Mechanical Engineers, from Irving,",
        "texts": [
            " The Rak 2 of 1928 had larger wings of about 1 m2 each. Judging from photographs, however, the design was very odd, using a fairly thin, well-cambered section fitted as if to give lift, but then set at a negative incidence that would have resulted in little vertical force at all. It is doubtful that either of these two vehicles could be considered to be serious contenders; more likely, they were just publicity vehicles. Prevost (1928) first described proposals for a venturi-bodied land speed record car (Figure 3.7.1), with the stated intention of preventing lift. In 1929, the Irving-designed Golden Arrow set a land speed record of 103 m/s (231 mph). This used a venturi-shaped underbody (Figure 3.7.2), which according to windtunnel tests, would give 2440 N downforce at the design speed of 112 m/s (250 mph) (Irving 1930). In Prevost's proposal the venturi had a large entry depth, but in Irving's design the venturi had acquired its modern form, with the entry barely any deeper than the throat, necessary because a deep entry gives front lift. 172 Tires, Suspension and Handling Automobile Engineer, letter from R. Prevost, September 1928.) J.S., \"The Golden Arrow and the World's Land Speed Record,\" Automobile Engineer, May 1930"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001834_j.proeng.2015.08.007-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001834_j.proeng.2015.08.007-Figure3-1.png",
        "caption": "Fig. 3. LENS samples preparation: (a) near-net-shaped deposition for tensile tests; (b) extraction of tensile specimens; (c) near-net-shaped deposition for fatigue tests; (d) extraction of fatigue specimens (top: from bulk deposition; bottom: from substrate).",
        "texts": [
            " Spherical gas atomized (GA) Ti-6Al-4V powder is used in both LENS and EBM fabrications, Fig. 2. Particle sizes are similar for the two techniques. The powder used in EBM, Fig. 2(b), contains 50% recycled powder [14]. LENS samples were fabricated at Ben\u00e9t Laboratories, using an Optomec L850-R system. Two sets of processing parameters were applied, Table 1. Near-net-shaped rectangular depositions were built on top of mill-annealed Ti-6Al-4V plates (substrate). The geometries of the depositions were designed for the convenience of extracting tensile specimens, Fig. 3(a, b), and fatigue specimens, Fig. 3(c, d). Post-LENS annealing was also performed to generate comparison with the asdeposited cases. The annealing treatment used was: 760\u00b0C +/- 4\u00b0C for 1 hour in vacuum, followed by air cooling. EBM samples were fabricated at Oak Ridge National Laboratory (ORNL) in two batches, B1 and B2, representing two different machine models A2 and Q10. The processing parameters were defined by the internal algorithm of the ARCAM machines. Similarly, near-net-shaped cylindrical and rectangular samples were designed for tensile and fatigue crack growth studies respectively, Fig",
            " Different from LENS fabrication which is typical of fast cooling, in EBM, the powder bed was held at 650-750\u00b0C through out the process, and was slowly cooled to room temperature when fabrication completed. Long period exposure under 650-750\u00b0C decomposed all the \u03b1' phases formed during solidification; and since the minimum cooling rate required to form martenstic microstructure in Ti-6Al-4V is 410\u00b0C/s [15], the slow cooling upon fabrication completion did not lead to any martensitic formation. The resulting microstrucure in EBM fabricated Ti6Al-4V was found to be fine \u03b1 + \u03b2 lamellae, Figs. 7(c, d). For LENS farbication, tensile tests were conducted only at horizontal orientation, Fig. 3(b). Tensile properties of LENS fabricated Ti-6Al-4V and a comparison with mill-annealed Ti-6Al-4V (substrate) are provided in Table 2. In general, the yield strength and ultimate tensile strength of LENS depositions are higher than those of the millannealed substrate. Comparing between LENS fabrications, LP as-deposited Ti-6Al-4V yieled higher strength, but significantly lower ductility due to the presence of \u03b1' martensite. After annealing, significant increase in ductility was observed as a result of \u03b1' decomposition into \u03b1 + \u03b2 lamellae"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000759_rob.20327-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000759_rob.20327-Figure5-1.png",
        "caption": "Figure 5. The quadrotor body diagram with the associated forces and frames.",
        "texts": [
            " Controller design for rotorcraft UAVs and MAVs is a complex matter and typically requires the availability of the mathematical model of its dynamics. A rotorcraft can be considered a rigid body that incorporates a mechanism for generating the required forces and torques. The derivation of the nonlinear dynamics is first performed in the bodyfixed coordinates B and then transformed into the NED inertial frame I. Let {e1, e2, e3} denote unit vectors along the respective inertial axes and {xb, yb, zb} denote unit vectors along the respective body axes, as defined in Figure 5. The equations of motion for a rigid body of mass m \u2208 R and inertia J \u2208 R 3\u00d73 subject to external force Fext \u2208 R 3 and torque \u03c4 \u2208 R 3 are given by the following Newton\u2013Euler Journal of Field Robotics DOI 10.1002/rob equations, expressed in the body frame B: mV\u0307 + \u00d7 mV = Fext, J \u0307 + \u00d7 J = \u03c4, (1) where V = (u, v, w) and = (p, q, r) are, respectively, the linear and angular velocities in the body-fixed reference frame. The translational force Fext combines gravity, main thrust, and other body force components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002539_j.isatra.2018.02.006-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002539_j.isatra.2018.02.006-Figure1-1.png",
        "caption": "Fig. 1. Cart-pole system.",
        "texts": [
            " In this section, we consider a special choice of the Lyapunov ign of an adaptive super-twisting decoupled terminal sliding mode 8), https://doi.org/10.1016/j.isatra.2018.02.006 function (18) which allows removing the singularity in the adaptation law. Let P \u00bc 1 0 0 P2 ; (27) with P2 >0: Due to the structure of H1; the adaptation law (17) is simplified to _bb1 \u00bc 1 G sgn\u00f0S1\u00de: (28) In order to validate the suggested control technique, a cartepole system is simulated and some comparisons between the suggested technique and the methods of [23] and [57] are presented. The dynamic behavior of the cartepole system illustrated in Fig. 1 can be presented in the form of (3) with the functions f01\u00f0x; t\u00de; b1\u00f0x; t\u00de; f02\u00f0x; t\u00de and b2\u00f0x; t\u00de as f01\u00f0x; t\u00de \u00bc mtg sin\u00f0x1\u00de mpL sin\u00f0x1\u00decos\u00f0x1\u00dex22 L 4 3 mt mpcos2\u00f0x1\u00de b1\u00f0x; t\u00de \u00bc cos\u00f0x1\u00de L 4 3 mt mpcos2\u00f0x1\u00de f02\u00f0x; t\u00de \u00bc 4 3 mpLx22 sin\u00f0x1\u00de \u00fempg sin\u00f0x1\u00decos\u00f0x1\u00de 4 3 mt mpcos2\u00f0x1\u00de b2\u00f0x; t\u00de \u00bc 4 3 4 3 mt mpcos2\u00f0x1\u00de (29) where x1\u00f0t\u00de represents the angular position of the pole from the vertical axis, x2\u00f0t\u00de signifies the angular velocity of the pole from the Please cite this article in press as: Ashtiani Haghighi D, Mobayen S, Des control scheme for a class of fourth-order systems, ISA Transactions (201 vertical axis, x3\u00f0t\u00de denotes the position of the cart, x4\u00f0t\u00de indicates the cart velocity, mt is the total mass of the system which contains the mass of the pole \u00f0mp\u00de and the mass of the cart \u00f0mc\u00de; and L is the half-length of the pole"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000252_taes.1984.310452-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000252_taes.1984.310452-Figure7-1.png",
        "caption": "Fig. 7. Joint three solution.",
        "texts": [
            " 6, we have four different arm configurations. Each arm configuration corresponds to From (23) and (24), and using (25), 01 is found to be different values of joint two as shown in Table II. (Px, Py' Pz ) Eo OA =d2 EF= px B ~~~~~AB=a2 EG =py ~~~fl ~~~~~BC =a3 DE =pz ZJ 132 ~~~~~~~CD= d AD = R = Vp7+pp2 +pp2 -2 AE =r = V~~ Am Configurations 02 ARM ELBOW ARM* ELBOW from the origin of (x2, Y2, Z2) to the point where the last three joint axes intersect. LEFT and ABOVE arm a-- 13-1 + -1 From the arm geometry in Fig. 7, we obtain the LEFT and BELOW arm a + p -1 -1 + 1 following equations for finding the solution for 03: RIGHT and ABOVE arm a + 1 + 1 +1 + 1 RIGHT and BELOW arm a-ot +1 -1 -I R = 2 + 2p +p - 2(36) Note: 00 < a s 3600 and 00.B' 900. a2 + (d2 + a2) - 2 cos (p = 2 2a2 4 + a3 From Table 11, 02 can be expressed in one equation sin9 = ARM ELBOW (37) for different arm and elbow configurations using thesi =AR ELO 1-co2p(7 ARM and ELBOW indicators as d_ 1a3 1 02 = a + (ARM. ELBOW) P= (x + K (27) sin ,13 = a o 2 =\\ (38) where the combined arm configuration indicator K = From Table III we obtain the equation for 03: ARM ELBOW will give an appropriate signed value 03 = (P (39) and the \"dot\" represents a multiplication operation on the indicators",
            " sin 1 (33) (3) Set joint 6 to align the given orientation vector (or sliding vector or Y6) and normal vector.cos 02 = cos (ox + K *)=cos aL cosC - (ARM - ELBOW) sin oa sin 13(34) Mathematically the above criteria, respectively, mean - -h (Z3 X a) given a = a aY' a From (33) and (34), we obtain the solution for 02: = ll given a = (ax,aaz)T (43) 02= atan2 [sin_021-0 c' ' . a = Z5, given a = (ax,ay,az)T (44) s = O _` given s = (s,sy3Sz)T and Joint Three Solution. For joint 3, we project the position vector p onto the x2-~Y2 plane as shown in Fig. n = (ni, ny, nz)T. (45) 7. From Fig. 7, we again have four different arm In (43), the vector cross product may be taken to be configurations. Each arm configuration corresponds to positive or negative. As a result, there are two possible LEE & ZIEGLER: ROBOT INVERSE KINEMATICS SOLUTION USING GEOMETRIC APPROACH 701 X2- Y2 plane d4 c A2BB = a2 A -? ~~~~~~~~~CD= d4 a92 B~B; -a = ~3 4 X3 r-,BAD= R = p2 + p + p-d219 ~~~~~Xy Z 2 LEFT and BELOW Arm C d4 D A 82 B 3 33=<- 900 x3 LEFT and BELOW Arm Arm Configurations (p4), 03 ARM ELBOW ARM. ELBOW vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003722_j.ymssp.2021.108319-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003722_j.ymssp.2021.108319-Figure3-1.png",
        "caption": "Fig. 3. Diagram of the 21 DOF gear dynamic model, in which ( xi, yi ) and \u03b8i are translational and torsional responses, respectively [2].",
        "texts": [
            " Two vibration sensors (B&K 4396 and B&K 4394 accelerometers) are mounted on the top of the gearbox casing in the positions shown in Fig. 2(b) to acquire the vibration signals for comparison analysis with simulations. Note that the sensitivity of the B&K 4396 accelerometer is 10.0mV/ms\u2212 2 and its nominal frequency range is 1\u201314,000 Hz, while for the B&K 4394, its sensitivity and frequency range are 1.00mV/ms\u2212 2 and 1\u201325,000 Hz, respectively. A 21-degree-of-freedom (DOF) dynamic model (shown in Fig. 3) was established, based on the gearbox test rig (shown in Fig. 2). The model includes the motor, shafts, gears, casing and couplings. The equation of motion for the system can be expressed in standard form, as shown in Eq. (3): Mx\u0308+Cx\u0307+Kx = f (3) where x represents the translational and angular displacements of the different nodes of the gear system, which are in the plane perpendicular to the shaft axes. Further details of the equation and parameter values are presented in Appendix A and study [2]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure11-1.png",
        "caption": "Fig. 11. (a) Representation of pedestal with outer race and (b) the bond graph sub-model of outer race.",
        "texts": [
            " The self-weight \u2212 M gSe: S is modeled at \u03071ym junction. Two Tf elements and 0 junctions are used to model the kinematics in Eq. (33). The motor speed is model by \u03c9Sf: i where it is assumed that the motor gives a controlled speed. If the motor is assumed to provide a torque then \u03c9Sf: i and coupling model are replaced by an effort source (Se). This sub-model has a multi-bond interface port numbered as 1 (shown within a circle) to connect it with several rolling element sub-models. The outer race (See Fig. 11(a)) is assumed to have no rotation. It is mounted on the bearing pedestal which has some structural stiffness and damping. Its sub-model is similar to that of the inner race and can be obtained from the later removing \u03b8 \u03071 i junction of Fig. 10(b) and all connected parts (eccentricity model, and drive and coupling) and labeling the remaining junctions appropriately, to obtain the sub-model shown in Fig. 11(b). In Fig. 11(b), the equivalent mass, mounting structural stiffness and damping, and the self-weight are represented with MI: p, KC: p, RR: p and \u2212 M gSe: p , respectively. For vibration analysis and bearing condition monitoring, the acceleration or velocity of the pedestal in the vertical direction is measured. Thus, an effort detector De (analogous to accelerometer when mass is constant) and a flow detector Df (analogous to velocity sensor) are implemented at appropriate locations in the model. A multi-bond interface port (port number 2) is used to connect this sub-model to the sub-models of rolling elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003726_j.ymssp.2015.05.015-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003726_j.ymssp.2015.05.015-Figure3-1.png",
        "caption": "Fig. 3. Time-varying gear mesh stiffness for different crack sizes.",
        "texts": [
            " Thus, the total mesh stiffness for one meshing tooth pair is: Kt \u00bc 1 1 Ktp \u00fe 1 K fp \u00fe 1 K tg \u00fe 1 K fg \u00fe 1 Kh \u00bc Km1 \u00f013\u00de where Km1 is the total mesh stiffness for the first tooth pair. In cases where there are two tooth pairs in contact, the same calculations are repeated for the second tooth pair to find Km2. Then we can obtain the equivalent mesh stiffness as follows: Km \u00bc Km1\u00feKm2 \u00f014\u00de A single-stage spur gear model was adopted in the present research work. The main gear modelling parameters that were used in this study were considered previously in [7,13], and can be seen in Table 3. The varying mesh stiffness obtained for all the studied crack sizes is shown in Fig. 3. In previous studies the angular dependency of the friction coefficient in the gear tooth contact has been studied [15,16]. The studies showed an angular dependency of the friction coefficient m with a variation of approximately 0.03\u20130.09. In the current study an assumption, previously adopted in gear modelling [7,16], of a constant friction coefficient has been adopted and a value of m\u00bc0.06 has been used. Here the term \u2018pinion\u2019 refers to the smaller gear, which is a driver gear in this study, and the term \u2018gear\u2019 refers to the larger gear, which is a driven gear in this study",
            " (a) Residual signal of crack case 6, (b) STFT of crack case 6 applied on residual signal, (c) residual signal of crack case 7, (d) STFT of crack case 7 applied on residual signal, (e) residual signal of crack case 9, and (f) STFT of crack case 9 applied on residual signal. moderate up to crack case 5, and after this case an increasing change can be seen. The frequency change shows a nonlinear behaviour which is consistent with the non-linear reduction in the mesh stiffness produced by the increasing crack size, see Fig. 3. Based on the simulation result shown in Fig. 10, it is therefore possible to detect all the crack cases. The change in frequency is, however, relatively small (2 Hz) for the first crack cases, up to case 5, compared to the later crack cases (50 Hz). The possibility of detecting experimentally the stiffness reduction of a tooth due to cracks is dependent on the ability of the used measurement system to measure small differences in frequency shifts within short periods of time. This study also shows that it is possible to recognise the change in the frequency content by applying the proposed approach on the residual signal, as can be seen in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003272_tvt.2020.2993725-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003272_tvt.2020.2993725-Figure5-1.png",
        "caption": "Fig. 5. Mechanical and electrical angles in three-phase 6/14 SRM [24].",
        "texts": [
            " (3) In (3), \u041f designates that the results from the ceil function for each prime factor are multiplied. If k is an integer multiple of one of the prime factors of m, the result of the multiplication is zero. Then, Nr is zero, which signifies that the selected configuration index cannot maintain a balanced and symmetric operation for the given number of stator poles and number of phases. If k is not an integer multiple of any of the prime factors of m, the result of the multiplication is one, and (3) turns into (2) calculating the number of rotor poles. Fig. 5 shows the mechanical and electrical angles of a novel 3-phase 6/14 SRM calculated from (5). The configuration index can be calculated as k = 7, which is not an integer multiple of the prime factor i = 3. It can be observed that a 6/14 SRM has similar electrical angles as the 12/8 SRM in Fig. 5. It also has higher number of strokes, which can potentially lead to lower torque ripple. Table 1 shows various SRM configurations calculated from (3). It shows the number of phases for a given number of stator poles and number of rotor poles. The empty cells show that the given number of stator and rotor poles do not provide a working configuration. The list can be expanded to higher numbers of stator and rotor poles. The pole configuration expression in (3) enables calculating various SRM configurations",
            " Most of the conventional SRM configurations have an even number of stator poles per phase; for example, for a 3-phase 12/8 SRM, Ns/m = 4 and for a 4-phase 24/18 SRM, Ns/m = 6. As shown in Table 1, pole configurations calculated by (3) include SRMs with an odd number of stator poles per phase, such as 3-phase 9/12, 4-phase 12/9, and 3-phase 15/10 SRMs. Fig. 6 shows the mechanical and electrical angles in a 3- phase 9/12 SRM, which has 3 stator poles per phase. It can be seen that the 9/12 SRM has similar electrical angles as the 12/8 SRM in Fig. 4 and the 6/14 SRM in Fig. 5. As shown in Fig. 4, when the coils of a phase of the 12/8 SRM are energized, four magnetic poles are created, which is equivalent to the number of stator poles per phase. Only the stator poles belonging to the excited phase generate the magnetic flux lines; making the mutual coupling between phases negligible, which is an important feature of SRMs. In the 12/8 SRM, the coils of the consecutive stator poles of a phase have opposite directions. This enables the flux pattern shown in Fig. 4. If the same coil pattern is applied to a 9/12 SRM, it would not be possible to have the number of magnetic poles equal to the number of stator poles per phase (Ns/m = 3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003898_j.msea.2019.138742-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003898_j.msea.2019.138742-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of (a) sample processing and (b) the scanning strategy.",
        "texts": [
            ", China) and corresponding chemical composition is listed in Table 1. The powder was obtained through electrode induction melting gas atomization (EIGA) technique, showing good sphericity (Fig. 1(a)) and approximately normal distribution (Fig. 1(b)) with median particle size of 34.3 \u03bcm. The wrought TA15 bars (\u03a645 \ufffd 100 mm) used for TA15 powder production was chosen as the reference material provided by the same company. Specimens with the dimension of 10 \ufffd 10 \ufffd 10 mm3 and cylindrical specimens with \u03a610 \ufffd 100 mm in the horizontal and vertical directions (Fig. 2(a)) were manufactured utilizing a SLM apparatus (EOSINT M280, EOS GmbH, Germany) equipped with a 200 W Yb fiber laser. Based on the preliminary processing optimization experiment, processing parameters were set as laser power of 190 W, laser scanning speed of 1050 mm/s, scan line hatch spacing of 100 \u03bcm, stripe width of 5 mm and powder layer thickness of 30 \u03bcm. The employed scanning strategy was round-trip scanning and rotation of 67\ufffd between two consecutive layers, as shown in Fig. 2(b). According to Archimedes method [36], the relative density of fabricated parts in SLM was measured and reached to Table 1 Chemical composition of TA15 powder used in the experiments. Element Ti Al V Zr Mo Si Fe C O N wt.% Balance 6.37 2.17 2.16 1.3 0.017 0.072 0.029 0.1 0.02 Fig. 1. (a) Morphology and (b) particle size distribution of TA15 powder. J. Jiang et al. Materials Science & Engineering A 772 (2020) 138742 99.98%. The horizontally and vertically fabricated samples are denoted as SLM-H and SLM-V, respectively",
            " To remove residual stress and improve plasticity of SLMed TA15 alloy, half of the fabricated specimens consisted of cubical and cylindrical samples were annealed at 800 \ufffdC for 2 h in argon atmosphere followed by air cooling. The annealing process was based on ASTM B367-13 standard [37]. SLM-H and SLM-V after annealing are denoted as HT-H and HT-V, respectively. The as-built and annealed cubic samples were used for microstructural characterization. Due to the special anisotropic building process of SLM, the horizontal and vertical planes of the cube (Fig. 2 (a)) are considered. Wrought TA15 samples were cut from TA15 bar for metallographic observation and phase identification. Microstructural observation was conducted using optical microscope (OM VHX-1000, Keyence), scanning electron microscope electron with backscatter diffractometer (SEM, EBSD, MIRA3, TESCAN) and transmission electron microscope (TEM, F20, FEI). Phase identification and crystallographic texture were performed on X-ray diffractometer (XRD, Rigaku D/MAX2500pc). The preparation of metallographic samples was based on ASTM E3-11 standard [38]",
            " preferential growth of crystals along the building direction in remolten pool of the previous layers [5,13]. Furthermore, it is worthy noted that there are Table 4 The sizes of \u03b1 laths. Type of \u03b1 Length Width Primary \u03b1 >20 \u03bcm 1\u20132 \u03bcm Secondary \u03b1 10\u201320 \u03bcm 0.5\u20131.5 \u03bcm Ternary \u03b1 1\u201310 \u03bcm 0.3\u20131 \u03bcm Quartic \u03b1 <1 \u03bcm 0.1\u20130.5 \u03bcm J. Jiang et al. Materials Science & Engineering A 772 (2020) 138742 some changes in the growth direction of prior \u03b2 grains and in the widths of columnar grains, which can be ascribed to the special scanning strategy (Fig. 2 (b)) in SLM with a rotation angle of 67\ufffd. Different from the chessboard pattern generated by 90\ufffd rotation in other published papers [4,13], most prior-\u03b2 grains present irregular shapes and a fraction of grains present approximately equiaxed shapes on the horizontal plane, as shown in Fig. 5(b). Additionally, a large number of fine acicular \u03b1\u02b9 martensite can be seen inside these columnar grains due to high temperature gradient resulted from the high cooling rate in SLM process [5]. On the vertical plane, these acicular structures are mostly distributed at an angle of \ufffd45\ufffd to the prior \u03b2 grain boundary (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure17-1.png",
        "caption": "Fig. 17. (a) Example describing the solid-to-solid contact model in ADAMS [41] and (b) wireframe model of a ball with a part of the cage and races showing the nodes used in the discretized model for contact detection.",
        "texts": [
            " The tangential forces are defined using Coulomb friction model. As per ADAMS implementation, three values of coefficients of friction at the contact point for slip velocity, less than the static transition velocity and greater than the friction transition velocity are defined in order to numerically integrate the equations of motion. These parameters are dependent on the material of bearing and types of lubricant used. As an illustration, the normal contact force between a sphere and a flat surface is calculated using the Adams solver [41] as (see Fig. 17(a)) ( )( ) = ( \u2212 ) \u2212 \u2212 \u0307 < \u2265 ( ) \u23aa \u23aa\u23a7\u23a8 \u23a9 F K x x STEP x x d R x x x x x x max 0, , , , ,0 if , 0 if , 37 e 1 1 1 1 1 where d, x, x1, R and e represent, respectively, the boundary penetration at which the ADAMS solver applies full damping, the distance variable that is used to compute an impact function, the stiffness of the boundary surface interaction, the free length of x (if x is less than x1 then ADAMS calculates a positive value for the force), the maximum damping coefficient and exponent of the force deformation characteristic. ADAMS uses the slave node-master surface concept from finite element method (FEM) for contact detection. The nodes and surfaces used for this purpose are obtained by discretization of the volume of the rigid bodies. A sample discretization of the volume is shown in Fig. 17(b). The friction/ traction force is calculated assuming that Coulomb force acts between the bodies. The coefficients of friction for every slip velocity are calculated by Adams solver using the four values of input, namely, static and dynamic coefficients of friction and static and dynamic transition velocities. This value is multiplied to the normal force to find the frictional force [41]. A number of models of rolling element bearing are available in literature where the localised faults are modelled as small notches of triangular or rectangular shape"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000273_tia.2009.2013550-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000273_tia.2009.2013550-Figure8-1.png",
        "caption": "Fig. 8. Eddy-current distribution of magnet (without magnet division, obtained by main calculation considering carrier, 6000 min\u22121).",
        "texts": [
            " In this case, the eddy currents flow through the whole part of the magnet because they are mainly produced by the carrier harmonic flux density, whose distribution varies due to one pole pitch, and it enters into the rotor deeply [4]. Furthermore, the frequency of the major carrier harmonics is higher than the slot harmonics. As a result, the eddy-current density of Fig. 7 is much higher than Fig. 6. C. Variation of Magnet Eddy-Current Loss Due to Divisions Next, let us investigate the effects of the magnet divisions. Fig. 8 shows the eddy-current distribution of model (a), which is without the magnet division, obtained by the main calculation considering the carrier. In this case, the eddy currents concentrate at the edge of the magnet due to the skin effect. The maximum eddy-current density is nearly twice of the case of 28 magnet divisions. On the other hand, it can be seen that the region where the eddy currents flow is restricted. Fig. 9 shows the variation of the calculated total iron loss due to the number of the magnet divisions along the axial length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000075_s11665-009-9535-2-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000075_s11665-009-9535-2-Figure3-1.png",
        "caption": "Fig. 3 Diagrammatic sketch showing dimension of tensile specimen",
        "texts": [
            " Thus, with the repeated singlelayers forming process, a rectangular block with dimension of 159 129 1 mm3 was prepared, and a gradient porosity microstructure along the speed gradient direction was obtained. In addition, to evaluate the influence of scan speed on the porosity and mechanical property of SLM-prepared samples, separate samples were fabricated under different scan speeds. Finally, porosities of samples produced at different scan speeds were measured by Archimedes law. Then, tensile samples were produced by wire-electrode cutting, and the dimension of tensile specimen is shown in Fig. 3. The tensile strengths were measured by Zwick/Roell Corporation Germany) with the loading rate of 2 mm/min. SLM specimens for metallographic examinations were cut from side view, and pre-grinding was conducted with SiC sandpaper to 800 grit finish. After plane grinding, polishing was done for the samples with Cr2O3 suspensions on woven synthetic pads. Then, the polished sample was rinsed using distilled water to wipe off any impurities on the polished surface. Aqua fortis was used as a corrosive agent"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003992_1350650117711595-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003992_1350650117711595-Figure8-1.png",
        "caption": "Figure 8. Solid model of: (a) first type of configuration; (b) second type of configuration (Source: Duzcukoglu et al.52).",
        "texts": [
            " The rise in the temperature of the gear surface was caused by the friction and hysteresis effects under repeated tooth loading. At low loads, gears with high fillet radius failed due to cracking at the pitch region whereas gears with low fillet radius failed by the cracking at the root due to high stress concentration. At all loads, the gears with high tooth fillet radius showed better service life. Drilling air-cooling holes on the tooth of gear In some studies, air-cooling holes were drilled at the different locations on the plastic gear tooth.51,52 Two types of gear tooth configurations were used as shown in Figure 8(a) and (b). In the first configuration, holes were drilled at the pitch diameter that went through the width and were perpendicular to the tooth axis. In the second configuration, a hole was drilled at a radial position and two smaller holes were drilled along the radial direction of each tooth. The gears with standard, the first type and the second type of tooth configuration were tested, and their performance was compared. The lowest tooth surface temperature was obtained in the second type of tooth configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001028_j.jmatprotec.2010.09.007-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001028_j.jmatprotec.2010.09.007-Figure2-1.png",
        "caption": "Fig. 2. Three domains, laser beam and powder jet.",
        "texts": [
            " the substrate, the melt pool and the solidified domain are distinuished. The process is modeled as a stationary problem, by fixing he frame of reference to the laser beam, i.e. the material flows hrough the domains. The melt pool flow is not considered in the urrent model. The laser source and the powder jet are described by two-dimensional source distribution which can be chosen arbirarily independent of their position along their main axes. Also the rientations and locations of these axes can be freely chosen. Fig. 2 hows the domains as well as the laser beam and powder jet. .1. Heat balance For all the domains, the basic heat equation can be written in erms of temperature T as: \u2202T \u2212\u2192 cp(T) \u2202t + cp(T) v \u00b7 \u2207T = \u2207 \u00b7 k(T)\u2207T (3) here k(T) (thermal conductivity), cp(T) (heat capacity) and (denity) are material property coefficients, which are functions of emperature T and/or space. The velocity vector \u2212\u2192v is the veloc- ssing Technology 211 (2011) 187\u2013196 ity of the material in a coordinate frame which is fixed to the laser beam",
            " Boundary equations To solve the heat balance in a domain, it is necessary to prescribe the boundary conditions along the complete boundary of the domain. The relevant heat fluxes and temperatures at the boundaries are; Initial temperature of the substrate, heat losses due to radiation, a heat flux from the laser and a heat flux associated with the hot particles arriving at the melt pool. Radiation losses will be in the order of a few percentage of the laser energy as shown by Hofman (2009) and are considered neglectable. The initial temperature of the substrate is used at the inflow boundary (area 1 of Fig. 2) of the substrate domain. On the other boundaries of the substrate as well as the outer surface of the solidified clad (area 2 of Fig. 2), the heat flux is assumed to be zero. This assumption is valid as long as the dimensions of the substrate in the model are relatively large and the boundary temperature does not increase much. At the top surface of the melt domain (area 3 of Fig. 2) the boundary condition is given by the interaction with the laser beam and the powder jet. The heat input is split-up into three parts. Firstly, the laser radiation passes through the powder jet and arrives at the melt pool attenuated. Secondly, the supplied powder after passing through the laser beam arrives at the melt pool at an elevated temperature. Lastly, as these boundaries are generally at elevated temperatures, an energy flux (qmass \u2212\u2192x ) associated with material flowing through this surface has to be taken into account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000953_tfuzz.2013.2280146-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000953_tfuzz.2013.2280146-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the electromechanical system.",
        "texts": [
            " It is noted that if \u03c31 and \u03c32 are too small, it may not be enough to prevent the parameter estimates from drifting. If ki (i = 1, . . . , n), Q, ci (i = 1, . . . , n), \u0393, and \u03b3 are big, the control energy is big. Therefore, in practical applications, the design parameters should be adjusted carefully to achieve suitable transient performance and control action. V. SIMULATION STUDY Example: To further show the effectiveness of the proposed adaptive fuzzy controller, we consider the electromechanical system shown in Fig. 1 [13], [28]. The dynamics of the electromechanical system is described by the following equation [13], [28]: { Dq\u0308 + Bq\u0307 + N sin(q) = \u03c4 M\u03c4\u0307 + H\u03c4 = V \u2212 Km q\u0307 (55) where D = J K \u03c4 + m L 2 0 3K \u03c4 + M 0 L 2 0 K \u03c4 + 2M 0 R 2 0 5K \u03c4 , N = m L 0 G 2K \u03c4 + M 0 L 0 G K \u03c4 , and B = B 0 K \u03c4 . J is the rotor inertia, m is the link mass, M0 is the load mass, L0 is the link length, R0 is the radius of the load, G is the gravity coefficient, B0 is the coefficient of viscous friction at the joint, q(t) is the angular motor position (and hence the position of the load), \u03c4 is the motor armature current, and K\u03c4 is the coefficient which characterizes the electromechanical conversion of armature current to torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003196_s11661-013-1968-4-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003196_s11661-013-1968-4-Figure3-1.png",
        "caption": "Fig. 3\u2014Schematic of SLM apparatus (a); SLM procedure for fabricating bulk-form Ti-based nanocomposite parts (b).",
        "texts": [
            " The ultrafine TiC nanoparticles were dispersed uniformly around Ti particles surface after the mechanical mixing process (Figure 2(c)). In contrast with the ball-milling process, the powder particles did not experience any deformation and structural change during the mixing process. The spherical Ti powder particles were METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, JANUARY 2014\u2014465 accordingly used, in order to obtain a sound flowability of the mixed TiC/Ti nanocomposite powder. The SLM apparatus, as schematically depicted in Figure 3(a), consisted mainly of a YLR-200 Ytterbium fiber laser with a power of ~200 W and a spot size of 70 lm (IPG Laser GmbH, Germany), an automatic powder layering mechanism, an inert argon gas protection system, and a computer system for process control. The real-time SLM process is illustrated in Figure 3(b). First, a Ti substrate was fixed on the building platform and levelled. The building chamber was then sealed and the argon gas with an outlet pressure of 30 mbar was fed inside, decreasing the O2 content below 10 ppm. Afterward, a thin layer of the powder with a thickness of 50 lm was deposited on the substrate by the layering mechanism. The laser beam then scanned the powder 466\u2014VOLUME 45A, JANUARY 2014 METALLURGICAL AND MATERIALS TRANSACTIONS A bed surface to form a two-dimensional profile according to computer-aided design data of the specimens"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002375_icra.2015.7139850-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002375_icra.2015.7139850-Figure1-1.png",
        "caption": "Fig. 1. a) a prototype quadrotor with manipulator, b) schematic model, c) a computed optimal trajectory viewed in Robot Operating System (ROS).",
        "texts": [],
        "surrounding_texts": [
            "I. INTRODUCTION\nThis work develops a nonlinear model-predictive control (NMPC) approach to enable agile pick-and-place capabilities for aerial vehicles equipped with manipulators. Aerial manipulation using vertical take-off and landing (VTOL) vehicles is a relatively new research area with a potential for various novel applications such as coordinated assembly, construction, and repair of structures at high altitudes, or operating in difficult-to-access, remote, or hazardous locations to e.g. install sensors or obtain samples. Autonomous control of such system is challenging primarily due to disturbances from interactions with the environment, due to additional dynamics caused by a moving manipulator, and due to difficulties associated with dexterous manipulation.\nInitial work related to aerial manipulation included slung load transportation with helicopters [6], [20], grasping with novel adaptive end-effectors [27], [26], construction using teams of quadcopters [18], or pole balancing tasks [7]. More recently, there has been a focus on autonomous construction and environment interaction, with initial demonstrations in laboratory settings. The Aerial Robotics Cooperative Assembly System (ARCAS) project [2], [12], [8], Mobile Manipulating Unmanned Aerial Vehicle project [25], [16], [17] and Airobots project [1], [31] have demonstrated complex manipulation and assembly tasks using multiple degrees of freedom manipulators. Other important developed capabilities include telemanipulation [22], [11] or avian-inspired agile grasping [30]. In addition to control-related challenges, accurate pose estimation of objects is of central importance and has been considered through image-based visual servoing [29] and marker-based pose computation [2], [7]. Real-time recognition and aerial manipulation of arbitrary\n1Gowtham Garimella and Marin Kobilarov are with the Department of Mechanical Engineering, Johns Hopkins University, 3400 N Charles Str, Baltimore, MD 21218, USA ggarime1|marin@jhu.edu\nunengineered objects in natural settings remains largely an open problem.\nControl strategies for aerial manipulation can be divided into coupled which consider the full multi-body system model [19], [14], [24], and decoupled based on separate controllers for the base body and manipulator [28]. The key difference is that the decoupled approach treats external forces from the arm or environment as disturbances to be compensated by the vehicle.\nIn this paper, we propose an optimal control algorithm for generating reference trajectories to pick an object using aerial vehicle. Experimental verification has been performed using a minimalist low-cost system based on a two-degree of freedom manipulator with a simple gripper. The task is made challenging by using a monocular camera to recognize and track the target object. To facilitate recognition, objects\n978-1-4799-6923-4/15/$31.00 \u00a92015 IEEE 4692",
            "are engineered with LED markers correspoding to known features. A detailed nonlinear model is employed by the optimal control framework to capture the interaction between the arm and quadcopter. Currently due to computational limitations, NMPC operates at 10Hz and is not used for realtime control. Hence a high frequency nonlinear controller is coupled with the optimal control framework to track the reference trajectories.\nThe paper is organized as follows. The dynamical multibody system modeling and numerical optimal control approach are described in \u00a7II and \u00a7III, respectively. Then we proceed to describe the experiments conducted to validate the optimal controller in \u00a7IV. Finally we provide the results of the experiments conducted and discuss future work in \u00a7V.\nThe aerial robot is modeled as a free-flying multi-body system consisting of n + 1 interconnected rigid bodies arranged in a tree structure. The configuration of body #i is denoted by gi \u2208 SE(3) and defined as\ngi = ( Ri pi 0 1 ) , g\u22121i = ( RT i \u2212RT i pi 0 1 ) .\nwhere pi \u2208 R3 denotes the position of its center of mass and and Ri \u2208 SO(3) denotes its orientation. Its body-fixed angular and linear velocities are denoted by \u03c9i \u2208 R3 and \u03bdi \u2208 R3. The pose inertia tensor of each body is denoted by the diagonal matrix Ii defined by\nIi = ( Ji 0 0 miI3, ) where Ji is the rotational inertia tensor, mi is its mass, and In denotes the n-x-n identity matrix. The system has n joints described by parameters r \u2208 Rn. Following standard notation [23], the relative transformation between the base body#0 and body#i is denoted by g0i : Rn \u2192 SE(3), i.e.\ngi = g0g0i(r).\nThe control inputs u \u2208 U \u2282 Rm=n+4 denote the four rotor speeds squared and the n joint torques. More specifically, ui = \u21262\ni for i = 1, . . . , 4 where \u2126i is the rotor speed of the i-th rotor, and u4+i denotes the i-th joint torque, for i = 1, . . . , n.\nThe configuration of the system is thus given by q , (g, r) \u2208 Q , SE(3) \u00d7 Rn, where g \u2208 SE(3) is a chosen reference frame moving with the robot. In this work we take the base body as a moving reference, i.e. g \u2261 g0. The velocity of the system is given by v , (V, r\u0307) \u2208 R6+n, where V \u2208 R6 denotes the body-fixed velocity of the moving frame g and r\u0307 \u2208 Rn denotes the joint angle velocities. The base velocity satisfies V\u0302 = g\u22121g\u0307 where the \u201chat\u201d operator V\u0302 for a given V = (\u03c9, \u03bd) is defined by\nV\u0302 =\n[ \u03c9\u0302 \u03bd\n01\u00d73 0\n] , \u03c9\u0302 =  0 \u2212w3 w3 w3 0 \u2212w1\n\u2212w2 w1 0\n . (1)\nWith these definitions, the full state of the system is x , (q, v) \u2208 X , Q\u00d7 R6+n.\nContinuous Equations of Motion: The coordinates for our setting are q = (g, r) where the pose g \u2208 SE(3) and r represents joint parameters. For optimal control purposes, it is necessary to avoid Euler angle singularities and, in addition, it is advantageous to avoid unit quaternion constraints. To achieve this, the dynamics is defined directly on state space X as:\ng\u0307 = gV\u0302 (2) M(r)v\u0307 + b(q, v) = Bu, (3)\nwhere the mass matrix M(r), bias term b(q, v), and constant control matrix B are computed analogously to standard methods such as the articulated composite body algorithm [5] or using spatial operator theory [10]. With our coordinatefree approach the mass matrix in fact only depends on the shape variables r rather than on q and for tree-structured systems can be computed readily according to\nM(r) =  I0 + n\u2211\ni=1\nAT i IiAi\n\u2211n i=1A\nT i IiJi\u2211n\ni=1 J T i IiAi\n\u2211n i=1 J T i IiJi\n (4)\nusing the adjoint notation Ai := Adg\u22121 0i (r), and Jacobian Ji := \u2211n j=1[g\u221210i (r)\u2202rjg0i(r)] \u2228,where g0i(r) is the relative transformation from the base body to body #i and Ii is the inertia tensor of body #i [23].\nThe bias term b(q, v) encodes all Coriolis, centripetal, gravity, and external forces. Finally, for a quadrotor model the constant control matrix B has the form\nB =  0 \u2212lkt 0 lkt \u2212lkt 0 lkt 0 km \u2212km km \u2212km 0 0 0 0 0 0 0 0 kt kt kt kt\n06\u00d7`\n0`\u00d76 I`\u00d7`\n ,\nwhere l, kt, km are known constants. This can be easily extended to other multi-rotor configurations.\nDiscrete Dynamics: For computational purposes we employ discrete-time state trajectories x0:N , {x0, . . . , xN} at equally spaced times t0, . . . , tN \u2261 tf with time step \u2206t =\ntf\u2212t0 N . The discrete state at index k approximates the\ncontinuous state at time tk = t0 + k\u2206t, i.e. xk \u2248 x(tk) and is defined by xk = (gk, rk, Vk,\u2206rk), where \u2206rk denotes the joint velocities at k-th stage. A simple discrete-time version of the continuous dynamics (2)\u2013(3) is then employed:\ngk+1 = gk cay (\u2206tVk+1) , (5) rk+1 = rk + \u2206t\u2206rk+1, (6) M(rk) vk+1 \u2212 vk\n\u2206t + b(qk, vk) = Buk. (7)\nThis is a first-order semi-implicit method since one first updates the velocity vk+1 using the dynamics (7) and then updates the configuration using the kinematics (5)\u2013(6). The method requires small time-steps to ensure stability (\u2206t \u2264"
        ]
    },
    {
        "image_filename": "designv10_1_0002492_j.rcim.2016.05.011-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002492_j.rcim.2016.05.011-Figure5-1.png",
        "caption": "Fig. 5. Robot base frame and the rotation of A1 axis.",
        "texts": [
            " Thus the robot base frame should be constructed in the measuring software of the laser tracker. The robot base frame was constructed in the measuring software (FARO CAM2) of the laser tracker in order to measure the positional errors of the TCP. Firstly a group of points on the mounting platform were measured and fitted to construct a plane, i.e. the XY plane of the robot base frame. Secondly a circle was fitted with a group of TCP positions measured while rotating the A1 axis, as is shown in Fig. 5. The normal direction of the circle was fitted in the measuring software as the A1 axis, also as the z axis of the robot base frame. The projection of the circle centre on the XY plane was the origin of the robot base frame. Thirdly, a circle was fitted using the same way while rotating the A6 axis. The projection of the circle centre on the XY plane was the point on the positive direction of the x axis of the robot base frame. Finally the robot base frame was constructed using the origin, the point on the x axis and the point on the XY plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001165_tie.2010.2046579-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001165_tie.2010.2046579-Figure2-1.png",
        "caption": "Fig. 2. Free-body diagram of the 3-DOF helicopter.",
        "texts": [
            " One end of the arm is attached to a counterweight, while two dc motors with propellers are installed at the other end to create forces that drive the propellers. Two motors\u2019 axes are parallel, and the thrust vector is normal to the frame. Three encoders are connected to the helicopter in order to measure the elevation, pitch, and travel angles of the body, and two voltage amplifiers are used to realize the control action in the system. The frontand back-motor voltages are the control input of the system. The free-body diagram of the 3-DOF helicopter [24] is shown in Fig. 2, and its spatial relations of the frames and angles are shown in Fig. 3. Applying the Euler\u2013Lagrange formula, the dynamics of the helicopter can be described by differential equations (see also in [13] and [15]). At first, we consider the elevation motion. The twisting moment of this axis is controlled by the composition of forces generated by the propellers J\u03b5\u03b5\u0308 = KfLa cos p(Ff + Fb) \u2212 mhgLa sin(\u03b5 + \u03b10) (1) where \u03b10 is the initial angle between the helicopter arm and its base. The pitch motion is described by the following: Jpp\u0308 = KfLh(Ff \u2212 Fb)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001812_jmes_jour_1962_004_018_02-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001812_jmes_jour_1962_004_018_02-Figure1-1.png",
        "caption": "Fig. 1. Co-ordinate system",
        "texts": [
            " Sibley and Orcutt (11) used an X-ray transmission technique to measure directly the minimum film thickness between slightly crowned discs. Several lubricants were used and the experiments covered a wide range of loads and speeds. Evidence of a hydrodynamic film in running gears has been provided by MacConochie and Cameron (12). A voltage discharge method was used to measure the oil film thickness and the results were consistent with elasto-hydrodynamic theory. For isothermal conditions and an incompressible lubricant a representative film thickness h (Fig. 1) can be written in dimensionless form as follows: h w 3 - 3 rlou .F] =' [fi E'R These groups will be written as H = h/R, W = w/E'R, U = 7,u/E'R and G = YE'. The independent dimensionless variables will be referred to as the load, speed and materials parameters respectively. Vol4 No 2 1962 at MCGILL UNIVERSITY LIBRARY on April 3, 2016jms.sagepub.comDownloaded from 122 D. DOWSON, G. R. HIGGINSON AND A. V. WHITAKER Notation 2b Width of Hertzian contact. El , E2 ModuIi of elasticity of rollers. G YE\u2018"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001439_j.cirp.2010.03.021-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001439_j.cirp.2010.03.021-Figure4-1.png",
        "caption": "Fig. 4. Experimental test rig for estimation of frictional torque in spindle bearings.",
        "texts": [
            " There are three main contributions to the total frictional torque in a ball\u2013groove contact [11]: (1) load friction caused by rolling and proportional to contact forces; (2) viscous friction caused by viscosity of lubricant\u2014nonlinearly proportional to speed; (3) spinning friction caused by kinematics of rolling elements (if contact angles differ from zero value, the rolling element necessarily spins in one of bearing grooves and creates heat). The friction in bearings is measured by monitoring the passive torque on an experimental test rig shown in Fig. 4. The friction is expressed as an empirical function of speed n (rpm), preload Fa (N), kinematic viscosity n (cSt = mm2 s 1) of the lubricant, and bearing parameters. A sample total friction torque Mtot (N mm) is given for the SKF 7010CD (50 mm bore, 158 contact angle) bearings with grease lubrication used in the experimental spindle (Fig. 5): Mtot \u00bc 8:41 10 4 Fa 4=3 \u00fe 6:75 10 11 \u00f0n n\u00de11=5 \u00fe 8:15 10 7 Fa n The viscosity n has been estimated through monitoring internal bearing temperature and known temperature\u2013viscosity properties of the lubricant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.9-1.png",
        "caption": "FIGURE 2.9. Global roll, pitch, and yaw rotations.",
        "texts": [],
        "surrounding_texts": [
            "44 2. Rotation Kinematics\nLet us now rotate B about two global axes repeatedly, such as turning \u03b1 about Z-axis followed by a rotation \u03b3 about X-axis, such that\n\u03b1 = 2\u03c0\nn1 \u03b3 =\n2\u03c0 n2 {n1, n2} \u2208 N. (2.48)\nWe may guess that repeating the rotations n = n1 \u00d7 n2 times will turn B back to its original configuration.\n[QX,\u03b3 QZ,\u03b1] n1\u00d7n2 = [I] (2.49)\nAs an example consider \u03b1 = 2\u03c0 3 and \u03b3 = 2\u03c0 4 . We need 13 times combined rotation to achieve the original configuration.\nGQB = QX,\u03b3 QZ,\u03b1 = \u23a1\u23a3 \u22120.5 \u22120.866 03 0 0 0 \u22121.0\n0.866 03 \u22120.5 0\n\u23a4\u23a6 (2.50)\nGQ13B = \u23a1\u23a3 0.9997 \u22120.01922 \u22120.01902 0.01902 0.99979 \u22120.0112 0.01922 0.01086 0.9998 \u23a4\u23a6 \u2248 I (2.51)\nWe may turn B back to its original configuration by lower number of combined rotations if n1 and n2 have a common divisor. For example if n1 = n2 = 4, we only need to apply the combined rotation three times. In a general case, determination of the required number n to repeat a general combined rotation GQB to turn back to the original orientation is an unsolved question.\nGQB = mY j=1 QXi,\u03b1j i = 1, 2, 3 (2.52)\n\u03b1j = 2\u03c0\nnj m,nj \u2208 N (2.53)\nGQn B = [I] n =? (2.54)\n2.3 Global Roll-Pitch-Yaw Angles\nThe rotation about the X-axis of the global coordinate frame is called a roll, the rotation about the Y -axis of the global coordinate frame is called a pitch, and the rotation about the Z-axis of the global coordinate frame is called a yaw. The global roll-pitch-yaw rotation matrix is:\nGQB = QZ,\u03b3QY,\u03b2QX,\u03b1 (2.55)\n= \u23a1\u23a3 c\u03b2c\u03b3 \u2212c\u03b1s\u03b3 + c\u03b3s\u03b1s\u03b2 s\u03b1s\u03b3 + c\u03b1c\u03b3s\u03b2 c\u03b2s\u03b3 c\u03b1c\u03b3 + s\u03b1s\u03b2s\u03b3 \u2212c\u03b3s\u03b1+ c\u03b1s\u03b2s\u03b3 \u2212s\u03b2 c\u03b2s\u03b1 c\u03b1c\u03b2 \u23a4\u23a6",
            "2. Rotation Kinematics 45\nFigures 2.9 illustrates 45 deg roll, pitch, and yaw rotations about the axes of a global coordinate frame. Given the roll, pitch, and yaw angles, we can compute the overall rotation matrix using Equation (2.55). Also we are able to compute the equivalent roll, pitch, and yaw angles when a rotation matrix is given. Suppose that rij indicates the element of row i and column j of the roll-pitch-yaw rotation matrix (2.55), then the roll angle is\n\u03b1 = tan\u22121 \u00b5 r32 r33 \u00b6 (2.56)\nand the pitch angle is \u03b2 = \u2212 sin\u22121 (r31) (2.57)\nand the yaw angle is\n\u03b3 = tan\u22121 \u00b5 r21 r11 \u00b6 (2.58)\nprovided that cos\u03b2 6= 0.\nExample 11 Determination of roll-pitch-yaw angles. Let us determine the required roll-pitch-yaw angles to make the x-axis of the body coordinate B parallel to u, while y-axis remains in (X,Y )-plane.\nu = I\u0302 + 2J\u0302 + 3K\u0302 (2.59)\nBecause x-axis must be along u, we have\nG\u0131\u0302 = u |u| = 1\u221a 14 I\u0302 + 2\u221a 14 J\u0302 + 3\u221a 14 K\u0302 (2.60)\nand because y-axis is in (X,Y )-plane, we have Gj\u0302 = \u00b3 I\u0302 \u00b7 j\u0302 \u00b4 I\u0302 + \u00b3 J\u0302 \u00b7 j\u0302 \u00b4 J\u0302 = cos \u03b8I\u0302 + sin \u03b8J\u0302. (2.61)",
            "46 2. Rotation Kinematics\nThe axes G\u0131\u0302 and Gj\u0302 must be orthogonal, therefore,\u23a1\u23a3 1/ \u221a 14 2/ \u221a 14\n3/ \u221a 14 \u23a4\u23a6 \u00b7 \u23a1\u23a3 cos \u03b8 sin \u03b8 0 \u23a4\u23a6 = 0 (2.62)\n\u03b8 = \u221226.56 deg . (2.63)\nWe may find Gk\u0302 by a cross product.\nGk\u0302 = G\u0131\u0302\u00d7 Gj\u0302 =\n\u23a1\u23a3 1/ \u221a 14 2/ \u221a 14\n3/ \u221a 14 \u23a4\u23a6\u00d7 \u23a1\u23a3 0.894 \u22120.447 0 \u23a4\u23a6 = \u23a1\u23a3 0.358 0.717 \u22120.597 \u23a4\u23a6 (2.64)\nHence, the transformation matrix GQB is:\nGQB = \u23a1\u23a3 I\u0302 \u00b7 \u0131\u0302 I\u0302 \u00b7 j\u0302 I\u0302 \u00b7 k\u0302 J\u0302 \u00b7 \u0131\u0302 J\u0302 \u00b7 j\u0302 J\u0302 \u00b7 k\u0302 K\u0302 \u00b7 \u0131\u0302 K\u0302 \u00b7 j\u0302 K\u0302 \u00b7 k\u0302 \u23a4\u23a6 = \u23a1\u23a3 1/ \u221a 14 0.894 0.358 2/ \u221a 14 \u22120.447 0.717 3/ \u221a 14 0 \u22120.597 \u23a4\u23a6 (2.65)\nNow it is possible to determine the required roll-pitch-yaw angles to move the body coordinate frame B from the coincidence orientation with G to the final orientation.\n\u03b1 = tan\u22121 \u00b5 r32 r33 \u00b6 = tan\u22121 \u00b5 0 \u22120.597 \u00b6 = 0 (2.66)\n\u03b2 = \u2212 sin\u22121 (r31) = \u2212 sin\u22121 \u00b3 3/ \u221a 14 \u00b4 \u2248 \u22120.93 rad (2.67)\n\u03b3 = tan\u22121 \u00b5 r21 r11 \u00b6 = tan\u22121 \u00c3 2/ \u221a 14 1/ \u221a 14 ! \u2248 1.1071 rad (2.68)\n2.4 Rotation About Local Cartesian Axes\nConsider a rigid body B with a space fixed point at O. The local body coordinate frame B(Oxyz) is coincident with a global coordinate frame G(OXY Z), where the origin of both frames are on the fixed point O. If the body undergoes a rotation \u03d5 about the z-axis of its local coordinate frame, as can be seen in the top view shown in Figure 2.10, then coordinates of any point of the rigid body in local and global coordinate frames are related by the following equation\nBr = Az,\u03d5 Gr. (2.69)\nThe vectors Gr and Br are the position vectors of the point in global and local frames respectively\nGr = \u00a3 X Y Z \u00a4T (2.70)\nBr = \u00a3 x y z \u00a4T (2.71)"
        ]
    },
    {
        "image_filename": "designv10_1_0000827_j.engfailanal.2014.04.005-Figure23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000827_j.engfailanal.2014.04.005-Figure23-1.png",
        "caption": "Fig. 23. (a) The spur gear rig. (b) The gear with tooth crack.",
        "texts": [
            " The former represent the lateral\u2013torsional coupling frequency and the later represent the lateral natural frequency. The vibration responses when the mean value of mesh stiffness are 3.5 107, 3.5 108 N/m are shown in Fig. 21. It is found that the amplitude of the vibration response decreases when the mesh stiffness increase from 5 107 N/m to 1 108 N/m. Fig. 22 is detail view of Fig. 21. By comparing Fig. 22(a) and (b), it can be found the frequency of impulses decreases as the mesh stiffness increases. 4.2. Experimental results A photograph of the spur gear rig is shown in Fig. 23(a) and the tested gear with tooth crack is shown in Fig. 23(b). The parameters of this test rig are shown in Table 5. The dimensions of the crack fault are 2 mm depth and 20 mm length across the tooth root (100% tooth root width).The vibration acceleration signals of the gear system under fault states can be collected using an accelerometer positioned on the top of the gearbox casing, the sampling frequency is 12.8 kHz, the rotational frequency of the driving gear fp1 is about 7.2 Hz, the rotational frequency of the driving gear fp2 is about 5.26 Hz, the mesh frequency is 394 Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001209_tmag.2010.2040144-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001209_tmag.2010.2040144-Figure2-1.png",
        "caption": "Fig. 2. Geometries of (a) straight and (b) arc coils.",
        "texts": [
            " Since the Helmholtz coil generates a uniform magnetic field intensity along the -axis, the Helmholtz coil can generate uniform magnetic torque to align a micro-robot located near the center of the coil along the -axis. This research develops saddle-shaped coils referred to as gradient and uniform saddle coils as shown in Fig. 1. Since each coil is intended to replace the -directional Maxwell and Helmholtz coils of the conventional MNS in [6], they should generate a uniform magnetic field gradient and intensity along the -direction, respectively. They are composed of the straight and arc coils as shown in Fig. 2(a) and (b), and the magnetic fields can be determined by the summation of each straight and arc coils. The magnetic fields of general straight and arc coils along the -axis in Fig. 2 can be expressed as follows: (7) (8) where , , , , , , , , and are , the length of the straight coil, the distance between the straight coils located along the -axis, the distance between the straight coils located along the -axis, the radius of the arc coil, and the starting and ending angles of the upper and lower arc coils, respectively. The signs of in (7) and in (8) correspond to the cases of the gradient saddle coil and the uniform saddle coil where the current in the upper and the lower part of the saddle coil flows in the opposite and the same direction, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001535_978-981-10-5355-9_1-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001535_978-981-10-5355-9_1-Figure14-1.png",
        "caption": "Fig. 14. A typical CCD based passive visual sensing device [86]",
        "texts": [
            " Instead of using an expensive high energy laser illuminator, an innovative vison-based sensing system using 50 mW laser diodes has been used to determine the weld pool geometry [85]. As shown in Fig. 13, the liquid GTAW weld pool, which has a mirror-like specular surface, reflects the incident laser pattern while the surface of the solid base metal is not specular. Therefore, dots or stripes projected on the weld pool are reflected and projected on the imaging screen, enabling indirect measurement of the weld pool geometry. Passive visual sensing uses the light from black body radiation of liquid metal and welding arc. As shown in Fig. 14, a typical passive visual sensing system composed of a CCD camera and filters has been used to capture the weld pool information during GMAW and GTAW processes [86]. For the pulsed GTAW process, clear images could be easily achieved during the time when the current is at the lowest (base current), as shown in Fig. 15 [87]. For the GMAW process, where it is more difficult to synchronize the camera with the higher frequency droplet spray transfer, an appropriate dimmer-filter system which significantly supresses interference from the welding arc is important"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003801_j.isatra.2016.09.013-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003801_j.isatra.2016.09.013-Figure1-1.png",
        "caption": "Fig. 1. Referential frames configuration.",
        "texts": [
            " Simulation results illustrating the performance of the proposed observer based control are given in Section 5. Finally, some conclusions are drawn. In this section, the dynamical model of fixed wing UAV moving in the space with the roll\u2013pitch\u2013yaw convention by the use of the 3 Euler angles \u00f0\u03d5;\u03b8;\u03c8 \u00deA \u00bd \u03c0;\u03c0 is introduced. The control of a fixed-wing UAV is through aileron, elevator and rudders, and the thrust generated by two engines. The dynamical behavior of a full 6 degree of freedom aircraft model using Newton\u2013Euler convention (see Fig. 1), is given by [3,20] _d \u00bc R1\u00f0\u03c6\u00dev \u00f01\u00de _\u03c6 \u00bc R 1 2 \u00f0\u03c6\u00de\u03c9 \u00f02\u00de F\u00feT\u00bcm\u00f0 _v\u00fe\u03c9 v\u00de mRT 1\u00f0\u03c6\u00deg \u00f03\u00de M\u00bc J _\u03c9\u00fe\u03c9 J\u03c9; \u00f04\u00de where d\u00bc \u00bdx; y; z T AR3 denotes the inertial position of the aircraft, \u03c6\u00bc \u00bd\u03d5;\u03b8;\u03c8 T is the attitude described by the set of the Euler angles, v\u00bc \u00bdu; v;w T AR3 corresponds to the non-inertial (body fixed frame coordinates) expression of the linear velocity and \u03c9\u00bc \u00bdp; q; r T AR3 represents the non-inertial expression of the angular velocity (see [20] for more details). Moreover, rotation matrix R1\u00f0\u03c6\u00deASO\u00f03\u00de maps body axis coordinates to inertial frame coordinates and the operator R2\u00f0\u03c6\u00deAR3 3 transforms the time derivative of the Euler angles set to the non-inertial expression of the angular velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002352_1077546317716315-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002352_1077546317716315-Figure3-1.png",
        "caption": "Figure 3. Schematic of a LOD on one race (enlarged view): (a) contact positions between the roller and LOD, and (b) LOD location.",
        "texts": [
            " To investigate vibration characteristics of a lubricated RB with a LOD on its races, the roller\u2013race contact deformation is lumped to a springdamping element, as shown in Figure 2, which is partially based on the assumptions presented by Sunnersjo\u0308 (1978). Here, the outer race is fixed in a rigid support, and the inner race is fixed rigidly with the shaft. The proposed model could describe the time-varying impact force (TVIF) caused by the LODs with different edge shapes. Based on the experimental results in Branch et al. (2013), the LOD sharp edges will be changed to some cylindrical-likely surfaces due to rollers\u2019 impacts, as shown in Figure 3, where the dash and solid lines represent the sharp and cylindrical edges, respectively. Consequently, the propagated LOD edges are considered as small smooth cylindrical surfaces here. Schematics illustrating the contact patterns between the roller and LOD are given in Figures 3 to 5. The contact pattern between the roller and LOD edge is determined by the following three parameters: (1) the ratio of LOD length to its width, which is calculated by d \u00bc L=B, in which L and B are the LOD length and width, respectively; (2) the ratio of roller size to LOD minimum size, which is calculated by rd \u00bc d=min\u00f0L,B\u00de, in which d is the roller diameter; and (3) the radius rd of cylindrical surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000793_pime_proc_1989_203_100_02-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000793_pime_proc_1989_203_100_02-Figure15-1.png",
        "caption": "Fig. 15 (a) Inclined crack in an elastic half-space subjected to a Hertz line load showing force doublets P-P and Q-Q",
        "texts": [
            " The finite element method has the advantage that standard computer packages are available, which simplifies programming, and the method can be extended, if necessary, into the plastic range. On the other hand, it places a very heavy demand on computing resources, since discrete elements are distributed throughout the whole volume of the body. In contrast, the other two methods only distribute discrete elements of either traction or displacement over the surface of the crack. In the dislocation method a mode I crack is represented by a distribution of \u2018climb dislocations\u2019 and a mode I1 crack by \u2018glide dislocations\u2019, as shown in Fig. 15. The distribution density along the line of the crack is then found to satisfy the boundary conditions on the crack surface, for example an open crack has stress-free surfaces. The method applies only to two-dimensional cracks. The body force method distributes doublets of force ( P and Q and shown in Fig. 15) over the face of the crack and again determines the density of distribution from the boundary condition. This method can be used for three-dimensional (thumbnail) cracks. The penetration of a fluid might influence crack propagation in three ways: (a) by reducing crack face friction; (b) by transmitting the contact pressure to the tip of the crack as suggested by Way (11): (c) by the mouth of the crack being closed by the contact and the trapped fluid generating a mode I stress intensity at the crack tip"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.24-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.24-1.png",
        "caption": "Fig. 10.24 The origin of hysteresis in stable ring positions: (a) Accumulated ring above the rotor causes newly emitted rings to \u2018expand\u2019, whereas (b) accumulated ring below the rotor causes newly emitted rings to contract. The diameter of newly emitted rings is the main factor in determining the direction of subsequent ring convection and provides a mechanism that strongly favors keeping the current position of the accumulating ring (Ref. 10.40)",
        "texts": [
            " So, as the rotor descends into its own wake, the helical pattern of tip vortices becomes more and more compressed, eventually merging and developing into a highly organised vortex ring (Figure 10.23). Tiltrotor Aircraft: Modelling and Flying Qualities 625 Brand and colleagues discuss the development of a phenomenological model of the rotor and its wake to capture these properties in vertical flight; the so-called \u2018vortex ring emitter model\u2019 replaces the helical vortex wake with a sequence of vortex rings, one per rev/per blade. The details of the model are given in Ref. 10.40 and they capture the hysteretic nature of the vortex ring as shown in Figure 10.24. VRS occurs as a bifurcation in the flowfield topology as the vortex ring flips into a position above the rotor. In Ref. 10.40, results are shown for the response to a step-wise reduction in collective pitch to bring the rotor into VRS. The paper discusses the situation when the step finally takes the rotor into the most significant phase of VRS (i.e. the phase with negative thrust damping with respect to descent rate). All prior collective pitch drops settled to a higher, but constant, descent rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure2.20-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure2.20-1.png",
        "caption": "Fig. 2.20 The three rotor disc degrees of freedom",
        "texts": [
            " We shall return to this assumption a little later on this Tour, but for now, we assume that the rotor flapping has time to achieve a new steady-state, one-per-rev motion following each incremental change in control and fuselage angular velocity. We write the rotor flapping motion in the quasi-steady-state form \ud835\udefd = \ud835\udefd0 + \ud835\udefd1c cos\ud835\udf13 + \ud835\udefd1s sin\ud835\udf13 (2.24) \ud835\udefd0 is the rotor coning and \ud835\udefd1c and \ud835\udefd1s the longitudinal and lateral flapping, respectively. The cyclic flapping can be interpreted as a tilt of the rotor disc in the longitudinal (forward) \ud835\udefd1c and lateral (port) \ud835\udefd1s planes. The coning has an obvious physical interpretation (see Figure 2.20). The quasi-steady coning and first harmonic flapping solution to Eq. (2.22) can be obtained by substituting Eqs. (2.23) and (2.24) into Eq. (2.22) and equating constant and first harmonic coefficients. Collecting terms, we can write \ud835\udefd0 = \ud835\udefe 8\ud835\udf062 \ud835\udefd ( \ud835\udf030 \u2212 4 3 \ud835\udf06i ) (2.25) \ud835\udefd1c = 1 1 + S2 \ud835\udefd { S\ud835\udefd\ud835\udf031c \u2212 \ud835\udf031s + ( S\ud835\udefd 16 \ud835\udefe \u2212 1 ) p + ( S\ud835\udefd + 16 \ud835\udefe ) q } (2.26) \ud835\udefd1s = 1 1 + S2 \ud835\udefd { S\ud835\udefd\ud835\udf031s + \ud835\udf031c + ( S\ud835\udefd + 16 \ud835\udefe ) p \u2212 ( S\ud835\udefd 16 \ud835\udefe \u2212 1 ) q } (2.27) where the stiffness number S\ud835\udefd = 8(\ud835\udf062 \ud835\udefd \u2212 1) \ud835\udefe (2.28) and p = p \u03a9 , q = q \u03a9 The stiffness number S\ud835\udefd is a useful nondimensional parameter in that it provides a measure of the ratio of hub stiffness to aerodynamic moments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000426_9781118680469-Figure6.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000426_9781118680469-Figure6.6-1.png",
        "caption": "FIGURE 6.6 Organization of bent-core molecules in tilted polar smectic (SmCP) phases indicating the origin of superstructural chirality. (a) Right-handed (left) and left-handed (right) Cartesian coordinate systems are defined by the relationship among three vectors. The geometries of molecules with opposite chirality are drawn in different colors (blue = (+) chirality, red= (\u2212) chirality). (b) The chirality (+) or (\u2212) of molecules can be determined by the rightor left-hand rule. (c) Symbolic representation of opposite handedness with the polar direction unidentified (see the definition of symbolic drawings in Fig. 6.4). (d) All four possible arrangements for bent-core molecules with macroscopic (+) (blue) and (\u2212) (red) chirality are illustrated with the inserted opposite polarity (green) in the middle of the symbolic drawings. To keep consistent with the early reports [23, 30], here the color code of chirality is opposite to the one previously reported [98, 99].",
        "texts": [
            " For example, in the orthogonal polar smectic phases (SmAP) phases, two-layer structures with six symbolic illustrations are possible depending on the polar direction with respect to the bend direction in adjacent layers (Fig. 6.5). In case (ii) that the director in layer structures is tilted away from the layer normal by a specific angle (0\u25e6 < < 90\u25e6), the supermolecular chirality appears. The opposite handedness, (+) and (\u2212), is determined by the relationship among the three 198 ELECTRIC- AND LIGHT-RESPONSIVE BENT-CORE LIQUID CRYSTALS vectors, b\u0302 = z\u0302 \u00d7 n\u0302, in a right- or left-handed system described by layer-normal z\u0302, the tilt-direction which is indicated by the molecular director n\u0302, and bend direction (b\u0302) (Fig. 6.6a, b, and c). The blue color represents (+) chirality, and the red color stands for (\u2212) chirality, which has nothing to do with the polar direction. This indicates that achiral bent-core molecules with zero polarity along the bend direction can still generate layer chirality as long as they have tilt organization. Changing either the bend direction or tilt direction reverses the handedness of layers, while changing both retains the handedness. However, depending on whether the polar direction, illustrated by green direction symbols, is parallel or antiparallel to the bend direction, four different drawings are used to describe either (+) or (\u2013) chirality (Fig. 6.6d). Based on the above definition, the six SmCP supermolecular isomers [96], consisting of two homogeneously chiral conglomerates, SmCaPA and SmCaPF, and two racemates, SmCsPA and SmCaPF, are illustrated in four cases: (i) unidentified polar direction and identified bend direction (Fig. 6.7a), (ii) polar direction parallel to bend direction (Fig. 6.7b), (iii) polar direction antiparallel to bend direction (Fig. 6.7c), and (iv) identified E-field direction and unknown bend direction (Fig. 6.7d). Herein the C subscripts, s and a, denote syn- and anti-clinicity, while the P subscripts, F and A, denote ferro- and antiferro-electricity (PF = FE, PA = AF), respectively [29]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000455_tac.2010.2043004-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000455_tac.2010.2043004-Figure1-1.png",
        "caption": "Fig. 1. Underactuated system with weak coupling.",
        "texts": [
            " Furthermore, one can choose appropriate design parameters to make as small as possible, that is, the tracking error can be steered to an arbitrarily small neighborhood of the origin in probability. IV. A PRACTICAL EXAMPLE OF MECHANICAL MOVEMENT AND SIMULATION This section is divided into two parts. 1) Part I: Let us consider the deterministic model frequently used in [1], [2], [8], [9]. The mechanical system consists of a mass on a horizontal smooth surface and an inverted pendulum supported by a massless rod as shown in Fig. 1. The mass is interconnected to the wall by a linear spring and to the inverted pendulum by a nonlinear spring which has cubic force-deformation relation. Let be the displacement of mass and be the angle of the pendulum from the vertical such that at and . The springs are unstretched. A control force acts on . The system has two degrees of freedom and is underactuated. Denote the units of these variables: mass and : ; displacement , length : ; angle : ; force : ; acceleration of gravity : ; second: . The equations of motion for the system are (26) where is the spring coefficient whose unit is (since ), and is another spring coefficient whose unit is , and in Fig. 1 is . Assume that in (26) are unknown constant parameters but belong to a known interval with . Inspired by two-mass spring system in [10], the stochastic noise process is introduced as follows. The spring coefficient has a specific nominal value which is considered uncertain, and ! . Let \" . For all , \" is the Gaussian white noise process with !\" and !\" \" . We can choose the value of parameter \" such that obeys the bound ! with a sufficiently high probability. This probability is increasing as \" by Chebyshev\u2019s inequality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure4-1.png",
        "caption": "Fig. 4. Three-dimensional, FEM models.",
        "texts": [
            " Loads between the pairs of the contact points can be calculated through conducting LTCA using the mathematical programming method [13,14] combined with FEM if the total load of the pair of gears along the line of action, gaps between the pairs of contact points and deformation influence coefficients of the pairs of contact points are known [11\u201314]. Then tooth MS, LSR and CS can be calculated when the loads between the pairs of contact points are known [11,12]. Apair of spur gearswith the parameters given in Table 1 is used as research objects in this paper. Tooth dimensions,materials (JIS), heat-treatment and the transmitted torque are also given in Table 1. FEM models of the pair of gears used for LTCA are illustrated in Fig. 4. Fig. 4(a) is a whole gear FEMmodel used for FEM analyses and Fig. 4(b) is used for an enlarged view of contact teeth. Fig. 5 is a section view of the engaged teeth at three different engagement positions. They are named Positions 1, 6 and 12 respectively. In LTCA, one engagement period of the pair of gears is divided into 12 tooth engagement positions fromengage-in to engage-out. Positions 1 to 7 are the double pair tooth engagement positions. It means that there are always two pairs of teeth in contact at these positions. Positions 8 to 12 are the single pair tooth engagement positions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001722_1.4027812-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001722_1.4027812-Figure4-1.png",
        "caption": "Fig. 4 Lumped-parameter planetary gear model from Ref. [10]",
        "texts": [
            " Planetary gear mathematical models are built using the same modeling strategies as those used for parallel-axis gear models. Readers unfamiliar with parallel-axis gear mathematical models are directed to the review articles by \u20acOzg\u20acuven and Houser [7], Blankenship and Singh [9], and Wang et al. [8]. A large amount of research on planetary gear dynamics and vibration has been performed using lumped-parameter models. The 2D planar lumped-parameter planetary gear model from Ref. [10] is shown in Fig. 4. The model includes the central members (carrier, ring gear, and sun gear) and an arbitrary number of planets (denoted by N). Planetary gears can have as little as three planets (the lowest number of planets that will take advantage of the multiple load paths) or more than ten planets, which occurs in highpower applications like aerospace engines and some helicopters. The stationary (inertial) basis is {E1, E2, E3} (not shown). The rotating {e1, e2, e3} basis (called {i, j, k} in Ref. [10]) is attached to, and rotates with, the carrier",
            " The constant forcing vector c is due to the centripetal accelerations of the planets. It is missing in Ref. [10] but included in Ref. [16]. Forcing due to the applied torque is contained in T(t). The vector F(t) is used in some models to represent forcing due to static transmission error or tooth modification excitations. Modeling of these effects is well developed for pairs of gears, but it is not mature or well validated for planetary gears with multiple interacting meshes. It is often assumed that the planetary gear in Fig. 4 has identical (mi\u00bcmp) equally spaced \u00f0wi \u00bc 2p\u00f0i 1\u00de=N\u00de planets, all support stiffnesses are isotropic khx\u00bc khy\u00bc kh, all planet support stiffnesses are equal kpi\u00bc kp, and all averaged sun\u2013planet (ksi\u00bc ksp) and ring\u2013planet (kri\u00bc krp) mesh stiffnesses are equal. With these assumptions, planetary gears are cyclically symmetric structures. The cyclic symmetry leads to well-defined vibration properties (discussed in Sec. 4) and qualitative features of the forced response (discussed in Sec. 6). More advanced mathematical models have been derived by extending planar lumped-parameter models to include additional features",
            " A trend in current planetary gear designs is to optimize the power density by using many planets. Aerospace and wind turbine gearboxes use planetary gears with as many as ten planets. This forces engineers to design planetary gears with load sharing strategies in mind and to manufacture high-quality planetary gear components. Planetary gears have distinct vibration mode structure because of their cyclic symmetry. This was first noticed in lumpedparameter models [10\u201312,14,16,18,21,55], like that shown in Fig. 4, and later validated with finite element/contact mechanics models [56,57] and experiments [58]. Cunliffe et al. [11] determined the vibration modes of a particular 13 DOF planetary gear. They grouped modes into low frequency \u201cbearing modes\u201d and high frequency \u201ctooth modes,\u201d but did not identify the vibration structure. Botman [12] determined the vibration of a 9\u00fe 3N (N is the number of planets) DOF planetary gear model, where each gear has two translational and one rotational DOF. Botman [12] first noticed the distinct vibration structure",
            " The mesh stiffness fluctuation will generally not have a rectangular or trapezoidal form for helical gear pairs or spur gear pairs with contact ratios greater than two. The mesh stiffness waveform can be calculated from finite element methods as done in Refs. [85] and [92]. The tooth mesh stiffness waveforms discussed above are for perfect planetary gears and teeth. Manufacturing and assembly errors can modulate the mesh stiffness waveform [45,87]. The tooth mesh stiffness waveform amplitude reduces for damaged gear teeth with root cracks [93\u201396]. The lumped-parameter planetary gear model in Fig. 4 with governing equations in Eq. (4a) is an example of a mathematical model described in this section with fluctuating mesh stiffnesses. Planetary gear models with time-varying stiffness more accurately reflect the physical behavior during planetary gear operation compared to those with constant stiffness and static transmission error excitation. They give accurate off-resonance response predictions where vibration amplitudes are small enough that the gear teeth always remain in contact. They also are used to identify regions of large amplitude response that occur near resonances",
            " Botman [47] observed nonlinear behavior for planetary gears in experiments measuring aerospace engine housing acceleration. These experiments showed obvious jump-up and jump-down frequencies during accelerating and decelerating speed sweeps. Tooth contact loss is the most studied nonlinearity in planetary gear dynamics. Contact loss is modeled by requiring the tooth mesh stiffnesses (or the corresponding mesh forces) vanish when the gear teeth separate, i.e., when the mesh deflection becomes positive. This prevents the meshes from exerting tensile forces. For the planar lumped-parameter planetary gear model in Fig. 4 with governing equations in Eq. (4a), the mesh stiffness matrix in this nonlinear case depends on the deformation of the system such that Km\u00f0t\u00de ! Km\u00f0q; t\u00de. Nonlinear models for planetary gear vibration that consider contact loss can be solved numerically using numerical integration or analytically using a variety of perturbation methods. August and Kasuba [43] analyzed a nonlinear, time-varying planetary gear model. They found that decreasing sun gear translational stiffness to zero (called \u201cfloating\u201d the sun) decreases the dynamic response"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002798_tec.2020.2964942-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002798_tec.2020.2964942-Figure3-1.png",
        "caption": "Fig. 3. Motor housing with integrated cooling channels, a) CAD and complete motor hardware \u2013 Technical University of Munich, TUfast Racing Team Formula Student [14], b) CAD \u2013 University of Nottingham [15]",
        "texts": [
            " heat treatment, post-AM [10]. Fig. 2b) shows an example comparing mechanical properties of parts fabricated using titanium alloy (Ti6Al4V) [60]. When analysing the experimental data, it is evident that the choice of AM and postprocessing techniques has a prominent impact on the overall mechanical properties of the fabricated parts [60]-[62]. Here, the use of AM have shown to be advantageous when compared with more conventional manufacturing techniques, subject to specific design requirements. Fig. 3 presents examples of machine housing for electric vehicle (EV) applications. Here, the computer aided designs (CADs) and prototype hardware are shown. In both cases an unique integrated channel design for liquid cooling has been incorporated within the housing reducing the total number of parts and improving the overall thermal management performance [14], [15]. In Fig 3a) the authors report 31% higher total mass flow and 20% improvement in total heat conduction and efficiency of the cooling system as compared with a more conventional design [14]. The authors do not provide details regarding the metal alloy used to fabricate the housing, but considering thermal conductivity of available alloys, it is most likely to be an aluminium alloy, e.g. AlSi10Mg. Reducing the mass of structural parts of the motor assembly is another area where AM has been successfully used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001025_j.euromechsol.2010.05.001-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001025_j.euromechsol.2010.05.001-Figure5-1.png",
        "caption": "Fig. 5. (a) Planet bearingmodelwith clearance; (b)Diagramof bearing forcewith clearance.",
        "texts": [
            ";N (10) When tooth wedging occurs, the drive- and back-side tooth forces at the jth SeP and ReP meshes are f dqj \u00bc hwqjk d qj\u00f0t\u00deddqj f bqj \u00bc hwqjk b qjd b;mod qj q \u00bc r; s; j \u00bc 1;.;N (11) where hwaj tracks whether tooth wedging occurs according to hwqj \u00bc ( 1 if dRqj > Dq 0 if dRqj < Dq ; q \u00bc r; s; j \u00bc 1;.;N (12) The linear bearings or fixed supports without clearance are modeled as one torsional and two translational springs. The nonlinear bearings are modeled as circumferentially distributed radial springs with uniform clearances as shown in Fig. 5. Forces develop only when the relative displacement between the connected bodies exceeds a specified clearance. For the jth planet bearing with bearing clearance Dcp as an example, the relativedisplacementbetween the carrier andplanet j is dcj \u00bc h xccosjj \u00fe ycsinjj xj 2 \u00fe xcsinjj \u00fe yccosjj \u00fe uc hj 2i1=2 (13) The direction of the developed force is determined by the contact angle wcj between e1 (Fig. 3) and the direction of relative motion between the carrier and planet j wcj \u00bc tan 1 xcsinjj \u00fe yccosjj \u00fe uc hj xccosjj \u00fe ycsinjj xj "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure1.14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure1.14-1.png",
        "caption": "Fig. 1.14",
        "texts": [
            "5 Statically Determinate Systems of Bars 31 displacement: u = |\u0394l1| = F l EA 1 tan\u03b1 , v = \u0394l2 sin\u03b1 + u tan\u03b1 = F l EA 1 + cos3 \u03b1 sin2 \u03b1 cos\u03b1 . (1.21) To determine the displacement of a pin of a truss with the aid of a displacement diagram is usually quite cumbersome and can be recommended only if the truss has very few members. In the case of trusses with many members it is advantageous to apply an energy method (see Chapter 6). The method described above can also be applied to structures which consist of bars and rigid bodies. E1.5Example 1.5 A rigid beam (weight W ) is mounted on three elastic bars (axial rigidity EA) as shown in Fig. 1.14a. Determine the angle of slope of the beam that is caused by its weight after the structure has been assembled. Solution First we calculate the forces in the bars with the aid of the equilibrium conditions (Fig. 1.14b): S1 = S2 = \u2212 W 4 cos\u03b1 , S3 = \u2212 W 2 . With l1 = l2 = l/ cos\u03b1 and l3 = l we obtain the elongations: \u0394l1 = \u0394l2 = S1 l1 EA = \u2212 W l 4EA cos2 \u03b1 , \u0394l3 = S3 l3 EA = \u2212 W l 2EA . Point B of the beam is displaced downward by vB = |\u0394l3|. To determine the vertical displacement vA of point A we sketch a displacement diagram (Fig. 1.14c). First we plot the changes \u0394l1 and \u0394l2 of the lengths in the direction of the respective bar. The lines perpendicular to these directions intersect at the displaced position A\u2032 of point A. Thus, its vertical displacement is given by vA = |\u0394l1|/ cos\u03b1. Since the displacements vA and vB do not coincide, the beam does not stay horizontal after the structure has been assembled. The angle of slope \u03b2 is obtained with the approximation tan\u03b2 \u2248 \u03b2 (small deformations) and l = a cot\u03b1 as (see Fig. 1.14d) \u03b2 = vB \u2212 vA a = 2 cos3 \u03b1\u2212 1 4 cos3 \u03b1 W cot\u03b1 EA . If cos3 \u03b1 > 1 2 (or cos3 \u03b1 < 1 2 ), then the beam is inclined to the right (left). In the special case cos3 \u03b1 = 1 2 , i.e. \u03b1 = 37.5\u25e6, it stays horizontal. E1.6 Example 1.6 The truss in Fig. 1.15a is subjected to a force F . Given: E = 2 \u00b7 102 GPa, F = 20 kN. Determine the cross-sectional area of the three members so that the stresses do not exceed the allowable stress \u03c3allow = 150 MPa and the displacement of support B is smaller than 0.5 \u2030 of the length of bar 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001031_pime_proc_1988_202_127_02-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001031_pime_proc_1988_202_127_02-Figure1-1.png",
        "caption": "Fig. 1 Displacement and force excitation",
        "texts": [],
        "surrounding_texts": [
            "The features of a thrust loaded ball bearing which determine its vibration forces are modelled as shown in Fig. 2. The bearing has N equispaced balls, all of which are in firm contact with inner and outer raceways and roll, without sliding, at a true epicyclic speed, given by (4) o = - 1-- , 2 \"'( \"fe,Sa) The reader is referred to the Notation for definitions of the variables used. Each ball is represented by a spring of stiffness k, (0 G j < N - 1) whose line of action passes through the centre of the inner and outer race contact areas. The analysis is restricted to applications in which bearing speeds are moderate, for which ball centrifugal force is negligible and hence inner and outer contacts are diametrically opposite. In this situation variations in spring force are only a function of ball-race contact compliance and amplitude of waviness. Waviness on the ball inner and outer raceways is assumed to be simple harmonic in the direction of rolling and independent of position, across the surface, normal to the direction of rolling. For inner and outer raceways these assumptions are reasonable for the longer wavelength surface features greater than about three times the ball-race contact width. For the balls, waviness of any wavelength occurs both in the direction of rolling and normal to the direction of rolling, and so the above assumptions are an approximation. The variation in elastic approach at the ball-raceway contacts for the above waviness model is independent of any oil film thickness and simply equal to the amplitude of waviness passing through the contacts."
        ]
    },
    {
        "image_filename": "designv10_1_0001794_j.ymssp.2012.11.004-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001794_j.ymssp.2012.11.004-Figure3-1.png",
        "caption": "Fig. 3. Geometry of crack: (a) crack location and (b) crack angle.",
        "texts": [
            " These findings show that the proposed demodulation analysis is effective to identify the modulating frequencies, even though they are very close to each other. Moreover, the simpler structure of envelope spectrum and instantaneous frequency spectrum is expected to be more helpful than the Fourier spectrum in applications. Fig. 2 shows the planetary gearbox test rig used for data collection. We manually introduced notch (to simulate crack) and tooth missing damage to one tooth of the planet and sun gear inside the 2nd stage planetary gearbox using EDM technique. Tables 2 and 3 list the gear parameters of the five gearboxes. Fig. 3 and Table 4 show and list the gear crack geometry respectively. During experiments, the rotating frequency of the input shaft connecting the sun gear of the 2nd stage planetary gearbox was set to 0.7778 Hz, and a load of 24,000 lb in. was applied to the output shaft connecting the planet carrier of the 2nd stage planetary gearbox. A torque sensor was mounted to the output shaft of the 2nd stage planetary gearbox (as shown in Fig. 4) to measure the torsional vibration. It has a sensitivity of 2.0 mV/V, a measurement range of 100,000 lb in"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.23-1.png",
        "caption": "Fig. 10.23 The merging of tip vortices below the rotor is the first stage of the vortex ring state (Ref. 10.40)",
        "texts": [
            " Brand points out that the tip vortices dominate the flow structure below a rotor and although the stream-tube model of flow (see Chapter 3), extending from above the rotor and accelerated below the rotor, can predict the induced power and rotor thrust reasonably well, it is not a correct physical model. \u2018The fundamental dynamic of VRS involves the tendency of these closely spaced vortices to completely reshape the cylindrical wake and form a stable system of co-rotating/merging wake elements\u2019. So, as the rotor descends into its own wake, the helical pattern of tip vortices becomes more and more compressed, eventually merging and developing into a highly organised vortex ring (Figure 10.23). Tiltrotor Aircraft: Modelling and Flying Qualities 625 Brand and colleagues discuss the development of a phenomenological model of the rotor and its wake to capture these properties in vertical flight; the so-called \u2018vortex ring emitter model\u2019 replaces the helical vortex wake with a sequence of vortex rings, one per rev/per blade. The details of the model are given in Ref. 10.40 and they capture the hysteretic nature of the vortex ring as shown in Figure 10.24. VRS occurs as a bifurcation in the flowfield topology as the vortex ring flips into a position above the rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002798_tec.2020.2964942-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002798_tec.2020.2964942-Figure6-1.png",
        "caption": "Fig. 6. Elements of thermal management systems for electrical machines, a) integrated liquid cooled HE (CAD of stator/winding together with HE and HE hardware) - University of Wisconsin-Madison [18], b) integrated aircooled HE/stator mechanical support (stator core pack and HE hardware) \u2013 Newcastle University [19], c) set of HG for enhanced heat transfer in electrical machines (hardware variants prior to final processing) \u2013 Newcastle University [20]",
        "texts": [
            " Some techniques on how to assess the diffusion bonding are discussed in [63]. Also, the authors report approximately 80% and 10% increase in output power for the wavy profile rotor with cladding, as compared to the solid and a more conventional squirrel cage rotor designs respectively. It has been shown earlier that the existing techniques for removing heat from the machine body greatly benefit from the use AM. As AM allows to rethink the manner in which electrical machines are thermally managed, less conventional solutions have been explored in some research. Fig. 6 presents a number of concept designs for enhanced heat removal specifically targeting motor stator/winding assembly. Fig. 6a) show a liquid cooled heat exchanger (HE) for direct heat evacuation from the winding body [18]. Here, HE is sharing the stator slot together with winding assembly. To assess the HE concept, the authors evaluated a number of alternative plastics including: ABS, Al-PC, CF-Nylon and PLA, with Al-PC being the preferred choice here [18]. A 44% reduction in winding operating temperature as compared with no HE alternative stator/winding assembly has been reported. Further development of the cooling concept makes use of ceramic material (Ceramco 3D, printable Alumina) showing an improvement to the plastic equivalents [65]. A concept of air-cooled HE for extracting heat from the complete stator/winding assembly is shown in Fig. 6b), where fully assembled HE occupies the inner bore of the stator core pack [19]. Such an arrangement provides a thermal path for an effective heat extraction. It is important to note that an outerrotor machine topology is considered here. The HE offers extremely high working surface area due to the application of design features possible only when using AM. Further to this, application of aluminium alloy (AlSi10Mg) enables achieving the required performance of HE. Here, an equivalent thermal conductance of stator to HE is equal 470W/m2 K for 1.5m/s air flow at 20\u00b0C, [19]. Fig. 6c) presents a family of heat guides (HGs) developed to enhance heat removal directly from the winding body [20]. AM has been used here to enable design solutions with high thermal conductivity and minimal additional power loss. As the HGs were designed to be placed in the stator slots, and consequently to be in direct contact with the winding body, providing a good balance between thermal and electrical properties of such an assembly was essential. It has been shown that the supplementary heat path between winding and the actively cooled machine housing (path introduced by HGs) results in 20% to 40% improvement in dissipation of the generated power loss from the stator/winding assembly [20]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure3.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure3.12-1.png",
        "caption": "Figure 3.12. The mechanical method of muscle action analysis applied to biceps and elbow flexion in the sagittal plane. It is assumed that in the anatomical position the biceps pulls upward toward its anatomical origin from its anatomical insertion (radial tuberosity). The motion can be visualized using a bicycle wheel with the axle aligned on the joint axis. If the the muscle were pulling on the wheel from its illustrated direction and orientations relative to that joint axis (visualize where the line of action crosses the medial-lateral and superior-inferior axes of the sagittal plane), the wheel would rotate to the left, corresponding to elbow flexion. Unfortunately, the actions of other muscles, external forces, or other body positions are not accounted for in these analyses. More thorough and mathematical biomechanical analyses of the whole body are required to determine the true actions of muscles.",
        "texts": [
            " Kinesiology professionals can only determine the true actions of muscle by examining several kinds of biomechanical studies that build on anatomical information. Functional anatomy, while not an oxymoron, is certainly a phrase that stretches the truth. Functional anatomy classifies muscles actions based on the mechanical method of muscle action analysis. This method essentially examines one muscle's line of action relative to one joint axis of rotation, and infers a joint action based on orientation and pulls of the muscle in the anatomical position (Figure 3.12). In the sagittal plane, the biceps brachii is classified as an elbow flexor because it is assumed that (1) the origins are at the shoulder joint, (2) the insertion is on the radial tuberosity, and (3) the anterior orientation and superior pull, as well as the superior orientation and posterior pull, would create elbow flexion. When a muscle is activated, however, it pulls both attachments approximately equally so that which end moves (if one does at all) depends on many biomechanical factors. Recall that there are three kinds of muscle actions, so that what the biceps brachii muscle does at the elbow in a particular situation depends on many biomechanical factors this book will explore"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001107_j.jsv.2007.12.013-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001107_j.jsv.2007.12.013-Figure1-1.png",
        "caption": "Fig. 1. Dynamic model of a spur gear pair.",
        "texts": [
            " Moreover, a reliability analysis is carried out in order to verify the robustness of optima obtained with GAs under perturbations due to manufacturing errors. ARTICLE IN PRESS G. Bonori et al. / Journal of Sound and Vibration 313 (2008) 603\u2013616 605 The key point of the present study is the vibration reduction, this is pursued by optimizing the system on static basis, i.e. minimizing the excitation source due to the static transmission error fluctuation. Therefore, a dynamic model is needed to check the effectiveness of the optimization on the gear vibration; the model represented in Fig. 1 is considered to this end. Such model considers spur gears as rigid disks, coupled along the line of action through a time varying mesh stiffness k\u00f0t\u00de and a constant mesh damping c; yg1\u00f0t\u00de is the angular position of the driver wheel (pinion), yg2\u00f0t\u00de is the angular position of the driven wheel (gear); Tg1\u00f0t\u00de is the driving torque, Tg2\u00f0t\u00de is the breaking torque; Ig1 and Ig2 are the rotary inertias; dg1 and dg2 are the base diameters. According to the literature [21] the relative dynamics of gears along the line of action can be represented by the following equation of motion: me \u20acx\u00f0t\u00de \u00fe c\u00f0 _x\u00f0t\u00de\u00de \u00fe k\u00f0t\u00def 1\u00f0x\u00f0t\u00de\u00de \u00fe kbs\u00f0t\u00def 2\u00f0x\u00f0t\u00de\u00de \u00bc Tg\u00f0t\u00de, (1) where \u00f0 \u00de \u00bc d\u00f0 \u00de=dt, me is the equivalent mass: me \u00bc d2 g1 4Ig1 \u00fe d2 g2 4Ig2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure5.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure5.18-1.png",
        "caption": "Fig. 5.18 Radii of curvature of a vehicle exiting a turn properly",
        "texts": [
            "22) \u03c11 = r + \u03b2\u03071 u/ cos\u03b21 = [ r u + (v\u0307 + a1r\u0307)u \u2212 (v + a1r)u\u0307 u3 ] cos\u03b21 (5.23) 5.2 The Kinematics of a Turning Vehicle 127 \u03c12 = r + \u03b2\u03072 u/ cos\u03b22 = [ r u + (v\u0307 \u2212 a2r\u0307)u \u2212 (v \u2212 a2r)u\u0307 u3 ] cos\u03b22 (5.24) 128 5 The Kinematics of Cornering 130 5 The Kinematics of Cornering cos\u03b2 = u\u221a u2 + v2 (5.25) cos\u03b21 = u\u221a (v + a1r)2 + u2 (5.26) cos\u03b22 = u\u221a (v \u2212 a2r)2 + u2 (5.27) \u03b2\u03071 u \u03c11 \u2212 r u (5.28) \u03b2\u03072 u \u03c12 \u2212 r u (5.29) where \u03c1i are the curvatures, that is the inverse of the radii of curvature. The kinematics of a vehicle exiting properly a turn is shown in Fig. 5.18. We see that many things go the other way around with respect to entering. In both cases, the knowledge of the inflection circle immediately makes clear the relationship between the position of the velocity center C and the centers of curvature E1 and E2. But things may go wrong. Bad kinematic behaviors are shown in Fig. 5.19. We see that the time derivatives of \u03b21 and \u03b22 are not as they should be. Indeed, point C is travelling also longitudinally. Again, the positions and orientations of the inflection circle immediately conveys the information about the unwanted kinematics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000335_j.aca.2011.07.024-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000335_j.aca.2011.07.024-Figure7-1.png",
        "caption": "Fig. 7. The expanded views of Abbott\u2019s (A) FreeStyle BGM test strip [97], (B) su",
        "texts": [
            " In order to confirm the sufficient filling of blood amples in the strips, fill detection electrodes are also employed n most commercial BGM strips. The automatic fill detection elimnates the visual confirmation error and reduces the testing time s the electrochemical assay starts immediately after the strip is ompletely filled with the blood sample. A small capillary chamber s located on the electrode substrate to work as reaction container. mixture of enzymes, mediators and other chemical components s coated within the capillary chamber in dry form. Fig. 7 shows the esigns of the Abbott\u2019s FreeStyle BGM test strip [97], the subcutaeous wired GOx electrode [91] and the FreeStyle Navigator sensor hip [82]. A working electrode is the channel to transmit glucose-derived lectrons from blood sample to the meter. It is generally made from creen-printed carbon ink or vapor-deposited gold or palladium. In GM strips, the area of the working electrode is kept constant durng mass-production to ensure high reproducibility. The distance etween the working and the auxiliary/reference electrode is minmized to decrease the required blood volume and inter-electrode lectrolytic resistance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000807_j.jelechem.2006.01.011-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000807_j.jelechem.2006.01.011-Figure2-1.png",
        "caption": "Fig. 2. Cyclic voltammograms of a OBMGCE in 0.1 M phosphate buffer (pH 8) at scan rates: (a) 5, (b) 10, (c) 20, (d) 30, (e) 40, (f) 50, (g) 60 and (h) 70 mV s 1.",
        "texts": [
            " The redox reactions in aqueous solutions for quinone derivatives occur with the participation of two electrons [1,2,19]. Based on the relation between formal potential of the redox couple, E0 0, and pH [25], depending on the number of protons taking part in the redox process with transfer of two electrons, the E0 0 will shift by 59 mV/pH (2 H+) and 29 mV/pH (1H+) [25]. So there is a transfer of two protons in the redox reaction in the pH range of 3.0\u201311.3 and one proton in the pH range of 11.3\u201313.0. Fig. 2 shows the cyclic voltammograms of the OBMGCE in 0.1 M phosphate buffer solution (pH 8) at various scan rates. The plot of anodic and cathodic peak current versus scan rate (not shown) yielded straight lines in the range 5\u2013500 mV s 1. This result confirms that the voltammetric behavior of the modified electrode is due to a reversible surface redox reaction [26]. The surface coverage (C) of the modified electrode was determined from the following equation, C = Q/nFA, where Q is the charge obtained by integrating the anodic or cathodic peak under the background correction and other symbols have their usual meanings, assuming an n value of 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure1-1.png",
        "caption": "Fig. 1. Image of contact teeth with misalignment error on the plane of action.",
        "texts": [
            " Definition of the misalignment error In the last research [12], since the effect of assembly errors of a pair of spur gears on tooth MS couldn't be investigated, this paper investigates this effect here. In the last research, it was found that themisalignment error of the gear shafts on the vertical plane of the plane of action of a pair of spur gears almost has no effect on tooth surface CS, so only themisalignment error of the gear shafts on the plane of action is used here to investigate the effect of it on toothMS. The misalignment error of the gear shafts on the plane of action can be expressed by an inclination angle of the contact teeth on the plane of action as shown in Fig. 1. 2.2. Definitions of the tooth modifications Fig. 2(a) is an image of the tooth profilemodificationmethod. An arc curvewith the radius R is used tomodify tooth profiles of spur gears (tooth tip and root are modified with the same quantity). Since this method can be realized easily, it is used very popularly for spur gears. In Fig. 2(a), themaximumquantity of the tooth profilemodification is illustrated. The effect of toothprofilemodification on tooth engagements is investigated through investigating the effect of themaximum quantity of the profile modification on toothMS, LSR and CS of the pair of gears when the pinion is modified"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001279_rpj-12-2015-0192-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001279_rpj-12-2015-0192-Figure8-1.png",
        "caption": "Figure 8 Schematic view of the substrate and samples with their correspodning build direction and height for (a) vertical samples and, (b) horizontal samples",
        "texts": [
            " 0 200 400 600 800 1000 1200 1400 S1 S2 S3 S4 S5 S6 S7 S tr en g th ( M P a ) Tensile yield Compressive yield D ow nl oa de d by F ud an U ni ve rs ity A t 1 7: 32 2 7 Fe br ua ry 2 01 7 (P T ) Page 13 of 34 3.3. Microhardness Microhardness measurements were conducted using a Vickers microhardness tester machine along the build direction of 17-4 PH SS samples for all the sets listed in Table 2. Because of different build orientations, the build heights are not the same for all samples, i.e.: the build height was 80 mm for the vertical samples (sets S1, S2, S5, S6, and S7) and 8 mm for the horizontal samples (sets S3 and S4) as described in Figure 8. Variation of Vickers hardness values versus distance from the substrate are plotted for the vertical samples in Figure 9 (a). Each point in the graph represents the Vickers pyramid number (HV) of an average value for at least three different measurements along the specimen length and at equidistant locations. The dashed blue line in Figure 9 (a) shows the highest Vickers hardness value for aged and solution-treated commercial 17-4 PH using Condition A (Hsiao et al., 2002). No significant trend in microhardness along the build direction for our tested samples can be identified. Also, we notice that S7 samples have microhardness values comparable with commercial parts. The average values for all samples are given in the bar chart in Figure 8 (b) with corresponding error bars. Average microhardness values for heat treated samples are significantly higher than those for as-built samples (S2 versus S1, S3 versus S4, and S6 versus S7) which indicates that the samples demonstrated temper hardening after solution annealing and aging typical of martensitic materials (Murr et al., 2012). This can be explained by the fact that the investigated samples were fabricated under argon atmosphere; thus, the dominant iron phase is martensite (Murr et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002117_j.mechmachtheory.2019.103597-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002117_j.mechmachtheory.2019.103597-Figure1-1.png",
        "caption": "Fig. 1. The contact angle of the ACBB with the combined loads.",
        "texts": [
            " The influences of the combined loads on the contact angle, load distribution and axial stiffness of the preloaded ACBB are studied. The results from the developed analytical method are compared with those from the traditional analytical method (SAM) and the quasi-static method (QAM). 2. Analytical calculation method of the load distribution 2.1. Contact angle The unloaded ACBBs have the radial and axial clearances, the inner ring will generate an axial displacement \u03b4a p relative to the outer ring when an axial force F p is applied as shown in Fig. 1 . According to the discussions in Refs. [19] and [32] , the relationship between the preload F p and the contact angle \u03b1p is represented as F p Z D 2 K = sin \u03b1p ( cos \u03b10 cos \u03b1p \u2212 1 )1 . 5 (1) where \u03b10 is the initial contact angle; D is the ball diameter; Z is the number of balls; K is the axial displacement parameter presented by Ref. [32] , whose value is depended on the total curvature B ( B = f i + f o \u22121), in which f i and f o are the groove curvature of the inner and outer rings, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002140_s0022112074001662-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002140_s0022112074001662-Figure1-1.png",
        "caption": "FIGURE 1. Schematic diagram illustrating the application of the oscillatory-boundary-layer technique.",
        "texts": [
            " Such a solution is rather restrictive in terms of the permitted variation of the wave form and wave amplitude over the body and its extension to non-spheroidal bodies appears to involve considerable algebraic complexity. The present paper takes a different approach to the general analysis of finite bodies by restricting attention to those organisms whose metachronal wavelength 2n/E is small compared with their overall dimensions. It follows that since the unsteady fluid motions generated by the cilia are generally attenuated like e--kg with distance y from the surface (see below) the thickness of this layer is small compared with the body size. The overall flow around the organism (see figure 1) will thus be comprised of a thin oscillatory boundary layer outside which the flow is predominantly steady. Since the Reynolds numbers based on propulsive velocity and overall dimensions are extremely small for most organisms, the latter is termed the complementary Stokes flow. The basic idea will then be to match fluid-mechanical solutions obtained for the motions within the boundary layer to this complementary Stokes flow in order t o predict the propulsive motions of the organism. In general such a procedure is independent of the particular means used to model the motions within the boundary layer",
            ") The complementary Stokes flow and the force Fc are then entirely defined except for the velocity a t infinity or propulsive velocity U . This is finally obtained by integration of TP using (64)-(66) to obtain FP and consequent application of the zero-total-force condition. Some simple examples of the implementation of the boundary-layer technique will be presented in the next section. In order to present some simple examples of the boundary-layer analysis of self-propulsion, a body whose mean surface shape is spherical is chosen because of the ease of construction of a complementary Stokes flow. This is indicated in figure 1, where our convention implies that the surface waves travel over the body in the direction of increasing 8. Further restricting the example to axisymmetric surface motions, let us examine several examples in which the complementary Stokes flow consists solely of the first-order spherical harmonic - q, = [ U - C(a/r)3 + D(a/r)] sin 8, function, so that qr = [ - u - 2c(a/r)3 - 2 ~ ( a / q j cos s,f where C and D are constants to be determined and U is the velocity in the 8 = 7~ direction as r -+ co (or the propulsive velocity in the 8 = 0 direction under a Galilean transformation)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002921_s41563-018-0062-0-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002921_s41563-018-0062-0-Figure1-1.png",
        "caption": "Fig. 1 | Global ZeeMs in prestrained elastic objects. a, Closing an elastic rod into a circular loop induces a compressive strain in the inner portion (solid line) and tensile strain on the outside (dashed line). b, The elastic",
        "texts": [
            " With no energy cost to rotate the molecules or spins collectively, the corresponding long wavelength distortion becomes a new hydrodynamic variable in the system. Generalizing the concept to elastic solids, here we propose a model, termed the 'embedded wheel', that allows the generation of soft motors into responsive materials. The idea is to induce and actively drive continuumelastic modes in objects that bear internally trapped mechanical prestrains. Consider the simplest of such objects, an elastic rod closed into a circular loop (Fig. 1a). By the process of closure, the initially cylindrical rod, now bent into a torus, displays topological prestrain and a broken symmetry\u2014the inner side experiences longitudinal compression, whereas the outer part is subject to tension (Fig. 1a). As in the hydrodynamic-mode scenario, the breaking of rotational symmetry around the rod's axis gives rise to a zero-energy mode; this corresponds to turning every crosssection around the long axis of the toroid (Fig. 1b). This collective deformation represents an embedded wheel that in an ideal elastic material, without defects and viscous losses, becomes a true zeroenergy mode. Such global zero-elastic-energy modes (ZEEMs) are not restricted to the toroidal geometry22,23 and are surprisingly common (Fig. 1c): from wrinkles on surfaces24, ripples on edge-stressed sheets7,24, isometric excess-angle cones25 and M\u00f6bius strips26 to plectonemic supercoils 'slithering' along closed DNA molecules27. Although ZEEMs resemble rigid rotations in that they conserve both the energy and the outer form of the object, they form a distinct class of motion that involves continuum material deformations. A particularly useful feature is their potential to be actively driven by dissipative self-organization. As a proof of concept, we demonstrate this effect in a simple ZEEM model system\u2014a toroidal polymer fibre between two heat baths that undergoes (non-rigid) rotation, performs mechanical work, stores energy and self-propels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002273_j.addma.2019.100958-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002273_j.addma.2019.100958-Figure5-1.png",
        "caption": "Fig. 5. Mechanisms of the protrusion at the rear of the molten pool due to the vapour recoil pressure and Marangoni convection.",
        "texts": [
            "1 m/s, with the height between the end of the droplet column and the top surface of the powder bed hdc remaining almost unchanged at approximately 200 \u03bcm, which demonstrates that the metal liquid column has reached a temporary equilibrium state. During the falling stage, as the hemispherical protrusion radius Rdc of the droplet column increases from 41.8 \u03bcm to 74.6 \u03bcm, deteriorations in the quasi-steady-state equilibrium for the droplet column can develop with an increase in the gravitational potential energy. Then, the metal liquid column is absorbed back into the molten pool at approximately t = 400 \u03bcs. As demonstrated in Fig. 5, the molten pool forms a protrusion under the combined effects of the Marangoni effect and the vapour recoil pressure during LPBF. For Inconel 718, the temperature coefficient of the surface tension d\u03c3/dT is negative [54], and the surface tension decreases as the molten pool temperature increases in the presence of laser radiation, which results in centrifugal Marangoni convection in the molten pool [28]. Furthermore, the lower surface tension reduces the kinetic energy required for spatter to escape"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002032_j.jmatprotec.2016.04.006-Figure27-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002032_j.jmatprotec.2016.04.006-Figure27-1.png",
        "caption": "Fig. 27. Distortion after deposition (5X).",
        "texts": [],
        "surrounding_texts": [
            "Afazov, S.M., Ratchev, S.M., Segal, J., 2012. Prediction and experimental validation of micro\u2010milling cutting forces of AISI H13 steel at hardness between 35 and 60 HRC. The International Journal of Advanced Manufacturing Technology 62, 887\u2010899. Banovic, S., DuPont, I., Marder, A., 2001. Dilution control in gas\u2010tungsten\u2010arc welds involving superaustenitic stainless steels and nickel\u2010based alloys. Metall and Materi Trans B 32, 1171\u20101176. Cawley, J.D., 1999. Solid freeform fabrication of ceramics. Current Opinion in Solid State and Materials Science 4, 483\u2010489. Chan, C., Mazumder, J., Chen, M.M., 1984. A two\u2010dimensional transient model for convection in laser melted pool. Metallurgical Transactions A 15, 2175\u20102184. Chande, T., Mazumder, J., 1984. Estimating effects of processing conditions and variable properties upon pool shape, cooling rates, and absorption coefficient in laser welding. Journal of applied physics 56, 1981\u20101986. Courtois, M., Carin, M., Le Masson, P., Gaied, S., Balabane, M., 2013. A new approach to compute multi\u2010reflections of laser beam in a keyhole for heat transfer and fluid flow modelling in laser welding. Journal of Physics D: Applied Physics 46, 505305. Fernandes de Lima, M.S., Sankare, S., 2014. Microstructure and mechanical behavior of laser additive manufactured AISI 316 stainless steel stringers. Materials & Design 55, 526\u2010532. Hoadley, A., Rappaz, M., 1992. A thermal model of laser cladding by powder injection. Metallurgical transactions B 23, 631\u2010642. Kou, S., Wang, Y., 1986. Three\u2010dimensional convection in laser melted pools. Metallurgical transactions A 17, 2265\u20102270. Liu, W., DuPont, J., 2003. Fabrication of functionally graded TiC/Ti composites by laser engineered net shaping. Scripta Materialia 48, 1337\u20101342. Ma, M., Wang, Z., Wang, D., Zeng, X., 2013. Control of shape and performance for direct laser fabrication of precision large\u2010scale metal parts with 316L Stainless Steel. Optics & Laser Technology 45, 209\u2010216. Mackwood, A., Crafer, R., 2005. Thermal modelling of laser welding and related processes: a literature review. Optics & Laser Technology 37, 99\u2010115. Manvatkar, V., Gokhale, A., Reddy, G.J., Venkataramana, A., De, A., 2011. Estimation of Melt Pool Dimensions, Thermal Cycle, and Hardness Distribution in the Laser\u2010Engineered Net Shaping Process of Austenitic Stainless Steel. Metallurgical and Materials Transactions A 42, 4080\u20104087. Metzbower, E., Bhadeshia, H., Phillips, R., 1994. Microstructures in hot wire laser beam welding of HY 80 Steel. Materials science and technology 10, 56\u201059. Miller, R., DebRoy, T., 1990. Energy absorption by metal\u2010vapor\u2010dominated plasma during carbon dioxide laser welding of steels. Journal of Applied Physics 68, 2045\u20102050. Nasr, M.N., Ng, E.\u2010G., Elbestawi, M., 2008. A modified time\u2010efficient FE approach for predicting machining\u2010induced residual stresses. Finite Elements in Analysis and Design 44, 149\u2010161. Nishi, T., Shibata, H., Waseda, Y., Ohta, H., 2003. Thermal conductivities of molten iron, cobalt, and nickel by laser flash method. Metallurgical and Materials Transactions A 34, 2801\u20102807. Pickin, C.G., Williams, S., Lunt, M., 2011. Characterisation of the cold metal transfer (CMT) process and its application for low dilution cladding. Journal of Materials Processing Technology 211, 496\u2010502. Schwam, D., Denney, P., Kottman, M., 2014. Rejuvenation of Steel Dies with Hot Wire Laser Cladding, NAMRI/SME. Shatla, M., Kerk, C., Altan, T., 2001. Process modeling in machining. Part I: determination of flow stress data. International Journal of Machine Tools and Manufacture 41, 1511\u20101534. Udvardy, S., Schwam, D., Denney, P., Kottman, M., 2014. Qualification of Additive Manufacturing Processes and Procedures for Repurposing and Rejuvenation of Tooling. Die Casting Engineer, 32\u201036. Zheng, S., P.Wen, J.Shan, 2014. Research on wire transfer and its stability in laser hot wire welding process. Chinese Journal of Laser, 101\u2010108. 14.82 \u2044 \u00a0 157.0 \u2044 \u00a0 Fig. 6. Thermocouple positions in the substrate (unit: mm). Fig. 7. The motion trail of the deposition. Fig. 9. Category of blocks. Fig. 10. The schematic of discretization. Fig. 12. Cross\u2010section of welding bead in one\u2010pass cladding experiment. Fig. 13. Temperature field of the welding bead by simulation (The absorptivity of laser power is 0.15). Fig. 17. Temperature distribution of the infinitesimal layer. Fig. 18. Temperature distribution calculated by two methods. Fig. 21. Temperature variation curves, as measured by thermocouples. Fig. 22. The temperature profile near the laser spot. Fig. 29. Distortion during deposition (the displacement of Point M). Fig. 30. LHW stress fields of (unit: Pa): during deposition (above); after deposition (below). Fig. 32. Temperature variation of heat affected zone. Fig. 33. SEM image of deposited material(Schwam et al., 2014) and temperature variation. Fig. 35. Processing window of stable hot\u2010wire deposition. Table 1 Chemical composition (weight percent) of H13 steel Element C Mn Si Cr Ni Mo Weight % 0.32\u20100.45 0.20\u20100.50 0.80\u20101.20 4.75\u20105.50 0.3 1.10\u20101.75 Element Mo V Cu P S Fe Weight % 1.10\u20101.75 0.80\u20101.20 0.25 0.25 0.03 Bal."
        ]
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure2.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure2.5-1.png",
        "caption": "Fig. 2.5 Rotor control through a swash plate",
        "texts": [
            " In this book, we shall be dealing with direct and coupled responses, sometimes described as on-axis and off-axis responses. On-axis responses will be discussed within a framework of response types \u2013 rate, attitude, and translational-rate responses will feature as types that characterise the initial response following a step control input. Further discussion is deferred until the modelling section within this Tour and later in Chapters 3\u20135. Some qualitative appreciation of vehicle dynamics can be gained, however, without recourse to detailed modelling. Rotor Controls Figure 2.5 illustrates the conventional main rotor collective and cyclic controls applied through a swash plate. Collective applies the same pitch angle to all blades and is the primary mechanism for direct lift or thrust control on the rotor. Cyclic is more complicated and can be fully appreciated only when the rotor is rotating. The cyclic operates through a swash plate or similar device (see Figure 2.5), which has nonrotating and rotating halves, the latter attached to the blades with pitch link rods, and the former to the control actuators. Tilting the swash plate gives rise to a one-per-rev sinusoidal variation in blade pitch with the maximum/minimum 14 Helicopter and Tiltrotor Flight Dynamics Fig. 2.6 Control actions as helicopter transitions into forward flight: (a) hover; (b) forward acceleration; (c) translational lift axis normal to the tilt direction. The rotor responds to collective and cyclic inputs by flapping as a disc, in coning, and tilting modes",
            "21) where \ud835\udf06i = vi \u03a9R We defer the discussion on rotor downwash until later in this chapter and Chapter 3; for the present purposes, we merely state that a uniform distribution over the disc is a reasonable approximation to support the arguments developed in this chapter. Eq. (2.19) can then be expanded and rearranged as \ud835\udefd\u2032\u2032 + \ud835\udefe 8 \ud835\udefd\u2032 + \ud835\udf062 \ud835\udefd \ud835\udefd = 2 \u03a9 (p cos\ud835\udf13 \u2212 q sin\ud835\udf13) + \ud835\udefe 8 ( \ud835\udf03 \u2212 4 3 \ud835\udf06i + p \u03a9 sin\ud835\udf13 + q \u03a9 cos\ud835\udf13 ) (2.22) The flapping Eq. (2.22) can tell us a great deal about the behaviour of a rotor in response to aerodynamic loads; the presence of the flap damping \ud835\udefd \u2032 alters the response characteristics significantly. We can write the applied blade pitch in the form (cf. Figure 2.5 and the early discussion on rotor controls) \ud835\udf03 = \ud835\udf030 + \ud835\udf031c cos\ud835\udf13 + \ud835\udf031s sin\ud835\udf13 (2.23) where \ud835\udf030 is the collective pitch and \ud835\udf031s and \ud835\udf031c the longitudinal and lateral cyclic pitch, respectively. The forcing function on the right-hand side of Eq. (2.22) is therefore made up of constant and first harmonic terms. In the general flight case, with the pilot active on his controls, the rotor controls \ud835\udf030, \ud835\udf031c, and \ud835\udf031s and the fuselage rates p and q will vary continuously with time. As a first approximation, we shall assume that these variations are slow compared with the rotor blade transient flapping",
            "278) with the positive sense defined by a positive increase in the corresponding rotor blade angle (see Figure 3.36). The automatic flight control system (AFCS) is usually made up of stability and control augmentation system Modelling Helicopter Flight Dynamics: Building a Simulation Model 131 (SCAS) functions, applied through series actuators, and autopilot functions applied through parallel actuators. In this section we consider only the modelling of the SCAS. Pitch and Roll Control The swash plate concept was introduced in Chapter 2 (Figure 2.5) as one of the key innovations in helicopter development, allowing one-per-rev variations in rotor blade pitch to be input in a quasi-steady manner from the actuators. The approximately 90\u2218 phase shift between cyclic pitch and the cyclic flapping response comes as a result of forcing the rotor with lift changes at resonance. In practice, cyclic pitch can be applied through a variety of mechanisms; the conventional swash plate is by far the most common, but Kaman helicopters incorporate aerodynamic surfaces in the form of trailing edge flaps and cyclic control in the Westland Lynx is effected through the dangleberry, with the blade control rods running inside the rotor shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure6.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure6.3-1.png",
        "caption": "FIGURE 6.3. Illustration of a 2R planar manipulator in two possible configurations: (a) elbow up and (b) elbow down.",
        "texts": [
            "36) therefore X2 + Y 2 = l21 + l22 + 2l1l2 cos \u03b82 (6.37) and cos \u03b82 = X2 + Y 2 \u2212 l21 \u2212 l22 2l1l2 (6.38) \u03b82 = cos\u22121 X2 + Y 2 \u2212 l21 \u2212 l22 2l1l2 . (6.39) However, we usually avoid using arcsin and arccos because of the inaccuracy. So, we employ the half angle formula tan2 \u03b8 2 = 1\u2212 cos \u03b8 1 + cos \u03b8 (6.40) to find \u03b82 using an atan2 function \u03b82 = \u00b12 atan2 s (l1 + l2) 2 \u2212 (X2 + Y 2) (X2 + Y 2)\u2212 (l1 \u2212 l2) 2 . (6.41) The \u00b1 is because of the square root, which generates two solutions. These two solutions are called elbow up and elbow down, as shown in Figure 6.3(a) and (b) respectively. The first joint variable \u03b81 of an elbow up configuration can geometrically be found from \u03b81 = atan2 Y X + atan2 l2 sin \u03b82 l1 + l2 cos \u03b82 (6.42) and for an elbow down configuration from \u03b81 = atan2 Y X \u2212 atan2 l2 sin \u03b82 l1 + l2 cos \u03b82 . (6.43) \u03b81 can also be found from the following alternative equation. \u03b81 = atan2 \u2212Xl2 sin \u03b82 + Y (l1 + l2 cos \u03b82) Y l2 sin \u03b82 +X (l1 + l2 cos \u03b82) (6.44) Most of the time, the value of \u03b81 should be corrected by adding or subtracting \u03c0 depending on the sign of X"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003726_j.ymssp.2015.05.015-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003726_j.ymssp.2015.05.015-Figure2-1.png",
        "caption": "Fig. 2. Geometrical parameters for fillet foundation deflection [13].",
        "texts": [
            " When the crack length is less than the whole tooth width, q\u00f0z\u00de \u00bc qo ffiffiffiffiffiffiffiffiffiffiffiffiffiffi Wc z Wc s ; zA 0 Wc\u00bd \u00f06\u00de q\u00f0z\u00de \u00bc 0 ; zA Wc W\u00bd \u00f07\u00de where Wc is the crack length, W is the whole tooth width, and qo is the maximum crack depth, see Fig. 1c. When the crack length extends through the whole tooth width, q\u00f0z\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2o q22 W z\u00feq22 s \u00f08\u00de where q2 is as shown in Fig. 1c. The effect of fillet foundation deflection on the gear mesh stiffness was studied in [12], and can be calculated as follows: \u03b4f \u00bc F cos 2 \u03b1m\u00f0 \u00de WE Ln uf Sf 2 \u00feMn uf Sf ( \u00fePn 1\u00feQn tan 2 \u03b1m\u00f0 \u00de ) \u00f09\u00de \u03b1mis the pressure angle, and uf and Sf are illustrated in Fig. 2. Ln;Mn; Pn; and Qncan be approximated using polynomial functions as follows [12]: Xn i hfi;\u03b8f \u00bc Ai=\u03b8 2 f \u00feBih 2 fi\u00feCihfi=\u03b8f \u00feDi=\u03b8f \u00feEihfi\u00feFi \u00f010\u00de Xn i represents the coefficients Ln;Mn; Pnand Qn. hfi \u00bc rf =rint; rf ; rint and \u03b8f are illustrated in Fig. 2. Please cite this article as: O.D. Mohammed, M. Rantatalo, Dynamic response and time-frequency analysis for gear tooth crack detection, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j.ymssp.2015.05.015i The coefficients Ai;Bi;Ci;Di; EiandFi are given in Table 2. Then the stiffness due to fillet foundation deflection can be obtained as: 1 Kf \u00bc \u03b4f F 1 \u00f011\u00de For a pinion it could be denoted as Kfp. The Hertzian contact stiffness Kh can be calculated as stated in [14] as follows: 1 Kh \u00bc 4 1 \u03bd2 \u03c0:E:W \u00f012\u00de After calculating the stiffness of a cracked pinion tooth, Ktp, due to bending, shear, and axial compression, and then calculating the stiffness due to the fillet foundation deflection, Kfp, we can perform the same calculations for an uncracked mating gear tooth to find Ktg and Kfg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003828_j.ijmecsci.2020.106180-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003828_j.ijmecsci.2020.106180-Figure11-1.png",
        "caption": "Figure 11: Force distribution on a) a single layer, and b) single unit cell of the gyroid lattice structure. By assuming the gyroid strut to act as a beam at an angle of \u03b8, A is assumed to be the free end, B is assumed to be the fixed",
        "texts": [
            " Similar to confined compression, the thicker struts at the 350 370 390 410 430 450 470 G2 G4 G24 (boarder) G24 (center) M ic ro h ar d n es s (H V ) boarders are restricting the thin inner struts from straining in the radial direction, and this might be the reason for the enhanced mechanical properties. G24 designs may be more suitable for load-bearing implants where high compressive strength and radial graded porosity is required. The improved ductility of G2 designs is related to the fact that these structures had the lowest percentage of internal defects. The force per unit cell can be estimated to be equal, assuming an infinite lattice structure formed of multiple gyroid unit cells. Therefore, it is assumed that all the struts will deform in the same way when loaded vertically [62]. In Figure 11, an approach to calculate the young's modulus depending on Bernoulli and Timoshenko beam theory was suggested by Yang et al. [47]. The total deflection in the one-fourth of the unit cell was calculated, assuming a simplified beam structure, as illustrated in Figure 11 (b). The ratio between the apparent analytical modulus of elasticity of the 0 20 40 60 80 100 0 0.1 0.2 0.3 0.4 0.5 0.6 En gi n ee ri n g St re ss ( M Pa ) Engineering Strain (mm/mm) G2 G4 G24 gyroid lattice structures (Ec) and the parent material modulus of elasticity (E) can be given by the following equation [47]: ( ) support. The force would cause a deflection \u03b4 and a moment (M) in the beam. To understand the effect of geometrical deviations in gyroid structures on the modulus of elasticity, an FEA model was developed to compare the designed gyroid lattice structures with scanned ones"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000456_tia.2007.900474-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000456_tia.2007.900474-Figure2-1.png",
        "caption": "Fig. 2. Switching states during current commutation. (a) Before current commutation. (b) During current commutation. (c) After current commutation. (d) Current commutation in three-phase switching mode.",
        "texts": [
            " The equations for the phase-winding terminal-to-ground (n0) voltages uan0, ubn0, and ucn0 are uan0 = uan + unn0 (4) ubn0 = ubn + unn0 (5) ucn0 = ucn + unn0 (6) where unn0 is the neutral point-to-ground voltage. The sum of the phase-winding terminal-to-ground voltages is uan0 + ubn0 + ucn0 =uan + ubn + ucn + 3unn0 = ea + eb + ec + 3unn0. (7) Thus, the neutral point-to-ground voltage is unn0 = 1 3 (uan0 + ubn0 + ucn0 \u2212 ea \u2212 eb \u2212 eb). (8) Based on the above equations, the phase-current commutation process can be analyzed. Fig. 2 shows the current paths during commutation between phases b and c when the switching states change from (100100) to (100001), where the digits are logical values which describe the states (\u201c1\u201d indicates ON and \u201c0\u201d indicates OFF) of the upper and lower switches for phases a, b, and c, respectively. At the instant of phasecurrent commutation, the three phase back-EMFs are ea = E, eb = \u2212E, and ec = \u2212E, where E is the peak value of the back-EMF waveform (Fig. 1). The back-EMFs are assumed to be constant during the phase-current commutation as in [1], although this is clearly not the case, as is evident from Fig. 1. During commutation [Fig. 2(b)], the rate of change of the phase currents is determined from the voltage equations dia dt = 1 3Ls Udc \u2212 4 3Ls E (9) dib dt = 1 3Ls Udc + 2 3Ls E (10) dic dt = \u2212 2 3Ls Udc + 2 3Ls E (11) where Udc is the dc-link voltage. In the above equations, it should be noted that the voltage drops across the power switches and diodes are assumed to be negligible. Further assumptions are that the stator windings are symmetrical and the phase inductances are constant and identical. As shown in Fig. 3, three conditions determine the phasecurrent variation during commutation [1]",
            " However, when the motor is operating at high speed (Udc < 4E), the rate of decrease of the current ib in phase b during commutation, which is associated with the conduction of the free-wheel diode, will be so high that the rate of increase of phase-c current ic cannot be increased sufficiently even if the dc-link voltage is fully utilized. In order to maintain ia constant during high-speed operation, the instant at which phase b is commutated off can be delayed and the machine can be operated in the three-phase switching mode, as illustrated in Fig. 2(d). The three phase currents will then be fully controllable throughout the commutation period, i.e., the uncontrollable commutation period, which is associated with the conduction of the free-wheel diodes, is now controllable. Hence, this concept is utilized to achieve improved DTC of a BLDC drive. The time which is taken for the current in phase b to decay to zero can be extended by controlling the switching of phase b via PWM, i.e., the usual two-phase switching mode is combined with a controllable three-phase switching mode during commutation periods",
            " The larger the torque-estimation error, the bigger the torque-ripple range. The only difference with the proposed torque-ripple reduction method is that conventional PWM chopping is employed during noncommutation periods and a hybrid two-phase/three-phase switching mode is employed during commutation periods. It should also be noted that, during the three-phase switching mode, the switching states are exactly the same as those which would be used in three-phase 180\u25e6-elec.-conduction BLDC operation, and as shown in Fig. 2(d), ia increases toward a positive value, while ib and ic increase toward negative values. Since, in this case, Udc > 2E at any instant, the rate of change of the three phase currents can be expressed as dia dt = 2 3Ls Udc \u2212 4 3Ls E (+ve value) (15) dib dt = \u2212 1 3Ls Udc + 2 3Ls E (\u2212ve value) (16) dic dt = \u2212 1 3Ls Udc + 2 3Ls E (\u2212ve value). (17) Therefore, it can be concluded that, during the commutation period, the current ia in the noncommutated phase increases when Udc > 4E and decreases when Udc < 4E"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure9.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure9.7-1.png",
        "caption": "Fig. 9.7 Roll rotations with and without suspension jacking",
        "texts": [
            "6 However, the vehicle does not care much about which point we applied the roll rotation. This is demonstrated in Fig. 9.6, where we superimposed the three vehicle rotations shown in Fig. 9.4. They are almost indistinguishable, suggesting that the notion of a roll axis about which the vehicle rolls is meaningless. For the vehicle, all points between, say, T and B are pretty much equivalent. In general, in addition to roll, there may be some suspension jacking, which results in a vehicle vertical displacement zi , as discussed in Sect. 3.8.10. Figure 9.7 shows the same axle with and without suspension jacking. The roll angle is the same. It is evident, particularly when comparing the two cases, as it is done in Fig. 9.7 (bottom), that the combination of roll and suspension jacking is like a rotation about a point Qz. 6In Fig. 9.5 it is also quite interesting to note the camber variations due to pure roll in each type of suspension. This topic has been addressed in Sect. 3.8.3. Fig. 9.6 Comparison of roll rotations about different points: they have almost the same effect on the vehicle We recall that suspension jacking occurs whenever the lateral forces exerted by the two tires of the same axle are not equal, which is always the case, indeed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002671_s40684-018-0006-9-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002671_s40684-018-0006-9-Figure2-1.png",
        "caption": "Fig. 2 Schematic diagram of SLM process parameters",
        "texts": [
            "18 Different definitions are first clarified, and existing research on part formation using volumetric energy density is then reviewed. Energy density normally consists of four independent process parameters, (1) laser powder Plaser (W), the power value of the laser beam; (2) scan speed vscan (mm/s), the velocity with which the laser beam traverses along the scan paths; (3) hatch space hspace (mm), the distance between two adjacent scan paths; and (4) layer thickness tlayer (mm), the thickness of a layer that equals the incremental amount of the lowering building bed. Fig. 2 illustrates these key parameters. The different combinations of these parameters greatly influence the part formation quality. In general, Plaser is selected based on material and equipment, tlayer is determined to ensure full laser penetration and powder melting, vscan can be adjusted accordingly, and hspace should be sufficiently small to ensure proper material connection. The interaction among them is complex yet critical to good part properties. Overlap ratio \u03b7o between two adjacent scan paths, and re-melting ratio \u03b7r between two adjacent layers are another two factors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001467_s10514-012-9294-z-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001467_s10514-012-9294-z-Figure1-1.png",
        "caption": "Fig. 1 The external forces and torques in (a) are solely responsible for the centroidal momentum rate change in (b). (c): Linear momentum rate change l\u0307 has a one-to-one correspondence with the GRF f . (d): The centroidal angular momentum rate change k\u0307 is determined by both f and CoP location p. (e): Conversely, p is determined by both l\u0307 and k\u0307",
        "texts": [
            " However, rotational dynamics of a robot plays a significant role in balance (Komura et al. 2005). Experiments on human balance control also show that humans tightly regulate angular momentum during gait (Popovic et al. 2004), which suggests the strong possibility that angular momentum may be important in humanoid movements. In fact, both angular and linear momenta must be regulated to completely control the CoP. The fundamental quantities and the relations between them are schematically depicted in Fig. 1 and described subsequently. Figure 1(a) shows all the external forces that act on a freely standing humanoid: the GRF f , the Ground Reaction Moment \u03c4n normal to the ground, and the weight mg of the robot, where m is the total robot mass and g is the acceleration due to gravity. According to D\u2019Alembert\u2019s principle, the sums of external moments and external forces, respectively, are equivalent to the rates of change of angular and linear momenta, respectively, of the robot. The mathematical expressions for these relationships are given by (1) and (2). Figure 1(b) depicts the robot\u2019s rate of change of angular momentum about the CoM, k\u0307, and linear momentum, l\u0307, respectively. k\u0307 = (p \u2212 rG) \u00d7 f + \u03c4n (1) l\u0307 = mg + f (2) In the above equations, rG is the CoM location and p is the CoP location. Together k and l is a 6 \u00d7 1 vector called the spatial centroidal momentum h = [kT lT ]T , which was studied in Orin and Goswami (2008). In this paper, we will call it spatial momentum, or simply the momentum of the robot. The aggregate momentum of a humanoid robot may be obtained by summing up all of the angular and linear momenta contributed by the individual link segments",
            " The centroidal momentum is this aggregate momentum of the robot projected to a reference point instantaneously located at its CoM. Note that the spatial centroidal momentunm is computed with respect to a frame which is aligned to the world frame and located at the overall CoM of the robot. Also the frame is instantaneously frozen with respect to the world frame. Indeed, as noted in Macchietto et al. (2009), the (spatial) momentum rate change has a one-to-one relationship with the GRF and CoP. From (2) and as shown in Fig. 1(c), l\u0307 is completely determined by f and vice versa. Furthermore, from (1) and Fig. 1(d), a complete description of k\u0307 needs both f and p. Conversely, p depends on both k\u0307 and l\u0307, which is shown in Fig. 1(e).1 This last sentence implies that a complete control of p is impossible without controlling both momenta. Based on this fundamental relation researchers have developed balance maintenance methods that controls both the linear and angular components of the spatial momentum (Kajita et al. 2003; Abdallah and Goswami 2005; Macchietto et al. 2009). We will call balance controllers of this approach momentum-based balance controllers. Some momentum-based balance control approaches define the desired rotational behavior of the controller in terms of the CoP (Abdallah and Goswami 2005; Macchietto et al",
            " Furthermore, our method computes contact forces at each support foot, and therefore can be used both during double-support and single-support and also on non-level, discrete, and non-stationary grounds, whereas Abdallah and Goswami (2005), Macchietto et al. (2009), Hofmann et al. (2009) consider only single-support. Table 1 illustrates how the existing methods treat momentum, GRF, and CoP in formulating balance and gait strategies. Robot gait planning methods using reduced models such as Kajita et al. (2001), Choi et al. (2007) (Table 1(a)) compute the necessary CoM trajectory which ensures balance for a specified desired CoP trajectory. This is done using reduced models such as the LIPM. As can be seen from Fig. 1(e) CoP depends on both linear and angular momenta rate changes, so CoM cannot be uniquely determined solely from CoP. This was possible in Kajita et al. (2001), Choi et al. (2007) because the reduced model used in those works approximated the robot as a point mass, which can only possess a zero angular momentum. In the Resolved Momentum Control approach (Kajita et al. 2003), both desired linear and angular momenta are used to determine joint motion for posture change (Table 1(b)). However, the admissibility of the CoP is not considered so the robot may lose balance if the values of input desired momenta are high"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001371_0278364916683443-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001371_0278364916683443-Figure5-1.png",
        "caption": "Fig. 5. (a) Render graphic of the electromagnetic system. (b) Photograph of the setup used in the demonstration. The setup comprises the catheter, the advancer gear box, the advancer motor, the electromagnets, and (not shown) the stereo-vision system. (c) Close-up of the catheter.",
        "texts": [
            " This results in a set of coil currents that maximizes the lower robustness bound for a desired equilibrium pose. To validate the derived electromagnetic catheter control three experiments were performed, each of them with a different control scheme: open-loop, closed-loop, and closedloop with stabilizing currents. In all cases, the catheter tip was directed to complete a trajectory composed of orthogonal squares measuring 4 \u00d7 4 cm2 in 250 s, which translates to a tip speed of 2.1 mm/s. The device used as a catheter model in this demonstration is shown in Figure 5. It is composed of a 0.55 mm diameter Nitinol wire surrounded by silicon tubing (i.d.: 0.75 mm, o.d.: 1.5 mm) with a cylindrical permanent magnet (d: 2.5 mm, h: 4 mm, NdFeB, HKCM Engineering) and a colored bead (d: 4.5 mm, h: 2.5 mm) placed at the tip. The total catheter length measures 13 cm when the tip is at the workspace origin. The calculated catheter parameters are provided in Table 1. The magnetic-manipulation system is composed of eight fluid cooled electromagnets with maximum permissible currents of \u00b120 A, arranged in a configuration similar to the system described in Kummer et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000088_027836499101000106-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000088_027836499101000106-Figure10-1.png",
        "caption": "Fig. 10. Coordinate systems of the three-link open-loop planar mechanism.",
        "texts": [
            " Two sets of typical optimal measurement configurations are shown in Figure 9 for this two-link planar mechanism. When the optimal configurations are selected, the maximum values of the determinant of det (E*T E*) becomes The corresponding observability index (0.1.) is It is interesting to see that the maximum observability value does not depend on the number of measurements performed. This result allows one to compare observability between two sets of measurement configurations that have distinct numbers of measurements. For the three-link open-loop planar mechanism shown in Figure 10, 12 geometric parameters are modeled; nine of them are shown to be observable. The position error model with nominal values of the geometric parameters is of the same form as in equation (12): at MICHIGAN STATE UNIV LIBRARIES on February 22, 2015ijr.sagepub.comDownloaded from 59 and For this mechanism, it can be shown that the maximum value of the determinant of E*T E* and the observability index are, Also it can be seen that a set of optimal measurement configurations can be obtained from the following formulations, similar to equation (16)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001967_s11071-018-4314-y-Figure30-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001967_s11071-018-4314-y-Figure30-1.png",
        "caption": "Fig. 30 Schematic of a angular misalignment [244] and b centroidal misalignment [245]",
        "texts": [
            " This work indicated that even smaller rolling element diameter errors have strongly influence the internal load distributions, stiffness and fatigue life of the bearing. Liu et al. [243] presented a theoreticalmodel to study the effects of the roundness errors of the components on the internal frictional torques of the needle roller bearings. 3.3 Misalignment Misalignment was also one of the most common distributed faults in REBs system even after using special alignment methods such as laser alignment, as shown in Fig. 30. Misalignment would generate a periodic unacceptable vibrations for REBs systems, which have significant effects on the load distribution and stability of REBs. Thus, it was also important to investigate the influence of misalignment on the contact mechanisms and vibrations of REBs. Numerous research works have been focused on those works as follows. Harris [244] proposed an analytical method to study the influence of inner race misalignment on the fatigue life of cylindrical roller bearings. An improved load\u2013 contact deflection relationship in the bearingwas established in this model",
            " This new stiffness model could be applied to formulate dynamic moment transmissibility and angular stiffness for REBs. Creju et al. [253] conducted a comprehensive dynamic model to performance the dynamic analysis for a TRB having axial load and angular misalignment. The contact surface geometries, gyroscopic moment, centrifugal forces, and lubricant film were formulated in this model. Lee and Lee [254] introduced a vibration model to predict the vibrations of misalignment rotor ball bearing systems. The angular, parallel, and combined misalignment were formulated in their model, as shown in Fig. 30. An experimental study was also conducted to validate the presented model. They indicated that the natural frequency increases with the effective bearing moment stiffness along the misalignment direction (Fig. 31). Nelias and Bercea [255] studied the influence of angular misalignment on the mechanical performance of TRBs. A generalized description for the static nonlinear behaviour for some double-row REBs was introduced. Their method may be adapted to single-row REBs. Liao and Lin [256] developed a new analytical method to study the influence of the angular misalignment of the inner race on the contact angles, contact deformations, and normal contact forces between the rolling element and races for a ball bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure19-1.png",
        "caption": "Fig. 19. Strain gauges on the compressive side of a tooth for compressive strain measurement.",
        "texts": [
            " It is found that calculated contact pattern is agreement with the measured one well. Root strains at the compressive side of tooth root are also measured (though tensile strains at the tooth root are more meaningful than the compressive strains for gear bending strength calculation, tensile strains are easily affected by tooth surface friction when lubricant is not enough in the measurement). Fig. 18 is comparisons between the measured root strains and the calculated ones at measurement positions of stain gauges 1\u20134 as shown in Fig. 19. It is also found that calculated root strains are agreement with the measured ones. Gears used as research objects for contact strength and bending strength calculations are given in Table 1. In Table 1, the wheel is cut by a hob under accuracy requirement of JIS fifth grade. Fig. 2 is the measured 3-D machining errors distributed on entire the tooth surface of the wheel. The pinion is ground under accuracy requirement of JIS zero grade. So machining errors of the pinion are ignored in the calculations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001315_978-1-4419-1117-9-Figure5.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001315_978-1-4419-1117-9-Figure5.9-1.png",
        "caption": "Fig. 5.9 CAD model of the spatial 3-dof parallel mechanism with prismatic actuators (Figure by Gabriel Cote\u0301)",
        "texts": [
            "63) with k52 and k54 are the stiffnesses of the virtual joints. Matrix J05 is the Jacobian matrix of the compliant constraining leg in this 4-dof case, while A and B are the Jacobian matrices of the structure without the constraining leg. The compliance comparison between the mechanism with rigid links (without virtual joints) and the mechanism with flexible links (with virtual joints) is given in Table 5.5. Again, the effect of the link flexibility is clearly demonstrated. This mechanism is illustrated in Fig. 5.9, the compliance matrix for the rigid mechanism can be written as Cc D J4.AJ4/ 1BCBT.AJ4/ TJT 4; (5.64) where C D diag\u0152c1; c2; c3 , with c1; c2, and c3 the compliance of the actuators and J4 is the Jacobian matrix of the constraining leg in this 3-dof case. Matrices A and B are the Jacobian matrices of the structure without the special leg. Similarly, the stiffness matrix for the mechanism with flexible links can be written as K D \u0152.J04/ TK4.J04/ 1 C ATB TKJB 1A ; (5.65) where K4 D diag\u0152k41; k42; k43; 0; 0; 0 ; (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001530_978-3-642-81857-8-Figure3.84-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001530_978-3-642-81857-8-Figure3.84-1.png",
        "caption": "Fig. 3.84. Case of one contact in assembly process-con",
        "texts": [
            " Case 1, when there is no contact between the hole and peg, represents free manipulator movement without reaction forces from the hole, so this situation does not differ dynamically from the task of transfer ring the working object in free space along desired trajectory and with a desired orientation. The manipulator dynamics is described by the mathematical model of open kinematic chain dynamics. Case 2 introduces the problem of the unknown reaction force acting on the manipulator via the object and influencing its dynamics. The prob lem of determining the reaction force in object-hole contact points arises. Fig. 3.84 illustrates the case of contact between the hole edge and the cylindrical surface of the peg, while Fig. 3.85 shows another possibility of single contact, namely, contact between the edge of the cylindrical base of the peg and the cylindrical surface of the hole. Both figures show the hole and peg section along the plane determined by the contact point and the symmetry axis of the hole cyl inder. Reaction forces at contact points are marked in figures. Three components of the reaction force at the point Kl or K2 are to be deter mined in the direction of the absolute coordinate system axes from Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.16-1.png",
        "caption": "FIGURE 5.16. The articulated and spherical manipulators are two common and practical manipulators.",
        "texts": [
            " Therefore, the transformation matrix i\u22121Ti for a link with \u03b1i = 90deg and P`R or P`P joints, known as P`R(90) or P`P(90), is i\u22121Ti = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 0 \u22121 0 0 1 0 di 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.42) while for a link with \u03b1i = \u221290 deg and P`R or P`P joints, known as 5. Forward Kinematics 253 yi-1 zi-1 xi-1 zixi xi-1 zi xi di Example 148 Assembling industrial links to make a manipulator. Industrial manipulators are usually made by connecting the introduced industrial links in Examples 142-147. A manipulator is a combination of three links that provide three DOF to a point in a Cartesian space. The articulated and spherical manipulators are two common and practical manipulators. Figure 5.16(a) and (b) show how we make these manipulators by connecting the proper industrial links. Example 149 Classification of industrial robot links. A robot link is identified by its joints at both ends, which determines the transformation matrix to go from the distal joint coordinate frame Bi to the proximal joint coordinate frame Bi\u22121. There are 12 types of links to make an industrial robot. The transformation matrix for each type depends solely on the proximal joint, and angle between the z-axes. The 12 types of 254 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003333_acsami.9b16770-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003333_acsami.9b16770-Figure9-1.png",
        "caption": "Figure 9. Magnetic actuation based on a hybrid bilayer structure of elastomer VHB (a kind of commercial tape from The 3M Company) and magnetic PNIPAAm hydrogels. (a) Schematic of magnetic navigation and magnetic shape morphing of a starlike bilayer. (b) The bilayer can move in the tube by using a magnet. During the motion process, the planar bilayer can bend upward as the AMF is applied. All scale bars are 10 mm. (Reproduced with permission from ref 116. Copyright 2019 American Chemical Society.)",
        "texts": [
            " The heat induced by the AMF led to volume contraction of the hydrogel. Thus, different distribution patterns of the magnetic hydrogel were fabricated on the elastomer VHB to form a two-layer structure for exhibiting shape-morphing structures (2D and 3D). In addition, by the design of the hinges, AMF-induced complicated folded origami structures can be realized. Finally, the author used a static magnetic field and an alternating magnetic field to achieve a combination of magnetic navigation and magnetic shape morphing, as shown in Figure 9. The AMF-induced actuation is expected to be applied to many fields such as biomedical engineering and soft robotics. Although past researches on hydrogel actuators have demonstrated the viability of multiple stimuli, a magnetic field is undoubtedly a promising option for future applications such as wearables and software robots. However, the application of magnetic hydrogels as actuators still faces major challenges including poor mechanical properties and durability in complicated environment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003657_j.measurement.2020.108855-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003657_j.measurement.2020.108855-Figure3-1.png",
        "caption": "Fig. 3. Coordinate system.",
        "texts": [
            "Yaw bearing are used to adjust the inflow angle stabilizing output [20], meanwhile automatically releasing the cable when twisted due to yawing movement. Load cases: yaw and pitch bearings have the characteristics of intermittent operation, frequent start and stop, large transmission torque and high transmission ratio. Therefore, small clearance is required for yaw bearing; compared with yaw bearing, pitch bearing is required to have zero clearance or small negative clearance due to larger impact load and larger vibration transmitted by blade compared with yaw bearing to reduce fretting wear of rolling working surface, as shown in Fig. 3 and Fig. 4. Because operating modes of slewing bearing are differing greatly from transmission system bearings, it is necessary to investigate typical failure modes of slewing bearings. Main faults of WTGS slewing bearings are summarized as follows. Plastic deformation: two types of plastic deformations will occur when loads exceed the elastic limit [21]. From a macro perspective, heavy loads or misalignment causes permanent deformation over large contact areas. Moreover, on a micro-scale, plastic deformation, such as indentation, will occur over tiny contact area [22]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002387_s11665-014-0993-9-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002387_s11665-014-0993-9-Figure1-1.png",
        "caption": "Fig. 1 Selective laser re-melting process",
        "texts": [
            " Keywords re-melting, selective laser melting, surface roughness Laser re-melting (LR) has been employed to assist many conventional metal processes for various purposes such as improving surface texture, mechanical properties, etc., to customize the microstructure and reduce residual stress on machined parts (Ref 1, 2). The process works by melting the surface up to the melting point of the metal, but lower than the evaporation point, in order to prevent the occurrence of cutting on the re-melted surface due to the increased temperature. After each track has been completed, the re-melted pool rapidly solidifies to generate a new surface profile as shown in Fig. 1. From an environmental perspective, the process is required to be fully shielded, using argon gas to avoid oxidation (Ref 3). An increase in oxygen ratio leads to insufficiently homogenous surface consolidation (i.e., more defects). This stems from the fact that the effects of surface tension on a liquid metal oxide will be less than on a liquid of metal without oxidation (Ref 4). Furthermore, the process has to be completed without any addition of new elements, in order to maintain the chemical composition of the surface (Ref 3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.17-1.png",
        "caption": "FIGURE 2.17. Local roll-pitch-yaw angles.",
        "texts": [
            "155) \u23a1\u23a3 \u03d5\u0307 \u03b8\u0307 \u03c8\u0307 \u23a4\u23a6 = \u23a1\u23a3 cos\u03c8 cos \u03b8 \u2212 sin\u03c8cos \u03b8 0 sin\u03c8 cos\u03c8 0 \u2212 tan \u03b8 cos\u03c8 tan \u03b8 sin\u03c8 1 \u23a4\u23a6\u23a1\u23a3 \u03c9x \u03c9y \u03c9z \u23a4\u23a6 . (2.156) In case of small Cardan angles, we have BAG = \u23a1\u23a3 1 \u03c8 \u2212\u03b8 \u2212\u03c8 1 \u03d5 \u03b8 \u2212\u03d5 1 \u23a4\u23a6 (2.157) and \u23a1\u23a3 \u03c9x \u03c9y \u03c9z \u23a4\u23a6 = \u23a1\u23a3 1 \u03c8 0 \u2212\u03c8 1 0 \u03b8 0 1 \u23a4\u23a6\u23a1\u23a3 \u03d5\u0307 \u03b8\u0307 \u03c8\u0307 \u23a4\u23a6 . (2.158) 62 2. Rotation Kinematics 2.7 Local Roll-Pitch-Yaw Angles Rotation about the x-axis of the local frame is called roll or bank, rotation about y-axis of the local frame is called pitch or attitude, and rotation about the z-axis of the local frame is called yaw, spin, or heading. The local roll-pitch-yaw angles are shown in Figure 2.17. The local roll-pitch-yaw rotation matrix is: BAG = Az,\u03c8Ay,\u03b8Ax,\u03d5 = \u23a1\u23a3 c\u03b8c\u03c8 c\u03d5s\u03c8 + s\u03b8c\u03c8s\u03d5 s\u03d5s\u03c8 \u2212 c\u03d5s\u03b8c\u03c8 \u2212c\u03b8s\u03c8 c\u03d5c\u03c8 \u2212 s\u03b8s\u03d5s\u03c8 c\u03c8s\u03d5+ c\u03d5s\u03b8s\u03c8 s\u03b8 \u2212c\u03b8s\u03d5 c\u03b8c\u03d5 \u23a4\u23a6 (2.159) Note the difference between roll-pitch-yaw and Euler angles, although we show both utilizing \u03d5, \u03b8, and \u03c8. Example 28 F Angular velocity and local roll-pitch-yaw rate. Using the roll-pitch-yaw frequencies, the angular velocity of a body B with respect to the global reference frame is G\u03c9B = \u03c9x\u0131\u0302+ \u03c9y j\u0302+ \u03c9z k\u0302 = \u03d5\u0307e\u0302\u03d5 + \u03b8\u0307e\u0302\u03b8 + \u03c8\u0307e\u0302\u03c8. (2.160) Relationships between the components of G\u03c9B in body frame and roll-pitchyaw components are found when the local roll unit vector e\u0302\u03d5 and pitch unit vector e\u0302\u03b8 are transformed to the body frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002342_j.jsv.2011.03.031-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002342_j.jsv.2011.03.031-Figure6-1.png",
        "caption": "Fig. 6. Dent on the rolling element. (a) Contact between the inner race and the dent on the ball surface. (b) Contact between the outer race and the dent on the ball surface.",
        "texts": [
            " It should be noted that not only does the radius of curvature change but so does the sign of curvature from positive to negative, because the dent on the inner race is a concave surface. Like the dent on the outer race, the direction of the contact force changes in the contact between the dent and the ball. The component of the force in the radial direction of the ball is given as FD,Ci \u00bc kd,id 3=2 Di\u00fe cos\u00f0yC ywj\u00de r\u00fe\u00f0xo xi\u00decosyj\u00fe\u00f0yo yi\u00desinyj wj : (28) The defect on the ball surface is modelled as a flattened ball, as shown in Fig. 6, where the flattened region is a sphere with a larger radius. The loss of contact will happen twice per complete rotation of the damaged rolling element, i.e. when the dent is in contact with the race and outer races. The dent has the form of a sphere with the radius R2 and R24rb. Due to the constant radius of the dent the contact stiffness is a constant, although it is different to that in the contact between the races and the rolling element. When the dent of the rolling element is in contact with the inner ring, the contact deformation is defined as dD,bi \u00bc r \u00f0Jwj\u00fer12J R2\u00de if r Jwj\u00fer12J\u00feR240, 0 else, ( (29) where r12 is the vector from the centre of the rolling element to the centre of the radii of the flattened curvature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001419_s0022112074001984-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001419_s0022112074001984-Figure4-1.png",
        "caption": "FIGURE 4. Lowest-order variation of A V = V / V , and c/c, with kh for a sheet in a channel, with the rate of working fixed at that for an isolated sheet. Here b = b, , k = k, and a = a,. The c/c, curve for a = 2 lies so close to the a = 0 curve that it is omitted for the sake of clarity.",
        "texts": [
            " Biharmonic analysis Using (28)) (20) and (62)) we define 1 sinh2kh-(kh)2 I1 1 +2am+a2,\u2019 sinh2 kh + (kh)2 sinh2 kh - (kh)2 sinh kh cosh kh - kh -a2+2a (63) 1 I- 1+a$\u2019 (64) AE, = nE,/(nE), kh + sinh kh cosh kh + 2a(kh)2 + a2[sinh kh cosh k7~ - kh] sinh2 kh - (kh)2 AE, = nEW/(nE), kh + sinh kh cosh kh + 2a (kh)2 + a2 [sinh kh cosh kh - kh] sinh2 kh - (kh)2 (65) 1 X 2( 1 +a%) \u2019 where the subscripts C and W refer to a sheet at the centre of a channel or near a single wall, respectively. For fixed wave size and shape, c/c, is obtained from (64) or (65); thence (63) determines AV. Typical results for a sheet in a channel are shown in figure 4. It should be noted that, since b < h, both the denominator and numerator of A V and A E approach zero in the biharmonic limit kh --f 0. If the b dependence is removed by factoring, then A V and A E become singular as 1/(hk)2 and l / (kh)3 , respectively, indicating the inapplicability of this limit. Note also that, with decreasing kh, c/c, decreases, while A V increases for a 2 0 but decreases when a > 0. The corresponding behaviour for a sheet near a single wall is very similar, the values of I A V I and c/c, being somewhat larger",
            " The results, illustrated in figure 6, indicate that, as kh decreases, the sheet must reduce the effective number of wavelengths. Thus the waves become larger owing to simultaneous increases in both amplitude and wavelength; and the beat frequency kc decreases. 5.2. Lubrication theory For a sheet swimming in a narrow channel or near a single wall such that kh < 1, we have, using (53), (54), (60), (61), and (62), 1 Allowing variations in wave speed alone to satisfy AE = 1, c/cm and AV are determined from (67) and (66), respectively, cf. figure 4. In figure 4, note the good agreement between the acceptable biharmonic limit kh - 1 and the lubrication-theory results. Note also that A V passes through an extremum as kh decreases. Indeed, it is readily shown that the extremal value is with h = 2b and c/c, = (3f) (bk)*( 1 + a2). Thus, if 1 - 23 < a < 1 + 24, this extremum is a maximum, cf. figure 7. Since V and E are independent of a in the lubrication-theory analysis, no optimization with respect to a is possible, cf. figure 5. However, if only the ivave size is allowed to vary subject to AE = 1, bk = b, k,, and constant effective length, cf"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001287_joe.2012.2201797-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001287_joe.2012.2201797-Figure1-1.png",
        "caption": "Fig. 1. Illustration of state variables in surge, sway, and yaw directions.",
        "texts": [
            " In Section III, the MPC approach is proposed to stabilize the tracking error dynamics. In Section IV, a recurrent neural network is applied for solving online optimization problems. In Section V, simulation results are provided. Finally, Section VI concludes the paper. A typical nonlinear model of an underactuated surface vessel dynamics is described as follows [36]: (1) where , and are the surge, sway, and yaw velocities, respectively; and , and are the surge displacement, sway displacement, and heading angle in earth fixed frame (see Fig. 1). The positive parameters denote the ship inertia and added mass effects. The positive parameters denote the hydrodynamic damping effects. The available controls are surge force and yaw moment . The objective is to exert control to force the ship to follow a predefined reference path. The system model (1) is not static feedback linearizable, nor can it be directly transformed to a chain form [37]. It was shown that any continuous or discontinuous time invariant feedback control law does not make the origin asymptotically stable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure2.23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure2.23-1.png",
        "caption": "Fig. 2.23 Field probes using fixed and rotating electrodes",
        "texts": [
            "22, which are based on the above calculations, enable a simple determination of the applied high voltage Vh from the measured low voltage Vm. In this context it has to be taken into account that the scale factor is dependent on the test frequency, if a measuring resistor is used. The main disadvantage of the arrangement shown in Fig. 2.21 is that it is only capable for measuring the field gradients occurring adjacent to earth potential. To measure also arbitrarily oriented field vectors in the space between HV and LV electrodes, spherical sensors are employed (Feser and Pfaff 1984). As illustrated in Fig. 2.23a, the surface of such a sphere is subdivided into six partial sensors to receive the three cartesian components of the electromagnetic field. To minimize the inevitable field disturbance caused by the metallic probe, it is battery powered and the whole components required for signal processing are integrated in the hollow sphere. The evaluated data are transmitted to earth potential via a fiber optic link. An essential benefit of the spherically shaped probe is that the admissible radius depending on the field strength to be measured can be calculated without large expenditure",
            " As the field probe provides a capacitive sensor it has to be taken into account that the induced charge and thus the measurable current i(t) is a consequence of the displacement flux which is correlated with the time dependent field strength E(t). Thus, only time dependent voltages, such as LI, SI, AC and other transients, induce a measurable displacement current. To measure also DC voltages, the desired alternating displacement current could be generated if the sensing electrode is periodically shielded by a rotating electrode connected to earth potential. This approach, schematically shown in Fig. 2.23b, is applied by the so-called field mill (Herb et al. 1937; Kleinw\u00e4chter 1970). Here the sensing electrode is established by two half-sectioned discs providing the measuring electrodes, which must be well isolated from each other. The vane electrode is connected to the guard electrode on earth potential. If the vane electrode is rotating in front of the measuring electrodes, an alternating displacement flux exposes these both electrodes 2.3 HV Measurement and Estimation of the Measuring Uncertainty 57 and induces thus an alternating current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000827_j.engfailanal.2014.04.005-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000827_j.engfailanal.2014.04.005-Figure2-1.png",
        "caption": "Fig. 2. Geometrical parameters for the fillet-foundation deflection.",
        "texts": [],
        "surrounding_texts": [
            "Base circle\n\u03c8 1\u03b1\n2\u03b1\nd\naF\nbF F\nxh h\nbr\nx\n\u03b1\nwhere subscripts 1 and 2 denote the driving and driven gears respectively, i = 1 represents the first pair of meshing teeth, i = 2 stands for the second pair of meshing teeth.\nThis so called potential energy method is time-saving comparing with ANSYS method. It is suitable to calculate the meshing stiffness when there is a crack fault in the gear pair [10].\n2.1. The improved energy method\nIn spite of those advantages of this method, it has a defect which needs to be corrected as follows. Before indicating the defect, a principle of mechanics about gears needs to be known. According to the knowledge of prin-\nciple of mechanics, the radius of gear base circle rb and root circle rf can be calculated as:\nrb \u00bc mz 2 cos\u00f0h\u00de; rf \u00bc mz 2 h a \u00fe c m \u00f011\u00de\nwhere m, z, h represent module, number of teeth and pressure angle, respectively. h a, c are addendum and tip clearance coefficients. If h a \u00bc 1, c \u00bc 0:25, h \u00bc 20 , when rb is equal to rf, the number of teeth z 42 can be obtained by using formula (11).\nThe potential energy method assumes the gear tooth as a variable cross-section cantilever beam which is fixed on the gear base circle. In this way, the potential energy stored in the part between base circle and root circle (the grid line portions as shown in Fig. 3) will be ignored. This defect must be corrected for further accurate calculation of time varying mesh stiffness.\nof the coefficients of Eq. (9).",
            "If the number of teeth is less than 42 (see in Fig. 3(a)), rb > rf the energy stored in the part between base and root circles must be added on the original foundation. If the number of teeth is more than 42 (see in Fig. 3(b)), the energy stored in the part between base circle and root circle must be subtracted on the original foundation.\nTherefore, when the number of teeth is less than 42, the formula of bending potential energy Ub (see in formula (2)) can be corrected as\nUb \u00bc Z d\n0\n\u00bdFb\u00f0d x\u00de Fah 2\n2EIx dx\u00fe1\nZ rb rf\n0\n\u00bdFb\u00f0d\u00fe x1\u00de Fah 2\n2EIx1\ndx1 \u00f012\u00de\nwhere Ix1 represents the area moment of inertia of the section where the distance from the tooth root is x1. Form the geometry of involute profile, d, x, hx can be expressed as\nd \u00bc rb\u00bdcos a1 \u00fe \u00f0a1 \u00fe a2\u00de sina1 cos a2 x \u00bc rb\u00bdcos a \u00f0a2 a\u00de sina cos a2 hx \u00bc rb\u00bd\u00f0a2 \u00fe a\u00de cos a sina 8>< >: \u00f013\u00de\nAfter simplify the formula (12), the bending mesh stiffness Kb can be expressed as\nkb \u00bc 1 Z a2\na1 3f1\u00fe cos a1\u00bd\u00f0a2 a1\u00de sin a cos a g2\u00f0a2 a\u00de cos a 2EL\u00bdsina\u00fe \u00f0a2 a\u00de cos a 3\nda\u00fe Z rb rf\n0\n\u00bd\u00f0d\u00fe x1\u00de cos a1 h sina1 2\nEIx1\ndx1 !, \u00f014\u00de",
            "where hx1 is the distance between the point on the tooth curve and the central line of the tooth, it can be expressed as hx1 \u00bc hb \u00fe R ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 x2 1 q , hb \u00bc rb sin\u00f0a2\u00de, R is root fillet radius.\nSimilarly, the shear mesh stiffness ks and axial compressive stiffness ka will be\nks \u00bc 1 Z a2\na1\n1:2\u00f01\u00fe v\u00de\u00f0a2 a\u00de cos a cos2 a1 EL sin a\u00fe a2 a\u00f0 \u00de cos a\u00bd da\u00fe Z rb rf 0 \u00f01:2 cos a1\u00de2 GAx1 dx1 !, \u00f015\u00de\nka \u00bc 1 Z a2\na1\n\u00f0a2 a\u00de cos a sin2 a1 2EL\u00bdsin a\u00fe \u00f0a2 a\u00de cos a da\u00fe Z rb rf 0 \u00f0sin a1\u00de2 EAx1 dx1 !, \u00f016\u00de\nwhere Ax1 represents the area of the section where the distance from the tooth root is x1. When the number of teeth is more than 42, the formula of bending potential energy Ub (see in formula (2)) can be corrected as\nUb \u00bc Z d\nrb rf\n\u00bdFb\u00f0d x\u00de Fah 2\n2EIx dx \u00f017\u00de\nThe formula of bending mesh stiffness Kb can be corrected as:\nkb \u00bc 1 Z a3\na1 3\u00f0a2 a\u00de cos af1\u00fe cos a1\u00bd\u00f0a2 a1\u00de sin a cos a g2 da 2EL\u00bdsina\u00fe \u00f0a2 a\u00de cos a 3\n!, \u00f018\u00de\nSimilarly, the shear mesh stiffness ks and axial compressive stiffness ka will be\nks \u00bc 1 Z a3\na1\n1:2\u00f01\u00fe v\u00de\u00f0a2 a\u00de cos a cos2 a1\nEL\u00bdsin a\u00fe \u00f0a2 a\u00de cos a da\n\u00f019\u00de\nka \u00bc 1 Z a3\na1\n\u00f0a2 a\u00de cos a sin2 a1\n2EL\u00bdsina\u00fe \u00f0a2 a\u00de cos a da\n!, \u00f020\u00de\nwhere a3 \u00bc af p 2z\u00fe \u00f0h hf \u00de , h = inv(a), hf = inv(af). a and af are the pressure angle of reference circle and root circle, respectively.\nNow, in order to confirm the accuracy of the improved time-varying mesh stiffness algorithm, three methods will be compared with ISO standard 6336-1-2006 which can be utilized to calculate the single stiffness c0 and mesh stiffness cc. As"
        ]
    },
    {
        "image_filename": "designv10_1_0001497_j.jmatprotec.2016.11.014-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001497_j.jmatprotec.2016.11.014-Figure2-1.png",
        "caption": "Fig. 2. Cathodes and anodes arrangements (bottom view): a) C1-A1, b) C1-A2, c) C2-A3 (cathode-to-anode distance in mm).",
        "texts": [
            " Additionally, the study focuses on the EP of internal surfaces since they are difficult to access by other technological means. This work is structured as follows. First, the experimental setup is presented in Section 2. The developed experimental methodology is given in Sections 3, 4\u20136 contain results, discussions, and conclusions of this study, respectively. 2. Experimental setup 2.1. Arrangements and design of electrodes and their intended use Three cathode-anode arrangements were designed for this study (Fig. 2). The first C1-A1 (a) arrangement was used for the current density (J) versus applied potential (Vapplied) characterization of the SLM-built Ti-6Al-4V specimens. The second C1-A2 (b) arrangement was designed to study the impact of major EP parameters on the roughness, mass and thickness reduction of specimens containing surfaces with different build orientations, as well as for the processing optimization. The third C2-A3 (c) arrangement was designed to simulate the polishing of an internal surface of a tube"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000915_j.ijmachtools.2006.09.025-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000915_j.ijmachtools.2006.09.025-Figure1-1.png",
        "caption": "Fig. 1. (a) Interaction of the laser irradiation and metal powder [4]. (b) Schemes of inter-particle contacts formation during metal laser sintering of single component powders [8].",
        "texts": [
            " Shiomi and Osakada [7] have developed a thermal model to calculate temperature and stress distribution for various track lengths. They have shown that the cracking of layer can be avoided by using smaller track length. In the present paper a FEM-based thermal model is developed to determine the non-uniform transient temperature distribution in the single powder layer of titanium due to laser irradiation for different laser power, beam diameter, laser on-time, laser off-time and hatch spacing. Localized heating of a small volume of powder during MLS is shown schematically in Fig. 1 [4]. The duration of laser beam at any powder particle is short, typically between 0.5 and 25ms. Therefore, the thermally induced binding reactions must be kinetically rapid. In principle, both single- and two-component powders can be subjected to MLS process [8]. In case of single-component powders the liquid phase arises due to the surface melting of particles and the powder is sintered by joining the solid non-melted cores of particles. Fig. 1(b) shows the possible ways of contact formation during MLS of single-component powders. Owing to random and complex nature of MLS process, following assumptions are made to make the problem mathematically tractable: 1. The input heat flux due to laser irradiation is treated as an internal heat generation in the powder layer. The heat flux from laser beam is taken as Gaussian distributed heat flux and given directly to the top of the powder layer. 2. The powder layer is assumed to be subjected to plane stress type of temperature variation because of the thickness of the powder layer is very small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001065_ecc.2013.6669644-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001065_ecc.2013.6669644-Figure5-1.png",
        "caption": "Fig. 5. Hardware development for a quadrotor UAV",
        "texts": [
            " In the proposed geometric nonlinear control system, there are only two controlled flight modes for position tracking and attitude tracking, and each controller has large region of attraction. Therefore, complex maneuvers can be easily generated in a unified way without need for timeconsuming planning efforts, as illustrated by this numerical example. This is another unique contribution of this paper. Preliminary experimental results are provided for the attitude tracking control of a hardware system illustrated at Figure 5. To test the attitude dynamics, it is attached to a spherical joint. As the center of rotation is below the center 0 1 2 3 4 0 0.2 0.4 0.6 0.8 (a) Attitude error function \u03a8 \u22120.2 0 0.2 \u22120.5 0 0.5 0 1 2 3 4 \u22121 0 1 (b) Position x, xd (m) \u22125 0 5 \u221220 0 20 0 1 2 3 4 \u221210 0 10 (c) Angular velocity \u2126,\u2126d (/sec) \u221210 0 10 f 1 \u221210 0 10 f 2 \u221210 0 10 f 3 0 1 2 3 4 \u221220 0 20 f 4 (d) Thrust of each rotor (N) Fig. 3. Flipping with integral terms (red,dotted:desired, blue,solid:actual) ~e1 ~e2~e3 Fig. 4. Snapshots of a flipping maneuver with integral terms: the red axis denotes the direction of the first body-fixed axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000437_027836499801700201-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000437_027836499801700201-Figure4-1.png",
        "caption": "Fig. 4. A PUMA-like robot mounted on a track.",
        "texts": [
            " Furthermore, priorities for the different task requirements can be assigned by selecting the appropriate task weighting factor Wt = diag{We, We}, The closed-loop, optimal, damped least squares solution of (37) is given by (Seraji and Colbaugh 1990) where K is the position feedback gain matrix. In practice, the inversion of the positive definite matrix [JT Wt J + Wv] is not needed, and 0 can be found using the Cholesky decomposition. Notice that (38) reduces to (24) when Wv = 0 and J is nonsingular. For the sake of illustration, we shall now consider a spatial three-jointed arm mounted on a 1-DOF mobile platform, as shown in Figure 4. This resembles a PUMA robot (without the wrist) mounted on a rail to provide base mobility. Let us denote the waist joint angle by 01, the shoulder joint angle by 92, and the elbow joint angle by 03, and let 04 represent the platform displacement in the x-direction of the world frame ~ W } in Figure 4. Therefore, the mobile arm has four degrees of freedom: the three revolute joints (01, 02, 03) for manipulation and one prismatic joint 04 for mobility. The forward kinematic equations relating the joint variables 0 = (01, 02, 03, 04)T to the tip Cartesian coordinates y = (x, y, z)T in the reference world frame are readily found to be where h is the shoulder height and t is the length of the upper arm (equal to the forearm length) and is set to unity for simplicity. Let us now consider the coordinated control of the arm and the platform. The robotic system in Figure 4 is kinematically redundant, and in this example the redundancy is resolved by controlling the &dquo;elbow angle&dquo; 0 between the upper arm and forearm in addition to the tip position Y. The elbow angle 0 determines the &dquo;reach&dquo; of the arm AP = 2\u00a3sin(\u00a7/2) = 2sin(\u00a7 /2). By introducing the elbow angle 0 as the fourth task variable, the forward kinematic model of the robot is augmented by The augmented differential kinematic model relating the rate of change of task variables to the joint velocities is found to be where the elements of J are obtained from (39) and (40)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000385_j.optlastec.2013.09.017-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000385_j.optlastec.2013.09.017-Figure2-1.png",
        "caption": "Fig. 2. Images of samples: (a) three-dimensional model, (b) photograph showing real-time selective laser melting process, (c) front view and (d) top view of SLM-processed tensile specimens, (e) three-dimensional model and (f) sliced two-dimensional (2D) layers of one real SLM-processed complex iron piece.",
        "texts": [
            " Before being installed, this platform was grit-blasted with alumina. At first, small iron cubes measuring 5 mm 5 mm 5 mm dimensions were preliminarily fabricated using several parameter sets in order to study the effect of processing parameters on the density of SLM-processed iron parts and to select \u201coptimal\u201d parameters to fabricate tensile specimens and the complex 3D piece. The preliminary criterion of \u201coptimal parameters\u201d is the acquisition of dense parts. Then the fabrication of the tensile specimens and the complex piece (see Fig. 2) was carried out using the \u201coptimal\u201d parameters, according to euro-norme 10002. Porous support layers (5 mm 5 mm 3 mm) were fabricated at the bottom of all the designed specimens in order to easily remove the specimens from the stainless steel building platform by a saw. The density of the SLM-fabricated samples was determined using the Archimedes method. The measuring details have been described in the literature [31]. The top-surface microstructure of the melted iron parts was observed using a scanning electron microscope (JEOL, JSM-5800LV)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure5.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure5.7-1.png",
        "caption": "Figure 5.7.1. Roll center for four-link solid axle.",
        "texts": [
            " Because the effect of a rising or falling roll center comes into play only as roll angle develops, it would be possible to treat the roll center height as fixed and to have an extra equivalent anti-roll bar. However, this would have to be nonlinear, probably with moment proportional to roll angle squared, and its properties could be established only by investigating the roll center movement. For a falling roll center it would have negative stiffness. 5.7 Solid-Axle Roll Centers This section deals with the determination of the roll center for solid axles with rigid link location. Leaf-spring axles are considered in the next section. Figure 5.7.1 shows a general four-link axle. The method is based on studying the support links to find two points A and B where forces are exerted by the axle on the body, the roll center necessarily lying on the line joining A and B, at the point where this line penetrates the transverse vertical plane of the wheel centers. Consider idealized springs at the wheels, or at least springs that do not act on the links. One link pair has an intersection point at A, so the combined force exerted by these links on the body must act through A (neglecting bush torques and link weight)",
            " This is an understeer effect for a rear axle, so The roll understeer coefficient (the rate of change of roll understeer with suspension roll angle) is therefore equal to the value of \u03c1A in radians, i.e., in this case value of the understeer coefficient is This is often expressed as a percentage roll understeer, i.e., 100\u03c1A%. The variation of roll steer coefficient with axle load is important. This is It can be examined easily by considering the change of \u03c1A from the motion of A and B with increasing load. If they move equally in the same direction then there is a change of roll center height but no change of roll steer. In some cases, for example the convergent four-link suspension of Figure 5.7.1, when the body moves down, A moves up and B moves down, giving a small change of roll center height but a large change of roll steer coefficient. Some positive sensitivity, i.e., increasing \u03c1A, may be desirable to help to compensate for the otherwise general trend toward oversteer with increasing load that occurs because of the tire characteristics. This can help with primary understeer but does not help with final understeer or oversteer. It might appear in the above discussion that the axle axis angle should be measured relative to the vehicle roll axis rather than to the horizontal",
            "44 m, point A is found 1.20 m behind the suspension plane at a height of 420 mm, and point B is 2.15 m in front at height 220 mm. What are the roll center height, net link load transfer factor and net link load transfer at 3200 N sprung mass side force? Q 5.7.3 Analyze the effect of vertical load on roll center height for the axles of Figure 4.6.1. Q 5.7.4 \"A solid axle is not subject to the link force jacking effect of independent suspensions.\" Discuss, with diagrams. Q 5.7.5 For a four link solid axle (Figure 5.7.1) explain how changes to the lateral spacing of the front ends of the bottom links will affect the roll center height. Q 5.8.1 Explain the roll center position of a leaf-spring mounted solid axle. Q 5.8.2 Explain the roll center position of a trailing twist axle. Q 5.9.1 Discuss various methods of experimental roll center measurement. Q 5.9.2 For the best method of experimental laboratory roll center measurement, consider the possible inaccuracies in relation to the force roll center for real cornering conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003361_j.msea.2017.05.061-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003361_j.msea.2017.05.061-Figure1-1.png",
        "caption": "Fig. 1. Simulation setup: (a) 3D finite element model and (b) scanning strategy.",
        "texts": [
            " The study conducts finite element simulation to predict the thermal behaviour of the parts prior to the experiment in order to narrow down the range of process parameters; it also investigates the microstructural and mechanical properties of as-fabricated composite samples. It examines the influence of cold working on various microstructural and mechanical properties as well as the correlation between microhardness improvement and the microstructural changes induced by cold working. The ANSYS Multiphysics finite element package was used to build the premier layer's scanning model and to conduct the heat transfer numerical simulation. A rectangular composite powder layer of 5\u00d71\u00d70.03 mm was built on a 5\u00d71\u00d70.12 mm aluminium substrate (Fig. 1a). The composite powder layer was meshed with a 0.015\u00d70.015\u00d70.015 mm SOLID70 hexahedron element to improve calculation accuracy; coarse mesh was used for the substrate. The premier layer that was built was reduced to three scanning tracks in order to reduce the simulation time; a bidirectional scanning strategy was employed to conduct the simulation (Fig. 1b). The heat flux followed a Gaussian distribution (Fig. 1a) and may be expressed as [17]: I r AP \u03c0r r r ( ) = 2 exp (\u2212 2 ) 0 2 2 0 2 (1) where A is absorptivity, P and r0 are laser power and laser spot radius, respectively; r denotes radial distance from the laser centre. This may be expressed as: r X a Y b r r= ( \u2212 ) + ( \u2212 ) (0\u2264 \u2264 )2 2 0 (2) where variables a and b may be determined as: \u23a7\u23a8\u23a9a b vt n l n h n nl vt n h n ( , ) = ( \u2212( \u22121) , ( \u22121) )( = 1, 3, 5, ...) ( \u2212 , ( \u22121) )( = 2, 4, 6, ...) (3) where v and t denote the scanning speed and scanning time, respectively; n and l represent track number and track length, respectively; and h is the hatch spacing",
            " The cold-working process was performed on both horizontally and vertically sectioned samples at room temperature using a universal testing machine (Autograph AG-1 20 kN, Shimadzu, Kyoto, Japan) with a strain rate of 0.5 mm/min until the strain reached 40%. A series of simulations were conducted with different combinations of various process parameters, including scanning speed (100\u20131000 mm/s) and hatch spacing (70, 100 and 130 \u00b5m). Fig. 4 shows the predicted thermal performance at the midpoint of track 1 (see Fig. 1b) under 200 W laser power and 100 \u00b5m hatch spacing. It is clear that the predicted maximum temperature at the molten pool region decreased from 2050 \u00b0C to 1899 \u00b0C when the scanning speed increased from 200 mm/s to 400 mm/s; the obvious decrease in molten pool dimensions was also caused by the increase in scanning speed (Fig. 4a and b). Fig. 4c shows the maximum temperature variation of the midpoint of track 1 when the scanning speed was varied from 100 mm/s to 1000 mm/s. Due to the heat accumulation, the predicted maximum temperature showed a slight increase along the scanning route; this trend was more obvious at low scanning speeds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001783_j.msea.2017.04.031-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001783_j.msea.2017.04.031-Figure2-1.png",
        "caption": "Fig. 2. (a) Schematic diagram of the horizontally and vertically SLM-built tensile samples. (b) Laser scan strategy applied in the SLM process.",
        "texts": [
            " A series of Ti-6Al-4V and 304 steel cubic samples with the same dimension of 10 mm\u00d710 mm\u00d710 mm were deposited using optimized SLM parameters for microstructure, texture and microhardness analyses. The laser power, scan speed, hatch space and layer thickness are 200 W, 1000 mm/s, 0.08 mm and 0.02 mm for Ti-6Al-4V, and 200 W, 800 mm/ s, 0.10 mm and 0.02 mm for 304 steel, respectively. Tensile test samples of each alloy designed according to ASTM E8/E8M\u201315a standard were horizontally and vertically built on the substrate, as schematically shown in Fig. 2a. Laser scanning direction changed between successive layers with the angle of 90\u00b0, as shown in Fig. 2b. During the SLM deposition, the building chamber was filled with argon and the oxygen content was strictly kept below 50 ppm. After the deposition, samples were cut from the substrate by wire electrical discharge. Then the SLMed Ti-6Al-4V and 304 steel samples were grinded and polished for relative density examination according to the method in Ref. [25], and for phase identification using a PANalytical X\u2032Pert PRO X-ray diffraction (XRD) with a Cu K-alpha radiation. For microstructure observations, etchings were conducted with a mixture of 2 ml hydrofluoric acid, 8 ml nitric acid and 90 ml deionized water for Ti-6Al-4V samples, and a mixture of 10 g ferric trichloride, 30 ml hydrochloric acid and 120 ml deionized water for 304 steel samples",
            " Meanwhile, the SLMed 304 steel sample is verified to be mainly composed of an FCC austenitic phase with the lattice parameter a=0.3571 nm. The phase identification results correspond well with the existing reports [20,22]. Microstructures of SLMed Ti-6Al-4V and 304 steel cubic samples are shown in Fig. 4. In Fig. 4a and d, it can be noticed that the microstructures on XOY sections of both alloys show chessboard patterns, which can be ascribed to the alternating scan strategy with the hatch angle of 90\u00b0 applied in the SLM processes (Fig. 2b). Acicular \u03b1\u2032 martensites within the columnar prior \u03b2 grains can be discerned on XOZ section of SLMed Ti-6Al-4V sample in Fig. 4b and c, which is consistent with the XRD results. The columnar prior \u03b2 grains are nearly parallel to the building direction and grow epitaxially over multiple layers. Similarly, the microstructure on XOZ section of SLMed 304 steel sample is filled with nearly vertical columnar structures in Fig. 4e. Inside the columnar structures are extremely fine cellular grains. The cellular grains with ~0",
            " 6c and d, there are no preponderant crystallographic orientations in the EBSD orientation maps of SLMed 304 steel samples, indicating that the texture may not be strong as well. The analysis results in Table 1 further manifest that the texture is weak, as the ODF intensity and volume fraction of the strongest crystallographic orientation (311)[130] are merely 20.83 and 7.68% respectively. The similar phenomenon is found in SLMed 316L austenitic stainless steel [16,17]. The cross scan strategy displayed in Fig. 2b can be perceived as the main cause of the weak texture in the 304 steel sample. Due to the change of scan directions between successive layers, the thermal gradient direction in horizontal plane changes. As a result, the variation of resultant thermal gradient direction can inhibit the continuous growth of columnar structures to a certain extent and avoid the formation of strong texture [17,20]. Evidently, the analysis results verify the weak texture characteristics in both alloys. Furthermore, by comparison with the 304 steel sample, the texture in the Ti-6Al-4V sample is even weaker due to the fact that it contains less preferred crystallographic orientations and lower corre- sponding volume fractions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure15-1.png",
        "caption": "Fig. 15. ADAMS MBS model of deep groove ball element bearing test rig.",
        "texts": [
            " A comprehensive chart of different types of bearing faults and the reasons for the faults can be found in SKF bearing damage chart. To model such types of defects, a multi-body simulation commercial software Adams is used here, where we can introduce different types of damages in the elements of bearing in component CAD models. In model development, a complete model of the test-rig including the rolling element bearing (here, deep groove ball bearing), which is first of its kind, has been developed using MBS ADAMS (Fig. 15). The inner race, outer race, ball and cage of the model are considered as rigid bodies. The traction between elements, nonlinear contact stiffness and damping, slip, imperfections due to manufacturing and faults are all included in the model. The model of the test rig consists of a rotor shaft connected to the motor through a flexible coupling, which offers significant torsional stiffness, but low bending stiffness in order to accommodate parallel and angular shaft misalignments. The rotor shaft is rigid both in torsion and bending"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000069_ip-epa:19981982-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000069_ip-epa:19981982-Figure10-1.png",
        "caption": "Fig. 10 Relations between the dflerent angles",
        "texts": [
            " To determine the electrical angle 0, for Park\u2019s rotor transformation, two other angles 6 and y have been computed. Indeed the three rotor currents are a function of the angle 6(t) for a balanced direct system by: cos(6) Irabc(t) = I r ( t ) . & C O S ( b - F) (9) i z/zf cos@ + F) A 3/2 Concordia\u2019s transformation allows to define currents lay and I,+: with I P T 6 = arctgI,, Park\u2019s transformation A(8,) leads to: y is the angle between d axis and vector I,. Knowing 6 and y. 0, is given by: Q , = b + y These relations are traduced in Fig. 10. The operating mode, I1 or 111, are dependent on the computation angle y. 7 Synchronisation on the network: mode II 7. I Or estimation In mode I1 the stator windings are open, stator currents is equal zero. The stator d and q fluxes are only dependent on the rotor currents, and 4 d s = M.Id? (pqs = M . I ~ T (14) (15) IqT 4 4 5 Idr d\u2019ds tg(y) = - = - The angle 0, is defined by the network and it is convenient to choice Vqs = V, and Vds = 0. #df and GqqS are obtained by integration of a and stator voltages and use of Park\u2019s transformation &e,)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000589_0077-7579(64)90001-8-Figure34-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000589_0077-7579(64)90001-8-Figure34-1.png",
        "caption": "Fig. 34. The light vector diagram of an A.L.D. homogeneous over 90 \u00b0 with a schematical representation of the two types of orientation performed by Daphnia magna.",
        "texts": [
            " RINGELBERG tion type (c). It was reported earlier (RINGELBERG, 1963) that Daphnia magna directed the body axis either to the ventral or to the dorsal screen edge. While these directions may be observed, especially with orienlation types (b) and (c), they are not the greatest in number. When the results of t962 and 1963 are summarized, it seems to be possible to propose at least two types of orientation mechanisms: First, a body directed to darkness while the eye is orientated to the ventral (now dorsal) contrast (fig.34a). Second, a body directed to the lighted area while the eye is orientated to the dorsal contrast (fig.34b). In the extreme cases (1962 animals) the behaviour is very consistent. The body is directed towards a restricted area in the light (355\u00b0-20 \u00b0) and the eye is orientated to the dorsal contrast or the body is directed to darkness (120\u00b0-140 \u00b0 ) and the eye is orientated to the ventral (now dorsal again) contrast. 1963 animals seem to represent a transitory state between these extremes. The behaviour is ambivalent in the homogeneous A.L.D. as well as when orientations are concerned. Ambivalent behaviour of another kind was sometimes observed in 1962 animals"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000655_1.4002333-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000655_1.4002333-Figure3-1.png",
        "caption": "Fig. 3 Load distribution in ball bearing and no and \u201eb\u2026 nomenclature of ball bearing for present s",
        "texts": [
            " The used relationship is expressed as follows 18 : Q = K 3/2 1 The radial deflection at any rolling element position refer to Fig. 2 is written as 18 = r cos \u2212 1 2 Pd 2 where r is the ring\u2019s radial shift at =0. If 0 is the initial position of the ith ball, the angular position i at any time t is defined by the following relation: i = 2 i Nb + ct + 0 3 where the angular velocity of cage is expressed in term of angular velocity of shaft and is defined as follows: c = 1 \u2212 d D s 2 4 Based on the geometry of the bearing, the normal load on the ball/raceway at position refer Fig. 3 is calculated by the following equation 18 : Q = Qmax 1 \u2212 1 2 1 \u2212 cos 3/2 5 where = 1 /2 1\u2212 Pd /2 r . In Fig. 3, it is clear that the applied radial load W is equal to the sum of the vertical components of the contact reactions. Mathematically, it is expressed as follows: W = =0 = 1 Q cos 6 The deflection of the ith ball in the radial direction is provided by the following expression refer to Fig. 1 c : i = Xs \u2212 Xb cos i + Ys \u2212 Yb sin i \u2212 c 7 nclature: \u201ea\u2026 load distribution in a ball bearing me imulation OCTOBER 2010, Vol. 132 / 041101-3 of Use: http://asme.org/terms w X t B p r s s o e b v t u m t d d w c o p b i w i i u t t f w d 0 Downloaded Fr here radial clearance c = Pd /2 1\u2212cos "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure17-1.png",
        "caption": "Fig. 17. Machining errors on reference face.",
        "texts": [],
        "surrounding_texts": [
            "LTCA and TSCS calculations of the pair of spur gears as shown in Table 1 are performed at the outer limit separately when MEmax = 0, 10, 20, 30 and 40 lm. Figs. 16 and 17 are ME of the wheel distributed on the reference face as shown in Fig. 6(a) when MEmax = 10 and 40 lm. Figs. 18 and 19 are contour lines of TSCS when MEmax = 10 and 40 lm. It is found that ME exerts great effect on TSCS distribution when Figs. 18 and 19 are compared with Fig. 15. Fig. 20 is a relationship between the maximum TSCS and MEmax. It is found that the maximum TSCS becomes greater when MEmax is increased. Influence factor of ME is introduced here to evaluate the effect of ME on TSCS quantitatively. So, it can be calculated through dividing the maximum TSCS of the gears when there are ME by the maximum TSCS of the gears when there are no ME, AE and TM. Relationship between the influence factor of ME and MEmax is also shown in Fig. 20. From Fig. 20, it is found that the influence factor of ME arrives at 2.2, a quite large number, when MEmax = 40 lm. Fig. 20 can be used as references when ISO 6336/2 [19] is used to calculate TSCS of a pair of spur gears with ME."
        ]
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure6-1.png",
        "caption": "Fig. 6. Face-contact model for loaded tooth-contact analysis.",
        "texts": [
            " 4, if the machined profile is on the outside of the theoretical profile, then ME is defined as positive, otherwise negative. Lead crowning and end relief are usually used for tooth modifications of a gear. In Fig. 5, one kind of lead crowning curve and two kinds of end relief curves are given. An arc is used for lead crowning. One arc with two straight lines and three straight lines are used for end relief. \u2018\u2018Q\u2019\u2019 is used to express the maximum quantity of lead crowning and end relief. Effects of the quantity Q of lead crowning on TSCS, TRBS, LRS and TE of the gears shall be investigated in this paper. Fig. 6 is a face-contact model used for LTCA of a pair of spur gears in this paper. Engagement of a pair of spur gears (Gear 1 and Gear 2) on the geometric contact line is shown in Fig. 6(b). Fig. 6(a) is a 3D view of the engaged tooth surface of Gear 1. In Fig. 6(a), loaded tooth contact is assumed to be on a reference face with a contact width Width. Of course, this reference face is a part of the tooth surface of Gear 1 and the geometric contact line is located at the center of this reference face. In Fig. 6(a), many lines parallel to the geometric contact line are made artificially. These lines (including the geometric contact line) are called reference lines and many points on the reference lines are made artificially. These points are called contact reference points, or simply say reference points. These reference points shall be used as contact points in LTCA. That is to say, tooth-contact on the reference face of Gear 1 shall be replaced by the contacts on the reference points when FEM is used to perform LTCA",
            " ; engT F k P 0; Y k P 0; ek P 0; d P 0; k \u00bc 1; 2; . . . ; n X n\u00fem P 0; m \u00bc 1; 2; . . . ; n\u00fe 1 In above equations, akj(1) and akj(2) are deformation influence coefficients of the pairs of contact points on engaged tooth surfaces of Gear 1 and Gear 2 separately. They are calculated by 3D FEM. P is total load of a pair of spur gears along the line of action. P can be calculated with Eq. (4). In Eq. (4), rb is radius of gear base circle. {e} is gap array that consists of all pairs of contact points on the reference face as shown in Fig. 6(a). {e} can be calculated geometrically. {F} is a array of contact loads between the pairs of contact points. d is relative deformation of the pair of gears along the line of action. When akj(1), akj(2), {e} and P are known, {F} and d can be calculated by solving the Eqs. (1)\u2013(3) with the modified simplex method of mathematical programming principle. Detailed procedures about the LTCA can be found in Ref. [17]. P \u00bc Transmitted Torque=rb \u00f04\u00de Hertz formula is often used to calculate TSCS of gears when tooth load is known. But it is difficult to be used here for a pair of gears with AE, ME and TM. So this paper calculates the TSCS of gears with a \u2018\u2018Unit Force\u2019\u2019 method. It means to calculate tooth load distributed on unit contact area of a tooth surface. That is to say, dividing the tooth load with a contact area on the reference face as shown in Fig. 6(a). For the pair of gears as shown in Table 1, TSCS at the outer limit of the single pair tooth-contact area as shown in Fig. 7 is greater than the one at the inner limit [17]. So, TSCS at the outer limit is calculated when the effects of ME, AE and TM on TSCS are investigated in this paper. When tooth load distributions are obtained in LTCA, TRBS are calculated with 3D FEM. For gears having contact ratios in the range 1 < e < 2, the maximum tensile root stress happens at outer limit contact of the gears",
            " The pinion is ground under accuracy requirement of JIS 0 grade. So machining errors of the pinion are ignored in the calculations. Torque conditions are also given in Table 1. These torques are used for all the calculations in the following. Fig. 14 is FEM models of the pair of gears used in LTCA. Fig. 14(a) is FEM mesh-dividing pattern of the wheel. The pinion is also divided similarly. Fig. 14(b) is FEM model in the part of tooth-contact. Four pairs of teeth are shown. The reference face as shown in Fig. 6(a) is fine divided with 48 meshes within the contact width \u2018\u2018Width\u2019\u2019 and 20 meshes within the face width. Nodes on inner hole surface (hub of the gears) as shown in Fig. 14(a) are fixed as the boundary conditions of FEM when deformation influence coefficients and TRBS are calculated. As it has been stated that the outer limit of the single pair tooth-contact is used as the \u2018\u2018worst load position\u2019\u2019 to do LTCA and TSCS calculations of the pair of gears as shown in Table 1. Fig. 15 is contour lines of calculated TSCS when there are no ME, AE and TM. This TSCS is distributed on the reference face as shown in Fig. 6(a). In Fig. 15, the horizontal axis (X-axis) is face width of the gears and the vertical axis (Y-axis) is contact width Width as shown in Fig. 6(a). Geometrical contact line of the gears is located at the center of contact width (Y = 0). Y < 0 is the side from the geometrical contact line to the root, Y > 0 is the side from the geometrical contact line to the tip. From Fig. 15, it is found that contact stress distributions are almost the same along the lead when there are no ME, AE and TM. LTCA and TSCS calculations of the pair of spur gears as shown in Table 1 are performed at the outer limit separately when MEmax = 0, 10, 20, 30 and 40 lm. Figs. 16 and 17 are ME of the wheel distributed on the reference face as shown in Fig. 6(a) when MEmax = 10 and 40 lm. Figs. 18 and 19 are contour lines of TSCS when MEmax = 10 and 40 lm. It is found that ME exerts great effect on TSCS distribution when Figs. 18 and 19 are compared with Fig. 15. Fig. 20 is a relationship between the maximum TSCS and MEmax. It is found that the maximum TSCS becomes greater when MEmax is increased. Influence factor of ME is introduced here to evaluate the effect of ME on TSCS quantitatively. So, it can be calculated through dividing the maximum TSCS of the gears when there are ME by the maximum TSCS of the gears when there are no ME, AE and TM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002251_s11071-013-1104-4-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002251_s11071-013-1104-4-Figure2-1.png",
        "caption": "Fig. 2 (a) Schematic of the backlash function, fh(x). (b) The approximated of the fh(x) based on a third-order polynomial",
        "texts": [
            " Dimensionless equation of motion can be obtained by defining: x = x\u0303/b, \u03c9n = \u221a km/m, \u03c4 = \u03c9nt \u03a9k = \u03c9k/\u03c9n, \u03a9e = \u03c9e/\u03c9n, \u03a9p = \u03c9p/\u03c9n \u03bc\u0303 = c/2m\u03c9n, k\u0303pr = kr/2m\u03c92 n F\u0303m = F\u0302m/bkm, F\u0303pr = F\u0302pr/bkm, F\u0303er = er/b The dimensionless equation of the gear pair could be written as d2x d\u03c4 2 + 2\u03bc\u0303 dx d\u03c4 + ( 1 + 2 \u221e\u2211 r=1 k\u0303pr cos(r\u03a9k\u03c4 + \u03c6kr) ) fh(x) = F\u0303m + \u221e\u2211 r=1 F\u0303pr cos(r\u03a9p\u03c4 + \u03c6pr) + \u221e\u2211 r=1 (r\u03a9e) 2F\u0303er cos(r\u03a9e\u03c4 + \u03c6er) (8) where fh(x) = \u23a7\u23a8 \u23a9 x \u2212 (1 \u2212 \u03b1) 1 < x \u03b1x \u22121 \u2264 x \u2264 1 x + (1 \u2212 \u03b1) 1 < \u2212x fh(x) is the nonlinear displacement function due to backlash. The third-order approximation polynomial can express the gear backlash clearance function fh(x). Therefore the third-order polynomial is taken to do the following analysis in this study. The particular case of \u03b1 = 0 for a gear pair system is studied. The approximated polynomial can be written as fh(x) = \u22120.1667x + 0.1667x3. Figure 2(a) and (b) shows the fh(x) and approximated function, respectively. Substituting fh(x) into Eq. (8), the equation of motion of the system can be obtained as d2x d\u03c4 2 + 2\u03bc\u0303 dx d\u03c4 + ( 1 + 2 \u221e\u2211 r=1 k\u0303pr cos(r\u03a9k\u03c4 + \u03c6kr) ) \u00d7 (\u22120.1667x + 0.1667x3) = F\u0303m + \u221e\u2211 r=1 F\u0303pr cos(r\u03a9p\u03c4 + \u03c6pr) + \u221e\u2211 r=1 (r\u03a9e) 2F\u0303er cos(r\u03a9e\u03c4 + \u03c6er) (9) The proposed study is focused on the homoclinic bifurcation and chaos of Eq. (9), which represents a generalized nonlinear time varying (NLTV) dynamic model of a spur gear pair. Both analytical and numerical solution techniques are employed to solve this equation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001277_j.procir.2016.11.009-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001277_j.procir.2016.11.009-Figure8-1.png",
        "caption": "Fig. 8. Illustration of the MTP machine given as industrial problem.",
        "texts": [
            " The delivery mechanisms for this pilot were mainly live videos and audio interactions with the engineering office from the academic lab through an advanced ICT configuration (Fig. 7). The students and the teaching staff were located in the lab. Various live cameras setups were used to show the lab demonstrators. At the same time, a presentation was shared through a web-conferencing tool, showing details. The industrial problem given for the presented Teaching Factory project, involved the case of designing a MultiTechnology Platform (MTP) that combines a milling working center with a robotic arm equipped with a laser head (Fig. 8). The simultaneous application of thermal load and vibration affect the performance of the machine in terms of dimensional accuracy and stability. The students had to design the swivel table in collaboration with the machine shop where the MTP would be installed. The industrial requirements were given in the form of specifications regarding the static compliance, thermal load and dynamic compliance of the final product. The pilot was organized in five collaborative cycles, through which the students would interact with the machine shop in order to solve the problem following the design cycle of the particular industrial practice (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001671_j.mechmachtheory.2018.10.007-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001671_j.mechmachtheory.2018.10.007-Figure1-1.png",
        "caption": "Fig. 1. Schematics of a circular spalling on the raceway for a ball bearing.",
        "texts": [
            " The relationship between the damage threshold and damage level is also used to determine the effective statistical features. The effective statistical features are applied to estimate the damage level. The test data given by the previous work in the list reference is utilized to verify the developed spalling propagation assessment algorithm. The results indicate that the established method can give a new approach to identify the spalling damage location and level for a ball bearing. While a spalling failure occurs on one bearing component, as depicted in Fig. 1 , the bearing vibration characteristics should be changed. As shown in Fig. 1 , D is the spalling depth and L is the spalling length. The vibration changes are determined by the spalling sizes and locations, which can be applied to detect the damage level and location. As to the study in Ref. [35] , the spalling profile can be a circular one. Thus, the spalling profile is formulated as a circular one. The spalling propagation is described by different damage level. Moreover, although the spalling is located in the center of the raceway as shown in Fig. 1 , the proposed method can also be used to detect the spalling cases with the damage area located in the motion line of the ball. To describe different damage level, a ratio parameter \u03b2 is determined as \u03b2= d d \u03c8 b \u00d7 100% (1) where d d is the damage radius, and \u03c8 b is the arc length of raceway groove, which is as follows: \u03c8 b = 2 R r acos ( D m \u2212 d 2 \u2212 2 \u03b3 2 R b ) (2) ( ( ( where R r is the raceway radius with the damage, D m is the pitch diameter, d 2 is the external diameter of inner raceway, R b is the ball radius, and \u03b3 is the bearing clearance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003657_j.measurement.2020.108855-Figure16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003657_j.measurement.2020.108855-Figure16-1.png",
        "caption": "Fig. 16. Vector method for fatigue prediction [56].",
        "texts": [
            " Based on model proposed by Leblanc and Nelias, Heras [55] obtained friction torque to consider full sliding in the roller\u2014raceway contact areas, which cannot be applied in large tilting moment cases. The purpose is to determine limitations of the analytical model and implement more revision, shown in Fig. 15. (3) Fatigue life Based on Hertz theory, Glodez\u030c [56 57] used vector method to calculate load distribution on the contact area, based on which stress-life method and strain-life method were used to calculate the fatigue life respectively, as shown in Fig. 16. Based on contact loads and stress distribution, Gao [58] discussed influences of geometric parameters, such as cross section, clearance and roller diameter et al, on bearing capacity and service life. Results revealed that ratio of curvatures and roller diameter had great impact on static carrying capability, whereas cross section clearance and initial contact load had more influence on service life. Based on ISO 281 rules, Gao [59] used Lundberg-Palmgren fatigue life theory to evaluate RCF reliability, considering geometric parameters of contact pairs, and material properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000584_j.jmatprotec.2013.11.014-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000584_j.jmatprotec.2013.11.014-Figure3-1.png",
        "caption": "Fig. 3. Schematic of vision sensor system.",
        "texts": [
            " It is noted that he work flat, driven by 3 independent stepping motors, has 3\u25e6 f freedom including moving in the Y-axis or X-axis, and rotating round the Z-axis. The mechanical part of the work flat is simply resented in Fig. 2. During the multi-layer deposition process, the elding gun is always stationary, and the work flat is lowered after layer is deposited. .2. Vision sensor design and image processing Owing to the variable NTSD in multi-layer deposition process, t should be monitored and controlled in real-time. Thus, a pasive vision sensor system is designed to observe the NTSD directly. s shown in Fig. 3, the vision sensor is placed opposite the welding ozzle. It consists of a CCD camera, a narrow-band and neural filter. he narrow-band filter was centered at 650 nm. With the approriate aperture of the CCD camera, a perfect bead image can be cquired. Fig. 4 displays the procedure of image processing for deposited bead height in GMAW-based LAM. Corresponding image processing algorithms, such as Gaussian filter, Sobel operator, and Hough transformation, were used to extract the characteristic information in the image, as seen in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002706_tmag.2014.2364988-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002706_tmag.2014.2364988-Figure15-1.png",
        "caption": "Fig. 15. Flux density distribution due to armature reaction for the 20-slot/18pole five-phase machine. (a) Conventional winding. (b) Proposed winding.",
        "texts": [],
        "surrounding_texts": [
            "The performance of both machines with different winding connections is quantitatively analysed using 2D FE simulation based on JMAG-Studio10.0. Both machines are simulated as motors running at the same rated speed of 600rpm. A. Simulation Results for The Three-Phase Machine Initially, to show the effect of the proposed winding on the stator MMF distribution, the flux distribution as well as the air gap flux density distribution variation with the peripheral angle are shown in Figs. 12 and 13 respectively, with the magnets removed from the model. It is clear that the 1 st component of the air gap flux density is completely cancelled in the air gap flux density. Moreover, the magnitude of the 5 th harmonic, torque producing flux component increased by approximately 3.5%. The machine is simulated with both winding configurations under rated phase current, rated speed, and maximum load angle assumed. The simulation results are given in Fig. 14 while the main conclusions are tabulated in Table V. Based on these results, the following conclusions can be drawn:  The induced eddy losses are generally decreased, with a significant reduction in both magnet and rotor core eddy losses.  The torque density is improved by approximately 3.5%; nearly the same as the enhancement obtained in the 5 th harmonic magnitude torque producing flux component. Moreover, the torque ripple magnitude is slightly reduced.  The THDs in both phase and line voltages are reduced with a slight increase in the fundamental voltage components.  A small zero sequence component, 0.07 pu, is induced in the delta connected winding. This component will depend on the magnitude of the third order harmonic voltage component of the three-phase voltages induced in the delta winding. This will be highly dependent on the PM design and magnetization direction. A parallel magnetization is used in the design to obtain a more sinusoidal voltage waveform and hence smaller zero sequence component. It is worth noting that this component will give rise to an increase in the total stator copper loss. However, it is evident from the simulation results that this effect is neglected. Moreover, stator cooling is generally simpler than rotor cooling. 0018-9464 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. TABLE V. SIMULATION RESULTS FOR THE THREE PHASE 12-SLOT/10-POLE MACHINE Conventional winding Proposed winding Average Torque (Nm) 13.8 14.3 (3.5% increase) Torque ripples (Nm) 1.87 (13.8%) 1.54 (10.8%) Copper loss (W) 40.5 40.6 Stator core loss (W) 21.6 16.5 (24% reduction) Magnet loss (W) 5.2 2.93 (44% reduction) Rotor loss (W) 14.14 5.63 (60% reduction) Fundamental phase voltage (V) 26.9 27.33 Phase voltage THD (%) 11.59 5.11 Fundamental line voltage (V) 46.59 47.35 Line Voltage THD (%) 5.14 3.36 Phase current harmonic component in delta winding (A) No delta winding I1 = 17.3A, I3 = 1.19A (a) B. Simulation Results for The Five-phase Machine Similar to the three-phase case, the flux distribution as well as the air gap flux density distribution with the peripheral angle for the designed five-phase machines are shown in Figs. 15 and 16 respectively, with the magnets removed from the model. It is clear that the fundamental air gap flux component is completely cancelled. Moreover, the magnitude of the 9 th harmonic, torque producing flux component, increased by approximately 1%, which yields an increased torque density by the same factor. This is clearly shown from the simulation results at rated conditions given in Table VI. The simulation results for rated conditions are also plotted in Fig. 17. Based on these results the following conclusions can be drawn:  The torque gain in the five-phase machine is smaller than the three-phase case. 0 0.005 0.01 0.015 0.02 12 13 14 15 16 Time, s T o rq u e , N m Conventional winding Proposed winding 0018-9464 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.  Although the operating frequency at rated speed is 1.8 times that in the three-phase machine, the corresponding eddy losses are smaller. This is because the space harmonics are inherently reduced using a multiphase winding when compared with the three-phase case.  The reduction in eddy loss is higher in the three-phase machine than in the five-phase machine.  The magnitude of the induced zero sequence component in the pentagon connected winding is neglected, 0.004pu, and its effect on the stator copper loss is also small.  Both phase and line voltage waveforms are highly improved and the corresponding THDs are significantly reduced. 0018-9464 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information."
        ]
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure1-1.png",
        "caption": "Fig. 1. Definition of assembly errors: (a) positions of gear shafts without assembly errors and (b) positions of gear shafts with assembly errors.",
        "texts": [
            " Tooth contact pattern and root stains of a pair of spur gears with AE are also calculated by the programs and compared with experimental results. It is found that the calculated results are agreement with the measured ones well. Finally, an example of calculating the real SCS and RBS of a pair of spur gears with ME, AE and TM is given in the paper. It is found that ME, AE and TM exert great effects on SCS and RBS of the gears. SCS and RBS of the same pair of gears are also calculated by ISO and JGMA standards for comparing with the FEM results. Fig. 1 is used to define AE of a pair of parallel-shaft gears. In Fig. 1(a), A0B0 and CD are shaft positions of a pair of parallel-shaft spur gears (Gear 1 and Gear 2) without AE. A0, B0, C, and D are four bearing positions to support the shafts A0B0 and CD. In Fig. 1(b), AB is the new position of A0B0 when there are AE. In order to define AE of the gears, a 3-D coordinate system (A0 XYZ) is built. XA0Y plane is a horizontal plane that passes through A0B0 and CD. It is called S-plane here. YA0Z plane is a vertical plane that passes through A0B0 and is perpendicular to the S-plane. It is called V-plane here. A0 is the origin. In the coordinate system (A0 XYZ), AE can be defined as center distance error XE on S-plane, center distance error ZE on V-plane, misalignment error h on S-plane and misalignment error / on V-plane as shown in Fig. 1(b). When XE, ZE, h and / are given, AB is positioned in the coordinate system (A0 XYZ). ME of gears are usually defined as profile deviation, helix deviations and pitch deviations in a two-dimensional (2-D), coordinate system. A gear checker can figure out these deviations. This paper defines ME of gears as 3-D shape deviation of tooth surfaces. This means that ME are the 3-D shape deviation of the machined tooth surface from the theoretical one along the line of action. Of course, this 3-D shape deviation includes profile deviation, helix deviations and pitch deviations of the gears",
            " In the 2-D coordinate system (O0 X0Y0), a line that passes through the point k and is parallel to the X0 axis is made. This line crosses the tooth profile of Gear 2 at the point k 0. k 0 is the responsive contact point of the point k on the tooth surface of Gear 2 and (k k 0) is used as a pair of contact points in LTCA with FEM. In the case that there are AE, the same idea can be used to find the responsive contact point of the point k on tooth surface of Gear 2. The following is descriptions how to find the responsive contact point of the point k. In 3-D coordinate system (A0 XYZ) as shown in Fig. 1, if position of the reference point k on the reference face of Gear 1 in the case that there are no AE is expressed as (Xk, Yk, Zk) and the new position of the point k when there are assembly errors XE, YE, h and / as shown in Fig. 1 is expressed as (XkE, YkE, ZkE), then (XkE, YkE, ZkE) can be calculated with Eq. (1) based on the principle of coordinate system transformations. X kE Y kE ZkE 2 64 3 75 \u00bc cos h sin h 0 sin h cos / cos h cos / sin / sin h sin / cos h sin / cos / 2 64 3 75 X k Y k Zk 2 64 3 75\u00fe X E 0 ZE 2 64 3 75 \u00f01\u00de A so-called Section 1 that passes through the point k(XkE, YkE, ZkE) and is parallel to the end face of Gear 2 (or parallel to the coordinate plane XA0Z as shown in Fig. 1) is made. Fig. 6 is the image of this Section 1. In Section 1, tooth profiles both of Gear 1 and Gear 2 are shown in bold solid lines. Since there are AE for Gear 1, tooth profile of Gear 1 in Section 1 is not an involute curves. But tooth profile of Gear 2 in Section 1 is still an involute curve. A 2-D coordinate system (O0 X0Y0) is made in Section 1. Where, O0 is the geometrical contact point on the tooth profile of Gear 2, X0 axis is the line of action of Gear 2 and Y0 axis is the vertical line to X0 axis. This 2-D system (O0 X0Y0) is also shown in Fig. 1(a). In Fig. 1(a), if the angle between X0 axis and S-plane is expressed as W (W = p/2 a0, a0 is pressure angle of the gears), position of the point k (XkE, YkE, ZkE) in the 2-D system (O0 X0Y0) is expressed as (X0k, Y0k) and position of the point O0 in the 3-D system (A0 XYZ) is expressed as (XO0, YkE, ZO0), then (X0k, Y0k) can be calculated with Eq. (2) based on the principle of coordinate system transformations. X 0k Y 0k \u00bc cos w sin w sin w cos w X kE X O0 ZkE ZO0 \u00f02\u00de On the other hand, in order to find the responsive contact point of the point k on tooth surface of Gear 2, a line that passes through the point k and is parallel to the X0 axis is made in the 2-D system (O0 X0Y0) as shown in Fig",
            " 8(b) and (c) are three teeth engagement and four teeth engagement FEM models built by the software automatically when a pair of high contact ratio gears is analyzed (see Fig. 9). Hertz formula is often used to calculate SCS of gears when tooth load is given. But it is difficult to be used here for a pair of gears with AE, ME and TM. So this paper calculates the SCS of gears with a \u2018\u2018Unit Force\u2019\u2019 method. It means to calculate tooth load distributed on unit contact area of a tooth surface. That is to say, dividing the tooth load with a contact area on the reference face as shown in Fig. 1(a). When the tooth load distributions are obtained in LTCA, RBS can be calculated with 3-D FEM and the model as shown in Fig. 20(a). Since there is no commercial FEM software available that can do this analysis, FEM software used for contact analysis and strength calculations of a pair of spur gears with AE, ME and TM are developed in a personal computer through many years\u2019 efforts based on the theory and methods presented in this paper. The following is the flowchart used for FEM software development",
            " Step 3: Input FEM mesh-dividing parameters for the gears Some parameters are used to control FEM mesh-dividing pattern of the gears. That is to say, to determine where should be fine divided and where should be roughly divided. Usually, tooth contact areas and tooth root are fine divided. FEM mesh-dividing pattern of the gears can be changed simply through changing values of these FEM mesh-dividing parameters. Step 4: Input machining error data file, assembly errors and tooth modification parameters A data file is used to input machining errors as shown in Fig. 2 when they are measured. Assembly errors as shown in Fig. 1(b) are inputted directly as parameters. Tooth modification equations as shown in Fig. 4 are installed in the software. Modification curve and modification quantity can be changed simply by two parameters, one is used to stand for type of the modification curve and the other is used to stand for the modification quantity. Step 5: Divide FEM meshes of the pinion and the wheel automatically Programs are developed to be able to divide FEM meshes of the pinion and the wheel automatically when structure dimensions, gearing parameters, tooth engagement position parameter and FEM mesh-dividing parameters are given",
            " Of course ME, AE and TM have been given before FEM mesh dividing. Step 6: Form pairs of contact points on contact reference faces Pairs of contact points on the contact reference faces as shown in Fig. 5 are made according to the methods stated in Sections 3.1 and 3.2. Step 7: Calculate backlash ek of every pair of contact points Backlash ek of every pair of contact points is calculated geometrically and automatically when the pair of spur gears with ME, AE and TM is positioned in 3-D coordinate system (A0 XYZ) as shown in Fig. 1 and pairs of contact points are made. Step 8: Calculate deformation influence coefficients of the contact points on the contact reference faces by 3-D, FEM When the pairs of contact points on Gear 1 and Gear 2 as shown in Fig. 5 are made, deformation influence coefficients of all the assumed contact points are calculated by 3-D, FEM. For an example, when to calculate deflection influence coefficients of a contact point on the reference face of Gear 1 as shown in Fig. 5(a), FEM model as shown in Fig",
            " Rademacher\u2019s calculation results are also given in Figs. 10 and 11. From Figs. 10 and 11, it is found that FEM results are well agreement with Rademacher\u2019s experimental results. Fig. 12 is FEM results of the maximum surface contact stresses obtained at the same time when FEM calculations are performed. Tooth contact pattern and root strains of a pair of spur gears as shown in Fig. 14 are measured when assembly errors h = 0.42 , / = 0.04 , XE = 2.1 mm and ZE = 0.2 mm are given to the gear shaft A0B0 in Fig. 1. These gears are ground under the accuracy requirement of JIS 1st grade. A so-called power-circulating form gear test rig is used to do the tests at a very low speed (1.65 rpm) under torque T = 294 N m. Fig. 15 is the test gearbox used in the test rig. In Fig. 15, a removable support is used to give AE to the shaft of Gear 1 by changing the position of this support. Fig. 16 is tooth contact pattern measured. Fig. 17 is the tooth contact pattern calculated under the same conditions. In Fig. 17, A is the areas of double pair tooth contact and B is the area of single pair tooth contact",
            " 13 by using the single pair tooth contact factors ZB (Pinion) or and ZD (Wheel), finally use the converted contact stress for surface contact strength calculation. JGMA standards use tooth contact stress at the pitch point for surface contact strength calculation. For the pair of gears as shown in Table 1, LTCA and SCS calculations are performed at outer limit and inner limit of the single pair tooth contact area when no ME, AE and TM are considered. Figs. 21 and 22 are contour lines of calculated SCS distributed on the reference face as shown in Fig. 1(a). In Figs. 21 and 22, the horizontal axis (X-axis) is face width of the gears and the vertical axis (Y-axis) is contact width width as shown in Fig. 1(a). Geometrical contact line of the gears is located at the center of contact width (Y = 0). Y < 0 is the side from the geometrical contact line to the root and Y > 0 is the side from the geometrical contact line to the tip. From Figs. 21 and 22, it is found that contact stress distributions are almost the same along the lead in Case 1. It is also found that the maximum SCS at the outer limit contact is greater than the one at the inner limit contact. So, outer limit contact is used as the position to calculate SCS for surface contact strength calculation of the pair of gears in this paper",
            " 21. But position of the maximum stress distribution line is moved to the side Y < 0 for the effect of misalignment error. Fig. 25 is contour lines of SCS when the misalignment error on the vertical plane of the plane of action is increased from 0.04 into 0.4 . It is found that tooth contact pattern has a bigger change by comparing Fig. 25 with Figs. 24 and 21, but the maximum SCS has a very little change. Fig. 26 is the machining error of the wheel distributed on the reference face as shown in Fig. 1(a). This machining error is used in LTCA and SCS calculations of the pair of gears. Fig. 27 is contour lines of SCS calculated in Case 4. It is found that machining errors have greater effects on tooth contact pattern and contact stress distribution by comparing Fig. 27 with Fig. 21. Fig. 28 is contour lines of SCS calculated in Case 5. It is found that tooth contact pattern is changed from a uniform contact into a center heavy contact for the effect of lead crowning. The maximum contact stress also has a bigger change from 1650 into 2064 MPa"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001165_tie.2010.2046579-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001165_tie.2010.2046579-Figure3-1.png",
        "caption": "Fig. 3. Spatial relations of the frames and angles.",
        "texts": [
            " One end of the arm is attached to a counterweight, while two dc motors with propellers are installed at the other end to create forces that drive the propellers. Two motors\u2019 axes are parallel, and the thrust vector is normal to the frame. Three encoders are connected to the helicopter in order to measure the elevation, pitch, and travel angles of the body, and two voltage amplifiers are used to realize the control action in the system. The frontand back-motor voltages are the control input of the system. The free-body diagram of the 3-DOF helicopter [24] is shown in Fig. 2, and its spatial relations of the frames and angles are shown in Fig. 3. Applying the Euler\u2013Lagrange formula, the dynamics of the helicopter can be described by differential equations (see also in [13] and [15]). At first, we consider the elevation motion. The twisting moment of this axis is controlled by the composition of forces generated by the propellers J\u03b5\u03b5\u0308 = KfLa cos p(Ff + Fb) \u2212 mhgLa sin(\u03b5 + \u03b10) (1) where \u03b10 is the initial angle between the helicopter arm and its base. The pitch motion is described by the following: Jpp\u0308 = KfLh(Ff \u2212 Fb). (2) When the force generated by the front motor is greater than that by the back one, the helicopter body will pitch in the positive direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001255_tro.2012.2217795-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001255_tro.2012.2217795-Figure2-1.png",
        "caption": "Fig. 2. Geometric model of a CDPR with two cables. (a) Operation mode I. (b) Operation mode II.",
        "texts": [
            " In particular, the possibility that both cables may be simultaneously parallel to k is discarded. Since the cable wrenches and the external load represent pure forces, and three screws of equal pitch are linearly dependent if and only if they belong to a planar pencil [40], G, A1 , A2 , B1 , and B2 must necessarily rest, at the equilibrium, in a plane parallel to k. Accordingly, xz and x\u2032z \u2032 must be superimposed. If y and y\u2032 point in the same direction, the robot is said to work in operation mode I [see Fig. 2(a)] and the rotation matrix between Oxyz and Gx\u2032y\u2032z \u2032 is RI = \u23a1 \u23a2\u23a3 c\u03b8 0 s\u03b8 0 1 0 \u2212s\u03b8 0 c\u03b8 \u23a4 \u23a5\u23a6 (21) whereas if y and y\u2032 point in opposite directions, the robot is said to work in operation mode II [see Fig. 2(b)] and the rotation matrix is RI I = \u23a1 \u23a2\u23a3 c\u03b8 0 s\u03b8 0 \u22121 0 s\u03b8 0 \u2212c\u03b8 \u23a4 \u23a5\u23a6 (22) where \u03b8 is the angle formed by x\u2032 with x through a positive rotation around y\u2032, and s\u03b8 and c\u03b8 stand for sin \u03b8 and cos \u03b8, respectively. If b\u2032 i is the coordinate vector of Bi in the Gx\u2032y\u2032z \u2032 frame, then ri = RI (\u03b8)b\u2032 i or ri = RI I (\u03b8)b\u2032 i . Distinguishing these two operation modes is important, since they provide distinct equilibrium configurations (and one set cannot be obtained from the other by planar movements). Indeed, when initially assembled, the CDPR moves to a pose corresponding to one operation mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000150_j.jmatprotec.2007.10.051-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000150_j.jmatprotec.2007.10.051-Figure11-1.png",
        "caption": "Fig. 11 \u2013 Simplified schematic representation of the combustion casing and internal flange together with three-dimensional axis designations (not to scale).",
        "texts": [],
        "surrounding_texts": [
            "The current trials have demonstrated the potential of SMD technology in the fabrication of complex engineering structures. Within the aerospace sector, the near net shape capability of additive SMD should offer obvious benefits in terms of improved materials yield and a reduction in mechanical surface removal operations\u2014both key factors controlling the cost of individual components. SMD provides a relatively rapid manufacturing process for large-scale features and can be automated through efficient multi-axis and multi-arm robotic controlled welding systems. n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 439\u2013448 446 j o u r n a l o f m a t e r i a l s p r o c e s s i However, detailed consideration must be given to the ultimate metallurgical and microstructural condition evolved during SMD manufacture. In particular, the present study has highlighted the presence of deleterious phases within the Alloy 718 MIG weld deposition structures (i.e. relatively brittle laves and phase segregation encouraged by extended time at high temperature during either deposition, through the cumulative exposure to transient deposition, or subsequent post-deposition heat treatment (PDHT)). The present study has confirmed previous reports (Cieslak et al., 1986; Jones et al., 1989), noting that these phases evolve in preferred orientations, potentially inducing an anisotropic mechanical response under subsequent loading. Volumetric changes associated with phase transformation may also have a local shearing effect across interfaces. In addition, associated discontinuities in the form of cracks and shrinkage porosity have been identified. In DS/ML weld deposition structures, the degree of reheating introduced during overlay operations appears to be critical for controlling the introduction of these defects (Metallographic Characterisation of IN718, 2003; Bowers et al., 1997; Qian and Lippold, 2003a,b). However, despite systematic optimization of the major weld control parameters such features persist. This may prove to be a significant limitation in considering MIG for aerospace applications. Added to this, the adverse effects of residual stress have also been demonstrated (affected during either machining or PDHT operations) through the introduction of macroscopic cracking in this feature of the demonstrator casing component. For high integrity components in aero gas turbines subjected to relatively demanding loading regimes, such phases as laves and delta must either be eliminated through precise thermo-mechanical processing or otherwise demonstrated to be \u201cbenign\u201d under typical service conditions (i.e. the component demonstrates sufficient \u201cphase tolerance\u201d and resists the formation of a critically sized crack from a pre-existing flaw over a specified period of operation). Given this philosophy, the major engine manufacturers appear to be adopting consistent strategies for additive manufacture (AM), restricting the techniques\u2019 potential use to non-critical component locations at this stage of process maturity (Kinsella, 2006). Even in the present example of the developmental combustor casing, the SMD flange was designed as an additive feature upon an internal wall pedestal, ensuring the flange itself would not experience design limiting hoop stresses. However, casing structures routinely experience at least one major fatigue cycle per flight; the thermal\u2013mechanical cycle imposed during normal engine use and shut down. High cycle fatigue may also be superimposed as a result of vibration. Therefore, improvements in additive technologies to avoid the introduction of crack initiating defects would clearly be advantageous. It is unlikely that MIG-based SMD used for hybrid near net shape components without a homogenisation treatment can eliminate the laves phase formation, due to the restrictions on pool size and hence the influence on freezing rate and segregation. To this end, methods of metal deposition, having smaller volumetric build unit sizes, may prove more suitable for the manufacture of higher integrity components. By controlling the build up of material on the microscopic scale (for example individual molten \u201cpools\u201d may be less than a millimetre diam- deposition) structure in Alloy 718. eter with some AM techniques) any incipient porosity, the evolving grain size and the internal microstructure are all fundamentally smaller. The resultant volume of material should also demonstrate more homogeneous mechanical properties and any long range residual stresses minimized. Macro-scale demonstration components are currently under manufacture for future detailed characterization (Fig. 14)."
        ]
    },
    {
        "image_filename": "designv10_1_0001859_j.msea.2018.10.051-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001859_j.msea.2018.10.051-Figure2-1.png",
        "caption": "Fig. 2. On the left is a schematic representation of the printed pillars along with location of EBSD and tensile testing coupons extracted through wire-EDM. On the right is a detailed view of the dogbone specimen's geometry (thickness is 1 mm); all units are in mm.",
        "texts": [
            " Five scan speed values and six laser power values were used (see Table 1), resulting in a total of 30 combinations. Substrate temperature was kept constant at 200 \u00b0C to match the preheat temperature commonly used in our SLM 125HL\u00ae system. Three combinations of laser power and laser scan speed were selected after implementing the Rosenthal model (see details on the model results below) and used to print samples with our SLM 125HL\u00ae LPBF machine. The builds were square pillars with a size of 12\u00d712\u00d750mm, printed vertically (e.g., parallel to the 50mm side), as shown in Fig. 2, using a 30 \u00b5m powder bed layer thickness and employing a 10mm stripe scanning strategy with a 90\u00b0 hatch rotation between consecutive layers. The powder used was gas-atomized 316 L stainless steel (d10 = 25.24 \u00b5m, d50 = 40.09 \u00b5m, d90 = 61.37 \u00b5m), provided by SLM Solutions, the manufacturer of the L-PBF system. The chemical composition of the powder, as provided by the manufacturer, is shown in Table 2. The build plate was preheated to 200 \u00b0C and kept at the same temperature for the entire duration of the printing process, which was carried out in an inert nitrogen atmosphere with oxygen concentration< 100 ppm. After being printed, the pillars were cut using a wire-EDM machine (Mitsubishi FA20S) in order to obtain smaller, square specimens for microstructural analysis, as well as dogbone specimens for tensile testing. As seen in Fig. 2, microstructural analysis was performed close to the top and the bottom of the build, while the tensile specimens were extracted from the central section of the pillars. Mass density was measured using image analysis on the same cross-sections used for microstructural analysis. Porosity quantification was performed after converting micrographs acquired with optical microscopy (Olympus BX53M) into binary images using ImageJ software. After being machined, dogbone specimens (geometry details are provided in Fig. 2) were polished down to a thickness of 1mm using SiC sand paper to avoid premature failure during tensile testing caused by the presence of surface defects. The samples were mounted in an Instron 8801 universal testing machine where they were uniaxially loaded in tension at a nominal strain rate of 10\u22123 s\u22121. The strainmeasuring unit was a standard video extensometer (SVE 2663, Instron), which tracks the relative displacement of two small dots, drawn on the two opposite ends of the gauge length using a marker prior to the beginning of the experiments",
            "5%) with circular pores generally smaller than 10 \u00b5m, most likely due to entrapment of gas bubbles during solidification. Only Sample 3 shows occasional signs of larger, non-spherical, lack-of-fusion pores, such as the one highlighted in Fig. 4. Kamath et al. [26] described such pores as the result of insufficient melt penetration in the z direction and Cherry et al. [27] showed how they can play a detrimental role to mechanical properties of manufactured parts. Representative EBSD orientation maps, which were acquired in two distinct locations for each sample (see Fig. 2) and color coded according to standard IPF color key with reference to the build direction z, are shown in Fig. 5. The majority of grains in all three builds have a preferred crystallographic orientation along<100> {001}. Thijs and coworkers [28] have shown how the strong directionality of heat flow during L-PBF produces highly anisotropic microstructures and, as a result, how most grains exhibit high aspect ratios and develop lengths of hundreds of microns, spanning across several printed layers without being limited by melt pool boundaries"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002031_tie.2016.2542787-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002031_tie.2016.2542787-Figure2-1.png",
        "caption": "Fig. 2. The architecture of the positioning motion system (driven by a DC motor) with digital servo amplifier (electrical driver)",
        "texts": [
            " On the other hand, as mentioned in Remark 1, though \u03931 will not dramatically affect the total adaptation gain \u0393 at steady state, a very large \u03931 is still not practical, since in the adaptive law (4), if the there exists a measurement noise of x(t), making x\u0303 inaccurate, then a large \u03931 will lead to significant errors of the derivation of estimations. The motion system considered here is a positioning system, in which an inertia load is directly driven by a dc motor. The structure of the system is presented in Fig. 2, and as described in [19], the motion dynamics of the inertia load can be given as my\u0308 = Ktu\u2212F(y\u0307)+ f (t,y, y\u0307), F(y\u0307) = vy\u0307+Ff (y\u0307), Ff (y\u0307) = a2[tanh(c2y\u0307)\u2212 tanh(c3y\u0307)] +a1 tanh(c1y\u0307), (39) where m and y represent the moment of inertia and the angular displacement, respectively; Kt is the torque constant with respect to the unit of input voltage; u is the control input; F(y\u0307) represents static friction force with respect to velocity, which includes viscous friction denoted by vy\u0307 and the Stribeck effect Ff (y\u0307), where v represents the combined coefficient of the modeled damping and viscous friction on the load and the actuator rotor, a1 and a2 represent different friction levels; and c1, c2, c3 denote various shape coefficients to approximate various friction effects; and f (t,y, y\u0307) represents other disturbances such as dynamic friction effects and other uncertain nonlinearities which cannot be modeled precisely"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure78-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure78-1.png",
        "caption": "Fig. 78 a View of the demonstration par; b result of the first attempt for manufacturing the AM part; c detailed view of the featured cutout [113]",
        "texts": [
            " In the process of arc additive manufacturing, the technology of \u201ccasting and forging\u201d was introduced to develop the integrated casting and forging additive. The system successfully produced high-performance metal forgings with a length of about 2.2 m, a weight of 260 kg, and a surface roughness of 0.02 mm [112]. Figure 77 shows the manufacturing process of the cast-forged integrated hybrid arc additive and the final formed part. Josef applied WAAM forming crane-related structures. The structure is complex and requires high mechanical properties [113]. This work (shown in Fig. 78) studies the feasibility of fabricating near-net-shaped structural members directly on sub-assemblies. It is suitable for crane structures without post-processing, using cold metal transfer process (CMT). Single- and multi-pass welding experiments were used to identify and validate appropriate process parameters, and then the parameters obtained were used to make wall structures. The optical measurement of the obtained geometry is performed to determine the mechanical properties of the full- welded metal in different directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001206_tmag.2012.2205014-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001206_tmag.2012.2205014-Figure1-1.png",
        "caption": "Fig. 1. Geometry definition for cylindrical magnets. The spherical coordinate definition is shown for the axially magnetized case only.",
        "texts": [
            " As this minimization is application specific, only the far-field optimal geometry for the dipole approximation will be considered in this paper and the quadrupole term term will be minimized by finding the value of that sets the contribution of the term to zero at every location in space. Cylindrical permanent magnets are most readily available in the axially magnetized and diametrically magnetized forms. Without loss of generality, the axis of the cylinder is aligned with the Cartesian -axis, as shown in Fig. 1. The parameter that characterizes the shape of the cylinder is the diameter-to-length aspect ratio . The following equations summarize some useful relationships using this parametrization, where is the radius of the minimum bounding sphere and is the volume of the cylinder: (11) For materials like NdFeB with small susceptibilities , (1) and (8) simplify to , which, given a minimum bounding sphere, maximizes when . However, maximizing the dipole moment of the magnet given a sphere size does not ensure a dipole approximation with minimal error; for that, a multipole expansion of the shape is required",
            " In the global frame, is the vector from the center of the magnetized material to the point of interest and will be described in a spherical frame with: measured from the global -axis and pointing in the positive direction, measured from the positive -axis and pointing in the positive direction, and taken as the magnitude of the vector with pointing in the direction (the difference in variable name is to avoid confusion when switching between spherical and coordinate-free descriptions). For reference, Fig. 1 shows the coordinate system with both the global and material coordinate systems aligned. 1) Axially Magnetized Cylinder: The multipole expansion defined by (5) is adapted to axially magnetized cylinders by taking to be on the top surface, on the bottom surface, and 0 on the cylindrical wall (12) where Using the substitution , can be further simplified odd even where (13) The magnetic field of an axially magnetized cylindrical magnet described in cylindrical coordinates is then (14) where is the magnitude of the dipole moment ",
            " The average error associated with the different optimal geometries is very close, with the cubic magnet having the least and the axially magnetized magnet having the most. Figs. 8 and 9 show the variation of error as a function of angle at a given distance. To determine the error at a given position, it is only necessary to multiply the average error given in Fig. 7 by the value in the error variation plot that corresponds to the angular position. axially magnetized cylindrical magnet with . The magnetization axis of the magnet corresponds to . See Fig. 1. to and . See Figs. 1 and 2. The diametrically magnetized cylinder has both the highest average error and the largest error range, which appears in conflict with the observations in the work by Fountain et al. [21], which shows diametrically magnetized magnets are preferable to the axially magnetized magnets. However, upon closer inspection, the least squares fit of the dipole approximation in the work by Fountain et al. is based on field measurements taken only along the magnetization axis of the magnet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure7.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure7.1-1.png",
        "caption": "Figure 7.1. The moment arms (d\u22a5) for the biceps femoris muscle. A moment arm is the right-angle distance from the line of action of the force to the axis of rotation.",
        "texts": [
            " The application of angular kinetics is illustrated with the principles of Inertia and Balance. The rotating effect of a force is called a torque or moment of force. Recall that a moment of force or torque is a vector quantity, and the usual two-dimensional convention is that counterclockwise rotations are positive. Torque is calculated as the product of force (F) and the moment arm. The moment arm or leverage is the perpendicular displacement (d\u22a5) from the line of action of the force and the axis of rotation (Figure 7.1). The biceps femoris pictured in Figure 7.1 has moment arms that create hip extension and knee flexion torques. An important point is that the moment arm is always the shortest displacement between the force line of action and axis of rotation. This text will use the term torque synony- mously with moment of force, even though there is a more specific mechanics-of-materials meaning for torque. CHAPTER 7 Angular Kinetics 169 In algebraic terms, the formula for torque is T = F \u2022 d\u22a5, so that typical units of torque are N\u2022m and lb\u2022ft. Like angular kinematics, the usual convention is to call counterclockwise (ccw) torques positive and clockwise ones negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.34-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.34-1.png",
        "caption": "FIGURE 5.34. A spherical wrist and its kinematics.",
        "texts": [
            " The manipulator is multibody so that it holds the main power units and provides a powerful motion for the wrist point. Figure 5.33 illustrates an example of an articulated manipulator with three DOF . This manipulator can rotate relative to the global frame by a base motor at M1, and caries the other motors at M2 and M3. Changeable wrists are complex multibodies that are made to provide three rotational DOF about the wrist point. The base of the wrist will be attached to the tip point of the manipulator. The wrist, the actual operator of the robot may also be called the end-effector, gripper, hand, or tool. Figure 5.34 illustrates a sample of a spherical wrist that is supposed to be attached to the manipulator in Figure 5.33. To solve the kinematics of a modular robot, we consider the manipulator and the wrist as individual multibodies. However, we attach a temporary coordinate frame at the tip point of the manipulator, and another temporary frame at the base point of the wrist. The coordinate frame at the temporary\u2019s tip point is called the takht, and the coordinate frame at the base of the wrist is called the neshin frame. Mating the neshin and takht frames assembles the robot kinematically. The kinematic mating of the wrist and arm is called assembling. The coordinate frame B8 in Figure 5.33 is the takht frame of the manipulator, and the coordinate frame B9 in Figure 5.34 is the neshin frame of the wrist. In the assembling process, the neshin coordinate frame B9 sits on the takht coordinate frame B8 such that z8 be coincident with z9, and 5. Forward Kinematics 281 x8 be coincident with x9. The articulated robot that is made by assembling the spherical wrist and articulated manipulator is shown in Figure 5.35. The assembled multibody will always have some additional coordinate frames. The extra frames require extra transformation matrices that can increase the number of required mathematical calculations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure2.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure2.10-1.png",
        "caption": "Fig. 2.10",
        "texts": [
            " The normal stresses for all section directions have the same value \u03c3\u03be = \u03c3\u03b7 = \u03c30 and no shear stresses appear (cf. Section 2.2.1). E2.2 Example 2.2 A plane stress state is given by \u03c3x = 50 MPa, \u03c3y = \u221220 MPa and \u03c4xy = 30 MPa. Using Mohr\u2019s circle, determine a) the principal stresses and principal directions, b) the normal and shear stress acting in a section whose normal forms the angle \u03d5 = 30\u25e6 with the x-axis. Display the results in sketches of the sections. Solution a) After having chosen a scale, Mohr\u2019s circle can be constructed from the given stresses (in Fig. 2.10a the given stresses are marked by green circles). From the circle, the principal stresses and directions can be directly identified: 2.2 Plane Stress 67 b) To determine the stresses in the inclined section we introduce a \u03be, \u03b7-coordinate system whose \u03be-axis coincides with the normal of the section. The unknown stresses \u03c3\u03be and \u03c4\u03be\u03b7 are obtained by plotting in Mohr\u2019s circle the angle 2\u03d5 in the reversed direction to \u03d5. Doing so we obtain: \u03c3\u03be = 58.5 MPa , \u03c4\u03be\u03b7 = \u221215.5 MPa . The stresses with their true directions and the associated sections are displayed in Fig. 2.10b. E2.3Example 2.3 The two principal stresses \u03c31 = 40 MPa and \u03c32 = \u221220 MPa of a plane stress state are known. Determine the orientation of a x, y-coordinate system with respect to the principal axes for which \u03c3x = 0 and \u03c4xy > 0. Calculate the stresses \u03c3y and \u03c4xy. Solution Using the given principal stresses \u03c31 and \u03c32, the properly scaled Mohr\u2019s circle can be drawn (Fig. 2.11a). From the circle the orientation of the unknown x, y-system can be obtained: the counterclockwise angle 2\u03d5 (from point \u03c31 to point P ) in Mohr\u2019s circle corresponds to the clockwise angle \u03d5 between the 1-axis and the x-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.14-1.png",
        "caption": "FIGURE 5.14. A perpendicular P\u22a5R(90) link.",
        "texts": [
            "39) The origin of the Bi\u22121 frame can be chosen at any point on the zi\u22121-axis or parallel to zi\u22121-axis arbitrarily. One simple setup is to locate the origin oi of a prismatic joint at the previous origin oi\u22121. This sets ai = 0 and furthermore, sets the initial value of the joint variable di = 0, which will vary when oi slides up and down parallel to the zi\u22121-axis. Example 146 Link with P\u22a5R or P\u22a5P joints. When the proximal joint of link (i) is prismatic and its distal joint is either revolute or prismatic, with perpendicular axes as shown in Figure 5.14, then \u03b1i = 90deg (or \u03b1i = \u221290 deg), \u03b8i = 0, ai is the distance between the joint axes on xi, and di is the only variable parameter. Therefore, the transformation matrix i\u22121Ti for a link with \u03b1i = 90deg and P\u22a5R or P\u22a5P joints, known as P\u22a5R(90) or P\u22a5P(90), is i\u22121Ti = \u23a1\u23a2\u23a2\u23a3 1 0 0 ai 0 0 \u22121 0 0 1 0 di 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.40) 252 5. Forward Kinematics while for a link with \u03b1i = \u221290 deg and P\u22a5R or P\u22a5P joints, known as P\u22a5R(\u221290) or P\u22a5P(\u221290), is i\u22121Ti = \u23a1\u23a2\u23a2\u23a3 1 0 0 ai 0 0 1 0 0 \u22121 0 di 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (5.41) Example 147 Link with P`R or P`P joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.15-1.png",
        "caption": "FIGURE 2.15. Application of Euler angles in describing the configuration of a top.",
        "texts": [
            " If \u03b8\u2192 0 then the Euler rotation matrix BAG = Az,\u03c8Ax,\u03b8Az,\u03d5 approaches to BAG = \u23a1\u23a3 c\u03d5c\u03c8 \u2212 s\u03d5s\u03c8 c\u03c8s\u03d5+ c\u03d5s\u03c8 0 \u2212c\u03d5s\u03c8 \u2212 c\u03c8s\u03d5 \u2212s\u03d5s\u03c8 + c\u03d5c\u03c8 0 0 0 1 \u23a4\u23a6 = \u23a1\u23a3 cos (\u03d5+ \u03c8) sin (\u03d5+ \u03c8) 0 \u2212 sin (\u03d5+ \u03c8) cos (\u03d5+ \u03c8) 0 0 0 1 \u23a4\u23a6 (2.121) and therefore, the angles \u03d5 and \u03c8 are indistinguishable even if the value of \u03d5 and \u03c8 are finite. Hence, the Euler set of angles in rotation matrix (2.106) is not unique when \u03b8 = 0. Example 23 Euler angles application in motion of rigid bodies. The zxz Euler angles are good parameters to describe the configuration of a rigid body with a fixed point. The Euler angles to show the configuration of a top are shown in Figure 2.15 as an example. Example 24 F Angular velocity vector in terms of Euler frequencies. A Eulerian local frame E (o, e\u0302\u03d5, e\u0302\u03b8, e\u0302\u03c8) can be introduced by defining unit vectors e\u0302\u03d5, e\u0302\u03b8, and e\u0302\u03c8 as shown in Figure 2.16. Although the Eulerian frame is not necessarily orthogonal, it is very useful in rigid body kinematic analysis. 2. Rotation Kinematics 57 The angular velocity vector G\u03c9B of the body frame B(Oxyz) with respect to the global frame G(OXY Z) can be written in Euler angles frame E as the sum of three Euler angle rate vectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003417_j.asej.2017.08.001-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003417_j.asej.2017.08.001-Figure3-1.png",
        "caption": "Fig. 3. Link frame assignment for 5DOF robot arm model.",
        "texts": [
            " The robotic arm can be modeled as an open-loop chain with many links connected in series by joints that are driven by stepper motors. Robot kinematics is related to the study of the geometry of the motion of a robot. Being more complex, difficult to solve, more common to be exist in research papers, the author choose the 5 DOF to be the testbed for simulation and implementation. Fig. 2 shows a five link robot which will be used to study the Soft-Computing based tool methods for solving the IK problem, its simulation results and experimental study. Fig. 3 shows link frame assignment for robot arm. Table 1 shows the DH parameters for the robot arm. Where ai-1 is the length of the common normal, ai-1 is the angle about common normal, from old Z-axis to new Z-axis, di is the offset along previous Z-axis to the common normal and bi is the angle about previous Z-axis from old X-axis to new X-axis. For the 5 DOF robot arm, the forward kinematic equations are [15]: r \u00bc l1 cos\u00f0h2\u00de \u00fe l2 cos\u00f0h2 \u00fe h3\u00de \u00fe l3 cos\u00f0h2 \u00fe h3 \u00fe h4\u00de \u00f01\u00de ZE \u00bc l0 \u00fe l1 sin\u00f0h2\u00de \u00fe l2 sin\u00f0h2 \u00fe h3\u00de \u00fe l3 sin\u00f0h2 \u00fe h3 \u00fe h4\u00de \u00f02\u00de Please cite this article in press as: El-Sherbiny A et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.39-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.39-1.png",
        "caption": "Fig. 17.39 Current transfer locus diagram",
        "texts": [
            " The equivalent circuit of the induction machine in Fig. 17.38 is similar to a transformer equivalent circuit. The stator leakage inductance, magnetizing inductance, and rotor leakage inductance calculated on the stator side are described by the reactance parameters X\u03c31, Xn, and X \u2032 \u03c32 for the frequency \u03c91. For the conversion of the rotor parameters to the stator side the factor \u03c91/\u03c92 is used. As a result the slip-dependent resistance R\u2032 2/s appears on the rotor side. The current transfer locus (Fig. 17.39) describes the operating behavior. The two significant points of this diagram are the idle speed point P0 (s = 0) and the point P\u221e (s = \u221e). Through a third point, e.g., the short-circuit point PK at standstill of the machine (s = 1) the circle is completely defined; its center is at point A and its diameter is given by the section P0 P\u03a6 . Similar to transformers, iron losses can be considered by using extra resistance in the cross branch in Fig. 17.38. Operating Characteristics The characteristic M(\u03a9) exhibits a breakdown torque Mk with the assigned breakdown slip sk"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000592_j.fss.2010.09.002-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000592_j.fss.2010.09.002-Figure1-1.png",
        "caption": "Fig. 1. Two inverted pendulums on carts.",
        "texts": [
            " Step 5: Li (s) is chosen so that L\u22121 i (s) is a proper stable transfer function and Hi (s)Li (s) is a proper SPR transfer function. Step 6: Construct the fuzzy controller (23) and (24), and the adaptation law (25) where Nussbaum function is chosen as N ( i ) = 2 i cos( i ). 4. Simulation examples In the following we will show two examples to verify the effectiveness of the proposed approach. Example 1. We consider two inverted pendulums, which are connected by a moving spring mounted on two carts [34]. Their configuration is shown in Fig. 1. We assume that the pivot position of the moving spring is a function of time that can change along the length l of the pendulums. The motion of the carts is specified. For this example we specify this motion as sinusoidal trajectories. The input to each pendulum is the torque ui , i = 1, 2 applied at the pivot point. The dynamic equations of the inverted double pendulums can be described as\u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 \u03081 = g cl 1 + 1 cml2 u1 + { k[a(t) \u2212 cl] cml2 [\u2212a(t) 1 + a(t) 2 \u2212 x1 + x2] } \u2212 (m/M)\u0307 2 1 sin( 1) \u03082 = g cl 2 + 1 cml2 u2 + { k[a(t) \u2212 cl] cml2 [\u2212a(t) 2 + a(t) 1 + x1 \u2212 x2] } \u2212 (m/M)\u0307 2 2 sin( 2) (38) where i and \u0307i are the angles and angular velocities of the pendulums, respectively, with respect to vertical axes, u1 and u2 are the control torques applied to the pendulums, c = m/(M + m), k and g are spring and gravity constants, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000051_s0360-3199(02)00027-7-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000051_s0360-3199(02)00027-7-Figure2-1.png",
        "caption": "Fig. 2. Outline of experimental apparatus.",
        "texts": [],
        "surrounding_texts": [
            "The water electrolysis of 10 wt% KOH aqueous solution was conducted under atmospheric pressure using Ni\u2013Cr\u2013Fe alloy (Inconel 600) as electrodes. In order to vary void fraction between electrodes, parameters as follows were controlled: current density, with or without separator, system temperature, and space, height, inclination angle, surface wettability of electrodes. As easily postulated from hydrodynamic and two-phase Gow point of view, the increase of void fraction would occur by following conditions; increasing current density, with separator, higher temperature, narrower space, larger height, horizontal setting of electrodes, and higher wettability. 1. DC power supplier 8. Liquid vessel ranged from 0.1 to 0:9 A=cm2. Hydrogen gas generated was collected to H2 collector bottle through water, while oxygen gas was released to open air. The temperature of the KOH aqueous solution was controlled to 20 \u25e6 C, 40 \u25e6 C, or 60 \u25e6 C by cartridge heaters. The inclination angle of electrodes was either vertical or horizontal. Rotation of the whole liquid container enabled horizontal setting of electrodes. The surface of electrodes was polished after several experiments to keep same overvoltage on electrodes. The surface wettability was tested to either lower surface wettability with silicone oil treatment or without treatment. The e0ciency of hydrogen production by water electrolysis was qualitatively evaluated and compared by the voltage value at a certain current density. Since the amount of hydrogen gas is proportional to electric current, the voltage value becomes good index to represent electric power necessary to produce a certain mass Gux of hydrogen when compared among data of the same current density. The voltage between electrodes was measured by voltmeter, while the DC current was estimated by measuring voltage drop of standard resistance (=0:5 mP). The experimental conditions are summarized in Table 1."
        ]
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.19-1.png",
        "caption": "FIGURE 5.19. Non-standard definition of DH parameters ai, \u03b1i, di, \u03b8i defined for joint i and link (i).",
        "texts": [
            " The parameters a2, a3, and a4 are constant while d, \u03b83, \u03b84, and \u03b81 are variable. Assuming \u03b81 is input and specified, we may solve for other unknown variables \u03b83, \u03b84, and d by equating corresponding elements of [T ] and I. Example 153 F Non-standard Denavit-Hartenberg notation. The Denavit-Hartenberg notation presented in this section is the standard DH method. However, we may adopt a different set of DH parameters, simply by setting the link coordinate frame Bi at proximal joint i instead of the distal joint i + 1 as shown in Figure 5.19. The zi-axis is along the axis of joint i and the xi-axis is along the common normal of the zi and zi+1 axes, directed from zi to zi+1 axes. The yi-axis makes the Bi frame a right-handed coordinate frame. The parameterization of this shift of coordinate frames are: 1. ai is the distance between the zi and zi+1 axes along the xi-axis. 2. \u03b1i is the angle from zi to zi+1 axes about the xi-axis. 3. di is the distance between the xi\u22121 and xi axes along the zi-axis. 258 5. Forward Kinematics 4. \u03b8i is the angle from the xi\u22121 and xi axes about the zi-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001550_1.4028484-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001550_1.4028484-Figure9-1.png",
        "caption": "Fig. 9 Typical simulation result: (a) temperature contour with melt pool geometry, (b) temperature profile, and (c) cooling rate",
        "texts": [
            "The substrate was treated as solidified materials from previous layer depositions. One example of actual process parameters obtained from the experiments has also been incorporated into the FE model: 632.6 mm/s scanning speed and 6.7 mA beam current. The beam diameter was approximately as 0.55 mm for the focus offset used in the experiment, 19 mA [46,47]. The electron acceleration voltage is always 60 kV. A single straight scan simulation was conducted and the temperature profile along the scanning path was extracted for further analysis. Figure 9 shows thermal characteristics in the EBAM process. Figure 9(a) shows the temperature contours in the entire model at the end of scanning; the melt pool shape and size are shown too, plotted with the threshold value of the melting point of Ti\u20136Al\u20134V. As expected, the high temperature zone, near the molten pool, is rather small, with the remaining part approaching a uniform temperature. Figure 9(b) illustrates the temperature profile along the center line of the scan path with the beam center at 0 of the horizontal axis. Extremely rapid temperature rise and fall near the beam center are noted, with the peak temperature reaching between 2700 C and 2800 C. In addition, a plateau is noted corresponding to the latent heat of fusion for the phase change. Figure 9(c) shows the heating and cooling rate history at one location from the scan path. The horizontal dashed line indicates the boundary between heating and cooling. The plateau is noted again in Fig. 9(c); it takes around 2\u20133 ls, which is generally just the duration that the cooling rate drops to a very low value. The abrupt drop in the heating period, which can be identified in the figure, indicates the phase change event. Another sharp transition occurred at around 9.5 ms indicates the change from the latent heat effect to solid-state cooling. 4.2 Typical Experimental Result. An example of typical temperature images from NIR during hatch melting is shown in Fig. 10(a). This particular example was at a build height of 26"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000726_j.mechmachtheory.2008.05.008-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000726_j.mechmachtheory.2008.05.008-Figure3-1.png",
        "caption": "Fig. 3. Contact loss modelling.",
        "texts": [
            " Backlash is defined as the excess of thickness space of a tooth compared to the conjugated tooth thickness. It can be introduced also by varying the centre distance on each gear stage. Backlash value must not be exaggerated for the work requirements, but it should be sufficient to create space for lubrication. To introduce the backlash defect into the model, we acts directly on the elastic meshing force ~f s\u00f0ds\u00f0t\u00de; bs\u00de. The contact loss is modelled by the discontinuity of the defined meshing force following the line of action [10]. Fig. 3 shows this discontinuity according to the teeth deflection ds(t). ~f s\u00f0ds\u00f0t\u00de; bs\u00de is the nonlinear symmetric function without zero value due to backlash and defined by ~f s\u00f0ds\u00f0t\u00de; bs\u00de \u00bc ks\u00f0t\u00de ~As\u00f0ds\u00f0t\u00de; bs\u00de ds\u00f0t\u00de \u00f06\u00de where 2 bs presents the backlash between teeth before meshing, as shown in Fig. 3. \u00c3s(ds(t), bs) is a nonlinear function defined on three domains. Practically, each teeth contact is characterized by three cases of teeth configurations. These cases are summarized in Table 1. The backlash introduced between teeth causes the contact loss especially for the system not or slightly loaded. This impact source results from an intense vibration, a noise and a great dynamic head. It assigns the gear system fidelity and lifespan. In the presence of backlash, the equations of motion of such systems become extremely nonlinear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002131_j.sna.2014.03.011-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002131_j.sna.2014.03.011-Figure3-1.png",
        "caption": "Fig. 3. The structure of control system for the quadrotor.",
        "texts": [
            " There exist finite positive constants MF, Md, MF0 , G, M G< \u221e and continuous functions F(x) and d(x) which satisfy he following inequalities: | F (x)| F(x) \u2264 MF, |d(x)| d(x, t) \u2264 Md, |F0(x)| F(x) \u2264 MF0 (7) G0(x) G(x) \u2264 MG, \u2223\u2223\u2223 G(x) G(x) \u2223\u2223\u2223 \u2264 M G (8) emark 1. Assumption 1 implies the mathematic modeling is relible, and there is no chance to produce an infinite control input. ssumption 2 implies the disturbances and modeling errors dealt n this work are bounded. 3. DOB-based controller design In this section, we aim to design a trajectory tracking control strategy which can effectively compensate for the lumped disturbance. As shown in Fig. 3, this control scheme is developed in a cascaded structure, which means the attitude controller works as the inner loop controller of the trajectory tracking controller. With such a scheme, the quadrotor is stabilized in the following way. The quadrotor dynamics is governed by R and H, which is expressed in (4) and (5). The control inputs Ui (i = 1, 2, 3, 4) for R are generated by rotors which have their own dynamics M as in (2). The controller A is designed to control the attitude q through U2, U3 and U4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002306_tie.2017.2681975-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002306_tie.2017.2681975-Figure8-1.png",
        "caption": "Figure. 8. Place of symmetry and the simulated coolant tubes in the 3D model.",
        "texts": [
            " This section presents two 3D CFD models of the direct cooling systems using polyalphaolefin-oil (case B) and distilled water (case C). Therefore, the main characteristics of the CFD models are presented first and later the results obtained are shown. First, the geometry is simplified in both cases in order to reduce the number of elements in the model and minimize the computational time. Consequently, an axial symmetry is considered, modelling only one stator and half of the rotor. In this sense, Fig. 8 shows the cutaway view where the symmetry plane is placed and also the assumed periodicity. In addition, a periodic behavior in the circumferential axis is assumed, where only one pole and one slot are modelled. For the physical setup, fluids (air, oil or water) have been considered incompressible and have been modelled with the properties given in table III, which also shows the thermophysical properties of different solids constituting the machine. The behaviour of fluids is obtained using Navier Stokes equations, which relate the speed and pressure of the fluids and combined with the initial and boundary conditions constitute the mathematical model for the fluid flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001404_j.engfailanal.2013.08.008-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001404_j.engfailanal.2013.08.008-Figure2-1.png",
        "caption": "Fig. 2. width,",
        "texts": [
            " The total stiffness of one tooth pair Kt could be calculated as follows: Kt \u00bc 1 1 Kp \u00fe 1 Kg \u00fe 1 Kh \u00bc Km1 \u00f04\u00de In cases where there were two pairs in contact, the same procedure was repeated for the second tooth pair to find Km2.Then we could calculate the equivalent mesh stiffness Km for the two pairs in contact as follows: Km \u00bc Km1 \u00fe Km2 \u00f05\u00de In this sub-section the approach presented in [3] is explained, as it is a more comprehensive approach and offers the possibility of simulating a parabolic crack distribution, see Fig. 2. This approach can be described as consisting of two parts: firstly, determination of the mesh stiffness with a constant crack depth for a thin slice along the tooth width, and secondly, determination of the mesh stiffness for all the slices along the tooth width which have a non-uniform crack depth. Moreover, the effects of fillet foundation deflection and Hertzian contact are taken into account, as explained in Sections 2.2.3 and 2.2.4. The stiffness of one tooth is a combination of the bending, shear, and axial compressive stiffnesses, with all of them acting in the direction of the applied load. By considering the tooth as a non-uniform cantilever beam with an effective length of d, see Fig. 2d, the deflections under the action of the force can be determined, and then the stiffness can be calculated. Note that, in this part of the stiffness calculations, the crack is assumed to have a constant crack depth, q(z), for each slice of width dW along the tooth width, as explained in Fig. 2a and b. Based on a calculation of the potential energy stored in a meshing gear tooth, it is feasible to obtain the bending, shear, and axial compressive stiffnesses as follows [3]: Z d 1 Ka \u00bc Z d 0 sin2\u00f0a1\u00de E:Ax dy \u00f08\u00de Kb is the bending stiffness, Ks is the shear stiffness and Ka is the axial compressive stiffness. h, hq, hc, hx, y, dy, d, and a1 are illustrated in Fig. 2d. Note that a1 varies with the gear tooth position. Also, the following notation is used: G shear modulus, G \u00bc E 2\u00f01\u00fet\u00de Ix area moment of inertia, Ix \u00bc \u00f01=12\u00de\u00f0hx \u00fe hx\u00de3dW; hx 6 hq \u00f01=12\u00de\u00f0hx \u00fe hq\u00de3dW; hx > hq ( Ax area of the section of distance \u2019y\u2019 measured from the load application point, Ax \u00bc \u00f0hx \u00fe hx\u00dedW; hx 6 hq \u00f0hx \u00fe hq\u00dedW; hx > hq hq = hc q(z). sin(ac), see Fig. 2d. q(z) and ac are the crack depth and crack angle, respectively, as shown in Fig. 2b. At a certain position, z, through the tooth width, we can find the stiffness of one slice resulting from the effect of all the stiffnesses calculated previously as follows: K\u00f0z\u00de \u00bc 1 1 Kb \u00fe 1 Ks \u00fe 1 Ka \u00f09\u00de The mesh stiffness model presented in [3] divides the tooth width into thin slices to represent the crack propagation through the tooth width, as shown in Fig. 2a. Consequently, for a small dW the crack depth is assumed to be a constant through the width for each slice, see Fig. 2b. By integrating the stiffness of all the slices along the width, the stiffness of the entire tooth can be evaluated as follows: Ktp \u00bc Z W 0 K\u00f0z\u00de \u00f010\u00de In [3] it is assumed that the distribution of the crack depth can follow a parabolic function along the tooth width, as shown in Fig. 2c for the crack section A\u2013A, which can be recognized in Fig. 2a. When the crack length is less than the whole tooth width, q\u00f0z\u00de \u00bc qo ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Wc z Wc s ; z 2 \u00bd0 Wc \u00f011\u00de q\u00f0z\u00de \u00bc 0; z 2 \u00bdWc W \u00f012\u00de where Wc is the crack length, W is the whole tooth width, and qo is the maximum crack depth, see Fig. 2c. When the crack length extends through the whole tooth width, q\u00f0z\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2 o q2 2 W z\u00fe q2 2 r \u00f013\u00de where q2 is shown in Fig. 2c. It was mentioned above that, in order to simplify the studied model, the crack is assumed to extend along the whole tooth width with a uniform crack depth distribution. Therefore, to apply method 1 on our model, qo will be equal to q2, which means that qz is constant and equal to qo. Sainsot et al. [29] studied the effect of fillet foundation deflection on the gear mesh stiffness, derived this deflection, and applied it for a gear body. The fillet foundation deflection can be calculated as follows [29]: df \u00bc F: cos2\u00f0am\u00de W:E L uf Sf 2 \u00feM uf Sf \u00fe P \u00f01\u00fe Q tan2\u00f0am\u00de\u00de ( ) \u00f014\u00de where the following notation is used: am is the pressure angle, uf and Sf are illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001235_j.jsv.2013.11.033-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001235_j.jsv.2013.11.033-Figure17-1.png",
        "caption": "Fig. 17. (a) Schematic of the test rig, (b) planetary gearbox test rig and (c) Seeded gear fault on the internal ring gear of the planetary gear-set.",
        "texts": [
            " Consequently, a selection of appropriate thresholds on the rms and CK1 value can allow for detection of gear faults and its position. Thus, from simulations of fixed axis as well as planetary gear-sets, it can be seen that a selection of appropriate thresholds on the rms and CKM values can enable detection of gear faults and its position using the proposed algorithm. The proposed Fast DTW algorithm along with fault identification using correlated kurtosis was applied on experimentally measured vibration signals from a planetary gearbox test rig shown in Fig. 17. The input shaft of the gearbox is connected to a 3-phase AC motor (4 kW 4 pole) controlled using a standard industrial drive. A generator, with a resistive load bank, is driven by the output shaft of the gearbox. The two tested gearboxes have back-to-back planetary gear-sets, each having four planets in an equally spaced configuration with number of ring gear teeth Nr\u00bc84, number of sun gear teeth Ns\u00bc28, and number of planet gear teeth Np\u00bc28. As a result of the back-to-back scheme, the overall gear ratio of the gearbox equals to G 1/G\u00bc4 1/4\u00bc1, where G represents the gear ratio of a single planetary gear-set. The vibration signals are measured at a sampling rate of 20 kHz using an accelerometer attached to the gearbox housing outside the ring gear. A seeded spalled gear tooth fault was introduced to one of the ring gear teeth (Fig. 17(c)) using electro-discharge machining (EDM). The vibration transmission function from the gear mesh to sensor location described in Step 2 in Section 2.4 can be experimentally obtained through demodulation of the measured vibration signal under healthy condition with controlled constant speed to determine the amplitude modulation (AM) function as illustrated in Fig. 8. The magnitude of this AM function is then normalized from 0 to 1. Fig. 18 shows the pre-defined AM function of the tested planetary gearboxes that is estimated from the envelope signal of the measured vibration of the test rig under presumed healthy condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure9.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure9.18-1.png",
        "caption": "Fig. 9.18 Shielding of the walls (courtesy of HSP Cologne). a Lower layer carrying the heat isolation (black). b Upper layer of perforated steel panels. c Check of electrical contact",
        "texts": [
            " The shielding of the walls shall enable multi-functions: In addition to the electromagnetic shielding, it shall be a heat isolation and a sound absorber. A perfect shielding of C100 dB up to 100 MHz\u2014as usual for EMC shielding of computer centres and EMC test areas\u2014is not necessary for a HV test room. The PD measurement according to IEC 60270 is usually performed at frequencies up to 1 MHz, and therefore, a damping B100 dB up to 5 MHz is sufficient for most laboratories. This can be reached with standard steel panels of two layers of galvanized steel (Fig. 9.18). The lower layer (Fig. 9.18a) carries the heat isolation (black, e.g. rock wool) which is at the same time the sound absorber. The upper layer is made of perforated steel panels and fixed to the lower panels (Fig. 9.18b, c). The panels of each layer among one another as well as of the two layers with each other should overlap and carefully screwed together for a reliable electric contact. Instead of screwing, welding of points every 50\u2013100 cm is even more reliable. The shielding of the ceiling (Fig. 9.19) may follow the same principle as that of the walls. But the ceiling usually contains panels of the heating system, the lighting system and the air conditioning (ventilation and aeration). The heating panels are also of steel and can be used as a part of the shielding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002503_j.oceaneng.2019.106309-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002503_j.oceaneng.2019.106309-Figure1-1.png",
        "caption": "Fig. 1. Reference frames, AUV image courtesy of http://seaeye.com.",
        "texts": [
            " Finally, conclusive remarks of this paper are given in Section 5. The AUV motion is generally described in 6-degrees of freedom (DOF) which includes translational component and rotational component. The translational component includes surge, sway and heave, which describe the AUV\u2019s position. The rotational component consists of roll, pitch and yaw, which describe the AUV\u2019s orientation. In order to study the motion model, an AUV can be regarded as a rigid body in 3-D space. For the convenience of clearly analyzing the 6-DOF motion of AUV, as depicted in Fig. 1, an inertial reference frame (i-frame) and a body-fixed frame (b-frame) are defined. The i-frame, which is denoted by (\ud835\udc42\ud835\udc3a, \ud835\udc4b\ud835\udc3a, \ud835\udc4c\ud835\udc3a, \ud835\udc4d\ud835\udc3a), is coincident with the East-North-Up (ENU) coordinate system in this paper. Within this frame, origin \ud835\udc42\ud835\udc3a is a point on the surface of the ocean, the \ud835\udc4b\ud835\udc3a-axis points towards the east, the \ud835\udc4c\ud835\udc3a-axis points towards the north, and the \ud835\udc4d\ud835\udc3a-axis points upwards perpendicular to the Earth\u2019s surface. The b-frame is a moving reference frame denoted by (\ud835\udc42\ud835\udc35 , \ud835\udc4b\ud835\udc35 , \ud835\udc4c\ud835\udc35 , \ud835\udc4d\ud835\udc35), the origin \ud835\udc42\ud835\udc35 of which coincides with the center of the AUV gravity",
            " The \ud835\udc4b\ud835\udc35-axis is directed from aft to fore along the longitudinal axis of the AUV, the \ud835\udc4c\ud835\udc35-axis points towards larboard, and the \ud835\udc4d\ud835\udc35-axis is directed from bottom to top. Ocean Engineering 189 (2019) 106309 The i-frame is used to record the global information of the AUV motion. Therefore, the motion of AUV need to be described as the motion of the b-frame with respect to the i-frame. In this paper, the Euler angle parameterization is used to describe the transformations between the two frames. As depicted in Fig. 1, the orientation of the b-frame with respect to the i-frame is expressed in terms of three successive rotations about the axes \ud835\udc4d\ud835\udc35 , \ud835\udc4c\ud835\udc35 and \ud835\udc4b\ud835\udc35 , which are yaw \ud835\udf19\ud835\udc67, pitch \ud835\udf19\ud835\udc66, and roll \ud835\udf19\ud835\udc65, respectively. Let \ud835\udc601 = [\ud835\udc65, \ud835\udc66, \ud835\udc67]\ud835\udc47 and \ud835\udc602 = [\ud835\udf19\ud835\udc65, \ud835\udf19\ud835\udc66, \ud835\udf19\ud835\udc67]\ud835\udc47 be the position vector and orientation vector of the AUV in the i-frame, where \ud835\udc65, \ud835\udc66 and \ud835\udc67 represent the three Cartesian coordinates, \ud835\udf19\ud835\udc65, \ud835\udf19\ud835\udc66 and \ud835\udf19\ud835\udc67 represent the three attitude components (roll, pitch, and yaw angles), respectively. In order to avoid the singularity problem of the Euler angle, the pitch angle \ud835\udf19\ud835\udc66 is bounded, satisfying \u2212\ud835\udf0b\u22152 < \ud835\udf19\ud835\udc66\ud835\udc5a\ud835\udc56\ud835\udc5b \u2264 \ud835\udf19\ud835\udc66 \u2264 \ud835\udf19\ud835\udc66\ud835\udc5a\ud835\udc4e\ud835\udc65 < \ud835\udf0b\u22152, where \ud835\udf19\ud835\udc66\ud835\udc5a\ud835\udc56\ud835\udc5b and \ud835\udf19\ud835\udc66\ud835\udc5a\ud835\udc4e\ud835\udc65 represent the predefined lower bound and upper bound of \ud835\udf19\ud835\udc66, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.28-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.28-1.png",
        "caption": "FIGURE 5.28. Hand of a robot in motion.",
        "texts": [],
        "surrounding_texts": [
            "would also be along the gripper axis at the rest position. If the first axis of rotation is perpendicular to the forearm axis then we consider the first rotation as Pitch. If the first rotation is a Roll, then the second rotation is perpendicular to the forearm axis and is a Pitch. There are two possible situations for the third rotation. It is a Roll, if it is about the gripper axis, and is a Yaw, if it is perpendicular to the axis of the first two rotations. Figure 5.27 and 5.28 illustrate a Roll-Pitch-Roll wrist at the rest position and in motion respectively. This type of wrist is also called Eulerian wrist just because Roll-Pitch-Roll reminds Z \u2212 x\u2212 z rotation axes. If the first rotation is a Pitch, the second rotation can be a Roll or a Yaw. If it is a Yaw, then the third rotation must be a Roll to have independent rotations. If it is a Roll, then the third rotation must be a Yaw. The PitchYaw-Roll and Pitch-Roll-Yaw are not distinguishable, and we may pick Pitch-Yaw-Roll as the only possible spherical wrist with the first rotation as a Pitch. Practically, we provide the Roll, Pitch, and Yaw rotations by introducing two links and three frames between the dead and living frames. The links will be connected by three revolute joints. The joint axes intersect at the wrist point, and are orthogonal when the wrist is at the rest position. It is simpler if we kinematically analyze a spherical wrist by defining three non-DH coordinate frames at the wrist point and determine their relative transformations. Figure 5.29 shows a Roll-Pitch-Roll wrist with three coordinate frames. The first orthogonal frame B0 (x0, y0, z0) is fixed to the forearm and acts as the wrist dead frame such that z0 is the joint axis of the forearm and a rotating link. The rotating link is the first wrist link and the joint is the first wrist joint. The direction of the axes x0 and y0 are arbitrary. The second frame B1 (x1, y1, z1) is defined such that z1 is",
            "5. Forward Kinematics 275\nalong the gripper axis at the rest position and x1 is the axis of the second joint. B1 always turns \u03d5 about z0 and \u03b8 about x1 relative to B0. The third frame B2 (x2, y2, z2) is the wrist living frame and is defined such that z2 is always along the gripper axis. If the third joint provides a Roll, then z2 is the joint axis, otherwise the third joint is Yaw and x2 is the joint axis. Therefore, B2 always turns \u03c8 about z2 or x2, relative to B1. Introducing the coordinate frames B1 and B2 simplifies the spherical wrist kinematics by not seeing the interior links of the wrist. Considering the definition and rotations of B2 relative to B1, and B1 relative to B0, there are only three types of practical spherical wrists as are classified in Table 7.11. These three wrists are shown in Figures 5.29-5.31.\nExample 160 DH frames and spherical wrist. Figures 5.27 and 5.28 depict a another illustrations of a spherical wrist of type 1. The common origin of frames B4, B5, and B6 is at the wrist point. The final frame, which is called the tool or end-effector frame, is denoted by three vectors, a, s, n, and is set at a symmetric point between the fingers of an empty hand or at the tip of the tools hold by the hand. The vector n is called tilt and is the normal vector perpendicular to the fingers or jaws. The vector s is called twist and is the slide vector showing the direction of fingers opening. The vector a is called turn and is the approach vector perpendicular to the palm of the hand. The placement of internal links\u2019 coordinate frames are predetermined by the DH method, however, for the end link the placement of the tool\u2019s frame Bn is somehow arbitrary and not clear. This arbitrariness may be resolved through simplifying choices or by placement at a distinguished location in",
            "276 5. Forward Kinematics\nthe gripper. It is easier to work with the coordinate system Bn if zn is made coincident with zn\u22121. This choice sets an = 0 and \u03b1n = 0.\nExample 161 Roll-Pitch-Roll or Eulerian wrist. Figure 5.29 illustrates a spherical wrist of type 1, Roll-Pitch-Yaw. B0 indicates its dead and B2 indicates its living coordinate frames. The transformation matrix 0R1, is a rotation \u03d5 about the dead axis z0 followed by a rotation \u03b8 about the x1-axis.\n0R1 = 1RT 0 = \u00a3 Rx1,\u03b8 R T z0,\u03d5 \u00a4T = \u00a3 Rx,\u03b8 R T Z,\u03d5 \u00a4T (5.127)\n= \u23a1\u23a2\u23a3 \u23a1\u23a3 1 0 0 0 cos \u03b8 sin \u03b8 0 \u2212 sin \u03b8 cos \u03b8 \u23a4\u23a6\u23a1\u23a3 cos\u03d5 \u2212 sin\u03d5 0 sin\u03d5 cos\u03d5 0 0 0 1 \u23a4\u23a6T \u23a4\u23a5\u23a6 T\n= \u23a1\u23a3 cos\u03d5 \u2212 cos \u03b8 sin\u03d5 sin \u03b8 sin\u03d5 sin\u03d5 cos \u03b8 cos\u03d5 \u2212 cos\u03d5 sin \u03b8 0 sin \u03b8 cos \u03b8 \u23a4\u23a6 The transformation matrix 1R2, is a rotation \u03c8 about the local axis z2.\n1R2 = 2RT 1 = RT z2,\u03c8 = RT z,\u03c8 = \u23a1\u23a3 cos\u03c8 \u2212 sin\u03c8 0 sin\u03c8 cos\u03c8 0 0 0 1 \u23a4\u23a6 (5.128)\nTherefore, the transformation matrix between the living and dead wrist"
        ]
    },
    {
        "image_filename": "designv10_1_0001994_tpas.1969.292379-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001994_tpas.1969.292379-Figure2-1.png",
        "caption": "Fig. 2. Root-locus contours.",
        "texts": [
            " The terminal voltage has been adjusted in accordance with (22). The dashed lines shown in Fig. 1 indicate the breakdown or maximum steadystate torque at the various operating frequencies. Negative torque output denotes induction generator action. The continuous contour shown in Fig. 1 forms the boundary between stable and unstable regions of operation. More specifically, this contour connects all operating points which yield a pair of complex-conjugate eigenvalues with a zero real part. The root-loci charts shown in Fig. 2 serve to demonstrate the significance of the closed contour given in Fig. 1. The three 1713 IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, NOVEMBER 1969 Te .0 -m I,gfRDECREASED TO 0.3 -1.0 0r 0.251- _ i .0 0.0L fR DECREASED TO 0.25 *W IAwmmmA\"A5_, Fig. 3. Frequency switching, analog computer study. root-locus plots in Fig. 2 correspond to initial operating points indicated in Fig. 1 as a, b, and c. These operating points occur at a constant loading condition of zero torque at frequencies of f, = 0.4, 0.30, and 0.25, respectively. Since the frequency ratio fR is defined as the ratio of applied frequency to base frequency, and since base frequency has been selected as 60 Hz, these operating points correspond to frequencies of operation of 24, 18, and 15 Hz. With fR = 0.40, in Fig. 2, the root-locus contour of the dominant pair of roots passes into the right-half plane indicating possible unstable points of operation. However, for the inertia being considered, the gain parameter l/2H is 5.0, thus, point a on this locus for zero-load torque is in the left-half plane corresponding to a stable operating condition. Since the remaining roots contain large negative real parts, these roots have negligible effect upon system response. The location of these roots have not been included in Fig. 2. With fR = 0.30 the root-locus contour again passes into the right-half plane. In addition, the gain parameter 1/2H = 5.0 fixes operating point b in the righthalf plane. Therefore, the system is unstable for zero-load torque with fR = 0.30. When fR = 0.25, the gain parameter 1/2H = 5.0 locates the dominant root in the left-half plane (point c). That is, the induction motor is again stable for fR = 0.25 and zero-load torque. In Fig. 2 the complete locus of the dominant root is plotted for a given operating frequency and loading condition. This locus was obtained by varying the gain constant 1/2H from zero to infinity. However, it is clear that the entire root locus need not be calculated at each operating point in order to establish system stability since only one set of points on the locus corresponds to a specified inertia constant H. In the foregoing stability analysis the equations which describe the dynamic performance of the induction machine have been linearized by the method of small displacements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003375_tnsre.2019.2895221-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003375_tnsre.2019.2895221-Figure2-1.png",
        "caption": "Fig. 2. Point cloud of level ground in different coordinate systems. Ground p and Camera p represent point cloud in the ground coordinate system and camera coordinate system respectively, and Ground CameraR was the rotation matrix from the camera coordinate system to the ground coordinate system.",
        "texts": [
            " See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. cloud can solve this problem. The leg of human can swing about 60\u00b0 within a gait cycle, which resulted in large orientation variation of the IMU-Camera. The output point cloud of depth camera was in the camera coordinate system. When the camera coordinate system changed, point cloud for the same object will also change. This phenomenon brings a difficulty to recognize the environment correctly. As shown in Fig. 2, the point cloud of level ground became an inclined plane rather than a horizontal plane in camera\u2019s view. Camera coordinate system changed when the camera rotated, but the ground coordinate system remained the same. In order to recognize environments correctly, the reference coordinate system of point cloud should be ground coordinate system rather than the camera coordinate system. The rotation offset of point cloud can be realized by changing the reference coordinate system as: Ground Ground Camera Camerap R p (1) where Ground p and Camera p were the point cloud in the ground coordinate system and camera coordinate system respectively, and Ground CameraR was the rotation matrix from camera coordinate system to ground coordinate system, which was calculated by the software of IMU vendor, Xsens Technologies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002607_j.jmatprotec.2012.05.012-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002607_j.jmatprotec.2012.05.012-Figure4-1.png",
        "caption": "Fig. 4. Schematics of conventional scanning strategy and inter-layer stagger scanning strategy.",
        "texts": [
            " This observation props us to take an investigation into the overlapping pattern during SLM process. 2. Experimental procedure A SLM machine Dimetal280 developed by South China University of Technology was used in the experiment. The source of r 2 o t a 7 1 o c m p i p g l b a d a i a p T t T m s c s r u 3 n a T C are not staggered and the continuity of layers depends on overlapping between tracks at the same position along fabrication direction. The zone between overlapping tracks of the fabricated entity, marked by black circle shown in Fig. 4a, may be with low adiation is a Ytterbium fiber laser with the maximal power of 00 W, a continuous wavelength of 1090 nm and beam coefficient f about 1.1; under direction of a dual axis mirror positioning sysem and a galvanometer optical scanner, the laser beam can move long the X-axis and the Y-axis; the focused laser spot is about 0 m after focusing of an F-theta lens with a focal distance of 63 mm. The proposed layer thickness is 20\u201350 m and the range f scanning speed is 50\u20132000 mm/s. These are the main technial parameters which are limited by the machine behavior of the achine and can be selected during fabrication",
            " The nonuniform distribution of energy becomes more serious when fabricating of the nineteenth layer (surface \u201cC\u201d). The surface topography of surface \u201cC\u201d shows an over-melted resultant. Essentially, the track overlapping implies an accumulation of energy. It can be deduced that the overlapping between tracks at the same position in adjacent layers respectively leads to over concentration of energy at the centre line of the fabricated track. Therefore, inter-layer stagger scanning strategy is preferred. Fig. 4 shows schematics of conventional scanning strategy and inter-layer stagger scanning strategy. As for a conventional scanning strategy, the tracks in adjacent layers (n layer and n + 1 layer) d s a d s l i n t l r s t \u201c \u201c a t p \u201c t t o s b o m t h l ensity or even pore generation. The tracks in adjacent layers are taggered if the scanning paths are staggered by a certain distance t path manipulation stage, shown in Fig. 4b. To assure an uniform istribution of energy, the staggered distance is always half track pace. Track in n layer overlaps with two stagger tracks in n + 1 ayer meanwhile it laterally overlaps with two neighbouring tracks n n layer. In this way, the zones between neighbouring tracks in layer are filled up with stagger tracks in n + 1 layer. Eventually, hese zones become the overlapping portions. Essentially, the track overlapping pattern produces a continuous ayer as well as a continuous entity. Cross section of a specimen fabicated using inter-layer stagger scanning strategy, shown in Fig",
            " Note that there are two parts of overlapping: intra-layer overlapping between neighbouring tracks in the same layer and inter-layer overlapping between tracks in adjacent layers. If overlapping rate is defined as the ratio of length of overlapping zone to the corresponding dimension of molten pool, then, intra-layer overlapping rate fs = s/D and inter-layer overlapping rate fh = h/H, where D and H are width and depth of track respectively, s is width of intra-layer overlapping zone, h is depth of inter-layer overlapping zone, shown in Fig. 4b. To obtain a continuous entity, the tracks must fill up nominal volume being fabricated. For a hypothesis that the molten pool contour is parabola, according to geometric relationship an approximate expression can be obtained as follows: < 0.5) 1/2 h + D 2 (2fh \u2212 1)1/2 \u2265 S 2 (0.5 < fh < 1) (1) F tegy. o w t{ { A e m l i t i i w c h d r m T l r r E l l i i t f c n o ig. 7. Three types of overlapping regime under inter-layer stagger scanning stra verlapping regime. here S is track space. Suppose layer thickness is represented by h, hen: S + s = D h + h = H (2) Substituting Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.32-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.32-1.png",
        "caption": "Fig. 4.32",
        "texts": [
            "3 it was shown that the assumptions concerning the displacements lead to shear stresses that are constant in a cross section (recall (4.23b)). This constant distribution of the shear stresses is only a first approximation. A better result can be obtained with the aid of the normal stresses (4.26) and the equilibrium conditions. At first, we restrict our attention to prismatic beams with solid cross sections, where the y-axis and the z-axis are assumed to be principal axes. In addition, we make the following assumptions: a) Only the component in z-direction of the shear stress \u03c4 is relevant (see Fig. 4.32a). b) The shear stress \u03c4 is independent of y, i.e., \u03c4 = \u03c4(z), analogously to the normal stress \u03c3 = \u03c3(z). Both assumptions are not exactly satisfied in reality. First, the shear stress always has the direction of the tangent to the boundary of an arbitrarily shaped cross section (Fig. 4.32b), and secondly, the shear stress depends to a certain degree on y. Therefore, the shear stress which is obtained using the above assumptions is only an average shear stress over the width b(z). In order to determine the shear stresses, we separate an element of length dx from the rest of the beam. Then we isolate a part of this element by an additional cut perpendicular to the z-axis at an arbitrary position z (Fig. 4.32c). Let us now consider the forces acting on this subelement. The unknown shear stresses \u03c4(z) act in z-direction at its front face. According to Section 2.1, these shear stresses are accompanied by shear stresses of equal magnitude acting in areas perpendicular to the front face (complementary shear stresses). Hence, the top face of the subelement is also acted upon by \u03c4(z), see Fig. 4.32c. Since only the forces in x-direction are needed in the following derivation, only the corresponding stresses are shown in Fig. 4.32c. The resultant of the shear stresses at the top surface is given by \u03c4(z) b(z)dx; it points into the direction of the negative x-axis. The two areas which are perpendicular to the x-axis (front and back surface) are subjected to the resultant forces \u222b A\u2217 \u03c3dA and \u222b A\u2217 (\u03c3 + (\u2202\u03c3/\u2202x)dx)dA. Here, the area A\u2217 is the area of the front surface of the subelement, i.e., it is that portion of the cross sectional area A which lies beyond the level z at which the shear stress is being evaluated, see Fig. 4.32d. The bottom face of the element (outer surface of the beam) is not subjected to a load. Hence, the equilibrium condition in 4.6 Influence of Shear 153 x-direction yields \u2212 \u03c4(z) b(z)dx\u2212 \u222b A\u2217 \u03c3 dA+ \u222b A\u2217 ( \u03c3 + \u2202\u03c3 \u2202x dx ) dA = 0 or \u03c4(z) b(z) = \u222b A\u2217 \u2202\u03c3 \u2202x dA. We denote the distance of the area element dA from the y-axis by \u03b6 (Fig. 4.32c). Then the flexural stress is given by \u03c3 = (M/I)\u03b6, see (4.26). The bending moment M is independent of y and z. Therefore, \u2202M/\u2202x = dM/dx. With dM/dx = V , we get \u2202\u03c3 \u2202x = V I \u03b6 (4.35) and therefore \u03c4(z) b(z) = V I \u222b A\u2217 \u03b6 dA. The integral on the right-hand side is the first moment S of the area A\u2217 with respect to the y-axis: S(z) = \u222b A\u2217 \u03b6 dA. (4.36) Hence, the shear stress distribution over a cross section is found to be \u03c4(z) = V S(z) I b(z) . (4.37) This equation is called the shear formula. It can be used to calculate the shear stress at any point of a beam with a solid cross section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002646_56911-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002646_56911-Figure2-1.png",
        "caption": "Figure 2. Coordinate system.",
        "texts": [],
        "surrounding_texts": [
            "A quadrotor is a cross-shaped aerial vehicle that is capable of vertical take-off and landing. It has four motors, each mounted per corner equidistant from the centre. The synchronized rotational speed (\u03c9) of all the motors is key to the control of the quadrotor.Vertical motion results from the simultaneous increase or decrease of the rotational speeds of all the rotors. The motion along any direction on the lateral axis is obtained by decreasing the rotational speed of the rotors along the desired direction of motion, and increasing the rotational speed of the rotors opposite to the desired direction of motion. Moment produced by rotation of rotors is used to initiate yaw. For instance, clockwise yaw is initiated by simultaneously increasing the rotation speed of the rotors creating a clockwise moment, and decreasing the rotation speed of the rotors creating counterclockwise moment. The motion of the quadrotor is described schematically in figure 1.Control of a quadrotor is a challenging task for the following reasons: high manoeuvrability, high non-linearity, intensely coupled multivariable and under-actuated condition with six degrees of freedom and only four actuators. A quadrotor is not a new concept. The first successful hovering of a quadrotor was achieved in October 1920 by Dr. George de Bothezat and Ivan Jerome [1]. Researchers have designed and implemented numerous quadrotor controllers such as PID/PD controllers, fuzzy controllers, sliding mode controllers, neuro-fuzzy controllers and Deepak Gautam and Cheolkeun Ha: Control of a Quadrotor Using a Smart Self-Tuning Fuzzy PID Controller 1www.intechopen.com Int. j. a v. robot. syst., 2013, Vol. 10, 380:2013 vision-based controllers. M. Santos et al. [2] proposed an intelligent system based on fuzzy logic to control a quadrotor. C. Coza et al. [3] used an adaptive fuzzy control algorithm to control a quadrotor in the presence of sinusoidal wind disturbance. The author addressed a robust method to prevent drift in the fuzzy membership centres. Y. A. Younes et al. [4] introduced a backstepping fuzzy logic controller as a new approach to controlling the attitude stabilization of a quadrotor. The backstepping controller parameters were scheduled utilizing fuzzy logic. M. H. Amoozgar et al. [5] proposed an adaptive PID controller for fault-tolerant control of a quadrotor helicopter in the presence of actuator faults. The PID gains were tuned using a fuzzy interface scheme. A. Sharma et al. presented and compared PID and fuzzy PID controllers to stabilize a quadrotor. Other authors [6\u20138] also addressed the fuzzy PID control algorithm to control a quadrotor. In this paper, modelling of a quadrotor, a control strategy using a self-tuning fuzzy PID algorithm and path planning using Dijkstra\u2019s algorithm are presented. A dynamic model is derived based on the Euler-Newton formulation. All the drags, aerodynamic, Coriolis and gyroscopic effects are neglected. The PID gain scheduling-based control algorithm is proposed for attitude stabilization and position control of the quadrotor. The tuning of PID gains is performed based on the self-tuning fuzzy controller. The tuning of the fuzzy parameters is performed using an EKF algorithm. Smart selection of the active fuzzy parameter followed by exclusive tuning of the active parameter is proposed to reduce the computational time. A path planning algorithm is proposed with two main objectives in mind: obstacle avoidance and shortest route calculation from any given initial position to the final position. Finally, a series of simulation results and conclusions are presented. 2. Mathematical Modelling The mathematical model of the quadrotor is derived based on the Newton-Euler formulation. Let E = {XE, YE, ZE} denote an inertial frame and B = {XB, YB, ZB} denote a body fixed frame. The body frame is related to the inertial frame by a position vector (x, y, z) and three Euler angles, (\u03d5, \u03b8, \u03c8) representing roll, pitch and yaw respectively. All equations are expressed in the inertial frame. The vehicle is assumed to be rigid and symmetrical. The centre of mass, centre of gravity and origin of body axis are assumed to be coincident. Let c\u03d5 represent cos \u03d5, and s\u03d5 represent sin \u03d5. Similar notation is used for \u03b8 and \u03c8. The rotation matrix from the body frame to the inertial frame E BR for the defined coordinate system is computed by multiplying the three matrices E BRX , E BRY and E BRX generated by rotations about the XB, YB and ZB axes respectively. E BR = E BRZ \u00d7 E BRY \u00d7 E BRX E BR =   c\u03c8 \u2212s\u03c8 0 s\u03c8 c\u03c8 0 0 0 1  \u00d7   c\u03b8 0 s\u03b8 0 1 0 \u2212s\u03b8 0 c\u03b8  \u00d7   1 0 0 0 c\u03d5 s\u03d5 0 \u2212s\u03d5 c\u03d5   E BR =   c \u03b8 c \u03c8 \u2212 s \u03d5 s \u03b8 c \u03c8 \u2212 c \u03d5 s \u03c8 c \u03d5 s \u03b8 c \u03c8 \u2212 s \u03d5 s \u03c8 c \u03b8 s \u03c8 \u2212 s \u03d5 s \u03b8 s \u03c8 + c \u03d5 c \u03c8 c \u03d5 s \u03b8 s \u03c8 + s \u03d5 c \u03c8 \u2212 s \u03b8 \u2212 s \u03d5 c \u03b8 c \u03d5c\u03b8   (1) The rotation of each rotor produces a vertical force towards the ZB direction and moment is produced opposite to the direction of rotation. Rotors are paired such that the total moment created is cancelled out. The rotor pair 2-4 produces clockwise moment, while the rotor pair 1-3 creates counterclockwise moment. Experimental observation at low speed showed that these moments are linearly dependent on the produced forces. The equation of motion can be written using force and moment balance as shown in equation 2 [9\u201311]   x\u0308 y\u0308 z\u0308 \u03d5\u0308 \u03b8\u0308 \u03c8\u0308   =   E BR     0 0 \u2211 Fi  \u2212   K1 x\u0307 K2y\u0307 K3 z\u0307      1 m \u2212   0 0 g      l (F1 \u2212 F2 \u2212 F3 + F4 + K4\u03c6\u0307) /IX l ( \u2212F1 \u2212 F2 + F3 + F4 + K5 \u03b8\u0307 ) /IY (CF1 \u2212 CF2 + CF3 \u2212 CF4 + K6\u03c8\u0307) /IZ   (2) where Mi = C \u00d7 Fi , Fi is the force from individual motors, Mi is the moment produced by rotation of the rotor for i = 1, ..., 4, C is the constant relating moment to force, m is the total mass of the UAV, g is the acceleration due to gravity, Ki is the coefficient of the drag opposing the motion of the quadrotor, for i = 1, 2, ..., 6. IX , IY , IZ are the moment of inertia of the UAV with respect to XB, YB, Int. j. adv. robot. syst., 2013, Vol. 10, 380:20132 www.intechopen.com ZB axes respectively. As the drags are negligible at low speed, for convenience the drag coefficients are assumed to be zero [9]. Moreover, inputs are defined as: U =   U1 U2 U3 U4   =   1 m 4 \u2211 i=1 Fi 1 IX (F1 \u2212 F2 \u2212 F3 + F4) 1 IY (\u2212F1 \u2212 F2 + F3 + F4) C IZ 4 \u2211 i=1 (\u22121)i+1Fi   (3) Substituting equation 3 to equation 2, the simplified form of the quadrotor dynamics is obtained as presented in equation 4.   x\u0308 = U1 (c \u03d5 s \u03b8 c \u03c8 \u2212 s \u03d5 s \u03c8) y\u0308 = U1 (c \u03d5 s \u03b8 s \u03c8 + s \u03d5 c \u03c8) z\u0308 = U1 (c \u03d5 c \u03b8)\u2212 g \u03d5\u0308 = U2l \u03b8\u0308 = U3l \u03c8\u0308 = U4 (4) Likewise, the motor is modelled considering a small motor with very low inductance and no gearbox. The motor dynamics is given by equation 5 [10, 11] J\u03c9\u0307 = \u2212KEKM R \u03c9 \u2212 d\u03c92 + KM R V (5) where J is the propeller inertia, \u03c9 is the rotational speed, KE is the back EMF constant, KM is the torque constant, R is the internal resistance of the motor, d is the aerodynamic drag factor and V is the motor input voltage. 3. Control and Path Planning Algorithm"
        ]
    },
    {
        "image_filename": "designv10_1_0002220_s00170-017-0703-5-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002220_s00170-017-0703-5-Figure6-1.png",
        "caption": "Fig. 6 A 3Dmodel with different building orientations",
        "texts": [
            " Integration of the results of calibration, validation, and uncertainty prediction can enhance our confidence in the UQ of AMprocess. To achieve the purpose of integration of calibration, validation, and uncertainty prediction, a roll-up method [128] has been recently developed. Resource allocation based on integration of model calibration, validation, and UQ can reduce the uncertainty in AM models in a symmetric way. Since the aleatory uncertainty is irreducible, the process parameters need to be optimized to reduce the effects of aleatory uncertainty on the variability of quantity of interest. As shown in Fig. 6, the optimal building orientation and slice thickness need to be determined to minimize the manufacturing error and standard deviation of the geometry error. The AM process optimization under uncertainty can be pursued in two directions: reliability-based design optimization (RBDO) [129] and robust design optimization (RDO) [130]. In RBDO, the process parameters are optimized while the optimization is subjected to reliability constraints regarding the QoIs. In RDO, the process parameters are optimized such that the QoIs are not sensitive to the variations in the manufacturing environment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002457_1.5085206-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002457_1.5085206-Figure1-1.png",
        "caption": "FIG. 1. Schematic of the SLM setup. Adapted with permission from K.-H. Leitz, P. Singer, A. Plankensteiner, B. Tabernig, H. Kestler, and L. Sigl, Met. Powder Rep. 72, 331\u2013338 (2017). Copyright 2017, Elsevier.",
        "texts": [
            " At the beginning of the process, a 3D computeraided design model describing both internal and external geometry features of the part is developed and sliced into a stack of 2D layers, which are loaded into the SLM equipment. A thin layer of powder material is then spread on a substrate plate via a powder delivery system and later melted together with a high-energy laser beam scanning over the selected area. By applying another thin layer of powder on top of the previously processed layer and repeating the scanning process, the successive layers are formed and metallurgically bonded with the previous layer. The designed part is, thus, fabricated layer by layer as shown in Fig. 1.1 Compared to conventional manufacturing techniques such as casting and forging, SLM holds advantages including (1) rapid prototyping, (2) the capability of producing components with customized or complex geometry, (3) the ability to produce novel structural designs for increased functionality, and (4) the joining of dissimilar metals through metallurgical means. Due to these advantages, SLM has been used for widespread practical industrial applications, such as aerospace, automotive, electronics, and biomedical devices"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000842_robot.2006.1641979-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000842_robot.2006.1641979-Figure5-1.png",
        "caption": "Fig. 5. Solution region for grasping a cylindrical object.",
        "texts": [
            " As mentioned in section I, another problem is that even if it were possible to compute and plan for all possible IK solutions to a single end-effector posture, there may actually be a wide continuous range of end-effector positions which allow solving the task. Consider the task of grasping a cylindrical object. The two configurations shown in Figure 2 are possible solutions but in addition, there are infinitely many more configurations that enable the robot to grasp the object. This set of configurations corresponds to a symmetric region in the C-space illustrated in Figure 5. AND INVERSE KINEMATICS We propose to avoid these difficulties by integrating the search for inverse kinematics solutions directly into the planning process. Currently, an efficient path planning method based on Rapidly-exploring Random Trees [13] is used to compute collision-free paths. We made the following modifications to the RRT search algorithm [14]: \u2022 No explicit goal configuration is computed. Instead, the planner evaluates workspace goal criteria for configurations generated during the search"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001535_978-981-10-5355-9_1-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001535_978-981-10-5355-9_1-Figure6-1.png",
        "caption": "Fig. 6. Schematic diagram of the PAW-based WAAM system and the details of plasma arc [23]",
        "texts": [
            " Preheating and trailing gas shielding may be used to control the inter pass temperature and to prevent oxidation, respectively. An experimental setup of twin-wire WAAM and the schematic diagram of the manufacturing process are shown in Fig. 5. PAW as a method for the AM of metallic materials has also been widely investigated [31\u201333]. Arc energy density in plasma welding can reach three times that of GTAW, causing less weld distortion and smaller welds with higher welding speeds [34]. A micro-PAW based WAAM system, as shown in Fig. 6, was introduced and the effects of process parameters on the mechanical properties and surface quality of fabricated parts have been investigated [23]. A recent article [19] systematically reviewed the published values for mechanical properties obtained for materials processed by various AM techniques, including powder bed fusion and directed energy deposition technologies. This review focuses on mechanical properties of metallic materials manufactured by WAAM. Based on the limited number of alloy systems for which mechanical properties are published, Table 1 summaries the existing alloy classes and references to published date, along with the process category"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000358_ac034204k-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000358_ac034204k-Figure4-1.png",
        "caption": "Figure 4. CVs obtained in 0.1 M NaOH solution (a) and 1 mM glucose (b) at 0.8% Ni-NDC film (A) and Ni-bulk (B) electrodes, respectively. Scan rate, 50 mV/s.",
        "texts": [
            " Sci. 1998, 409, 358-371. Analytical Chemistry, Vol. 75, No. 19, October 1, 2003 5193 states including metallic nickel, NiO, Ni2O3, and Ni(OH)2) highly dispersed and embedded homogeneously in disordered graphitelike carbon. Electrochemical Properties. To evaluate the 0.8% Ni-NDC film electrode as an amperometric detector for carbohydrate detection, it was studied with regard to the electrooxidation of mono- and disugars as target compounds compared with the Nibulk electrode. Cyclic Voltammograms. Figure 4 shows cyclic voltammograms obtained in 0.1 M NaOH solution (a) and in the presence of 1 mM glucose (b) at the 0.8% Ni-NDC film (A) and Ni-bulk (B) electrodes. The anodic and cathodic peaks in 0.1 N NaOH alkaline solution (curve a) are assigned to the Ni(II)/Ni(III) redox couple, which is thought to catalyze the oxidation of small organic molecules at the Ni electrodes.9,32-34 The peak current of glucose (corrected for the background current of 0.1 M NaOH) is 3.5 and 32 \u00b5A at the 0.8% Ni-NDC film and bulk electrodes, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002581_j.jmatprotec.2016.11.013-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002581_j.jmatprotec.2016.11.013-Figure2-1.png",
        "caption": "Fig. 2. Part built orientation angl",
        "texts": [
            " It is noteworthy that the response to the laser processing arkedly depends upon the physical properties of the powder nd the related results cannot be generalized for all materials Aboulkhair et al., 2016). Aim of this work is to develop a model ble to predict the roughness obtainable on AlSi10Mg processed by LM, taking into account the above mentioned problems, namely he staircase effect typical of AM and the defects typical of this Al lloy. . Theoretical model The first processing step, typical of the layer by layer fabrication, s characterized by the orientation of the virtual model onto the ase plate, with respect to the stratification direction d\u0302. In Fig. 2a his direction corresponds to the axis and the object is rotated by he orientation angles \u03d5 , \u03d5 , \u03d5\u03c2 , thus determining the direction long which the layers are generated. Each surface can be locally efined by its normal n\u0302: the angle between n\u0302 and d\u0302 is the local tratification angle. In Fig. 2b two surfaces, characterized by two ifferent , are reported. As shown in Fig. 2 the staircase effect influences the part suraces: each stair step can be considered as a triangle characterized y two side lengths, one equal to the layer thickness L and the other ependent upon the angle . A representation is reported in Fig. 3. Let\u2019s consider a generic profile composed by a repetition of the tair step with a period equal to e1 + e2. In order to evaluate the oughness profile and according to the ISO Standard definition (ISO and local stratification angle (b). 4287, 1997), the reference line is calculated as reported in the following"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002817_jmes_jour_1964_006_046_02-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002817_jmes_jour_1964_006_046_02-Figure1-1.png",
        "caption": "Fig. 1. Column of bonded rubber blocks subjected to compressive and shear loads between $at surfaces",
        "texts": [
            " I Second moment of area of the block crosssection. l Height of the column. s z \u2018Shape factor\u2019 of the rubber block (10). Distance from one end of the column. Elastic constants E, G E,, Ga K, T K\u2018, T\u2019 K\u2019,, Young\u2019s modulus and shear modulus of the Apparent values of Young\u2019s modulus and shear Shear stiffness and bending stiffness of a single Reduced shear and bending stiffnesses for a Apparent value of reduced shear stiffness. rubber. modulus. unit. column of unit height. Three loading conditions are treated below. The first is illustrated in Fig. 1, the column being located and compressed between flat parallel surfaces. The behaviour of a column compressed between parallel knife-edges then follows from symmetry considerations. Finally, the effect of introducing rigid separating struts between the knifeedges and the column is considered. The units are assumed to deform in two ways; by simple shear, in which one plate is displaced parallel to the other in its own plane; and by bending, in which one plate is rotated with respect to the other about an axis of symmetry in its own plane",
            " For example, K is given by AE/Sh for a relatively thin block of cross-sectional area A and thickness h (8). The corresponding relation for T is more complex. It is shown elsewhere (7) to take the general form T = EI( 1 + Bs2)/h where s is the \u2018shape factor\u2019 of the block, describing the restricting effect of the bonded surfaces, and B is a numerical constant, about 0-5. For a block of circular cross-section, of radius a, s is given by a/2h. Column between flat surfaces The following relation for the lateral deflection ym at the centre of the column sketched in Fig. 1 is obtained from Haringx\u2019s treatment (3) : where P and S are the applied compressive and shear loads, Vo16 No 4 1964 at UNIV NEBRASKA LIBRARIES on January 5, 2016jms.sagepub.comDownloaded from 320 A. N. GENT E is the height of the column (2Z in Haringx's notation), and q is given by ,.=;(l+;) . . . (3) ql r The deflection ym becomes infinitely large when - = -9 4 2 i.e., when the compressive load P attains a value P,, given by This corresponds to the buckling condition. For a column compressed between parallel knife-edges, the maximum lateral displacement ym and the critical compressive load P, are obtained by substituting 21 for E on the right-hand sides of equations (2) and (4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000570_med.2006.328749-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000570_med.2006.328749-Figure2-1.png",
        "caption": "Fig. 2. Propellers that can be rotated an angle \u03b1 to produce a force F in an arbitrary direction.",
        "texts": [
            " \u2022 Control surfaces can be mounted at different locations to produce lift and drag forces. For underwater vehicles these could be fins for diving, rolling, and pitching, rudders for steering, etc. Table I implies that the forces and moments in 6 DOF due to the force vector f = [Fx, Fy, Fz]> can be written: \u03c4 = \u2219 f r\u00d7 f \u00b8 = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 Fx Fy Fz Fzly\u2212F ylz Fxlz\u2212F zlx Fylx\u2212Fxly \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (5) where r = [lx, ly, lz] > are the moment arms. For azimuth thrusters the control force F will be a function of the rotation angle \u03b1; see Figure 2. Consequently, an azimuth thruster in the horizontal plane will have two force components Fx = F cos\u03b1 and Fy = F sin\u03b1, while the main propeller aft of the ship only produces a longitudinal force Fx = F, see Table I. A more general representation of control forces and moments is: \u03c4 = T(\u03b1)f , f =Ku (6) where u \u2208Rr and \u03b1\u2208Rp are control inputs defined as: \u03b1=[\u03b11, ..., \u03b1p] >, u=[u1, ..., ur] > (7) and f \u2208Rr is a vector of control forces. A. Force Coefficient Matrix The force coefficient matrix K \u2208Rr\u00d7r is diagonal: K =diag{k1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.7-1.png",
        "caption": "Fig. 3.7 Aerodynamic loads on a typical aerofoil section",
        "texts": [
            "18) The blade radial distance has now been written with a subscript b to distinguish it from similar variables. We have neglected the blade weight force in Eq. (3.18); the mean lift and acceleration forces are typically one or two orders of magnitude higher. We follow the normal convention of setting the blade azimuth angle, \ud835\udf13 , to zero at the rear of the disc, with a positive direction following the rotor. The analysis in this book applies 82 Helicopter and Tiltrotor Flight Dynamics to a rotor rotating anticlockwise when viewed from above. From Figure 3.7, the aerodynamic load fz (rb, t) can be written in terms of the lift and drag forces as fz = \u2212\ud835\udcc1 cos\ud835\udf19 \u2212 d sin\ud835\udf19 \u2248 \u2212\ud835\udcc1 \u2212 d\ud835\udf19 (3.19) where \ud835\udf19 is the incidence angle between the rotor inflow and the plane normal to the rotor shaft. We are now working in the blade axes system, of course, as defined in Section 3A.4, where the z direction lies normal to the plane of no-pitch. The acceleration normal to the blade element, azb, includes the component of the gyroscopic effect due to the rotation of the fuselage and hub, and is given approximately by (see Section 3A",
            " Up to moderate forward speeds, the extent of this region is small and the associated dynamic pressures low, justifying its omission from the analysis of rotor forces. At higher speeds, the importance of the reversed flow region increases, resulting in an increment to the collective pitch required to provide the rotor thrust, but decreasing the profile drag and hence rotor torque. These approximations make it possible to derive manageable analytic expressions for the flapping and rotor loads. Referring to Figure 3.7, the aerodynamic loads can be written in the form Lift\u2236 \ud835\udcc1(\ud835\udf13, rb) = 1 2 \ud835\udf0c(U2 T + U2 P)ca0 ( \ud835\udf03 + UP UT ) (3.21) Drag\u2236 d(\ud835\udf13, rb) = 1 2 \ud835\udf0c(U2 T + U2 P)c\ud835\udeff (3.22) where \ud835\udeff = \ud835\udeff0 + \ud835\udeff2C2 T (3.23) 84 Helicopter and Tiltrotor Flight Dynamics We have assumed that the blade profile drag coefficient \ud835\udeff can be written in terms of a mean value plus a thrust-dependent term to account for blade incidence changes (Refs. 3.6, 3.7). The nondimensional in-plane and normal velocity components can be written as UT = rb(1 + \ud835\udf14x\ud835\udefd) + \ud835\udf07 sin\ud835\udf13 (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure1-1.png",
        "caption": "Fig. 1. Definition of assembly errors: (a) positions of gear shafts without assembly errors, (b) positions of gear shafts with assembly errors and (c) other coordinate system used to define the misalignment errors \u2018\u2018e2\u2019\u2019 and \u2018\u2018e3\u2019\u2019.",
        "texts": [
            " Methods for LSR calculation of a pair of spur gears with ME, AE and TM are also presented in this paper. Effects of ME, AE and TM on LSR are analyzed quantitatively. It is found that ME has great effect on LSR. Methods for TE calculation of a pair of spur gears with ME, AE and TM are also presented in this paper. Effects of ME, AE and TM on TE of gears are also analyzed quantitatively. It is found that ME not only changes waveform of TE easily, but also makes TE greater when ME is increased. AE and TM also make TE greater when they are increased, but do not change waveform of TE. Fig. 1 is used to define AE of a pair of parallel-shaft gears. In Fig. 1(a), A0B0 and CD are shaft positions of a pair of parallel-shaft spur gears (Gear 1 and Gear 2) without AE. A0, B0, C, and D are four bearing positions to support the shafts A0B0 and CD. In Fig. 1(b), AB is the new position of A0B0 when there are AE. In order to define AE of the gears, a three-dimensional (3D), coordinate system (A0\u2013XYZ) is built. XA0Y plane is a horizontal plane that passes through A0B0 and CD. It is called S-plane here. YA0Z plane is a vertical plane that passes through A0B0 and is perpendicular to the S-plane. It is called V-plane here. A0 is the origin. In the coordinate system (A0\u2013XYZ), AE can be defined as center distance error XE on S-plane, center distance error ZE on V-plane, misalignment error h on S-plane and misalignment error / on V-plane as shown in Fig. 1(b). When XE, ZE, h and / are given, AB is positioned in the coordinate system (A0\u2013XYZ). Fig. 1(c) is the other 3D coordinate system used in this paper. The plane of action of the pair of spur gears is used as a horizontal coordinate plane and misalignment error of the gear shafts on this plane is expressed as \u2018\u2018e3\u2019\u2019. The vertical plane of the plane of action is used as the vertical coordinate plane and misalignment error of the gear shafts on this plane is expressed as \u2018\u2018e2\u2019\u2019. Effects of \u2018\u2018e2\u2019\u2019 and \u2018\u2018e3\u2019\u2019 on TSCS, TRBS, LSR and TE shall be investigated in this paper. ME of gears defined as 3D shape deviation of tooth surfaces in this paper",
            " (2) is available in LTCA: Transmission error \u00bc d=rb \u00f05\u00de Total load on each tooth surface is calculated when 3D tooth load distribution on each tooth surface is available in LTCA at double pair tooth-contact positions 1\u20136. Then tooth LSR is calculated by Eq. (6): Tooth load sharing ratio \u00bc Total load on each tooth=P \u00f06\u00de As introduced in Ref. [17], special FEM software was developed and following experiments have been done to prove reliability of the special FEM software. Tooth-contact pattern and root strains of a pair of spur gears as shown in Fig. 8 are measured when assembly errors h = 0.42 , / = 0.04 , XE = 2.1 mm and ZE = 0.2 mm are given to the gear shaft A0B0 as shown in Fig. 1(b). These gears are ground under the accuracy requirement of JIS 1st grade. A so-called power- circulating form gear test rig is used to do the tests at a very load speed (1.65 rpm) under torque T = 294 N m. Fig. 9 is the test gearbox used in the test rig. In Fig. 9, a removable support is used to give AE to the shaft of Gear 1 by changing the position of this support. Fig. 10 is tooth-contact pattern measured. Fig. 11 is the tooth-contact pattern calculated under the same conditions. In Fig. 11, A is the areas of double pair toothcontact and B is the area of single pair tooth-contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001620_978-90-481-8764-5_2-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001620_978-90-481-8764-5_2-Figure1-1.png",
        "caption": "Fig. 1 Coordinate system",
        "texts": [
            " A disturbance observer(DOB) based controller using the derived dynamic models is also proposed for hovering control. And a vision based localization for the developed QRT UAV are introduced. The performance of the proposed control scheme is verified through experiments using QRT UAVs. Section 2 shows the basic structure and the dynamics of the UAV. The DOB for flight control algorithms is given in Section 3. Section 4 shows the experimental setup and experimental results including the vision based localization schemes, and followed by concluding remarks in Section 5. Reprinted from the journal 11 Figure 1 shows coordinate systems of QRT UAVs. The motion of QRT UAVs is induced by the combination of quad rotors as shown in Fig. 2. The state vectors for the QRT UAVs are described as following: \u03b7 = [\u03b7T 1 , \u03b7 T 2 ]T; \u03b71 = [x, y, z]T; \u03b72 = [\u03c6, \u03b8, \u03c8]T; \u03bd = [\u03bdT 1 , \u03bd T 2 ]T; \u03bd1 = [vx, vy, vz]T; \u03bd2 = [\u03c9x, \u03c9y, \u03c9z]T; where the position and orientation of a QRT UAV, \u03b7, are described relative to the inertial reference frame, while the linear and angular velocities of a QRT UAVs, \u03bd, are expressed in the body-fixed frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002940_app.1960.070030805-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002940_app.1960.070030805-Figure1-1.png",
        "caption": "Fig. 1. Simple extension tear test piece.",
        "texts": [],
        "surrounding_texts": [
            "In previous papers (I to V of this a tear criterion for rubbers has been proposed based on an energy balance approach. This equates the energy required to form new surfaces (the tearing energy) with the loss of elastic strain energy in the test piece. The tearing energy T is assumed to be characteristic of the material and so independent of the overall shape of the test piece. It is thus the fundamental property controlling tear behavior. The correctness of this approach was investigated by making tear measurements on test pieces of different shapes but of the same material and examining the constancy of the T values obtained.lV6 The results weie consistent with the theory but not wholly conclusive, due primarily to the particular tearing behavior of the materials used (natural rubber gum vulcanizates) . Another limitation was that accurate T values could be obtained only if they could be calculated directly from the measured tearing forces or elongations, add the required relationships were known for only two types of test piece. Clearly, the more test pieces available for comparison and the more they differ from each other in shape, the more stringent the test of the basic theory. In the present paper a third test piece is described, the necessary theory given, and experimental results presented on the three test pieces. By comparing the results from these test pieces, which are of widely different shapes, a critical test of the theory is possible. The choice of the experimental material is influenced by several factors. Previous measurements have been made on natural rubber gum compounds,\u2019 which have the advantage of possessing excellent elastic properties but whose rupture characteristics are such that tearing occurs at a critical load. In contrast, a gum GR-S tears more or less steadily at a rate depending on the a characteristic which is experimentally advantageous for the particular test pieces de- scribed here. It was therefore used in this investigation."
        ]
    },
    {
        "image_filename": "designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure2-1.png",
        "caption": "Fig. 2. Image of tooth profile modification, tooth lead crowning and tooth lead relieving.",
        "texts": [
            " In the last research, it was found that themisalignment error of the gear shafts on the vertical plane of the plane of action of a pair of spur gears almost has no effect on tooth surface CS, so only themisalignment error of the gear shafts on the plane of action is used here to investigate the effect of it on toothMS. The misalignment error of the gear shafts on the plane of action can be expressed by an inclination angle of the contact teeth on the plane of action as shown in Fig. 1. 2.2. Definitions of the tooth modifications Fig. 2(a) is an image of the tooth profilemodificationmethod. An arc curvewith the radius R is used tomodify tooth profiles of spur gears (tooth tip and root are modified with the same quantity). Since this method can be realized easily, it is used very popularly for spur gears. In Fig. 2(a), themaximumquantity of the tooth profilemodification is illustrated. The effect of toothprofilemodification on tooth engagements is investigated through investigating the effect of themaximum quantity of the profile modification on toothMS, LSR and CS of the pair of gears when the pinion is modified. Fig. 2(b) is an image of tooth lead crowning. Thismethod is used for tooth longitudinalmodification. An arc curve is used tomodify the tooth lead. Though the lead crowning was investigated in the last research, since the effect of the lead crowning on tooth MS couldn't be investigated in the last research, it is investigated here. The maximum quantity of the lead crowing is also illustrated in Fig. 2(b). Fig. 2(c) shows amethod also used for tooth longitudinal modification. It is called lead relieving. In Fig. 2(c), straight lines are used to relief the tooth lead. The maximum relieving quantity and relieving length of the teeth are illustrated in Fig. 2(c). The effect of the lead relieving on tooth engagements is investigated through investigating the effect of the relieving length on toothMS, LSR and CS of the pair of gears under the condition that the maximum relieving quantity is fixed at 15 \u03bcm. 3. LTCA of a pair of spur gears with misalignment error and tooth modifications In previous research [11,12], a face-contact model of contact teeth and self-developed FEM software were used to conduct LTCA, MS, LSR and CS calculations of a pair of spur gears withmachining errors, assembly errors and toothmodifications",
            " Since the tooth side heavier contacts make the tooth loads concentrate on the tooth side, greater contact deformation of the contact teeth shall happen than the uniform contact, then tooth MS becomes smaller than the uniform contact. Fig. 10(a) and (b) is the tooth CS on the first and second pairs of contact teeth respectively when the pair of gears engages at Position 6 and the misalignment error is 0.004\u00b0. 7. Effect of the tooth profile modification on tooth engagements LTCA is made and the tooth MS, LSR and CS are calculated for the pair of gears with tooth profile modifications. Tooth profile modifications are made only for the pinion using arc curves as introduced in Fig. 2(a). Calculation results are given in the following. Fig. 11(a) is a comparison of the toothMS curves between the ideal gears and the pair of gearswith tooth profilemodifications. The maximum quantities of the tooth profile modifications are also illustrated in Fig. 11(a). In Fig. 11(a), it is found that value of the tooth MS curves becomes smaller and smaller gradually when themaximumquantities of the tooth profile modifications are changed from 0 \u03bcm into 1 and then 2 \u03bcm. In this case, since the maximum quantities of the tooth profile modifications are not so large, these tooth profile modifications cannot change tooth contact states (from a double pair tooth contact into a single pair tooth contact), only changed tooth LSR of the double pair tooth contact as shown in Fig",
            " 15(a) and (b) is the tooth CS on the first and second pairs of contact teeth respectively when the pair of gears engages at Position 6 and the maximum quantity of the lead crowning is 5 \u03bcm. Lead relieving was used for spur gears very early in order to reduce tooth side heavier contacts resulted from the misalignment errors of gear shafts. So, the effect of the lead relieving on tooth engagements is investigated here through performing LTCA, MS, LSR and CS calculations. When doing this investigation, the lead relieving is made only for the pinion using the method illustrated in Fig. 2(c). Also, the relieving quantity of the pinion is fixed at 15 \u03bcm and the relieving length is varied from 2 to 10 mm. Calculation results are given in the following. Fig. 16(a) is a comparison of the toothMS curves between the ideal gears and the pair of gears with lead relieving. Fig. 16(b) is the relationships among the MS value at Position 7, the fluctuation D and the relieving length. From Fig. 16, it is found that the MS value and the fluctuation D become smaller when the pinion is relieved and the relieving length becomes longer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003750_s00170-017-1303-0-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003750_s00170-017-1303-0-Figure3-1.png",
        "caption": "Fig. 3 A simplified airfoil blade",
        "texts": [
            " This paper investigates the profile errors and surface microstructures of the stainless steel 316L parts produced by the SLM process. The residual stress distribution among the scanning and build directions has been measured using the XRD method. A correlation between the surface microstructure and residual stress distribution has been made. Simplified airfoil blade geometries were selected for this study. The dimensions of a typical airfoil blade were simplified into inclination angle, center distance, and leading-edge diameter and trailing-edge diameter as shown in Fig. 3. Four groups of samples A\u2013D were designed, and each group consisted of nine samples as shown in Fig. 4. These groups were used for studying the effect of two factors: (i) part dimensions; and (ii) part location on the build plate. Group A to study the inclination angle, group C to study the center distance, and group D to study the thickness (trailing- and leading-edge diameters). Group B consists of identical samples to study the part location on the build plate. Table 1 illustrates the dimensions of the samples in each group"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001991_j.jbiomech.2011.02.072-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001991_j.jbiomech.2011.02.072-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the biomechanical walking model. Human body was modeled with two massless, compliant legs with curved feet. The parameters K, C, y, L and R indicate the spring constant, damping constant, leg angle with respect to the vertical axis, compliant leg length and radius of the curved foot, respectively. The subscripts \u20181\u2019 and \u20182\u2019 indicate the trailing leg and the leading leg, respectively.",
        "texts": [
            " Optical marker positions and GRFs were 5th-order Butterworth low-pass filtered with cutoff frequencies of 10 Hz for the motion capture data and 30 Hz for the force plate data. The velocity and the trajectory of the CoM were calculated by integrating the accelerations obtained from the GRF data (Donelan et al., 2002a; Yeom and Park, 2010). To calculate leg stiffness as a function of walking speed, the human body was modeled as a lumped mass on top of two massless, compliant legs connected to a curved foot (Fig. 1). We added a damper to an existing compliant walking model (Geyer et al., 2006; Whittington and Thelen, 2009). The compliant leg was defined as a radial telescoping leg that deflects in the linear direction but can transmit forces in tangential directions (Whittington and Thelen, 2009). A passive spring provided a compliant mechanism to absorb collision impacts and to generate push-off impulses, whereas the damper restrained excessive motion of the CoM. Both the spring and damper were assumed to be time-invariant linear components at a given walking speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003080_j.phpro.2014.08.099-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003080_j.phpro.2014.08.099-Figure10-1.png",
        "caption": "Fig. 10. Macrographs of web support structure with dimension of 1.45 mm.",
        "texts": [
            " As it can be noticed from Table 4, the web supports were quite easily removed. Most supports were very loose and could be removed without tools or removed easily with pliers. Table 4 also shows that generally the smaller the angle is the easier it is to remove the support structure. It can be also said that the diameter of the support affects its removability. A support with a larger diameter is easier to remove than a support with a small diameter. Fig. 9 shows macrographs of web support structures with dimension of 1.3 mm and Fig. 10 represents macrograph of web support structures with dimension of 1.45 mm. As it can be seen from Fig. 9 and Fig. 10, some of the support structures were already detached during the cutting of the pieces which indicates that the supports would be easy to remove. When the digital model is compared to the manufactured piece, it can be seen that there are nearly no deformations and also the teeth between the support and the part are manufactured well (see Fig. 11). Most of the support structures in samples 3 and 4 were tightly attached to the main part after cutting. Sample 3 had no missing supports and sample 4 only lost six small pieces of tubes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002656_j.resmic.2012.10.016-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002656_j.resmic.2012.10.016-Figure1-1.png",
        "caption": "Fig. 1. Swimming bacteria undergo rheotaxis in bulk fluids and near walls. (a) Schematic for rheotaxis in bulk fluids: the chirality of a left-handed flagellum leads to a lift force (in the \u00fez direction as indicated on the figure) that is opposed by the drag on the cell body, thereby producing a torque on the cell that rotates the bacterium so that it can partially swim against the flow direction ( z). Figure reproduced with permission from Marcos et al. (2012). (b) Near a solid surface, E. coli (K12) exhibit rheotaxis against flow (arrows) when the shear rate is less than 6.4 s 1. Figure reproduced with permission from Kaya and Koser (2012). Copyright 2012 Cell Press.",
        "texts": [
            " A surprising consequence of this physical mechanism is that swimming bacteria can drift across streamlines of an external flow, which is not expected in low Reynolds number environments in which the flows are laminar (Marcos et al., 2012). Experiments on Bacillus subtilis show that in bulk fluids far from surfaces, hydrodynamic stresses on helical flagella produce a net lift force that is balanced by viscous drag (Marcos et al., 2009), whereas the cell body feels only drag. The combined forces on bundle and body induce a torque that rotates the cell body against the direction of flow, allowing the bacterium to swim upstream against the gradient in shear stress in rheotaxis as shown in Fig. 1a (Marcos et al., 2012). As bacteria swim near solid surfaces, as required for biofilm formation, hydrodynamic interactions with the surface modify the physics of flagellated swimming. Bacteria swimming near a solid surface also exhibit rheotaxis, rapidly and continuously swimming against the direction of moderate flow rates (corresponding to shear rates of up to 6.4 s 1) as shown in Fig. 1b (Kaya and Koser, 2012). In addition to flow, however, hydrodynamic interactions with the nearby surface can also reorient bacteria: specifically, hydrodynamic drag due to the surface on the back of the cell, downstream, rotates the cell body to point directly upstream and thereby allows the bacterium to swim against the direction of flow (Kaya and Koser, 2009). Physical interactions between appendages, bacteria, and surfaces leading to rheotaxis may thus allow biofilm-forming bacteria to rapidly spread on surfaces against adverse flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002352_1077546317716315-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002352_1077546317716315-Figure4-1.png",
        "caption": "Figure 4. Schematic of the contact pattern (enlarged view): (a) sharp edge, (b) very small cylindrical edge, and (c) small cylindrical edge.",
        "texts": [],
        "surrounding_texts": [
            "For an unlubricated healthy RB, the contact deformation ih between the inner race and roller can be given by (Chen, 2007) ih \u00bc 2Q le 1 2 E0 ln 4RihRrh b2ih \u00fe 0:814 \u00f01\u00de where Q is the external force, le is the equivalent contact length, Rrh is the radius of the healthy roller, is the Poisson\u2019s ratio, E0 is the equivalent elastic modulus, and bih is the semi-width of the contact surface between the unlubricated healthy inner race and roller, which is given by bih \u00bc 1:59 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q le RihRrh Rih \u00fe Rrh 1 2 E0 s \u00f02\u00de Then, the contact stiffness coefficient between the unlubricated healthy inner race and roller Kih is calculated by Kih \u00bc Q ih \u00f03\u00de Moreover, the contact deformation oh between the unlubricated healthy outer race and roller can be given by (Chen, 2007) oh \u00bc 2Q le 1 2 E0 1 ln boh\u00f0 \u00de \u00f04\u00de where boh is the semi-width of the contact surface between the unlubricated healthy outer race and roller, which is given by boh \u00bc 1:59 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q le RohRrh Roh Rrh 1 2 E0 s \u00f05\u00de Then, the contact stiffness coefficient between the unlubricated healthy outer race and roller Koh can be calculated by Koh \u00bc Q oh \u00f06\u00de The total contact stiffness coefficient Keh between two unlubricated healthy races and one roller can be given by Keh \u00bc KihKoh Kih \u00fe Koh \u00f07\u00de"
        ]
    },
    {
        "image_filename": "designv10_1_0001315_978-1-4419-1117-9-Figure5.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001315_978-1-4419-1117-9-Figure5.3-1.png",
        "caption": "Fig. 5.3 Position of the attachment points: (a) on the base, (b) on the platform",
        "texts": [],
        "surrounding_texts": [
            "A 6-dof parallel mechanism and its joint distributions both on the base and on the platform are shown in Figs. 5.1\u20135.3. This mechanism consists of six identical variable length links, connecting the fixed base to a moving platform. The kinematic chains associated with the six legs, from base to platform, consist of a fixed Hooke joint, a moving link, an actuated prismatic joint, a second moving link, and a spherical joint attached to the platform. It is also assumed that the vertices on the base and on the platform are located on circles of radii Rb and Rp, respectively.\nA fixed reference frame O xyz is connected to the base of the mechanism and a moving coordinate frame P x0y0z0 is connected to the platform. In Fig. 5.2, the points of attachment of the actuated legs to the base are represented with Bi and the points of attachment of all legs to the platform are represented with Pi , with i D 1; : : : ; 6, while point P is located at the center of the platform with the coordinate of P.x; y; z/.\nThe Cartesian coordinates of the platform are given by the position of point P with respect to the fixed frame, and the orientation of the platform (orientation of frame P x0y0z0 with respect to the fixed frame), represented by three Euler angles ; , and or by the rotation matrix Q.",
            "Fig. 5.2 Schematic representation of the spatial 6-dof parallel mechanism with prismatic actuators\nX\u2019\nB1\nB6\nB2\nB3\nB4 B5\nP1P2\nP3\nP4 P5\nP6\nZ\nX\nY O\nP Y\u2019\nZ\u2019\nIf the coordinates of point Bi in the fixed frame are represented by vector bi , then we have\npi D 2 4 xi yi zi 3 5 ; r 0 i D 2 4 Rp cos pi Rp sin pi 0 3 5 ; p D 2 4 x y z 3 5 ; bi D 2 4 Rb cos bi Rb sin bi 0 3 5 ; (5.1)",
            "where pi is the position vector of point Pi expressed in the fixed coordinate frame whose coordinates are defined as .xi ; yi ; zi /, r0i is the position vector of point Pi expressed in the moving coordinate frame, and p is the position vector of point P expressed in the fixed frame as defined above, and\nbi D 2 66666664 b1 b2 b3 b4\nb5\nb6\n3 77777775 D 2 66666664\nb\n2 =3 b\n2 =3C b\n4 =3 b\n4 =3C b\nb\n3 77777775 ; pi D 2 66666664 p1 p2 p3 p4\np5\np6\n3 77777775 D 2 66666664\np\n2 =3 p\n2 =3C p\n4 =3 p\n4 =3C p\np\n3 77777775 : (5.2)\nSimilarly, the solution of the inverse kinematic of this mechanism can be written as\n2i D .pi bi /T.pi bi /; i D 1; : : : ; 6: (5.3)\nSince the mechanism is actuated in parallel, one has the velocity equation as\nAt D B P ; (5.4)\nwhere vectors P and t are defined as\nP D P 1 P 6\nT ; (5.5)\nt D !T PpT T ; (5.6)\nwhere ! and Pp are the angular velocity and velocity of one point of the platform, respectively, and\nA D m1 m2 m3 m4 m5 m6\nT (5.7)\nB D diag\u0152 1; 2; 3; 4; 5; 6 (5.8)\nand mi is a six-dimensional vector expressed as\nmi D\n.Qr0i / .pi bi /\n.pi bi /\n: (5.9)"
        ]
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure37-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure37-1.png",
        "caption": "Fig. 37 Isometric view (3D) of schematic representation of the forged area at each step [56]",
        "texts": [
            " The combination of forging and WAAM can be during WAAM forming [56], or can be processed after WAAM forming, such as a WAAM technology based on hot forging proposed by Duarte VR. During WAAM, the material is locally forged immediately after deposition, and in situ viscoplastic deformation occurs at high temperatures. In the subsequent layer deposition, recrystallization of the previously solidified structure occurred, thereby refining the microstructure. The design of the device is shown in the Fig. 37, and the formed samples are mechanically characterized. The samples have obtained improvements in yield strength and ultimate tensile strength. In order to combine WAAM and forging processes, Bambach [57] proposed two process chains. The first is to first use WAAM to form semi-finished products, and then use forging to form a complete workpiece; the second is to forge into semi-finished products first, and then use WAAM to add more complex features on the final workpiece to the semi- finished products to obtain the final parts, shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002292_j.msea.2014.03.077-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002292_j.msea.2014.03.077-Figure3-1.png",
        "caption": "Fig. 3. Top view and dimensions of the dog-bone specimens where the shaded area represents the clad: (a) tensile specimen and (b) fatigue specimen.",
        "texts": [
            " Fourteen depth points were measured for each of the four variables in the vertical direction through the clad, heat affected region, and substrate at a spacing of 0.5 mm for a total distance of 7.0 mm. Each of the fourteen depth points were measured in three principal directions (two in-plane directions and one normal to the surface). Axial tension testing was performed using a 250 kN MTS testing machine using a strain rate of 1.0 mm/min, in accordance with ASTM standard 8M (dimensions shown in Fig. 3a). Strain was measured using a 25 mm MTS extensometer. Four specimens were tested for each variable. For comparison, the tensile properties of both the substrate (AISI 4340) and substrate with a grind-out were also tested. Axial constant amplitude fatigue testing was performed using a 100 kN MTS testing machine using an R ratio of 0.1 and test frequency of 10 Hz, in accordance with ASTM standard E466 (dimensions shown in Fig. 3b). Testing was performed at room temperature. For each variable, three to four specimens were tested over four different stress levels to produce a preliminary fatigue life curve, in accordance with ASTM standard E739. For comparison, the fatigue life of both the substrate and substrate with a grind-out were also tested. Fracture surface images were obtained using a Phillips XL30 Scanning Electron Microscope. Table 2 Laser processing parameters used for the laser cladding experiment. Laser power (kW) Powder flow rate (g/min) Laser traverse speed (mm/min) Laser spot size (mm) Overlap width (mm) 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003808_j.mechmachtheory.2018.03.001-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003808_j.mechmachtheory.2018.03.001-Figure3-1.png",
        "caption": "Fig. 3. Schematic illustration of normal forces to the contact between the raceways: (a) without angular contact; (b) with angular contact; (c) front view with Azimuth angle of a generic ball.",
        "texts": [
            " (4) and (5) , the damping coefficient for inner and outer raceways can be directly obtained for each ball. F d = F dynamic = F restoring + F dissipati v e (5) Nonato and Cavalca [36,38,40,41] derived the model for a pure radial ball bearing, which allowed for the simplification of a total force between inner and outer raceway, resulting in a single set of nonlinear force parameters. However, for an angular contact ball bearing it is necessary to take into account that forces and displacements in each contact are noncollinear Fig. 3 ), requiring the reduced model to be fitted for each inner and outer contacts. Eqs. (4) and (5) are used during the optimization to calculate the nonlinear parameters. Unlike the pure radial cases, different contact angles impact the damping at each circumferential location, due to variation in the velocity at the contacts. Therefore, a set of nonlinear force parameters has to be defined for inner and outer raceways contacts at each element. The model presented here for the angular contact ball bearing is based on forces equilibrium equations at each instant of time for every rotation condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002203_j.ymssp.2013.06.040-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002203_j.ymssp.2013.06.040-Figure1-1.png",
        "caption": "Fig. 1. Modelling of gear tooth crack. (a) Modelling of cracked tooth, (b) modelling of one slice of width dW, (c) crack depth distribution along the tooth width, and (d) tooth notation [4].",
        "texts": [
            " A calculation model for gear mesh stiffness using a parabolic distribution of the tooth crack propagation is presented in [4] and can be described as consisting of two parts: determination of the mesh stiffness with a constant crack depth for a thin slice along the tooth width and determination of the mesh stiffness for all the slices along the tooth width which have a non-uniform crack depth. Moreover, the effects of fillet foundation deflection and Hertzian contact are taken into account, as explained in Sections 2.3 and 2.4. By considering the tooth as a non-uniform cantilever beam with an effective length of \u2018d\u2019, see Fig. 1d, the deflections under the action of the force can be determined, and then the stiffness can be calculated. Note that, in this part of the stiffness calculations, the crack is assumed to have a constant crack depth, q(z), for each slice, dW, along the tooth width, as explained in Fig. 1a and b. Based on the calculation of the potential energy stored in a meshing gear tooth, it is feasible to obtain the bending, shear, and axial compressive stiffnesses as follows [4]: 1 Kb \u00bc Z d 0 \u00f0x cos \u00f0\u03b11\u00de h sin \u00f0\u03b11\u00de\u00de2 EIx dx \u00f01\u00de 1 Ks \u00bc Z d 0 1:2 cos 2\u00f0\u03b11\u00de GAx dx \u00f02\u00de 1 Ka \u00bc Z d 0 sin 2\u00f0\u03b11\u00de EAx dx \u00f03\u00de where the following notation is used: Kb: Bending stiffness. Ks: Shear stiffness. Ka: Axial compressive stiffness. h, hc, hx, x, dx, d, and \u03b11 are illustrated in Fig. 1d. Note that \u03b11 varies with the gear tooth position. E: Young\u2032s modulus. G: Shear modulus, G\u00bc E 2\u00f01\u00fe\u03c5\u00de \u03c5: Poisson ratio. Ix: Area moment of inertia, Ix \u00bc \u00f01=12\u00de\u00f0hx\u00fehx\u00de3 dW ; hxrhq \u00f01=12\u00de\u00f0hx\u00fehq\u00de3 dW ; hx4hq ( Ax: Area of the section of distance \u2018x\u2019 measured from the load application point, Ax \u00bc \u00f0hx\u00fehx\u00de dW ; hxrhq \u00f0hx\u00fehq\u00de dW ; hx4hq ( hq\u00bchc q(z) sin(\u03b1c), hq represents the reduced dimension of the tooth thickness when a crack is existing. Chen and Shao [4] and Tian [21] used this reduced dimension for calculating Ix and Ax. They used hq instead of hx in case of hx4hq. q(z) and \u03b1c are the crack depth and crack angle, respectively, as shown in Fig. 1b. At a certain position, \u2018z\u2019, through the tooth width, we can find the stiffness of one slice resulting from the effect of all the stiffnesses calculated previously as follows: K\u00f0z\u00de \u00bc 1= 1 Kb \u00fe 1 Ks \u00fe 1 Ka \u00f04\u00de The mesh stiffness model presented in [4] divides the tooth width into thin slices to represent the crack propagation through the tooth width, as shown in Fig. 1a. Consequently, for a small dW the crack depth is assumed to be a constant through the width for each slice, see Fig. 1b. By integrating the stiffness of all the slices along the width, the stiffness of the entire tooth can be evaluated as follows: Ktp \u00bc Z W 0 K\u00f0z\u00de \u00f05\u00de In [4] it is assumed that the distribution of the crack depth follows a parabolic function along the tooth width, as shown in Fig. 1c for the crack section A-A, which can be recognised in Fig. 1a. When the crack length is less than the whole tooth width: q\u00f0z\u00de \u00bc qo ffiffiffiffiffiffiffiffiffiffiffiffiffi Wc z Wc s ; zA 0 Wc\u00bd \u00f06\u00de q\u00f0z\u00de \u00bc 0; zA \u00bdWc W \u00f07\u00de where Wc is the crack length, W is the whole tooth width, and qo is the maximum crack depth, see Fig. 1c. When the crack length extends through the whole tooth width: q\u00f0z\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2o q22 W z\u00feq22 s \u00f08\u00de where q2 is shown in Fig. 1c. Sainsot et al. [31] studied the effect of fillet foundation deflection on the gear mesh stiffness, derived this deflection, and applied it for a gear body. The fillet foundation deflection can be calculated as follows [31]: \u03b4f \u00bc F U cos 2\u00f0\u03b1m\u00de W UE Ln uf Sf 2 \u00feMn uf Sf \u00fePn\u00f01\u00feQn tan 2\u00f0\u03b1m\u00de\u00de ( ) \u00f09\u00de where the following notation is used: \u03b1m is the pressure angle. uf and Sf are illustrated in Fig. 2. Ln; Mn; Pn; and Qn can be approximated using polynomial functions as follows [31]: Xn i \u00f0hf i; \u03b8f \u00de \u00bc Ai=\u03b8 2 f \u00feBih 2 f i\u00feCihf i=\u03b8f \u00feDi=\u03b8f \u00feEihf i\u00feFi \u00f010\u00de Xn i represents the coefficients Ln; Mn; Pn; and Qn",
            " As it is difficult to define analytically the exact crack length corresponding to a certain crack depth, and because the study of crack growth with time is out of the scope of the present research study, we have considered the propagation cases proposed in [30]. The propagation cases utilised for the study of this scenario are shown in Table 6. The values of q2 have been obtained from the intersections of the parabolic lines with the vertical axis at points a\u2013j, as illustrated in Fig. 8a, the section A-A can be recognised in Fig. 1a, and the time-varying mesh stiffnesses for all the studied cases are shown in Fig. 8b. A high backup ratio with a crack angle of 701 is considered here. The dynamic response of a gear system can be extracted using dynamic lumped parameters modelling to study the effect of tooth crack propagation on the obtained vibration response from a fault detection point of view. A dynamic simulation of a six DOF model has been performed based on the time-varying mesh stiffness model which was explained earlier"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000440_science.165.3891.358-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000440_science.165.3891.358-Figure1-1.png",
        "caption": "Fig. 1. Induction by gibberellic acid (GA) of a-amylase in isolated aleurone layers. The GA was removed after 9 hours of incubation, and then added back at 15 hours (arrow). The synthesis of a-amylase is dependent upon the continued presence of GA. [From Chrispeels and Varner (10)]",
        "texts": [
            "o rg D ow nl oa de d fr om o n Ju ly 2 6, 2 01 5 w w w .s ci en ce m ag .o rg D ow nl oa de d fr om o n Ju ly 2 6, 2 01 5 w w w .s ci en ce m ag .o rg D ow nl oa de d fr om o n Ju ly 2 6, 2 01 5 w w w .s ci en ce m ag .o rg D ow nl oa de d fr om Evidence for Induced Enzyme Synthesis As little as 10-10 mole of gibberellic acid per liter promotes release of reducing sugars by endosperm of barley half seeds (5) because of increased formation and secretion of a-amylase by aleurone cells surrounding the endosperm (Fig. 1) (6, 7). The a-amylase increase is inhibited by the following: (i) anaerobiosis and dinitrophenol (8). which suggests a requirement for phosphorylative energy; (ii) p-fluorophenylalanine and cycloheximide (7) and therefore requires protein synthesis; (iii) and actinomycin D and 6-methyl purine (9, 10), which suggests a requirement for RNA synthesis. Labeled amino acids are incorporated throughout the polypeptide chain (9). Thus at least part of the increased a-amylase activity is due to de novo synthesis of a-amylase molecule"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002714_j.triboint.2011.08.019-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002714_j.triboint.2011.08.019-Figure3-1.png",
        "caption": "Fig. 3. Ball loading at angular position Cj.",
        "texts": [
            " In according with the relative axial displacement of the inner and outer rings da, the axial distance between the position of inner and outer raceway groove curvature centers at any ball is A1j \u00bc BDsina0\u00feda \u00f03\u00de Further, in according with the relative radial displacement of the ring centers dr, the radial distance between the position of the groove curvature centers at any ball is A2j \u00bc BDcosa0\u00fedr coscj \u00f04\u00de New variables X1j and X2j are defined as seen from Fig. 2 cosaoj \u00bc X2j \u00f0f o 0:5\u00deD\u00fedoj sinaoj \u00bc X1j \u00f0f o 0:5\u00deD\u00fedoj cosaij \u00bc A2j X2j \u00f0f i 0:5\u00deD\u00fedij sinaij \u00bc A1j X1j \u00f0f i 0:5\u00deD\u00fedij 8>>>>< >>>>: \u00f05\u00de Using the Pythagorean theorem, it can be seen from Fig. 2 that \u00f0A1j X1j\u00de 2 \u00fe\u00f0A2j X2j\u00de 2 \u00bd\u00f0f i 0:5\u00deD\u00fedij 2 \u00bc 0 \u00f06\u00de X2 1j\u00fe\u00f0X 2 2j \u00bd\u00f0f o 0:5\u00deD\u00fedoj 2 \u00bc 0 \u00f07\u00de Considering the plane passing through the bearing axis with the center of a ball located at azimuth Cj, the load diagram of Fig. 3 can be obtained. If \u2018\u2018outer raceway control\u2019\u2019 is approximated at a given ball location, the ball gyroscopic moment is resisted entirely by friction force at the ball-outer raceway contacts, then in Fig. 3, lij\u00bc0 and loj\u00bc2. The normal ball loads in accordance with normal contact deformations are as follows: Qoj \u00bc Kod 1:5 oj \u00f08\u00de Qij \u00bc Kid 1:5 ij \u00f09\u00de From Fig. 3, considering the equilibrium of forces in the horizontal and vertical directions Qij sinaij Qoj sinaoj Mgj D \u00f0lij cosaij loj cosaoj\u00de \u00bc 0 \u00f010\u00de Qij cosaij Qoj cosaoj\u00fe Mgj D \u00f0lij sinaij loj sinaoj\u00de\u00feFcj \u00bc 0 \u00f011\u00de With (5)\u2013(7), (10) and (11), X1j, X2j, aij and aoj may be solved simultaneously at each ball angular location once values for da and dr are assumed. The Newton\u2013Raphson method can be used for solution of simultaneous nonlinear Eq. [22]. The centrifugal force mentioned above is calculated as follows: Fcj \u00bc 1 2 dmo2 jm \u00f012\u00de in which dm is the pitch diameter of the bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure42-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure42-1.png",
        "caption": "Fig. 42 Idle time selection for WAAM: method based on finite element simulation. aHeat source model used for WAAM simulation and moving coordinate system; b idle time calculation procedure; c actual manufactured part [60]",
        "texts": [
            " This method uses a finite element model to simulate the temperature field of the workpiece during the process and calculates the appropriate idle time. The proposed algorithm calculates idle time values specific to each layer to allow for conditions that satisfy a constant interlayer temperature. Such parameters are measured by observing the top surface of the current layer. This allows for an increase in the size of the weld pool during the deposition process, which results in component collapse and non-uniform mechanical properties along the building direction, shown in Fig. 42. As can be seen from the above discussion, alloys such as titanium alloys, nickel alloys, aluminum alloys, and stainless steels are suitable for large-scale workpiece forming of WAAM, especially titanium alloys and nickel alloys widely used in the aviation industry. However, the current research has not developed a specific alloy material specifically for WAAM, and it is difficult to achieve the requirements of multi-functionality and complexity. Therefore, by studying the metal arc additive manufacturing mechanism, it has become a top priority to develop serialized, professional, low-cost, high-strength metal materials with good molding properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure2.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure2.19-1.png",
        "caption": "Fig. 2.19 Components of rotor blade incidence",
        "texts": [
            " The blades will then flap to restore the zero hub moment condition. For small flap angles, the equation of flap motion can now be written in the approximate form \ud835\udefd\u2032\u2032 + \ud835\udf062 \ud835\udefd \ud835\udefd = 2 \u03a9 (p cos\ud835\udf13 \u2212 q sin\ud835\udf13) + 1 I\ud835\udefd\u03a92 R \u222b 0 \ud835\udcc1(r, \ud835\udf13)rdr (2.16) \ud835\udcc1(r, \ud835\udf13) = 1 2 \ud835\udf0cV2ca0\ud835\udefc (2.17) where V is the resultant velocity of the airflow, \ud835\udf0c the air density, and c the blade chord. The lift is assumed to be proportional to the incidence of the airflow to the chord line, \ud835\udefc, up to stalling incidence, with lift curve slope a0. In Figure 2.19 the incidence is shown to comprise two components, one from the applied blade pitch angle \ud835\udf03 and one from the induced inflow \ud835\udf19, given by \ud835\udf19 = tan\u22121 UP UT \u2248 UP UT (2.18) where UT and UP are the in-plane and normal velocity components respectively (the bar signifies nondimensionalisation with \u03a9R). Using the simplification that UP \u226aUT, Eq. 2.16 can be written as \ud835\udefd\u2032\u2032 + \ud835\udf062 \ud835\udefd \ud835\udefd = 2 \u03a9 (p cos\ud835\udf13 \u2212 q sin\ud835\udf13) + \ud835\udefe 2 1 \u222b 0 (U 2 T\ud835\udf03 + UTUP) r dr (2.19) Helicopter and Tiltrotor Flight Dynamics \u2013 An Introductory Tour 29 where r = r\u2215R and the Lock number, \ud835\udefe , is defined as (Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure2.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure2.2-1.png",
        "caption": "Fig. 2.2 Wheel with tire: nomenclature and reference system",
        "texts": [
            " For simplicity, the road is assumed to have a hard and flat surface, like a geometric plane. This is a good model for any road with high quality asphalt paving, since the texture of the road surface is not relevant for the definition of the rim kinematics (while it highly affects grip [8]). The rim R is assumed to be a rigid body, and hence, in principle, it has six degrees of freedom. However, only two degrees of freedom (instead of six) are really relevant for the rim position because the road is flat and the wheel rim is axisymmetrical. Let Q be a point on the rim axis yc (Fig. 2.2). Typically, although not strictly necessary, a sort of midpoint is taken. The position of the rim with respect to the flat road depends only on the height h of Q and on the camber angle \u03b3 (i.e., the inclination) of the rim axis yc. More precisely, h is the distance of Q from the road plane and \u03b3 is the angle between the rim axis and the road plane. Now, we can address how to describe the rim velocity field. The rim, being a rigid body, has a well defined angular velocity . Therefore, the velocity of any point P of the (space moving with the) rim is given by the well known equation [7, p. 124] VP = VQ + \u00d7 QP (2.1) where VQ is the velocity of Q and QP is the vector connecting Q to P . The three components of VQ and the three components of are, e.g., the six parameters which completely determine the rim velocity field. A moving reference system S = (x, y, z;O) is depicted in Fig. 2.2. It is defined in a fairly intuitive way. The y-axis is the intersection between a vertical plane containing the rim axis yc and the road plane. The x-axis is given by the intersection of the road plane with a plane containing Q and normal to yc. Axes x and y define the origin O as a point on the road. The z-axis is vertical, that is perpendicular to the road, with the positive direction upward.3 The unit vectors marking the positive directions are (i, j,k), as shown in Fig. 2.2. 3S is the system recommended by ISO (see, e.g., [14, Appendix 1]). 10 2 Mechanics of the Wheel with Tire An observation is in order here. The directions (i, j,k) have a physical meaning, in the sense that they clearly mark some of the peculiar features of the rim with respect to the road. As a matter of fact, k is perpendicular to the road, i is perpendicular to both k and the rim axis jc, j follows accordingly. However, the position of the Cartesian axes (x, y, z) is arbitrary, since there is no physical reason to select a point as the origin O . This is an aspect whose implications are often underestimated. The moving reference system S = (x, y, z;O) allows a more precise description of the rim kinematics. On the other hand, a reference system Sf = (xf , yf , zf ;Of ) fixed to the road is not very useful in this context. Let jc be the direction of the rim axis yc jc = cos\u03b3 j + sin\u03b3 k (2.2) where the camber angle \u03b3 of Fig. 2.2 is positive. The total rim angular velocity is = \u03b3\u0307 i + \u03b8\u0307 jc + \u03b6\u0307k = \u03b3\u0307 i + \u03c9cjc + \u03c9zk = \u03b3\u0307 i + \u03c9c cos\u03b3 j + (\u03c9c sin\u03b3 + \u03c9z)k = \u03a9x i + \u03a9yj + \u03a9zk (2.3) where \u03b3\u0307 is the time derivative of the camber angle, \u03c9c = \u03b8\u0307 is the angular velocity of the rim about its spindle axis, and \u03c9z = \u03b6\u0307 is the yaw rate, that is the angular velocity of the reference system S. 2.2 Rim Position and Motion 11 It is worth noting that there are two distinct contributions to the spin velocity \u03a9zk of the rim, a camber contribution and a turn contribution4 \u03a9z = \u03c9c sin\u03b3 + \u03c9z (2.4) Therefore, the same value of \u03a9z can be the result of different operating conditions for the tire, depending on the amount of the camber angle \u03b3 and of the yaw rate \u03c9z. By definition, the position vector OQ is (Fig. 2.2) OQ = h(\u2212 tan\u03b3 j + k) (2.5) This expression can be differentiated with respect to time to obtain VQ \u2212 VO = h\u0307(\u2212 tan\u03b3 j + k) + h ( \u03c9z tan\u03b3 i \u2212 \u03b3\u0307 cos2 \u03b3 j ) = h\u03c9z tan\u03b3 i \u2212 ( h\u0307 tan\u03b3 + h \u03b3\u0307 cos2 \u03b3 ) j + h\u0307k (2.6) since dj/dt = \u2212\u03c9zi. Even in steady-state conditions, that is h\u0307 = \u03b3\u0307 = 0, we have VQ = VO +h\u03c9z tan\u03b3 i and hence the two velocities are not exactly the same, unless also \u03b3 = 0. The camber angle \u03b3 is usually very small in cars, but may be quite large in motorcycles. The velocity of point O has, in general, longitudinal and lateral components Vo = VO = Vox i + Voy j (2",
            " It is assumed here that the carcass and the belt have negligible inertia, in the sense that the inertial effects are small in comparison with other causes of deformation. This is quite correct if the road is flat and the wheel motion is not \u201ctoo fast\u201d. Tires are made from rubber, that is elastomeric materials to which they owe a large part of their grip capacity [17]. Grip implies contact between two surfaces: one is the tire surface and the other is the road surface. The contact patch (or footprint) P is the region where the tire is in contact with the road surface. In Fig. 2.2 the contact patch is schematically shown as a single region. However, most tires have a tread pattern, with lugs and voids, and hence the contact patch is the union of many small regions (Fig. 2.5). It should be emphasized that the shape and size of the contact patch, and also its position with respect to the reference system, depend on the tire operating conditions. Grip depends, among other things, on the type of road surface, its roughness, and whether it is wet or not. More precisely, grip comes basically from road roughness effects and molecular adhesion",
            " Traditionally, the components of F and MO have the following names: Fx longitudinal force; Fy lateral force; Fz vertical load or normal force; Mx overturning moment; My rolling resistance moment; Mz self-aligning torque, called vertical moment here. The names of the force components simply reaffirm their direction with respect to the chosen reference system S and hence with respect to the rim. On the other hand, 2.5 Footprint Force 15 the names of the moment components, which would suggest a physical interpretation, are all quite questionable. Their values depend on the arbitrarily selected point O , and hence are arbitrary by definition. For instance, let us discuss the name \u201cself-aligning torque\u201d of Mz, with reference to Fig. 2.2 and Eq. (2.10). The typical explanation for the name is that \u201cMz produces a restoring moment on the tire to realign the direction of travel with the direction of heading\u201d, which, more precisely, means that Mz and the slip angle \u03b1 are both clockwise or both counterclockwise. But the sign and magnitude of Mz depend on the position of O , which could be anywhere! The selected origin O has nothing special, not at all. Therefore, the very same physical phenomenon, like in Fig. 2.2, may be described with O anywhere and hence by any value of Mz. The inescapable conclusion is that the name \u201cself-aligning torque\u201d is totally meaningless and even misleading.5 For these reasons, here we prefer to call Mz the vertical moment. Similar considerations apply to Mx . It is a classical result that any set of forces and couples in space, like (F,MO), is statically equivalent to a unique wrench [18]. However, in tire mechanics it is more convenient, although not mandatory, to represent the force-couple system (F,MO) by two properly located perpendicular forces (Fig. 2.2): a vertical force Fp = Fzk having the line of action passing through the point with coordinates (ex, ey,0) such that Mx = Fzey and My = \u2212Fzex (2.9) and a tangential force Ft = Fx i + Fyj lying in the xy-plane and having the line of action with distance |dt | from O (properly located according to the sign of dt ) Mz = \u221a F 2 x + F 2 y dt = |Ft |dt (2.10) We remark that the two \u201cdisplaced\u201d forces Fp and Ft (Fig. 2.2) are completely equivalent to F and MO . These forces are transferred to the rigid rim (apart for a small fraction due to the inertia and weight of the tire carcass and belt). Indeed, the equivalence of the distributed loads in the contact patch to concentrated forces and/or couples makes sense precisely because the rim is a rigid body. For instance, the torque T = T jc that the distributed loads in the contact patch, and hence the force-couple system (F,MO), exert with respect to the wheel axis yc is given by T = T jc = ((QO \u00d7 F + MO) \u00b7 jc ) jc = ( \u2212Fx h cos\u03b3 + My cos\u03b3 + Mz sin\u03b3 ) jc (2.11) 5What is relevant in vehicle dynamics is the moment of (F,MO) with respect to the steering axis of the wheel. But this is another story. 16 2 Mechanics of the Wheel with Tire where (2.2) and (2.5) were employed. This expression is particularly simple because the yc-axis intersects the z-axis and is perpendicular to the x-axis (Fig. 2.2). If \u03b3 = 0, Eq. (2.11) becomes T = \u2212Fxh + My = \u2212Fxh \u2212 Fzex (2.12) To perform some further mathematical investigations, it is necessary to discard completely the road roughness (Fig. 2.6) and to assume the road surface in the contact patch to be perfectly flat, exactly like a geometric plane (Fig. 2.2).6 This is a fairly unrealistic assumption whose implications should not be underestimated. Owing to the assumed flatness of the contact patch P , we have that the pressure p(x, y)k, by definition normal to the surface, is always vertical and hence forms a parallel distributed load. Moreover, the flatness of P implies that the tangential stress t(x, y) = tx i + tyj forms a planar distributed load. Parallel and planar distributed loads share the common feature that the resultant force and the resultant couple vector are perpendicular to each other, and therefore each force-couple system at O can be further reduced to a single resultant force applied along the line of action (in general not passing through O)",
            " A few formulae should clarify the matter. The resultant force Fp and couple MO p of the distributed pressure p(x, y) are given by Fp = Fzk = k \u222b\u222b P p(x, y)dxdy MO p = Mx i + Myj = \u222b\u222b P (xi + yj) \u00d7 kp(x, y)dxdy (2.13) where Mx = \u222b\u222b P yp(x, y)dxdy = Fzey, My = \u2212 \u222b\u222b P xp(x, y)dxdy = \u2212Fzex (2.14) As expected, Fp and MO p are perpendicular. As shown in (2.14), the force-couple resultant (Fp,MO p ) can be reduced to a single force Fp having a vertical line of action passing through the point with coordinates (ex, ey,0), as shown in Fig. 2.2. 6More precisely, it is necessary to have a mathematical description of the shape of the road surface in the contact patch. The plane just happens to be the simplest. 2.6 Tire Global Mechanical Behavior 17 The resultant tangential force Ft and couple MO t of the distributed tangential stress t(x, y) = tx i + tyj are given by Ft = Fx i + Fyj = \u222b\u222b P ( tx(x, y)i + ty(x, y)j ) dxdy MO t = Mzk = \u222b\u222b P (xi + yj) \u00d7 (tx i + tyj)dxdy = k \u222b\u222b P ( xty(x, y) \u2212 ytx(x, t) ) dxdy = kdt \u221a F 2 x + F 2 y (2.15) where Fx = \u222b\u222b P tx(x, y)dxdy, Fy = \u222b\u222b P ty(x, y)dxdy (2.16) Also in this case Ft and MO t are perpendicular. As shown in (2.15), the force-couple resultant (Ft ,MO t ) can be reduced to a tangential force Ft , lying in the xy-plane and having a line of action with distance |dt | from O (properly located according to the sign of dt ), as shown in Fig. 2.2. Obviously the more general (2.8) still holds F = Fp + Ft MO = MO p + MO t (2.17) The analysis developed so far provides the tools for quite a precise description of the global mechanical behavior of a real wheel with tire interacting with a road. More precisely, as already stated at p. 8, we are interested in the relationship between the motion and position of the rim and the force exchanged with the road in the contact patch: rim kinematics \u21d0\u21d2 force and moment We assume as given, and constant in time, both the wheel with tire (including its inflating pressure and temperature field) and the road type (including its roughness)",
            "29) 7We have basically a steady-state behavior even if the operating conditions do not change \u201ctoo fast\u201d. 2.6 Tire Global Mechanical Behavior 23 which means that Fx = 0 if Vox \u03c9c = fx ( h,\u03b3, Voy \u03c9c , \u03a9z \u03c9c ) (2.30) Under many circumstances there is experimental evidence that the relation above almost does not depend on Voy and can be recast in the following more explicit form8 Vox \u03c9c = rr (h, \u03b3 ) + \u03c9z \u03c9c cr(h, \u03b3 ) (2.31) that is Vox = \u03c9crr(h, \u03b3 ) + \u03c9zcr(h, \u03b3 ) (2.32) This equation strongly suggests to take into account a special point C on the y-axis such that (Fig. 2.11 and also Fig. 2.2) OC = cr(h, \u03b3 )j (2.33) where cr is a (short) signed length. Point C would be the point of contact in case of a rigid wheel. Quite often point O and C have almost the same velocity, although their distance cr may not be negligible (Fig. 2.11). Equation (2.31) can be rearranged to get Vox \u2212 \u03c9zcr(h, \u03b3 ) \u03c9c = Vcx \u03c9c = rr (h, \u03b3 ) (2.34) This is quite a remarkable result and clarifies the role of point C: the condition Fx = 0 requires Vcx = \u03c9crr (h, \u03b3 ), regardless of the value of \u03c9z (and also of Voy )",
            " Therefore they do not provide any direct information on the amount of sliding at any point of the contact patch. In this regard their names may be misleading. More precisely, sliding or adhesion is a local property of any point in the contact patch, whereas slip is a global property of the rim motion. They are completely different concepts. The slip angle \u03b1 is defined as the angle between the rolling velocity Vr and the speed of travel Vc. However, according to (2.48) and (2.43), when \u03b3\u0307 \u2248 0 it is almost equal to the angle between i and Vc (Fig. 2.2)10 tan\u03b1 = \u2212Vcy Vcx (2.68) that is Vcy = \u2212Vcx tan\u03b1. For convenience, \u03b1 is positive when measured clockwise, that is when it is like in Fig. 2.2.11 Of course, a non-sliding rigid wheel has a slip angle constantly equal to zero. On the other hand, a tire may very well exhibit slip angles. However, as will be shown, 10Common definitions of the slip angle, like \u201c\u03b1 being the difference in wheel heading and direction\u201d are not sufficiently precise. 11All other angles are positive angles if measured counterclockwise, as usually done in mathematical writing. 2.8 Grip Forces and Tire Slips 31 a wheel with tire can exchange with the road very high longitudinal and lateral forces still with small slip angles (as shown in the important Fig",
            "45) \u2022 lateral slips: \u03c3y11 = (v + ra1) cos(\u03b411) \u2212 (u \u2212 rt1/2) sin(\u03b411) \u03c911r1 \u03c3y12 = (v + ra1) cos(\u03b412) \u2212 (u + rt1/2) sin(\u03b412) \u03c912r1 \u03c3y21 = (v \u2212 ra2) cos(\u03b421) \u2212 (u \u2212 rt2/2) sin(\u03b421) \u03c921r2 \u03c3y22 = (v \u2212 ra2) cos(\u03b422) \u2212 (u \u2212 rt2/2) sin(\u03b422) \u03c922r2 (3.46) According to (2.57), the evaluation of the spin slips \u03d5ij requires also the knowledge of the camber angles \u03b3ij , of the wheel yaw rates \u03b6\u0307ij = r + \u03b4\u0307ij and of the camber reduction factors \u03b5i \u03d5ij = \u2212 r + \u03b4\u0307ij + \u03c9ij sin\u03b3ij (1 \u2212 \u03b5i) \u03c9ij ri (3.47) The sign conventions are like in Fig. 2.2. Therefore, under static conditions, the two wheels of the same axle have camber angles of opposite sign \u03b3 0 i1 = \u2212\u03b3 0 i2 (3.48) This is contrary to common practice, but more consistent and more convenient for a systematic treatment. The kinematic equations for camber variations due to roll motion will be discussed in Sect. 3.8.3. Similarly, the kinematic equations for roll steer will be given in (3.123). Their presentation must be delayed till the suspension analysis has been completed. 58 3 Vehicle Model for Handling and Performance Owing to (3",
            " In other words, in straight running, the aerodynamic force Fa is given as two vertical loads Za 1 and Za 2 acting directly on the front and rear tires, respectively, plus the aerodynamic drag Xa acting at road level. The road-tire friction forces Ftij are the resultant of the tangential stress in each footprint, as shown in (2.15). Typically, for each tire, the tangential force Ftij is split into a longitudinal component Fxij and a lateral component Fyij , as shown in Fig. 3.7. It is very important to note that these two components refer to the wheel reference system shown in Fig. 2.2, not to the vehicle frame. If \u03b4ij is the steering angle of a wheel, the components of the tangential force in the vehicle frame S are given by Ftij = Xij i + Yij j where Xij = Fxij cos(\u03b4ij ) \u2212 Fyij sin(\u03b4ij ) Yij = Fxij sin(\u03b4ij ) + Fyij cos(\u03b4ij ) (3.58) with obvious simplifications if \u03b4ij is very small. To deal with shorter expressions, it is convenient to define X1 = X11 + X12, X2 = X21 + X22 Y1 = Y11 + Y12, Y2 = Y21 + Y22 \u0394X1 = X12 \u2212 X11 2 , \u0394X2 = X22 \u2212 X21 2 \u0394Y1 = Y12 \u2212 Y11 2 , \u0394Y2 = Y22 \u2212 Y21 2 (3",
            " In a first order analysis, the investigation is limited to the series expansion \u0394\u03b3ij \u2248 \u2202\u03b3ij \u2202\u03c6s i \u03c6s i + \u2202\u03b3ij \u2202\u0394ti \u0394ti + \u2202\u03b3ij \u2202\u03c6 p i \u03c6 p i + \u2202\u03b3ij \u2202z p i z p i (3.81) where all derivatives are evaluated at the reference configuration. From Fig. 3.8 and also with the aid of Fig. 3.9, we obtain the following general results for any 70 3 Vehicle Model for Handling and Performance symmetric planar suspension (cf. Fig. 9.5) \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u2202\u03b3i1 \u2202\u03c6s i = \u2202\u03b3i2 \u2202\u03c6s i = \u2212 ti/2 \u2212 ci ci = \u2212qi \u2212 bi bi \u2202\u03b3i1 \u2202\u0394ti = \u2212 \u2202\u03b3i2 \u2202\u0394ti = 1 2bi \u2202\u03b3i1 \u2202\u03c6 p i = \u2202\u03b3i2 \u2202\u03c6 p i = 1 \u2202\u03b3ij \u2202z p i = 0 (3.82) The sign convention for the camber variations \u0394\u03b3ij is like in Fig. 2.2. Therefore, in Fig. 3.9(b) we have \u0394\u03b3i1 < 0 and \u0394\u03b3i2 > 0. Equations (3.81) and (3.82) yield \u0394\u03b3i1 \u2248 \u2212 ( qi \u2212 bi bi ) \u03c6s i + \u03c6 p i + 1 2bi \u0394ti \u0394\u03b3i2 \u2248 \u2212 ( qi \u2212 bi bi ) \u03c6s i + \u03c6 p i \u2212 1 2bi \u0394ti (3.83) This is quite a remarkable formula. It is simple, yet profound. For instance, the two suspension schemes of Fig. 3.8, which look so different, do have indeed very different values of the first two partial derivatives in (3.82). On the other hand, it should not be forgotten that (3.81) is merely a kinematic relationship",
            " The belt slides on the rigid body (to simulate rolling) and is equipped with infinitely many flexible bristles (like a brush) which touch the road in the contact patch. As shown in Fig. 10.2, the contact patch P is assumed to be a convex, simply connected region. Therefore, it is quite different from a real contact patch, like the one in Fig. 2.5 at p. 14, which usually has lugs and voids. It is useful to define a reference system S\u0302 = (x\u0302, y\u0302, z\u0302;D), with directions (i, j,k) and origin at point D. Usually D is the center of the contact patch, as in Fig. 10.2. Directions (i, j,k) resemble those of Fig. 2.2, in the sense that k is perpendicular to the road and i is the direction of the wheel pure rolling. More precisely, the contact patch is defined as the region between the leading edge x\u0302 = x\u03020(y\u0302) and the trailing edge x\u0302 = \u2212x\u03020(y\u0302), that is P = {(x\u0302, y\u0302) : x\u0302 \u2208 [\u2212x\u03020(y\u0302), x\u03020(y\u0302) ] , y\u0302 \u2208 [\u2212b, b]} (10.1) 10.1 Brush Model Definition 293 It is assumed for simplicity that the shape and size of the contact patch are not affected by the operating conditions, including the camber angle \u03b3 . Of course, this is not true in real tires"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002089_tia.2010.2103915-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002089_tia.2010.2103915-Figure13-1.png",
        "caption": "Fig. 13. Distributions of the armature-reaction flux (\u03b2 = 90\u25e6).",
        "texts": [
            " The 25th eddy currents caused by the inverter carrier in the IPM flow in a large loop, which is similar to that of the third harmonic. On the other hand, the positions of the 25th harmonic loops in the SPM are different from those of the third harmonic. However, the width of the loops is also similar to that of the third harmonic. The difference between the slot-harmonic eddy currents in the IPM and those in the SPM can be explained by the time variation in the flux produced by the armature currents [1]. Fig. 13 shows the distributions of the armature-reaction flux in the IPM and SPM motors. In this case, the current angle \u03b2 is set at 90\u25e6 for simplicity. In the case of the IPM, the armature flux enters into only one magnet at this rotor position. It alternately varies due to the rotation of the rotor. This variation is caused by the permeance distribution of the rotor along the circumferential direction. In this case, the flux density in one magnet is nearly uniform. Consequently, the eddy currents flow in the large loop, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002342_j.jsv.2011.03.031-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002342_j.jsv.2011.03.031-Figure1-1.png",
        "caption": "Fig. 1. Developed bearing model.",
        "texts": [
            " [6] combined this 2 DOF model with an analytical approach to model the nonlinear dynamic behaviour of a bearing due to localised surface defects. In this model the effect of the radial internal clearance was taken into account. Liew [7] presented four different bearing models in order to model bearing vibrations. The most comprehensive model includes the rollingelement centrifugal load, the angular contact and the radial clearance, and is a 5 DOF model. The 5 DOF bearing model includes not only the radial displacement of the inner race, but also the axial displacement and the rotation around the x and y axes, Fig. 1. Building on the 2 DOF model developed by Liew, Feng [8] developed a bearing-pedestal model with 4 DOF, as it includes a pedestal 2 DOF. The model takes into consideration the slippage in the rolling elements, the effect of mass unbalance in the rotor and the possibility of introducing a localised fault in the inner or outer race. Arslan and Aktu\u0308rk [9] developed a shaft-bearing system with bearing defects. The model has 3 DOF, 2 DOF for the radial displacement and 1 DOF for the axial displacement",
            " As well as testing the feasibility of the envelope analysis and the wavelet transform for the bearing-fault identification during run-up, the contribution of this research is an improved dynamic model of a faulty bearing for the simulation of vibrational signals during run-up. The main goal was to include detailed fault modelling in the dynamical model of the bearing, the nonstationary speed of the shaft and the deformable outer race. The deformable outer race is modelled with FEs. Based on previous studies [7,13\u201315], a multiple-degree-of-freedom model of a radial ball bearing was developed, shown in Fig. 1, to determine the vibration of a faulty bearing during run-up. The following assumptions were made: 1 The rolling elements, the inner and outer races and the rotor have motions in the plane of the bearing only. 2. The balls are assumed to have masses, and the vibrations of the balls are considered in the radial direction. The centrifugal load on the balls is taken into account. 3. Deformations in the contact occur according to the Hertzian theory of elasticity. The effect of the elastohydrodynamic lubricated (EHL) contact is neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002833_physrevapplied.5.017001-Figure20-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002833_physrevapplied.5.017001-Figure20-1.png",
        "caption": "FIG. 20. Various structures formed by LC elastomers adhered to a polystyrene layer. Bends, folds, and twists are introduced, as well as a four-arm grabbing structure. Reproduced (adapted) from Ref. [164] with permission of The Royal Society of Chemistry.",
        "texts": [
            " When heated, the LC elastomer attempts to contract along its alignment director but is inhibited by the polystyrene layer. In regions of thin polystyrene the balancing of deformation energy causes small wrinkles, but as the polystyrene becomes thicker, the wavelength and amplitude of the wrinkles increase until the sheet folds. The authors show that applying polystyrene films on opposite layers can make further complex shapes. A four-arm grabbing actuator is made by selectively patterning the arms of a cross (Fig. 20). The polystyrene is placed on top of the LC, where the alignment director is parallel to the direction of the intended bend, while it is placed under the LC with perpendicular alignment. When heated, both sets of arms curl upward in a grasping motion. This pattern can be extended to a planar LC elastomerpolystyrene bilayer, which results in an actuator that functions like a leaf\u2013closing when the temperature rises too high and opening when it falls. Shape memory alloys have long been a promising material in the field of shape-morphable structures but have been hindered by their lack of flexibility"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001003_s10846-012-9708-3-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001003_s10846-012-9708-3-Figure1-1.png",
        "caption": "Fig. 1 Quadrotor body-fixed and inertial coordinate systems",
        "texts": [
            "it To identify the quadrotor dynamics, we will refer to the rigid-body dynamics and then we will discuss the forces and moments acting on it. This will allow us to find a non-linear model for the quadrotor that we will linearise around the hovering point. 1.1 Rigid Body Dynamics First we have to define the reference frames. We will consider two right-handed coordinate systems. The first one is an earth-fixed inertial frame (INF) coordinate system. The second is a body-fixed one, with its linear velocity vector V = [ u v w ]T and its angular velocity vector = [ p q r ]T (Fig. 1). Initially the two frames coincide. The attitude of the body-fixed frame (BFF) is defined by successive rotations of its three axes around the INF axes. For this purpose we will express the rotations with Euler\u2019s angles: \u03c6 (roll), \u03b8 (pitch) and \u03c8 (yaw). The torque moment is defined as the time derivative of the angular momentum as follows: n M = d L dt = d dt ( I \u00b7 ) (1) with the inertia tensor defined as I = \u23a1 \u23a3 Ixx Ixy Ixz Iyx Iyy Iyz Izx Izy Izz \u23a4 \u23a6 = \u23a1 \u23a3 Ixx 0 0 0 Iyy 0 0 0 Izz \u23a4 \u23a6 (2) The fact that \u2200i = j \u21d2 Iij = 0 derives from the assumption that the mass distribution of the aerial vehicle is symmetric"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003807_j.triboint.2017.12.027-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003807_j.triboint.2017.12.027-Figure3-1.png",
        "caption": "Figure 3: Sliding speed and normal forces on the tooth contact [2].",
        "texts": [
            " PV = PVZ0 + PVZP + PVL + PVD + PVX no-load losses load dependent losses power loss gears bearings auxiliaryseals Figure 2: Power loss contributions [43]. The load dependent losses are directly influenced by the applied load torque while the load independent mechanisms depend mainly on the rotational speed, gearbox geometry and oil physical properties (density, viscosity...) [4]. The load dependent losses are due to gears (PVZP) and rolling bearings (PVL). The load independent or no-load losses are due to seals (PVD) as well as rolling bearings (PVL) and gears churning losses (PVZ0). At each point along the path of contact, see Figure 3, the load-dependent gear friction power loss is given by equation (24). PVZP(x) = FN(x) \u00b7 \u00b5Z(x) \u00b7 vg(x) (24) If the coefficient of friction is considered constant along the path of contact (\u00b5mZ), the power loss can be calculated with equation (25). PVZP = \u00b5mZ \u00b7 Fbt \u00b7 vtb\ufe38 \ufe37\ufe37 \ufe38 Pin \u00b7 1 pb \u222b b 0 \u222b E A fN(x, y) Fbt \u00b7 vg(x, y) vtb dxdy\ufe38 \ufe37\ufe37 \ufe38 HVL (25) Equation (25) is valid both for spur and helical gears where \u00b5mZ is the average coefficient of friction, Pin the input power and HVL is the gear loss factor depending on the gear tooth geometry [44]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000759_rob.20327-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000759_rob.20327-Figure2-1.png",
        "caption": "Figure 2. The quadrotor micro air vehicle equipped with the developed autopilot. The total weight of the aerial platform is about 650 g.",
        "texts": [
            " To demonstrate autonomous flight of a rotorcraft MAV (RMAV), the vehicle platform should be suitably integrated with subsystems as well as hardware and software. The choice of the air vehicle and avionics is a crucial step toward the development of an autonomous platform. That choice is mainly dependent on the intendent application as well as performance, cost, and weight. In this section, we will describe the air vehicle and introduce the major subsystems implemented in our RMAV system, shown in Figure 2. Safety and performance requirements drove the selection of the quadrotor vehicle as a safe, easy-to-use platform with very limited maintenance requirements. A versatile hobby quadrotor, the X-3D-BL produced by Ascending Technolo- gies GmbH in Germany, is adopted as a vehicle platform for our research. The vehicle design consists of a carbonfiber airframe with two pairs of counterrotating, fixed-pitch blades as shown in Figure 2. The vehicle is 53 cm rotor tip to rotor tip and weighs 400 g, including the battery. Its payload capacity is about 300 g. The propulsion system consists of four brushless motors, powered by a 2,100-mAh threecell lithium polymer battery. The flight time in hovering is about 12 min with full payload. The original hobby quadrotor includes a controller board called X-3D that runs three independent PD loops at 1 kHz, one for each rotational axis (roll, pitch, and yaw). Angular velocities are obtained from three gyroscopes (Murata ENC-03R), and angles are computed by integrating gyroscope measurements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001434_0094-114x(80)90021-x-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001434_0094-114x(80)90021-x-Figure4-1.png",
        "caption": "Figure 4.",
        "texts": [
            " As already suggested, alternative equations are available and, in some cases, one of them will be necessary to locate the appropriate quadrant for a joint angle which might be sought for a particular configuration. No attempt is made here to determine explicit input-output relationships for all joint angles. These remarks apply, in general, to each of the linkages examined in this paper. 2. The general p l a n e - s y m m e t r i c case A model of a general plane-symmetric 6-R linkage is shown in Fig. 4. More common examples of special cases are illustrated by the models of Fig. 5. As for the line-symmetric loop, so for the general form of this linkage, offsets are non-zero and skew angles not rightangles. Again, readers are directed away from Bricard's explanation of the loop's mobility to that of Waldron[8, 10] for the corresponding 6-H chain. For the general Bricard loop, we have the dimensional conditions, say, O61 = a12 a56 ~-- a23 a45 = 034 a6z + al2 = ~r a56 + a23 = 7r an5 + a34 = 7r R t = R4 = 0 R6 = R2 R5 = R3 and two independent closure equations 06+ 02 = 2~r (2",
            " Bian qua dtautres chercheurs [2,7,11-133 aient con~ent~ ces r~canismes et/ou aient ar~plifi~ lea aspects g~om~triques de ces octa~dres d~formables, aucune publication n'a analys~ le mouvement relatif entre lea membres. L'obJet de cat article eat d'utiliser la ~thode des 6quations de clSture [3,6,8] pour d~crire pleinement 1as cinq m~canismes distincts. Cette analyse compl~ta le travail sur les m~canisnms surcontraints connus qui ne contiennent qua lea couples tournants [5,6]. 286 La premiere cha~ne de Bricard est la boucle g~n~rale ~ ligne de sym~trie (Fig. 2), con- ditionn~e par les ~quations (1.1-5). La deuxi~me est le m~canisme g~n~ral ~ plan de sym~trie (Fig. 4), qui eat sujet aux ~quations (2.1-5). Le troisi~me type distinct est le m~canisme tri~dre unique (Figs. 7,8), conditionn~ par les ~quations (3.1-5). On peut d~river tout droit le restant des trois octa~dres d~formables de Bricard [i~, mais l'un d'eux est un cas special de la cha~ne A ligne de sym~trie susmentionn~e. La quatri~me boucle (Figs. 16,17) est d~riv~e d'un octa~dre ~ plan de sym~trie, ~ais n'a pas elle-m~me un plan de sym~trie. Elle est conditionn~e par les ~quations (4.1-5). La cinqui~me cha~ne estle m~canisme \"doublement aplatissable\" (Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure7.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure7.4-1.png",
        "caption": "Figure 7.4.1. Single-degree-of-freedom yaw model.",
        "texts": [
            " The forced response to a step input force F is Unsteady-State Handling 439 The initial lateral acceleration is as would be expected. The final drift speed is which is proportional to V, because this gives the necessary value of \u03b2 = F/C0. The lateral displacement response to the step force input is found by integrat- ing y and evaluating the constant of integration from the initial condition y = 0, to give Thus the sideslip motion is characterized by no stiffness and no oscillation, but strong positive damping. 7.4 1-dof Yaw In the one-degree-of-freedom yaw model the vehicle is considered pinned at From Figure 7.4.1 the slip angles are 440 Tires, Suspension and Handling where \u03c8 is the heading angle and is the yaw angular speed. The equation of motion in yaw is where are the first- and second-moment vehicle cornering stiffnesses. Unsteady-State Handling 441 By comparison with the standard one-degree-of-freedom vibration equation of Section 7.2, which was the yaw stiffness is C1 and the yaw damping coefficient is C2/V. For static stability the yaw stiffness should be restoring, i.e., C1 should be negative. Since, from Chapter 6, the understeer gradient is static stability requires positive k, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001302_j.foodchem.2012.01.003-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001302_j.foodchem.2012.01.003-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the batch injection cell containing the three-electrode system.",
        "texts": [
            " Injections of standard solutions or samples were conducted using an Eppendorf electronic micropipette (Multipette stream), which permits injections from 10 to 1000 lL (using a 1 mL Combitip ) at a programmable dispensing rate (from 28 to 330 lL s 1). The working, counter, and reference electrodes were respectively, Prussian-blue (PB)-modified graphite-composite electrode, platinum wire, and Ag/AgCl/saturated KCl. Amperometric measurements were performed using a homemade electrochemical batch-injection cell adapted from a previous report (Tormin, Gimenes, Richter, & Munoz, 2011). Fig. 1 illustrates a schematic diagram of the batch-injection cell that consists of a 180 mL glass cylinder (internal diameter = 7 cm) and two polyethylene covers, which were firmly fitted on the top and bottom of the cylinder. On the top, the polyethylene cover contained three holes for the counter and reference electrodes and the micropipette tip. The distance between the electronic micropipette tip (external diameter = 6.6 mm) and the center of the working electrode (positioned oppositely to the micropipette tip) was adjusted around 2 mm distant in a wall-jet configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure2.14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure2.14-1.png",
        "caption": "Fig. 2.14 Two different operating conditions, but with the same spin slip \u03d5",
        "texts": [
            "51) can be recast as cr = cr(Fz, \u03b3 ), rr = rr (Fz, \u03b3 ), sr = sr (Fz, \u03b3 ), \u03b5r = \u03b5r(Fz, \u03b3 ) (2.73) It is often overlooked that Fx , Fy and Mz (Eqs. (2.70) and (2.72)) depend on both the camber angle \u03b3 and the spin slip \u03d5. In other words, two operating conditions with the same \u03d5, but obtained with different \u03b3 \u2019s, do not provide the same values of Fx , Fy and Mz, even if Fz, \u03c3x and \u03c3y are the same. For instance, the same value of \u03d5 can be obtained with no camber \u03b3 and positive yaw rate \u03c9z or with positive \u03b3 and no \u03c9z, as shown in Fig. 2.14. The two contact patches are certainly not equal to each other, and so the forces and moments. The same value of \u03d5 means that the rim has the same motion, but not the same position, if \u03b3 is different. We remind that the moment Mz in (2.72) is with respect to a vertical axis passing through a point O chosen in quite an arbitrary way. Therefore, any attempt to attach a physical interpretation to Mz must take care of the position selected for O . 2.9 Tire Testing 33 Unfortunately, it is common practice to employ the following functions, instead of (2",
            " 10.32(d) and 10.33 gives an idea of the effect of the shape of the contact patch. In the second case the lengths of the axes have been inverted, while all other parameters are unchanged. Nevertheless, the normalized lateral force is much lower (0.36 vs 0.61). In the brush model developed here, the lateral force and the vertical moment depend on \u03d5, but not directly on \u03b3 . Therefore, there is no distinction between operating conditions with the same spin slip \u03d5, but different camber angle \u03b3 as in Fig. 2.14. This is a limitation of the model with respect to what stated at p. 32. It should be appreciated that a cambered wheel under pure spin slip cannot be in free rolling conditions. According to (2.11), there must be a torque T = Mz sin\u03b3 jc = T jc with respect to the wheel axis. Conversely, T = 0 requires a longitudinal force Fx and hence a longitudinal slip \u03c3x . From the tire point of view, there are fundamentally two kinds of vehicles: cars, trucks and the like, whose tires may operate at relatively large values of translational slip and small values of spin slip, and motorcycles, bicycles and other tilting vehicles, whose tires typically operate with high camber angles and small translational slips"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000901_1.1830045-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000901_1.1830045-Figure8-1.png",
        "caption": "Fig. 8 Four quadratic curves of a three-cable mechanism \u201ef\u00c40 deg, static state\u2026",
        "texts": [
            " Singularity loci should also be part of this boundary. As we saw in Section 6, the whole workspace is a union of a set of three-cable subworkspaces. Thus, we must consider the singu- Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 09/04/20 larity loci for every three-cable combination. These loci are the same as those from a mechanism using standard prismatic actuators: they can be any quadratic curve @13#. Figure 7 is an example of singularity loci for the same threecable mechanism. Figure 8 shows all the potential boundaries of the static state workspace, i.e., three two-cable equilibrium hyperbolas and the singularity loci ~dotted curve for singularity loci!. The method that we propose for the determination of the workspace boundaries is simple. The first step is the creation of every two-cable combination hyperbola of equilibrium and every threecable combination singularity curve. Then, we intersect the curves with each other to create a set of sections, i.e., curves segments ~we will not elaborate on this"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000727_48.107144-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000727_48.107144-Figure7-1.png",
        "caption": "Fig. 7. Heading angle (rad).",
        "texts": [
            " Case 3: We consider the vehicle with X u , = 1646 kglm, Y, , = 2273 kglm, and N,, = 5457 kg/m2. We implemented the control system with the learning algorithm, assuming that the current velocity changes from 0.1 to 0.4 m/s in the X direction at a time of 30 s. The results of the computer simulations are shown in Figs. 4-7. Figs. 4-6 show the vehicle trajectory in the X-Y plane for each case. In these figures, the dotted lines, which overlap the desired trajectory, indicate the trajectory with the on-line direct learning algorithm. Fig. 7 shows the heading angle of YUH: A NEURAL NET CONTROLLER FOR UNDERWATER ROBOTIC VEHICLES 165 the vehicle with the learning algorithm. Each case shows almost the same result in the heading angle except case 3, which shows the small oscillation after 30 s due to the sudden change in the current velocity. Results show the robustness of the control system to the changes in the vehicle and its environment. However, when without the learning algorithm and we used the weights that were adjusted during the first implementation, the vehicle moved far away from the desired trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure12-1.png",
        "caption": "Fig. 12. (a) Schema of cage with rolling elements and (b) bond graph sub-model of cage.",
        "texts": [
            " For vibration analysis and bearing condition monitoring, the acceleration or velocity of the pedestal in the vertical direction is measured. Thus, an effort detector De (analogous to accelerometer when mass is constant) and a flow detector Df (analogous to velocity sensor) are implemented at appropriate locations in the model. A multi-bond interface port (port number 2) is used to connect this sub-model to the sub-models of rolling elements. The cage is modeled here as a 3 DOF rigid body whose primary purpose is to maintain a fixed angular spacing between the balls (Fig. 12(a)). The actual cage has a space within which the balls are held. Here, we simplify that geometry and assume that the ball is attached to the cage through a revolute joint so that it can freely rotate about the axis of the pin-joint, i.e., an axis parallel to z-axis. This assumption holds because in a deep groove ball bearing, balls normally do not rotate about other axes. It is also assumed that a contact stiffness and damping exists to restrain relative translational between the ball and the cage. The clearance (like backlash) between the ball and the cage can be modeled by properly modifying the contact stiffness and damping element's constitutive relations. In bond graph sub-model of the cage is given in Fig. 12(b), where JI: c, MI: c and \u2212 M gSe: c , respectively represent the polar moment of inertia, mass and weight of the cage. For the i-th ball, the components of the velocity at the pin between the cage and the ball are \u03b8 \u03b8 \u03c0 \u03b8 \u03b8 \u03c0\u0307 = \u0307 \u2212 \u0307 + \u0307 = \u0307 + \u0307 + ( ) \u239b \u239d\u239c \u239e \u23a0\u239f \u239b \u239d\u239c \u239e \u23a0\u239fx x r i n y y r i n sin 2 and cos 2 34 ji c c c c b ji c c c c b where ( )= \u2026 \u2212i n0 1b is an enumeration of the balls with nb being the number of balls, rc is the pitch circle or mean radius, \u03b8c is the cage rotation angle, ( )x y,c c defines the cage center position and ( )x y,ji ji is the i-th ball center (i.e., pin or revolute joint) position on the cage. The pin joint constrains the motion between the cage and the rolling element. In Fig. 12(b), this constraint is modeled by flexible contact or pin flexibility through KC: j and RR: j elements and the kinematic relation given in Eq. (34) is represented through two TF elements and other junction structures. The cage sub-model is interfaced to nb number of sub-models for rolling elements through nb number of multi-ports numbered 3 to ( )+ \u2212n3 1b . The bond graph sub-model of rolling element (here, ball) is shown in Fig. 13. It has two non-linear contact springs (C K: b), two linear contact dampers (R R: b) and two dampers (R R: f ) for friction/traction force modeling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000190_bf01342668-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000190_bf01342668-Figure1-1.png",
        "caption": "Fig. 1. Arrangement of the spherical treadmill in the anechoic, light-tight chamber. Loudspeakers (L) are shown in their usual positions for 135 ~ angular separation. A pulsed-infrared scanning system (IR) measures animal position for compensatory feedback to motors (M) which drive the 50-cm-diameter sphere (S). The television camera (TV) is for observation in lighted conditions. Further description in the text",
        "texts": [
            ", FRG); the position of the latter is sensed in two dimensions (X, 7) by reflected infrared light (power LED, wavelength band 940 \u2022 23 nm) which is pulsed (at 330 Hz) by two orthogonally aligned sets of rotating slits ( ' IR, SLITS'; Figs. 1 and 2). Pulse timings with respect to sync-pulses in the X and Y directions encode departure of the animal from center of the scanning field and allow analog generation (via ramp-and-hold circuits) of position feedback signals (lower loops in Fig. 2) which arive the motors to compensate movement. Negative velocity feedback in the X and Y directions, for damping of the compensation, is provided by tachometers on the shafts of ' the two orthogonally aligned drive motors (M in Fig. 1 ; 0SR in Fig. 2). The main weight of the sphere is borne on a multidirectional roller s)Lstem. The dynamics of the compensation are treated below. For continuous monitoring of walking velocity during operation of the treadmill, a 26-ram-diameter rubber wheel turning an 'ant ipodal ' tachometer was lightly spring-loaded against the bottom of the sphere, and mounted on a vertical crank (5-ram offset) so that it followed the walking direction, which was itself monitored by a continuous (360 ~ except for a few degrees of dead space) potentiometer on the crank axis (designed and built by E",
            " To gate the stimulus sound either (i) only during motion of the sphere or (ii) only during pauses between walking bouts, the above velocity signal generated a logical voltage level that could be used to gate or blank the acoustical signal. 30-cm-thick castellated glass-wool material (reflection < 1% at frequencies above 300 Hz) on all six surfaces (Gr/inzweig & Hartmann GmbH). The main sources of possible reflections are the suspended floor grid, bars supporting the door, the cameras, and the sphere. Air temperature in the anechoic chamber was 19-23 ~ relative humidity (in winter) about 30%. 4. Calling-Song Stimuli Sound stimuli, delivered via loudspeakers (Piezo Horntweeter Type PHS, Visaton; L in Fig. 1) placed in the horizontal plane of the animal, 1.5 to 2 m from the sphere as shown in Figs. 1 and 5C, were either male G. campestris calling song (taped in the field at 21 ~ and reproduced with a bandwidth of 14 kHz; see Fig. 5D) or simulated songs. The tape-recorded G. campestris calling song ordinarily consists (see, for example, Weber 1978) of 'chirps ' , each containing 4 'syllables' of ca. 5-kHz sound; the syllables last ca. 10-15 ms and are repeated at intervals of ca. 30 ms. Chirps are repeated every 250-500 ms, depending upon temperature",
            " The simulated songs were generated by modulating a 5-kHz sinusoidal signal with timing and logic devices designed by P. Heinecke, Seewiesen. Sound intensity (for continuous tones) was measured by placing a half-inch Brfiel & Kjaer microphone near the position of the animal. Intensity variations within the 20-cmdiameter field near the top of the sphere were on the order of \u2022 dB or less, so that no prominent standing-wave effects were discernible. Calling-song intensities refer to the peak of the syllable envelope. 3. Experimental Conditions As sketched in Fig. 1, the experiments are done with the Kramer treadmilI centered in a 4 \u2022 4-m x 3-m-high anechoic chamber with 5. Special Sources o f Disturbance In addition to the fundamental question of animal-substrate inertial dynamics to be treated below, several other sources of disturbance 218 T. Weber et al. : Auditory Behavior of the Cricket. I are inherent in spherical treadmills of this kind, and ought to be taken into account. The standard (50-cm-diameter) polycarbonate sphere (streetlamp globe; Powerlight GmbH, Berlin) ordinarily used with these compensating systems is made by replacing the hole for the light fixture with a piece cut from a second globe"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.32-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.32-1.png",
        "caption": "FIGURE 5.32. A practical spherical wrist.",
        "texts": [
            " 0R1 = 1RT 0 = \u00a3 Rx1,\u03b8 R T z0,\u03d5 \u00a4T = \u00a3 Rx,\u03b8 R T Z,\u03d5 \u00a4T (5.134) = \u23a1\u23a2\u23a3 \u23a1\u23a3 1 0 0 0 c\u03b8 s\u03b8 0 \u2212s\u03b8 c\u03b8 \u23a4\u23a6\u23a1\u23a3 c\u03d5 \u2212s\u03d5 0 s\u03d5 c\u03d5 0 0 0 1 \u23a4\u23a6T \u23a4\u23a5\u23a6 T = \u23a1\u23a3 cos\u03d5 \u2212 cos \u03b8 sin\u03d5 sin \u03b8 sin\u03d5 sin\u03d5 cos \u03b8 cos\u03d5 \u2212 cos\u03d5 sin \u03b8 0 sin \u03b8 cos \u03b8 \u23a4\u23a6 Therefore, the transformation matrix between the living and dead wrist frames is: 0R2 = 0R1 1R2 = \u00a3 Rx1,\u03b8 R T z0,\u03d5 \u00a4T RT z2,\u03c8 = Rz0,\u03d5R T x1,\u03b8 R T z2,\u03c8 = RZ,\u03d5R T x,\u03b8 R T z,\u03c8 (5.135) = \u23a1\u23a3 c\u03c8c\u03d5\u2212 c\u03b8s\u03c8s\u03d5 \u2212c\u03d5s\u03c8 \u2212 c\u03b8c\u03c8s\u03d5 s\u03b8s\u03d5 c\u03c8s\u03d5+ c\u03b8c\u03d5s\u03c8 c\u03b8c\u03c8c\u03d5\u2212 s\u03c8s\u03d5 \u2212c\u03d5s\u03b8 s\u03b8s\u03c8 c\u03c8s\u03b8 c\u03b8 \u23a4\u23a6 Example 164 Practical design of a spherical wrist. Figure 5.32 illustrates a practical Eulerian spherical wrist. The three rotations of Roll-Pitch-Roll are controlled by three coaxes shafts. The first rotation is a Roll of B4 about z4. The second rotation is a Pitch of B5 about z5. The third rotations is a roll of B6 about z6. 280 5. Forward Kinematics 5.5 Assembling Kinematics Most modern industrial robots have a main manipulator and a series of interchangeable wrists. The manipulator is multibody so that it holds the main power units and provides a powerful motion for the wrist point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.23-1.png",
        "caption": "Fig. 3.23 Flap and lag mode eigenvalues",
        "texts": [
            " Because of the lower inherent damping in lag, the Coriolis moment tends to be more significant in the lag equation due to flap motion. In addition, the lag aerodynamic moment ML will be strongly influenced by in-plane lift forces caused by application of blade pitch and variations in induced inflow. The impact of these effects will be felt in the frequency range associated with the coupled rotor/fuselage motions. In terms of MBCs, the regressing and advancing lag modes will be located at (1\u2212 \ud835\udf06\ud835\udf01 ) and (1+ \ud835\udf06\ud835\udf01 ), respectively. A typical layout of the uncoupled flap and lag modes is shown on the complex eigenvalue plane in Figure 3.23. The flap modes are well damped and located far into the left plane. In contrast, the lag modes are often weakly damped, even with mechanical dampers, and are more susceptible to being driven unstable. The most common form of stability problem associated with the lag DoF is ground resonance, whereby the coupled rotor/fuselage/undercarriage system develops a form of flutter; the in-plane rotation of the rotor centre of mass resonates with the fuselage/undercarriage system. Another potential problem, seemingly less well understood, arises through the coupling of rotor and fuselage motions in flight"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure6-1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure6-1-1.png",
        "caption": "Fig. 6-1 dq windings at t\u00a0=\u00a00\u2212. d-axis",
        "texts": [
            " 6-1 EFFECT OF DETUNING DUE TO INCORRECT ROTOR TIME CONSTANT \u03c4r We will define a detuning factor to be the ratio of the actual and the estimated rotor time constants as k r r \u03c4 \u03c4 \u03c4 = , , est (6-1) where the estimated quantities are indicated by the subscript \u201cest.\u201d To analytically study the sensitivity of the vector control to k\u03c4, we will simplify our system by assuming that the rotor of the induction machine is blocked from turning, that is, \u03c9mech\u00a0=\u00a00. Also, we will assume an openloop system, where the command (reference) currents are isd* and isq* . As shown in Fig. 6-1 at t\u00a0=\u00a00\u2212, the stator a-axis, the rotor A-axis, and the d-axis are all aligned with \u03bbr , which is built up to its rated value. 97 6 Detuning Effects in Induction Motor Vector Control Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink\u00ae, First Edition. Ned Mohan. \u00a9 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. 98 DETuNINg EFFECTS IN INDuCTIoN MoTor VECTor CoNTrol Also initially, i isd sd= * , and \u03b8da\u00a0=\u00a0\u03b8da,est\u00a0=\u00a00. Initially, the torque component of the stator current is assumed to be zero, that is i isq sq * = = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003937_j.engfailanal.2017.08.028-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003937_j.engfailanal.2017.08.028-Figure1-1.png",
        "caption": "Fig. 1. Geometric parameters of the fillet-foundation deflection.",
        "texts": [
            " This tooth fillet-foundation stiffness calculation method for health gears was established based on the theory of Muskhelishvili [27]. This method is based on the assumptions that the stress variation of the root circle is linear and constant, and then the formula to calculate the gear body deformation can be deduced. It is calculated as [26], \u239c \u239f= \u23a1 \u23a3 \u23a2 \u239b \u239d \u239e \u23a0 + + + \u23a4 \u23a6 \u23a5\u03b4 E F b \u03b1 L u S M u S P Q \u03b11 cos [1 tan ]f m f f f f m 2 2 2 (1) where, b is the width of the tooth. The parameters uf and Sf are given in Fig. 1. And the symbols, L, M, P and Q, are functions of h and \u03b8. They are expressed as [26], = + + + + +X h\u03b8 A \u03b8 B h C h \u03b8 D \u03b8 E h F( )i f i f i i f i f i i 2 2 (2) However, the effective load bearing area of the gear between the gear tooth and the gear body will be reduced when the tooth root crack appears, and thus the contribution of the gear body deformation to the gear tooth displacement will be increased, which thereby results in the reduction of the gear tooth fillet-foundation stiffness. Therefore, in order to put forward the calculation method of the gear tooth fillet-foundation stiffness with tooth root crack and to improve further the accuracy of gear mesh stiffness calculation, two improved models are proposed to calculate the stiffness of gear tooth fillet-foundation in this paper based on the model proposed in [26]",
            " Thus the stiffness of the gear tooth fillet-foundation with tooth root crack can be expressed as, = \u2212K K x(1 )f (3) where, Kf is the stiffness of healthy gear tooth fillet-foundation; And x is the ratio of the crack length and the total length of the potential crack path, which is calculated as, =x l L 0 (4) where, the symbol l0 is the tooth root crack length; L denotes the total length of the tooth root crack. This model is simple to use for the calculation of gear mesh stiffness with respect to gear tooth root crack. As shown in Fig. 2, geometric parameters of the fillet-foundation deflection will change in the presence of tooth root crack. It is assumed that the stiffness of the gear fillet-foundation is related to the variations of geometric parameters of the fillet-foundation due to the tooth root crack. Compared with the geometric parameters as shown in Fig. 1, the load bearing area is changed from Sf to Sf\u2032, and uf is changed to uf\u2032 due to the presence of the gear tooth root crack. A rectangular coordinate system is established as shown in Fig. 2. Here, Rb is the radius of base circle, and Rg is the radius of dedendum circle; L denotes the total length of the fictitious crack crossing over the whole tooth thickness and l0 is the length of the practical crack; \u03b1m is action angle of the mesh force; The coordinate of point OA is (0, \u2212Rg); While the coordinate of point D is (xD, yD), X is the ratio of the practical crack length to the fictitious crack length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003288_j.engfailanal.2014.01.008-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003288_j.engfailanal.2014.01.008-Figure1-1.png",
        "caption": "Fig. 1. Contact lines, friction forces and normal forces in helical gears. Dash line: Contact line on the right side of the pitch line. Dash double-dot line: Contact line on the left side of the pitch line.",
        "texts": [
            " By incorporating the time-varying sliding friction and mesh stiffness, the dynamic model of helical gears with sliding friction is developed in Section 4. The effect of spalling defect on the dynamic characteristics of helical gears under sliding friction are illustrated in detail in Section 5. Finally, some conclusions will be drawn in Section 6. The overall contact ratio between 1 and 4 is normally used in a helical gear system. The number of contact lines present in the contact zone depends upon the basic parameters of gears, such as normal module, helix angle, face width and transmission ratio. Fig. 1 shows an example of the corresponding zone of contact in a helical gear pair. Here, points C and D are the starting and ending points of one complete mesh event; P is the pitch point, where the friction force changes direction. Because of the different characteristics of the contact line in helical gears, helical gears are separated here into two groups according to the relationship between the face width and the line of action (Fig. 2). When b tan bb > LCD, the maximum length of contact line can be express as LCD csc bb, which is defined as group 1",
            " Otherwise, the maximum length of contact line will become b sec bb, and is defined as group 2. In order to obtain a general formulation to determine time-varying contact line, frictional force and torque in a helical gear system, the following elaboration of our method is provided. Due to the reversal of the sliding velocity before and after the pitch plane, each contact line is divided into two segments, to facilitate the computation of friction force and torque. One is the left side contact line relative to the pitch plane (dash double-dot line in Fig. 1), and the other is the right side contact line (dash line in Fig. 1). The friction moments about the gear centers depend on the position of the contact points. By assuming that the friction force on the contact line is distributed uniformly, the moment arm of the friction force is found by taking the center point of each segment of the contact line. Based on the analysis of relative sliding velocity between two meshing teeth, the direction of the frictional force during all of the line of action has been determined by the position before and after the pitch line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure5-1.png",
        "caption": "Fig. 5. Fault angular width in terms of inner and outer races.",
        "texts": [
            " In case of inner race fault, the spall rotates with inner race and its position changes continually. Thus, \u03d5d value is dependent on the angle of shaft rotation which can be expressed as \u03d5 \u03c9 \u03d5= + ( )t , 12d i 0 where \u03d50 is the initial location of spall. For simulation, \u03d5d is modified by deducting full rotations out of it. The contact deformation is given as \u03b4 \u03b8 \u03b8 \u03b4= ( + \u2212 \u2212 ) ( )x y cmax cos sin ,0 , 13d j d j fi where \u03b4 \u03d5 \u03b8 \u03d5 \u03d5 = < < +\u2206 \u23aa \u23a7\u23a8\u23a9 C if , 0 otherwise. f d d j d d A spall in the ball rotates at the same speed as that of ball. At any instant, the angular position of the spall (See Fig. 5) can be expressed as \u03d5 \u03c9 \u03d5 \u03d5= \u2212 + ( ) \u239b \u239d \u239c\u239c \u239b \u239d\u239c \u239e \u23a0\u239f \u239e \u23a0 \u239f\u239f D d d D t 2 1 cos 14 s i 2 0 where \u03d50 is the initial position of spall. Note that the ball rotates in opposite direction to that of shaft rotation. For ball fault, the angular width of ball fault in terms of inner and outer races (Fig. 5) can be expressed as \u03d5 \u03d5= \u2206 ( )d D/ , 15bi d i \u03d5 \u03d5= \u2206 ( )d D/ . 16bo d o where Di and Do are the diameters of inner and outer races, respectively, and = ( + )D D D /2.i o For each complete rotation of ball, loss of contact is detected twice, once contact with inner race is lost and once contact with outer race is lost. The inner race and the outer race have different curvatures and hence, the angular fault widths are different for the two contact losses. This difference in curvature also influences the depth of ball's entry into the spalls on the inner and outer races"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.9-1.png",
        "caption": "Fig. 3.9 Suggested selection of internal coordinates: (a) roll angle \u03c6s i due to suspension deflections only, (b) track variation \u0394ti , (c) roll angle \u03c6 p i due to tire deformations only, (d) vertical displacement z p i due to tire deformations only",
        "texts": [
            " Also shown in Fig. 3.8 are points Q1 and Q2. They are given by the intersection of the straight lines connecting Ai and Bi on both sides. Because of symmetry, they lay on the centerline at heights q1 and q2. Points Q1 and Q2 are the so-called roll centers and their role in vehicle dynamics will be addressed shortly. For each axle, four \u201cinternal\u201d coordinates are necessary to monitor the suspension conditions with respect to a reference configuration. A possible selection of coordinates may be as follows (Fig. 3.9) \u2022 body roll angle \u03c6s i due to suspension deflections only; \u2022 body vertical displacement zs i due to suspension deflections only (which results in track variation \u0394ti ); \u2022 body roll angle \u03c6 p i due to tire deformations only; \u2022 body vertical displacement z p i due to tire deformations only. Figure 3.9 shows how each single coordinate changes the vehicle configuration for a swing axle suspension.4 These four coordinates are, by definition, independent. It will depend on the vehicle dynamics whether they change or not. In other words, the kinematic schemes of Fig. 3.9 have nothing to do with real operating conditions. It is therefore legitimate, but not mandatory at all, to define, e.g., the roll \u03c6s i of the vehicle body keeping the track ti fixed and without any tire deformation, as in Fig. 3.9. 4A more precise definition of roll angle is given in Sect. 9.2. 3.8 Suspension First-Order Analysis 69 The first order relationship between zs i and \u0394ti is given by (Fig. 3.9) zs i = \u2212 ci 2bi \u0394ti = \u2212 ti 4qi \u0394ti (3.80) which, because of symmetry, does not depend on \u03c6s i and \u03c6 p i . Any other kinematic quantity is, by definition, a function of the selected set of coordinates (\u03c6s i ,\u0394ti, \u03c6 p i , z p i ). It is quite important to monitor the variation of the wheel camber angle \u03b3ij as a function of the selected coordinates (\u03c6s i ,\u0394ti, \u03c6 p i , z p i ). In a first order analysis, the investigation is limited to the series expansion \u0394\u03b3ij \u2248 \u2202\u03b3ij \u2202\u03c6s i \u03c6s i + \u2202\u03b3ij \u2202\u0394ti \u0394ti + \u2202\u03b3ij \u2202\u03c6 p i \u03c6 p i + \u2202\u03b3ij \u2202z p i z p i (3.81) where all derivatives are evaluated at the reference configuration. From Fig. 3.8 and also with the aid of Fig. 3.9, we obtain the following general results for any 70 3 Vehicle Model for Handling and Performance symmetric planar suspension (cf. Fig. 9.5) \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u2202\u03b3i1 \u2202\u03c6s i = \u2202\u03b3i2 \u2202\u03c6s i = \u2212 ti/2 \u2212 ci ci = \u2212qi \u2212 bi bi \u2202\u03b3i1 \u2202\u0394ti = \u2212 \u2202\u03b3i2 \u2202\u0394ti = 1 2bi \u2202\u03b3i1 \u2202\u03c6 p i = \u2202\u03b3i2 \u2202\u03c6 p i = 1 \u2202\u03b3ij \u2202z p i = 0 (3.82) The sign convention for the camber variations \u0394\u03b3ij is like in Fig. 2.2. Therefore, in Fig. 3.9(b) we have \u0394\u03b3i1 < 0 and \u0394\u03b3i2 > 0. Equations (3.81) and (3.82) yield \u0394\u03b3i1 \u2248 \u2212 ( qi \u2212 bi bi ) \u03c6s i + \u03c6 p i + 1 2bi \u0394ti \u0394\u03b3i2 \u2248 \u2212 ( qi \u2212 bi bi ) \u03c6s i + \u03c6 p i \u2212 1 2bi \u0394ti (3.83) This is quite a remarkable formula. It is simple, yet profound. For instance, the two suspension schemes of Fig. 3.8, which look so different, do have indeed very different values of the first two partial derivatives in (3.82). On the other hand, it should not be forgotten that (3.81) is merely a kinematic relationship. There is no dynamics in it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002790_j.addma.2018.05.040-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002790_j.addma.2018.05.040-Figure3-1.png",
        "caption": "Figure 3. (a) Schematic representation of three different orientations used in this study; (b) dimensions of tensile samples machined from cylindrical rods built in three different orientations.",
        "texts": [
            " The average porosity was found by evaluating the porosities at three different sections (parallel to the build plate) across the build direction of samples. An overview of all the samples at three different planes were captured to compute percentage porosity on each surface based on variation of grey-scale intensities between pores and material. In order to inspect the effect of build orientation of SLM samples, the relative density and the tensile behaviour of the samples (diameter 20 mm, length 95 mm) printed in three different orientations, i.e. vertical, horizontal and inclined (45o to the build plate) orientations, as shown in Figure 3 (a), were studied. These samples were fabricated using scan strategy \u2018H\u2019, scan speed 1000 mm/s, laser power 285 W, hatch spacing 100 \u00b5m, and powder layer thickness 40 \u00b5m. The as-fabricated samples were machined down to tensile specimen dimensions as shown in Figure 3 (b) based on ASTM E8M standard with gauge length 5 times the gauge diameter [39]. Moreover, the relative density of the tensile specimen in the gauge region was computed using X-Ray Computed Tomography (CT) scans for which GE Phoenix X-ray CT machine was ACCEPTED M ANUSCRIP T employed. The CT scanning was done with a voxel size of 11 \u00b5m, scan voltage of 220 kV and scan current of 55 \u00b5A. The 3D scans of the samples were analysed using myVGL studio and Avizo 3D software. The porosity in each sample was determined based on the grey-scale intensities",
            " (a) Scan strategy (Scan \u2018O\u2019) with scanning vectors along +45\u00b0 for odd numbered layers (left) and -45\u00b0 for even numbered layers (right); (b) Scan strategy (Scan \u2018X\u2019) of a single odd numbered layers (left) and even numbered layers (right) with the first laser scan (solid lines) followed by the second intermediate laser scan (dashed line); (c) Scan strategy (Scan \u2018H\u2019) with scanning vectors along +45\u00b0 for odd numbered layers (left) and -45\u00b0 for even numbered layers (right). [Grey represents powder layers and yellow represents scan vectors.] .................................................................................................................................................... 9 Figure 3. (a) Schematic representation of three different orientations used in this study; (b) dimensions of tensile samples machined from cylindrical rods built in three different orientations. .............................................................................................................................. 10 Figure 4: (a) Stitched optical microscope images showing the relative density (%) variation across the AlSi12 samples printed with varying scan speeds and scan strategies; (b) average relative density of the as-built samples printed at varying scan speeds and scan strategies "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001389_iros.2011.6094506-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001389_iros.2011.6094506-Figure2-1.png",
        "caption": "Fig. 2. Dynamics of a quadrocopter, acting under inputs of thrust (f ), and two angular accelerations q\u0307 and p\u0307; and under the influence of gravity g. The base vectors x, y and z of the inertial reference frame are also shown.",
        "texts": [
            " In Section III we present algorithms to estimate the ball state and predict the ball\u2019s trajectory, estimate the racket\u2019s coefficient of restitution and estimate an aiming bias. Then an algorithm to generate a trajectory for the quadrocopter is given in Section IV, followed by a discussion on the system architecture and experimental setup in Section V. Results from experiments are presented in Section VI. We attempt to explain why the system fails on occasion in Section VII and conclude in Section VIII. We model the quadrocopter with three inputs (refer to Fig. 2): the angular accelerations q\u0307 and p\u0307, taken respectively about the vehicle\u2019s x and y axes, and the mass-normalised collective thrust, f . The thrust points along the racket normal, n. The attitude of the quadrocopter is expressed using the z-y-x Euler angles, rotating from the inertial frame to the 978-1-61284-456-5/11/$26.00 \u00a92011 IEEE 5113 body-fixed frame by yaw (\u03c8) first, then pitch (\u03b8) and finally by roll (\u03c6) \u2013 for simplicity, throughout this paper the yaw is assumed to be controlled to zero by a separate controller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.30-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.30-1.png",
        "caption": "Fig. 17.30 Three-phase power transformer for public energy supply > 150 MVA (SIEMENS)",
        "texts": [],
        "surrounding_texts": [
            "If the excited current is time varying then it generates a time-varying voltage that, when transferred to the primary side of the transformer, takes the following form\nVm = w1 d\u03a6m dt = \u2212 d\u03a8m dt . (17.129)\nIf the flux changes to a sine function then the inducted voltage will also have a sine waveform with the same frequency as the drawn current. The effective (RMS) value of the voltage is described as\nVm = \u03c9\u221a 2 w1\u03a6m = 4.44 fw1 B\u0302 AFe . (17.130)\nThe generated voltage is proportional to the working frequency f , the winding number w1, the magnetic induction magnitude B\u0302, and the cross-section AFe.\nNo-Load and Short-Circuit Conditions When the secondary winding of the transformer works in the open circuit, this means that I2 = 0, and the voltage at the output clamps of transformer is approximated by the formula\nV 20 \u2248 V 1/n . (17.131)\nIn this case, the current I0 in the primary winding is moved back by about 90\u25e6 with respect to the supply voltage. The active power for such a working condition of the transformer reflects mainly the eddy current and hysteresis losses due to magnetization of the core, and the reactive power results from the almost purely inductive character of the device. The relations for these working conditions are expressed in the following form\nP = V1 I0 cos \u03d50 , Q = V1 I0 sin \u03d50 (17.132)\nfor the active and reactive power, respectively. The characteristic value for the transformer is an open-circuit current, which is defined as the ratio of the current I0 in the open-circuit condition to the nominal current of the transformer\ni0 = I0\nIN . (17.133)\nThis factor amounts to only a few percent. The P and Q quantities in the open-circuit condition serve as the basis for calculating the mentioned parameter RL, which reflects the losses in the core, and Xm, which describes the main inductance in the transformer circuit.\nThe no-load characteristics V1 = f (I0) exhibit the saturation features of the transformer, which must be taken into account during transformer design.\nIf a transformer works in short-circuit conditions of the secondary winding the following conditions are fulfilled\nV 2 = 0 , I2s \u2248 \u2212nI1 . (17.134)\nThe flux produced by the current flowing in the primary winding is almost completely compensated by the flux produced by the current in the secondary winding.\nThe wire resistances and leakage reactance can be roughly obtained with the help of the following expressions\nZs = Rs + jXs , Rs = R1 +n2 R2 , Xs = \u03c9 ( L\u03c31 +n2 L\u03c32 ) . (17.135)\nFigure 17.26 illustrates a further connection between the quantities in graphical form and introduces the term relative short-circuit voltage, which is defined as\nvs = Xs IN/V N . (17.136)\nFor a power transformer these values can be up to 6%.\nPhasor Diagram In order to better understand the phenomena arising in the transformer, a phasor diagram is often used. In such a case the secondary-side quantities are transferred to the primary winding of the transformer and the relationship between currents and voltages at the clamps of the transformer are as follows\nV 1 = (R1 + j\u03c9Ls)I1 + j\u03c9Lm I\u03bc , V 2 = j\u03c9Lm I\u03bc + (R\u2032 2 + j\u03c9L \u2032 \u03c32)I \u2032 2 , (17.137)\nwhere I\u03bc = I1 + I \u2032 2 is defined as a magnetization current. If the additional core losses represented by the\nPart C 1 7 .2",
            "resistance RL are taken into account, the behaviors of the currents and voltages at the transformer are described by the phasor diagram in Fig. 17.27.\nIt can be seen that the magnetization current is shifted back by 90\u25e6 with respect to the main voltage, denoted by V m = j\u03c9Lm I\u03bc. The whole current I0 characterizes properties of the main flux in the transformer and can be divided into two geometric components: the primary and the related secondary current.\nTransformer are called auto-transformer if the primary windings is part of the secondary windings or vice versa. The windings of the auto-transformer do not have galvanic separation, as shown in Fig. 17.28. Auto-transformers have lower leakage reactances, lower losses, and smaller exciting current when the voltage ratio does not differ too greatly from 1 : 1. The disad-",
            "Denotation Phasor\nIndex Switching group PW SW\n2V\n2W2U\nCircuit picture Ratio\nPW SW\nDd 0\nYy 0\n0\n5\nDy 5\nYd 5\nYz 5\n1V\n1U 1W\n1U\n1V\n1W\n2U\n2V\n2W\nVL1/VL2\n1U\n1V\n1W\n2U\n2V\n2W\n1U\n1V\n1W\n2U\n2V\n2W\n1U\n1V\n1W\n2U\n2V\n2W\n1U\n1V\n1W\n2U\n2V\n2W\nN1/N2\nN1/N2\n3N1/N2\nN1/ 3N2\n2N1/ 3N2\n2W2U\n2V\n2U\n2V\n2W\n2U\n2W\n2V\n2W\n2U\n2V\n1V\n1W 1U\n1W\n1V\n1U\n1W\n1V\n1U\n1W1U\n1V\nFig. 17.32 Connection groups of three-phase transformers [17.1]\nvantage is the direct electric connection between the high- and low-voltage sides.\nThe instrument transformer is a device that uses the principles of a transformer to convert network currents and voltages into quantities that can be processed by other measurement instruments, protective or metering devices or control systems (Fig. 17.29). The norm for voltage measurement is 100 V, whereas for current measurement it is either 1 or 5 A. The secondary side of the instrument transformer is galvanically separated and, in particular, this property makes it possible to measure high-voltage systems. The total measurement error of these devices depends on the sum of the magnitude error and angle error. Depending on the accuracy levels of the instrument,\nthey are grouped into several classes which characterize the allowable percentage error (class 0.1, 0.2, or 1.0).\nCurrent Transformers The primary and secondary windings in a current transformer are coupled by a ferromagnetic sheeting or toroidal core with low leakage inductivity. If high currents are measured, the core with the secondary winding is mounted around the primary winding. This way the primary winding usually consists of one turn. The resistance (burden) connected to the secondary side is used for the current measurement.\nSince the accuracy is strongly depending on the existing of the current I0, metal sheeting with high permeability in the operating range is used. Additional errors occur, when the core gets saturated by primary currents containing DC components.\nPart C 1 7 .2"
        ]
    },
    {
        "image_filename": "designv10_1_0000790_s00170-013-5261-x-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000790_s00170-013-5261-x-Figure10-1.png",
        "caption": "Fig. 10 Longitudinal residual stress predictions from transient mechanical model (a) and efficient \u201cengineering\u201d FE model (b) (a scaling factor of 5 is used for the distorted shape)",
        "texts": [
            " Thus, to simplify the model, there was no temperature change outside the plastic zone during the deposition process. By keeping this at room temperature, the material in the plastic zone is effectively restrained in the longitudinal direction. Hence, application of the peak temperature in the plastic zone enables the equivalent plastic strain to be calculated which is important for generating the residual stress. The mechanical results from the efficient \u201cengineering\u201d FE model were compared with the results from the transient model. Panels a and b of Fig. 10 show the predicted longitudinal residual stress of the four-layer wall after the clamps were removed from the two model types and indicate nearly identical stress distributions. Tensile stresses were generated along the deposited wall due to material contraction during solidification, which consequently generated a balancing compressive residual stress in the base plate. Significant outof-plane distortion of the component can be observed after removal of the clamps. The out-of-plane displacement along the long edge was compared for the two models"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000535_978-1-4020-8482-9-Figure5.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000535_978-1-4020-8482-9-Figure5.1-1.png",
        "caption": "Fig. 5.1 Stable parameter regimes for (a) \u22114 i=1 \u03b2 2 i < R 4 ; (b) max1\u2264i\u22644 |\u03b2i| < R 4 ; (c) max1\u2264i\u22644 |\u03b2i| < R 2 ; and (d) rp2 \u2265 \u22114 i=1 1+sign\u03b2i",
        "texts": [
            " It is of great interest in estimating the parameter values for the stability of aircrafts in the vertical direction. The larger the stable parameter regimes, the better 130 5 Special Lurie-Type Control Systems 2 \u03b2i \u03c1i the designing technical characteristics. The typical stable parameter regimes in the literature are given below: (a) min 1\u2264i\u22644 \u03c12 i r2 p2 2 \u221216 4 \u2211 i=1 \u03b2 2 i > 0; (b) min 1\u2264i\u22644 \u03c1i r p2 \u22124 max 1\u2264i\u22644 |\u03b2i| > 0; (c) min 1\u2264i\u22644 \u03c12 i r2 p2 2 \u22124 4 \u2211 i=1 \u03b2 2 i > 0. Let R = min1\u2264i\u22644 \u03c1i r p2. Then the geometrical meaning of the above cases are demonstrated in Fig. 5.1a\u2013c. The result given in Corollary 5.27 substantially increases the stable parameter regimes, as shown in Fig. 5.1d. Note that Fig. 5.1a\u2013c are all compact set, but Fig. 5.1d is unbounded set. 5.5 Two Special Systems Consider the following special Lurie system [78]: x\u0307 = Ax+ h f (xn), (5.19) where f \u2208 F\u221e, A \u2208 Rn\u00d7n, h = (h1, . . . ,hn)T \u2208 Rn. 5.5 Two Special Systems 131 Theorem 5.28. If aii < 0 (i = 1,2, . . . ,n), ai j \u2265 0 (i = j, i, j = 1, . . . ,n), hn < 0, hi \u2265 0 (i = 1,2, . . . ,n\u22121), and (a1n,a2n, . . . ,ann) = \u03bb (h1, . . . ,hn), \u03bb > 0, then the zero solution of system (5.19) is absolutely stable if and only if A is a Hurwitz matrix. Proof. Necessity. Let f (xn) = xn, system (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003546_tmag.2015.2446951-Figure18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003546_tmag.2015.2446951-Figure18-1.png",
        "caption": "Fig. 18. HSSPM prototype machine with 12/10 stator/rotor poles. (a) 12 pole stator. (b) 10 pole rotor.",
        "texts": [
            " (a) (a) (b) 0 60 120 180 240 300 360 0 0.5 1 1.5 2 2.5 Rotor position (\u00b0elec.) E le ct ro m ag ne ti c to rq ue ( N m ) HSSPM (100W) HSSPM (500W) VFM (100W) VFM (500W) 0018-9464 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 9 The machine operating principle is validated using a proof of principle prototype with 90mm stator outer diameter and 25mm stack length in Fig. 18. In order to save manufacturing costs, only the novel HSSPM machine is experimentally validated. The prototype consists of a simple aluminium stator frame. The tooth wound coils, laminated steel stator and the stator slot magnets are insulated using fibre glass. The back-EMF waveforms simulated in 2D FE and experimentally measured at 500rpm rotor speed are compared in Fig. 19. The static torque with armature and DC currents is shown in Fig. 20. It is worth mentioning that the armature current for the purpose of static torque validation is also a DC current chosen such that ia = Idc and ib = ic = -0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002925_1.4040615-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002925_1.4040615-Figure2-1.png",
        "caption": "Fig. 2 Schematic diagram of the location of flash-lamps and camera used to capture in situ powder bed images [44]",
        "texts": [
            " A digital single-lens reflex camera (DSLR, Nikon D800E) along with multiple flash-lamps placed inside the build chamber is used to capture the layer-by-layer powder bed images. Images are captured at two instances in every layer, namely, post laser scan and post re-coat. The camera shutter is controlled by a proximity sensor that registers the location of the recoater blade. Five images of the powder bed images are captured under bright-field and dark-field flash settings. The layout of the camera and flash-lamp location is shown in Fig. 2, and the representative images under the five light schemes are shown in Fig. 3. In this work, images from the bright-field light scheme in Fig. 3(a) are analyzed. Details of the experimental setup are available in Ref. [44]. As shown in Fig. 4, the LPBF process data are analyzed in two phases, namely, (1) offline analysis of XCT data in Sec. 4.1; and (2) analysis of in situ images of the powder bed in Sec. 4.2. 4.1 Phase 1: Offline Analysis of Porosity. This section aims to analyze the effect of hatch spacing (H), laser velocity (V), and laser power (P) on the count, size, and location of pores"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000029_j.jmatprotec.2009.09.011-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000029_j.jmatprotec.2009.09.011-Figure5-1.png",
        "caption": "Fig. 5. Top/side Ra measurement of thin wall part.",
        "texts": [
            " A variety of Ramp Up and Ramp Down pulses were generated when producing thin wall parts measuring 25 mm in length from four 100 m powder layers. Parts were built on a 10 mm thick steel substrate. The pulse shapes employed were progressively increased in duration and overall energy. The effects of pulse shaping on part top/side arithmetic average surface roughness (Ra) and width were tested. Sample surface Ra was measured three times for each sample using a Talysurf CLI 2000. The Talysurf evaluated 12.5 mm of the samples surface with a cut-off length of 2.5 mm. Fig. 5 illustrates the surfaces of the thin wall part that were measured for roughness. Sample width was measured using digital callipers along three segments of the sample\u2019s length. The most effective pulse shapes were identified and used to produce larger thin wall test parts 25 mm in length built from 80 m to 100 m powder layers. These were tested for Ra in multiple directions (including vertical side Ra). Laser repetition rate and scan speeds remained fixed at 40 Hz and 400 mm/min, respectively throughout all experimentation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure7.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure7.11-1.png",
        "caption": "Figure 7.11. Application of static equilibrium and a reaction board to calculate whole body center of gravity. Summing torques about the reaction board edge at the feet and solving for the moment arm (d\u22a5) for gravity locates the center of gravity.",
        "texts": [
            " The segmental method uses anthropometric data and mathematically breaks up the body into segments to calculate the center of gravity. The reaction board method requires a rigid board with special feet and a scale (2D) or scales (3D) to measure the ground reaction force under the feet of the board. The \u201cfeet\u201d of a reaction board are knife-like edges or small points similar to the point of a nail. A 2D reaction board, a free-body diagram, and static equilibrium equations to calculate the center of gravity in the sagittal plane are illustrated in Figure 7.11. Note that the weight force of the board itself is not included. This force can be easily added to the computation, but an efficient biomechanist zeros the scale with the board in place to exclude extra terms from the calculations. The subject in Figure 7.11 weighs 185 pounds, the distance between the edges is 7 feet, and the scale reading is 72.7 pounds. With only three forces acting on this system and everything known but the location of the center of gravity, it is rather simple to apply the static equilibrium equation for torque and solve for the center of gravity (d\u22a5). Note how the sign of the torque created by the subject's body is negative according to convention, so a negative d\u22a5 (to the left) of the reaction board edge fits this standard, and horizontal displacement to the left is negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure8.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure8.4-1.png",
        "caption": "Figure 8.4. The water nearest a surfboard forms a boundary layer that flows more slowly (VB) past the board than the free stream velocity (VFS) because of friction with the board and fluid friction.",
        "texts": [
            " Surface drag can be thought of as a fluid friction force, much like solid friction force studied in chapter 6. Surface drag is also commonly called friction drag or skin friction drag. It results from the frictional force between fluid molecules moving past the surface of an object and the frictional force between the various layers of the fluid. Viscosity is the internal resistance of a fluid to flow. Air has a lower viscosity than water, which has a lower viscosity than maple syrup. Suppose a surfer is floating on their board waiting for the right wave (Figure 8.4). The fluid flow below the apparently stationary surfboard creates surface drag from the flow of the ocean under the board. Water molecules immediately adjacent to the board are slowed by shear forces between them and the molecules of the board. So the fluid close to the board moves slower than the ocean water farther from the board. In fact, there is a region of water layers close to the board that moves more slowly because of viscous (fluid friction) forces between the fluid particles. This region of fluid affected by surface drag and viscosity near an object is called the boundary layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000827_j.engfailanal.2014.04.005-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000827_j.engfailanal.2014.04.005-Figure10-1.png",
        "caption": "Fig. 10. Dynamic model of bearing.",
        "texts": [
            " (28) is \u00f0Me T \u00feMe R\u00de \u20acqe xGe _qe \u00fe Keqe \u00bc Q e \u00f029\u00de All the matrices of Eq. (29) presented in Appendix A are symmetric except the gyroscopic matrix Ge which is skew symmetric, they are given in Appendix A by Eqs. (A.1)\u2013(A.4). According to relative principle, the element matrix can be assembled to total matrix MR, stiffness matrix KR and gyroscopic matrix GR of rotor. 3.1.2. The dynamic model of discrete bearings The bearings utilized in this paper can be simplified as a spring-damper system as shown in Fig. 10. The central coordinate of the bearing support is [xb yb], and shaft neck is [xs ys], the vibration differential equation of the bearing support can be expressed as Mbx 0 0 Mby \u20acxb \u20acyb \u00fe cxx cxy cyx cyy _xb _xs _yb _ys \u00fe kxx kxy kyx kyy xb xs yb ys \u00fe cbxx cbxy cbyx cbyy _xb _yb \u00fe kbxx kbxy kbyx kbyy xb yb \u00bc 0 0 \u00f030\u00de If the bearing support is approximated rigid, then xb = 0, yb = 0, then the generalized force of the bearing support acting on the shaft neck can be expressed as Q 1 Q 2 \u00bc cxx cxy cyx cyy _xs _ys kxx kxy kyx kyy xs ys \u00f031\u00de Further assume that the support is isotropic and no coupling, the formula (31) can then be expressed as Q 1 Q 2 \u00bc cxx 0 0 cyy _xs _ys kxx 0 0 kyy xs ys \u00f032\u00de 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001934_j.msea.2019.03.096-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001934_j.msea.2019.03.096-Figure2-1.png",
        "caption": "Fig. 2. The geometry and meshed FE model established for the thermal analysis.",
        "texts": [
            " The tensile properties of both the FTLD-IN718 and GDLD-IN718 were measured using a universal testing machine (Zwick Z100) operating at a constant tensile rate of 0.1mm/min. The thermal analysis of the LMD process was carried out on a 3D FE model, the model substrate was set as 25\u00d730\u00d710mm3, and the single track additive layer was set as a thickness of 0.9 mm. Based on the experimental measurement, the widths of FTLD-IN718 and GDLDIN718 were established as 5.6 mm and 4.8mm, respectively. The meshed FE model is shown in Fig. 2 and the thermal material data of IN718 used in the simulation are listed in Table 1. Two types of surface heating sources were established, resembling the focused laser beams of GDLB and FTLB, of which the energy intensity q (x, y) satisfies the following Eqs. (1) and (2), respectively. \u239c \u239f= \u239b \u239d \u2212 \u2212 + \u2212 \u239e \u23a0 q x y \u03b7 P S x x y y \u03c3 ( , ) exp (( ) ( ) ) e 0 2 0 2 2 (1) \u23a7 \u23a8 \u23aa \u23aa \u23a9 \u23aa \u23aa = < \u2212 = \u2212 \u226a \u226a + = > + \u2212 \u2212 + \u2212 + \u2212 \u2212 \u2212 \u2212 + \u2212 \u2212 ( ) ( ) ( ) q x y \u03b7 y y q x y \u03b7 y y y q x y \u03b7 y y ( , ) exp , 2 ( , ) exp , 2 2 ( , ) exp , 2 P S x x y y \u03c3 P S x x \u03c3 P S x x y y \u03c3 (( ) ( 2) ) 0 ( ) 0 0 (( ) ( 2) ) 0 e 0 2 0 2 2 e 0 2 2 e 0 2 0 2 2 (2) Where P is the total laser power, Se the effective area of the focused laser beam, x, y the Cartesian coordinate position inner the laser beam and x0 and y0 the center position of the laser beam, \u03b7 the laser absorptivity (which were set as 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.10-1.png",
        "caption": "Fig. 3.10 The forces and moments acting on a rotor hub",
        "texts": [
            " Of course, a hingeless rotor will not need to flap nearly as much and the pilot might be expected to make smaller control inputs than with an articulated rotor, to produce the same hub moment and hence to fly the same manoeuvre. The coupled rotor\u2013body motions, whether quasi-steady or with first- or second-order flapping dynamics, are formed from coupling the hub motions with the rotor and driving the hub, and hence the fuselage, with the rotor forces. The expressions for the hub forces and moments in MBC form will now be derived. Rotor Forces and Moments Returning to the fundamental frames of reference given in Section 3A, in association with Figure 3.10, we note that the hub forces in the hub\u2013wind frame can be written as Xhw = Nb\u2211 i=1 R \u222b 0 {\u2212( fz \u2212 mazb)i\ud835\udefdi cos\ud835\udf13i \u2212 ( fy \u2212 mayb)i sin\ud835\udf13i + maxb cos\ud835\udf13i}drb (3.73) Yhw = Nb\u2211 i=1 R \u222b 0 {( fz \u2212 mazb)i\ud835\udefdi sin\ud835\udf13i \u2212 ( fy \u2212 mayb)i cos\ud835\udf13i \u2212 maxb sin\ud835\udf13i}drb (3.74) Zhw = Nb\u2211 i=1 R \u222b 0 ( fz \u2212 mazb + maxb\ud835\udefdi)idrb (3.75) The expressions for the inertial accelerations of the blade element are derived in Section 3A. The aerodynamic loading is approximated by a simple lift and drag pair, with overall inflow angle assumed small, so that fz = \u2212\ud835\udcc1 cos\ud835\udf19 \u2212 d sin\ud835\udf19 \u2248 \u2212\ud835\udcc1 \u2212 d\ud835\udf19 (3",
            " The equivalent K\ud835\udefd for a hingeless rotor can be three to four times that for an articulated rotor, and it is this amplification, rather than any significant difference in the magnitude of the flapping for the different rotor types, that produces the greater hub moments with hingeless rotors. Modelling Helicopter Flight Dynamics: Building a Simulation Model 97 Rotor Torque The remaining moment produced by the rotor is the rotor torque and this produces a dominant component about the shaft axis, plus smaller components in pitch and roll due to the inclination of the disc to the plane normal to the shaft. Referring to Figure 3.10, the torque moment, approximated by the yawing moment in the hub\u2013wind axes, can be obtained by integrating the moments of the in-plane loads about the shaft axis Nh = Nb\u2211 i=1 R \u222b 0 rb( fy \u2212 mayb)idrb (3.107) We can neglect all the inertia terms except the accelerating torque caused by the rotor angular acceleration, hence reducing Eq. (3.107) to the form, Nh = Nb\u2211 i=1 R \u222b 0 {rb(d \u2212 \ud835\udcc1\ud835\udf19)}drb + IR\u03a9\u0307 (3.108) where IR is the moment of inertia of the rotor blades and hub about the shaft axis, plus any additional rotating components in the transmission system",
            "3 Non-rotating gimbal axis system for the right (counter-clockwise) rotor in helicopter (left) and airplane (right) modes xg yg yg xg zg zg zg zga1 b1 b1 a1 Fig. 10A.4 Non-rotating gimbal axis system for the left (clockwise) rotor in helicopter (left) and airplane (right) modes 702 Helicopter and Tiltrotor Flight Dynamics xb1 xb1 yb1 \u03c8 \u03c8 \u03a9 \u03a9 yb1 Fig. 10A.5 Rotating blade axes on starboard and port proprotors There are differences from the axes systems described in Chapter 3. The blade axes shown in Figure 3.10 have been rotated to conform with the FLIGHTLAB methodology. The blade axes systems are also different on the two rotors as shown in Figure 10A.5. On the counter-clockwise right rotor (left hand side as we look at Figure 10A.5), ybl is in the direction of rotor rotation (as with the clockwise rotor) and the zbl direction is forward, out of the page. In Figure 3.10 the corresponding yb and zb directions are reversed, rotated 180 deg about the xb axis, relative to those in Figure 10A.5. The body-fixed fuselage axes system, centred at the fuselage-wing-empennage centre of gravity, is shown in Figure 10A.1 with the usual orientation (i.e. as in Chapter 3) of xb forward, yb to starboard and zb down. To obtain the hub-fixed axes centred at the hub centre, the x-z plane is rotated 180 deg clockwise about the y-axis (as in Figure 3A.3) so that, in helicopter mode, the xh axis points rearward (\ud835\udf13 = 0) and the zh axis point upwards"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000832_icems.2009.5382812-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000832_icems.2009.5382812-Figure8-1.png",
        "caption": "Fig. 8. Magnetic flux distribution at maximum linkage magnetic flux.",
        "texts": [
            " A B C D E G H ( kA/m ) J ( T ) F Magnetic field analysis using the finite element method was performed for the novel motor to verify the change of the linkage magnetic flux by the permanent magnet. The model for analysis determined the principle model. The magnetization direction of the magnet in an analysis model is the same as Fig. 6. The magnetization direction of the constant magnetized magnet is the direction of d-axis, and is the upward direction. The magnetization direction of the variable magnetized magnet is the right-angled to q-axis. Firstly, the N pole is formed at d-axis side to produce the maximum of linkage magnetic flux. The analysis results at this state are shown in Fig. 8 and Fig. 9. The magnetic flux distribution of Fig. 8 shows that magnetic flux increases by addition of the magnetic flux of the variable magnetized magnet and the constant magnetized magnet. Fig. 9 shows the air gap magnetic flux density distribution. The air-gap magnetic flux density is about 0.55 T at the average in the state of the maximum linkage magnetic flux. If the polarity of the variable magnetized magnet is reversed, the linkage magnetic flux by the permanent magnets will become the minimum. The analysis results at this state are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000927_0094-114x(82)90042-8-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000927_0094-114x(82)90042-8-Figure8-1.png",
        "caption": "Figure 8. Special configuration RCCC mechanism.",
        "texts": [
            " More recently Gilmartin and Hunt[l, 6] discussed this type of configuration. Here a more complete explanation is given for the RCCC mechanism with the aid of screw theory. An RCCC mechanism with the following dimensions has an stationary and uncertainty 126 (260l, ~1 deg 180 120 60 0 - 6 0 (-Ioo) \u00b0 I00 - S4 m 5 0 - 0 50 5 0 - 100 150 to ; (a) 85 deg i 390 ~s deg ! 390 L ~ ~- deg Figure 7. Displacement functions. configuration illustrated by Figs. 8(a-b) a12 = 1.Om a12 = 60 \u00b0 a23 = 1.5 az3 = 60 \u00b0 a34 = 2.0 0'34 = 90 \u00b0 a41 = 3.0 a41 = 90 \u00b0 $44 = 2.5m Figure 8(a) illustrates a stationary configuration of the input crank a34 Links a~2 and a23 are parallel, and the axes of _S,, _$2 and _$3 are normal to the plane defined by al2 and a23. The screws representing the slider displacements of the three cylindric joints are linearly dependent. The four 6 x 6 determinants of the 7 \u00d7 6 matrix which include the Pliicker coordinates of the slider displacements are thus simulataneously zero. The remaining three 6 \u00d7 6 determinants are not zero, and, therefore, alLfour rotational displacements are simultaneously inactive. The links a j2 and a23 are, however, free to slide. A stationary configuration of the input crank a34 occurs when 04 = 300 \u00b0, and the slider displacements $1, $2 and 5'3 have values in the range _+ ~, as illustrated by Figs. 9(a-f). However when the slider displacement $2= 0 then aj2 and a23 become coaxial, see Fig. 8(b), and the axes $1, _$2 and _$3 have a common perpendicular line. The screws representing the motions of the three cylindric pairs now belong to a system with 127 -aa4 order four, and the mechanism has an uncertainty configuration. The axis of the screw which is reciprocal to all the seven screws representing the joint motions is along the (_a12, _a23) line as illustrated by Fig. 8(h). The mechanism can now be moved out of this position by rotating the input crank back out of its limit position. Theoretically when 04 = 60 \u00b0, the input crank is stationary. A further uncertainty configuration occurs when 04 = 180 \u00b0. The slider displacements have infinite values. Clearly such configurations can never be reached in practice. The use of the Gramian for determining special configurations of overconstrained singleloop mechanism is illustrated using as an example the 4R planar mechanism (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure12.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure12.6-1.png",
        "caption": "Figure 12.6 (a) Coordinate system and configuration of a planar array transducer symmetrically located on the x-y plane. (b) Coordinate system for 3D beamforming process for the planar array shown in (a).",
        "texts": [
            " The beam output of the transmitted pulse by a linear phase array probe is defined by the following equation: B(\u03b8i, f ) = \u2211 n Sn(\u03b8i, f )ej2\u03c0f \u03c4n, (12.14) where Sn(\u03b8i, f ) is the Fourier transform of the nth transducer signal sn(\u03b8i, m). Equation (12.14) is identical to Eq. (12.25) in Section 12.2.4.4. The time delay \u03c4n is a function of the transducer location and the steering angle \u03b8i and was defined before by Eq. (12.4). 12.2.4.3 Multifocus Transmit Beamformer for Planar Phase Array The left-hand side of Figure 12.6 depicts the configuration of a linear phase array probe in Cartesian coordinates. The same coordinate system located at the center of the planar array defines the parameters (i.e., A,B, \u03b8, \u03c6) of the 3D beamformer at the right-hand side of Figure 12.6. The broadband characteristics of the transmitted pulses are the same as in the case of the linear phase array and are expressed by Eq. (12.1), and the time series defining transmitted pulses for the active aperture of the phase array planar array include also time delays to account for their range focusing and angular steering characteristics. These time series are expressed by Sl,n(\u03b8i, \u03c6q, Rs,m) = Sref(\u03b8i, \u03c6q, Rs, m + \u03c4l,n)wl,n, (12.15a) where Sref(\u03b8i, \u03c6q, Rs, m + \u03c4l,n) is defined by Eq. (12.2) with \u03c4l,n(A, B,Rs) being the time-delay steering defined by the angles (A, B) and the focus range Rs and (l, n) are NEXT-GENERATION 3D/4D ULTRASOUND IMAGING TECHNOLOGY 381 the indexes for a transducer located at the (lth row, nth column) of the planar array, \u03c4l,n is the shift of the reference signal needed to create the signal for the (l, n)th transducer to achieve focus at Rs and (\u03b8i, \u03c6q) steering angle in 3D space, defined in Figure 12.6, wl,n is the spatial window value for the (l, n)th transducer, and \u03b4l,nx and \u03b4l,ny are the x and y locations, respectively, of the (l, n)th transducer. Estimates of \u03c4l,n(A, B,Rs) are provided from the following expression (12.15b): \u03c4l,n(A, B, Rs) = \u221a R2 s + \u03b42 l,nx + \u03b42 l,ny \u2212 2\u03b4l,nx cos A \u2212 2\u03b4l,ny cos B \u2212 Rs c . (12.15b) Sl,n(\u03b8i, \u03c6q, m) = \u2211 all Rs |\u03b8i ,\u03c6q Sl,n(\u03b8i, \u03c6q, Rs, m). (12.16) Implementation of a spatial window wl,n on the planar array requires the application of the decomposition process of the 2D planar array beamformer into two line array beamforming processes that have been introduced in [3]",
            "23) and the 3D beam power pattern image is obtained from P(px, py, pz) = \u2211 all \u03b8i ,\u03c6q P ( px, py, pz, \u03b8i, \u03c6q ) , (12.24) which represents the 3D image of the summation of all the illuminations of the 3D steering angles. Figure 12.7 shows the 3D beam power pattern distribution from the illumination of a volume of size (10 cm \u00d7 10 cm \u00d7 10 cm) by a planar array with 12 \u00d7 12 transducers having 0.4-mm transducer spacing. The beam steering with multiple range focusing is at a 3D angle (75 \u25e6 , 75 \u25e6) as defined by the parameters depicted in the coordinate system of Figure 12.6. The center frequency and bandwidth of the transmitted signal are 2 and 2 MHz, respectively. As in the case of the linear array active beamformer, the maximum temporal length of the active beam time series of the planar array can be estimated from \u03c4max = 2 ( N 2 + 0.5 )\u221a 2\u03b4 fs c , (12.25) Figure 12.7 3D beam power pattern distribution from the illumination of a volume of size (10 cm \u00d7 10 cm \u00d7 10 cm) by a planar array with 12 \u00d7 12 transducers having 0.4-mm transducer spacing. The beam steering with multiple range focusing is at a 3D angle (75\u25e6 , 75\u25e6) as defined by the parameters depicted in the coordinate system of Figure 12.6. The center frequency and bandwidth of the transmitted signal are 2 and 2 MHz, respectively. 384 DIGITAL 3D/4D ULTRASOUND IMAGING ARRAY where the multiplication factor \u221a 2 takes into account the transducer spacing along the diagonal direction. Then the lower boundary or the starting temporal sample of the synchronized active transducer signals is smin = spos \u2212 \u03c4max. (12.26) Finally, the beam output of the transmitted pulse by an active planar array probe is defined by B(\u03b8i, \u03c6q, Rs, f ) = \u2211 l \u2211 m Sl,n(\u03b8i, \u03c6q, f ) ej2\u03c0f \u03c4l,n(\u03b8i ,\u03c6q ,Rs ), (12",
            " The beamforming energy transmission is done through the 12 \u00d7 12 elements at the center of the array, while the receiving 3D beamformer through the 32 \u00d7 32 elements of the full phase array. The receiving data acquisition unit digitizes the sensed ultrasound reflections via the A/DC peripheral of the unit, under a similar arrangement as was defined in the previous sections. The angular subsectors depicted in Figure 12.10, are arranged in column-row configuration. Each angular subsector occupies the region bounded by the A and B angles, as defined in Figure 12.6. In Figure 12.10, the angular sector 70\u25e6 \u2264 A \u2264 110\u25e6, 70\u25e6 \u2264 B \u2264 110\u25e6 is shown to be divided into 9 angular subsectors consisting of 3 rows and 3 columns. Each subsector occupies 10\u25e6 of A angle and 10\u25e6 of B angle, with their coordinate system defined in Figure 12.6. As discussed in the previous sections, each subsector is illuminated by separate transmissions. There are, therefore, the same number of sets of received signals as the number of subsectors. The image of each angular subsector is also reconstructed separately using the corresponding set of received data. Volumetric reconstruction of each subsector is derived from the 3D beamforming process applied on all the received sensor time series of the planar array. The number of beams to be formed by the receiving beamformer is specified by the size of the angular subsector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure6.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure6.19-1.png",
        "caption": "Figure 6.19. Mechanical work is calculated as displacement of the object in the direction of the force. This calculation is accurate if the 80-N force is constant during horizontal displacement of the dolly. If you were pulling this dolly, what angle of pull would you use?",
        "texts": [
            " This example also assumes that the energy losses in the pulleys are negligible as they change the direction of the force created by the patient. Note that mechanical work can only be done on an object when it is moved relative to the line of action of the force. A more complete algebraic definition of mechanical work in the horizontal (x) direction that takes into account the component of motion in the direction of the force on an object would be W = (F cos ) \u2022 dx. For example, a person pulling a load horizontally on a dolly given the data in Figure 6.19 would do 435 Nm or Joules of work. Only the horizontal component of the force times the displacement of object determines the work done. Note also that the angle of pull in this example is like the muscle angle of pull analyzed earlier. The smaller the angle of pull, the greater the horizontal component of the force that does work to move the load. The vertical component of pull does not do any mechanical work, although it may decrease the weight of the dolly or load and, thereby decrease the rolling friction to be overcome"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001030_s11071-014-1440-z-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001030_s11071-014-1440-z-Figure1-1.png",
        "caption": "Fig. 1 Geometry of an air-breathing hypersonic vehicle",
        "texts": [
            " 3, a nonlinear controller is developed for the COM with input constraint and aerodynamic uncertainty based on RBFNN and robust adaptive dynamic surface control. Then in Sect. 4, the stability of rigid body system is analyzed based on Lyapunov theory. Simulation results and analysis are presented in Sect. 5. The paper ends with conclusions in Sect. 6. The model adopted in the paper is originated from a first principles model developed in [1,14]. It is constructed for longitudinal dynamics of a FAHV. A sketch of the vehicle geometry showing the location of control surfaces is given in Fig. 1, which is according to [50]. The equations of motion derived using Lagrange\u2019s equations which include flexible effects by modeling the vehicle as a single flexible structure with mass-normalized mode shapes. In the equations of motion, the scramjet engine model is taken from [51]. Since aerodynamic forces and moments are calculated using oblique shock and Prandtl\u2013Meyer theory, relation between control inputs and controlled outputs does not admit a closed-form representation. A simplified model has been derived for controller design and stability analysis in [50]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001505_j.automatica.2008.07.019-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001505_j.automatica.2008.07.019-Figure1-1.png",
        "caption": "Fig. 1. Schematic of tripled inverted pendulums.",
        "texts": [
            " In addition, using Vj and the proof of Case 2, we can easily prove that all signals of the subsystems satisfying |sj,nj | 6 \u03bej are bounded. Accordingly, all signals of the overall closed-loop system are bounded. Therefore, we can conclude from Cases 1, 2, and 3 that all the closed-loop signals are semi-globally bounded. Furthermore, the stabilization errors can be made arbitrarily small by appropriately adjusting the design parameters. To validate the effectiveness of the proposed method, we consider the stabilization problem of the tripled inverted pendulums with unknown non-symmetric dead-zone control inputs shown in Fig. 1. The tripled inverted pendulums subject to non-symmetric dead-zone control inputs can be described by \u03b8\u03081 = g l sin \u03b81 + Z1(u1) + k1a2 m1l2 (sin \u03b82 cos \u03b82 \u2212 sin \u03b81 cos \u03b81), \u03b8\u03082 = g l sin \u03b82 + Z2(u2) + k1a2 m2l2 (sin \u03b81 cos \u03b81 \u2212 sin \u03b82 cos \u03b82) + k2a2 m2l2 (sin \u03b83 cos \u03b83 \u2212 sin \u03b82 cos \u03b82), \u03b8\u03083 = g l sin \u03b83 + Z3(u3) + k2a2 m3l2 (sin \u03b82 cos \u03b82 \u2212 sin \u03b83 cos \u03b83), (32) where \u03b8i is the angle of the ith pendulum, g is the gravitational acceleration (kg m/s2), mi is the mass of the ith rod (kg), l is the length of each rod (m), a is the distance from the pivot to the center of gravity of the rod (m), k1 and k2 are the spring constants, and Zi(ui) denotes the output of the dead-zone where i = 1, 2, 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001620_978-90-481-8764-5_2-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001620_978-90-481-8764-5_2-Figure8-1.png",
        "caption": "Fig. 8 The scheme of the vision based localization",
        "texts": [
            " The UAVs are also equipped with an IMU(Inertial Measurement Unit) composed of three rate gyros for sensing attitude, eight IRs and four ultrasonic range sensors for obstacle detection, and one additional ultrasonic sensor for altitude measuring. A CCD camera with wireless RF(Radio Frequency) transmitter is mounted on the top of the UAV for the observation task. Table 1 gives 22 Reprinted from the journal the specification of the developed UAV. Figure 7 shows the schematic view of the embedded controller using a TMS320F2812 DSP controller. 4.2 Vision Based Localization Figure 8 shows the scheme of the vision based localization. As the payload of the UAV is limited, red and green LED markers are attached at the bottom of the UAV, and a CCD camera is put on the ground. The CCD camera gets the image of the LED markers, and the image processor analyzes the color distribution of the markers, extract the center of each marker and finds the position and orientation of the markers as shown in Fig. 9 [19]. It takes 25ms for the image processing, and 5ms for serial communication"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002117_j.mechmachtheory.2019.103597-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002117_j.mechmachtheory.2019.103597-Figure3-1.png",
        "caption": "Fig. 3. The ball distribution and coordinate system of the ACBB.",
        "texts": [
            " The normal displacement of the inner ring relative to the outer ring is given as \u03b4\u03c8 = \u03b4max [ 1 \u2212 1 1 + \u03b4a tan \u03b1 \u03b4r (1 \u2212 cos \u03c8) ] (3) where \u03b4\u03c8 , \u03b4a , and \u03b4r are the normal displacement, axial displacement and radial displacement, respectively; and \u03b4max is the maximum normal displacement when the corresponding azimuth \u03c8 is equals to 0 \u00b0, in which \u03b4max = \u03b4a sin \u03b1+ \u03b4r cos \u03b1. According to the contact relationships between the ball and rings, the normal contact load applied on the inner ring is represented as Q \u03c8 = Q max [ 1 \u2212 1 1 + \u03b4a tan \u03b1 \u03b4r (1 \u2212 cos \u03c8) ] 3 / 2 (4) Moreover, Q is equal to 0 when the ball azimuth is greater than the load angle l . The load angle l is given by \u03c8 l = cos \u22121 (\u2212\u03b4a tan \u03b1/ \u03b4r ) (5) 2.3. Load distribution from the QAM According to the quasi-statics model of the ACBB in Refs. [23\u201327] , as shown in Fig. 3 , the rotational center of the bearing is defined as the original point of the coordinate o ; the rotational plane of the bearing is defined as the plane xoy ; and the axial direction of the bearing is defined as z -axis. Moreover, in Fig. 3 , \u03b8 x and \u03b8 y are the angular position coordinates of the inner ring respected to the x and y axises, respectively; the balls are numbered by 1\u2013q; \u03d5 is the angular difference between two adjacent balls; \u03d5q is the azimuth of the q th ball; and the ball distribution and coordinate system definition of the bearing are given in Fig. 3 . When the ACBB is subjected to the combined loads, the inner ring will produce the axial displacement \u03b4a and radial displacement \u03b4rq . The positions of the shifted ball center and groove curvature centers for the q th ball are depicted in Fig. 4 . Here, the ball center will be moved to O b from O b \u2019 ; the curvature center of the groove of the inner ring will be moved to O i from O i \u2019 . The loads applied on the q th ball are depicted in Fig. 5 . The geometry and compatibility equations for the ACBB are represented as ( A 1 q \u2212 X 1 q ) 2 + ( A 2 q \u2212 X 2 q ) 2 \u2212 [ ( f i \u2212 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003504_ijaac.2016.076453-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003504_ijaac.2016.076453-Figure1-1.png",
        "caption": "Figure 1 Configuration of quadrotor MUAV",
        "texts": [
            " Section 3 provides detail description of control methodologies classified according to three control design domains. An extensive discussion is provided in Section 4, where all research questions are addressed. Finally, concluding remarks are presented in Section 5. Quadrotor is the most commonly used configuration of MUAV for variety of applications (Corke, 2011). Quadrotor has four rotors that are at equally spaced distance lcg from centre of gravity, and are mounted at ends of a cross airframe structure. The quadrotor model is shown in Figure 1. The axes convention for body frame is according to NED frame. The rotors are connected to electric motors. The rotor speed is \u03c9i and thrust of each rotor in the upward direction is \u03a4i. The rotor\u2019s thrust creates torque, which is opposed by aerodynamic drag Qi. Rotor\u2019s thrust and drag are given a 2 2 i i i i T k\u03c9 Q b\u03c9 = = (1) where i = 1 to 4, k is the lift constant and b is the drag constant. Total thrust of quadrotor is sum of all rotors\u2019 thrust, i.e. 4 1 ii T T = =\u2211 (2) Each rotor rotates in direction opposite to adjacent rotors",
            " External torques vector \u0393, which consists of torques about the quadrotor\u2019s x-axis (\u03c4\u03c6), y-axis (\u03c4\u03b8) and z-axis (\u03c4\u03c8) is given as: ( ) ( ) ( ) ( ) 2 2 4 2 4 2 2 2 1 3 1 3 4 4 1 1 \u0393 cg cg \u03b8 cg cg \u03c8 i ii i \u03c4 l T T l k \u03c9 \u03c9 \u03c4 l T T l k \u03c9 \u03c9 \u03c4 Q Q = = \u23a1 \u23a4\u23a1 \u23a4\u2212 \u2212\u23a1 \u23a4 \u23a2 \u23a5\u23a2 \u23a5\u23a2 \u23a5= = \u2212 = \u2212\u23a2 \u23a5\u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5\u23a2 \u23a5\u23a3 \u23a6 \u23a2 \u23a5\u23a2 \u23a5\u23a3 \u23a6 \u23a3 \u23a6\u2211 \u2211 \u03c6 (3) Quadrotor MUAV is an underactuated mechanical aerial vehicle, which has less control inputs than output system states, that makes MUAV control a challenging task. Many researchers have formulated dynamic models of MUAV. For modelling of quadrotor two frames of references are used; inertial frame, which is defined by the ground and body frame; which is defined by the orientation of quadrotor as shown in Figure 1. The absolute linear and angular positions of quadrotor with reference to inertial frame are defined as \u03be = [x y z]T and \u03b7 = [\u03c6 \u03b8 \u03c8]T respectively where \u03c6 is roll angle (rotation around the x-axis), \u03b8 is pitch angle (rotation around the y-axis) and \u03c8 is yaw angle (rotation around the z-axis). The linear motion of the quadrotor in inertial frame is given by Newton\u2019s second law m m= \u2212 B\u03be G RT (4) 0 0 10 0 m g T \u23a1 \u23a4 \u23a1 \u23a4 \u23a2 \u23a5 \u23a2 \u23a5= \u2212\u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5\u23a3 \u23a6 \u23a3 \u23a6 \u03be R (5) where TB is the thrust vector in the body coordinate frame, whereas R represent a rotation matrix from the body frame to the inertial frame, given as"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001967_s11071-018-4314-y-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001967_s11071-018-4314-y-Figure5-1.png",
        "caption": "Fig. 5 Schematic of a penny-shaped crack [59]",
        "texts": [
            " The influences of the crack depth, contact load, crack shape and crack surface friction coefficient on the stress intensity factors were analysed. The results indicated that the classicHertzian contact pressure between the rolling element and inner race could be significantly influenced by the rolling cracked rolling element. Wen et al. [59] introduced a 3D FE model based on a purely linear elastic quasi-static method to predict the propagation of the subsurface penny-shaped crack under a moving compressive load. The profile of the penny-shaped crack is plotted in Fig. 5. The contact and friction between the crack faces were considered in this model. The influences of the ratio of the crack depth to its length, crack-front angle, normalized load position, and frictional coefficient on the stress intensity factors were studied. They found that the shearing-mode failure could occur along the loading path direction. Potoc\u030cnik et al. [60] used a 3D FE calculation procedure to predict the subsurface elliptical crack propagation in the raceway segment of a large slewing ball bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001722_1.4027812-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001722_1.4027812-Figure2-1.png",
        "caption": "Fig. 2 Finite element/contact mechanics model of a planetary gear from a helicopter application using Calyx [6]. The colors show the stress contours and the instantaneous contact pressure at a sun-planet mesh.",
        "texts": [
            " They can incorporate finite element models of the housing and carrier built using conventional finite element software. These methods historically have had only basic tooth mesh modeling, although more recently the focus has been on better mesh modeling. Multibody dynamics methods can provide quick answers that can be used to assess different designs, but they are less effective for root cause failure analyses because of simplifications of the gear mesh. There are also finite element/contact mechanics tools, for example, Calyx [6], shown in Fig. 2, which can be used for high fidelity contact modeling and analysis. Although accurate contact between bodies is captured, this solution often requires long computation times. Interestingly, lumped-parameters models (i.e., models based on mass-spring representations for rigid body gears) are not widely used in industry, and underutilized when they are. In contrast to their use in applications, these models have been widely used in planetary gear research, where they have been shown to compare well with experiments and detailed finite element/contact mechanics models"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002361_j.actamat.2019.05.008-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002361_j.actamat.2019.05.008-Figure5-1.png",
        "caption": "Fig. 5. Phase composition and crystallographic information of the as-printed sample normal to the building direction: (a) XRD patterns showing phase constitutions of the powder, as-printed sample and heat-treated sample, (b) an inverse pole figure (IPF) map of the as-printed Tie22Ale25Nb showing the grain distribution and orientation, (c) nano-scale O phase distribution, (d) the grain size distribution and the inset showing inverse pole figure (IPF) of O phase and b phase, (e) EBSD image quality (IQ) map with LAGBs and high-AGBs (HAGBs) superimposed, (f) variation in growth rate along melt pool boundary.",
        "texts": [
            " 4(b) shows cellular structures with a size of ~1 mm. Such microstructure differs from those produced by conventional manufacturing approaches, such as powder metallurgy and forging [13,27]. High cooling rate and track-by-track manufacturing manner of the SLM processing are the underlying reasons for the microstructural characteristics of the as-printed Tie22Ale25Nb. XRD and EBSD experiments have been conducted to understand the phase constitution and microstructural features of the asprinted samples. The XRD patterns shown in Fig. 5(a) illustrate that both the raw powder and the as-printed sample mainly consist of B2/b phase and O phase. It should be noted that the weak (100)B2 superlattice peak can be found at the 2q angle of ~27.5 , confirming the existence of B2 phase. To further distinguish between the B2 phase and the b phase, the as-printed sample was heat-treated at the B2 phase region (1200 C/4 h) to obtain a microstructure dominated by the B2 phase. Compared with the original XRD data, the diffraction peaks of the B2 phase in the heat-treated condition shift slightly to the lower 2q angles, implying that the b phase has transformed into the B2 phase after the heat treatment. Based on these results, it can be proposed that the as-printed sample mainly consists of the b phase, along with a small volume fraction of the B2 phase and O phase. EBSD result in Fig. 5(b) illustrates that grains grow along the melt tracks and exhibit a ripple pattern rather than a conventional planar morphology [28]. Meanwhile, the grains existing in the melt track boundaries are much smaller than those existing in the central area of melt tracks. Fig. 5(c) reveals that very fine O phase grains prefer to grow along the melt track boundaries. The corresponding grain size distribution and the crystal orientation map of b phase and O phase are revealed in Fig. 5(d). The average grain size of b phase is calculated to be ~38 mm; the majority of b phase is presented in green-blue color in the EBSD results, suggesting that b phase tends to grow along (101) and (111) directions. In contrast, the very fine O phase shows non-preferred growth direction. The EBSD image quality (IQ) map shown in Fig. 5(e) further indicates that as-printed Tie22Ale25Nb IMC contains a large fraction of lowangle grain boundaries (LAGBs, 2 e15 , ~23.3% of the total GBs), which mainly distribute along the melt track boundaries. As mentioned, the grains along the melt track boundaries are much smaller than those of central area (Fig. 5(e)). As shown in Fig. 5(f), the grain growth rate (R), which varies with molten pool boundaries, can be expressed as [29]: R \u00bc v cos a (2) where v is the laser scanning speed, and a refers to the angle between the laser scanning direction and the direction normal to the pool boundary. By such definition, the values of the a angle equal to 0 and 90 at center line and fusion line, respectively. Therefore, the growth rate at fusion line should be zero (minimum), while that at the center line it can achieve the maximum value (v)",
            " The contributions of these two parts to peak broadening follow linear relationship, as expressed by the following equations. dhkl \u00bc dD; hkl \u00fe d \u03b5; hkl (4) dD; hkl \u00bc l D cosqhkl (5) d \u03b5; hkl \u00bc 2\u03b5 tanqhkl (6) where l\u00bc 0.154 nm is the wavelength of the Cu Ka radiation, D is the average crystallite size, q is the Bragg diffraction angle of the (hkl) peak and \u03b5 is the micro-strain. Size induced peak broadening effect is evident only for the grain size less than about 100 nm [46]. In this study, the average grain size of the b phase measured by EBSD is about 38 mm (Fig. 5(b)). Therefore, micro-strain is considered as the main reason for peak broadening, and Eq. (4) can be rewritten as: dhkl cosqhklz2\u03b5 sinqhkl (7) The value of dhkl can be obtained based on Eq. (8). dhkl \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2hkl \u00f0as printed\u00de d2hkl \u00f0powder\u00de q (8) where dhkl (as-printed) and dhkl (powder) are the full width at half maximum (FWHM) of the as-printed sample and original power, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002714_j.triboint.2011.08.019-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002714_j.triboint.2011.08.019-Figure2-1.png",
        "caption": "Fig. 2. Position of ball bearing center and raceway groove curvature centers.",
        "texts": [
            " Under zero load the centers of the raceway groove curvature radius are separated by a distance BD defined by (as shown in Fig. 1 a) BD\u00bc \u00f0r0i\u00fer0o 2rb\u00de \u00bc \u00f0f i\u00fe f o 1\u00deD \u00f02\u00de where rb is the radius of ball, while D is the diameter of the ball. f is defined by f\u00bcr 0 /D. Under an applied load, a centrifugal force acts on the ball, and then because the inner and outer raceway contact angles are dissimilar, the line of action between raceway groove curvature radius centers is not collinear with BD, but is discontinuous as indicated by Fig. 2. It is assumed in Fig. 2 that the outer raceway groove curvature center is fixed in space and the inner raceway groove curvature center moves relative to that fixed center. Moreover, the ball center shifts by virtue of the dissimilar contact angles. In according with the relative axial displacement of the inner and outer rings da, the axial distance between the position of inner and outer raceway groove curvature centers at any ball is A1j \u00bc BDsina0\u00feda \u00f03\u00de Further, in according with the relative radial displacement of the ring centers dr, the radial distance between the position of the groove curvature centers at any ball is A2j \u00bc BDcosa0\u00fedr coscj \u00f04\u00de New variables X1j and X2j are defined as seen from Fig. 2 cosaoj \u00bc X2j \u00f0f o 0:5\u00deD\u00fedoj sinaoj \u00bc X1j \u00f0f o 0:5\u00deD\u00fedoj cosaij \u00bc A2j X2j \u00f0f i 0:5\u00deD\u00fedij sinaij \u00bc A1j X1j \u00f0f i 0:5\u00deD\u00fedij 8>>>>< >>>>: \u00f05\u00de Using the Pythagorean theorem, it can be seen from Fig. 2 that \u00f0A1j X1j\u00de 2 \u00fe\u00f0A2j X2j\u00de 2 \u00bd\u00f0f i 0:5\u00deD\u00fedij 2 \u00bc 0 \u00f06\u00de X2 1j\u00fe\u00f0X 2 2j \u00bd\u00f0f o 0:5\u00deD\u00fedoj 2 \u00bc 0 \u00f07\u00de Considering the plane passing through the bearing axis with the center of a ball located at azimuth Cj, the load diagram of Fig. 3 can be obtained. If \u2018\u2018outer raceway control\u2019\u2019 is approximated at a given ball location, the ball gyroscopic moment is resisted entirely by friction force at the ball-outer raceway contacts, then in Fig. 3, lij\u00bc0 and loj\u00bc2. The normal ball loads in accordance with normal contact deformations are as follows: Qoj \u00bc Kod 1:5 oj \u00f08\u00de Qij \u00bc Kid 1:5 ij \u00f09\u00de From Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003443_bf02120338-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003443_bf02120338-Figure1-1.png",
        "caption": "Fig. 1. Ske tch of a s imple c ross - spr ing p ivo t . The two m e m b e r s a and h are c o n n e c t e d t o g e t h e r by the two flat spr ings c and d. The cen t ra l line c repre-",
        "texts": [
            " For the par t icu la r case of a small \" p u r e \" bending m o m e n t the centre of ro ta t ion coincides wi th the initial midpo in t of the spring. Such a spr ing e lement does not allow of a n y d isp lacements in its longi tudinal direct ion and is, moreover , c o m p a r a t i v e l y rigid wi th respect to bending in its own plane. On the o ther hand, however , i t is readi ly subject to distort ions due to la tera l forces or twis t ing moments . - - 3 1 3 - - These objections can be met by applying a second flat spring crossing the first one at an angle of, for instance, 90 degrees (fig. 1). We then have what is called a cross-spring pivot. To a first approximation (see section 2) it only allows of a rotation about the axis through the point of \"intersection\" of the two springs; otherwise, it is to be regarded as rigid. When, however, buckling phenomena arise the rigidity of a flat spring with respect to bending in its own plane is only limited. Consequently, in order to give greater stability to the structure two pairs of such crossed springs are generally employed, the two axes of rotation coinciding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.6-1.png",
        "caption": "Fig. 3.6 The centre-spring equivalent rotor analogue",
        "texts": [
            " It will be shown that the first mode frequency is always close to one-per-rev, and combined with the predominant forcing at one-per-rev the first flap mode generally does approximate the zero and one-per-rev blade dynamics and hub moments reasonably well, for the frequency range of interest in flight dynamics. The approximate model used in the Helisim formulation simplifies the first mode formulation even further to accommodate teetering and articulated rotors as well. The articulation and elasticity is assumed to be concentrated in a hinged spring at the centre of rotation (Figure 3.6), otherwise the blade is straight and rigid; thus S1 = r R (3.17) Such a shape, although not orthogonal to the elastic modes, does satisfy Eq. (3.11) in a distributional sense. The centre-spring model is used below to represent all classes of retention system and contrasts with the offset-hinge and spring model used in several other studies. In the offset-hinge model, the hinge offset is largely determined from the natural frequency whereas in the centre-spring model, the stiffness is provided by the hinge spring. In many ways the models are equivalent, but they differ in some important features. It will be helpful to derive some of the characteristics of blade flapping before we compare the effectiveness of the different formulations. Further discussion is therefore deferred until later in this section. The Centre-Spring Equivalent Rotor Reference to Figure 3.6 shows that the equation of motion for the blade flap angle \ud835\udefd i(t) of the ith blade can be obtained by taking moments about the centre hinge with spring strength K\ud835\udefd ; thus R \u222b 0 rb{fz(rb) \u2212 mazb}drb + K\ud835\udefd\ud835\udefdi = 0 (3.18) The blade radial distance has now been written with a subscript b to distinguish it from similar variables. We have neglected the blade weight force in Eq. (3.18); the mean lift and acceleration forces are typically one or two orders of magnitude higher. We follow the normal convention of setting the blade azimuth angle, \ud835\udf13 , to zero at the rear of the disc, with a positive direction following the rotor",
            "13, upper) has a two-per-rev rotorspeed variation superimposed on the mean value, which is the rotation speed of the input shaft (b in figure) (Ref. 10.21). The extent of the fluctuations depends on the orientation angle \ud835\udefd as shown; \ud835\udf13 is the rotation angle. For the CV joint, which can be engineered as a double Hooke joint (Figure 10.13, lower), the rotation speed of the output shaft is a constant \u03a9. Later we will show one of the designs for the hub of the ERICA tiltrotor, to illustrate innovation in compact complexity. It is helpful to recall the behaviour of our familiar articulated centre-spring rotor (Figure 3.6), in response to a step cyclic input (say +\ud835\udf031s), in hover. For our simulation, the input shaft is held fixed. The rotor blade flaps up and, after a well damped transient, settles into one-per-rev flapping with maximum at the front of the disc and minimum at the rear (so, \u2212\ud835\udefd1c). The blade incidence, and therefore blade lift, at any radial station is constant around the disc azimuth, the cyclic pitch and flap rate cancelling each other out at every azimuth. Strictly, the (unsteady) lift and moment due to the pitch and plunge motions we are describing are different, but at the reduced frequency associated with one-per-rev oscillations, the differences are small enough to be ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003791_j.jsv.2016.01.016-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003791_j.jsv.2016.01.016-Figure14-1.png",
        "caption": "Fig. 14. The faulty planet gear with a cracked tooth.",
        "texts": [
            " It can be seen that additional frequency components appear at orders of 87, 114, etc. These orders reflect the fault characteristics of a sun gear local fault in the epicyclic gearbox and the results are consistent with the spectral structures described in Section 4.2. In addition, components also exist at orders of 97, 100 and 101 which are not integer multiples of the number of planet gears. This may be caused by small angular shifts of planet gears. Since the noise in the experiment is quite heavy, there are some frequency components with small amplitudes in the spectrum. Fig. 14 shows a cracked planet gear. The cracked flank of the planet gear tooth meshes with the ring gear in this experiment. A collected vibration signal and its spectrum are illustrated in Fig. 15. We can see that, frequency components with sizable amplitudes appear at orders of 94.5, 100, 101, 106.5, and so on in Fig. 15(b). The frequency components reflecting planet gear fault characteristics appear at orders of 94.5, 106.5, etc. This is consistent with the deduced spectral structures in Section 4.3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure4.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure4.3-1.png",
        "caption": "Fig. 4.3 The general trim condition of an aircraft",
        "texts": [
            "22) are of the same order and the neglected in-plane lift forces have a significant influence on the resulting bank angle. From the force and moment balance can be derived the required control angles \u2013 main/tail rotor collectives producing the required thrusts and the lateral cyclic from the lateral disc tilt. The elementary analysis outlined above illustrates the primary mechanisms of trim and provides some insight into the required pilot trim strategy, but is too crude to be of any real practical use. The most general trim condition resembles a spin mode illustrated in Figure 4.3. The spin axis is always directed vertically in the trim, thus ensuring that the rates of change of the Euler angles \ud835\udf03 and \ud835\udf19 are both zero, and hence the gravitational force components are constant. The aircraft can be climbing or descending and flying out of lateral balance with sideslip. The general condition requires that the rate of change of magnitude of the velocity vector is identically zero. Considering Eqs. (3.1)\u2013(3.6) from Chapter 3, we see that the trim forms reduce to \u2212(WeQe \u2212 VeRe) + Xe Ma \u2212 g sin\u0398e = 0 (4",
            "29) Qe = \u03a8\u0307e sin\u03a6e cos\u0398e (4.30) Re = \u03a8\u0307e cos\u03a6e cos\u0398e (4.31) The combination of 13 unknowns and 9 equations means that to define a unique solution, four of the variables may be viewed as arbitrary and must be prescribed. The prescription is itself somewhat arbitrary, although Modelling Helicopter Flight Dynamics: Trim and Stability Analysis 171 particular groupings have become more popular and convenient than others. We shall concern ourselves with the classic case where the four prescribed trim states are defined as in Figure 4.3, i.e. Vfe flight speed \ud835\udefe fe flight path angle \u03a9ae = \u03a8\u0307e turn rate \ud835\udefde Sideslip In Appendix 4C, the relationships between the prescribed trim conditions and the body axis aerodynamic velocities are derived. In particular, an expression for the track angle between the projection of the fuselage x-axis and the projection of the flight velocity vector, both onto the horizontal plane, is given by the numerical solution of a nonlinear equation. Since the trim Eqs. (4.23)\u2013(4.28) are nonlinear, and are usually solved iteratively, initial values of some of the unknown flight states need to be estimated before they are calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003594_j.jallcom.2020.154350-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003594_j.jallcom.2020.154350-Figure10-1.png",
        "caption": "Fig. 10. EBSD analysis of the SLMed sample on the top surface: (a) the orientation map, (b) pole figures and (c) inverse pole figures.",
        "texts": [
            " Therefore, the deformation of SLMed Cu-Cr-Zr alloy may be induced by a combination of dislocation glide and twinning, which will be further studied in our future work. The EDS results (Fig. 9) demonstrate that the elements of Zr and Cr are distributed uniformly in the Cu substrate, thereby indicating the homogeneous deposition during the SLM process. The pits on the surface of the EDS sample (Fig. 9 (a)) were caused during the preparation of the EDS testing sample and have no effects on the results of the EDS tests. 12 Considering the discrepancy in the peak intensities in Fig. 7 (b), probable texture may present in the SLMed sample. Fig. 10 (a) demonstrates the EBSD orientation map of the SLMed sample on the top surface and the homologous pole figures (PFs) and inverse pole figures (IPFs) are displayed in Fig. 10 (b) and (c). Most grains in Fig. 10 (a) appear green. Hence, the grains in the sample preferentially orient their <110> direction along the building direction (BD). According to the Fig. 10 (b), the maximum texture intensity value is 6.4, which also suggests the existence of the strong texture with the <110> direction parallel to BD. The formation of texture in SLM is associated with the specific temperature field, which is strongly affected by the scanning strategy and the material properties. During SLM process, the higher thermal conductivity of the substrate relative to the powders leads to the heat of the melt pool mainly conducting toward the entity that is with lower temperature",
            " For materials with high thermal conductivity, such as the copper alloy studied in this paper, the strong thermal gradients within the molten pools result in the intense texture that is caused by the fierce competitive growth of grains. Jadhav et al. [42] observed similar phenomena while investigating the texture evolution on pure copper in SLM. They 13 explained that the solidification morphology leads to the strong texture at the top surface, which is strongly influenced by the temperature gradients within the melt pools. According to the IPF (Fig. 10 (c)), there are very weak <100> and <111> textures parallel to the directions of TD and SD. This is mainly ascribed to the scanning strategy used in this experiment. Under such condition, it is not easy to form texture along a single direction. Fig. 11 presents the engineering stress-strain curves of the tensile specimens corresponding to the SLMed parts and the wrought copper alloy. Benefiting from the excellent density, the SLMed parts exhibit comparable elastic modulus (E) and ultimate tensile strength (UTS) to the wrought copper alloy, as listed in Table 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure20-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure20-1.png",
        "caption": "Fig. 20. FEM models: (a) elements = 57,472, nodes = 67,320.",
        "texts": [
            " Hertz formula is often used to calculate SCS of gears when tooth load is given. But it is difficult to be used here for a pair of gears with AE, ME and TM. So this paper calculates the SCS of gears with a \u2018\u2018Unit Force\u2019\u2019 method. It means to calculate tooth load distributed on unit contact area of a tooth surface. That is to say, dividing the tooth load with a contact area on the reference face as shown in Fig. 1(a). When the tooth load distributions are obtained in LTCA, RBS can be calculated with 3-D FEM and the model as shown in Fig. 20(a). Since there is no commercial FEM software available that can do this analysis, FEM software used for contact analysis and strength calculations of a pair of spur gears with AE, ME and TM are developed in a personal computer through many years\u2019 efforts based on the theory and methods presented in this paper. The following is the flowchart used for FEM software development. Every step in the flowchart is explained in the following: Step 1 : Input gearing parameters and structure dimensions of a pair of gears The FEM software is built to be able to conduct contact analysis and strength calculations of a pair of spur gears with arbitrary structure dimensions as shown in Fig",
            " 1 and pairs of contact points are made. Step 8: Calculate deformation influence coefficients of the contact points on the contact reference faces by 3-D, FEM When the pairs of contact points on Gear 1 and Gear 2 as shown in Fig. 5 are made, deformation influence coefficients of all the assumed contact points are calculated by 3-D, FEM. For an example, when to calculate deflection influence coefficients of a contact point on the reference face of Gear 1 as shown in Fig. 5(a), FEM model as shown in Fig. 20(a) is used and a unit force is applied on the contact point along the line of action, then deformations of the contact point and other contact points on the reference face along the lines of action are calculated with a 3-D, FEM. This calculation is repeated for all the remained contact points on the reference face as shown in Fig. 5(a). Then deformation influence coefficient matrix of Gear 1 is formed by these calculated deformations. The same calculations are made for Gear 2. Step 9: Input loaded torque Torque is inputted here for LTCA using in the equations of mathematical programming method",
            " 7(b)) are obtained here. Step 11: Output tooth load distribution of the pair of gears with AE, ME and TM Tooth contact pattern and tooth load distribution of the pair of gears with AE, ME and TM can be obtained. Step 12: Calculate contact stresses on tooth surfaces and calculate tooth root stresses with 3D-FEM Tooth contact stresses are calculated by the method stated in Section 3.6 when load distribution on each tooth is known. Tooth root stresses are calculated by 3D-FEM with the model as shown in Fig. 20(a). Step 13: Stop It is well-known that tooth contact length (see \u2018\u20182a\u2019\u2019 in Fig. 28) of a lead-crowned gear shall become shorter when the quantity \u2018\u2018Q\u2019\u2019 of lead crowning becomes greater. Rademacher [15] investigated the relationship among tooth contact length, quantity \u2018\u2018Q\u2019\u2019 of lead crowning and loaded torque by a lot of experimental measurements and some theoretical calculations. Rademacher\u2019s experimental results are used here to compare with the results calculated by the FEM presented in this paper",
            " The detailed information can be found in Ref. [23]. N1 to N8 are the shape functions of the nodes at the corners, N9 to N11 are the shape functions of the nodes inside the element. N 1\u00f0n; g; f\u00de \u00bc \u00f01 n\u00de\u00f01 g\u00de\u00f01\u00fe f\u00de=8 N 2\u00f0n; g; f\u00de \u00bc \u00f01\u00fe n\u00de\u00f01 g\u00de\u00f01\u00fe f\u00de=8 N 3\u00f0n; g; f\u00de \u00bc \u00f01\u00fe n\u00de\u00f01\u00fe g\u00de\u00f01\u00fe f\u00de=8 N 4\u00f0n; g; f\u00de \u00bc \u00f01 n\u00de\u00f01\u00fe g\u00de\u00f01\u00fe f\u00de=8 N 5\u00f0n; g; f\u00de \u00bc \u00f01 n\u00de\u00f01 g\u00de\u00f01 f\u00de=8 N 6\u00f0n; g; f\u00de \u00bc \u00f01\u00fe n\u00de\u00f01 g\u00de\u00f01 f\u00de=8 N 7\u00f0n; g; f\u00de \u00bc \u00f01\u00fe n\u00de\u00f01\u00fe g\u00de\u00f01 f\u00de=8 N 8\u00f0n; g; f\u00de \u00bc \u00f01 n\u00de\u00f01\u00fe g\u00de\u00f01 f\u00de=8 N 9\u00f0n; g; f\u00de \u00bc 1 n2 N 10\u00f0n; g; f\u00de \u00bc 1 g2 N 11\u00f0n; g; f\u00de \u00bc 1 f2 \u00f021\u00de Fig. 20 is FEM models of the pair of gears. Fig. 20(a) is FEM mesh-dividing pattern of the wheel. The pinion is also divided similarly. Fig. 20(b) is FEM model in the part of tooth contact. Four pairs of teeth are shown. The reference face as shown in Fig. 5(a) is fine divided with 48 meshes within the contact width \u2018\u2018width\u2019\u2019 and 20 meshes within the face width. Nodes on inner hole surface (hub of the gears) as shown in Fig. 20(a) are fixed as the boundary conditions when deformation influence coefficients and RBS calculations are performed. Calculations are conducted at six cases. Case 1 is the case that no ME, AE and TM are considered in the calculations. Case 2 is the case that only 0.04 misalignment error of the gear shafts on the plane of action of the gears is given. Case 3 is the case that only 0.04 misalignment error of the gear shafts on the vertical plane of the plane of action is given. Case 4 is the case that only machining error as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000337_1.1555660-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000337_1.1555660-Figure11-1.png",
        "caption": "Fig. 11 Four-dof torsional model for automotive transmission neutral rattle study with viscous damping ~from Singh, Xie, and Comparin @27#!",
        "texts": [
            " On the other hand, the other phenomenon of a nonlinear geared system is related to gear rattle in manual automotive transmissions. Related investigations have been made for a number of different geared systems with backlash and multistage clutch stiffness @178\u2013180#. The rattle problem in lightly-loaded geared drives with low frequency external torque excitations was also studied @22,181,182#. Singh, Xie, and Comparin @27# investigated a four-dof nonlinear model for automotive transmission neutral rattle problems, as shown in Fig. 11. The corresponding model was then taken by Padmanabhan and Singh @11# as an example to explain some of their observations. Later, Karagiannis and Pfeiffer @60# and Pfeiffer and Kunert @183# also developed gear rattle models based on the principles of multi-body dynamics. Solutions were obtained with a patching scheme where a coefficient of restitution term was used for impact conditions. Chaos was found in their simulations, which was further examined by means of the Fokker-Planck equations. Kataoka, Ohno and Sugimoto @184# used the method of harmonic balance to predict torque impulses and its dependence on the two-stage clutch stiffness ratio"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure9.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure9.11-1.png",
        "caption": "Fig. 9.11 Two forces acting on a surface [73]",
        "texts": [
            " The change management is a continuous process that takes into account the fact that the SE environment can be improved based on change requests that could be introduced by stakeholders. The practical value of SE is illustrated with the following two use cases. Vuillemin et al. describe an application of model based SE for a force fighting issue in the aerospace domain. The challenge to be tackled consists of investigating the system behaviour when two forces acting in the same direction or in opposite directions are applied on a surface. This can be caused among others by errors such as signal conversion errors or by adjustment tolerances [73]. Figure 9.11 depicts a schematic presentation of the system. In order to solve the issue aforementioned, the RFLP approach has been applied. Thus, the systems requirements have been formulated by the authors in textual form. The next step has been the functional analysis. The mission of the system as well as the functions and corresponding I/O interfaces have been determined and the connections of functions as well as their sequences have been modeled [73]. A logical architecture of the aileron has been created as a block diagram on which all relevant components of the system are represented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000252_taes.1984.310452-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000252_taes.1984.310452-Figure5-1.png",
        "caption": "Fig. 5. Joint one solution.",
        "texts": [
            " (4) BELOW ARM (elbow below wrist): Position of the which corresponds to the position vector of T: wrist of the RIGHT (LEFT) arm with respect to the shoulder coordinate system has positive (negative) Pxl C1 (a2C2 + a3 C23 + d4S23) - d2S1 coordinate value along the Y2 axis. Py| = S, (a2C2 + a3C23 + d4S23) + d2CiI. (14) (5) WRIST DOWN: The s unit vector of the hand Pz L d4C23 - a3S23 - a2S2 coordinate system and the y5 unit vector of the (x5, y5, z5) coordinate system have a positive dot product. Joint One Solution. If we project the position vector (6) WRIST UP: The s unit vector of the hand coordinate p onto the x0 -Yo plane as in Fig. 5, we obtain the system and the y5 unit vector of the (x5, Y5, Z5) following equations for solving 01: coordinate system have a negative dot product. 0L = p - t; 0R = ff + (0 + t (15) (Note that the definition of the arm configurations with r\\/p2 2 2 2 2 respect to the link coordinate systems may have to be r= p +p -d2; R p +py (16) slightly modified if one uses different link coordinate p ( systems.) sin (P = cos p = (17) With respect to the above definition of various arm configurations, two arm configuration indicators (ARM sina=d2; r (18) and ELBOW) are defined for each arm configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001140_1.4025746-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001140_1.4025746-Figure3-1.png",
        "caption": "Fig. 3 The geometry of the domain; (a) the domain overview, (b) horizontal view of the domain cross-section, and (c) longitudinal view of the domain cross-section",
        "texts": [
            " The kinetic energy of electrons is transformed into heat upon striking the target material. The emitting electrons start to preheat the substrate (stainless steel plate) to a specific temperature. By reaching the desired temperature, the electron beam fully melts the powder where a solid is needed and partially where a solid is not presented. The detailed description of the EBM VR process is presented in Ref. [22]. Figure 2 shows the flowchart of the experimental procedure of the EBM VR process. Numerical Modeling Figure 3 shows the defined geometry used in this study. In order to avoid any possible bonding between substrate and solidified powders, it is required to have a thick layer of powder on the substrate. Therefore, a 3-mm layer of Ti-6Al-4V powder was placed layer-by-layer on a stainless steel substrate of 10 mm thick. The width and length of the whole geometry were selected to be 6 mm by 10 mm, respectively. An electron beam was moved along the Y-axis at the top surface, where the beginning and end points of the scanning trace were 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003791_j.jsv.2016.01.016-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003791_j.jsv.2016.01.016-Figure7-1.png",
        "caption": "Fig. 7. Different faulty flanks of the planet gear tooth.",
        "texts": [
            " Moreover, the amplitudes at orders of 99 and 102 which are integer multiples of Np in Fig. 6(b) are smaller than the amplitudes at the same orders in Fig. 5(b). Obviously, even though the angular shift is very small, the spectral structure turns to be quite complicated. In this section, suppose that a single local fault occurs on one tooth flank of the ith planet gear. If the faulty flank of the planet gear tooth meshes with the ring gear, the other healthy flank meshes with the sun gear, which is shown as label (a) in Fig. 7. Vice versa, if the faulty flank of the planet gear tooth meshes with the sun gear, the other healthy flank meshes with the ring gear, shown as label (b) in Fig. 7. No matter on which tooth flank the planet gear fault appears, the fault characteristic frequency is the same, i.e. \u03c9f p \u00bc \u03c9m Zp \u00bc Zr Zp \u03c9c. The Fourier series of the vibration signals Ari\u00f0t\u00devfprpi\u00f0t\u00de and Asi\u00f0t\u00devfpspi\u00f0t\u00de are written as: Ari\u00f0t\u00devfprpi\u00f0t\u00de \u00bc Ar1 t \u03c8 i \u00fe\u03b4pi \u03c9c 1\u00feam t \u03c8 i \u00fe\u03b4pi \u03c9p \u00fe\u03c9c Vrp1 cos \u03c9m t \u03c8 i \u00fe\u03b4pi \u03c9c \u00febm t \u03c8 i \u00fe\u03b4pi \u03c9p \u00fe\u03c9c \u00bc XQ q \u00bc Q XH h \u00bc H XN n \u00bc N XL l \u00bc L XqiAmhBmlFrine j\u00f0nZr \u00feq\u00fe\u00f0l\u00feh\u00deZrZp\u00de\u03c9cte j\u00f0nZr \u00feq\u00fe l\u00feh\u00de\u00f0\u03c8 i \u00fe\u03b4pi\u00de \u00bc XQ q \u00bc Q XH h \u00bc H XN n \u00bc N XL l \u00bc L XqiAmhBmlFrine j\u00f0nZr \u00feq\u00fe\u00f0l\u00feh\u00deZrZp\u00de\u03c9cte j\u00f0nZr \u00feq\u00fe l\u00feh\u00de2\u03c0\u00f0i 1\u00de Np e j\u00f0nZr \u00feq\u00fe\u00f0l\u00feh\u00de\u00de\u03b4pi (21) Asi\u00f0t\u00devfpspi\u00f0t\u00de \u00bc kAr1 t \u03c8 i \u00fe\u03b4pi \u03c9c 1\u00feam t\u00fe \u03c8 i \u00fe\u03b4pi \u03c9p \u00fe\u03c9c Vsp1 cos \u03c9m t\u00fe\u03c8 i \u00fe\u03b4pi \u03c9s \u03c9c \u00fe\u03b3i\u00febm t\u00fe \u03c8 i \u00fe\u03b4pi \u03c9p \u00fe\u03c9c \u00bc k XQ q \u00bc Q XH h \u00bc H XN n \u00bc N XL l \u00bc L XqiAmhBmlF sin e j\u00f0nZr \u00feq\u00fe\u00f0l\u00feh\u00deZrZp\u00de\u03c9ctejn\u03b3i ej\u00f0nZs q\u00fe l\u00feh\u00de\u00f0\u03c8 i \u00fe\u03b4pi\u00de \u00bc k XQ q \u00bc Q XH h \u00bc H XN n \u00bc N XL l \u00bc L XqiAmhBmlF sin e j\u00f0nZr \u00feq\u00fe\u00f0l\u00feh\u00deZrZp\u00de\u03c9ctejn\u03b3iej\u00f0nZs q\u00fe l\u00feh\u00de2\u03c0\u00f0i 1\u00de Np ej\u00f0nZs q\u00fe l\u00feh\u00de\u03b4pi (22) where vfprpi\u00f0t\u00de and vfpspi\u00f0t\u00de are the vibrations excited by the faulty tooth flank of the ith planet gear meshing with the ring gear and the sun gear, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000244_j.eswa.2009.06.009-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000244_j.eswa.2009.06.009-Figure3-1.png",
        "caption": "Fig. 3. The steep turn Maneuv",
        "texts": [
            " There are some basic maneuvers described in the aviation literature. One of them is steep turns. Steep turns aim to see the domination of the pilot over the control surfaces of the plane in basic training. There are several types of steep turn maneuvers. The one that is used here is a 270 turn which starts at a particular heading angle and finishes at a heading angle which is 270 from the start. As an example if the UAV starts a 270 right steep turn at 350 heading angle, 50 knots and 330 ft altitude as shown in Fig. 3, it must complete a 270 right turn and finish the turn at 260 heading angle, 50 knot airspeed and 330 ft also. It is to be noted that 330 ft is a rather low altitude for the Aerosonde considered. A steep turn at lower altitudes need more skills and can be dangerous because it is more difficult to keep the altitude level. If the controller can manage to complete the described turn with the same speed and the altitude values as at the start of the turn, this would indicate that the control surfaces of the UAV are effectively controlled by the FLCs and that the UAV can accomplish any other kind of maneuver demanded (turns, dives and climbs) with the same success as long as the maneuver is within its flight envelop"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000827_j.engfailanal.2014.04.005-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000827_j.engfailanal.2014.04.005-Figure5-1.png",
        "caption": "Fig. 5. A crack tooth model.",
        "texts": [
            " In conclusion, the method 3 proposed in this paper is most accurate for calculating time varying mesh stiffness. 2.2. Calculation of mesh stiffness of gear with tooth root crack A tooth root crack typically starts at the point of the largest stress in the material. Lewicki [20] indicates that crack propagation paths are smooth, continuous, and in most cases, rather straight with only a slight curvature. This paper also assumes the cracked tooth as a cantilevered beam, the intersection angle v between the crack and the central line of the tooth is a constant (see in Fig. 5), and the curve of the tooth profile remain perfect. In this case the Hertzian contact stiffness kh and axial compressive stiffness ka will not change at all, and they also can be calculated according to Eqs. (1), (16) and (20). However, the bending and shear stiffness will change due to the influence of the crack. When the crack is present, the effective area moment of inertia and area of the cross section at a distance of x from the tooth root will be calculated as Eqs. (24) and (25), respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000827_j.engfailanal.2014.04.005-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000827_j.engfailanal.2014.04.005-Figure11-1.png",
        "caption": "Fig. 11. Typical dynamic model of gear pair.",
        "texts": [
            " The central coordinate of the bearing support is [xb yb], and shaft neck is [xs ys], the vibration differential equation of the bearing support can be expressed as Mbx 0 0 Mby \u20acxb \u20acyb \u00fe cxx cxy cyx cyy _xb _xs _yb _ys \u00fe kxx kxy kyx kyy xb xs yb ys \u00fe cbxx cbxy cbyx cbyy _xb _yb \u00fe kbxx kbxy kbyx kbyy xb yb \u00bc 0 0 \u00f030\u00de If the bearing support is approximated rigid, then xb = 0, yb = 0, then the generalized force of the bearing support acting on the shaft neck can be expressed as Q 1 Q 2 \u00bc cxx cxy cyx cyy _xs _ys kxx kxy kyx kyy xs ys \u00f031\u00de Further assume that the support is isotropic and no coupling, the formula (31) can then be expressed as Q 1 Q 2 \u00bc cxx 0 0 cyy _xs _ys kxx 0 0 kyy xs ys \u00f032\u00de 3.2. Modeling of gear pair system In recent decades, the gear dynamic analysis has drawn wide attention. As research continues, the gear dynamic model becomes more and more complex [23]. The dynamic model of gear pair system utilized in this paper is ten degrees of freedom nonlinear model [16] which will be introduced as follows. 3.2.1. Nonlinear model of gear pair system A symbolic representation of a single stage gear system is illustrated in Fig. 11. A pair of meshing gears is modeled by rigid disks representing their mass/moment of inertia. The disks are linked by line elements that represent the stiffness and the damping. As shown in Fig. 11, a displacement vector of a gear pair can be defined from the pressure line co-ordinate system, the central coordinate vector can be expressed as qG \u00bc u1 v1 h1 hu1 hv1 u2 v2 h2 hu2 hv2\u00bd T where u, v, hu, hv are the lateral degrees of freedom and h1, h2 are the torsional degree of freedom. Subscripts 1 and 2 indicate the driving and driven gears. O1 and O2 are centers of the gears when they are stationary, O01 and O02 are centers of the gears when they are rotating, and G1 and G2 geometrical centers of the gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure6.31-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure6.31-1.png",
        "caption": "Fig. 6.31",
        "texts": [
            "17 Determine the support reaction B of the beam (flexural rigidity EI) and the angle of slope \u03d5B due to the applied moment MA (Fig. 6.29). A B C a MA a Fig. 6.29 Results: see (B) B = 3MA 2a , \u03d5B = \u2212MAa 12EI . 6.6 Supplementary Examples 281 E6.18Example 6.18 A circular arch is subjected to a force F as shown in Fig. 6.30. Determine the displacement of the point of application of the force due to bending. EI s F R Fig. 6.30 Results: see (A) fH = FR3 4EI , fV = \u03c0FR3 4EI . E6.19Example 6.19 The two beams (modulus of elasticity E) of the frame shown in Fig. 6.31 have rectangular cross sections with constant width b. The depth h is constant (h = h0) in region AB, whereas in region BC it has a linear taper (h = h(x)). A constant line load q0 acts in region BC. Calculate the vertical displacement wC of point C. Neglect axial deformations. Result: see (B) wC = 1.2 q0l 4 EI0 . E6.20 Example 6.20 A rectangular frame (flexural rigidity EI, axial rigidity \u2192 \u221e) is subjected to a uniform line load q0 (Fig. 6.32). Determine the bending moment in the frame. 2b q0 2a q0 A C Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002972_jfm.2015.372-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002972_jfm.2015.372-Figure1-1.png",
        "caption": "FIGURE 1. Problem definition: a dilute suspension of slender active particles with positions x= (x, y, z) and orientations p= (sin \u03b8 cos\u03c6, sin \u03b8 sin\u03c6, cos \u03b8) is confined between two parallel flat plates (z=\u00b1H) and subject to an imposed pressure-driven parabolic flow.",
        "texts": [
            " The effects of an external Poiseuille flow are discussed in \u00a7 4, where a numerical solution of the governing equations captures upstream swimming and shear trapping in the relevant parameter ranges, and where both effects are also explained theoretically using asymptotic analyses in the weakand strong-flow regimes. We summarize our results in \u00a7 5 and discuss them in the light of the recent literature in the field. 2.1. Problem definition and kinetic model We analyse the dynamics in a dilute suspension of self-propelled slender particles confined between two parallel flat plates and placed in an externally imposed pressuredriven flow as illustrated in figure 1. The channel half-width is denoted by H, and is assumed to be much greater than the characteristic length L of the particles (H/L 1), so that the finite size of the particles can be neglected. The external flow follows the parabolic Poiseuille profile U(x)=U(z) y\u0302=Um[1\u2212 (z/H)2] y\u0302, (2.1) with maximum velocity Um at the centreline (z = 0). The shear rate varies linearly with position z across the channel: S(z)= dU dz =\u2212\u03b3\u0307w z H , (2.2) where \u03b3\u0307w= 2Um/H is the maximum absolute shear rate attained at the walls (z=\u00b1H)",
            " Cl\u00e9ment, R. Stocker, R. Rusconi and J. Guasto for useful conversations on this problem. D.S. gratefully acknowledges funding from NSF CAREER grant no. CBET-1151590. In this appendix, we compare the no-flux boundary condition of (2.8), which is central to our model, with the reflection boundary condition used in previous works (Bearon et al. 2011; Ezhilan et al. 2012). The reflection boundary condition ensures that \u03a8 (\u00b11, \u03b8, \u03c6)=\u03a8 (\u00b11, \u03c0 \u2212 \u03b8, \u03c6) (A 1) at the channel walls, where \u03b8 and \u03c6 are defined in figure 1. Calculating the first three orientational moments of (A 1) yields the following conditions to be enforced at z= \u00b11: dc dz = 0, (A 2) mz = 0, dmy dz = 0, (A 3a,b) dDzz dz = 0, dDyy dz = 0, Dyz = 0. (A 4a\u2212c) While (A 2)\u2013(A 4) are easily shown to imply that the no-flux conditions (2.25)\u2013(2.27) on c, my, Dyy and Dzz are also satisfied, they are much more stringent conditions, with a significant impact on the distribution of particles near the wall. First, in the absence of flow, we see that (3.4)\u2013(3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.19-1.png",
        "caption": "FIGURE 2.19. A position vector r, in a local and a global frame.",
        "texts": [
            " Alternatively, rotation of a local frame when the position vector Br of a point P is fixed in the local frame and rotates with the local frame, is called active transformation. Surprisingly, the passive and active transformations are mathematically equivalent. In other words, the rotation matrix for a rotated frame and rotated vector (active transformation) is the same as the rotation matrix for a rotated frame and fixed vector (passive transformation). Proof. Consider a rotated local frame B(Oxyz) with respect to a fixed global frame G(OXY Z), as shown in Figure 2.19. P is a fixed point in the global frame, and so is its global position vector Gr. Position vector of P can be decomposed in either a local or global coordinate frame, denoted by Br and Gr respectively. 74 2. Rotation Kinematics The transformation from Gr to Br is equivalent to the required rotation of the body frame B(Oxyz) to be coincided with the global frame G(OXY Z). This is a passive transformation because the local frame cannot move the vector Gr. In a passive transformation, we usually have the coordinates of P in a global frame and we need its coordinates in a local frame; hence, we use the following equation: Br = BRG Gr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000501_pime_proc_1985_199_092_02-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000501_pime_proc_1985_199_092_02-Figure4-1.png",
        "caption": "Fig. 4 Phasor sum for the compressor drive geaibox",
        "texts": [
            " Consider the spectrum obtained for a compressor drive gearbox containing three planets and 134 teeth on the annulus gear (1). The spacing of the planet gears is assumed equal. Hence for this gearbox N = 3,Z, = 134, P I = 0, P, = 2x13 and P , = -2n/3. Substituting these values into Equation (12) and reducing the result to the range between -n and TI Proc Instn Mech Engrs Vol 199 No C1 gives, for the meshing component at rn = 1 and n = 0: Q i i o = 0 Q210 = 2~/3(134) = -2n/3 Q310 = -27~/3(134) = 2 ~ / 3 From the phasor sum of these components illustrated in Fig. 4a, it can be seen that the amplitude of the spectrum at the meshing frequency will be zero. For the first lowcr sideband at m = 1 and n = - 1 : Q i i - t = 0 Q21 - = 2n/3(133) = 27113 Q31 1 = -2n/3(133) = -2n/3 The resultant of the phasor sum shown in Fig. 4b is also zero, hence the amplitude of the spectrum at the first lower sideband will be zero. For the first upper sideband at rn = 1 and n = 1 : Q i i i = 0 Q z l l = 2n/3(135) = 0 Q 3 1 1 = -2~/3(135) = 0 As shown in Fig. 4c, the resultant of this phasor sum has maximum amplitude bccause all components are in phase. After repeating the above calculations and normalizing by dividing by N , the results in Table 1 are obtained. Note that only the vibration at the first upper sideband and every third sideband around are non-zero. It is not possible to predict thc relative amplitudes of the surviving components because these are determined by the sideband pattern of Ao( f \u2019 ) , which is not known Table I Compressor drive gearbox N = 3 Z,=134 m = l n I Q,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000317_0278364909353351-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000317_0278364909353351-Figure7-1.png",
        "caption": "Fig. 7. CAD model of a second-generation prototype 07g2 produced with an extended fabrication process featuring an additional layer. This robot type was used in the competition of 2007. (a) Top/side view, (b) bottom/side view. (1) Gold base frame resting on dimple feet, (2) nickel attractor attached to base frame, (3) nickel swinging mass separated by (4) a 10\u201320 m gap and suspended above ground by (5) a meander gold spring which in turn is attached to the base frame about 6 m above ground, (6) air gap between compression spring and nickel hammer allowing for larger springs and masses, (7) 5 m 5 m 0 75\u20132 0 m dimple.",
        "texts": [
            " Hence, it is sufficient to ensure induced displacement of the hammer in a ground state for computed forces at a given magnetic field strength. A good trade-off with large safety factors was achieved with the first design. at NEW MEXICO STATE UNIV LIBRARY on September 12, 2014ijr.sagepub.comDownloaded from As soon as it became clear that the first prototype 07v6b could be successfully fabricated and driven well within hardware and software capabilities, the fabrication process was expanded with an additional sacrificial layer. The new process allows for complex designs featuring multi-layered overhanging structures (Figure 7, label 6). The space gain makes symmetric arrangements of mass and spring possible leading to significant improvements in robot performance, as discussed in Section 5.1. Other changes included increasing the gap size between magnetic hammer and attractor mass from initially 10 to up to 20 m in later variations in order to allow for larger hammer strokes. As a result, stronger impact and inertial forces leading to higher device speeds could be achieved. The first design 07v6b-MH (Figure 5) was fabricated with a custom surface micromachining process with thick photoresist and electroplating",
            " The high mass and low Young\u2019s modulus of gold compared with other common materials in microtechnology also offers lower natural frequencies thanks to higher hammer mass and lower spring stiffness. Electrical conductivity is required for each device and spacer layer in order to enable electrodepositing of all of the following metal layers. Nickel was chosen for the magnetic bodies due to its ease of deposition. Implementing a material with higher susceptibility will increase interbody forces, but shape anisotropy plays an important role in limiting the field strength. The secondgeneration symmetric robots, e.g. 07g2 shown in Figure 7, were fabricated with a similar but extended process. Current efforts aim at the development of fabrication processes with better yield and higher device homogeneity. The robots are fabricated in batches of 10 tethered to larger gold/nickel strips when released (Figure 8(b)) which greatly facilitates their handling with tweezers and attachment for characterization of stationary devices. A laser mill allows for fast and precise separation of the devices as well as postprocessing where necessary (i",
            " Individual agent addressability based on selective frequency response has been one of the primary design criteria for the MagMite platform (Section 2.2). Multi-agent control has been achieved several times but remains fragile for practical reasons such as handling and positioning of the robots as well as up to recently insufficient understanding of the distinct driving characteristics (Figure 12). For multi-agent control studies, at NEW MEXICO STATE UNIV LIBRARY on September 12, 2014ijr.sagepub.comDownloaded from we used the two different designs 07v6b-MH (Figure 5) and 07g2-MH (Figure 7). Preliminary data illustrating the feasibility of this approach has been presented before in Frutiger et al. (2008b) and Kratochvil et al. (2009) and a representative illustration is shown in Figure 20 where two robots have been driven independently using time-division multiplexing signals. As for all results the performance of our agents is best captured in video but for illustration here the time sequence has been compressed into an overlayed picture and shows three distinct periods of movement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000422_asia.200900143-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000422_asia.200900143-Figure3-1.png",
        "caption": "Figure 3. Platinum/gold rods with short, magnetized nickel segments (length<diameter). A) These rods move autonomously in hydrogen peroxide solution. B) When an external magnetic field is applied, particles align and move perpendicular to the applied field. Adapted from Ref. [26], [28], and [37].",
        "texts": [
            " The simplest method to achieve wireless control is by incorporating ferromagnetic sections such as nickel metal between the platinum and the gold segments and consequently achieving control by a magnetic field.[26] The shape and length of this segment must be controlled by electroplating to later enable control of the direction of the nanorobot.[36, 37] Such nanorobots could be controlled wirelessly by an external magnetic field using a simple NeFeB magnet. It was observed that a magnetic field did not influence nanorod speed but only controlled the direction of the nanorods, orienting them perpendicular to the magnetic field (Figure 3).[26,28, 38] Nanorobots could electrostatically attach to different cargoes and utilize a magnetic field, as follows. After the corresponding metals were electrodeposited, electropolymeriza- tion was carried out in order to deposit a polypyrrole (PPy) segment from 100 to 800 nm in length on one side of the nanorod. This PPy segment carries a negative charge. Therefore, positively charged magnetic spherical polystyrene beads can be picked up as cargo (Figure 4 A).[38] A modification of this work was carried out by electrodepositing two nickel segments giving Pt/Ni/Au/Ni/Au/PPy nanorobots"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001140_1.4025746-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001140_1.4025746-Figure17-1.png",
        "caption": "Fig. 17 The effect of powder bed density on molten pool dimension",
        "texts": [
            " As shown, by changing the packing style from SC to BCC and FCC at any temperature, the powder bed density increases and, as a result, the thermal conductivity increases. The amount of conductive thermal conductivity is a function of solid Ti-6Al-4 V thermal conductivity (k0) and the contact size ratio (rC). As mentioned earlier, the contact size ratio was assumed to be equal 0.2. As shown in Table 1, by increasing the temperature, the thermal conductivity of solid Ti-6Al-4V increases. Therefore, the influence of the powder bed density on the powder bed conductive heat transfer (kCD) is more dominant at higher temperatures. Figure 17 shows the effect of powder bed density on the molten pool dimensions at the powder bed top surface. An increase in the powder bed density is associated with a higher thermal conductivity that leads to faster heat dissipation from the molten pool center to the surrounding loose powders. With a constant heat input applied on all of the powder bed densities, and by increasing the powder bed density, more heat can be dissipated form the molten pool to the surrounding area. Therefore, there is an inversely proportionate relationship between the powder bed density and the maximum temperature of the molten pool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003272_tvt.2020.2993725-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003272_tvt.2020.2993725-Figure7-1.png",
        "caption": "Fig. 7. Flux patterns in 3-phase 9/12 SRM with mutually coupled coil connections [27].",
        "texts": [
            " If the same coil pattern is applied to a 9/12 SRM, it would not be possible to have the number of magnetic poles equal to the number of stator poles per phase (Ns/m = 3). As circled in Fig. 6, the opposing flux direction cannot be maintained, since one of the flux loops opposes the coil direction. As a result, the dotted flux line in Fig. 6 would not be generated and a 9/12 SRM would have an unbalanced operation. In SRMs with an odd number of stator poles per phase, balanced magnetic poles can be generated by using a mutually coupled coil configuration as shown in Fig. 7 [26]. In this case, all coils of each phase have the same polarity. As a result, the flux completes its path through the stator poles of the neighboring phases and the magnetic poles are symmetrically distributed around the stator circumference. In mutually-coupled SRMs, the mutual inductance cannot be neglected. As discussed in [26], mutually-coupled SRMs are modeled and controlled differently compared to non-coupled SRMs, but they can utilize the 3-phase bridge inverter topology used in AC machines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002748_j.triboint.2015.07.021-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002748_j.triboint.2015.07.021-Figure3-1.png",
        "caption": "Fig. 3. Ball on raceway contact spots, (a) outer raceway, (b) inner raceway.",
        "texts": [
            " 2, we can develop the following formulations: Daj \u00bc \u00f0ri\u00fero d\u00de sin \u03b10\u00fe\u0394z Drj \u00bc \u00f0ri\u00fero d\u00de cos \u03b10\u00fe\u0394y cos \u03c6j\u00fe\u0394x sin \u03c6j ( \u00f01\u00de Xaj \u00bc \u00f0ro 0:5d\u00de cos \u03b10\u00fe\u03940 jz Xrj \u00bc \u00f0ro 0:5d\u00de sin \u03b10\u00fe\u03940 jy ( \u00f02\u00de tan \u03b1oj \u00bc Xaj Xrj \u00f03\u00de tan \u03b1ij \u00bc Da Xaj Dr Xrj \u00f04\u00de Then, we can get the deformations between the jth ball and the raceways as: \u03b4ij \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0Daj Xaj\u00de2\u00fe\u00f0Drj Xrj\u00de2 q \u00f0ri 0:5d\u00de \u03b4oj \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xaj 2\u00feXrj 2 q \u00f0ro 0:5d\u00de 8>< >: \u00f05\u00de According to Hertz theory, the contact force between ball and raceway can be obtained through contact deformations as follows: Qi=o \u00bc ki=o\u03b4 1:5 i=o \u00f06\u00de In order to determine the traction forces in the ball-on-raceway contacts, we have to firstly obtain the ball and raceway surface velocities. As shown in Fig. 3, at any point (x\u2033o, y\u2033o) in the ball/outerraceway contact elliptical spot, the sliding speed due to translational speed differential between ball and raceway is given by: \u0394V !x\u2033 0 \u00bc 0:5dm\u03c9c\u00fe\u00f0\u03c9y0 sin \u03b1o\u00fe\u03c9z0 cos \u03b1o\u00fe\u03c9c cos \u03b1o\u00de \u00f0r2o x\u20332o \u00de1=2 \u00f0r2o a2o\u00de1=2\u00fe \u00f00:5d\u00de2 a2o h i1=2 \u0394V !y\u2033 o \u00bc \u03c9x0 \u00f0r2o x\u20332o \u00de1=2 \u00f0r2o a2o\u00de1=2\u00fe \u00f00:5d\u00de2 a2o h i1=2 8>>>>< >>>>: \u00f07\u00de Similarly, at any point (x\u2033i, y\u2033i) in the ball/inner-raceway contact elliptical spot, the sliding speed due to translational speed differential is given by: \u0394V "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001794_j.ymssp.2012.11.004-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001794_j.ymssp.2012.11.004-Figure2-1.png",
        "caption": "Fig. 2. Planetary gearbox test rig.",
        "texts": [
            " For example, in the zoomed-in envelope spectrum (Fig. 1(g)) and instantaneous frequency spectrum (Fig. 1(i)), the dominant peaks correspond exactly to the two modulating frequencies f1 and f2. These findings show that the proposed demodulation analysis is effective to identify the modulating frequencies, even though they are very close to each other. Moreover, the simpler structure of envelope spectrum and instantaneous frequency spectrum is expected to be more helpful than the Fourier spectrum in applications. Fig. 2 shows the planetary gearbox test rig used for data collection. We manually introduced notch (to simulate crack) and tooth missing damage to one tooth of the planet and sun gear inside the 2nd stage planetary gearbox using EDM technique. Tables 2 and 3 list the gear parameters of the five gearboxes. Fig. 3 and Table 4 show and list the gear crack geometry respectively. During experiments, the rotating frequency of the input shaft connecting the sun gear of the 2nd stage planetary gearbox was set to 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002145_20100901-3-it-2016.00302-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002145_20100901-3-it-2016.00302-Figure4-1.png",
        "caption": "Fig. 4. A reference frame is attached to the shin Rsh. The motion of the stance shin is limited to the motion produce by a fictitious stance ankle with degrees of freedom q1 = \u03c6xsh and q2 = \u03c6ysh.",
        "texts": [
            " where l, L, and h are the distances along the x, y and z axes between the origin of the reference frame Rst and the ankle. From the ZMP conditions in (26), it follows that both Fmx st and Fmy st must be zero when the size of the supporting foot is zero. From (36), we obtain u1 = u2 = 0, and therefore the stance ankle joint must be passive. With the foot reduced to a point, the reference frame used to define the contact constraint is moved to the end of the leg, with its z-axis aligned along the shin as depicted in Fig. 4. The reference frame is relabeled as Rsh; its position and orientation are denoted by psh and \u03c6sh, respectively. In order to simplify the definition of the holonomic constraint, we chose to define the angles such that the orientation of the frame Rsh with respect to the frame R0 is 0Ash = Rot(z, \u03c6zsh)Rot(x, \u03c6 x sh)Rot(y, \u03c6 y sh). Consequently, the angle \u03c6zsh defines the orientation of a fictitious foot, and \u03c6xsh and \u03c6ysh are the angles of the fictitious ankle. Recalling that we assume no yaw rotation for the stance leg end, the appropriate holonomic constraint is \u03b7sh(qe) = [ psh(qe) \u03c6zsh(qe) ] = constant",
            " The width of the hips is nonzero. The stance leg is assumed to act as a passive pivot in the sagittal and frontal planes, with no rotation about the z-axis (i.e., no yaw motion). Indeed, the small link in the diagram that appears to form a foot has zero length and no mass. Its purpose is to indicate the two DOF at the leg-ground contact point corresponding to motion in the frontal (q1) and sagittal (q2) planes; in addition, it shows that there is no yaw rotation about the stance leg end per Sect. 4.4 and Fig. 4. The angles q1 and q2 are unactuated. The remaining joints are independently actuated. In single support, the robot is underactuated, having 8 DOF and 6 independent actuators. The physical parameters of the robot are given in Table 1. Studied Gait: The walking gait consists of phases of single support, alternating on the left and right legs, with transitions determined by the height of the swing leg above the ground becoming zero. The impact of the swing leg with the ground is assumed to be rigid as in Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure14-1.png",
        "caption": "Fig. 14. Free-body diagrams for chain CVT model: (a) forces on a chain link; (b) chain link interaction; (c) link-pulley contact description [16].",
        "texts": [
            " The authors reported that pulley deformation has a decisive influence on the relative contact dynamics between a chain link and the pulley sheave. It was observed that the efficiency of a chain CVT drive with flexible sheaves was lower than with rigid sheaves. This was attributed to substantial radial movements of the chain links in the pulley grooves for the case with higher pulley flexibility. The authors also discussed the influence of chain\u2019s pitch on the vibratory behavior of transmission. It was proposed that an unintegrated chain pitch reduced vibration amplitudes but also included a wider excitation band. Fig. 14[16] depicts representative free-body diagrams of a planar multibody chain CVT model. Sedlmayr and Pfeiffer [77\u201380] studied spatial dynamics of CVT chain drives. The authors modeled the links and pulleys as elastic bodies and also included pulley misalignment effects. Since even a small pulley misalignment could yield significant tensile forces in the chain, the authors proposed a spatial chain CVT model. The pulley deformation was modeled using a static finite element approximation and the reciprocal theorem of elasticity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure5-1.png",
        "caption": "Fig. 5. Engagement positions of the contact teeth.",
        "texts": [
            " Then tooth MS, LSR and CS can be calculated when the loads between the pairs of contact points are known [11,12]. Apair of spur gearswith the parameters given in Table 1 is used as research objects in this paper. Tooth dimensions,materials (JIS), heat-treatment and the transmitted torque are also given in Table 1. FEM models of the pair of gears used for LTCA are illustrated in Fig. 4. Fig. 4(a) is a whole gear FEMmodel used for FEM analyses and Fig. 4(b) is used for an enlarged view of contact teeth. Fig. 5 is a section view of the engaged teeth at three different engagement positions. They are named Positions 1, 6 and 12 respectively. In LTCA, one engagement period of the pair of gears is divided into 12 tooth engagement positions fromengage-in to engage-out. Positions 1 to 7 are the double pair tooth engagement positions. It means that there are always two pairs of teeth in contact at these positions. Positions 8 to 12 are the single pair tooth engagement positions. It means that there is only one pair of teeth in contact at these positions. FEM mesh-dividing is made at these 12 positions separately when conducting LTCA of the pair of gears. Also, tooth MS, LSR and CS are calculated separately at these 12 positions. Based on the above statements, it can be known that Fig. 5(a) shows two pairs of teeth contacted at the double pair tooth engagement position. Since this position is also the beginning of tooth contact, it is named Position 1. Fig. 5(b) shows also two pairs of teeth contacted at the double pair tooth engagement position. At this position, the double pair tooth engagement position shall be ended. Fig. 5(c) shows one pair of teeth contacted at the single pair tooth engagement position. This position is also the last position of the single pair tooth engagement. It is named Position 12. FEM models in Figs. 4 and 5 are used to calculate deformation influence coefficients and gaps between the pairs of the contact points with FEM. Hubs of the gear and pinion are fixed as boundary conditions when the deformation influence coefficients are calculated using FEM. LTCA ismade for a pair of ideal gears withoutmachining errors, assembly errors and toothmodifications at first in order tomake a comparison with the effects of tooth profile modification and lead relieving on tooth engagements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure13.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure13.7-1.png",
        "caption": "Figure 13.7 Geometric illustration of relative and transformation errors in the location parameter vector \u03b8 . The manifold S(\u03b8\u0302) represents rigid translations and rotations of the coordinate estimates \u03b8\u0302 , and the point on S(\u03b8\u0302) closest to \u03b8 represents the optimally transformed estimate, \u03b8\u0302 r . The error vector \u03be = \u03b8 \u2212 \u03b8\u0302 may be decomposed into \u03be = wr + wt , where wr = \u03b8 \u2212 \u03b8\u0302 r is the relative error vector and wt = \u03b8\u0302 r \u2212 \u03b8\u0302 . wt and wr may be approximated, respectively, by w\u0303t and w\u0303r , the projections of the error vector \u03be onto the transformation subspace R(W) and the relative subspace R(W)\u22a5.",
        "texts": [
            "54) RELATIVE AND TRANSFORMATION ERROR DECOMPOSITION 429 denote the transformed scene estimate. The optimal \u03b10 may be found using the Procrustes method of Section 13.3.1.3. As the translation and rotation components of \u03b8\u0302 have been optimally corrected in \u03b8\u0302 r , the error \u03b5r ||\u03b8 \u2212 \u03b8\u0302 r ||2 (13.55) represents the relative error, or the error in the \u201cshape\u201d of the estimate \u03b8\u0302 . We define the transformation error \u03b5t as the portion of the total error due to miss estimation of the transformation parameters \u03b5t \u03b5 \u2212 \u03b5r . (13.56) These errors are illustrated graphically in Figure 13.7. Also depicted in this figure is the four-dimensional nonlinear manifold S(\u03b8\u0302) of equivalent shapes given by all possible translations, rotations, and scalings of \u03b8\u0302 . The point on S(\u03b8\u0302) closest to \u03b8 is \u03b8\u0302 r . A linear subspace interpretation of the relative-absolute decomposition is obtained by linearizing S(\u03b8\u0302) through the transformation operator T\u03b1 . This linearization is appropriate for small-deviation analysis such as the CRB and for analyzing algorithm performance in high SNR settings. The subspace interpretation allows us to simplify the expressions for \u03b5r , \u03b5t and their expected values",
            " (13.62) The range of W , R(W), is a linear subspace approximation of the transformation space S(\u03b8\u0302) while the orthogonal complement R(W)\u22a5 represents the subspace of relative configurations. These subspaces facilitate calculating approximations of the transformation and relative errors, which may now be interpreted as projections of the total error vector \u03be onto R(W) and R(W)\u22a5. Let PW = WWT and P \u22a5 W = I \u2212 WWT denote the projection operators onto R(W) and R(W)\u22a5, respectively. Thus, as depicted in Figure 13.7, the linear approximation \u03b5\u0303r of the relative error \u03b5r is given by \u03b5\u0303r ||\u03b8 \u2212 \u03b8\u0303 r ||2 = ||P \u22a5 W\u03be ||2, (13.63) and the corresponding linear approximation \u03b5\u0303t of the transformation error is given as \u03b5\u0303t \u03b5 \u2212 \u03b5\u0303r = ||\u03be ||2 \u2212 ||P \u22a5 W\u03be ||2 = ||PW\u03be ||2. (13.64) For an unbiased estimator \u03b8\u0302 , we may express the expected values of the three estimation errors \u03b5, \u03b5\u0303r , and \u03b5\u0303t in terms of the estimator covariance matrix \u03b8\u0302 = E[\u03be\u03beT]. Let t = E[\u03b2\u0302\u03b2\u0302 T ] = WT \u03b8\u0302W (13.65) RELATIVE AND TRANSFORMATION ERROR DECOMPOSITION 431 denote the covariance matrix of the transformation coefficients, and let r = E[(P \u22a5 W\u03be)(P \u22a5 W \u03be)T] = P \u22a5 W \u03b8\u0302P \u22a5 W (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure5.17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure5.17-1.png",
        "caption": "Fig. 5.17",
        "texts": [
            " Result: see (B) \u03d1E = 62M0 l \u03c0 G r40 . E5.8 Example 5.8 A thin-walled tube (Fig. 5.16) is subjected to a torque MT . Given: a = 20 cm, t = 2 mm, \u03c4allow = 40 MPa, l = 5m, G = 0.8 \u00b7 105 MPa. Determine the allowable magnitude MTallow of the torque and the corresponding angle of twist \u03d1 for a) a closed cross section and b) an open cross section. MT MT t 2t2t 2t a t 2t l a t t Fig. 5.16 Results: see (A) a) MTallow = 6400 Nm, \u03d1 = 1.07\u25e6, b) MTallow = 96 Nm, \u03d1 = 35.8\u25e6. 5.5 Supplementary Examples 221 E5.9Example 5.9 The assembly shown in Fig. 5.17 consists of a thinwalled elastic tube (shear modulus G) and a rigid lever. The lever is subjected to a couple. Calculate the displacement of point D. Result: see (B) wD = 7 P a3 Gb3 t . E5.10Example 5.10 A rectangular lever has the thin-walled closed cross section (wall thickness t = h/20) shown in Fig. 5.18. It is loaded by a force F at the free end. Determine the equivalent stress \u03c3e at point P . Use the maximum-shear-stress theory. Result: see (B) \u03c3e = 20.2 F l h3 . E5.11 Example 5.11 A leaf spring (t b) is subjected to an eccentrically acting force F as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000736_0278364904047392-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000736_0278364904047392-Figure4-1.png",
        "caption": "Fig. 4. Planar two-wheeled mobile robot.",
        "texts": [
            " The method uses a linear least-squares estimator to compute c and \u03c6 in real time. This allows a rover to optimize its wheel traction to locally changing terrain conditions. In this paper, however, we assume a priori knowledge of c and \u03c6 for simplicity. To solve the optimization problem discussed above, the local wheel\u2013terrain contact angles must be known. Here, we present a method for estimating wheel\u2013terrain contact angles from simple on-board rover sensors. Consider a planar two-wheeled system on uneven terrain (see Figure 4). In this analysis the terrain is assumed to be rigid, and the wheels are assumed to make point contact with the terrain. For rigid wheels on deformable terrain, the singlepoint assumption no longer holds. However, an \u201ceffective\u201d wheel\u2013terrain contact angle is defined as the angular direction at Universitats-Landesbibliothek on December 12, 2013ijr.sagepub.comDownloaded from of travel imposed on the wheel by the terrain during motion (see Figure 5). In Figure 4, the rear and front wheels make contact with the terrain at angles \u03b31 and \u03b32 from the horizontal, respectively. The vehicle pitch, \u03b1, is also defined with respect to the horizontal. The wheel centers have speeds \u03bd1 and \u03bd2. These speeds are in a direction parallel to the local wheel\u2013terrain tangent due to the rigid terrain assumption. The distance between the wheel centers is defined as l. For this system, the following kinematic equations can be written: \u03bd1 cos (\u03b31 \u2212 \u03b1) = \u03bd2 cos (\u03b32 \u2212 \u03b1) (13) \u03bd2 sin (\u03b32 \u2212 \u03b1) \u2212 \u03bd1 sin (\u03b31 \u2212 \u03b1) = l\u03b1\u0307",
            " Thus, new measurement updates for the filter are not taken when these special cases are detected. See Figure 7 for a pictorial diagram of the EKF estimation process (adapted from Welch and Bishop 1999). The rough-terrain control algorithm is summarized in Figure 8. The performance of the multicriteria rough-terrain control algorithm and traditional individual-wheel velocity control were compared in simulation. The simulated system was a planar, two-wheeled 10 kg vehicle similar to that shown in Figure 4. The rigid wheel radius r was 10 cm and its wheel width w was 15 cm. The wheel spacing l was 0.8 m. Measured quantities were vehicle pitch and wheel angular velocities. Sensor noise was modeled by white noise of standard deviation approximately equal to 5% of the full-range values. The force distribution equations for the simulated system can be written as   cos(\u03b31) \u2212 sin(\u03b31) cos(\u03b32) \u2212 sin(\u03b32) sin(\u03b31) cos(\u03b31) sin(\u03b32) cos(\u03b32) V y 1 \u2212V x 1 V y 2 \u2212V x 2     T1 N1 T2 N2   =   Fx Fy Mz   . (31) This system of equations possesses (2n \u2212 3) = 1 degree of redundancy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002981_j.corsci.2020.109149-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002981_j.corsci.2020.109149-Figure1-1.png",
        "caption": "Figure 1: a) Build orientations studied for selective laser melted 316L tensile specimen produced: vertical (90\u00b0), horizontal (0\u00b0) and 45\u00b0 relative to build substrate. The red arrows highlight the cross-sections utilised for microstructure characterisation and polarisation testing for each tensile specimen. b) Points gauged to obtain the average residual stress value for each build orientation specimen.",
        "texts": [
            " Tensile specimens of 5 mm x 10 mm x 50 mm and cuboids of 50 mm x 50 mm x 12 mm were prepared to be suitable for tensile testing and residual stress measurements, respectively. For the SLM process, laser diameter was fixed at 100 \u03bcm and the oxygen level inside the build chamber was maintained < 0.30 % by inert nitrogen-purging. Laser power was maintained at 205 W, laser scan speed at 960 mm/s, and the distance between the core of two consecutive passes (hatch distance) was maintained at 110 \u00b5m with a layer height of 40 \u00b5m. The specimens were manufactured at varied build orientations, namely, vertical (90\u00b0), horizontal (0\u00b0) and 45\u00b0 as shown in Figure 1a. The build orientation angles were relative to a wrought 316L substrate (sourced from Interalloy (Victoria, Australia)). Support structures were not utilised (or required) to manufacture the specimens, regardless of build orientation angle. The SLM 316L samples were investigated on the cross-section surface perpendicular (vertical and 45\u00ba) and parallel (horizontal) to their respective production build orientation (indicated in Figure 1a), whilst the wrought 316L sample was analysed for the surface perpendicular to their rolling direction. All samples were metallographically prepared by Jo ur na l P r -p ro of successively grinding the surface to a P2500 grit finish (utilising silicon carbide paper) and polishing them to 1 \u00b5m surface finish (utilising diamond particle suspension). Posteriorly to surface preparation, each sample was individually subjected to ultrasonic bath cleaning in order to remove any residual contaminants from the surface",
            " Residual stress measurements were performed on the electropolished surface of SLM 316L specimens fabricated at horizontal, vertical and 45\u00ba orientations. The electropolishing was carried out by exposing the investigated specimen surface to a solution of choline chloride and ethylene glycol (2:1 molar ratio) under 6 V (DC power supply) for 45 minutes. After that, five different points were chosen for each build orientation specimen and residual stress measurements were carried out on the surface of those points in all the samples (Figure 1b). A Bruker\u00ae D8 Discover X-ray diffractometer equipped with a centric Eulerian cradle and Vantec-500 2D detector operating with a characteristic Cu K radiation source with a wavelength () of 1.5405 \u00c5 was utilised. An accelerating X-ray voltage of 40 kV and beam current of 40 mA were used. To investigate the SLM 316L specimens, the -Fe (220) diffraction peak was chosen with the 2 range between 73\u00ba \u2013 76\u00ba at a step size of 0.1\u00ba. The irradiated X-ray beam was 2 mm in diameter and the sample was rotated about the \u03a6 axes Jo ur al Pre -p ro of and tilted about \u0471 axes to evaluate all the components of the stress tensor",
            " The magnitude of residual stress was determined using the sin2\u0471 method at six \u03a6 angles (0\u00ba, 45\u00ba, 90\u00ba, 180\u00ba, 225\u00ba, 270\u00ba) and seven \u0471 directions (0\u00ba - 60\u00ba). A Bruker\u00ae Diffrac.Leptos software (version 7.10) was used to calculate the residual stresses where the utilised X-ray elastic constants are s1 = -1.35 x 10-6 1/MPa, \u00bd s2 = 6.18 x 10-6 1/MPa, Young\u2019s modulus (E) = 207.04 GPa, Poisson ratio () = 0.280 and an anisotropy factor of 1. Due to the anisotropic nature of residual stresses in metal AM [21,34], the residual stress values utilised herein were averaged from points carefully chosen from each specimen as shown in Figure 1b. Cyclic-potentiodynamic polarisation (CPP) was carried out for metallographically prepared (to a P1200 grit finish) SLM (vertical, 45\u00ba, horizontal) and wrought 316L stainless steel samples. Electrochemical measurements were carried out in a three-electrode system utilising a flat cell containing saturated calomel electrode (SCE) as reference and platinum mesh as the counter electrode (CE). The 316L specimens behaved as the working electrode (WE) with 1 cm2 exposed area tailored from the same cross-sections analysed for microstructure characterisation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure6.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure6.11-1.png",
        "caption": "Figure 6.11. Forces of contact between objects are usually resolved into the right-angle components of normal reaction (FN) and friction.",
        "texts": [
            " These curves allow for calculation of several variables related to angular kinetics from linear measurements. Rightangle trigonometry is also quite useful in studying the forces between two objects in contact, or precise kinematic calculations. objects in contact is also analyzed by resolv- ing the forces into right-angle components. These components use a local frame of reference like the two-dimensional muscle angle of pull above, because using horizontal and vertical components are not always convenient (Figure 6.11). The forces between two objects in contact are resolved into the normal reaction and friction. The normal reaction is the force at right angles to the surfaces in contact, while friction is the force acting in parallel to the surfaces. Friction is the force resisting the sliding of the surfaces past each other. When the two surfaces are dry, the force of friction (F) is equal to the product of the coefficient of friction ( ) and the normal reaction (FN), or F = \u2022 FN. The coefficient of friction depends on the texture and nature of the two surfaces, and is determined by experimental testing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001321_icra.2014.6907261-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001321_icra.2014.6907261-Figure5-1.png",
        "caption": "Fig. 5. Double support posture stabilization. Depending on the CoM and the desired offset o\u2032R, the position of one foot is retargeted and the joint angles of the corresponding leg chain are recomputed so that the resulting posture is statically stable.",
        "texts": [
            " It remains to describe how to generate statically stable robot postures after posture mapping and determination of the CoM position and support mode. Our approach finds a new target for either one foot or both feet so that the given offset (see Sec. V-A) is fulfilled. 1) Double Support: In the double support mode, one foot is repositioned so that the CoM, projected on the connection line between the feet, equals to the desired offset factor. The repositioning in double support mode is illustrated in Fig. 5. Here, the left foot position pLFoot is shifted in the direction of the CoM position pCoM to its new target position p\u2032LFoot so that the desired offset o\u2032R is met. Whether the right or the left foot is moved, depends on the desired offset o\u2032R and on the current offset oR which is calculated from the given pose. If o\u2032R < oR, the left foot is repositioned, otherwise the right foot. Afterwards our approach calculates new target orientations for the feet so that they have the same orientation and span a plane on the ground"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001135_tfuzz.2015.2396075-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001135_tfuzz.2015.2396075-Figure8-1.png",
        "caption": "Fig. 8. Robot manipulator with the dead-zone output mechanism.",
        "texts": [
            " Specifically, these four controllers for the comparison are given by \u2022 Quadratic Lyapunov function (QLF)-based controller with time delay compensator (TDC); \u2022 QLF-based controller without TDC; \u2022 The proposed barrier Lyapunov function (BLF)-based controller with TDC; \u2022 BLF-based controller without TDC. The simulation results are presented in the Fig. 7, which numerically verify that the proposed BLF-based controller with TDC obtains the best tracking control performance among these four controllers. Example 2(Practical Example): Consider a robot manipulator with the dead-zone output mechanism depicted in Fig. 8. Note that its dynamics can be modeled as the following second-order Lagrangian equation [54] Jq\u0308 +Bq\u0307 +Mgl sin(q) = u(t), Q(t) = DZ(q) (63) where q1 = q and q2 = q\u0307 represent the angle and angular velocity of the link, respectively. B is the overall damping coefficient and J is the total rotational inertias of motor. The link\u2019s total mass is M . The distance from the joint axis to center of mass is denoted as l. g is the gravitational acceleration. In this simulation, the aforementioned physical parameters are given as J = 1, B = 2,Mgl = 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001868_s00158-010-0496-8-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001868_s00158-010-0496-8-Figure4-1.png",
        "caption": "Fig. 4 Two-mass inverted pendulum model",
        "texts": [
            " Kudoh and Komura (2003) presented C2 continuous gait motion for biped robots using an enhanced IPM, named the angular-momentum-inducing inverted pendulum model (AMIPM), which considered angular momentum around the COG as shown in Fig. 3. The gait motion consisted of single support and double support phases. The proposed method was used to control walking motion in the sagittal and frontal planes separately. Park and Kim (1998) proposed a method called the gravity-compensated inverted pendulum model (GCIPM) to design the gait pattern. This method extended the IPM by including the effect of the free motion leg dynamics as shown in Fig. 4. The 7-DOF mechanical system was simplified into two different masses instead of a single mass in the IPM. One mass was for the free leg, and the other for the rest of the body. The mass for the free leg was assumed to concentrate at its foot, which moved along a parabolic trajectory controlled by step length and maximum foot height. In contrast, the mass for the rest of the body was modeled as in linear IPM. The walking motion was modeled as successive swinging motion in the sagittal plane, and the trajectory of the COG was analytically obtained by solving the linear equations of the two mass IPM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000736_0278364904047392-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000736_0278364904047392-Figure2-1.png",
        "caption": "Fig. 2. Wheel\u2013terrain interface on uneven terrain.",
        "texts": [
            " Vectors from the points Pi to the vehicle center of mass are denoted Vi = [V x i V y i ]T , i = {1, . . . ,n} and are expressed in the corresponding local frame {xyzi} fixed at Pi . The 3 \u00d7 1 vector F is expressed in the inertial frame {xyzo} and represents the summed effects of vehicle gravitational forces, inertial forces, forces due to manipulation, and forces due to interaction with the environment or other robots. A wheel\u2013terrain contact force exists at each point Pi and is denoted f i = [TiNi]T (see Figure 2). The vector is expressed in the local frame {xyzi} and can be decomposed into a tractive force Ti tangent to the wheel\u2013terrain contact plane and a normal force Ni normal to the wheel\u2013terrain contact plane. It is assumed that there are no moments acting at the wheel\u2013 terrain interface. The angles \u03b3i , i = {1, . . . , n} represent the angle between the horizontal and the wheel\u2013terrain contact plane. For the planar system above, quasi-static force balance equations can be written as [ 0R1 0R2 \u00b7 \u00b7 \u00b7 0Rn V y 1 \u2212V x 1 V y 2 \u2212V x 2 \u00b7 \u00b7 \u00b7 V y n \u2212V x n ]   f1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000717_j.conengprac.2010.06.007-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000717_j.conengprac.2010.06.007-Figure5-1.png",
        "caption": "Fig. 5. Experiment arrangement.",
        "texts": [
            " Given the reference and the information generated by the artificial vision system, the algorithm calculates the thrust necessary to keep the model at the required position and heading. All information is sent by radio-frequency signals to a receptor onboard the model. The receptor is integrated with electronic devices which cause the propellers to work in the desired way. There is also real-time feedback in the control system with the actual rotation values. The topology of the experimental set-up is illustrated in Fig. 5. A full description of the experimental facilities is given in Tannuri and Morishita (2006). In this paper, the performance of the SMC is experimentally evaluated through two sets of tests: set-point changes and variations in the operational condition. The former tests are intended to verify the stability and ability of the controller to work according to the specifications. The latter tests check the robustness of the SMC by changing the load of the model and environmental conditions. The set-point change tests were carried out by considering maneuvers in the surge, sway, and yaw directions, as indicated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.1-1.png",
        "caption": "Fig. 3.1 Steering axis",
        "texts": [
            " Mathematically these additional assumptions amount to having the vehicle always in its reference configuration, as shown in Fig. 1.4, with the exception of the steering angles \u03b4ij of each wheel (\u03b411 being front-left, \u03b412 front-right, etc.). More precisely, a1, a2, l, t1, t2 and h are all constant during the vehicle motion. This is fairly reasonable if the motion is not too harsh, that is if accelerations are not too big and do not change abruptly. Typically, the steering axis (pivot line) is something like in Fig. 3.1, with a caster angle and a kingpin inclination angle. Therefore, there are a trail and a scrub radius. They are key quantities in the design of the steering system. However, their effects on the dynamics of the whole vehicle may be neglected in some cases, particularly with small steering angles and perfectly rigid steering systems (as assumed here). The net effect of all these hypotheses is that the vehicle body has a planar motion parallel to the road. This is quite a remarkable fact since it greatly simplifies the analysis",
            "74\u2032) Now, in the framework of the linear single track model, we relax the assumption of rigid steering system. This means making a few changes in the congruence Eq. (6.148), since \u03b41 and \u03c41\u03b4v are no longer equal to each other. As shown in Fig. 6.45, the steering system now has a finite angular stiffness ks1 with respect to the axis about which the front wheel steers. In a turn, the lateral force Y1 exerts a vertical moment with respect to the steering axis A because of the pneumatic trail tc1 and also of the trail ts1 due to the suspension layout (see Fig. 3.1). The effect of this vertical moment Y1(tc1 + ts1) on a compliant steering system is to make the front wheel to steer less than \u03c41\u03b4v . More precisely, we have that (Fig. 6.45) \u03b41 = \u03c41\u03b4v \u2212 Y1(tc1 + ts1) ks1 (6.194) The computation of the pneumatic trail tc1 is discussed at p. 312. Accordingly, the congruence equations (6.148) of the linear single track model become \u03b11 = \u03b41 \u2212 v + ra1 u \u03b12 = \u03c7\u03c41\u03b4v \u2212 v \u2212 ra2 u (6.195) with the additional equation (6.194). On the other hand, the equilibrium equations m(v\u0307 + ur) = Y = Y1 + Y2 Jzr\u0307 = N = Y1a1 \u2212 Y2a2 (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003847_s10846-016-0333-4-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003847_s10846-016-0333-4-Figure4-1.png",
        "caption": "Fig. 4 Formation of momentum drag",
        "texts": [
            " In this paper, x = 0 holds for all position for simplification, which means gust only vary with time. Step 1-5 are implemented offline, step 6 must be implemented during simulation according to variation of time. Similarly, wind speed of y axis can also be acquired. The wind field applied in simulation in this work is shown in Figs. 2 and 3. 3 2.4 Wind Impact on Quadrotor In order to quantify boundary of force and moment disturbance [Dx, Dy, D\u03c6, D\u03b8 ] of airflow on quadrotor, momentum drag theory is introduced, which is presented in [16\u201318]. From the Fig. 4, it is easy to conclude that momentum drag exist as long as there is relative motion between propeller and atmosphere, and the changeful feature of wind gust will make the variation of momentum drag much more rapid and complex. The momentum drag N is presented as N = mV\u221e = k(\u03c1A\u03c90)V\u221e (9) where, \u03c90 = \u221a T 2\u03c1A (10) Where T stands for thrust generated by propeller A is the area of propeller disk, \u03c1 is air density, V\u221e is velocity of freestream. The impact of airflow on quadrotor is comprised of two parts: momentum drag and moment disturbance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002342_j.jsv.2011.03.031-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002342_j.jsv.2011.03.031-Figure3-1.png",
        "caption": "Fig. 3. Contact geometry and deformation on the outer ring in a dent.",
        "texts": [
            " In order to model the behaviour of the rolling element so as to reflect the actual path that the rolling element takes while rolling into and out of the dent, the dent was modelled as an ellipsoidal depression on the inner and outer races, while the dent on the rolling element was modelled as a flattened sphere. Another important aspect of this model is that due to the different geometry of the contact between the dent and the bearing component the contact stiffness changes due to the different geometrical properties in the contact. Let there be a defect on the surface of the outer race at an angle j from the horizontal axis, as shown in Fig. 3. The dent has an angle length of jd. If the rolling-element position yj coincides with the dent-angle range joyjoj\u00fejD the contact deformation will be smaller for the dent depth Dd at the position jc where C is the contact point. The contact deformation between the rolling element and the dent is now calculated as dDo\u00fe \u00bc Jrj\u00feqbCJ \u00f0R\u00f0jC\u00de\u00feDdo\u00f0jC\u00de\u00de if Jrj\u00feqbCJ \u00f0R\u00f0jC\u00de\u00feDd\u00f0jC\u00de\u00de40, 0 otherwise, ( (20) where Dd is the depth of the dent at the contact position jc . It should be noted that the contact deformation in the dent is given by simple equation (20), although behind these equations are hidden extensive trigonometric equations, that are beyond the scope of this paper",
            " For the ball\u2019s outer race contact the radii of curvature ri are rI1 \u00bc rb, rI2 \u00bc rb, rII1 \u00bc RD, rII2 \u00bc R\u00f0y\u00de: (23) When the ball strikes the dent, the radius of curvature rII2 changes to rII2 \u00bc RD \u00bc ab \u00f0a2sin2t\u00feb2cos2t\u00de3=2 , (24) where a is the semi major axis, b is the semi minor axis of the ellipsoid and t is a parameter given by the polar angle f from the ellipse centre as t\u00bc tan 1 a b tanf : (25) Although the radius of curvature RII1 changes, it is assumed that the change of this radius is negligible in order to avoid problems during the transition from the race into the dent. With the known sum and curvature difference the contact stiffness kd,o in the dent can be calculated according to Hertzian theory. From Eq. (24) it is clear that the contact stiffness is a continuous function of the angle f. Fig. 3 shows that the contact force does not act in the direction of rj under the angle yj but under the angle yC , and thus the contact force in the radial direction is FD,Co \u00bc kd,od 3=2 Do\u00fe cos\u00f0yj yC\u00de: (26) The tangential component of the contact force in the dent is neglected because the cage ensures the angular position of the rolling elements, but is taken into account as the loading on the outer race. Let there be a defect on the surface of the inner race as shown in Fig. 5. This defect will rotate with the angular speed of the shaft oS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001404_j.engfailanal.2013.08.008-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001404_j.engfailanal.2013.08.008-Figure10-1.png",
        "caption": "Fig. 10. Dynamic model of a reduction gear system with 6 DOF.",
        "texts": [
            " Dynamic simulation was applied to simulate the effect of using method 3, which is the new method proposed in this paper in preference to method 1, which is the basic approach for analytical mesh stiffness evaluation for gears with a cracked tooth. The dynamic response of a gear system can be extracted using dynamic lumped parameter modelling, to study the effect of tooth crack propagation on the obtained vibration response from a fault detection point of view. A dynamic simulation of a 6 DOF model was performed based on the time-varying mesh stiffness model explained above. The dynamic model used is shown in Fig. 10; it is the same as the model adopted in [3,31,32]. The model represents 6 DOF and is explained in the equations below, through which the friction force caused by sliding between the mating teeth is introduced. The parameters of the dynamic model are given in Table 5. The gear system works under a torque, Tg, of 60 N m applied on the driven gear. It is assumed that the radial stiffness and damping in the bearings of the pinion and gear have the same values as those given in Table 5. The moments can be obtained due to the friction force Mp and Mg by multiplying Fp and Fg respectively, by the distance from the point of contact measured perpendicularly to the centre of each disc, see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000109_s0007-8506(07)63450-7-Figure35-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000109_s0007-8506(07)63450-7-Figure35-1.png",
        "caption": "Figure 35: Micro-assembly system operating in ultrahigh vacuum with tools for surface activated bonding [ 961.",
        "texts": [
            " Image data is used to compute the relative positions of the parts. A micro-assembly system for MEMS, using the surface activated bonding (SAB) technique has been developed at RCAST, University of Tokyo [96]. The basic concept of SAB is that two atomically clean solid surfaces under contact can develop a very strong adhesive force. Atomically clean surfaces can be obtained by energetic particle bombardment in ultrahigh vacuum (UHV). The micro-assembly system developed for this purpose is shown in figure 35. It consists of an UHV chamber, a multi-axis manipulator, a SEM, and an Ar-FAB source. The two parts to be bonded together are brought in eachother's vicinity by the multi-axial stage (14 degrees of freedom (dofs)) and the manipulator (3 dofs). Their positions are monitored by the SEM. The surface of the specimen is then sputter-cleaned by Ar-FAB irradiation of about 1-2 keV for several minutes. After the native oxide or contamination layer is removed, they are brought into contact under slight pressure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001786_anie.201705667-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001786_anie.201705667-Figure1-1.png",
        "caption": "Figure 1. Schematic illustrations of the generation of the helical micromotors: (a) microfluidic spinning and spiraling system with shuttered UV lithography for the generation of helical microfiber with discrete polymerization units; (b) helical micromotors were released from the microfibers by using alginate lyase to degrade the microfibers.",
        "texts": [
            " [32-39] However, due to the limitation of the flow forms in the microfluidic lithography channel, which were usually with dispersed emulsions or continuous coflow, the recent microfluidic lithography approaches cannot generate complex 3D microparticles, especially those with helical structures. In addition, the potential value of the microfluidic-generated microparticles as bioinspired micromotors remains unexplored. Here, we present a flow lithography integrated microfluidic spinning and spiraling system for the continuous generation of helical microparticles as bioinspired micromotors, as shown schematically in Figure 1. Spinning and spiraling occurred first when the inner Na-alginate and poly-(ethylene glycol) diacrylate (PEG-DA) mixed liquid flow was injected into a [a] Dr. Y. R. Yu,[+] Dr. L. R. Shang,[+] Dr. W. Gao, Dr. Z. Zhao, Dr. H, Wang, and Prof. Y. J. Zhao State Key Laboratory of Bioelectronics, School of Biological Science and Medical Engineering, Southeast University, Nanjing 210096, China E-mail: yjzhao@seu.edu.cn [+]These authors contributed equally to this work. Supporting information for this article is given via a link at the end of the document. This article is protected by copyright. All rights reserved. calcium chloride (CaCl2) solution, which formed a spiraled microfiber due to the immediate gelation and unbalanced fluidic friction between the gelation microfiber and its surrounding fluid.[40,41] This spiraled microfiber was then flowed over a microscope objective and exposed through a photomask to shuttered ultraviolet (UV) light that polymerized the exposed area of PEG-DA in the microfiber (Figure 1a). Finally, discrete helical PEG micromotors were achieved when the gelation calcium alginate was degraded (Figure 1b). As the fabrication processes could be precisely tuned by adjusting the flow rates and the illuminating frequency, the length, diameter and pitch of the helical micromotors were highly controllable. In addition, benefit from the online gelation and polymerization, the resultant helical micromotors could be formed with the same Janus, triplex, and core-shell cross-sectional structures as their injection flows; these have not been achieved by other methods. Because of the spatially controlled encapsulation of functional nanoparticles in these microstructures, the helical micromotors can perform locomotion not only by magnetically actuated rotation or corkscrew motion but through chemically powered catalytic reaction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000052_1.3629602-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000052_1.3629602-Figure3-1.png",
        "caption": "Fig. 3 Bricard mechanism",
        "texts": [
            " T h e data used to draw these curves were accurate to within 0.0001 deg and 0.0001 in. T o achieve tliis accuracy it was necessary to make only four iterations at each position. The rate of convergence of the iteration process can be seen from the data in Table 1. I t lists the correction factors, the ddi and ds;, for each of the four iterations made in position one. These data are typical for the many problems tried and show a very satisfactory rate of convergence. Fig. 6 shows the results of the computer analysis of the Bricard mechanism shown in Fig. 3, equation (4) . These graphs were also plotted from data accurate within 0.0001 deg. As expected, the iteration process converged in four iterations for each position until reached 105 deg; it failed to converge for 110 deg. As shown in Fig. 6 both 02 and 04 approach a vertical asymptote at 0i = 106.4 deg. This implies that the relative velocities of joint 2 and joint 4 are both undefined at that position and, b y definition, the mechanism has a deadpoint. This explains why the process failed to converge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000736_0278364904047392-Figure19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000736_0278364904047392-Figure19-1.png",
        "caption": "Fig. 19. Microrover during thrust force measurement experiment.",
        "texts": [
            " In these experiments, estimates of the terrain parameters c and \u03c6 were based on results obtained from parameter identification experiments. Results of a representative experiment are shown in Figure 18. A second experiment was performed to quantify the thrust increase generated by the rough-terrain control algorithm. A weighted aluminum sled was attached to a force/torque sensor at Universitats-Landesbibliothek on December 12, 2013ijr.sagepub.comDownloaded from mounted at the front of the rover, as shown in Figure 19. The force exerted on the sled was measured during the ditch traverse with a six-axis force/torque sensor. Results of a representative pair of trials are shown in Figure 20. It can be seen that the rough-terrain control system generated greater thrust than the velocity-controlled system during the majority of the traverse. Again, this thrust increase is due to optimization of the wheel-torque distribution by the rough-terrain control algorithm. The average thrust improvement was 82%, a substantial improvement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure13.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure13.2-1.png",
        "caption": "Figure 13.2 Illustrations of basic measurement systems. (a) TOA and RSS measurements depend on the distance between the transmitter and receiver, which are described by position vectors pt and pr , respectively. (b) The AOA measurement \u03c6rt between transmitter t and receiver r is made in node r\u2019s local coordinate system, which is offset by an angle \u03b3r from the global coordinate system.",
        "texts": [
            " Common 412 SELF-LOCALIZATION OF SENSOR NETWORKS measurement types include TOA, AOA, and RSS. In these methods, a calibration signal is emitted, in turn, from each sensor in the network and received by a subset of its neighbors. The calibration signal may be any modality that is appropriate for the sensing application, hardware, and environmental conditions. Acoustic and radio-frequency (RF) calibration signals are common modalities. Time-of-arrival measurements depend on the transmitter\u2013receiver distance (Fig. 13.2a) and the emission time of the calibration signal. For a receiving sensor node r at location pr = [xr yr ]T and a transmitting sensor t at location pt = [xt yt ]T, the measured quantity is zt,r = \u03c4t + ||pt \u2212 pr ||2 c + \u03b7t,r (TOA), (13.1) where c is the propagation velocity of the calibration signal, \u03c4t is the emission time of the signal from node t , and \u03b7t,r is a random variable modeling measurement noise. In this model, \u03c4t and c are assumed known, and we estimate {pi}Si=1 from the collection of available TOA measurement pairs z = {zt,r}. TOA measurements are effectively measurements of range. In AOA, measurements are of the form zt,r = \u2220(pt , pr ) \u2212 \u03b3r + \u03b7t,r (AOA), (13.2) where, as illustrated in Figure 13.2b, \u2220(pt , pr ) denotes the global frame angle between the receiver and transmitter of the calibration signal, \u03b3r is the orientation of the MEASUREMENT TYPES AND PERFORMANCE BOUNDS 413 receiver\u2019s local measurement coordinate system with respect to the global coordinate system, and \u03b7t,r again represents measurement noise. The orientations {\u03b3r} are assumed known in the AOA model. Received signal strength measurements are typically acquired on a logarithmic scale [e.g., power ratio in decibels refenced to 1 mW (dBm)] and follow a log-distance path loss model [12]: zt,r = Pt \u2212 Ld0 \u2212 10\u03b1 log10 ||pt \u2212 pr ||2 d0 + \u03b7t,r (RSS), (13",
            " The ISOMAP algorithm [18] extends CS to this scenario by replacing missing distances with the shortest path distance between associated nodes. 422 SELF-LOCALIZATION OF SENSOR NETWORKS 13.3.1.2 Subspace-Based Multiangulation This section describes a closedform technique\u2014dubbed robust angulation using subspace techniques (RAST)\u2014for performing localization from AOA or ADOA measurements [19]. Each sensor\u2019s location is described by a position vector pi \u2208 R 2 in a global coordinate system. Each sensor r also maintains a local coordinate system centered at pr and rotated by an amount \u03b3r from the global system (Fig. 13.2b). In the global coordinate system, the AOA at receiving node r , of a transmission from node t , is \u03b8rt = \u03c6rt + \u03b3r , (13.30) where \u03c6rt is the measurement in r\u2019s local coordinate system. We consider the AOA measurement model, where the orientation angles {\u03b3r} are known. In this case, the local angle measurements {\u03c6rt } may be converted to global frame arrival angles {\u03b8rt} via (13.30). From each angle \u03b8rt , a unit vector urt = [ sin \u03b8rt \u2212 cos \u03b8rt ] (13.31) is formed that, as illustrated in Figure 13.2b, is orthogonal to the difference of the position vectors uT rt (pt \u2212 pr ) = 0. (13.32) Equation (13.32) forms the basis for the construction of a system of homogeneous equations that can be simultaneously solved in order to obtain position estimates of all sensors in the network. As in Section 13.2.2.1, we let M denote the set of M ordered measurement pairs. In expanding (13.32) into matrix form for all measurements, we first form the matrix U = {Uij }, which is an M \u00d7 M block diagonal matrix, where each block is an element of R 2\u00d71"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.11-1.png",
        "caption": "FIGURE 2.11. Arm of Example 14.",
        "texts": [
            " If a local coordinate frame Oxyz has been rotated 60 deg about the zaxis and a point P in the global coordinate frame OXY Z is at (4, 3, 2), its coordinates in the local coordinate frame Oxyz are:\u23a1\u23a3 x y z \u23a4\u23a6 = \u23a1\u23a3 cos 60 sin 60 0 \u2212 sin 60 cos 60 0 0 0 1 \u23a4\u23a6\u23a1\u23a3 4 3 2 \u23a4\u23a6 = \u23a1\u23a3 4.60 \u22121.97 2.0 \u23a4\u23a6 (2.89) Example 13 Local rotation, global position. If a local coordinate frame Oxyz has been rotated 60 deg about the z-axis and a point P in the local coordinate frame Oxyz is at (4, 3, 2), its position in the global coordinate frame OXY Z is at:\u23a1\u23a3 X Y Z \u23a4\u23a6 = \u23a1\u23a3 cos 60 sin 60 0 \u2212 sin 60 cos 60 0 0 0 1 \u23a4\u23a6T \u23a1\u23a3 4 3 2 \u23a4\u23a6 = \u23a1\u23a3 \u22120.604.96 2.0 \u23a4\u23a6 (2.90) Example 14 Successive local rotation, global position. The arm shown in Figure 2.11 has two actuators. The first actuator rotates the arm \u221290 deg about y-axis and then the second actuator rotates the arm 90 deg about x-axis. If the end point P is at BrP = \u00a3 9.5 \u221210.1 10.1 \u00a4T (2.91) then its position in the global coordinate frame is at: Gr2 = [Ax,90Ay,\u221290] \u22121 BrP = A\u22121y,\u221290A \u22121 x,90 BrP = AT y,\u221290A T x,90 BrP = \u23a1\u23a3 10.1 \u221210.1 9.5 \u23a4\u23a6 (2.92) 50 2. Rotation Kinematics 2.5 Successive Rotation About Local Cartesian Axes The final global position of a point P in a rigid body B with position vector r, after some rotations A1, A2, A3, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002462_tase.2020.3001183-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002462_tase.2020.3001183-Figure2-1.png",
        "caption": "Fig. 2. Underactuated unicycle-like underwater vehicle. Blue color indicates the actuated degrees of freedom.",
        "texts": [
            " Initially, the mathematical model of the underactuated underwater vehicle is presented. The pose vector of the vehicle with respect to the inertial frame I is denoted by \u03b7tot = [\u03b7T 1 \u03b7T 2 ]T \u2208 R 6, including the position (i.e., \u03b71 = [x y z]T ) and orientation (i.e., \u03b72 = [\u03c6 \u03b8 \u03c8]T ) vectors. The vtot = [vT 1 vT 2 ]T \u2208 R 6 is the velocity vector of the vehicle expressed in body fixed frame V and includes the linear (i.e., v1 = [u v w]T ) and angular (i.e., v2 = [p q r ]T ) velocity vectors (see Fig. 2). In this work, we consider one of the most common types of underactuated underwater vehicles, namely unicycle-like vehicles (see Fig. 2). The considered unicycle-like vehicles are equipped with a set of thrusters that are effective only in surge, heave, and yaw motion (see Fig. 2), meaning that the vehicle is underactuated along the sway axis. Remark 1: The unicycle-like underactuated underwater vehicles considered in this work are usually designed with metacentric restoring forces in order to regulate roll and pitch angles. Thus, the angles \u03c6 and \u03b8 and angular velocities p and q are negligible, and we can consider them to be equal to zero [29]. In addition, the vehicle is symmetric about the xz plane and close to symmetric about the yz plane. Therefore, we can safely assume that motions in heave, roll, and pitch are decoupled [30]",
            " Without loss of generality and based on the aforementioned considerations, the dynamic equations of the considered underwater robotic vehicle can be given as follows [30]: x\u0307 = u cos\u03c8 \u2212 v sin\u03c8 (1a) y\u0307 = u sin\u03c8 + v cos\u03c8 (1b) z\u0307 = w (1c) \u03c8\u0307 = r (1d) u\u0307 = 1 m11 m22vr + Xuu + Xu|u||u|u + \u03c4X (1e) v\u0307 = 1 m22 \u2212m11ur + Yvv + Yv|v||v|v (1f) w\u0307 = 1 m33 (W \u2212 B)+ Zww + Zw|w||w|w + \u03c4Z (1g) r\u0307 = 1 m44 (m11 \u2212 m22)uv + Nrr + Nr |r ||r |r + \u03c4N (1h) where m11, m22, m33, and m44 are the terms of the inertia matrix, including the added mass, W and B are the vehicle weight and the buoyancy force, Xu , Xu|u|, Yv , Yv|v|, Zw , Zw|w|, Nr , and Nr |r | are negative hydrodynamic damping coefficients, and \u03c4X , \u03c4Z , and \u03c4N are the control inputs of the system and Authorized licensed use limited to: University of Southern Queensland. Downloaded on July 04,2020 at 08:13:32 UTC from IEEE Xplore. Restrictions apply. consist of body forces and torque generated by the thrusters along the surge, heave, and yaw directions. Remark 2: In this work, we consider one of the most common types of underactuated underwater vehicles, namely the unicycle-like vehicles (see Fig. 2). In particular, the unicycle-like underactuated vehicles considered in this class are actuated by forces \u03c4X and \u03c4Z along the longitudinal (surge) and vertical (heave) axes, respectively, and a torque \u03c4N about the vertical (yaw) axis (see Fig. 2). The aforementioned forces \u03c4X and \u03c4Z and torque \u03c4N define the input control variables of the corresponding dynamic system (1), which, in this case, is unactuated in the sway degree of freedom (i.e., \u03c4Y = 0). The dynamic equations of (1) can be rewritten as \u03b7\u0307 = J(\u03b7)v + g(\u03b7, v) (2a) v\u0307 = M\u22121 \u03c4+C(v, v)v +D(v)v+g (2b) v\u0307 = 1 m22 \u2212m11ur + Yvv + Yv|v||v|v (2c) where the following holds. 1) \u03b7 = [x y z \u03c8] \u2208 R 4 is the pose vector expressed in I. 2) v = [u, w, r ] \u2208 R 3 is the velocity vector of the vehicle along actuated degrees of freedom, expressed in the body-fixed frame V "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003021_j.optlaseng.2019.105950-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003021_j.optlaseng.2019.105950-Figure8-1.png",
        "caption": "Fig. 8. Experimental validation for GPR model: (a) track width, (b) track height. Part I refers to the experimental parameter sets of which the cross section shape is smaller than a \u201dsemicircle \u201d, while Part II refers to those larger than a \u201dsemicircle \u201d. The parameter sets of Part I are within the parameter range of the simulation, while the parameter sets of Part II are out of the parameter range of the simulation.",
        "texts": [
            " Experimental validation for GPR model To evaluate the practicality of the GPR model, the experimental reults are used to validate the GPR model. Figs. 8 (a) and (b) show the omparison of the GPR track width and height with experimental reults. Each figure can be divided into two parts: Part I refers to the exerimental parameter sets of which the cross section shape is smaller han a \u201dsemicircle \u201d, while Part II refer to those larger than a \u201dsemicirle \u201d. The parameter sets of Part I are within the parameter range of the imulation, while the parameter sets of Part II are out of the parameer range of the simulation. For Fig. 8 (a) Part I, the average relative rror is 6.04% and the maximum relative error is 12.9%, which means he GPR model of track width fits the experimental results with paramter sets in the simulation range well. Similarly, the conclusion is also pplicable to the GPR model of track height, since the average relative rror between the predicted track height and the experimental result is .46% and the maximum relative error is 24.5%, as shown in Fig. 8 (b). owever, for the experimental parameter sets in Part II, whether the aximum or the average relative errors for track width and height are oo high to be acceptable for the GPR model. That is, the GPR models do ot perform well within these parameter sets. It should be mentioned hat these parameter sets belong to those which can not be simulated usng the powder-scale model. From these results, it can be concluded that he GPR model for track width and height can predict the geometrical c p c s v p p t 5 t d v b o b t s t r t T p 6 d t g d d o a haracteristics with the parameter sets which can be simulated using the owder-scale model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003040_tase.2014.2379615-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003040_tase.2014.2379615-Figure3-1.png",
        "caption": "Fig. 3. Description of quaternion.",
        "texts": [
            " 1, the orientation of with respect to is characterized by a unit vector along the Euler axis and the rotation angle about that axis, as follows: The reference coordinate system can be shown in (1) (2) where the corresponding direction cosine matrix , and (3) Note that , , and are not independent of each other, but constrained by the relationship (4) Then, we define the four Euler parameters as follows: Next, we define a vector such that is the vector part and is the scalar component, the detailed description of quaternion is also shown in Fig. 3. Note that the Euler parameters are not independent of each other, but constrained by the relationship due to (4) [39], [40], [42]. Based on what has been shown earlier, we chose quaternions to avoid singularity problem. The attitude kinematics and dy- namics of a rigid spacecraft can be modeled as (see [12], [23], [40], and [42]) (5) (6) here, the unit quaternion represents the attitude orientation of the spacecraft. is the positive definite inertia matrix. denotes the angular velocity vector. is the actuator effectiveness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000927_0094-114x(82)90042-8-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000927_0094-114x(82)90042-8-Figure1-1.png",
        "caption": "Figure 1. Uncertainty configuration--spatial.",
        "texts": [
            " However, more important this procedure can be used to monitor special configurations of any overconstrained spatial mechanism. For example, the six screws representing the instantaneous motion of an overconstrained 6,1ink spatial mechanism belonging to the system of order five. The Gramian obtained is a 6 x 6 matrix, and special configurations can be determined by monitoring the 6, 5 \u00d7 5 Gramians. Clearly this procedure can be applied to determine special configurations of overconstrained 5-1ink and 4-1ink mechanisms by montiroing respectively 5,4 \u00d7 4 Gramians and 4,3 x 3 Gramians. Figure 1 illustrates an uncertainty configuration of a spatial 5-1ink RCRCR mechanism. (A planar representation of the RCRCR mechanism labeled with dual angle sides &ii =aii + ~ aij and dual exterior angles #j = 0~ + \u00a2 Sj (~2 = 0) is illustrated by Fig. 2). For this case all the seven screws are reciprocal to the single screw ~ as illustrated. The rank of the matrix of the screws expressed in Pliicker coordinates is 5, and, therefore, all the 6 \u00d7 6 determinants of the 7 \u00d7 6 matrix of the Pliicker coordinates are instantaneously zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003439_j.cad.2015.06.007-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003439_j.cad.2015.06.007-Figure1-1.png",
        "caption": "Fig. 1. An example of overhang model and associated warping defect.",
        "texts": [
            " In general, the abovementioned studies have not comprehensively addressed the aspect of the need of supports for an overhang and for suitable support types. EBAM has a potential to be a cost-effective alternative to conventional discrete component manufacture for high-value, smallbatch, and custom-designed metallic parts. However, one of the challenges in part designs is inevitable overhang geometries. The overhang area will require support structures, or there will be defects around the overhang area, shown in Fig. 1, including size inaccuracy and, most noticeably, distortions. Furthermore, postprocessing for support removal can be labor intense and time consuming. There are commercial software packages, e.g., [24], which can generate support structures with a variety of options (patterns/size); however, there is no clear guideline of support design, relying on trial and error and experiences. Moreover, it needs to be pointed out that those support designs were developed more for the weight-carrying purpose, to avoid overhang area deformation due to gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003115_j.mechmachtheory.2019.03.014-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003115_j.mechmachtheory.2019.03.014-Figure5-1.png",
        "caption": "Fig. 5. Beam model of an internal gear tooth.",
        "texts": [
            " 2 ( 1 + v ) ( \u03b12 \u2212 \u03b1) cos \u03b1cos 2 \u03b11 EbH d \u03b1 (20) 1 k a = \u222b \u2212\u03b14 \u2212\u03b11 ( \u03b12 \u2212 \u03b1) cos \u03b1sin 2 \u03b11 2 EbH d \u03b1 (21) According to [13,14] , the external-external mesh stiffness is derived. These analytical formulas can be utilized to evaluate the TVMS with the changed tooth profiles. As for the mesh stiffness of external-internal spur gears, it can be divided into the external and internal stiffness. The external stiffness has been analyzed in Section 2.1 . For the internal gear, the detailed derivation of the stiffness can be found in [12] . Here, we employ it to derive the stiffness of the internal gear analytically, as shown in Fig. 5 . The meshing force F is decomposed into two orthogonal force F a and F b : { F a = F sin ( \u03b11 + \u03b80 ) F b = F cos ( \u03b11 + \u03b80 ) (22) The Hertzian contact stiffness and the flexible base stiffness are the same as the external gear. Besides, the bending, shear, and axial compressive stiffness correspond to Eqs. (11) \u2013(13) , where the geometric parameters h, h x , d, x, I x , A x can be expressed as: h = R b [ sin ( \u03b11 + \u03b80 ) \u2212 ( \u03b11 + \u03b12 ) cos ( \u03b11 + \u03b80 )] (23) h x = R b [ sin (\u03b1+ \u03b80 ) \u2212 (\u03b1 + \u03b12 ) cos (\u03b1 + \u03b80 )] (24) d = R b [( \u03b1 f + \u03b12 ) sin ( \u03b1 f + \u03b80 ) + cos ( \u03b1 f + \u03b80 ) \u2212 ( \u03b11 + \u03b12 ) sin ( \u03b11 + \u03b80 ) \u2212 cos ( \u03b11 + \u03b80 )] (25) x = R b [( \u03b1 f + \u03b12 ) sin ( \u03b1 f + \u03b80 ) + cos ( \u03b1 f + \u03b80 ) \u2212 (\u03b1 + \u03b12 ) sin (\u03b1 + \u03b80 ) \u2212 cos (\u03b1 + \u03b80 )] (26) I x = 1 12 (2 h x ) 3 b, A x = (2 h x ) b (27) The derived bending, shear, and axial compressive stiffness are then calculated as: 1 k b = \u222b \u03b11 \u03b1 f D 2 \u00d7 12 ( \u2212\u03b1 \u2212 \u03b12 ) D 2 Eb [ 2 D 1 \u2212 2 ( \u03b1 + \u03b12 ) D 2 ] 3 d \u03b1 (28) 1 k s = \u222b \u03b11 \u03b1 f 1 ",
            " 11\u201314 does not refer specifically to the pressure angle of the pitch circle, but the pressure angles of different meshing points on the same involute profile. The wear depth of the planet-ring gear is shown in Figs. 13 and 14 . It is worth noticing that the wear depth is also proportional to the number of meshing cycles, agreeing with Eq. (45) . Similarly, the tooth wear depth of the ring gear should be n (the number of planets) times of the theoretical value and the direction of the tooth wear depth is along with the force F , as shown in Fig. 5 . By comparing with the sun-planet tooth wear depth shown in Figs. 11 and 12 , the wear depth of the planet-ring gear presented in Figs. 13 and 14 indicate the same conclusion that the tooth wear depth at the tooth root is larger than that at the tooth tip, and the tooth surface shows no wear in 20 \u00b0. The tooth wear condition of the sun gear is much more severe compared with the planet gear and ring gear. It should be noted when a tooth of the sun gear meshes N s times ( N s = 1 \u00d7 10 8 , N s = 3 \u00d7 10 8 and N s = 6 \u00d7 10 8 ), a tooth of the ring gear meshes N r = N r \u00d7 z s z r times ( z s , z r are the tooth number of the sun gear and ring gear respectively), i",
            " Thus, this section only considers the influence of tooth wear on the stiffness of the ring gear. The variation of geometric parameters of the internal gear with tooth wear is expressed as follows: h = R b [ sin ( \u03b11 + \u03b80 ) \u2212 ( \u03b11 + \u03b12 ) cos ( \u03b11 + \u03b80 )] \u2212 h wear ( \u03b11 ) cos ( \u03b11 + \u03b80 ) (55) I x = 1 12 (2 h x \u2212 h wear cos (\u03b1 + \u03b80 )) 3 b, A x = (2 h x \u2212 h wear cos (\u03b1 + \u03b80 )) b (56) { h wear ( \u03b11 ) = h wear _ pr ( \u03b11 ) h wear = h wear _ pr (\u03b1) (57) where h wear _ pr (\u03b1) is the wear depth of the planet-ring gears at the angle \u03b1, as shown in Fig. 5 , and the direction of the wear depth is along the direction of force F . Therefore, the internal gear stiffness with the tooth wear is derived as: 1 k b = \u222b \u03b11 \u03b1 f D 2 \u00d7 12 ( \u2212\u03b1 \u2212 \u03b12 ) D 2 Eb [ 2 D 1 \u2212 2 ( \u03b1 + \u03b12 ) D 2 \u2212 h wear D 2 R b ]3 d \u03b1 (58) 1 k s = \u222b \u03b11 \u03b1 f 1 . 2 D 4 2 ( \u2212\u03b1 \u2212 \u03b12 ) D 2 Gb [ 2 D 1 \u2212 2 ( \u03b1 + \u03b12 ) D 2 \u2212 h wear D 2 R b ]d \u03b1 (59) 1 k a = \u222b \u03b11 \u03b1 f D 3 2 ( \u2212\u03b1 \u2212 \u03b12 ) D 2 Eb [ 2 D 1 \u2212 2 ( \u03b1 + \u03b12 ) D 2 \u2212 h wear D 2 R ]d \u03b1 (60) b where D = D 4 ( D 2 + ( \u03b12 + \u03b1) D 1 \u2212 D 4 \u2212 ( \u03b12 + \u03b11 ) D 3 ) \u2212 D 3 ( D 3 \u2212 ( \u03b12 + \u03b11 ) D 4 \u2212 D 4 \u00d7 h wear ( \u03b11 ) R b ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000655_1.4002333-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000655_1.4002333-Figure2-1.png",
        "caption": "Fig. 2 Radial deflection at a rolling element position",
        "texts": [
            " \u2022 Damping due to the presence of friction at various interfaces cage-ball, inner race-shaft, and outer race-housing is neglected. ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 03/09/2015 Terms 2.1 Total Deflection of Ball in Radial Direction. Hertzian load-deformation relationship is used in calculation of deformation at the contacts formed between ball and races of the bearing under investigation. The used relationship is expressed as follows 18 : Q = K 3/2 1 The radial deflection at any rolling element position refer to Fig. 2 is written as 18 = r cos \u2212 1 2 Pd 2 where r is the ring\u2019s radial shift at =0. If 0 is the initial position of the ith ball, the angular position i at any time t is defined by the following relation: i = 2 i Nb + ct + 0 3 where the angular velocity of cage is expressed in term of angular velocity of shaft and is defined as follows: c = 1 \u2212 d D s 2 4 Based on the geometry of the bearing, the normal load on the ball/raceway at position refer Fig. 3 is calculated by the following equation 18 : Q = Qmax 1 \u2212 1 2 1 \u2212 cos 3/2 5 where = 1 /2 1\u2212 Pd /2 r "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.5-1.png",
        "caption": "Fig. 3.5 Velocity center C, acceleration center K and inflection circle",
        "texts": [
            "34) which, in case of planar motion, simplifies into aP = aG + r\u0307k \u00d7 GP \u2212 r2GP (3.35) The acceleration field of a rigid body in planar motion is like a pure rotation around the acceleration center K , that is a point which has aK = 0. According to (3.35), 3.2 Vehicle Congruence (Kinematic) Equations 55 the acceleration aP of any point P must be given by aP = r\u0307k \u00d7 KP \u2212 r2KP (3.36) Therefore, the angle \u03be between aP and PK is such that tan(\u03be) = r\u0307 r2 (3.37) By setting P = G in (3.36), as shown in Fig. 3.5 aG = r\u0307k \u00d7 KG \u2212 r2KG (3.38) we obtain that |KG| = aG\u221a r\u03072 + r4 (3.39) or, more precisely GK = axr 2 \u2212 ay r\u0307 r4 + r\u03072 + ax r\u0307 + ayr 2 r4 + r\u03072 (3.40) The acceleration center lies necessarily on the inflection circle, which is the set of all points whose trajectories have an inflection point (Fig. 3.5). Actually, the velocity center C does not belong to the inflection circle, although it looks like. Point K spans the inflection circle depending on the value of the ratio r\u0307/r2, as shown in Fig. 3.5. This topic will be addressed in detail in Chap. 5, entirely devoted to the kinematics of cornering. 56 3 Vehicle Model for Handling and Performance So far only the kinematics of the vehicle body has been addressed. Roughly speaking, it is what that mostly matters to the driver. However, vehicle engineers are also interested in the kinematics of the wheels, since it strongly affects the forces exerted by the tires. According to (3.3), the velocity of the center P11 of the left front wheel is given by V11 = VG + rk \u00d7 GP11 = (ui + vj) + rk \u00d7 ( a1i + t1 2 j ) (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.9-1.png",
        "caption": "Fig. 3.9 Eigenvalues of a multiblade coordinate rotor system",
        "texts": [
            "60) Some physical understanding of the MBC dynamics can be gleaned from a closer examination of the hover condition. The free response of the MBC then reveals the coning and differential coning as independent, uncoupled, DoFs with damping \ud835\udefe/8 and natural frequency \ud835\udf06\ud835\udefd , or approximately one-per-rev. The cyclic mode equations are coupled and can be expanded as \ud835\udefd\u2032\u20321c + \ud835\udefe 8 \ud835\udefd\u20321c + (\ud835\udf062 \ud835\udefd \u2212 1)\ud835\udefd1c + 2\ud835\udefd\u20321s + \ud835\udefe 8 \ud835\udefd1s = 0 (3.61) \ud835\udefd\u2032\u20321s + \ud835\udefe 8 \ud835\udefd\u20321s + (\ud835\udf062 \ud835\udefd \u2212 1)\ud835\udefd1s \u2212 2\ud835\udefd\u20321c + \ud835\udefe 8 \ud835\udefd1c = 0 (3.62) The eigenvalues of this cyclic flapping system are given by the roots of the following equation, and are shown sketched in Figure 3.9: ( \ud835\udf062 + \ud835\udefe 8 \ud835\udf06 + \ud835\udf062 \ud835\udefd \u2212 1 )2 + ( 2\ud835\udf06 + \ud835\udefe 8 )2 = 0 (3.63) The two modes have been described as the flap precession (or regressing flap mode) and nutation (or advancing flap mode) to highlight the analogy with a gyroscope; both have the same damping factor as the coning mode but their frequencies are widely separated, the precession lying approximately at (\ud835\udf06\ud835\udefd \u2212 1) and the nutation well beyond this at (\ud835\udf06\ud835\udefd + 1). While the nutation flap mode is unlikely to couple with the fuselage motions, the regressing flap mode frequency can be of the same order as the highest frequency fuselage modes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002032_j.jmatprotec.2016.04.006-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002032_j.jmatprotec.2016.04.006-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the LHW process.",
        "texts": [
            " An LHW experiment is designed and conducted. A HIGHYAG NIMO G laser device attached to a FANUC R\u20102000iB robot is the main heat source. A Lincoln welding machine is used to heat the wire as the supplementary heat source. The workpiece is deposited layer by layer. Each layer is cladded pass by pass. Four built\u2010in thermocouples are installed in the substrate to capture the temperature variation curves. The distortion of the substrate is measured during the deposition. 2.1 Laser hot\u2010wire process The schematic of the LHW process is shown in Fig 1. Filler wire is transferred from roller to the substrate by a wire feeder. Laser power is used as the main heat source to melt the base metal and wire. In addition to the laser, voltage is applied between feeder and substrate. The wire is heated by the Joule heat of the electric current. Both the laser device and wire feeder are integrated together and move synchronously. Inert gas is used to protect molten metal against oxidation. All the motions are controlled by the computer system. With the assumption of volume conservation, the wire feed speed and laser travel speed should follow the equation below: (1) 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure4-1.png",
        "caption": "Fig. 4. Ball about to fall into a spall.",
        "texts": [
            " Its equation of motion can be written as ( ) ( )\u00a8 = \u2212 + \u0307 \u2212 \u0307 \u2212 ( )M y K y y R y y m g. 10R R R o R R o R R Localised faults are modelled as proposed in [28]. Accordingly, constant angular width \u03d5(\u2206 )d and depth ( )Cd of the fault is assumed. Thus, the linear fault widths for inner, outer and ball fault are different. The fault models are the same for the 5-DOF simplified rolling element bearing model developed in this section and the bond graph model developed in the next section. A fault in the outer race is modelled as a small rectangular spall in the race (Fig. 4). When any ball approaches a specific angular position \u03d5d at which the balls\u2019 path encounters a spall on the outer race, there is a loss of contact and upon exiting this spall, the contact is established again. These sudden contact losses and gains result in a large amount of periodic impulsive forces. The contact deformation in the case of outer fault can be calculated as \u03b4 \u03b8 \u03b8 \u03b4= ( + \u2212 \u2212 ) ( )x y cmax cos sin ,0 , 11d j d j fo where \u03b4 \u03d5 \u03b8 \u03d5 \u03d5 = < < +\u2206 \u23aa \u23a7\u23a8\u23a9 C if , 0 otherwise. f d d j d d and = \u2212x x xd i o, = \u2212y y yd i o",
            " For inner race contact with the ball, ( )\u03b4= ( \u2212 ) + \u2212 \u2212x x y y D/2b i 2 b i 2 where = + = ( + )D D d r r2i i b is the pitch circle diameter. The normal and tangential forces at point Q can be represented likewise. The contact compression at the points of contact P and Q depend on the relative position of the ball with respect to the inner and outer race centres. These relative positions are influenced by inner and outer race motions and the cage rotation that governs the ball's angular position. The maximum deformation occurs in a ball when it is in the load zone (See Fig. 4). Commonly, rolling element bearing faults are caused by fatigue and fracture failures from wear and tear or due to incorrect operation such as large unbalance, shaft misalignment, etc. In most rolling element bearing fault models available in literature, raceway fault is modelled by a triangular or rectangular notch or a pit of regular shape in order to generate periodic/non-periodic impulses at constant/variable speed rotor operation [26\u201328,36]. The fault model for inner and outer race faults are discussed in Section 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003815_s102745101901004x-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003815_s102745101901004x-Figure2-1.png",
        "caption": "Fig. 2. Robot work space layout.",
        "texts": [
            " Otherwise, it alarms that: \u201cbit of error occurred in the operation interface and the path planning fails, please rearrange the model location and re-plan the path\u201d. On the alarm prompt, clicking a point in the left part of layout statement, displays the position of the error. With a click erring location can be modified, deleted, or re-adjust to reposition the part or to re-plan and simulate to prevent the actual robot from the occurrence of joint limit, collision, termination of execution, etc. The robot work space layout is shown in Fig. 2. JOURNAL OF SURFACE INVESTIGATION: X-RAY, SYNCHRO The three-dimensional model is imported into the DingzhiPNT off-line path programming software. Subsequently, simulation is performed in the following steps: setting of parameters, slicing, layering, generating the path and simulating the torch walk. In the process of WAAM-CMT, different process parameters directly affect the forming effect of the parts being formed. WAAM-CMT is driven by the three-dimensional data of the parts, which controls arcing and a subsequent liquid metal deposition layer by layer on the point, line and body as the requirements of the path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000874_ip-epa:20045185-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000874_ip-epa:20045185-Figure6-1.png",
        "caption": "Fig. 6 LIM with a disk-type secondary plate used in this experiment",
        "texts": [
            " Correspondingly, the thrust also decreases, yielding lower speed. On the other hand, with the proposed scheme the flux level is kept constant and no discrepancy is observed between the thrust command and the produced thrust. Note however, that the d-axis-current command level increases with the speed to compensate for the end effect. The proposed scheme produces a higher final speed. IEE Proc.-Electr. Power Appl., Vol. 152, No. 6, November 2005 1569 The linear motor used in this experiment is shown in Fig. 6. The primary yoke was mounted on a fixed pole, while the secondary circuit comprising aluminum plate and steel was mounted on a big flywheel. The dimensions of the LIM are shown in Table 1. Figure 7 shows a block diagram illustrating the proposed vector control. In Fig. 7, PI gains for the flux, thrust and current controllers were selected as PI1\u00bc (200p+100000)/p, PI2\u00bc (0.015p+15)/p, and PI3\u00bc (25p\u00bc 80000)/p, respectively. The validity of the proposed model is demonstrated first by comparing the measured current and the calculated currents based on two models, while increasing the speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003041_s11837-015-1298-7-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003041_s11837-015-1298-7-Figure8-1.png",
        "caption": "Fig. 8. Fracture surface observation of fatigue crack growth specimen tested at R = 0.3 on LS-START orientation. The fatigue crack growth direction is top to bottom. Note unfused regions in boxed regions.",
        "texts": [
            " Typical fracture surface examinations revealed defects of various types and sizes in the as-deposited materials. Figure 7 shows the fracture surface of the LT-BOTH sample tested to failure in fatigue at R = 0.3. Defects are evident perpendicular to the build direction at various locations (e.g., START, END, and MIDDLE of build) and consist of Evaluation of Orientation Dependence of Fracture Toughness and Fatigue Crack Propagation Behavior of As-Deposited ARCAM EBM Ti-6Al-4V unmelted particles. Figure 8 shows both low- and high-magnification SEM images of the fatigue crack growth fracture surface of an LS-START specimen. Similar types of defects are exhibited at various locations with respect to the build\u2014the regions of unmelted particles are always present perpendicular to the build direction as shown in both Figs. 7 and 8. Also detected were regions of porosity and what appears to be other poorly fused regions (Fig. 8c). These fracture surface images are provided to indicate that whereas the as-deposited properties approach those of conventionally processed materi- als (cf. Table IV), optimized EBM processing (e.g., control of melt pool size) and/or postprocessing should further improve and reduce the anisotropy of properties caused by embedded defects. Early work on LENS-processed material revealed improved properties after HIP due to the elimination of porosity and beneficial microstructure changes.25 Current and next-generation EBM machines may also provide better control of the processing conditions and melt pool size and geometry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001834_j.proeng.2015.08.007-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001834_j.proeng.2015.08.007-Figure1-1.png",
        "caption": "Fig. 1. Working principles of (a) LENS [1]; (b) EBM.",
        "texts": [
            " Systematic investigation of the influence of processing parameters on microstructure evolution, tensile properties, and fatigue properties were performed. The effects of post-deposition heat treatments were also studied. LENS technique was originally developed at Sandia National Laboratories and was commercialized by Optomec, Inc. in 1997 [12]. In the same year, the Swedish company ARCAM AB was founded, and published its first patent for EBM technique in 2001 [13]. Schematic representations illustrating the working principles of LENS and EBM are shown in Fig. 1 [1]. During LENS process, the laser beam creates a melting pool on a substrate placed onto the x-y table, material powder is then injected into the melting pool to fuse and solidify into a bead. At the same time, the substrate moves with the x-y table (in x-y directions), enabling the selective deposition of one layer. Then, the laser beam and material deposition head move together upward (in z direction) to start the deposition of the second layer. This procedure is repeated until a 3D geometry is completed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure1.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure1.9-1.png",
        "caption": "FIGURE 1.9. Structure and terminology of an R`R\u22a5R elbow manipulator.",
        "texts": [
            " RkRkP The SCARA arm (Selective Compliant Articulated Robot for Assembly) shown in Figure 1.8 is a popular manipulator, which, as its name suggests, is made for assembly operations. 2. R`R\u22a5R The R`R\u22a5R configuration, illustrated in Figure 1.6, is called elbow, revolute, articulated, or anthropomorphic. It is a suitable configuration for industrial robots. Almost 25% of industrial robots, PUMA for instance, are made of this kind. Because of its importance, a better illustration of an articulated robot is shown in Figure 1.9 to indicate the name of different components. 3. R`R\u22a5P The spherical configuration is a suitable configuration for small robots. Almost 15% of industrial robots, Stanford arm for instance, are made of this configuration. The R`R\u22a5P configuration is illustrated in Figure 1.10. By replacing the third joint of an articulate manipulator with a prismatic joint, we obtain the spherical manipulator. The term spherical manipulator derives from the fact that the spherical coordinates define the position of the end-effector with respect to its base frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000979_s0022112065000915-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000979_s0022112065000915-Figure2-1.png",
        "caption": "FIGURE 2. Motion of a helicoidal filament; point P moves toward P\u2018.",
        "texts": [
            "18) that, under some conditions, The meaning of this relation is mysterious, beyond the remark that a plane filament will develop equal and opposite amounts of the quantity A. The equations also indicate that if K\u2019 and T\u2018 are everywhere zero at some time, they will remain zero at later times. This means that a helical vortex filament, having constant R and T will satisfy (2.1). Since R is constant, it will comply even with (1.2), provided that a is constant. In space, the helicoidal filament will move with a translation velocity V, and a rotation producing a tangential velocity V,. The following relation can be found: The direction of motion is shown in figure 2. Incidentally, two intertwined, thin filaments of opposite vorticity will move toward each other. VE/VT = T/Ki . (3.3) If A = 0, the filament is plane and the only solution is given by R = 0, (3.4) +K\u2018 = 0. K\u201d\u2019 K\u20193 K\u2019K\u201d - + - - 2 - K K 3 K2 Equation (3.5) can be integrated twice, with the result dK (cK + bK2- K3))\u2019 (3.5) where b and c are integration constants. I f c =k 0, the ends of the filament cannot be straight. Indeed, the limit K+O leads to K = ~ C ( S - S ~ ) ~ . I f c = 0, the equation can be integrated exactly to (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001194_j.jmatprotec.2017.11.032-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001194_j.jmatprotec.2017.11.032-Figure2-1.png",
        "caption": "Fig. 2. SLM sample preparation: (a) H13 powder was coated on an H13 bulk; (b) melt pool formed during laser irradiation along the scanning direction; and, (c) after the melt pool solidified, un-melted powder was removed, leaving a single melt track.",
        "texts": [
            "54 ( )R s (12) The saturated vapor pressure over the surface temperature T can be expressed as: \u239c \u239f= \u239b \u239d \u2212 \u239e \u23a0 RTT ( )s v b b 0 (13) Here, P0 is the pressure of the surroundings, R is the gas constant, Lv is the latent heat of evaporation, and Tb is the boiling temperature of the material. The value is shown in Table 2. The equations above were discretized and then solved using the finite difference method in FLOW3D, a commercial computational fluid dynamic (CFD) software. For sample preparation, a layer of H13 powder was coated on an H13 metal plate, as shown in Fig. 2(a).The SLM process was conducted by an EOS AM250 with an Nd-YAG laser as the heat source. The laser power, laser spot size and laser scanning speed were set as 200 W, 52 \u03bcm and 1000 mm/s, respectively. Fig. 2(b) illustrates that the laserscanning strategy involves only one direction and one-time scanning. After the track is formed, un-melted powder is removed by high pressure air, as shown in Fig. 2(c). To distinguish a clear boundary between the re-melting zone and the original bulk, post-treatment is required. Firstly, the SLM sample was cut in half by a cutting machine; then, the cross section of the sample was sequentially ground with #240, #600, #800, #1200, #2500 and #4000 sandpaper, and etched by the mixture of 6% HNO3 and alcohol for 60 s, then polished with 1 \u03bcm diamond slurry until no obvious scratches were visible. Finally, a mechanical vibratory-polishing machine with 0.05 \u03bcm SiO2 was used for 2 h until a mirror-like surface was achieved",
            " The commercial H13 powder was examined by particle size analyzer, where the D10, D50, and D90 of the H13 powder were found to measure 19 \u03bcm, 29 \u03bcm and 43 \u03bcm in diameter, respectively. To better match to the experiment conditions, the simulation used the same powder distribution as the input parameters. The calculation domain here was set to 5 \u00d7 10\u22126 m3. To validate the model, whether the calculated powder still maintains the same distribution in the calculated area must first be confirmed; then, it must be verified that no powder-size segregation in the specified areas has occurred. Fig. 2 shows t that different colors represent different powder sizes. According to the color distribution of the entire area, the particles appear to be well dispersed, which means no powder-size segregation occurred. Then, the plane was divided into three small regions, labeled A, B and C, after which the powder-size distribution was respectively calculated. The results are also shown in Fig. 3, and as can be seen, the powder-size distribution of the three regions corresponds with the actual powder distribution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002270_j.addma.2019.100805-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002270_j.addma.2019.100805-Figure2-1.png",
        "caption": "Figure 2. Dimensions for mechanical testing samples: (a) fatigue testing, (b) tensile testing and (c) mini-Charpy testing.",
        "texts": [
            " Porosity analysis was then conducted using Micro-Computed Tomography (\u00b5-CT) in an Xradia MicroXCT-400 with the samples positioned to achieve a pixel resolution of 4.7 \u00b5m (beam energy of 60 kVp / 166 uA, 3000 projections, 10 s exposures). Reconstruction and data analysis were done using XMReconstructor 7.0.2817 and Avizo, respectively. Electric discharge machining was used to fabricate specimens for tensile and miniaturized Charpy impact tests. The uniaxial fatigue test specimens were machined into shape via lathe machining and finished with a surface polish using FEPA 1200 grit SiC paper. The dimensions of these specimens are shown in Figure 2. If the long axis of a test sample is aligned with the X direction (i.e. machined out of sub-blocks from Figure 1c), the sample is designated as an X sample (for simplicity, this will include the tensile test coupons which were machined either as XZ samples or XY samples as per the designation by the ASTM coordinate system [24]). Likewise, if the long axis of a test sample is aligned with the Z direction (machined from sub-blocks in Figure 1d), the sample is designated as a Z sample, including all tensile test samples which were machined as ZX samples"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002230_tcyb.2020.2972582-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002230_tcyb.2020.2972582-Figure2-1.png",
        "caption": "Fig. 2. Simplified structure of lower limb exoskeleton.",
        "texts": [],
        "surrounding_texts": [
            "Index Terms\u2014Adaptive fuzzy control, decoupling control, lower limb exoskeleton, multi-input\u2013multi-output (MIMO) nonlinear systems, reduced fuzzy system.\nI. INTRODUCTION\nEXOSKELETON can be seen as a biped robot designed to track the human\u2019s movement smoothly. Recently, lower limb exoskeletons have been widely studied in the robotic field and have a broad spectrum of applications in rehabilitation, assisting human walking, military, etc. The Berkeley lower\nManuscript received August 8, 2018; revised December 16, 2019; accepted February 4, 2020. This work was supported in part by the Minister of Science and Technology, Taiwan, under Grant MOST 108-2221-E-011-159, and in part by the \u201cCenter for Cyber-Physical System Innovation\u201d from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education in Taiwan. This article was recommended by Associate Editor I. Bukovsky. (Corresponding author: Shun-Feng Su.)\nWei Sun is with the School of Mathematics Science, Liaocheng University, Liaocheng 252000, China (e-mail: sunw8617@163.com).\nJhih-Wei Lin and Shun-Feng Su are with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan (e-mail: b9907134@gmail.com; sfsu@mail.ntust.edu.tw).\nNing Wang is with the Marine Engineering College, Dalian Maritime University, Dalian 116026, China (e-mail: n.wang.dmu.cn@gmail.com).\nMeng Joo Er is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: emjer@ntu.edu.sg).\nColor versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org.\nDigital Object Identifier 10.1109/TCYB.2020.2972582\nextremity exoskeleton (BLEEX) is a well-known autonomous lower limb exoskeleton that augments human strength and endurances during locomotion [1]. By combining the strength capabilities of robotics with some artificial intelligence and adaptability of humans, BLEEX allows people to carry heavy loads. Hybrid assistive limb (HAL) is a walking aid system for individuals with gait disorders [2]. Effective physical support is provided from the HAL by the autonomous control system. Another category is the lower limb rehabilitation exoskeleton which is developed for the training of stroke survivors. With the combination of a treadmill and suspension system, the goal of physical rehabilitation is to help survivors regain the use of impaired limbs [3]. The studies [4]\u2013[9] and the references therein also made significant contributions to the research of exoskeleton.\nIn the literature, several intelligent control schemes have been proposed for controlling exoskeleton systems [10]\u2013[13]. More specifically, for a BLEEX, a sensitivity amplification controller is presented in [10] to track the human\u2019s trajectory without installing any sensor between the human and the exoskeleton. In [11], a repetitive learning control scheme is designed for the tracking control of a lower limb exoskeleton called CASWELL. By using learning control approaches, an adaptive control scheme is developed in [12] for the exoskeleton system such that the corresponding leg can move on a desired periodic trajectory. Also in [13], a combination of a linear PID control method and a neural compensator strategy is proposed for an upper limb exoskeleton. However, it can be seen that an exoskeleton system is a multi-input\u2013multi-output (MIMO) system. The above approaches do not address this issue in their studies.\nMIMO uncertain nonlinear systems have attracted much attention [14]\u2013[17] in the past two decades. Although considerable efforts have been made to guarantee stability and robustness for the related control design, it is still a challenging issue because various kinds of uncertainties exist in systems, such as coupling effects, external disturbance, parameter variations, and system model errors. In general, the uncertainty of a system may be classified into two types: 1) structured uncertainties or parametric uncertainties, and 2) unstructured uncertainties. Usual adaptive control methods can be used to deal with structured uncertainties. However, in practice, plants may contain unstructured uncertainties, both the adaptive control method and the robust control approach may not be able to have satisfactory control performances for this kind of plant. Adaptive fuzzy control [18]\u2013[22] and neural\n2168-2267 c\u00a9 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information.\nAuthorized licensed use limited to: University of Canberra. Downloaded on April 28,2020 at 04:29:58 UTC from IEEE Xplore. Restrictions apply.",
            "networks control [23]\u2013[25] have been developed to solve this problem. Besides, backstepping techniques have been successfully applied to adaptive fuzzy control of MIMO nonlinear systems [26]\u2013[28]. However, it is worth noting that the adaptive fuzzy control methods therein have a common restriction that the structure of the controlled systems must be in the lower triangular or nested lower triangular structure, which greatly limits their applicability to more complex nonlinear systems. Sliding-mode control schemes are also proposed in [29] and [30] for MIMO nonlinear systems. By using neural networks and adaptive fuzzy hierarchical sliding-mode control, the research is extended to MIMO nonstrict-feedback nonlinear time-delay systems in [31] and [32]. Based on command filtered design, the adaptive fuzzy tracking control for MIMO uncertain switched nonstrict-feedback nonlinear systems is investigated in [33]. The studies in [34]\u2013[37] and the references therein also report several control strategies for MIMO systems.\nFor the MIMO nonlinear systems control, one main concern is the coupling problem. Almost disturbance decoupling control for single-input\u2013single-output nonlinear systems is considered in [38] and [39]. Then, in [40]\u2013[42], the approach is extended to MIMO nonlinear systems with a nested lower triangular form. A generalized inversion method is developed for the linearization and decoupling control for a general nonlinear system in [43]. In [44], the decoupling control and robust deadbeat control technique is proposed for a twin-rotor system. To attenuate the coupling effects, an approach using H\u221e control and indirect adaptive fuzzy control is proposed in [45]. However, in our experiments, it can be observed that when the coupling state of the system has a large change, a rather large control input will be required to reduce the tracking error when the H\u221e tracking method is employed. This phenomenon is not acceptable for our practical control plant. Instead of H\u221e control, an indirect adaptive control is considered to approximate the coupling parameters. When the system considers all possible fuzzy rules, the number of rules for the coupling terms may become very large and, as a result, the learning process may become inefficient. This phenomenon can be seen in our simulation. Since adaptive fuzzy control is an online control system, the learning efficiency is also an important issue. Thus, in this article, a reduced adaptive fuzzy control scheme is proposed to approximate the coupling terms. It can be found that the proposed control method not only achieves better control effects but also has good learning efficiency as shown in our simulation.\nThe structure of the control plant used in this article is similar to that of the active leg exoskeleton used in [3] and the lokomat in [7]. The loads are not fixed and will be heavier than normal applications when the robot is used to assist patients walk. The fundamental structure of a lower limb exoskeleton robot is a 2-DOF robot, which is a typical MIMO uncertain nonlinear system. Hence, such an unknown system is not easy to control by using PID tuning control and the coupling effects may also have a certain influence. The existing decoupling control method cannot be used in our control model because the system is not in a lower triangular or nested lower triangular structure. From our experiments, the H\u221e control approach\nand robust control method may yield violent changes in control inputs when an intense disturbance occurs. In this article, a reduced adaptive fuzzy decoupling control is designed for lower limb exoskeletons. It can be seen that the proposed control scheme achieves outstanding control effects from both theoretical analysis and practical experiments.\nThis article is organized as follows. After the introduction section, the dynamic model and the motion planner of lower limb exoskeletons are briefly introduced in Section II. The proposed reduced adaptive fuzzy decoupling control is presented in Section III. To demonstrate the effectiveness of the proposed design schemes, numerical simulations and corresponding comparisons are given in Section IV. In Section V, the proposed control method is applied to our lower limb exoskeleton system and the corresponding experimental results are presented in this section. Finally, concluding remarks are given in Section VI.\nThe 2-DOF lower limb exoskeleton system considered in this article is shown in Figs. 1 and 2, and the dynamic equation is expressed as [46]\nM(\u03b8)\u03b8\u0308 + C(\u03b8, \u03b8\u0307 )\u03b8\u0307 + G(\u03b8) = u (1)\nAuthorized licensed use limited to: University of Canberra. Downloaded on April 28,2020 at 04:29:58 UTC from IEEE Xplore. Restrictions apply.",
            "where \u03b8 = [\u03b81, \u03b82]T is the angular position vector, M(\u03b8) is the inertia matrix, C(\u03b8, \u03b8\u0307 )\u03b8\u0307 is the centrifugal and Coriolis force vector, G(\u03b8) is the gravity torque vector, u = [u1, u2]T is the actuator torque vector, and\nM(\u03b8) = [ m1l2c1 + m2L\u03041 + I1 + I2 m2L\u03042 + I2\nm2L\u03042 + I2 m2l2c2 + I2\n]\nC(\u03b8, \u03b8\u0307 ) = [\u2212l1lc2\u03b8\u03072m2s2 \u2212l1lc2m2s2(\u03b8\u03071 + \u03b8\u03072)\nl1lc2\u03b8\u03071m2s2 0\n]\nG(\u03b8) = [ (m1lc1 + m2l1)gc1 + m2glc2c12\nm2glc2c12\n]\nwith L\u03041 = l21 + l2c2 + 2l1lc2c2, L\u03042 = l2c2 + l1lc1c2, ci = cos \u03b8i, si = sin \u03b8i, c12 = cos(\u03b81 + \u03b82), and the relevant parameters of the lower limb exoskeleton system considered are shown in Table I. Define x11 = \u03b81, x12 = \u03b8\u03071, x21 = \u03b82, x22 = \u03b8\u03072, y1 = x11, and y2 = x21, and premultiplying M\u22121(\u03b8) on both sides of (1), we then have[\ny\u03081 y\u03082\n] = \u2212M\u22121(\u03b8) ( C(\u03b8, \u03b8\u0307 )\u03b8\u0307 + G(\u03b8) )+ M\u22121(\u03b8)u\n[\nf1 f2\n] + [\ng11 g12 g21 g22 ][ u1 u2 ] . (2)\nFor an exoskeleton system, similar to that of [47] and [48], a human walking gait pattern must be used as the system tracking reference. The entire period of a gait cycle of the hip and the knee joints is calculated. Since the 2-DOF lower limb exoskeleton is controlled by two motors, the end-effector trajectory must be designed by using inverse kinematic [49] to the joint degrees. The coordinates of the end-effector point on the x-direction and the y-direction are, respectively, designed as\npx = ax0 + ax1 cos(wxt) + bx1 sin(wxt) + ax2 cos(2wxt)\n+ bx2 sin(2wxt) + ax3 cos(3wxt) + bx3 sin(3wxt)\npy = ay0 + ay1 cos ( wyt )+ by1 sin ( wyt )+ ay2 cos ( 2wyt ) + by2 sin ( 2wyt )+ ay3 cos ( 3wyt )+ by3 sin ( 3wyt\n) + ay4 cos ( 4wyt )+ by4 sin ( 4wyt )+ ay5 cos ( 5wyt\n) + by5 sin ( 5wyt\n) with the following parameters:\nax0 = 5.422, ax1 = 25.82, bx1 = 12.61, ax2 = 6.249 bx2 = \u22126.304, ax3 = 0.8893, bx3 = \u22120.8885, wx = 0.1256\nay0 = \u221277.98, ay1 = 2.084, by1 = \u22124.941, ay2 = \u22120.9565 by2 = 2.420, ay3 = 1.993, by3 = 0.7234, ay4 = 0.5084 by4 = \u22120.6855, ay5 = \u22120.005, by5 = \u22120.1436\nwy = 0.1257.\nThe details can be referred to in [50]. In inverse kinematic, the desired joint rotational degrees are designed as\nym1 = arc cos\n\u00d7 \u239b \u239c\u239c\u239c\u239c\u239d px ( l1+ p2 x+p2 y\u2212l21\u2212l22 2l1 ) +pyl2 \u221a 1\u2212 ( p2 x+p2 y\u2212l21\u2212l22 2l1l2 )2 p2 x+p2 y \u239e \u239f\u239f\u239f\u239f\u23a0\nym2 = arc cos\n( p2\nx + p2 y \u2212 l21 \u2212 l22 2l1l2\n) .\nGiven a reference trajectory ym = [ym1, ym2]T , the objective of this article is to design an adaptive fuzzy controller u such that the system output y = [y1, y2]T follows the reference signal ym, while all other signals in the closed-loop system are bounded.\nTo show the general applicability of the proposed control methods, the following MIMO uncertain nonlinear system, which is the general form of model (2), is considered:\ny(r1) 1 = f1(x) + p\u2211 j=1 g1j(x)uj\n...\ny (rp) p = fp(x) + p\u2211 j=1 gpj(x)uj (3)\nwhere x = [x1, x2, . . . , xp]T with xi = [xi1, xi2, . . . , xiri ] T = [yi, y\u0307i, . . . , y(ri\u22121) i ]T for i = 1, . . . , p is the state vector, u = [u1, . . . , up]T is the control input vector, y = [y1, . . . , yp]T is the output vector, and fi(x) and gij(x) for i, j = 1, . . . , p are smooth unknown nonlinear functions. The control objective is to design a control law u for the system (3) such that the system output y follows the reference signal ym = [ym1, . . . , ymp]T .\nThe MIMO system (3) can be divided into the following p MISO systems:\ny(ri) i = fi(x) + gii(x)ui + p\u2211 j=1,j =i gij(x)uj, i = 1, . . . , p. (4)\nBased on the traditional adaptive fuzzy control, the fuzzy systems f\u0302i(x|\u03b8fi) = \u03beT s (x)\u03b8fi and g\u0302ii(x|\u03b8gii) = \u03beT s (x)\u03b8gii can be used to online approximate the unknown functions fi and gii, respectively. With the same approximation philosophy of adaptive fuzzy control, the coupling terms \u2211p j=1,j =i gij(x)uj can also be approximated by using similar adaptive fuzzy systems. However, it can be expected that when a fuzzy system is used\nAuthorized licensed use limited to: University of Canberra. Downloaded on April 28,2020 at 04:29:58 UTC from IEEE Xplore. Restrictions apply."
        ]
    },
    {
        "image_filename": "designv10_1_0000520_s0094-114x(02)00120-9-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000520_s0094-114x(02)00120-9-Figure12-1.png",
        "caption": "Fig. 12. Geared chain and its graphs. (a) Functional schematic, (b) graph (labelled), (c) graph (unlabelled), (d) graph (unlevelled), (e) rotation graph and (f) displacement graph.",
        "texts": [
            " Johnson and Towfigh [27] represented a meshing pair of gears by an equivalent four-bar linkage and used the technique of structural synthesis of linkages for creative design of singlefreedom epicyclic gear trains. Levai [32] classified PGTs and stated that the simple PGT consisting of two central gears, one or more planet gears and one arm comes in 34 different types. Buchsbaum and Freudenstein [37] introduced graph theory to the study of structure of geared kinematic chains. They represented such a chain by a graph and derived conditions to be satisfied by the graph of a geared kinematic chain. Fig. 12(a) shows the functional schematic of a six-link, singlefreedom geared chain with four-gear pairs. Here, links are numbered and the letters, A, B, C, indicate the level in space of axes of rotation of gears. Fig. 12(b) shows the graph of the geared chain where the thick edges represent gear pairs and labeled thin edges represent revolute pairs with the corresponding axis-levels. The sub-graph obtained by deletion of geared edges from the graph of the geared chain is a tree and each fundamental circuit associated with the tree contains a geared edge as a chord [37]. For example, geared edge 1\u20136 in Fig. 12(b) is chord for the circuit 1326. Fig. 12(c) and (d) show unlabelled and unleveled graphs of the geared chain of Fig. 12(a). In every fundamental circuit there will be one vertex such that edges on one side of it are all at one level and those on the other side are all at another common different level. Such a vertex is called transfer vertex. In Fig. 12(d) the transfer vertices are marked on the corresponding geared edges. As per definition in [38] both rotation and displacement graphs are open graphs. A partly computerized procedure was developed in [37] for structural synthesis of geared chains and applied to the case of chains with up to three geared pairs. Subsequently, Freudenstein [38] established the correspondence between the graph representation and the displacement equations of the mechanism. He also defined rotation and displacement graphs of the geared chain with a view to characterize rotation and displacement isomorphism",
            " Lloyd [76] provides a systematic procedure to enumerate all possible epicyclic gear transmissions (EGTs) in which clutches are used in addition to brakes as the speed controlling members. The concept of ports which helps in finding the number of clutches and brakes that a system must contain is also introduced. Structural synthesis based on inspection of three-epicyclic, six-speed system is also attempted. Ravisankar and Mruthyunjaya [92] defined closed rotation and displacement graphs for epicyclic gear trains. These are shown in Fig. 12(e) and (f). They also presented the first fully computerized method based on graph theory and matrix representation for structural synthesis of geared kinematic chains which can be used to derive epicyclic gear drives. Isomorphism detection was based on comparison of CPAMs, the adjacency matrices being written down denoting revolute edges, geared edges and levels associated with different revolute edges by different numerical labels. Method was applied to synthesize the structure of single-freedom geared chains with up to four gear pairs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000805_1.2717228-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000805_1.2717228-Figure4-1.png",
        "caption": "Fig. 4 Selection of actuated joints for the 3-R\u0301\u0301 \u201eRRR\u2026ER\u0301\u0301 parallel mechanism with both spherical and translational modes: \u201ea\u2026 in translation mode, \u201eb\u2026 in lockup^translation configuration, \u201ec\u2026 in lockup configuration, \u201ed\u2026 in lockup^rotation configuration, and \u201ee\u2026 in spherical mode",
        "texts": [
            " 2 can be obtained. ithout considering the variation of legs, as it can be seen from able 4, one can obtain 43 types of three-legged parallel mechaisms with both spherical and translational modes with identical ypes of legs. According to the validity condition for actuated joints of transational parallel mechanisms 20 and spherical parallel mechaisms 8 , one can find that the three joints located on the base can e used as actuated joints in both the translational mode Fig. a and the spherical mode Fig. 4 e of the 3-R\u0301\u0301 RRR ER\u0301\u0301 arallel mechanism. Moreover, these three joints can be used to ontrol the rotation of each leg about the axes of its corresponding wo coaxial R joints in a lockup configuration Fig. 4 c , where he DOF of the moving platform is zero. However, these three ctuated joints cannot fully control the motion of the moving platorm in the lockup\u2194translation configuration Fig. 3 b or the ockup\u2194rotation configuration Fig. 3 d , where the instantaeous DOF of the moving platform is four. This requires that four oints, including the three joints located on the base and the secnd joint in one of the legs, should be actuated Figs. 4 b and d . The above analysis shows that four joints should be actuted in order to change the parallel mechanism with both spherical nd translational modes from one operation mode to another"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001853_tsmc.2017.2650219-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001853_tsmc.2017.2650219-Figure2-1.png",
        "caption": "Fig. 2. Geometrical illustration of LOS guidance.",
        "texts": [
            " If \u03b5 is a reconstruction error satisfying |\u03b5| \u2264 \u03b5\u2217, then there exists an ESN in the form of (2) such that [44] f (\u03be) = WTX(\u03be)+ \u03b5, \u2200\u03be \u2208 \u2282 R n (3) where W is bounded by ||W|| \u2264 W\u2217 with W\u2217 being a positive constant. The output weight of ESN can be expressed as W = arg min W\u0302\u2208Rn { sup \u03be\u2208 f (\u03be)\u2212 W\u0302TX(\u03be) } (4) where W\u0302 is an estimate of W. The update law for W\u0302 will be designed in Section IV. III. PROBLEM FORMULATION The general motion of an ASV can be expressed using an earth-fixed frame {E} and a body-fixed frame {B} (see Fig. 2). Let (xi, yi) be the position of the vehicle; and \u03c8iB is the heading angle that represents the rotation matrix from {B} to {E}. Let ui, \u03c5i, and ri be the surge velocity, sway velocity, and the angular rate, respectively. According to [45], the dynamical model of the ith ASV can be described as \u23a7 \u23a8 \u23a9 x\u0307i = ui cos\u03c8iB \u2212 \u03c5i sin\u03c8iB y\u0307i = ui sin\u03c8iB + \u03c5i cos\u03c8iB \u03c8\u0307iB = ri (5) and \u23a7 \u23a8 \u23a9 miuu\u0307i = fiu(ui, \u03c5i, ri)+ \u03c4iu + \u03c4iuw mi\u03c5\u03c5\u0307i = fi\u03c5(ui, \u03c5i, ri)+ \u03c4i\u03c5w mir\u03c8\u0307i = fir(ui, \u03c5i, ri)+ \u03c4ir + \u03c4irw (6) where miu = mi \u2212 X\u0307u\u0307, mi\u03c5 = mi \u2212 X\u0307\u03c5\u0307 , and mir = Iz \u2212 X\u0307r\u0307 with mi being the vehicle mass, Iz being the moment of inertia with regard to z-axis, and X\u0307u\u0307, X\u0307\u03c5\u0307 , and X\u0307r\u0307 being the hydrodynamic derivatives; fiu(\u00b7), fi\u03c5(\u00b7), and fir(\u00b7) are nonlinear functions including Coriolis/centripetal force, and hydrodynamic damping effects; \u03c4iuw(t), \u03c4i\u03c5w(t), and \u03c4irw(t) denote the ocean disturbances induced by wind, waves, and ocean currents; \u03c4iu and \u03c4ir denote the surge force and yaw moment, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000426_9781118680469-Figure1.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000426_9781118680469-Figure1.4-1.png",
        "caption": "FIGURE 1.4 Thermoresponsive self-folding SU-8- polycaprolactone thin films. (a) fabrication: (i) A sacrificial layer was spin coated on a clean Si wafer. SU-8 panels were patterned using conventional photolithography. (ii) PCL was deposited in hinge gaps. (iii) 2D templates were lifted off via dissolution of the PVA layer in water and self-assembly occurred on heating above 58 \u25e6C. (b, i\u2013iii) Schematic demonstrating self-folding of a cubic container. External \u201clocking\u201d hinges are colored in pairs to denote corresponding meeting edges. (c) Video capture sequence (over 15 s) showing a 1 mm sized, six-windowed polymeric container self-folding at 60 \u25e6C. Reproduced from Reference 27b, with kind permission from Springer Science & Business Media. Copyright 2010.",
        "texts": [
            " used continuous volume expansion with temperature and demonstrated thermoresponsive rolling-unrolling of polydimethylsiloxane\u2013gold bilayers tubes at 60\u201370 \u25e6C [24a, 24b] which is due to different temperature expansion coefficients. Gracias et al. used melting of polymer, which form a droplet and forces patterned polymer films to fold. This was demonstrated on the example of patterned SU-8 photoresist\u2013polycaprolactone film, which irreversibly folds at 60 \u25e6C [31] due to melting of polycaprolactone (Fig. 1.4). In order to reduce the transition temperature and make film more suitable bio-related applications, Gracais et al. used photoresist hinges which are sensitive to temperature around 40 \u25e6C [32]. The metal-polymer grippers irreversibly fold in response to temperature as well. Lendlein et al. demonstrated the possibilities to design thermoresponsive macroscopic self-folding objects using shape-memory polymers based on different poly(\u03b5caprolactone) [12]. At low temperature, the materials are in their temporary shape"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.54-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.54-1.png",
        "caption": "Fig. 10.54 Proprotor tilt during pitch-up manoeuvre (Ref. 10.62)",
        "texts": [
            " As already covered in the modelling and simulation part of this chapter, this in-plane component of thrust leads the disc tilt and, at the high inflow conditions typical of a tiltrotor, can dominate the pitch and yaw damping contributions from the rotor. In the case of pitch, this then results in a smaller manoeuvre margin than for a conventional propeller airplane. Figure 10.53 shows that after settling to a pitch rate response of about 4 deg/s and incidence change of about 5 deg, the climb angle continues to increase in this 0.7 g manoeuvre. Velocity (w) perturbations in the rotor plane effectively act as a longitudinal cyclic input, causing the proprotor to tilt in the direction of the aircraft pitch change as illustrated in Figure 10.54 (Ref. 10.62). The applied aerodynamic moment is then greater than that required to precess the gimbaled rotor,3 leading to an increased flapping in the direction of motion. This is also illustrated in Figure 10.54 where, after an aft step input in elevator, the initial response of the rotor disk is to lag the rotor shaft (i.e., flap forward counteracting the pitch rate q). However, velocity perturbations in the rotor plane (w) result in the rotor advancing the shaft, further adding to the destabilising effect of the static stability derivative Mw, i.e. a positive contribution from the proprotor. Overall, Mw is negative (stabilising) for the FXV-15 in airplane mode due to the strong effect of the horizontal tail",
            " The short-period mode is characterised by significant changes in the pitch rate of course, but also the body axis normal velocity (aircraft incidence) and velocity perturbations in the rotor plane. These velocity perturbations effectively act as cyclic inputs, causing the proprotor to flap in the same direction as the aircraft pitch rate. The aerodynamic moment, the Mw effect, is then greater than that required to precess the gimballed proprotor, leading to increased flapping in the direction of rotation (recall Figure 10.54). The total angular rate of the proprotor is the sum of the fuselage pitch rate and the gimbal longitudinal flapping rate. This creates a large out-of-plane aerodynamic moment acting on the rotor. In his seminal work (Refs. 10.88 and 10.89), Miller showed that for a gimballed proprotor, cyclic rotor yoke in-plane/chordwise bending moments are directly related to the out-of-plane (flap) moments on the rotor. These in-plane bending loads in a pull-up manoeuvre are significant and can limit manoeuvrability"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001748_j.oceaneng.2017.09.062-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001748_j.oceaneng.2017.09.062-Figure1-1.png",
        "caption": "Fig. 1. Earth-fixed OXoYo and body-fixed AXY coordinate frames of an MV.",
        "texts": [
            " The rest of this paper is organized as follows. In Section 2, problem formulation and preliminaries are addressed. The ATC, DO-ATC and UOATC schemes together with theoretical analyses on finite-time stability are given in Section 3. Simulation results and discussions are presented in Section 4. Conclusions are drawn in Section 5. 2. Problem formulation and preliminaries 2.1. Problem formulation The problem addressed in this paper can be clearly formulated by considering two coordinate frames shown in Fig. 1, where OXoYo and BXY denote the earth- and body-fixed coordinate frames, respectively, the axes OXo and OYo are directed to the north and east, respectively, the axes AX and AY are directed to fore and starboard, respectively, and xg is the distance between the geometric center B and the gravity center G. Usually, the vessel is port-starboard symmetric (Fossen, 2002), the kinematics and dynamics of an MV moving in the planar space can be expressed as follows: _\u03b7 \u00bc R\u00f0\u03c8\u00de\u03bd M _\u03bd \u00bc N \u00f0\u03b7; \u03bd\u00de \u00fe \u03c4\u00fe \u03c4\u03b4 (1) where here, \u03b7 \u00bc \u00bdx; y;\u03c8 T is the 3-DOF position \u00f0x; y\u00de and heading angle \u00f0\u03c8\u00de of the MV, \u03bd \u00bc \u00bdu; \u03bd; r T is the corresponding linear velocities \u00f0u; \u03bd\u00de, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure1.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure1.5-1.png",
        "caption": "Fig. 1.5 Example of a double wishbone front suspension [6]",
        "texts": [
            "3 Yet, suspensions cannot be completely disregarded, at least not in vehicles with four or more wheels. This aspect will be thoroughly discussed. The vehicle shown in Fig. 1.4 has a swing arm rear suspension and a double wishbone front suspension. Perhaps, about the worst and the best kind of independent suspensions [3]. They were selected to help explaining some concepts, and should not be considered as an example of a good vehicle design. An example of a double wishbone front suspension is shown in Fig. 1.5. 1. Arnold M, Burgermeister B, F\u00fchrer C, Hippmann G, Rill G (2011) Numerical methods in vehicle system dynamics: state of the art and current developments. Veh Syst Dyn 49(7):1159\u2013 1207 2. Cao D, Song X, Ahmadian M (2011) Editors\u2019 perspectives: road vehicle suspension design, dynamics, and control. Veh Syst Dyn 49(1\u20132):3\u201328 3. Genta G, Morello L (2009) The automotive chassis. Springer, Berlin 4. Guiggiani M, Mori LF (2008) Suggestions on how not to mishandle mathematical formul\u00e6. TUGboat 29:255\u2013263 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002798_tec.2020.2964942-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002798_tec.2020.2964942-Figure7-1.png",
        "caption": "Fig. 7. Examples of rolling bearing cages fabricated using AM \u2013 Oak Ridge National Laboratory [21]",
        "texts": [
            " Here, the lower improvement bound corresponds with a higher operating frequency, whereas the higher performance increase is at low frequency. Rolling bearings are another important mechanical part, of the electrical machine assembly. There also has been some attention related to rolling bearings in the context of AM. These high-precision components would not normally be associated with AM. This is due to limitations of the existing AM technology. Nevertheless, the available literature shows feasibility work on low-volume fabrication of roll-bearings using AM [21], [22]. Examples of rolling bearing cages from the study are shown in Fig. 7. The stainless steel (316L) was used in AM. The initial outcomes showed that the surface finish of parts is one of the numerous challenges when considering AM of rolling bearings. Even though the initial 0885-8969 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. results are far from being perfect, large companies supplying high-precision components have been working on developing such technology [22]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002280_j.oceaneng.2015.07.039-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002280_j.oceaneng.2015.07.039-Figure2-1.png",
        "caption": "Fig. 2. The schematics of the trajectory tracking guidance based on the virtual vehicle method.",
        "texts": [
            " (I) The predefined desired trajectory can be described as a sufficiently smooth time-function on the horizontal (yaw) plane, which is generated by the movement of the virtual vehicle with the time parameters t. And there exists the first three orders continuous time-derivatives at least. (II) The reference point on the desired trajectory coincides with the center of gravity (CG) G of the virtual vehicle. (III) The surge (longitudinal) velocity uR of the virtual vehicle is constant positive (uR40), i.e., the virtual vehicle cannot reverse. Lemma 6. (Repoulias and Papadopoulos, 2005, 2007. In Fig. 2, the virtual vehicle sailing along the reference trajectory satisfies all conditions of Assumption 2 and Assumption 3. The CG G of the virtual vehicle denotes dR\u00f0t\u00de \u00bc \u00bdxR\u00f0t\u00de; yR\u00f0t\u00de T (simplifying dR \u00bc \u00bdxR ; yR T) in the inertial coordinate frame {I}. Then, the kinematics of the virtual vehicle can be described by the following kinematic variables: (i) The total speed of the virtual vehicle is vP \u00bc \u2016vP\u2016\u00bc \u2016 _dR\u2016\u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi _x2R\u00fe _y2R q , and its first- and second-order time-deri- vative can be given by differentiating the total speed _vP \u00bc _dR ; \u20acdR D E vP \u00f016a\u00de \u20acvP \u00bc _dR ; ::: dR D E \u00fe \u20acdR ; \u20acdR D E _v2P vP \u00f016b\u00de The sway velocity vR is vR \u00bc 7 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v2P u2 R q , where \u201c7\u201d indi- cates that the virtual vehicle may turn right or left depending on the predefined trajectory",
            " Considering the dynamics of the virtual vehicle, the surge velocity and acceleration can be derived _uR \u00bc \u00f0m\u030211 m\u030222\u00de 1\u00bdm\u030211uRv 1 P _vP u 1 R \u00f0m\u030222vP _vP Y\u0302vv2R Y\u0302vj vj v2R vRj j\u00de m\u030211v 2 P vR\u00f0_xR \u20acyR \u20acxR _yR\u00de \u00f018a\u00de \u20acuR \u00bc \u00f0m\u030211 m\u030222\u00de 1\u00bdm\u030211 _uRv 1 P _vP\u00fem\u030211uRv 1 P \u20acvP m\u030211uRv 2 P _v2P\u00feu 2 R \u00f0m\u030222vP _vP Y\u0302vv2R Y\u0302vj vj v2R vRj j\u00de _uR u 1 R \u00f0m\u030222 _v 2 P\u00fem\u030222vP \u20acvP 2Y\u0302vvR _vR 3Y\u0302vj vj v2R _vRsgn\u00f0vR\u00de\u00de m\u030211v 2 P _vR\u00f0_xR \u20acyR \u20acxR _yR\u00de \u00fe2m\u030211v 3 P _vPvR\u00f0_xR \u20acyR \u20acxR _yR\u00de m\u030211v 2 P vR\u00f0_xR ::: yR ::: xR _yR\u00de \u00f018b\u00de where \u201c4\u201d denotes the nominal value of the hydrodynamic coefficients for an underactuated UUV. (ii) The sideslip angle and course angle are given by their definitions: \u03b2\u00bc arctan vR uR \u00f019\u00de \u03b3 \u00bc arctan _yR _xR \u00f020\u00de (iii) The yaw angle is solved from Fig. 2 \u03c8R \u00bc \u03b3 \u03b2\u00bc arctan _yR _xR arctan vR uR \u00f021\u00de And, the yaw angular velocity and acceleration can be solved by differentiating the above equation rR \u00bc _\u03c8R \u00bc _\u03b3 _\u03b2\u00bc\u03c9 _vRuR _uRvR v2P \u00f022a\u00de \u03c9\u00bc _\u03b3 \u00bc _xR \u20acyR \u20acxR _yR v2P \u00f022b\u00de _rR \u00bc \u20ac\u03c8R \u00bc \u20ac\u03b3 \u20ac\u03b2\u00bc _\u03c9 \u20acvRuR \u20acuRvR v2P \u00fe2 _vRuR _uRvR v3P _vP \u00f022c\u00de _\u03c9\u00bc \u20ac\u03b3 \u00bc _xR ::: yR ::: xR _yR v2P 2 _\u03b3 _vP vP \u00f022d\u00de where \u03c9 denotes the course angular velocity, and _\u03c9 is the course angular acceleration. In this subsection, the trajectory tracking error differential equations are established based on the tracking guidance laws (16)\u2013(22) and the motion model of the vehicle, which can build up the relationship between the motion states of the actual UUV and the predefined desired trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003978_tie.2016.2565442-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003978_tie.2016.2565442-Figure3-1.png",
        "caption": "Fig. 3. SLIM models with the laminated back iron secondary",
        "texts": [
            " When the primary is supplied by an inverter, the air-gap flux is produced between the primary and secondary. Through the reaction between the air-gap flux and the eddy current in the secondary, two types of forces, i.e. thrust (Fx) and vertical forces (Fz), are produced. Thrust is a tractive force and it is used to drive the train. Vertical force usually is the attractive force which increases the running resistance and the pressure of the rails. Another type of the secondary, i.e. the laminated back iron secondary, is also applied and shown in Fig.3. Comparing to the solid secondary, two changes are as follows: 1). The equivalent conductivity of the laminated back iron decreases with the increase of the lamination number owing to the change of the edge transvers effect. 2). The equivalent air-gap decreases with the increase of the lamination number, because the back iron magnetic reluctance decrease which is caused by the increase of the field penetration depth. III. METHODS OF NUMERICAL ANALYSIS The following assumptions are proposed: 1) Nonlinear magnetic characteristic is considered in the back iron of the secondary and the primary core, as well as B-H curves are set up"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000910_tec.2015.2401398-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000910_tec.2015.2401398-Figure2-1.png",
        "caption": "Fig. 2. Radial force in stator yoke (fr s ) and stator teeth of A-, B-, and C-phases (frA , frB , and frC ).",
        "texts": [
            " In three-phase SRM, three teeth are excited in one electrical period; thus, the third harmonic component is apparent. Moreover, from (2), third harmonic frequency of the acoustic noise and vibration at 1500 r/min is 1800 Hz, which corresponds to the natural frequency of a test machine. Therefore, the acoustic noise and vibration is the maximum at 1500 r/min. In experiments, serious acoustic noise was observed at 1500 r/min. This paper focuses on the reduction of the acoustic noise and vibration at this most serious operating point. Fig. 2 shows a cross section of a SRM. A vibration pickup is attached on the stator outer surface in the radial direction of an A-phase tooth. The waveform of the vibration has three peaks in one electrical cycle. The vibration occurs when A-, B-, and C-phases are excited sequentially. Thus, the vibration occurs not only by A-phase force, but also by B- and C-phases forces. Let us define the radial force frs as the sum of all radial forces frA , frB , and frC as fr = frA + frB + frC (4) where frA , frB , and frC are the radial forces generated on the stator teeth of A-, B-, and C-phases, respectively. The force sum frS can be considered as the force acting on the stator yoke, indicated by the ellipse in Fig. 2. Fig. 3 shows the waveforms of the A-phase current, inductance, radial forces acting on the each stator tooth frA , frB , and frC , radial force sum frS , and vibration at rectangular current excitation in FEM analysis. The inductance waveform shows the aligned position of A-phase at 0\u00b0, 360\u00b0, and 720\u00b0 in two electrical cycles. When the inductance is increasing, the rectangular current is provided with inverter chopping. The radial force frA at A-phase tooth is the maximum at the angle of 340\u00b0 just before the current starts to decrease"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002366_j.jmatprotec.2020.116689-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002366_j.jmatprotec.2020.116689-Figure7-1.png",
        "caption": "Fig. 7. Illustration of the forging process: (a) 17 MN hydraulic isothermal forging press equipped with a handling robot and an inert gas chamber, (b) billet geometry and (c) final forged part in a die set.",
        "texts": [
            " In previous studies of the authors, the hot deformation behavior of WAAM material was analyzed by means of high-temperature compression testing using small cylindrical samples. It was shown that WAAM material has a good hot workability, lower flow stresses and activation energies for hot forming as well as faster globularization kinetics compared to conventional wrought material with a lamellar microstructure (Sizova et al., 2019). To investigate the mechanical properties isothermal forging experiments were performed. The dogbone billet was produced from WAAM material. The geometry of billet is shown in Fig. 7b. The forging of the blade was carried out in a single step using a hydraulic isothermal forging press (Fig. 7a). The die temperature was approximately 950 \u00b0C. The temperature of the billet as measured during forging was approximately 940 \u00b0C. The deformation speed was approximately 0.1 mm/s. The set-up for isothermal forging was also presented in a previous study of the authors (Sizova et al., 2019). The turbine blade with a total length of about 160 mm was produced in a single forging step (Fig. 8a). The maximum experimental forging force reached at the end of the forging was around 2200 kN (Fig. 8b). Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001530_978-3-642-81857-8-Figure3.92-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001530_978-3-642-81857-8-Figure3.92-1.png",
        "caption": "Fig. 3.92. Manipulator with two degrees of freedom",
        "texts": [
            " form, a control has been determined for a simple manipulator with two d~grees of freedom, using parallel processing with two microprocessors. 328 We stress that this manipulator is of no greater practical signi ficance and that two microprocessors are not needed for the control of such a system. The control was intended to demonstrate how decentrali zed and global control, as well the decentralized observer, can be im plemented by parallel processing [33J. The scheme of the manipulator for which the control has been implemen ted is shown inFig. 3.92. For actuators we used D.C. servomotors PRINTED t,lOTORS LTD., type G9M4T, the model of whi ch is given by (1.2.1), where _ i _ (i \u00b7i i T n i - 3, x - q, q , i R) , so that N = 2x3 =:.6. The manipulator parameters are shown in Table 3.22. The actuator models are given in Table 3.22. In the system S we measured only the manipu~ator angles ql, q2. \u00b71 \u00b72 The other state vector coordinates (angular velocities q ,q and the rotor currents ii, i~) were not accessible to measurement. Thus, the subsystem outputs are given by yi qi, k i = 1, i = 1,2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000584_j.jmatprotec.2013.11.014-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000584_j.jmatprotec.2013.11.014-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of work flat.",
        "texts": [
            " It is responsibility to implement several functions: ontrol of the movement of the work flat using a data acquisition ard, image display and processing, arc on/off control, adjustment f arc current and voltage, and human\u2013machine interface designed o provide the user with all necessary information. It is noted that he work flat, driven by 3 independent stepping motors, has 3\u25e6 f freedom including moving in the Y-axis or X-axis, and rotating round the Z-axis. The mechanical part of the work flat is simply resented in Fig. 2. During the multi-layer deposition process, the elding gun is always stationary, and the work flat is lowered after layer is deposited. .2. Vision sensor design and image processing Owing to the variable NTSD in multi-layer deposition process, t should be monitored and controlled in real-time. Thus, a pasive vision sensor system is designed to observe the NTSD directly. s shown in Fig. 3, the vision sensor is placed opposite the welding ozzle. It consists of a CCD camera, a narrow-band and neural filter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003808_j.mechmachtheory.2018.03.001-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003808_j.mechmachtheory.2018.03.001-Figure2-1.png",
        "caption": "Fig. 2. (a) Scheme of the oil film thickness h(x,y) in the contact area and the initial geometry (dashed line), the deformed geometry (dotted line) and deformed and displaced geometry (solid line) [adapted from [39] ]; (b) approximation of the oil film by springs and dampers.",
        "texts": [
            " The third term contains information about the Couette flow due to the average velocity between the contacting surfaces. Finally, the last term, referred to as squeeze term, represents the impact of gross variation in film thickness with time due to rigid body motion between element and raceway. The piezo-viscosity and piezo-density formulations were obtained from the work of Roelands [30] , and Dowson and Higginson [31] . The film thickness, h(x,y) is described in Eq. (2) by the curvature ratios ( R x , R y ), the approach between the rigid bodies ( h 0 ) and the reduced elastic modulus ( E \u2032 ). Fig. 2 (a) illustrates the film thickness scheme. h ( x, y ) = h o + x 2 2 R x + y 2 2 R y + 2 \u03c0E \u2032 \u222b \u222b p ( x \u2032 , y \u2032 ) dx \u2032 \u221a ( x \u2212 x \u2032 ) 2 + ( y \u2212 y \u2032 ) 2 d x \u2032 d y \u2032 (2) For the dynamic EHD formulation employed in this work, a harmonic external excitation Eq. (3) is considered, adding a sinusoidal force term to the static load balance, with amplitude proportional to the total contact force and frequency related to the rotation speed of the inner ring, as defined in [38] . Eq. (3) shows the contact system motion equation to be solved in parallel to the multi-level algorithm for EHD problem, where m is the mass of each single rolling element, h 0 is the approach between the bodies, p ( x, y, t ) is the pressure distribution over the contact area, S is the contact domain, f ( t ) is the harmonic external force applied to the contact, A h is the amplitude and e the excitation frequency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003274_j.optlastec.2020.106477-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003274_j.optlastec.2020.106477-Figure11-1.png",
        "caption": "Fig. 11. Residual stress measurement positions.",
        "texts": [
            "3, and Young\u2019s modulus = 211,000 MPa. To avoid the influence of stress relief, the base plate and samples were not separated in the measurement, which is consistent with the simulation condition. Although it was designed this way for fair comparison, it should be acknowledged that the residual stress obtained this way could be different from the residual stress obtained after the separation. The residual stress was measured at various height positions for the area of interest of each selected layer, which is shown in Fig. 11. The X-Ray irradiation area is around 1 mm \u00d7 2 mm located on the center of the sample surface, and this match up with the area of interest shown in the simulation setting. To measure the in-depth stress, electropolishing was employed to remove the material layers from the top, as illustrated in Fig. 11. Electropolishing was conducted at a voltage of 20 V, with a saturated brine solution. Seven measurement depths were taken at 2.0, 1.8, 1.6, 1.4, 1.2, 1.0, and 0.8 mm, respectively. To minimize the surrounding material loss and stress redistribution, care was taken to submerge the samples into the solution by 1 mm in each operation. The compensation approach developed by Moore and Evans [47] to deal with stress relaxation due to layer removal was adopted to correct the measured residual stress. Therefore, the residual stresses reported in the following are actually the corrected results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001949_13552541211218216-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001949_13552541211218216-Figure6-1.png",
        "caption": "Figure 6 A set of cylindrical parts fabricated perpendicular to gas flow showing no delamination",
        "texts": [
            " Similar concepts were reported in previous studies in which temperature gradient has been introduced as the first source of thermal stress (Mercelis and Kruth, 2006; Shiomi et al., 2004). The temperature profile of the powder bed at the end of SLM process, shown in Figure 5, confirms the inhomogeneous temperature distribution. This shows that the right side of the bed (where argon enters) has a lower temperature than that of the left side. It should be noted that although this image has been taken at the end of the process, it still indicates temperature differences between the two sides, implying higher temperature variations existed within the SLM process. Figure 6 shows that laying the parts perpendicular to gas flow leads to an obvious reduction in deformations, i.e. this figure shows almost no delaminations for the parts. This result (b) Effect of SLM layout on the quality of stainless steel parts S. Dadbakhsh, L. Hao and N. Sewell Volume 18 \u00b7 Number 3 \u00b7 2012 \u00b7 241\u2013249 can be attributed to a lower temperature gradient produced in each part due to the laying direction. Thus, one may conclude that to produce less thermal stress (and subsequently delamination) the parts should be laid on the bed with a view of producing a less temperature gradient, which here appears to be perpendicular to gas flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000096_tnn.2006.878122-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000096_tnn.2006.878122-Figure7-1.png",
        "caption": "Fig. 7. Phase-plane portrait of uncontrolled wing-rock motion system.",
        "texts": [
            " These aircrafts may become unstable due to oscillation, mainly a rolling motion known as wing-rock motion [24], [25]. A dynamic system of the wing-rock motion system can be written in a state variable form as (40) where is the roll angle and the parameters , are nonlinear functions of the angle of attack. The aerodynamic parameters are given by , , , , , and . The open-loop system time response with was simulated for two initial conditions: a small initial condition ( , s ) and a large initial condition ( , s ). The phase-plane plot is shown in Fig. 7. For the small initial condition, a limit cycle oscillation is obtained, and for the large initial condition, the roll angle is divergent. Thus, it is shown that the uncontrolled nonlinear wing-rock motion system will be unstable for some initial conditions. The system dynamic function would be online estimated by the WNN identifier. A WNN identifier with five hidden nodes is utilized to approach the system dynamic function of the wingrock motion system. In addition, the control parameters are selected as , , and for "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003887_j.ijmecsci.2019.05.012-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003887_j.ijmecsci.2019.05.012-Figure4-1.png",
        "caption": "Fig. 4. Dynamic model of a one-stage nonlinear spur gear system.",
        "texts": [
            " Thus, for the crack length L c < L , the crack curve solid curve) can be described by, ( \ud835\udc67 ) = \ud835\udc5e 0 \u221a \ud835\udc3f \ud835\udc50 \u2212 \ud835\udc67 \ud835\udc3f \ud835\udc50 , \ud835\udc67 \u2208 [ 0 , \ud835\udc3f \ud835\udc50 ] (13) ( \ud835\udc67 ) = 0 , \ud835\udc67 \u2208 [ \ud835\udc3f \ud835\udc50 , \ud835\udc3f ] (14) While for the crack extending through the entire tooth width, the rack curve (dash curve) can be described by, ( \ud835\udc67 ) = \u221a \ud835\udc5e 2 2 \u2212 \ud835\udc5e 2 0 \ud835\udc3f \ud835\udc67 + \ud835\udc5e 2 0 (15) Thus, the equivalent mesh stiffness of a single tooth pair can be cal- ulated by, 1 \ud835\udc58 \ud835\udc52 = 1 \ud835\udc58 \u210e + 1 \ud835\udc58 \ud835\udc4f 1 ,\ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59 + 1 \ud835\udc58 \ud835\udc60 1 ,\ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59 + 1 \ud835\udc58 \ud835\udc4e 1 + 1 \ud835\udc58 \ud835\udc531 + 1 \ud835\udc58 \ud835\udc4f 2 + 1 \ud835\udc58 \ud835\udc60 2 + 1 \ud835\udc58 \ud835\udc4e 2 + 1 \ud835\udc58 \ud835\udc532 (16) Finally, the total mesh stiffness for the double-tooth-pair meshing duation can be calculated by the summation of two tooth pairs\u2019 stiffness. he contact ratio determines the meshing duration of single pair/double airs in one mesh period. In this study, the contact ratio is assumed to e independent from the tooth deformation. . Modeling of spur gear pair system The dynamic model of the spur gear system adopted in the present nalysis is depicted in Fig. 4 . The spur gear pair is modeled using two v T t a o i e \ud835\udc53 c a p s s n d e m t i isks coupled by mesh stiffness, mesh damping and static transmission rror excitation. Both gears are supported by rolling element bearings. he model consists of four degrees of freedom, namely, two lateral moions y 1 and y 2 , and two angular motions \ud835\udf031 and \ud835\udf032 . k g and c g are the ear mesh stiffness and damping, while 2 b g is the gear backlash. e repesents the static transmission error. T i , m i , I i and R i denote the torque, ass, mass moment of inertia and basic circle radius, respectively",
            " \ud835\udc54 \u23a4 \u23a5 \u23a5 \u23a6 + \u23a1 \u23a2 \u23a2 \u23a3 \ud835\udc50 \ud835\udc4f 1 0 \ud835\udc50 \ud835\udc54 0 \ud835\udc50 \ud835\udc4f 2 \u2212 \ud835\udc50 \ud835\udc54 0 0 \ud835\udc50 \ud835\udc54 \u23a4 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a3 ?\u0307? 1 ?\u0307? 2 ?\u0307? \ud835\udc54 \u23a4 \u23a5 \u23a5 \u23a6 + \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 \ud835\udc58 \ud835\udc4f 1 0 \ud835\udc58 \ud835\udc54 ( \ud835\udc61 ) 0 \ud835\udc58 \ud835\udc4f 2 \u2212 \ud835\udc58 \ud835\udc54 ( \ud835\udc61 ) 0 0 \ud835\udc58 \ud835\udc54 ( \ud835\udc61 ) \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 \ud835\udc53 \ud835\udc4f 1 ( \ud835\udc66 1 ) \ud835\udc53 \ud835\udc4f 2 ( \ud835\udc66 2 ) \ud835\udc53 \ud835\udc54 ( \ud835\udc66 \ud835\udc54 ) \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 \ud835\udc39 \ud835\udc4f 1 \ud835\udc39 \ud835\udc4f 2 \ud835\udc39 \ud835\udc5a \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 + \u23a1 \u23a2 \u23a2 \u23a3 0 0 \ud835\udc5a \ud835\udc54 \ud835\udc52 0 \u03a92 \u210e \u23a4 \u23a5 \u23a5 \u23a6 sin ( \u03a9\u210e \ud835\udc61 + \ud835\udf19\u210e ) (33) . Effect of crack propagation on gear mesh stiffness In this section, the effect of the tooth crack propagation on the gear esh stiffness is investigated. The dynamic model of gear system utilized n present study is depicted in Fig. 4 . Corresponding parameters of the ear pair are listed in Table 2 . To be mentioned, only one tooth for gear is assumed to be cracked in this study. Thus, the frequency of tooth rack is same as the shaft revolution frequency. Fig. 7 (a) shows five crack cases in the crack section A-A, and coresponding case data can be found in Table 3 . From cases 1 to 5, the ooth root crack is estimated to propagate along both tooth width and rack depth simultaneously, which is more reasonable to reflect the ocurrence and growth of tooth crack than the assumption with uniformly istributed crack depth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001025_j.euromechsol.2010.05.001-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001025_j.euromechsol.2010.05.001-Figure3-1.png",
        "caption": "Fig. 3. Coordinates for the jth suneplanet mesh.",
        "texts": [
            " These errors are not included in the model. Because friction is usually small for well-lubricated gears, it is modeled through modal damping. Particularly for the low-speed cases examined in the current paper, the specific dissipation model will not significantly affect the results. The coordinates are shown in Fig. 2. Translational displacements xl, yl, (l\u00bc c, r, s) are assigned to the carrier, ring, and sun, respectively, with respect to the basis {Ei} (i\u00bc 1, 2, 3) that is fixed to the carrier as shown in Fig. 3. The originO is at the center of the planetarygear. The radial and tangential displacements of the planets are denoted by xj, hj, j \u00bc 1, ., N with respect to the basis {ei} rotating with the carrier and oriented for each planet as shown in Fig. 3. The rotational displacements are uv\u00bc rvqv, v\u00bc c, r, s, 1,.,N, where qv is the rotation in radians and rv is the base circle radius for the sun, ring, andplanets and the radius to the planet center for the carrier. Throughout this paper, thesubscript j\u00bc1,.,Ndenotesplanets1 toN; l\u00bc c, r, sdenotes the carrier, ring, and sun; and the superscripts d, b, w denote driveside tooth contact, back-side tooth contact, and tooth wedging. The tooth contact model captures four possible situations: drive-side tooth contact, back-side tooth contact, no contact, and tooth wedging (simultaneous drive-side and back-side contact)",
            " This parametric excitation is introduced through time-varying mesh stiffnesses kdqj (t) at the SeP and ReP meshes. They are calculated by finite element analysis (Vijayakar, 2005) fully discussed in Section 3, which includes the elastic deformation of the gear teeth and gear bodies. The back-side mesh deflection dbsj at the jth SeP mesh is derived from the relative displacement between two points A and B on the sun and planet j base circles, respectively, along the back-side line of action as shown in Fig. 3. The back-side line of action and the line of action have equal pressure angles. The displacements of A and B and the back-side mesh deflection are dA \u00bc xsE1 \u00fe ysE2 useb1 dB \u00bc xje1 \u00fe hje2 \u00fe ujeb1 (4) dbsj \u00bc \u00f0dA dB\u00deeb1 \u00bc xssinj b sj yscosj b sj xjsinas\u00fehjcosas uj us; jb sj \u00bc jj\u00feas (5) where thebasisfegbi isorientedasshowninFig. 3,eb1 isalongthebackside line of action,as is the pressure angle of the SePmeshes, andjj is the fixed angular position of planet j in the carrier reference frame. Similarly, the back-sidemesh deflection at the jth ring-planetmesh is dbrj \u00bc xrsinj b rj yrcosj b rj\u00fexjsinar\u00fehjcosar\u00feuj ur; jb rj \u00bc jj ar (6) Back-side tooth contact takes place when the back-side mesh deflection exceeds the backlashes bq (q\u00bc r, s) for the sun and ring. The back-side tooth force is f bqj \u00bc hbqjk b qj dbqj bq ; q \u00bc r; s (7) hbqj \u00bc ( 1 if dbqj > bq 0 if dbqj < bq ; j \u00bc 1;",
            " The nonlinear bearings are modeled as circumferentially distributed radial springs with uniform clearances as shown in Fig. 5. Forces develop only when the relative displacement between the connected bodies exceeds a specified clearance. For the jth planet bearing with bearing clearance Dcp as an example, the relativedisplacementbetween the carrier andplanet j is dcj \u00bc h xccosjj \u00fe ycsinjj xj 2 \u00fe xcsinjj \u00fe yccosjj \u00fe uc hj 2i1=2 (13) The direction of the developed force is determined by the contact angle wcj between e1 (Fig. 3) and the direction of relative motion between the carrier and planet j wcj \u00bc tan 1 xcsinjj \u00fe yccosjj \u00fe uc hj xccosjj \u00fe ycsinjj xj ! (14) c\u20acxc \u00fe kcxc PN j\u00bc1 kpmcj dcj Dcp cos wcj \u00fe jj \u00fe kcrmcr\u00f0dcr Dcr\u00decosw mc\u20acyc \u00fe kcyc \u00fe XN j\u00bc1 kpmcj dcj Dcp sin wcj \u00fe jj \u00fe kcrmcr\u00f0dcr Dcr\u00desinw Ic=r2c \u20acuc \u00fe kcuuc \u00fe XN j\u00bc1 kpmcj dcj Dcp sinwcj \u00bc f uc \u00fe f ua \u00f0t\u00de The bearing forces that are the projections of this bearing force in the xc, yc, uc, xj, hj directions are f xcj \u00bc mcjkp dcj Dcp cos wcj \u00fe jj f ycj \u00bc mcjkp dcj Dcp sin wcj \u00fe jj f ucj \u00bc mcjkp dcj Dcp sinwcj f xpj \u00bc mcjkp dcj Dcp coswcj f hpj \u00bc mcjkp dcj Dcp sinwcj (15) The planet bearing stiffness is denoted by kp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000055_s0022-460x(78)80044-3-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000055_s0022-460x(78)80044-3-Figure3-1.png",
        "caption": "Figure 3. The inner ring centre of a rolling bearing with radial clearance undergoing a small, arbitrary displacement from O to 0\".",
        "texts": [
            " For these reasons it has not been considered realistic to aim at making quantitative comparisons between theoretical and experimental results, but merely to demonstrate that the predicted phenomena associated with VC vibrations actually occur in practice. Experimental runs were made in a rig resembling the set-up of Figure I. An accelerometer was positioned on the bearing pedestal. Figure 2 shows the spectrogram obtained from a slow running roller bearing (type N206) with a 75 kg load. Peaks at roller passage frequency and the first few harmonics thereof can be seen clearly. 2. THE FORCE-DEFORMATION RELATIONSHIP FOR ROLLER BEARING ASSEMBLIES Consider the roller bearing in Figure 3(a). The angular position of the cage separating the rolling elements is defined by ~, and the gaps between the rollers by V ( V = 27r/N, where ROLLING BEARING VIBRATIONS 365 N is the number of rollers). The bearing has a radial clearance of 2e. The dashed circle in Figure 3(b) is identical to the dashed circle in Figure 3(a), while the full line circle in Figure 3(b) is identical to the circle having the radius R + e in Figure 3(a). Now, assume that the centre of the shaft and inner ring (i.e., the centre of the dashed circle) is moved from O to O' as indicated in Figure 3(b). This causes the two circles to interfere over a part of the circumference. Returning to Figure 3(a), it is clear that this interference will cause an elastic deformation (for small displacements) of rollers and rings. Dowson has shown [4] that for roller bearing races mounted firmly against a solid steel shaft and bearing housing the only significant deformations are the local deformations at the contact points between rollers and rings. He also showed that the local stiffness is near-linear and can be well approximated by K = 1.07 x 10n~ (1) for steel components, where L is the roller length",
            " (12) For such a preloaded bearing, the stiffness is constant and time invariant and no VC vibrations would be generated. Equation (12) also shows that the stiffness does not increase with the preload, once condition (I0) is fulfilled. One should therefore avoid excessive preload since this often causes problems of increased friction and overheating, while no increase of assembly stiffness is gained. This conclusion is valid only as long as the local stiffness is independent of deformation. The case where e = 0 can be analysed in a similar way. From Figure 3(b) it is clear that if e = 0 the contact zone will cover exactly half the circumference of the outer race for all (small) displacements. If the bearing has an even number of rollers, then N[2 rollers will always be in contact with both races. For this condition, equations (7) yield Kx = Ky = KN]4. (13) Hence, also in this case the force-deformation relationship is linear and time invariant and no VC vibrations would be generated. Note that with e = 0 and an odd number of rollers VC vibrations will still be excited"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001836_jestpe.2014.2299765-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001836_jestpe.2014.2299765-Figure11-1.png",
        "caption": "Fig. 11. PMSM (TEFC-design) lumped-parameter thermal model (shown in a simplified form).",
        "texts": [
            " 2 includes online loss calculations in combination with lumped-parameter thermal models. Copper loss PCu is calculated with (3), iron loss PFe with (5), while rotor loss Pr is neglected. Note that the dependency of Rs on winding temperature Twinding is considered by thermal model feedback. Furthermore, motor voltages ud and uq in (5) are obtained directly from the FOC-block PI current control loops. All loss components are supplied to a lumped-parameter thermal model of the totally enclosed fan cooled (TEFC) motor, which was implemented according to [39]. Fig. 11 shows the structure of the thermal model in a simplified form. The nodes represent average temperatures of the frame Tframe, stator core Tcore, stator winding Twinding, and rotor Trotor. Thermal resistances and capacitances were calculated from material properties, motor geometry, and basic experimental data according to [19], [39], and [40]. Note that the thermal resistance between motor frame and ambient is dependent on the rotor speed due to the shaft-mounted fan. The cooling air speed and corresponding convection coefficient were determined experimentally, but remain a large source of uncertainty"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.16-1.png",
        "caption": "Fig. 10.16 Exploded view of the CV joint on the ERICA tiltrotor concept developed in the European NICETRIP project (courtesy Airbus and Leonardo Helicopters, Refs. 10.27)",
        "texts": [
            " \ud835\udeff3 is also included on the V-22 CV gimbal, where the pitch link/horn geometry applies flap when cyclic pitch is input, such that the effective phase lag between cyclic pitch and flap is about \u2212102 deg (Ref. 10.26). The design of CV-jointed tiltrotor hubs requires innovation to enable the control functions and joints to fit into a limited space. The need for compactness is in tension with the requirement for mechanisms that provide for a large rotor blade pitch angle range, which can be as great as 60 deg. As an example, Figure 10.16 shows an exploded view of the DART rotor system for the ERICA tiltrotor concept (Ref. 10.27), including the CV joint above the yoke. 616 Helicopter and Tiltrotor Flight Dynamics Later in this chapter, the topic of load alleviation in tiltrotor aircraft and its impact on flying qualities will be examined. The dynamics of blade motion will be revisited then to highlight the contributions of the lift forces to the inplane loadings. The oscillatory inplane bending loads increase in magnitude as out-of-plane flapping occurs, particularly in manoeuvring flight, and methods to minimise these loads have become important in tiltrotor flight dynamics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001434_0094-114x(80)90021-x-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001434_0094-114x(80)90021-x-Figure1-1.png",
        "caption": "Figure 1.",
        "texts": [
            " Apart from the fact that the Bricard linkages present a considerable algebraic challenge, and that their solutions will complete the assault on the known loops of their general character, it is hoped that the following analysis will clear away the misconceptions concerning them and even, for many workers perhaps, bring them out of the kinematic unknown. In addition, the results should be of value to those involved in a current resurgence of interest in line geometry. Bottema has also expressed curiosity about the relative motion between links of the octahedral chains in the closing paragraph of [7], from which paper possible applications of the linkages to structural organic chemistry may be inferred. In the analysis to follow, we shall use a terminology which is well known and most clearly defined by an illustration, such as Fig. 1. For brevity, we shall write cosine as c and sine as s. There will be other special conventions for the octahedral linkages which will be described at the appropriate places. We shall refer to the 6-bar closure eqns (A6.1-A6.12) in the form given in the Appendix. The reader is reminded in this context that eqns (A6.1-A6.9) are \"rotational\" equations, derivable from a spherical indicatrix and, as they stand, representing at most three independent equations. Equations (A6.10-A6.12) are \"translational\" equations, generally independent and derivable, in principle, as dual relationships from the rotational set"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001620_978-90-481-8764-5_2-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001620_978-90-481-8764-5_2-Figure4-1.png",
        "caption": "Fig. 4 PID controller for controlling the altitude and attitude of a QRT UAV",
        "texts": [
            "\u23a1 \u23a2\u23a2\u23a3 m(z\u0308+ g) Ixx\u03c6\u0308 Iyy\u03b8\u0308 Izz\u03c8\u0308 \u23a4 \u23a5\u23a5\u23a6+ = \u23a1 \u23a2\u23a2\u23a3 u1 u2 u3 u4 \u23a4 \u23a5\u23a5\u23a6 , (29) 16 Reprinted from the journal where the disturbance, , is defined as = \u23a1 \u23a2\u23a2\u23a3 \u03b43 \u03b44 + (Izz \u2212 Iyy)\u03c9y\u03c9z \u03b45 + (Ixx \u2212 Izz)\u03c9z\u03c9x \u03b46 \u23a4 \u23a5\u23a5\u23a6 . (30) Description Value Weight 2.2 kg And \u03b4i mainly comes from the dynamic inconsistency. For the hovering control, the amount of disturbance is relatively small. Hence, it does not give instability, but poor performance, which may violate the assumption, \u03c6 \u2248 0 and \u03b8 \u2248 0. This phenomenon can be resolved using DOB control input. 3.1 Basic Controller The control algorithms for the altitude and attitude, roll, pitch and yaw, of the UAV are designed based on PID controllers as shown in Fig. 4. The control input u1 for controlling the altitude z of the UAV with respect to the reference input zd is designed as u1 = Kp1(zd \u2212 z)+ Kd1 d(zd \u2212 z) dt + KI1 \u222b t 0 (zd \u2212 z)d\u03c4. (31) The control inputs u j ( j = 2, 3, 4) for controlling the attitude (\u03c6, \u03b8, \u03c8) of the UAV with respect to the reference inputs (\u03c6, \u03b8, \u03c8)d are designed, respectively given as: INSJoystick Encoder Main Controller (TMS320F2812 DSP) PWMRF (RS232C) RS232C Altitude Sensor (Ultrasonic) DI/O Obstacle Detector (Infrared) CAN Camera RS232C RS232C DC Motor Driving System Motor #1 Motor #2 Motor #3 Motor #4 Driver #1 Driver #2 Driver #3 Driver #4 18 Reprinted from the journal u j are the PD control inputs for avoiding obstacles in roll and pitch axis given as: u2 = [Kpr(drd \u2212 dr)\u2212 Kdrd\u0307r]U(drd \u2212 dr)\u2212 [Kpl(dld \u2212 dl)\u2212 Kdld\u0307l]U(dld \u2212 dl) u3 = [Kpb (dbd \u2212 db )\u2212 Kdb d\u0307b ]U(dbd \u2212 db )\u2212 [Kpf (d f d \u2212 d f )\u2212 Kdf d\u0307 f ]U(d f d \u2212 d f ) u4 = 0 (33) where dmd (m = f,b , l, r) are reference distances for avoiding obstacles to forward, backward, left, and right direction, and dm (m = f,b , l, r) are distances of obstacles to the four direction",
            " Figures 13\u201315 show three angle rates and angles for pitch, roll, and yaw controls. As shown in the Fig. 16, the performance of the altitude control is very satisfactory, even though the sonar sensor is used. The results show that the proposed algorithm for both the altitude and attitude control of the UAV works well. For the hovering control, in this paper, a DOB controller with PID is proposed. With DOB, we can derive the linear equation, Eq. 37 using internal loop compensator, Eq. 36. As depicted in Fig. 4, a PID controller is used for the altitude and attitude of QRT UAVs. For the yaw controller, the I-gain is set to 0, because of the sensor noise. Normally the electrical compass is used for sensing the yaw motion, but the electrical compass is easily affected from other electrical systems, e.g., motor and battery. In this study, a QRT UAV is developed for calamity observation in indoor environments. The hovering robot captures the image of targets under harmful environments, and sends the image to the operator on the safe site"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000628_j.automatica.2011.01.024-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000628_j.automatica.2011.01.024-Figure4-1.png",
        "caption": "Fig. 4. Assumption (7) for a convex domain D.",
        "texts": [
            " Now we summarize the above discussion by imposing the cumulative assumption, which covers Assumptions 2 and 3. Assumption 4. There exists a regular interval [d\u2212, d+] that contains the required distance d0 and the distances from the points on the initial circles to the boundary \u2202D. If the domain D is convex, this assumption is implied by the following inequality min  d0; d(0) \u2212 2R  > max  R \u2212 R\u2212; dsafe  , where R\u2212 := inf r\u2217\u2208\u2202D R\u03ba(r\u2217). (7) Here dmin-in := d(0) \u2212 2R is the tight lower bound of the distances d = d\u2217 encountered when moving along feasible initial circles1 (see Fig. 4). Inequality (7) means that the vehicle is capable of maintaining both the given speed v and any of these distances d\u2217, as well as the required one d\u2217 := d0, since the minimal curvature radius d\u2217+R\u2212 of the corresponding trajectory exceeds theminimal turning radius R of the vehicle. Furthermore, (7) means that this trajectory meets the safety requirement d\u2217 > dsafe. Nowwe are in a position to state themain result concerning the border patrolling problem. Theorem 3. Let Assumptions 1 and 4 hold and the parameters \u03b3 > 0 and \u03b4 > 0 of the control rule (4) and (5) be chosen so that the following inequality is true, where \u03bb is the constant related to the interval from Assumption 4 by Definition 2, 1 + \u03b3 2 (1 \u2212 \u03bb)2u2 < \u00b5 := v \u03b4\u03b3  (5) = v v\u2217  ",
            " 2 Due to access to only d and d\u0307, the vehicle is unable to distinguish between the cases (c1) and (c2) from Fig. 5. Due to this deficiency in the sensor data, it has to apply a common control in both cases, which in the case (c2), results in a less effective maneuver than in the case (c1). Since neither the initial orientation nor location on the initial d(0)-equidistant curve are measured, the expected operational zone of the vehicle is the domain limited by the min{d(0) \u2212 2R, d0}and max{d(0) + 2R, d0}-equidistant curves, see Fig. 4. Our proposed strategy consists in switching between the obstacle avoidance law (4), with d(t) replaced by di(t) := distDi [r(t)] for a properly chosen i, and straight moves to the target: u(t) = 0. (9) As before, the obstacle avoidance maneuver is associated with the safety margin dsafe > 0 and the desired distance d0 > dsafe to the obstacle. The rule for switching between (9) and (4) employs two more parameters \u03f5 > 0 and C > d0 + \u03f5. (10) Here C is the distance to an obstacle at which avoidance is commenced; the maneuver termination is allowed only if the vehicle is close enough to the obstacle: di \u2264 d0 + \u03f5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003950_j.ymssp.2018.09.027-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003950_j.ymssp.2018.09.027-Figure2-1.png",
        "caption": "Fig. 2. The contact model of a spur gear pair with tooth pitting and spalling.",
        "texts": [
            " In practice, tooth pitting and spalling are normally first initiated on the smaller gear (which undergoes more revolutions and therefore more stress cycles) and close to the tooth pitch line [1], see Fig. 1. The size of what delineates pitting and spalling has not been uniformly defined and both terms are often used interchangeably. Based on [20,21], the size of pitting can range from 0.01 mm (micro-pitting) to 0.8 mm (macro-pitting) in diameter, and the size of tooth spall is considerably larger than tooth pitting. The contact model of a spur gear pair with lubrication under tooth pitting and spalling is shown in Fig. 2, where the contact line just crosses the defect area near the dedendum of tooth 1. In practice, a gear transmission is always lubricated in order to reduce contact friction and wear [9,10]. As defined in [10,20], micro-pitting is usually in very small size, therefore, its effect can be modeled as the increase of the tooth surface roughness. The tooth spalling (or macro-pitting) is often in large size which is capable of blocking the formation of a lubricant film and reducing the effective tooth contact length, see Fig. 2. The reduced tooth contact length directly decreases the strength of the contacting teeth on supporting the dynamic loads, which is generally modeled by decreased gear TVMS within the spalling area [23]. The mating process of a spur gear pair with tooth contact friction forces is shown in Fig. 3. The line of action B1B2 is tangent to the base circles of the pinion and gear at points B1 and B2. Line segment P1P2 is the actual effective contact locus, where point P1 is the starting contact point (approach point), and P2 corresponds to the separation point. a0 is the pressure angle,x1 andx2 are rotational speeds. Fpg is the total dynamic mesh force of the mating process (along the action line B1B2). Fg1 and Fp1, Fg2 and Fp2, represent the tooth contact friction forces of each mating tooth pair. The mating tooth can be simplified as equivalent cylinders in contact with time-varying radii of the tooth curvatures r1 and r2 (Fig. 2) or rp1, rp2, rg1, rg2 (Fig. 3) and forming a lubrication filmwith width of 2b.up1 \u00bc x1 rp1, ug1 \u00bc x2 rg1 are the moving speeds of the contact point of each surface along the off-line of action [24]. For ordinary spur gear pairs with contact ratio less than 2, the length of the time-varying radii (rpi, rgi) can be determined from rpi \u00bc rbp hpi \u00fe tan\u00f0\\B1OPP1\u00de rgi \u00bc \u00f0rpp \u00fe rpg\u00desina0 rpi ( i \u00bc 1; 2; \u00f01\u00de in which i denotes the ith gear tooth, hpi is the contact angle of the ith tooth pair. For a spur gear pair, the contact angle of the followed second gear tooth lags with respect to the first gear tooth pair by hp1 2p=N where N is the number of gear teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.63-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.63-1.png",
        "caption": "FIGURE 5.63. Assembled spherical wrist.",
        "texts": [
            " A spherical wrist has three revolute joints in such a way that their joint axes intersect at a common point, called the wrist point. Each revolute joint of the wrist attaches two links. Disassembled links of a spherical wrist are shown in Figure 5.62. Define the required DH coordinate frames to the links in (a), (b), and (c) consistently. Find the transformation matrices 3T4 for (a), 4T5 for (b), and 5T6 for (c). 22. F Assembled spherical wrist. 5. Forward Kinematics 319 Label the coordinate frames attached to the spherical wrist in Figure 5.63 according to the frames that you installed in Exercise 21. Determine the transformation matrices 3T6 and 3T7 for the wrist. 23. F A 5 DOF robot. Figure 5.64 illustrates a five DOF robot having a spherical wrist. (a) Follow the DH rules and complete the link coordinate frames such that the hand of the robot at the rest position is straight with the forearm. (b) Determine the link-joint table for the manipulator. (c) Determine the DH transformation matrices. 320 5. Forward Kinematics (d) Determine the forward kinematics final transformation matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002032_j.jmatprotec.2016.04.006-Figure23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002032_j.jmatprotec.2016.04.006-Figure23-1.png",
        "caption": "Fig. 23. Temperature field of the whole model (unit: ).",
        "texts": [
            "1 Temperature variation and validation Temperature variation curves captured by thermocouples are presented in Fig 21. For any one of the four curves, each layer contains one peak when the laser travels through the area on top of the thermocouple. All the data is recorded by the dedicated data acquisition system. The computed temperature profile near the laser spot area is presented at two scales in Fig22.. The maximum temperature value is approximately 3877 \uff0cand the molten pool is not bilaterally symmetric due to the asymmetry of the thermal boundary conditions. Fig 23. shows the temperature field of the whole part during the deposition. The maximum temperature occurs in the molten pool, whereas the temperature in substrate is below the phase transformation point. As shown in Fig 24., the temperatures variation curves at the four nodes where the thermocouples are located are calculated. Comparison charts for each thermocouple are presented in Fig 25.. For TC1, 2 and 4, the calculated value is a slightly higher than the experimental value. However, TC3 shows a value equal to the experimental value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.14-1.png",
        "caption": "Fig. 3.14 Flow through a rotor in forward flight",
        "texts": [
            " Young\u2019s approximation estimates that the autorotation line is crossed at \ud835\udf07d \ud835\udf06ih = 1.8 (3.135) parachute. We return to the modelling of vortex ring state in the context of tiltrotor aircraft Chapter 10. Modelling Helicopter Flight Dynamics: Building a Simulation Model 101 Momentum Theory in Forward Flight In high-speed flight, the downwash field of a rotor is like that of a fixed-wing aircraft with circular planform and the momentum approximations for deriving the induced flow at the wing apply (Ref. 3.13). Figure 3.14 illustrates the flow streamtube, with freestream velocity V at angle of incidence \ud835\udefc to the disc, and the actuator disc inducing a velocity vi at the rotor. The induced flow in the far wake is again twice the flow at the rotor (wing) and the conservation laws give the mass flux as m\u0307 = \ud835\udf0cAdVres (3.136) and hence the rotor thrust (or wing lift) as T = m\u03072vi = 2\ud835\udf0cAdVresvi (3.137) where the resultant velocity at the rotor is given by V2 res = (V cos \ud835\udefcd)2 + (V sin \ud835\udefcd + vi)2 (3.138) Normalizing velocities and rotor thrust in the usual way gives the general expression 102 Helicopter and Tiltrotor Flight Dynamics where \ud835\udf07 = V cos \ud835\udefcd \u03a9R , \ud835\udf07z = \u2212 V sin \ud835\udefcd \u03a9R (3.140) and where \ud835\udefcd is the disc incidence, shown in Figure 3.14. Strictly, Eq. (3.139) applies to high-speed flight, where the downwash velocities are much smaller than in hover, but the solution also reduces to the cases of hover and axial motion in the limit when \ud835\udf07= 0. In fact, this general equation is a reasonable approximation to the mean value of rotor inflow across a wide range of flight conditions, including steep descent, and provides an estimate of the induced power required. Summarizing, we see that the rotor inflow can be approximated in hover and high-speed flight by the formulae V = 0, vi = \u221a( T 2Ad\ud835\udf0c ) (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure9-1.png",
        "caption": "Fig. 9. 5\u20135\u20134 RPR-equivalent PMs with one U joint. (a) 2-uPRS/uvSvPR. (b) 2-uRPS/uvSvPR. (c) 2-uRRS/uvSvPR. (d) 2-uRRS/uvSvRR. (e) 2-SuPR/vRPuvU. (f) 2-SuRR/vRRuvU.",
        "texts": [
            " RPR-equivalent PMs in subcategory 5\u20135\u20134 can be constructed with two 5-DOF limbs in Table II and one 4- DOF limb in Table III. The first combination is {L1} = {R(O,u)}{G(v)} and {L2} = {G(u)}{S(Fa)} {L3} = {G(u)}{S(Fb)}, with Fa \u2208 axis(B, u) and Fb \u2208 axis(B, v). The second combination is {L1} = {G(u)}{R(B,v)}, and {L2} = {S(Da)}{G(v)}, {L3} = {S(Db)}{G(v)} with Da \u2208 axis(O, u) and Db \u2208 axis(O, u), which is a kinematic inversion of the first family. Architectures with limbs generating {X(u)}{X(v)} are also neglected. Fig. 9 shows six RPR-equivalent PMs in this category. Note that Fig. 9(e) and (f) belongs to the second family. Table VI enumerates 49 RPR-equivalent PMs in the first family in 5\u20135\u20134 category. The dimension of the three limb bonds of a nonoverconstrained RPR-equivalent PM must be five. Using the 5-D limb bond in Table III, one can construct a nonoverconstrained RPRequivalent PM A. {L1} = {G(u)}{S(F)}, {L2} = {S(Da)}{G(v)}, and {L3} = {S(Db)}{G(v)} Like the 4\u20134\u20134 subcategory, the PM in 5\u20135\u20135 subcategory can be constructed by two combinations, respectively. The first combination is {L1} = {G(u)}{S(F)} and {L2} = {S(Da)}{G(v)}, {L3} = {S(Db)}{G(v)} with Da \u2208 axis(O, u) and Db \u2208 axis(O, u)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001303_am100413u-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001303_am100413u-Figure1-1.png",
        "caption": "FIGURE 1. Schematic diagram of GOx/ZnO-NWs/Au/PET bioelectrode used in the present study for glucose monitoring. The Au-coated PET substrate is deposited with ZnO nanowires (NWs) immobilized with glucose oxidase (GOx) in a phosphate buffer saline solution mixed with Nafion.",
        "texts": [
            " In the present work, we demonstrate a working enzymatic glucose sensor based on ZnO nanowires (NWs) electrochemically deposited on a Au-coated polyester (PET) substrate. Glucose oxidase (GOx) has been immobilized on the ZnO NWs by simple physical adsorption, and the glucose sensing performance of the resulting GOx/ZnO-NWs/Au/PET bioelectrode has been characterized. The GOx/ZnO-NWs/Au/PET bioelectrode is found to be very sensitive to glucose, and it exhibits a very small Michaelis-Menten constant (1.57 mM) and fast response (<5 s). Figure 1 shows a schematic diagram of the bioelectrode fabricated in the present work. A flexible PET substrate (1 \u00d7 1 mm2, 0.2 mm thick) was first coated with a 2 nm thick Au layer by using a magnetron sputter-coater (Denton Desk II). The Aucoated PET substrate was then used as the working electrode for depositing ZnO NWs electrochemically in a conventional three-electrode cell with a Ag/AgCl reference electrode and a Pt wire as the counter electrode. A CH Instruments 660A electrochemical workstation was employed for the electrodeposition of ZnO NWs by amperometry at a constant applied potential of -0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003503_j.measurement.2016.03.001-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003503_j.measurement.2016.03.001-Figure7-1.png",
        "caption": "Fig. 7. Strain gauge location and orientation near crack tip.",
        "texts": [
            " The strain filed in the region II for plane stress state condition can be written as [4,7,34]; Eexx \u00bc A0r 1 2 cos h 2 \u00f01 m\u00de \u00f01\u00fe t\u00de sin h 2 sin 3h 2 \u00fe 2B0 \u00fe A1r 1 2 cos h 2 \u00f01 t\u00de \u00f01\u00fe t\u00de sin2 h 2 ; Eeyy \u00bc A0r 1 2 cos h 2 \u00f01 m\u00de \u00f01\u00fe t\u00de sin h 2 sin 3h 2 2tB0 \u00fe A1r 1 2 cos h 2 \u00f01 t\u00de \u00f01\u00fe t\u00de sin2 h 2 ; 2Gcxy \u00bc A0r 1=2 sin h cos 3h 2 A1r1=2 sin h cos h 2 \u00f013\u00de where A0, A1 and B0 are unknown coefficients which can be evaluated with the help of geometry and boundary conditions of the specimen and coordinate r and h of point P as shown in Fig. 6. The definition of KI, it is related to A0 coefficient in the above series and can be written as [4,34]; KI \u00bc ffiffiffiffiffiffi 2p p A0 \u00f014\u00de The unknown coefficient A0 can be evaluated with the help of single strain gauge location at point P with a orientation from the horizontal axis X as shown in Fig. 7 and consequently KI. The strain component in the direction of x0 at a point P by using strain transformation can be written as [34]; 2Gex0x0 \u00bcA0r 1=2 kcos h 2 1 2 sinhsin 3h 2 cos2a\u00fe1 2 sinhcos 3h 2 sin2a \u00feB0\u00f0k\u00fecos2a\u00de\u00feA1r1=2 cos h 2 k\u00fe sin2 h 2 cos2a 1 2 sinhsin2a \u00f015\u00de where k \u00bc 1 t 1\u00fet and t is the Poisson\u2019s ratio of material of the specimen.The unknown coefficient B0 can be eliminated from the Eq. (15) by placing strain gauge at an angle a as given below [4,34]; cos 2a \u00bc k \u00bc 1 t 1\u00fe t \u00f016\u00de The another unknown coefficient A1 in Eq",
            " During the experiment gear has to be fixed at particular meshing position then torque is applied on pinion with the help of lever arrangement on the pinion in anticlockwise direction. In this experiment the limitations of the space for pasting the strain gauge on the gear tooth small strain gauges have been used. During pasting the CF350-3AA strain gauges all the precautions and cares were taken. Strain gauge installation and experiment were performed at room temperature. First surface was abraded, degreased and cleaned with cleaning solution. The strain gauge was aligned with right position on the surface (as shown in Fig. 7) and was pasted with the help of M-Bond 200 bonding adhesive. After pasting the strain gauge the silicone paste was used to protect them from environment. Data acquisition system was used to record the output voltage of the strain gauge and after that strain was calculated with the help of gauge factor provided by gauge manufacture as 2. Spur gear and pinion specimen of steel material were manufactured on CNC wire EDM. The main parameter of gear and pinion are shown in Table 2. The artificial crack was inserted with the help of CNC wire EDM at the tooth root of pinion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001177_j.ins.2010.08.009-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001177_j.ins.2010.08.009-Figure4-1.png",
        "caption": "Fig. 4. An articulated two-link manipulator.",
        "texts": [
            " For evaluating the performance of the controller, we can use the performance criteria as follows: (a) Integral of the absolute value of the error (IAE) (b) Integral of the time multiplied by the absolute value of the error (ITAE) (c) Integral of the square value (ISV) of the control input Cont MIM AFTS MIM AFSM SISO AFTS SISO AFSM ISV \u00bc Z tf 0 u2\u00f0t\u00dedt: \u00f057\u00de Both IAE and ITAE are used as objective numerical measures of tracking performance for an entire error curve, where tf represents the total running time. The criterion IAE will give an intermediate result. In ITAE, time appears as a factor; it will heavily emphasize errors that occur late in time. The criterion ISV shows the consumption of energy. Consider the two-link manipulators, as shown in Fig. 4. The dynamical equation of the manipulators can be described as [39,40] H11 H12 H21 H22 \u20acq1 \u20acq2 \u00fe h _q2 h\u00f0 _q1 \u00fe _q2\u00de h _q1 0 _q1 _q2 \u00fe G1 G2 \u00fe Td1 Td2 \u00bc s1 s2 ; where formance indices. roller Joint Example 1 Example 2 IAE (rad) ITAE (rad-s) ISV (N-m)2 IAE (rad) ITAE (rad-s) ISV (N-m)2 O Joint 1 0.4325 2.2045 85,392 0.5256 3.6151 113,030 MC Joint 2 0.1889 0.8472 16,772 0.1235 0.4425 11,909 O Joint 1 1.0809 8.1813 74,148 1.3626 11.4203 103,790 C Joint 2 0.5385 4.1116 13,008 0.3188 1.9016 9064 Joint 1 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002140_s0022112074001662-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002140_s0022112074001662-Figure3-1.png",
        "caption": "FIGURE 3. Diagram dernoristrating how the elliptic locus of a surface particle varies with the pmameters K and 8,. Loci are shown for K = - 1 to + 1 in steps of 0.5 arid for 0 , = 0 to 277 in steps of i7r. The mean surface is horizontal, the fluid above it and the surface waves travelling to the right. An example of a ciliary tip locus (symplectic) is indicated below.",
        "texts": [
            ") (77- 1)\u2019 i(7 - 7) { ( 7 2 - 1) (72- 1 ) y tan8, = - sin8, = Thus the parameter 7 defines both K , the amplitude-ratio parameter, and 8,, the phase angle; indeed the inverse of (40) and (41) is (42) (1 - K2)* - cos8, + iK sin 8, K cos 8, - i sin 8, 7 = This complex quantity 7 will thus be termed the wave-form parameter. Each surface particle performs an elliptical orbit whose shape and orientation is easily related to and completely described by the two parameters K and 8, or alternatively by the wave-form parameter r. The variations are illustrated in figure 3, where the fluid should be envisaged as lying above a horizontal material surface whose fluctuations in position are travelling towards the righthand side of the page. In the envelope model of ciliary motion these orbits may be considered as the loci of the cilium tips. Other properties of the fluid motion are easily calculated. The rate 2 of dissipation of energy per unit area of the mean surface may be evaluated as J!3 = (2dp /k) A2[77 + pll, (43) p being the dynamic viscosity. This is, of course, equal to the rate at which work is done by the surface on the fluid in producing the motion",
            " But these values appear too small to justify any preference for antiplectic metachronism in micro-organisms. Finally, it is readily demonstrated from the above relations that the mass flow in the positive-x direction relative to the fluid a t infinity is given by 41Cf/wl2 -+ - (I - K2)* cos 0, as W -f 0. (48) Values of this quantity are identical to those shown in a later graph, figure 9. Note that the maxima are different from these of figure 4. It can also be shown that & is directly proportional to the area described by the ciliary loci of figure 3. 5. Oscillating-boundary-layer theory Having developed the basic equations in \u00a7\u00a7 2 and 3 and delineated the features of the infinite-sheet solution in the last section, we have laid the foundations for the development of governing equations for the oscillatory boundary layer on a finite body in accordance with the ideas outlined in the introduction. The basic approach will involve a generalization of the infinite-sheet solution so as to permit the wave form I- and amplitude A of the surface motions to be slowly varying functions of the position x on the mean surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000168_roman.2001.981968-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000168_roman.2001.981968-Figure1-1.png",
        "caption": "Figure 1: The miniature four rotors helicopter",
        "texts": [
            " Based on this nonlinear model, we design in Section I11 a dynamic feedback control law which renders the system linear, controllable and noninteractive. In section IV, some simulations are carried out, allowing the analysis of the stability - robustness of the proposed controller in the presence of wind, turbulences and parametric uncertainties. Finally, in section V, our conclusions and directions for future work are presented. - 586 - 2 Dynamic modeling of a 4 rotors helicopter In this section we develop the dynamic model describ ing the UAV position and attitude. The considered UAV is a miniature four rotors helicopter (Figure 1). Each rotor consists of an electric DC motor, a drive gear and a rotor blade. Forward motion is accom:$shed by increasing the speed of the rear rotor while simultaneously reducing the fornard rotor by the same amount. Aft, left and right motion work in the same way. Yaw command is accomplished by accelerating the two clockwise turning rotors while decelerating the counter-clockwise turning rotors. The equations describing the attitude and position of an UAV are basically those of a rotating rigid body with six degrees of freedom [3][10]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001398_jestpe.2018.2811538-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001398_jestpe.2018.2811538-Figure4-1.png",
        "caption": "Fig. 4. FEA model of the 12-slot/8-pole SMPMSM in healthy (left) and faulty (right) conditions",
        "texts": [
            " Influence of the ITSC on the machine chractersitics is first investigated without controller effect under two different fault severities. Based on the discussions above, a 9-slot/8-pole SMPMSM with the given specifications in Table I is selected for fault analysis. A perfect short circuit with \ud835\udc5f\ud835\udc53 = 0  is assumed in open circuit analysis and the increase in the phase resistance due to locally elevated temperatures is ignored. These assumptions are made to perform a worst case analysis for a relatively fault tolerant PM machine. FEA models and phase inductances of the healthy machine are shown in Fig. 4 and Fig. 5, respectively. As the mutual inductances are much lower than the self-inductance, magnetic couplings between phases are ignored. After this simplification, the short circuit current can be represented by (3), which shows both back-emf and phase A current contribute to short circuit current. af ah af ah sc af af af af e j M i i r j L r j L          (3) At low rotational speeds \ud835\udc5f\ud835\udc4e\ud835\udc53 \u226b \ud835\udf14\ud835\udc3f\ud835\udc4e\ud835\udc53, short circuit current is limited by the resistance of the faulty turns and increases both with rotational speed and load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure2-1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure2-1-1.png",
        "caption": "Fig. 2-1 Stator windings.",
        "texts": [
            " 2-2 SINUSOIDALLY DISTRIBUTED STATOR WINDINGS In the following analysis, we will also assume that the magnetic material in the stator and the rotor is operated in its linear region and has an infinite permeability. 6 2 Induction Machine Equations in Phase Quantities: Assisted by Space Vectors Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink\u00ae, First Edition. Ned Mohan. \u00a9 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. SINuSoIdallY dISTrIbuTEd STaTor WINdINgS 7 In ac machines of Fig. 2-1a, windings for each phase ideally should produce a sinusoidally distributed radial field (F, H, and B) in the air gap. Theoretically, this requires a sinusoidally distributed winding in each phase. If each phase winding has a total of Ns turns (i.e., 2Ns conductors), the conductor density ns(\u03b8) in phase-a of Fig. 2-1b can be defined as n N s s( ) sin , .\u03b8 \u03b8 \u03b8 \u03c0= \u2264 \u2264 2 0 (2-1) The angle \u03b8 is measured in the counter-clockwise direction with respect to the phase-a magnetic axis. rather than restricting the conductor density expression to a region 0\u00a0<\u00a0\u03b8\u00a0<\u00a0\u03c0, we can interpret the negative of the conductor density in the region \u03c0\u00a0<\u00a0\u03b8\u00a0<\u00a02\u03c0 in Eq. (2-1) as being associated with carrying the current in the opposite direction, as indicated in Fig. 2-1b. In a multi-pole machine (with p\u00a0 >\u00a0 2), the peak conductor density remains Ns/2, as in Eq. (2-1) for a two-pole machine, but the angle \u03b8 is expressed in electrical radians. Therefore, we will always express angles in all equations throughout this book by \u03b8 in electrical radians, thus making the expressions for field distributions and space vectors applicable to two-pole as well as multi-pole machines. For further discussion on this, please refer to example 9-2 in reference [1]. The current ia through this sinusoidally distributed winding results in the air gap a magnetic field (mmf, flux density, and field intensity) that is co-sinusoidally distributed with respect to the position \u03b8 away from the magnetic axis of the phase 8 INduCTIoN MaCHINE EQuaTIoNS IN PHaSE QuaNTITIES H N p a s g a( ) cos\u03b8 \u03b8= i (2-2) B H N p a o a o s g a( ) cos\u03b8 \u00b5 \u03b8 \u00b5 \u03b8= ( )=       i (2-3) and F H N p a g a s a\u03b8 \u03b8 \u03b8( )= ( )= i cos "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000703_j.automatica.2004.08.005-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000703_j.automatica.2004.08.005-Figure1-1.png",
        "caption": "Fig. 1. Interpretation of tracking errors.",
        "texts": [
            " The main ideas to solve the control objective are as follows: (1) Introduce a coordinate to change the ship position (x, y) such that the ship model (1) can be transformed to a diagonal form to overcome difficulties caused by non-zero off-diagonal terms in the system matrices. (2) Interpret tracking errors in a frame attached to the path such that the tracking error dynamics are of a triangular form to which the backstepping technique can be applied. (3) Use the orientation tracking error as a virtual control to stabilize the cross-track error. Introduce the following coordinate transformation (changing the ship position, see Fig. 1): x\u0304 = x + cos( ), y\u0304 = y + sin( ), v\u0304 = v + r, (12) where =m23/m22. Using the above change of coordinates, the ship dynamics (1) can be written as \u02d9\u0304x = u cos( ) \u2212 v\u0304 sin( ), \u02d9\u0304y = u sin( ) + v\u0304 cos( ), \u0307 = r, u\u0307 = \u0304u \u02d9\u0304v = \u2212 ur \u2212 v\u0304 + r, r\u0307 = \u0304r (13) where we have chosen primary controls u and r as u = m11\u0304u \u2212 m22vr \u2212 ((m23 + m32)/2)r2 + d11u, r = (m22m33 \u2212 m23m32)\u0304r/m22 \u2212 ((m11m22 \u2212 m2 22) \u00d7 uv + (m11m32 \u2212 m22(m23 + m32)/2)ur + (m32d22 \u2212 m22d32)v \u2212 (m22d33 \u2212 m32d23)r)/m22 (14) with \u0304u and \u0304r being considered as new controls to be designed later. Remark 3. After ship system (1) is transformed to the diagonal form (13), the methods mentioned in the Introduction can be used to obtain controllers for specific tasks such as stabilization and model reference trajectory tracking if (x\u0304, y\u0304) are considered as the ship position instead of x, y. We now interpret the path-tracking errors in a frame attached to the path (Samson, 1991; Pettersen, 1996) as follows (see Fig. 1) [xe, ye, \u0304e]T = JT( )[x\u0304 \u2212 xd, y\u0304 \u2212 yd, \u2212 d]T, (15) where d is the angle between the path and the X-axis defined by d = arctan(y\u2032 d(s)/x \u2032 d(s)) (16) with x\u2032 d(s) and y\u2032 d(s) being defined in (7). In Fig. 1, OXY is the earth-fixed frame; ObXbYb is a frame attached to the path such that ObXb and ObYb are parallel to the surge and sway axes of the ship; u\u0304d is tangential to the path; Oc is the center of gravity; and Os is referred to as the center of oscillation of the ship. Therefore xe, ye and \u0304e can be referred to as tangential tracking error, cross-tracking error and heading error, respectively. Differentiating (15) along the solutions of the first three equations of (13) results in the kinematic error dynamics x\u0307e = u \u2212 u\u0304d cos(\u0304e) + rye, y\u0307e = v\u0304 + u\u0304d sin(\u0304e) \u2212 rxe, \u02d9\u0304 e = r \u2212 r\u0304d, (17) where u\u0304d and r\u0304d are given in (7)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000109_s0007-8506(07)63450-7-Figure39-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000109_s0007-8506(07)63450-7-Figure39-1.png",
        "caption": "Figure 39: Beam transformation system for high-power laser diode bars [ 1031.",
        "texts": [
            " The assembly of microcomponents onto a preprocessed substrate can be decomposed into a series of operations like picking components, dispensing adhesives, positioning, assembly and inspection steps at chip level. The main challenges, apart from developing suitable processing steps, for a successful development of such processing centres are contamination control, standard mechanical and software interfaces, process control, production 468 Keynote Papers beam by means of an actively aligned fast-axis collimation (FAC) lens, as shown in figure 39. The central part of the assembly system is a 6-axis positioning system. The most critical step in the assembly process is the adjustment and fixing of the FAC lens. To give an idea, for a 200 pm fibre coupled system a 1 pm FAC height decentring results in about 50% excess loss. Assembly is carried out in closed loop with feedback from an intensity profile measurement. In its final position, the lens is glued to the heat sink while the laser operates at maximum output power. 10 EXAMPLES OF ASSEMBLED MICROPRODUCTS Siemens developed a small-signal relay fabricated by silicon micromachining and using an electrostatic actuator [I 051"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002943_j.jsv.2014.10.004-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002943_j.jsv.2014.10.004-Figure1-1.png",
        "caption": "Fig. 1. Diagram illustrating the ball bearing and the coordinate system used to describe relative displacements (\u03b4x,\u03b4y,\u03b4x) and rotations (\u03b8x,\u03b8y) between the inner and outer raceways; (left) radial view; (right) axial view.",
        "texts": [
            " Concluding remarks are presented in Section 5. This section presents the analytical formulation of the load distribution and varying effective stiffness of a ball bearing assembly with a raceway defect of varying circumferential extent, depth, and surface roughness. The varying stiffness is calculated as a function of cage angular position while assuming the cage is stationary. An outer raceway defect is considered in this paper and the method can easily be adapted to the case of an inner raceway defect. Fig. 1 presents a diagram of a ball bearing with an outer raceway defect as well as the coordinate system and nomenclature used in the formulation of the bearing stiffness matrix. The relative displacements and rotations between the inner and outer raceways are contained in a vector q defined as q\u00bc \u00bd\u03b4x \u03b4y \u03b4z \u03b8x \u03b8y T; (1) where \u03b4x, \u03b4y and \u03b4z are the relative displacements in the x, y and z directions, and \u03b8x and \u03b8y are the relative rotations around the x and y axes. The bearing is subjected to static loads and moments which are contained in a vector F defined as F\u00bc \u00bdFx Fy Fz Mx My T; (2) where Fx, Fy and Fz are the static force loads in the radial (x, y) and axial (z) directions, and Mx and My are the static moment loads around the x and y axes. The shaft in Fig. 1 rotates at a run speed \u03c9s \u00bc 2\u03c0f s. For a bearing with pitch diameter Dp, a loaded contact angle \u03b1, a ball diameter Db, the resulting nominal cage speed \u03c9c \u00bc 2\u03c0f c is given by \u03c9c \u00bc \u03c9s 2 1 Db cos \u03b1 Dp : (3) The angular position \u03d5j of ball j shown in Fig. 1 is defined as \u03d5j \u00bc\u03d5c\u00fe 2\u03c0\u00f0j 1\u00de Nb ; j\u00bc 1 to Nb; (4) with \u03d5c the cage angular position and Nb the number of balls. Eq. (4) defines the cage angular position to coincide with ball j\u00bc1. For the case of an outer raceway defect considered here, the defect frequency is given by the outer raceway ball pass frequency f bpo \u00bcNbf c: (5) In the diagram of the bearing shown in Fig. 1, the outer raceway defect has a circumferential extent defined by \u0394\u03d5f and is centered at an angle \u03d5f. The defect location \u03d5f is constant for an outer raceway defect but rotates at the shaft speed \u03c9s for an inner raceway defect, such that \u03d5f \u00f0t\u00de \u00bc\u03d5f \u00f00\u00de\u00fe\u03c9st. The parametric study presented in Section 3 considers square-shaped outer raceway defects of depth h for which a defect depth profile d\u00f0\u03d5j\u00de is generated as d\u00f0\u03d5j\u00de \u00bc min h; r2b ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b 0:25R2 o\u00f0\u03d5j \u03d5f \u00fe0:5\u0394\u03d5f \u00de2 q if \u03d5f 0:5\u0394\u03d5f o\u03d5jr\u03d5f min h; r2b ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b 0:25R2 o\u00f0\u03d5f \u00fe0:5\u0394\u03d5f \u03d5j\u00de2 q if \u03d5f o\u03d5jo\u03d5f \u00fe0:5\u0394\u03d5f 0 if \u03d5f \u00fe0:5\u0394\u03d5f r\u03d5jr\u03d5f 0:5\u0394\u03d5f 8>>< >>: (6) where d\u00f0\u03d5j\u00de is the defect depth at the ball angular position \u03d5j, rb is the ball radius, and Ro is the outer raceway radius",
            " Note that for the smaller defect with \u0394\u03d5f \u00bc 51, the ball's size prevents it from touching the bottom of the defect. In this section, the Hertzian contact deformations for the defect-free bearing case [27] are modified to account for the presence of a raceway defect with a depth profile d\u00f0\u03d5j\u00de. The contact deformation \u03b4j for ball j is given by \u03b4j \u00bc A A0; \u03b4j40 0; \u03b4jr0; ( (7) where A and A0 are the loaded and unloaded relative distance between the inner and outer raceway groove curvature centers ai and ao, respectively, as illustrated in Fig. 1. The loaded relative distance A is defined as A\u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u03b4n2 rj \u00fe\u03b4n2 zj q ; (8) where \u03b4n rj \u00bc A0 cos \u03b10\u00fe\u03b4rj (9) \u03b4n zj \u00bc A0 sin \u03b10\u00fe\u03b4zj: (10) In Eq. (9), the effective displacement \u03b4rj and \u03b4zj of ball j in the radial and axial directions are calculated from the relative bearing displacements q as \u03b4rj \u00bc \u03b4x cos \u03d5j\u00fe\u03b4y sin \u03d5j rL d\u00f0\u03d5j\u00de cos\u03b10 (11) \u03b4zj \u00bc \u03b4z\u00ferd\u00f0\u03b8x sin\u03d5j \u03b8y cos\u03d5j\u00de d\u00f0\u03d5j\u00de sin\u03b10; (12) where d\u00f0\u03d5j\u00de is the defect depth profile evaluated at the ball angular position \u03d5j, rL the radial clearance, and rd the radial distance of the inner raceway groove curvature center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002403_tmag.2017.2658634-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002403_tmag.2017.2658634-Figure7-1.png",
        "caption": "Fig. 7. Flux lines and flux density distribution under open circuit. (a) Proposed PMV machine. (b) Regular SPMV machine.",
        "texts": [
            " 5-7, open-circuit characteristics of the two machines are shown at a speed of 600 r/min. As shown in Fig. 5, expressions (7) and (8) are validated in the spectra analysis of airgap flux density. And the assumption that the proposed machine can be treated as the superposition of two machines is validated, too. The enlarged flux density of proposed machine is responsible for the enhancement of electromagnetic performance, and EMF from consequent or Halbach part share same frequency. Meanwhile, it\u2019s seen from Fig. 7 that leakage flux of the proposed machine is obviously decreased and the utilization of silicon steel for the proposed machine is much better while the tooth tips are slightly saturated. When \u03b2 is selected to be 40%, the torque versus current curves of the proposed and regular PMV machine are shown in Fig. 8, and the corresponding torque ripple values are also given. As shown, the average torque of proposed machine is much larger than the regular one under same current values. It\u2019s worth noting that the proposed PMV machine produces 54"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000878_j.jmapro.2014.04.001-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000878_j.jmapro.2014.04.001-Figure2-1.png",
        "caption": "Fig. 2. The hexahedral mesh structure of the metal powder bed.",
        "texts": [
            "7\u2212 R) (8) The modelling is carried out using the commercially available finite element package. In this study, the FEA method is used to calculate the temperature distribution of laser irradiated SS316L powder bed. An Nd-YAG-laser beam is used to melt the powder bed thickness of 0.5 mm. The melting process is briefly illustrated in Fig. 1, where the theoretically Gaussian beam is applied on the powder surface. Eventually laser beam moves over a distance of 10 mm along the x axis. The hexahedral mesh structure of the metal powder SS316L bed is shown in Fig. 2. The mesh size chosen is 50 m. On the travelling path of the laser, the size of elements is optimized, balancing the demand for simulating precision and computational efficiency, which turns out to be smaller than that in other regions. The phys- erimental investigations on laser melting of stainless steel 316L apro.2014.04.001 ical parameters of SS316L [17] has been used to develop a model is shown in Table 2. The geometry of the FEM model represents a single powder layer (thickness 100 m) together with substrate materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000499_j.phpro.2010.08.065-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000499_j.phpro.2010.08.065-Figure12-1.png",
        "caption": "Fig. 12. Capillary stability of segmental cylinder of a liquid on a solid substrate (hatched): (a) non-disturbed; (b) disturbed; (c) stability map",
        "texts": [
            " The Plateau-Rayleigh analysis of the capillary instability of an infinitely long circular cylinder of a liquid indicates that such a cylinder is stable against axial harmonic disturbances of its radius with wavelengths \u03bb less than the circumference of the cylinder. The necessary and sufficient condition of stability is [24] 1> \u03bb \u03c0D , (25) where D is the diameter. The melt cylinder is not free at SLM but is bounded to the substrate. Therefore, below the similar problem is studied for a segmental cylinder of a liquid attached to a solid substrate by a contact band with a fixed width as shown in Fig. 12. The contact width is specified by angle \u03a6 in Fig. 12 (a). The segmental cylinder is stable if the disturbance increases its surface. This gives the stability condition [25] \u03a6\u2212\u03a6+\u03a6 \u03a6\u2212\u03a6+\u03a6> \u03bb \u03c0 2sin3)2cos2(2 2sin)2cos1(2D , (26) applicable at \u03a6 > \u03c0/2. According to Ref. [25] the segmental cylinder is stable at any wavelength if \u03a6 < \u03c0/2 (less than a half cylinder). In the limit of circular cylinder, \u03a6 = \u03c0, Eq. (26) gives 3 2> \u03bb \u03c0D , (27) which differs from the result of Plateau and Rayleigh by Eq. (25) for the free circular cylinder because the segmental cylinder with \u03a6 = \u03c0 is still attached to the substrate by a line and deforms with the loss of the axial symmetry. Figure 12 (c) compares Eqs. (25) and (26) and shows that the segmental cylinder is more stable that the free circular one: in the filled domain of the parameters the free circular cylinder is instable while the segmental cylinder is instable only near the bottom right corner of this rectangle in the zone limited by the curve drawn according to Eq. (26). Circles on the stability map in Fig. 12 (c) correspond to parameters of stable experimentally observed single vectors [3]. The six circles on the top half of the map are obtained for steel 316L with the layer thickness of 50 \u03bcm and the nominal laser power of 50 W. The numbers near these points mean the scanning velocity. The lowest circle is obtained for a Co-Cr alloy at a considerably greater scanning velocity. All the experimental points are situated in the stability domain as predicted by Eq. (26). Crosses correspond to numerical experiments with various powder thickness L (marked near them) shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002474_j.mechmachtheory.2014.09.011-Figure3-1.png",
        "caption": "Fig. 3. Face-contact model of a pair of spur gears used for loaded tooth contact analysis.",
        "texts": [
            " LTCA of a pair of spur gears with misalignment error and tooth modifications In previous research [11,12], a face-contact model of contact teeth and self-developed FEM software were used to conduct LTCA, MS, LSR and CS calculations of a pair of spur gears withmachining errors, assembly errors and toothmodifications. But effects of these errors and modifications on tooth engagements couldn't be investigated completely. So, in the paper, the same FEM model and software are used again to finish the research that couldn't be finished in the last research. It has been confirmed in the previous research [11,12] that the FEMmodel and software canmake correct calculations of toothMS, LSR and CS of a pair of spur gears with errors and modifications. Fig. 3 is an image of the face-contact model used for LTCA of a pair of spur gears. This face-contact model is different from a linecontact model in that tooth contact is assumed to be on a reference facewith a contact width \u201cWidth\u201d on the contact tooth surfaces as shown in Fig. 3(a). The line-contact model only assumes that tooth contact is only on the geometric contact lines. When FEM is used for LTCA, face contact of the contact teeth on the reference faces is replaced by the contact of many pairs of contact points on the reference faces as shown in Fig. 3. In Fig. 3(b), (k\u2013k\u2032) is an optional pair of contact points on the reference faces. k is the point on the reference face of Gear \u2780, and k\u2032 is the responsive contact point on the reference face of Gear \u2781. \u03b5k is a gap between the pair of points (k\u2013k\u2032). Loads between the pairs of the contact points can be calculated through conducting LTCA using the mathematical programming method [13,14] combined with FEM if the total load of the pair of gears along the line of action, gaps between the pairs of contact points and deformation influence coefficients of the pairs of contact points are known [11\u201314]",
            " 7, the abscissa is tooth engagement positions. It is also expressed by the contact ratio (=1.60) of the pair of the gears. The ordinate of Fig. 7 is the calculated LSR of the contact teeth. Fig. 8 shows contour line graphs of tooth CS of the ideal gears at Position 6. Since Position 6 is a double pair tooth contact position, Fig. 8(b) and (c) is the CS on the first and second pairs of contact teeth respectively. In Fig. 8, the abscissa is the tooth longitudinal dimension and the ordinate is the contact width \u201cWidth\u201d as shown in Fig. 3. From Fig. 8, it is found that CS of the ideal gears are uniform distributions along the longitude. Geometrical contact lines of the first and second pairs of contact teeth are also illustrated in Fig. 8. It is found that the maximum CS of the first and second pairs of contact teeth happened on the geometrical contact lines. Also, the maximum CS of the first pair of contact teeth is about 2 times greater than that of the second pair of contact teeth. In the last research [12], effects of the misalignment errors of a pair of gears on tooth CS, root bending stresses and LSR were investigated",
            " Tooth MS of a pair of gears is an important factor to affect dynamic behavior of the pair of gears. Of course, it is necessary to know the value of tooth MS in advance if vibration analyses are made for a pair of gears or a geared mechanical system. Though there are many researches on tooth MS analyses of a pair of gears, very a few investigated the relationship between tooth MS and transmitted torque. This is because this investigation is a difficult thing to do if a face-contact model of the contact teeth as shown in Fig. 3 is not used. So, this paper conducts this investigation here using the face-contactmodel of the contact teeth and FEM. Calculation results are given in the following. The similar research was also conducted by Kiekbusch et al. [21]. Since a different method was used by Kiekbusch, a different expression method is used for calculation results of tooth MS. Fig. 19(a) shows MS curves of the ideal gears under several different torque loads. Fig. 19(b) is a relationship between MS at Position 7 and the torque loads"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003293_s00170-015-7989-y-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003293_s00170-015-7989-y-Figure7-1.png",
        "caption": "Fig. 7 Dimensions of the steel tube and the substrate",
        "texts": [
            " A new stress equilibrium is reached after each pass, and the updated residual stresses and distortion are calculated with the use of the finite element method. The proposed methodology is applied for predicting the residual stresses and distortion of a steel tube that is fabricated by laser cladding on a substrate of the same material and is then subjected to surface finishing by HSM. The tube is 25 mm high with an outer diameter of 52.4 mm, while its thickness is equal to 2.2 mm. The substrate\u2019s dimensions are 200\u00d7200\u00d710 mm with the cylinder positioned at its center. The whole structure is illustrated in Fig. 7. In laser cladding, the material is fed coaxially with the laser beam in the form of powder and is delivered on the substrate. The powder melts when coming in contact with the substrate which is heated by the laser beam, forming a bell-shaped melt pool. As the laser moves, the already scanned regions are gradually cooling and the material solidifies. HSM is an advanced machining process utilizing a different chip formation mechanism than conventional machining [27]. HSM exhibits great potential and is considered as a key technology for manufacturing applications [27, 28]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000477_0079-6425(63)90037-9-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000477_0079-6425(63)90037-9-Figure7-1.png",
        "caption": "Fig. 7. Diagramatic representation of steady state growth of a lamellar eutectic. (From Tiller Liquid Metals and Solidification 1958, American Society for Metals, Metals Park, Ohio.~18~)",
        "texts": [
            " Lamplough and Scott H2~ (1914) repeated Vogel's experiments and supported Vogel's view of simultaneous growth of the two phases, and also observed that increasing the growth rate led to a finer eutectic structure. Straumanis and Brakss tl~ (1935) later verified that the mechanism of growth of lamellar eutectic alloys was by the simultaneous edgewise growth of both phases by conducting experiments in which the heat flow direction was controlled. An idealized drawing representing the growth of a lamellar eutectic alloy is given in Fig. 7. The average composition of the solid is exactly the same as the composition of the liquid from which it freezes, although the component phases ~. and ~, of the solid can be of widely different compositions. Dt~ring solidification the ~. phase rejects atoms of B and the 13 phase rejects atoms of A. Under steady state growth conditions, the rate of rejection of B atoms by the ~. phase is equal to the rate of rejection of A atoms by the ~3 phase. For any particular growth rate, lateral concentration gradients are set up ahead of the interface in Fig. 7 to give the required amount of diffusion of the two species of atoms to stabilize the steady state interlamellar spacing. A mathematical analysis of the diffusion problem associated with this co-operative type of growth phenomenon is extremely difficult, and as yet the exact solution of the Laplace equation has never been evaluated quantitatively. There have been three different attempts, however, to obtain approximate numerical solutions of the diffusion equations for the analogous solid state reaction of the eutectoid decomposition of austenite to pear}ire",
            " The value of AT will then be constant across the interface for any particular growth rate. The rejection of B atom_, from the ~ lamellae will be approximately uniform across the whole width of the phase, and similarly for the rejection of A atoms from the ,3 lamellae. If no lateral diffusion of the rejected solute elements were allowed, for example by having imaginary membranes extending in the liquid from the positions E U T E C T I C A L L O Y S O L I D I F I C A T I O N 111 of the interphase boundaries in Fig. 7, the solute build-up ahead of the lamellae would attain the steady state values given by the formulae: C~ = CE (1 --k~) I-- Rx) / . ~ e x p - - - - D - - -- CE (2a) C L = CE(1 --k~.~) (-- Rx) ,~ k5 exp D i CE (2b) where x = distance measured from solid-liquid interface k s = partition coefficient of B in u. k a = partition coefficient of A in ~ D = liquid diffusion coefficient. In general C~ ~: C~. If we now imagine the real case where the membranes are removed, there will be lateral diffusion between the two regions rich in solute and under steady state conditions the build up of solute ahead of the two phases will be much less than that given by equations (2a) and (2b)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure24.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure24.12-1.png",
        "caption": "Fig. 24.12 The fourth design: \u2018Sharkie\u2019",
        "texts": [
            " There is a stickman, which is a tissue paper container, lain on the top of \u2018Desire\u2019. The happy and bright smile on the stickman may cheer users with some positive emotions. Users can play with the stickman and have more interactions with their companion. The tissue paper 24 Consumer Goods 717 container has two choices of scents, which are chocolate and milk. A temporary waste storage, hidden at the bottom of the container, is designed for users to throw their waste easily and conveniently. 718 C.-H. Chen et al. The fourth design, \u2018Sharkie\u2019 (see Fig. 24.12), is a shark-shaped biscuit container with white colour and glossy surface. It is a screw lock container. There are some functions available. Users can estimate the level of cookies inside \u2018Sharkie\u2019 through the transparent eyes. \u2018Sharkie\u2019s mouth is a tissue paper holder. There is an inbuilt cutter in the fin for users to open food packaging. As shown in Fig. 24.12, users can slide the food packaging downward through the inbuilt cutter to create a small opening in the packaging. The cutter is built in the fin to ensure safety of users especially children. The slit is designed narrow enough to avoid children to put in their fingers. The fin comes with a variety of scents for users to choose, including fruits, sweet, mint, coffee, perfume, etc. The fifth design, \u2018FreshMint\u2019 (see Fig. 24.13), is a tooth-shaped biscuit container with glossy surface. It is a snap-fit container"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001645_j.jmatprotec.2017.06.044-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001645_j.jmatprotec.2017.06.044-Figure6-1.png",
        "caption": "Fig. 6. The temperature gradient along Y direction using different laser parameters.",
        "texts": [
            " (2007)\u2019s research, the dimensionless Marangoni number Ma can be assessed by: )( ))()(( w w dx dT dT d M a     (4) where dT/dx is the temperature gradient within the melt pool, w is the linear size of the pool, \u03ba is the thermal diffusivity and \u03bc is the dynamic viscosity. As such, the Ma is determined by the temperature gradient dT/dx, the dimension of melt pool and the dynamic viscosity of liquid simultaneously. The dynamic viscosity \u03bc of the melt can be determined as (Gu et al., 2012):  Tk m B15 16  (5) where m is the atomic mass, kB represents the Boltzmann constant. The temperature gradients along Y direction using different laser parameters are calculated and given in Fig. 6 quantificationally. It can be seen that, there is an enormous difference in the maximal temperature gradient between powder zone and as-fabricated zone; the temperature gradients in all regions constantly reduce with the applied \u03c9 decreasing. As the \u03c9 is applied at 120 J/mm3, the maximal temperature gradient in powder zone and as-fabricated zone is 1.47 \u00d7 107 K/m and 4.65 \u00d7 106 K/m, respectively. Meanwhile, a small scan speed v corresponds to an elevated operative T, due to the longer dwelling time of the laser beam on the surface of melt pool",
            " As such, an enormous temperature gradient, a significantly reduced dynamic viscosity \u03bc and a large dimension of melt pool can lead to an enhanced Ma (Eq. (4)), hence reinforcing the ability of melt flow strongly. Fig. 7 gives the velocity field within the cross-sections of the melt pool using different processing parameters. It can be seen that, when the \u03c9 is 120 J/mm3, the maximal melt flow velocity within melt pool is calculated about 15.7 m/s (Fig. 7(a)); the location of the maximal melt flow velocity is located at 21.2 \u03bcm, which is highly corresponding to the location of the maximal temperature gradient as shown in Fig. 6. From Fig. 7(a), it can be seen that the Marangoni flow exhibits a radially outward flow pattern and, the upward direction of the melt in the region, Z\u226527.5 \u03bcm, with the average melt velocity of 4 m/s indicates the formation of the evaporation phenomenon caused by the overheating of the melt irradiated by the laser beam. This can cause significant spatter phenomenon during selective laser melting and induce liquid fluctuation phenomenon. Generally, the orientation of Marangoni convection implies the direction of heat and mass transfer within the melt"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000736_0278364904047392-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000736_0278364904047392-Figure6-1.png",
        "caption": "Fig. 6. Physical interpretations of cos\u03b8 = 0.",
        "texts": [
            " (16) and (17) do not yield a solution, since, if \u03b1\u0307 = \u03bd1 = \u03bd2 = 0, both a and b are undefined. Physically, the lack of a solution results from the fact that a stationary rover can have an infinite set of possible contact angles at each wheel. The second special case occurs when cos\u03b8 equals zero. In this case, \u03b32 = \u00b1\u03c0/2 + \u03b1 from the definition of \u03b8 , and eq. (18) yields the solution \u03b31 = \u00b1\u03c0/2 + \u03b1. Physically, this corresponds to two possible cases: the rover undergoing pure translation or pure rotation (see Figure 6). While these cases are unlikely to occur in practice, they are easily detectable. For the case of pure rotation, \u03bd1 = \u2212\u03bd2. The solutions for \u03b31 and \u03b32 can be written by inspection as \u03b31 = \u03b1 + \u03c0 2 sgn (\u03b1\u0307) (20) at Universitats-Landesbibliothek on December 12, 2013ijr.sagepub.comDownloaded from \u03b32 = \u03b1 \u2212 \u03c0 2 sgn (\u03b1\u0307) . (21) For the case of pure translation, \u03b1\u0307 = 0, and \u03bd1= \u03bd2. Thus, h is undefined and the system of eqs. (16) and (17) has no solution. However, for low-speed rovers considered in this work, the terrain profile varies slowly with respect to the data sampling rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000472_tsmc.1981.4308713-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000472_tsmc.1981.4308713-Figure1-1.png",
        "caption": "Fig. 1. Length a, and twist a, of a link.",
        "texts": [
            " The base of the manipulator is link 0 and is not considered one of the six links. Link 1 is connected to the base link by joint 1. There is no joint at the end of the final link. The only significance of links is that they maintain a fixed relationship between the manipulator joints at each end of the link (7). Any link can be characterized by two dimensions: the common normal distance a, and an the angle between the axes in a plane perpendicular to an. It is customary to call an \"the length\" and a,n \"the twist\" of the link (see Fig. 1). Generally, two links are connected at each joint axis (see Fig. 2). The axis will have two normals connected to it, one for each link. The relative position of two such connected links is given by d,, the distance between the normals along the joint n axis, and 0On the angle between the normals measured in a plane normal to the axis. dn and 0,n are called 'the distance\" and \"the angle\" between the links, respectively. In order to describe the relationship between links, we will assign coordinate frames to each link"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000337_1.1555660-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000337_1.1555660-Figure9-1.png",
        "caption": "Fig. 9 Modeling schemes used to describe compliant gear bodies: a! ring theory, b! plate theory, and c! numerically obtained eigensolutions or shape functions ~from Vinayak and Singh @4#!",
        "texts": [
            " However, gear dynamics research focused mainly on the mathematical analysis of systems with rigid gear bodies @1,146#. Limited studies on multi-mesh systems with gears have been made, as reported by Vinayak, Singh, and Padmanabhan @5#, which included shaft and bearing deformations and rigid gears. Based on the above discussions, Vinayak and Singh @4# extended the multi-body dynamics modeling strategy for rigid gears to include compliant gear bodies in multi-mesh transmissions, the modeling schemes of which are shown in Fig. 9. They applied their previous ideas @5,147# to rigid gears and compliant gear-like disks separately. The combination of distributed gear mesh stiffness with gear blank compliance models in a multi-body dynamics framework resulted in a set of non-linear differential equations with time-varying coefficients. Recently, Parker, Vijayakar, and Imajo @148# used a finite element/contact mechanics model to study the dynamic response of a spur gear pair with compliant gear bodies, which will be reviewed in the following section, due to the consideration of tooth separation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000110_ac00289a042-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000110_ac00289a042-Figure2-1.png",
        "caption": "Figure 2. A coordinate system for Weling me two-dimensional sensor.",
        "texts": [
            " For substrate concentrations specified in the external medium, the concentrations in the gel are determined by (1) the permeability of the gel, membrane, and adjacent medium to each substrate, (2) the enzyme activity, and (3) the aspect ratio, or ratio of the cross-sectional area of the annular end of the gel layer to the area of the cylindrical face covered by the hydrophobic membrane. These factors ultimately determine the sensor response. ANALYTICAL CHEMISTRY, VOL. 57. NO. 12, OCTOBER 1985 2353 We consider a glucose sensor as shown in Figure 2, having an internal cylindrical oxygen sensor of radius r, and length L that is surrounded by a gel of inner radius r, and outer radius r,. The oxygen sensor is electrochemically active only on its curved surface. The gel contains immobilized glucose oxidase and excess catalase. A hydrophobic layer of specified oxygen permeability is in contact with the outer cylindrical surface of the gel. The analysis here is based on diffusion and reaction of glucose and oxygen within the gel. The chemical reaction given in eq 1 can he generalized as follows Y glucose + O2 - products (2) where Y is a stoichiometry coefficient that has a value of 2 in this case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001642_tie.2017.2674634-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001642_tie.2017.2674634-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor schematic.",
        "texts": [
            " In Section II, the mathematical model of quadrotors is given. Then, the controller design procedure is shown in Section III. Furthermore, the stability analysis is given in Section IV, and the experimental results are presented in Section V. Finally, conclusions are drawn in Section VI. Notations. The norms used in this paper are denoted as: \u2016x\u2016 =\u221a x2 1 + \u00b7 \u00b7 \u00b7+ x2 n, for x \u2208 Rn\u00d71 and \u2016y\u2016\u221e = supt\u2265t0 \u2016y(t)\u2016, for y(t) \u2208 Rn\u00d71. The rotational dynamics of the rigid body of a quadrotor will be considered here. As shown in Fig. 1, an inertial reference frame I = {oI , xI , yI , zI} and a body-fixed frame B = {oB , xB , yB , zB} with the origin locating at the mass center of the rigid body are defined. The orientation from the body-fixed frame B to the inertial reference frame can be represented by a rotation matrix R \u2208 SO(3), which is a group of 3\u00d73 orthogonal matrix with determinant 1 and satisfies that R\u0307 = RS(\u03c9b), (1) where \u03c9b = [\u03c9bi]3\u00d71 \u2208 R3\u00d71 indicates the angular speed expressed in B and S(x) =   0 \u2212x3 x2 x3 0 \u2212x1 \u2212x2 x1 0   "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001255_tro.2012.2217795-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001255_tro.2012.2217795-Figure1-1.png",
        "caption": "Fig. 1. Geometric model of a CDPR with three cables.",
        "texts": [
            ", [26], [28], and [30]), but they do not provide the entire set of equilibrium configurations and they may cause unstable configurations to be inadvertently addressed as stable. The complex spatial behavior of the robot is described, and complete static and stability analyses are presented. To show the generality of the stability algorithm, this is also applied to exemplifying robots with three and four cables. In all numerical examples that are presented in the text, measurements are expressed in SI units, with angles being computed in radians. Fig. 1 shows the model of an underconstrained n\u2013n CDPR, for the case n = 3. The ith cable (i = 1, . . . , n) exits from the fixed base at point Ai , and it is connected to the mobile platform at point Bi . The cable length is \u03c1i , with \u03c1i > 0. Oxyz is a Cartesian coordinate frame that is fixed to the base, with i, j, and k being unit vectors along the coordinate axes. Gx\u2032y\u2032z \u2032 is a Cartesian frame that is attached to the end effector. Without loss of generality, O is chosen to coincide with A1 . The platform pose is described by X = [x;\u03a6], where x is the position vector of G in the fixed frame, and \u03a6 is the array grouping the variables parameterizing the platform orientation with respect to Oxyz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure10-1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure10-1-1.png",
        "caption": "Fig. 10-1 Permanent-magnet synchronous machine (shown with p\u00a0=\u00a02).",
        "texts": [
            " 10-1 INTRODUCTION In the previous course [1], we looked at permanent-magnet synchronous motor drives, also known as \u201cbrushless-dc motor\u201d drives in steady state, where without the help of dq analysis, it was not possible to discuss dynamic control of such drives. In this chapter, we will make use of the dq-analysis of induction machines, which is easily extended to analyze and control synchronous machines. 10-2 d-q ANALYSIS OF PERMANENT MAGNET (NONSALIENT-POLE) SYNCHRONOUS MACHINES In synchronous motors with surface-mounted permanent magnets, the rotor can be considered magnetically round (non-salient) that has the same reluctance along any axis through the center of the machine. A simplified representation of the rotor magnets is shown in Fig. 10-1a. The three-phase stator windings are sinusoidally distributed in space, like in an induction machine, with Ns number of turns per phase. In Fig. 10-1b, d-axis is always aligned with the rotor magnetic axis, with the q-axis 90\u00b0 ahead in the direction of rotation, assumed to be counter-clockwise. The stator three-phase windings are represented by equivalent d- and q-axis windings; each winding has 3 2/ Ns turns, which are sinusoidally distributed. 143 10 Vector Control of Permanent-Magnet Synchronous Motor Drives Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink\u00ae, First Edition. Ned Mohan. \u00a9 2014 John Wiley & Sons, Inc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure3-1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure3-1-1.png",
        "caption": "Fig. 3-1 Representation of stator mmf by equivalent dq windings.",
        "texts": [
            " In most textbooks, this analysis is discussed as a mathematical transformation called the Park\u2019s transformation. In this chapter, we will take a physical approach to this transformation, which is much easier to visualize and arrive at identical results. 28 3 Dynamic Analysis of Induction Machines in Terms of dq Windings Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink\u00ae, First Edition. Ned Mohan. \u00a9 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. 3-2-1 Stator dq Winding Representation In Fig. 3-1a at time t, phase currents ia (t), ib (t), and ic (t) are represented by a stator current space vector i ts( ). A collinear magnetomotive force (mmf) space vector F ts( ) is related to i ts( ) by a factor of (Ns/p), where Ns equals the number of turns per phase and p equals the number of poles: i t i t i t e i t es a a b j c j( ) ( ) ( ) ( )/ /= + +2 3 4 3\u03c0 \u03c0 (3-1) and F t N p i ts a s s a( ) ( ).= (3-2) dq WINDING REPRESENTATION 29 30 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS We should note that the space vector i ts( ) in Fig. 3-1 is written without a superscript \u201ca.\u201d The reason is that a reference axis is needed only to express it mathematically by means of complex numbers. However, i ts( ) in Fig. 3-1 depends on the instantaneous values of phase currents and is independent of the choice of the reference axis to draw it. In the previous course for analyzing ac machines under balanced sinusoidal steady-state conditions, we replaced the three windings by a single hypothetical equivalent winding that produced the same mmf distribution in the air gap. This single winding was sinusoidally distributed with the same number of turns Ns (as any phase winding), with its magnetic axis along the stator current space vector and a current \u020as (peak value of is ) flowing through it. However, for dynamic analysis and control of ac machines, we need two orthogonal windings such that the torque and the flux within the machine can be controlled independently. At any instant of time, the air gap mmf distribution by three phase-windings can also be produced by a set of two orthogonal windings shown in Fig. 3-1b, each sinusoidally distributed with 3 2/ Ns turns: one winding along the d-axis, and the other along the q-axis. The reason for choosing 3 2/ Ns turns will be explained shortly. This dq winding set may be at any arbitrary angle \u03b8da with respect to the phase-a axis. However, the currents isd and isq in these two windings must have specific values, which can be obtained by equating the mmf produced by the dq windings to that produced by the three phase windings and represented by a single winding with Ns turns in Eq. (3-2) 3 2/ , N p i ji N p is sd sq s s d+( )= (3-3) where the stator current space vector is expressed using the d-axis as the reference axis, hence the superscript \u201cd.\u201d Eq. (3-3) results in i ji isd sq s d+( )= 2 3 , (3-4) which shows that the dq winding currents are 2 3/ times the projections of i ts( ) vector along the d- and q-axis, as shown in Fig. 3-1c: dq WINDING REPRESENTATION 31 i i t dsd s= \u00d72 3/ ( )projection of along the -axis (3-5) and i i t qsq s= \u00d72 3/ ( ) .projection of along the -axis (3-6) The factor 2 3/ , reciprocal of the factor 3 2/ used in choosing the number of turns for the dq windings, ensures that the dq-winding currents produce the same mmf distribution as the three-phase winding currents. In Fig. 3-1b, the d and the q windings are mutually decoupled magnetically due to their orthogonal orientation. Choosing 3 2/ Ns turns for each of these windings results in their magnetizing inductance to be Lm (same as the per-phase magnetizing inductance in Chapter 2 for three-phase windings with ia\u00a0+\u00a0ib\u00a0+\u00a0ic\u00a0=\u00a00) for the following reason: the inductance of a winding is proportional to the square of the number of turns and therefore, the magnetizing inductance of any dq winding (noting that there is no mutual inductance between the two orthogonal windings) is dq L L m m winding magnetizing inductance -phase= = ( / ) ( / ) , , 3 2 3 2 2 1 1 2 12 -phase using Eq -=Lm ( ",
            " The phase currents in these equivalent rotor phase windings can be represented by a rotor current space vector, where 32 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS i t i t i t e i t er A A B j C j( ) ( ) ( ) ( ) ,/ /= + +2 3 4 3\u03c0 \u03c0 (3-8) where i t F t N p r A r A s ( ) ( ) / .= (3-9) The mmf F tr ( ) and the rotor current i tr ( ) in Fig. 3-2 can also be produced by the components ird (t) and irq (t) flowing through their respective windings as shown. (Note that the d- and the q-axis are the same as those chosen for the stator in Fig. 3-1. Otherwise, all benefits of the dq-analysis will be lost.) Similar to the stator case, each of the dq windings on the rotor has 3 2/ Ns turns, and a magnetizing inductance of Lm, which is the same as that for the stator dq windings because of the same number of turns (by choice) and the same magnetic path for flux lines. Each of these rotor equivalent windings has a resistance Rr and a leakage inductance L\u2113r (equal to \u2032Rr and \u2032L r , respectively, in the perphase equivalent circuit of induction machines in the previous course)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002621_rob.21673-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002621_rob.21673-Figure17-1.png",
        "caption": "Figure 17. Linear inverted pendulum with spring and damper.",
        "texts": [
            " The Zero Moment Point (ZMP) error generated from the change of CoM height can be compensated for by applying Preview Control again as a dynamic filter (Stasse et al., 2008). When the robot is walking in place with vertical CoM motion, which is a sine wave, the measured ZMP with compensation and the measured ZMP with no compensation can be represented as shown in Figure 16. It can be seen that the measured ZMP with compensation is closer to the reference ZMP. The robot is modeled as linear inverted pendulum with spring and damper and the model is represented in Figure 17. This model is generally used for feedback controller (I. Kim & Oh, 2013), but if the step length becomes Journal of Field Robotics DOI 10.1002/rob longer and the mass of robot increases, compliance becomes a larger problem due to deflections of the links. Thus, an inverse model method was devised to modify the CoM trajectory that was generated in the Preview Control. This method applies a feedforward controller for the walking pattern; the transfer function can be calculated as G(s) = x ref CoM xinv CoM = k ml2 + c ml2 s s2 + c ml2 s + k ml2 \u2212 g l , where k, c, m, l, and g are the spring coefficient, damping coefficient, total mass, and acceleration due to gravity, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.17-1.png",
        "caption": "Fig. 3.17 Local momentum theory applied to a rotor disc",
        "texts": [
            " These can be sufficient to stall the blade in certain conditions and are important for predicting rotor stall boundaries and the resulting flight dynamics at the flight envelope limits. We shall return to this last topic later in the discussion on advanced, high-fidelity modelling. Before leaving inflow, however, we shall examine the theoretical developments needed to improve the prediction of the nonuniform and unsteady components. 106 Helicopter and Tiltrotor Flight Dynamics Local-Differential Momentum Theory and Dynamic Inflow We begin by considering the simple momentum theory applied to the rotor disc element shown in Figure 3.17. We make the gross assumption that the relationship between the change in momentum and the work done by the load across the element applies locally as well as globally, giving the equations for the mass flow through the element and the thrust differential as shown in Eqs. (3.161) and (3.162). dm\u0307 = \ud835\udf0cVrbdrb d\ud835\udf13 (3.161) dT = dm\u03072vi (3.162) Using the two-dimensional blade element theory, these can be combined into the form Nb 2\ud835\udf0b (1 2 \ud835\udf0ca0c(\ud835\udf03U 2 T + UTUp)drb d\ud835\udf13 ) = 2\ud835\udf0crb(\ud835\udf072 + (\ud835\udf06i \u2212 \ud835\udf07z)2)1\u22152\ud835\udf06i drb d\ud835\udf13 (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002473_amr.633.135-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002473_amr.633.135-Figure6-1.png",
        "caption": "Fig. 6. Parametric optimisation geometry. Cutaways included to show internal features",
        "texts": [
            " Topographic optimisation offers an excellent opportunity to identify morphologies that are fundamentally efficient for the specific design scenario; however, contemporary algorithms generate results that include geometric features that do not correctly represent the optimal geometry, notably checkerboard effects, where the solution geometry incorrectly includes cubic facets due to discretization process (Fig. 5). To overcome these geometric effects, it is appropriate to apply topographic methods initially, in order to identify a preferred morphology, and then to develop a parametric model based on the topographically optimal result (Fig. 6). Input Data. Robust optimisation outcomes can only be achieved if based on a comprehensive understanding of the associated mechanical properties and manufacturing limitations. For aerospace applications the dominant failure mode is often fatigue, and the fatigue strength, including effects of surface finish (as manufactured or machined) and post production processing (shot blasting, hot isostatic pressing, heat treatment as outline above) must be quantified. Although fatigue is often the dominant failure mode for high-value aerospace components, all possible failure modes must be 140 Advances in Engineering Materials, Product and Systems Design accommodated, as the optimisation process may reveal latent failure modes that were not previously relevant",
            " Case Study: Geometric Optimisation of High-Value Aerospace Bracket. The design method of Fig. 4 is applied to identify the optimal design for a high-value aerospace application: a structural hinge assembly. Based on the quantified mechanical properties, allowable design volume and physical constraints; a topographic optimization algorithm was applied for four distinct load cases (Fig. 5). A component that can accommodate these distinct loads is defined by superposition, resulting in a CAD geometry that is appropriate for parametric optimisation (Fig. 6). The CAD geometry of Fig. 6 includes several features that do not exist in the topographically optimal morphology. These include features important for component manufacture, hollow truss structures and internal scaffolds based on micro-scale optimization: \u2022 Internal gussets used to allow manufacture of overhang features. \u2022 Truss-like morphology with hollow elements. \u2022 Bulkhead features to provide compressive strength. \u2022 Annular reinforcement to resist local buckling. These features should be added based on design experience",
            " The highvalue aerospace component designed in this work has been subject to manufacturability optimisation. In particular, regions with undesirable inclination angle have been identified and overcome by geometry modification or the use of support material (Fig. 8): \u2022 Geometry modification \u2013 the inclination angle of the upper truss element is highly acute. To avoid the necessity of support material, the horizontal element was inclined slightly. Note that this inclination introduces staircase effects (Fig. 8, inset). Advanced Materials Research Vol. 633 143 \u2022 Internal gussets \u2013 Fig. 6 showed the example of added internal gussets to allow for the manufacture of the optimized overhang features, thereby minimizing the use of support material. \u2022 Minor support \u2013 the annular reinforcement rings initially required support material to allow manufacture. The detail design was modified to reduce the necessity for support material, however, minor use of support structures was still required. \u2022 Large scale support \u2013 the annular feature geometry is set by the mating components, and cannot be modified"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001140_1.4025746-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001140_1.4025746-Figure12-1.png",
        "caption": "Fig. 12 The effect of electron beam scanning speed on the molten pool half width with 14 mA as an electron beam current, (a) scanning speed 5 100 mm/s, (b) scanning speed 5 300 mm/s, and (c) scanning speed 5 500 mm/s",
        "texts": [
            " The top side compares the numerical and experimental results of the molten pool size, while the bottom side shows the numerically obtained temperature distribution in and around the molten pool. Results and Discussions The Influence of EBM VR Parameters. As shown in Fig. 10, the molten pool width increases by increasing the electron beam current. The increase of the electron beam current from 8 to 14 mA at a constant electron beam scanning speed of 100 mm/s is associated with an increase of the heat input applied to the powder bed surface, where more heat was distributed on the same volume of material. Therefore, the highest beam current results in the largest molten pool size. Figure 12 compares the effect of electron beam scanning speed on the molten pool dimensions at the powder bed top surface, where the electron beam current was set at 14 mA. The black arrow shows the electron beam scanning direction and the dashed line is the representative of Y\u00bc 6 mm. By increasing the electron beam scanning speed, the heat input decreases, and lower heat is provided to increase the temperature of the same volume of material. Therefore, a smaller amount of material reaches the melting temperature that is associated with a decrease in the molten pool width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003767_tie.2019.2947845-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003767_tie.2019.2947845-Figure1-1.png",
        "caption": "Fig. 1. Illustration of UMV path following.",
        "texts": [
            " As a consequence, in combination with the FSO-HLOS guidance and the FUO-based FHC-FSC, the entire HLOS-based finite-time path following (HLOS-FPF) framework for the UMV with complex unknowns is eventually established, and guarantees that both guidance deviations and tracking control errors are globally finite-time stable, such that accurate path-following can be achieved via heading-surge collaborative guidance. The rest of this paper is arranged as follows. Key preliminaries and path-following derivations are formulated in Section II. In Section III, the finite-time sideslip observerbased hyperbolic-tangential LOS guidance scheme is developed. Finite-time tracking controllers of surge and heading, as well as stability analysis, are synthesized in Section IV. Simulation results and comprehensive comparisons are provided in Section V, and conclusions are drawn in Section VI. As shown in Fig. 1, the UMV can be modeled by \u03b7\u0307 = R(\u03c8)\u03bd M\u03bd\u0307 = f (\u03bd ) + \u03c4 + \u03c4 \u03b4(t,\u03bd) (1) where \u03b7 = [x, y, \u03c8]T , \u03bd = [u, v, r]T , rotation matrix R(\u03c8) = [ cos\u03c8 \u2212 sin\u03c8 0 sin\u03c8 cos\u03c8 0 0 0 1 ] , inertia matrix M = diag (m11,m22,m33), control inputs \u03c4 = [\u03c4u, 0, \u03c4r] T , complex unknowns \u03c4 \u03b4 = [\u03c4\u03b4u , \u03c4\u03b4v , \u03c4\u03b4r ] T , nominal dynamics f (\u03bd) = [fu, fv, fr] T with fu = m22vr\u2212d11u, fv = \u2212m11ur\u2212d22v, and fr = \u2212(m22\u2212 m11)uv \u2212 d33r, where d11, d22, and d33 are dampings. Assumption 2.1: Unknowns \u03c4 \u03b4 are differentiable, i.e., \u2016\u03c4\u0307 \u03b4\u2016 \u2264 D (2) for a bounded constant D <\u221e. As shown in Fig. 1, a \u201cvirtual ship1\u201d (xp(\u03b8), yp(\u03b8)) on the predefined path parameterized by a time-dependent variable 1The virtual ship is regarded as a virtually desired point with appropriate dynamics along the path, and works like an imaginary target ship. 0278-0046 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. \u03b8(t) is the tracking target. In this context, a path-tangent (PT) frame is built originating at virtual ship"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000110_ac00289a042-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000110_ac00289a042-Figure1-1.png",
        "caption": "Figure 1. (a) The previous sensor design. Glucose and oxygen both diffuse in the same direction, mainly perpendicular to the plane of the electroda surface. Analogous diffusion regimes have been used for spherical sensors. (b) The two-dimensional design. Glucose and oxygen diffuse axially into the enzyme gel but only oxygen can diffuse radially into the gel through the hydrophobic membrane.",
        "texts": [],
        "surrounding_texts": [
            "All previous designs have required that both oxygen and glucose diffuse into the membrane from the same direction. As shown in Figure la, diffusion to and within the membrane has been mainly perpendicular to the plane of the membrane, for both substrates. This is the case for planar as well as spherical sensors. Such a diffusion regime ideally allows the enzymatic and electrochemical reactions to occur uniformly in the plane of the membrane and across the electrode surface, with substrate concentration gradients developing perpendicular to this plane. The new design is shown schematically in Figure lb. The sensor is a small cylinder made of concentric layers of materials open to the sample medium at one end. The core is a short segment of platinum wire, inactive at the exposed end, which serves as a cylindrical oxygen sensor. When this platinum electrode is properly polarized, oxygen is electrochemically consumed on its curved surface, resulting in a steady oxygen flux from the sample medium that is both radial toward the curved electrode surface and axial from the region in front of the sensor. Adjacent to the electrode is a concentric layer of hydrophilic gel containing the immobilized enzymes. Surrounding this gel layer is a hydrophobic, oxygen-permeable layer or tube, made of a material such as silicone rubber that is impermeable to glucose, which serves as a selectively permeable membrane. Both glucose and oxygen can therefore diffuse into the gel layer through the exposed annular end along a direction parallel to the axis of the cylinder, but only oxygen has radial access to the gel through the membranecovered surface. This gives rise to a two-dimensional supply of oxygen to the enzyme region (radial and axial) and only a one-dimensional supply of glucose (axial). For substrate concentrations specified in the external medium, the concentrations in the gel are determined by (1) the permeability of the gel, membrane, and adjacent medium to each substrate, (2) the enzyme activity, and (3) the aspect ratio, or ratio of the cross-sectional area of the annular end of the gel layer to the area of the cylindrical face covered by the hydrophobic membrane. These factors ultimately determine the sensor response. ANALYTICAL CHEMISTRY, VOL. 57. NO. 12, OCTOBER 1985 2353"
        ]
    },
    {
        "image_filename": "designv10_1_0002714_j.triboint.2011.08.019-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002714_j.triboint.2011.08.019-Figure10-1.png",
        "caption": "Fig. 10. Temperature measuring points on the ball\u2013screw.",
        "texts": [
            " By adjusting the setting pressure of the relief valves amounted on the outlets of hydraulic cylinder, axial load applied for the ball\u2013screw system is adjustable within the range of 1\u20134 KN. Furthermore, there is no lubricant in the bearing housing in order to let the heat flow in the inner raceway of ball bearings totally conduct through the ball\u2013screw. In order to research the thermal characteristics of ball\u2013screw, some other sensors and instruments are employed except for the experimental bench. The infrared radiation thermometers with a resolution of 0.1 1C (as shown in Fig. 10), and corresponding intelligent thermal resistance modulators are used to measure the temperatures of measuring points. The values of temperature sensors are acquired by NI PXI-4351 module installed in PXI-9230 signal acquisition system. Fig. 11 shows the ball\u2013screw system of the experimental bench. The comprehensive coefficient of heat convection with the ambient air is as, and the temperature of the ambient air is Tf. The equation of heat conduction is @2T @x2 \u00bc rc k @T @t \u00fe 4as kd \u00f0T T f \u00de \u00f038\u00de where T is the temperature of the ball\u2013screw, which is the function of time t and the distance x"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure26-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure26-1.png",
        "caption": "Fig. 26. Machining errors on the reference face.",
        "texts": [
            " It is found that tooth contact pattern and the maximum contact stress almost have no changes in this case by comparing Fig. 24 with Fig. 21. But position of the maximum stress distribution line is moved to the side Y < 0 for the effect of misalignment error. Fig. 25 is contour lines of SCS when the misalignment error on the vertical plane of the plane of action is increased from 0.04 into 0.4 . It is found that tooth contact pattern has a bigger change by comparing Fig. 25 with Figs. 24 and 21, but the maximum SCS has a very little change. Fig. 26 is the machining error of the wheel distributed on the reference face as shown in Fig. 1(a). This machining error is used in LTCA and SCS calculations of the pair of gears. Fig. 27 is contour lines of SCS calculated in Case 4. It is found that machining errors have greater effects on tooth contact pattern and contact stress distribution by comparing Fig. 27 with Fig. 21. Fig. 28 is contour lines of SCS calculated in Case 5. It is found that tooth contact pattern is changed from a uniform contact into a center heavy contact for the effect of lead crowning"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003293_s00170-015-7989-y-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003293_s00170-015-7989-y-Figure8-1.png",
        "caption": "Fig. 8 Meshed tube and substrate",
        "texts": [
            " Virfac\u00ae software developed by GeonX is used for performing a transient simulation of the laser cladding process under a fully implicit time integration scheme. The whole model is meshed using hexahedral elements with each node having 1 temperature and 3 translational degrees of freedom (DOFs). A dense mesh is applied to the tube region with the tube being divided in 14 sections in the z-direction and 4928 elements in total. A coarser mesh of 10,836 elements is applied to the substrate in order to reduce computational complexity, as shown in Fig. 8. The mesh on the substrate is getting finer as we move from the substrate\u2019s edges to the interface with the tube. As the model has been developed for methodology demonstration purposes, systematic finite element model development, with the execution of convergence tests, has not been followed. The elements in the tube are inactive at the beginning of the simulation and are activated when required (i.e., when material is added). To achieve this, the simulation uses the quiet element method for the activation of elements [31]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure3.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure3.9-1.png",
        "caption": "Fig. 3.9 Principle design of cylinder-type test transformers. a Single winding and core on ground potential. b Divided windings and core on half potential",
        "texts": [
            " Consequently, the thermal behaviour is limited, which limits also generation of higher reactive test power (Table 3.1). Usually they are provided for short-term operation up to 10 h (Fig. 3.8), long-term operation would require a forced cooling of the oil, e.g. with external coolers connected by houses. In any case, the duty cycle of this type of test transformers should be carefully considered. The insulating cylinder has on both sides metallic covers. The lower cover carries the active part. There are two principles of the design of the active part, one is with one common coaxial LV and HV winding (Fig. 3.9a) and the core on ground potential, the other one is with divided windings and the core on half potential (Fig. 3.9b). The latter requires an insulating support for the core, but it is better adapted to the geometry of the cylinder. The lower windings have the LV potential on its outer side and the HV \u2018\u2018half\u2019\u2019 potential on its inner side. The core is connected to this \u2018\u2018half\u2019\u2019 potential as well as a transfer winding for the upper windings. There, the exciter winding is next to the core, whereas the second HV \u2018\u2018half\u2019\u2019-potential winding is on the outer side. This means, between the two HV 100 h 10 1 0.1 0.01 available test duration 0 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.31-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.31-1.png",
        "caption": "FIGURE 5.31. Spherical wrist of the Pitch-Yaw-Roll type.",
        "texts": [
            " 0R1 = 1RT 0 = \u00a3 Rx1,\u03b8 R T z0,\u03d5 \u00a4T = \u00a3 Rx,\u03b8 R T Z,\u03d5 \u00a4T (5.131) = \u23a1\u23a2\u23a3 \u23a1\u23a3 1 0 0 0 c\u03b8 s\u03b8 0 \u2212s\u03b8 c\u03b8 \u23a4\u23a6\u23a1\u23a3 c\u03d5 \u2212s\u03d5 0 s\u03d5 c\u03d5 0 0 0 1 \u23a4\u23a6T \u23a4\u23a5\u23a6 T = \u23a1\u23a3 cos\u03d5 \u2212 cos \u03b8 sin\u03d5 sin \u03b8 sin\u03d5 sin\u03d5 cos \u03b8 cos\u03d5 \u2212 cos\u03d5 sin \u03b8 0 sin \u03b8 cos \u03b8 \u23a4\u23a6 Therefore, the transformation matrix between the living and dead wrist frames is: 0R2 = 0R1 1R2 = \u00a3 Rx1,\u03b8 R T z0,\u03d5 \u00a4T RT x2,\u03c8 = Rz0,\u03d5R T x1,\u03b8 R T x2,\u03c8 = RZ,\u03d5R T x,\u03b8 R T x,\u03c8 (5.132) = \u23a1\u23a3 c\u03d5 s\u03b8s\u03c8s\u03d5\u2212 c\u03b8c\u03c8s\u03d5 c\u03b8s\u03c8s\u03d5+ c\u03c8s\u03b8s\u03d5 s\u03d5 c\u03b8c\u03c8c\u03d5\u2212 c\u03d5s\u03b8s\u03c8 \u2212c\u03b8c\u03d5s\u03c8 \u2212 c\u03c8c\u03d5s\u03b8 0 c\u03b8s\u03c8 + c\u03c8s\u03b8 c\u03b8c\u03c8 \u2212 s\u03b8s\u03c8 \u23a4\u23a6 Example 163 Pitch-Yaw-Roll spherical wrist. Figure 5.31 illustrates a spherical wrist of the type 3, Pitch-Yaw-Roll. B0 indicates its dead and B2 indicates its living coordinate frames. The transformation matrix 1R2, is a rotation \u03c8 about the local z2-axis. 1R2 = 2RT 1 = RT z2,\u03c8 = RT z,\u03c8 = \u23a1\u23a3 cos\u03c8 \u2212 sin\u03c8 0 sin\u03c8 cos\u03c8 0 0 0 1 \u23a4\u23a6 (5.133) 5. Forward Kinematics 279 To determine the transformation matrix 0R1, we turn B1 first \u03d5deg about the z0-axis, and then \u03b8 deg about the x1-axis. 0R1 = 1RT 0 = \u00a3 Rx1,\u03b8 R T z0,\u03d5 \u00a4T = \u00a3 Rx,\u03b8 R T Z,\u03d5 \u00a4T (5.134) = \u23a1\u23a2\u23a3 \u23a1\u23a3 1 0 0 0 c\u03b8 s\u03b8 0 \u2212s\u03b8 c\u03b8 \u23a4\u23a6\u23a1\u23a3 c\u03d5 \u2212s\u03d5 0 s\u03d5 c\u03d5 0 0 0 1 \u23a4\u23a6T \u23a4\u23a5\u23a6 T = \u23a1\u23a3 cos\u03d5 \u2212 cos \u03b8 sin\u03d5 sin \u03b8 sin\u03d5 sin\u03d5 cos \u03b8 cos\u03d5 \u2212 cos\u03d5 sin \u03b8 0 sin \u03b8 cos \u03b8 \u23a4\u23a6 Therefore, the transformation matrix between the living and dead wrist frames is: 0R2 = 0R1 1R2 = \u00a3 Rx1,\u03b8 R T z0,\u03d5 \u00a4T RT z2,\u03c8 = Rz0,\u03d5R T x1,\u03b8 R T z2,\u03c8 = RZ,\u03d5R T x,\u03b8 R T z,\u03c8 (5",
            " Attach the 2 DOF RkP manipulator of Exercise 27 to the 2R horizontal manipulator of Exercise 28 and make a SCARA manipulator. Solve the forward kinematics problem for the manipulator. 30. F Roll-Pitch-Yaw spherical wrist kinematics. Attach the required DH coordinate frames to the Roll-Pitch-Yaw spherical wrist of Figure 5.30, similar to 5.28, and determine the forward kinematics of the wrist. 31. F Pitch-Yaw-Roll spherical wrist kinematics. Attach the required coordinate DH frames to the Pitch-Yaw-Roll spherical wrist of Figure 5.31, similar to 5.28, and determine the forward kinematics of the wrist. 32. F Assembling a R-P-Y wrist to a spherical arm. Assemble the Roll-Pitch-Yaw spherical wrist of Figure 5.30 to the spherical manipulator of Figure 5.40 and determine the forward kinematics of the robot. 322 5. Forward Kinematics z0 x5 z1 z2 z3 z4 z5 z6 z7 x0 y0 x1 x3 x4 x6 y7 x2 x7 1\u03b8 3\u03b8 2\u03b8 4\u03b8 5\u03b8 6\u03b8 7\u03b8 1 2 3 4 5 6 0 7 Camera Gripper x8 y8 z8 a b FIGURE 5.67. The space shuttle remote manipulator system (SSRMS) with a camere attached to the link (4). 33. F Assembling a P-Y-R wrist to a spherical arm. Assemble the Pitch-Yaw-Roll spherical wrist of Figure 5.31 to the spherical manipulator of Figure 5.40 and determine the forward kinematics of the robot. 34. F SCARA robot with a spherical wrist. Attach the spherical wrist of Exercise 22 to the SCARA manipulator of Exercise 29 and make a 7DOF robot. Change yourDH coordinate frames in the exercises accordingly and solve the forward kinematics problem of the robot. 35. F Modular articulated manipulators by screws. Solve Exercise 15 by screws. 36. F Modular spherical manipulators by screws. Solve Exercise 18 by screws",
            " 3T4 = \u23a1\u23a2\u23a2\u23a3 c\u03b84 0 \u2212s\u03b84 0 s\u03b84 0 c\u03b84 0 0 \u22121 0 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 4T5 = \u23a1\u23a2\u23a2\u23a3 c\u03b85 0 s\u03b85 0 s\u03b85 0 \u2212c\u03b85 0 0 1 0 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 5T6 = \u23a1\u23a2\u23a2\u23a3 c\u03b86 \u2212s\u03b86 0 0 s\u03b86 c\u03b86 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 18. F Roll-Pitch-Yaw spherical wrist kinematics. Attach the required DH coordinate frames to the Roll-Pitch-Yaw spherical wrist of Figure 5.30, similar to 5.28, and determine the forward and inverse kinematics of the wrist. 19. F Pitch-Yaw-Roll spherical wrist kinematics. Attach the required coordinate DH frames to the Pitch-Yaw-Roll spherical wrist of Figure 5.31, similar to 5.28, and determine the forward and inverse kinematics of the wrist. 20. SCARA robot inverse kinematics. Consider the RkRkRkP robot shown in Figure 5.23 with the following transformation matrices. Solve the inverse kinematics and find \u03b81, \u03b82, \u03b83 and d for a given 0T4. 0T1 = \u23a1\u23a2\u23a2\u23a3 cos \u03b81 \u2212 sin \u03b81 0 l1 cos \u03b81 sin \u03b81 cos \u03b81 0 l1 sin \u03b81 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 1T2 = \u23a1\u23a2\u23a2\u23a3 cos \u03b82 \u2212 sin \u03b82 0 l2 cos \u03b82 sin \u03b82 cos \u03b82 0 l2 sin \u03b82 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 378 6. Inverse Kinematics 2T3 = \u23a1\u23a2\u23a2\u23a3 cos \u03b83 \u2212 sin \u03b83 0 0 sin \u03b83 cos \u03b83 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 3T4 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 0T4 = 0T1 1T2 2T3 3T4 = \u23a1\u23a2\u23a2\u23a3 c\u03b8123 \u2212s\u03b8123 0 l1c\u03b81 + l2c\u03b812 s\u03b8123 c\u03b8123 0 l1s\u03b81 + l2s\u03b812 0 0 1 d 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u03b8123 = \u03b81 + \u03b82 + \u03b83 \u03b812 = \u03b81 + \u03b82 21"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000519_j.jsv.2008.06.043-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000519_j.jsv.2008.06.043-Figure1-1.png",
        "caption": "Fig. 1. Basic frequency in a bearing.",
        "texts": [
            " A modified Newmark time integration technique used to solve the equations of motion numerically [22]. The classical Floquet theory is applied to the proposed model to investigate the linear stability of the bearing system including local defects on raceways and rolling elements. Finally, the basic routes to chaos in rolling bearing systems are discussed in details. There are some basic motions in rolling element bearings which demonstrate dynamics of the elements of rotating bearing and each has its specific frequency. These frequencies are illustrated in Fig. 1. They are cage ARTICLE IN PRESS A. Rafsanjani et al. / Journal of Sound and Vibration 319 (2009) 1150\u20131174 1153 frequency (oc); ball passing inner race frequency (obpi), ball passing outer race frequency (obpo) and ball spin frequency (ob). These frequencies are known as defect frequencies of rolling element bearings (see Appendix A for more details). Any defect in bearing elements, results in an increase of vibration energy at defect frequencies or combination of them [23]. For normal speeds, these defect frequencies lie in the low-frequency range and are usually less than 500Hz [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001525_tia.2009.2036507-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001525_tia.2009.2036507-Figure11-1.png",
        "caption": "Fig. 11. (a) Construction of a harmonic gear with pw = 1 without flexible rotor. (b) Exploded view of (a).",
        "texts": [
            " Whereas a flexible rotor can be realized using the same technology that is employed in mechanical harmonic gears, a simplified construction for gears with pw = 1 is discussed. Furthermore, a magnetic coupling to connect the low-speed output rotor to an external load is also proposed. For harmonic gears which exhibit only one sinusoidal cycle in the air gap between the low-speed rotor and the stator (pw = 1), the flexible rotor can be replaced by a conventional solid permanent-magnet rotor, which is positioned via a bearing on an eccentricity of the high-speed rotor, as shown in Fig. 11, such that the gear is akin to a magnetic version of the mechanical cycloid gear and may exhibit higher level of mechanically and magnetically generated acoustic noise. However, since the low-speed rotor is mounted eccentrically to the high-speed rotor, a mechanical system is required to connect the low-speed eccentric rotor to an external concentric shaft [10]. The requirement for a coupling between the flexible structure and an output shaft can be overcome if a dual-stage harmonic gear is employed, as shown in Fig",
            " The high-speed and flexible rotors are common to both stages, although the flexible rotor carries a different number of magnet poles in each of the two stages. As discussed previously, the rotation of the high-speed rotor results in a geared rotation of the flexible rotor in the first stage, which, in turn, results in a geared rotation of the output rotor in the second stage. However, because the intermediate flexible rotor is no longer connected to an external load, the total torque, which is applied to it, is equal to zero under steady-state operating conditions. This arrangement can also be employed in the gear, which is shown in Fig. 11, in order to transmit the low-speed output rotation to the load without transmitting the eccentric motion of the low-speed rotor. In order to simplify the discussion, it is assumed that a magnet combination is adopted in each of the two stages, which results in maximum torque transmission, as demonstrated previously, i.e., q1,2 = p1,2 + pw (6) where p1 and p2 represent the number of pole pairs on the intermediate rotor in the first and second stages, respectively, and q1 and q2 represent the number of pole pairs on the stator and low-speed rotor, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002891_j.optlastec.2020.106287-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002891_j.optlastec.2020.106287-Figure3-1.png",
        "caption": "Fig. 3. Diagram of the single-track.",
        "texts": [
            " Thus, a single time step of numerical simulation was completed. According to the mass conservation principle, total birth elements number Si by each time step was represented by the following equation: =S l l l q t/i x y z m p (11) where lx, ly, lz is the length of the grid element after discretization in the x, y and z directions respectively, \u03b1 is the powder utilization and values 0.8 based on previous study, t is time step length. The meshed model for the single-track cladding simulation is shown in Fig. 3. Substrate size was 0.01 * 0.025 * 0.006 m3 and the cladding size was 0.003 * 0.02 * 0.002 m3. Mesh size of the cladding in x and z direction was set to be 0.00005 m and as 0.0001 m in y direction. Meanwhile, to reduce the calculation time and improve the calculation efficiency, the substrate was meshed including a free mesh and a special hexahedral mesh, as shown in Fig. 3. Solid70 was adopted as a type thermal analysis element in this paper. The substrate and powder material used in this paper were all 316 stainless steel and the particle size of the powder was 75\u2013150 \u03bcm. The thermophysical parameters of 316 stainless steel used in this paper are listed in Table 1 [20,21]. The solidus temperature of the 316 stainless steel material is 1399 \u00b0C and its liquidus temperature is 1430 \u00b0C. Besides, its latent heat is \u00d73 105 J/kg. The laser radius Rb was equal to 2.5 mm in this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.10-1.png",
        "caption": "Fig. 3.10 Fictitious loads to obtain roll and vertical stiffnesses",
        "texts": [
            ", that a suspension scheme has a typical value of the partial derivative \u2202\u03b3ij /\u2202\u03c6s i , without specifying which are the other three internal coordinates. This is clearly meaningless. The value of the partial derivative is very much affected by which other coordinates are kept constant. Three internal coordinates are necessary to monitor the vehicle condition with respect to a reference (often static) configuration. A suitable choice may be to take as coordinates the vehicle body roll angle \u03c6 and the front and rear vertical displacements z1, z2 of the vehicle centerline (Fig. 3.10). An alternative selection could be the roll angle \u03c6 and the track variations \u0394t1 and \u0394t2. These three coordinates are, of course, independent. Whether they change or not will depend on the vehicle dynamics. The total roll angle \u03c6 of the vehicle body is given by \u03c6 = \u03c6s 1 + \u03c6 p 1 = \u03c6s 2 + \u03c6 p 2 (3.84) 3.8 Suspension First-Order Analysis 71 that is, by the roll angle due to the suspension deflection plus the roll angle due to the tire deformation. Similarly, the front and rear vertical displacements z1, z2 of the vehicle centerline are z1 = zs 1 + z p 1 and z2 = zs 2 + z p 2 (3",
            "85) precisely relate the eight suspension internal coordinates to the three vehicle internal coordinates. The goal of this section is to define the stiffness associated to each internal coordinate. It is important to realize that the symmetric behavior of the two suspensions of the same axle plays a key role here. If, for some reason, the two suspensions were different, then we should also have to consider the cross-coupled stiffnesses. To this end, we assume to apply first a (small) pure rolling moment Lbi to the vehicle body. As shown in Fig. 3.10, application of a (small) pure rolling moment Lbi to the vehicle body results in a (small) pure roll rotation \u03c6\u0302i such that5 Lb = k\u03c6\u03c6\u0302 = (k\u03c61 + k\u03c62)\u03c6\u0302 (3.86) 5The symbol \u03c6\u0302 (instead of just \u03c6) is used to stress that this is not the roll angle under operating conditions. 72 3 Vehicle Model for Handling and Performance where k\u03c6 is, by definition, the global roll stiffness of the vehicle. Moreover, by measuring the corresponding load transfers \u0394ZL 1 t1 = k\u03c61 \u03c6\u0302 and \u0394ZL 2 t2 = k\u03c62 \u03c6\u0302 (3.87) also the front and rear vehicle roll stiffnesses k\u03c61 and k\u03c62 can be obtained",
            " Once k p \u03c6i are known, the suspension roll stiffness ks \u03c6i for each axle can be obtained from (3.88). Similarly, to obtain the vertical stiffnesses, small vertical loads Zb i are assumed to be applied over each axle. 6This is true only if the left and right suspensions have perfectly symmetric behavior. For instance, the so-called contractive suspensions do not behave the same way and, therefore, a pure rolling moment also yields some vertical displacement. 3.8 Suspension First-Order Analysis 73 As shown in Fig. 3.10, application to the vehicle body centerline, exactly over the front axle, of an upward (small) vertical load Zb 1k results only in a (small) vertical displacement z\u03021 such that Zb 1 = kz1 z\u03021 (3.91) which defines the global front vertical stiffness kz1 . Doing the same on the rear axle provides Zb 2 = kz2 z\u03022 (3.92) which defines the rear vertical stiffness kz2 . Again, to single out the suspension and tire contributions, first observe that the two tires of each axle have a vertical stiffness k p zi = 2pi (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001121_iembs.2007.4352899-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001121_iembs.2007.4352899-Figure1-1.png",
        "caption": "Fig. 1. Configuration of bicycle model parameters during insertion of flexible bevel tip needle (redrawn after [4]).",
        "texts": [
            " In this paper, we present a kinematic model quantitatively describing the needle trajectory, based on the duty cycle of spinning and natural curvature of the needle. The model is then validated using experimental results. A. Needle Steering Model via Duty-Cycled Spinning A nonholonomic model for bevel-tip needle steering was presented and validated in [4]. Though the work presented did not involve spinning, the model includes a term for rotational speed and therefore is already suited to modeling the spinning behavior. As seen in Fig. 1, this model follows a variation of the standard kinematic bicycle model with constant front wheel angle, \u03c6, wheel to wheel distance, l1, back wheel to needle tip distance, l2, insertion speed, u1, and rotation speed, u2. Assuming u1 and u2 are control inputs, the kinematic model follows as 1-4244-0788-5/07/$20.00 \u00a92007 IEEE 2756 ( ) ( ) ( ) ( ) ( ), 0 32 )\u02c6\u02c6( 2211 tpeltRtn egtg abab tVuVu abab += = + (1) where Rab(t) and pab(t) are the 3-dimensional rotation and translation components, respectively, of the homogeneous transformation matrix gab(t), and n(t) represents the needle tip coordinates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.8-1.png",
        "caption": "FIGURE 2.8. The arm of Example 7.",
        "texts": [
            " When we find the coordinates of points of the rigid body after the first rotation, our situation before the second rotation is similar to what we had before the first rotation. Example 6 Successive global rotation matrix. The global rotation matrix after a rotation QZ,\u03b1 followed by QY,\u03b2 and then QX,\u03b3 is: GQB = QX,\u03b3QY,\u03b2QZ,\u03b1 (2.38) = \u23a1\u23a3 c\u03b1c\u03b2 \u2212c\u03b2s\u03b1 s\u03b2 c\u03b3s\u03b1+ c\u03b1s\u03b2s\u03b3 c\u03b1c\u03b3 \u2212 s\u03b1s\u03b2s\u03b3 \u2212c\u03b2s\u03b3 s\u03b1s\u03b3 \u2212 c\u03b1c\u03b3s\u03b2 c\u03b1s\u03b3 + c\u03b3s\u03b1s\u03b2 c\u03b2c\u03b3 \u23a4\u23a6 Example 7 Successive global rotations, global position. The end point P of the arm shown in Figure 2.8 is located at:\u23a1\u23a3 X1 Y1 Z1 \u23a4\u23a6 = \u23a1\u23a3 0 l cos \u03b8 l sin \u03b8 \u23a4\u23a6 = \u23a1\u23a3 0 1 cos 75 1 sin 75 \u23a4\u23a6 = \u23a1\u23a3 0.0 0.26 0.97 \u23a4\u23a6 (2.39) The rotation matrix to find the new position of the end point after \u221229 deg rotation about the X-axis, followed by 30 deg about the Z-axis, and again 132 deg about the X-axis is GQB = QX,132QZ,30QX,\u221229 = \u23a1\u23a3 0.87 \u22120.44 \u22120.24 \u22120.33 \u22120.15 \u22120.93 0.37 0.89 \u22120.27 \u23a4\u23a6 (2.40) and its new position is at:\u23a1\u23a3 X2 Y2 Z2 \u23a4\u23a6 = \u23a1\u23a3 0.87 \u22120.44 \u22120.24 \u22120.33 \u22120.15 \u22120.93 0.37 0.89 \u22120.27 \u23a4\u23a6\u23a1\u23a3 0.0 0.26 0.97 \u23a4\u23a6 = \u23a1\u23a3 \u22120"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.13-1.png",
        "caption": "Fig. 10.13 Simple representations of the Cardano/Hooke joint (upper) and the double Cardano/Hooke joint (lower); the latter enables constant velocity and angular momentum to be transferred through a mechanism (based on Ref. 10.21)",
        "texts": [
            "9; to NASA and the US Army for various images of the XV-15 and the large civil tiltrotor; to Leonardo Helicopters and Jay Miller/AHS for images of the AW609; to Airbus Helicopters and Leonardo Helicopters for the image of the DART rotor; to Bob Fortenbaugh (author), Bell Helicopters, and Leonardo Helicopters, and the RAeS for the use of Figure 10.6; to Jay Miller for the use of the image of the V-22 Osprey; to ART for the use of the image of the FLIGHTLAB model editor (Figure 10.2); to Pierangelo Masarati and Springer for the use of Figure 10.13; to Troy Gaffey, Bell Helicopters and the AHS for quoted text on gimbal flap-lag coupling and Figure 10.30 from Ref 10.4; to the AHS and authors of Ref. 10.29 for Figure 10.18; to Mark Potsdam, NASA and the AHS, for material from Refs 10.31 and 10.32; to Wayne Johnson and NASA for material from Ref. 10.33; to Albert Brand and Ron Kisor, Bell Helicopters, and the AHS for the use of material from Refs. 10.39 and 10.40; to the RHILP and ACT-TILT project teams for use of material from the University of Liverpool\u2019s research publications from these projects and to the RAeS and AHS for use of material from the author\u2019s related publications; to Dwayne Kimbal and the AHS for Figures 10",
            " Without stiffness, there is no natural frequency as such, and the notion of phase resonance is meaningless, so we might not expect to find the same situation as with an articulated rotor, i.e. cyclic pitch at one/rev leading to cyclic flap at one/rev, lagging 90 deg. However, this outcome is preserved in gimbal rotors, but for different physical reasons, as will be explained. The orientation of the angular velocity normal to the gimbal plane is crucial to this behaviour. In practice, the gimbal joint that achieves this is likely be very complicated, but a simple illustration is useful. In the case of the Cardano or Hooke joint (Figure 10.13), the output drive (a in Figure 10.13, upper) has a two-per-rev rotorspeed variation superimposed on the mean value, which is the rotation speed of the input shaft (b in figure) (Ref. 10.21). The extent of the fluctuations depends on the orientation angle \ud835\udefd as shown; \ud835\udf13 is the rotation angle. For the CV joint, which can be engineered as a double Hooke joint (Figure 10.13, lower), the rotation speed of the output shaft is a constant \u03a9. Later we will show one of the designs for the hub of the ERICA tiltrotor, to illustrate innovation in compact complexity. It is helpful to recall the behaviour of our familiar articulated centre-spring rotor (Figure 3.6), in response to a step cyclic input (say +\ud835\udf031s), in hover. For our simulation, the input shaft is held fixed. The rotor blade flaps up and, after a well damped transient, settles into one-per-rev flapping with maximum at the front of the disc and minimum at the rear (so, \u2212\ud835\udefd1c)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001776_iros.2009.5354199-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001776_iros.2009.5354199-Figure4-1.png",
        "caption": "Fig. 4 Experimental results showing a plot of predicted versus actual rod shape using a model, which incorporates gravity versus one without gravity. The top line shows the analytical model which does not include gravity, while the bottom line shows the proposed model, offset vertically to make the physical rod visible.",
        "texts": [
            " Therefore, after running the ODE, the error ( )fs\u2212\u03c4 m where \u03c4 specifies the applied tip moment allows a root-finding solver to guess a new ( )0lu initial value until the error between computed and applied tip moment is sufficiently small. IV. IMPLEMENTATION AND EXPERIMENTAL VALIDATION A rod composed of a nickel-titanium alloy termed Nitinol provides a good candidate for the backbone of a continuum robot, due to its ability to flex a large amount (up to 1% strain) without a permanent (plastic) deformation. However, its temperature-dependent modulus requires measurement of E and application at a constant temperature. A rod of diameter 1.56 mm, 40 cm in length, with a mass density of 6.80 g/cc as shown in Fig. 4 provided an experimental platform on which to validate the theory presented in this proposal. To determine the modulus of elasticity of the rod, the data (tip mass vs. deflection) was fit to the model, yielding E = 54 GPa. For a circular cross-section rod, 4 64I d\u03c0= and 4 32J d\u03c0= where d specifies the rod diameter. In this case, 40.291 pmI = and 40.581 pmJ = . Choosing Poisson\u2019s ratio 0.3\u03bd = , the shear modulus ( )1 20.8 GPaG E \u03bd= + = . A. Experimental procedure Fig. 4 shows the experimental setup, in which this rod was mounted horizontally on a sheet of acrylic with a laser-cut 1 mm grid. A friction-fit assembly located precisely with respect to the grid securely held the rod. A mass was attached to its tip with a string; 1 cm of the rod was used to fix the rod, leaving 39 cm of bending length. The measured position of the tip was compared to its predicted value; the distance between the two as a percentage of rod length gives the percent error. Table II summarizes the results, showing high accuracy in the model\u2019s predictions with an average tip position error of 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000477_0079-6425(63)90037-9-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000477_0079-6425(63)90037-9-Figure17-1.png",
        "caption": "Fig. 17. Diagram showing the simplified nucleation and growth mechanism of lamellar eutectic alloys. (From Tiller Liquid Metals and Solidification !958, American Society for Metals, Metals Park, Ohio.~18~)",
        "texts": [
            " A slight modification of this growth model was given recently, Us> in which the nucleation and growth of the first two plates of the eutectic structure occurred in exactly the same way as described above, bu~ ~then further plates of both phases grew by the mutual overlapping of one phase over the edge of the other phase, thus avoiding the problem of repeated nucleation inherent in the early theories. In the light of the observations of Sundquist and Mondolfo mentioned above, the overlapping ability of both phases appears to be essential for the growth of a eutectic crystal in which the lamellae of each phase have a constant crystallographic orientation. This sequence of heterogenous nucleation, overlap, and edgewise growth of both phases is illustrated in Fig. 17. It is extremely unlikely that this simple model of nucleation and growth actually occurs in practice, and a more realistic model founded upon experimental observations has been developed as follows. Impurity particles will undoubtedly be present in the bulk eutectic liquid and some of these will act as heterogeneous nucleation centres when the eutectic liquid is undercooled. Which of the solid phases will be nucleated first upon the most potent heterogeneous nuclei will probably depend to a certain extent upon the epitaxial correspondence that can be attained between the nucleation centre and the two solid phases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure4.21-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure4.21-1.png",
        "caption": "Fig. 4.21 Source of rotor hub couple due to inclination of rotor torque to the shaft",
        "texts": [
            " Before leaving the roll and pitch moment derivatives, it is important that we consider the influence of the in-plane rotor loads on the moments transmitted to the fuselage. In our previous discussion of the force derivatives Xq and Yp, we have seen how the Amer effect reduces the effective rotor damping, most significantly on teetering rotors in low-thrust flight conditions. An additional effect stems from the orientation of the in-plane loads relative to the shaft when the rotor disc is tilted with one-per-rev flapping. The effect is illustrated in Figure 4.21, showing the component of rotor torque oriented as a pitching moment with lateral flapping (the same effect gives a rolling moment with longitudinal flapping). The incremental hub moments can be written in terms of the product of the steady torque component and the disc tilt; hence, for four-bladed rotors (\ud835\udeffL)torque = \u2212 QR 2 \ud835\udefd1c (4.90) (\ud835\udeffM)torque = QR 2 \ud835\udefd1s (4.91) These moments will then combine with the thrust vector tilt and hub moment to give the total rotor moment. To examine the contribution of all three effects to the derivatives, we compare the breakdown for the Puma and Lynx"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000793_pime_proc_1989_203_100_02-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000793_pime_proc_1989_203_100_02-Figure8-1.png",
        "caption": "Fig. 8 (a) Rolling contact of a cylinder with an elastic-plastic half-space. Contact stresses c, cYy, uzz and z,, which exceed the elastic limit introduce residual compressive stresses p,, and pyy",
        "texts": [
            " Cyclic plasticity (plastic shakedown) The steady cyclic state consists of a closed plastic stress-strain loop with no net accumulation of uni-directional plastic strain (Fig. 7c). 3. Plastic deformation-in the early cycles makes the surfaces more conforming which, for a given load, reduces the intensity of contact stress. Each of these influences on shakedown have been investigated. By considering the line contact of elastic-perfectly plastic cylinders in plane strain (or a cylinder in contact with a plane; Fig. 8a), strain hardening and changing conformity are eliminated, leaving only the effect of residual stress. In these circumstances equilibrium with the free surface of the cylinders (which are assumed to deform as half-spaces) restricts the possible residual stresses to the two components p d z ) and pyy(z) , which act parallel to the surface and vary with depth z only. Plastic deformation is inhibited in the steady state by the development of compressive (negative) values of p,, and pyv in the sub-surface layer where initial yielding has taken place. The influence of these residual stresses on the subsurface contact stresses at a depth z = 0 . 5 ~ is shown in Fig. 8b. The perfectly plastic model of material behaviour greatly overestimates the plastic deformation compared Part C: Journal of Mechanical Engineering Science @ IMechE 1989 at UNIV OF WISCONSIN on September 8, 2014pic.sagepub.comDownloaded from THE STRENGTH OF SURFACES IN ROLLING CONTACT 157 (b) Sub-surface stresses at depth z = 0 . 5 ~ in a free rolling contact (Q = 0), showing the effect of residual stresses pxx and pyy with that found in an experiment. It also leads to difficulties of indeterminancy and lack of uniqueness of deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.42-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.42-1.png",
        "caption": "Fig. 17.42 Synchronous generator (ABB)",
        "texts": [
            " Because the rotor is subjected to changing magnetic fields, it is constructed of thin laminations to reduce eddy-current losses. A DC current must be supplied to the field circuit on the rotor. Since the rotor is rotating, a special arrange- ment is required to provide the DC power to its field windings. There are two approaches to supply this DC power: \u2022 From an external DC source to the rotor by means of slip rings and brushes\u2022 From a special DC source mounted directly on the shaft of the synchronous generator The largest electrical machines in the world are synchronous generators (Fig. 17.42). Some can produce as much power as 1700 MW. They are constructed as (twoor four-pole) turbogenerators and are driven, for example, by steam turbines. The power of a synchronous machine is limited by its possible rotor dimension (mechanical stress) and allowable armature current (temperature) (Table 17.3). The limiting power values of two-pole turbogenerators at 50 Hz are described below. Part C 1 7 .3 Operating Characteristics In order to analyze the electrical behavior, d\u2013q system modeling can be used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001620_978-90-481-8764-5_2-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001620_978-90-481-8764-5_2-Figure2-1.png",
        "caption": "Fig. 2 QRT motion principle",
        "texts": [
            " The performance of the proposed control scheme is verified through experiments using QRT UAVs. Section 2 shows the basic structure and the dynamics of the UAV. The DOB for flight control algorithms is given in Section 3. Section 4 shows the experimental setup and experimental results including the vision based localization schemes, and followed by concluding remarks in Section 5. Reprinted from the journal 11 Figure 1 shows coordinate systems of QRT UAVs. The motion of QRT UAVs is induced by the combination of quad rotors as shown in Fig. 2. The state vectors for the QRT UAVs are described as following: \u03b7 = [\u03b7T 1 , \u03b7 T 2 ]T; \u03b71 = [x, y, z]T; \u03b72 = [\u03c6, \u03b8, \u03c8]T; \u03bd = [\u03bdT 1 , \u03bd T 2 ]T; \u03bd1 = [vx, vy, vz]T; \u03bd2 = [\u03c9x, \u03c9y, \u03c9z]T; where the position and orientation of a QRT UAV, \u03b7, are described relative to the inertial reference frame, while the linear and angular velocities of a QRT UAVs, \u03bd, are expressed in the body-fixed frame. x, y, and z mean the linear positions of a QRT UAV with respect to inertial reference frame. \u03c6, \u03b8 , and \u03c8 represent the roll, pitch, and yaw angles of the QRT UAV in the inertial reference frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001525_tia.2009.2036507-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001525_tia.2009.2036507-Figure8-1.png",
        "caption": "Fig. 8. Components of force on the magnets of the low-speed rotor.",
        "texts": [
            " It can also be seen that, contrary to (2), the space harmonic, which corresponds to m = 1 and k = 1, is significantly lower than the one which corresponds to m = 1 and k = 2. Unfortunately, a simple explanation of this phenomenon is yet to be proposed. Finally, although the flux density of the active asynchronous harmonic is relatively low, the transmitted torque is high since it is proportional to the product of the air-gap flux density and the number of pole pairs of the active harmonic. Two-dimensional finite-element analysis has been employed to compute the torque on each component in the gear. As shown in Fig. 8, the total force Fr, which is exerted on each magnet of the low-speed rotor, has components Fn and Ft, which are normal and tangential to the bearing outer circumference, respectively. The tangential component Ft enables the low-speed rotor to slide over the high-speed rotor and therefore contributes to the torque on the low-speed rotor. The normal component Fn is transmitted through the bearing and contributes to a torque on the high-speed rotor, because Fn is generally not applied through the center of rotation of the high-speed rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001277_j.procir.2016.11.009-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001277_j.procir.2016.11.009-Figure9-1.png",
        "caption": "Fig. 9. The five steps followed in the Teaching Factory course.",
        "texts": [
            " The simultaneous application of thermal load and vibration affect the performance of the machine in terms of dimensional accuracy and stability. The students had to design the swivel table in collaboration with the machine shop where the MTP would be installed. The industrial requirements were given in the form of specifications regarding the static compliance, thermal load and dynamic compliance of the final product. The pilot was organized in five collaborative cycles, through which the students would interact with the machine shop in order to solve the problem following the design cycle of the particular industrial practice (Fig. 9). The real-life industrial problem was presented to the students on the academia side. The second cycle focused on the definition of the design specifications based on the prerequisites defined in the first cycle. The feedback that the students received from the machine shop during the first two cycles was used for drafting an initial design within the third cycle of the pilot. The fourth cycle was focused on the detailed dynamic and thermal analysis of the selected design. Finally, during the fifth cycle the students presented their final solution as a result of this collaborative design process (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure9.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure9.3-1.png",
        "caption": "Fig. 9.3 Definition of yaw, pitch and roll",
        "texts": [
            ", their order is important) Human beings are comfortable with two-dimensional rotations, and Euler was, perhaps, no exception when he invented the technique of three elemental rotations, often referred to as Euler angles. The basic idea is to generate a sequence of four Cartesian reference systems Si , each one sharing one axis with the preceding system and another axis with the next one. Therefore, we can go from one system to the next by means of a two-dimensional rotation about their common axis.2 In vehicle dynamics it is convenient to use the following sequence of reference systems (Fig. 9.3) (i0, j0,k0) \u03c8\u2212\u2192 k0=k1 (i1, j1,k1) \u03b8\u2212\u2192 j1=j2 (i2, j2,k2) \u03c6\u2212\u2192 i2=i3 (i3, j3,k3) (9.1) to go from the ground-fixed reference system S0, with directions (i0, j0,k0), to the vehicle-fixed reference system S3, with directions (i3, j3,k3). This vehicle-fixed reference system has been already introduced in Fig. 1.4, although with a slightly different notation (no subscripts). When the vehicle is at rest, direction k3 = k is orthogonal to the road (hence directed like k0) and direction i3 = i is parallel to the road and pointing forward (hence like i1, Fig",
            "2) often called the line of nodes, which is orthogonal to both k0 = k1 and i2 = i3. This direction j1 = j2 is the link between the ground-fixed and the vehicle-fixed reference systems. This way, we have that we can go from S0 to S1 with an elemental rotation 2More precisely, the axis must share the same direction. The origin can be different. 274 9 Handling with Roll Motion \u03c8 about k0 = k1, and so on. Any two consecutive reference systems differ by a two-dimensional rotation, as shown in (9.1). More precisely, as shown in Fig. 9.3, the first rotation \u03c8 (yaw) is about the third axis k0 = k1, which S0 and S1 have in common, the second rotation \u03b8 (pitch) is about the second axis j1 = j2, shared by S1 and S2, and the third rotation \u03c6 (roll) is about the first common axis i2 = i3 of S2 and S3. This is why this sequence of elemental rotations is marked (3,2,1), or yaw, pitch and roll.3 In vehicle dynamics, the pitch and roll angles are very small. 3Classical Euler angles use the sequence (3,1,3). 9.3 Angular Velocity 275 With this sequence of reference systems, the angular velocity of the vehicle body is given by = \u03c6\u0307i2(\u03c8, \u03b8) + \u03b8\u0307 j1(\u03c8) + \u03c8\u0307k0 (9.3) This is a simple and intuitive equation, but it has the drawback that the three unit vectors are not mutually orthogonal (Fig. 9.3). Therefore, our goal is to obtain the following equation4 = pi3 + qj3 + rk3 (9.4) where the vector is expressed in terms of its components in the vehicle-fixed reference system S3.5 The expressions of p, q and r can be easily obtained by means of the rotation matrices\u23a1 \u23a3pq r \u23a4 \u23a6= R1(\u03c6) \u23a1 \u23a3\u03c6\u03070 0 \u23a4 \u23a6+ R1(\u03c6)R2(\u03b8) \u23a1 \u23a30 \u03b8\u0307 0 \u23a4 \u23a6+ R1(\u03c6)R2(\u03b8)R3(\u03c8) \u23a1 \u23a30 0 \u03c8\u0307 \u23a4 \u23a6 = \u23a1 \u23a3\u03c6\u03070 0 \u23a4 \u23a6+ R1(\u03c6) \u23a1 \u23a30 \u03b8\u0307 0 \u23a4 \u23a6+ R1(\u03c6)R2(\u03b8) \u23a1 \u23a30 0 \u03c8\u0307 \u23a4 \u23a6 (9.5) where, as well known, the rotation matrices for elemental rotations are as follows, for a generic angle \u03b1 \u2013 rotation around the first axis R1(\u03b1) = \u23a1 \u23a31 0 0 0 cos\u03b1 sin\u03b1 0 \u2212 sin\u03b1 cos\u03b1 \u23a4 \u23a6 (9",
            "16) The vehicle lateral velocity v was introduced in (3.1) in the case of negligible roll motion. Now we need to extend that definition when the roll motion is taken into account. This task is not as simple as it may seem. Intuitively, we would like to obtain an expression of v independent of \u03c6. Therefore, we are looking for a point which, broadly speaking, follows the vehicle motion, without being subject to roll. A point that is like G, except that it does not roll. More precisely, we are looking for the origin O1 of the reference system S1 in Fig. 9.3, that is a reference system which yaws, but does not pitch and roll. For simplicity, we assume the tires are perfectly rigid in this chapter. Roll motion is part of vehicle dynamics. However, it is useful to start with a purely kinematic analysis to get an idea of the several effects of roll motion. This kinematic analysis should be seen as a primer for better investigating roll dynamics. Figure 3.11 shows how to determine the no-roll centers Qi for a swing arm suspension and a double wishbone suspension"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure5.8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure5.8-1.png",
        "caption": "Figure 5.8.2. Trailing twist axle: (a) rear view, (b) beam free-body diagram, (c) bending-moment diagram.",
        "texts": [
            " This complicates the issue considerably. In the case of location by longitudinal leaf-springs, the load transfer properties depend on the bending and torsional stiffness of the springs and bushes, 254 Tires, Suspension and Handling which comes into play only once the body rolls; so it is necessary to separate out the roll stiffness effects as an equivalent anti-roll bar, to leave the effective roll center height. As an example to find a first approximation to the roll center position, consider the simplified case of Figure 5.8.1. First, consider the case of perfect torsional rigidity of the straight spring ABC, and complete rigidity of link DC and the bushes at A, C and D, other than their basic design motion. In such a case, a force could be applied to the body at any height without any roll rotation being possible. This is equivalent to a perfectly rigid anti-roll bar. To completely eliminate anti-roll bar effects, which must be done to find the roll center, compliance must be introduced into the system, in particular for the bushes about axes AC or AD",
            " Otherwise the result will be some intermediate position. If the rod is at a different height from B, this calls for increased lateral deflection of the leaf-springs and therefore Suspension Characteristics 255 results in an additional roll stiffness, which must be treated as an equivalent antiroll bar. In the case of the trailing twist axle the crossmember acts in torsion giving an anti-roll bar effect, so to eliminate this we must consider a zero torsion stiffness crossmember, still with bending stiffness. Figure 5.8.2(a) shows a rear view of a simplified case with horizontal arms and small roll angle. The tire lateral forces are L and L . The crossbeam has the free-body diagram in rear view of Figure 5.8.2(b). The wheel vertical forces are reacted separately by springs on the trailing arms. The tire side forces exert moments Ls and L s on the ends of the beam. For beam rotational equilibrium there must be vertical end forces as shown. This gives the beam the bending-moment diagram of Figure 5.8.2(c). When L L the central bending moment is small in this view. A similar argument applies in plan view. In conjunction with the zero torsion specification, this means that each half of the suspension exerts negligible moment about an axis from its own front bush through the mid-point of the crossbeam. Therefore this axis can be projected into the transverse plane of the wheel centers to find the force center, as for a trailing arm. The approximations are increasingly in error as the lateral acceleration increases, so this is only the initial position of the roll center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.56-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.56-1.png",
        "caption": "FIGURE 5.56. A 2 DOF polar manipulator.",
        "texts": [
            "54(a) and (b) and find their rest positions. (c) Determine the global coordinates of the tip point of the manipulator in 5.54(a) and (b)at the position shown. 8. Frame at center. Let us attach the link\u2019s coordinate frame at the geometric center of the link, ai/2. Using the rigid motion and homogeneous matrices, develop the transformation matrices 0T1, 1T2, and 0T2 for the manipulator of Figure 5.55. 9. A polar manipulator. Determine the link\u2019s transformation matrices 1T2, 2T3, and 1T3 for the polar manipulator shown in Figure 5.56. 10. Ground and end-effector replacement of polar manipulator. Determine the transformation matrices transformation matrices 3T2, 2T1, and 3T1 for the manipulator of Figure 5.56. 11. A planar Cartesian manipulator. Determine the link\u2019s transformation matrices 1T2, 2T3, and 1T3 for the planar Cartesian manipulator shown in Figure 5.57. Hint: The coordinate frames are not based on DH rules. 12. F Manipulator designing. Use the industrial robot links and make a manipulator to have 5. Forward Kinematics 313 x2 y2 y0 x1 a 1 y1 a2 2\u03b8 314 5. Forward Kinematics z2 x3 x1 x2 z3 z1 d2 d3 5. Forward Kinematics 315 z0 P FIGURE 5.58. A planar manipulator with 4 DOF . (b) Determine the link-joint table for the manipulator",
            "59 shows a 3 degree of freedom manipulator. (a) Follow the DH rules and complete the link coordinate frames. (b) Determine the link-joint table for the manipulator. (c) Determine the DH transformation matrices. (d) Determine the coordinates of point P as functions of the joint coordinates. (e) Attach a tool coordinate frame at P and solve the forward kinematics to determine the orientation of the frame. 316 5. Forward Kinematics x0 y0 x1 a l z0 P Spherical manipulators are made by attaching a polar manipulator shown in Figure 5.56, to a one-link R`R(\u221290) manipulator shown in Figure 5.51 (b). Attach the polar manipulator to the one-link R`R(\u221290) arm and make a spherical manipulator. Make the required changes to the coordinate frames Exercises 3 and 9 to find the link\u2019s transformation matrices of the spherical manipulator. Examine the rest position of the manipulator. 19. F Non-industrial links and DH parameters. Figure 5.61 illustrates a set of non-industrial connected links. Complete the DH coordinate frames and assign the DH parameters",
            " Find an equation to relate the angular acceleration of link (i) to the angular acceleration of link (i \u2212 2), and the angular acceleration of link (i) to the angular acceleration of link (i+ 2). 6. F Acceleration in different frames. For the 2R planar manipulator shown in Figure 12.7, find 0 1a2, 1 0a2, 0 2a1, 2 0a1, 2 0a2, and 0 1a1. 7. Slider-crank mechanism dynamics. A planar slider-crank mechanism is shown in Figure 12.23. Set up the link coordinate frames, develop the Newton-Euler equations of motion, and find the driving moment at the base revolute joint. 8. PR manipulator dynamics. Find the equations of motion for the planar polar manipulator shown in Figure 5.56. Eliminate the joints\u2019 constraint force and moment to derive the equations for the actuators\u2019 force or moment. 9. A planar Cartesian manipulator. Determine the equations of motion of the planar Cartesian manipulator shown in Figure 12.24. Hint : The coordinate frames are not based on DH rules. 10. F Global differential of a link momentum. In recursive Newton-Euler equations of motion, why we do not use the following Newton equation? iF = Gd dt iF = Gd dt m iv = m iv\u0307 + i 0\u03c9i \u00d7m iv 11. 3R planar manipulator dynamics",
            " Determine the Newton-Euler equations of motion for the planar Cartesian manipulator shown in Figure 5.57. 13. Articulated manipulator. Figure 12.25 illustrates an articulated manipulator with massless arms and two massive points m1 and m2. (a) Follow the DH rules and complete the link coordinate frames. (b) Determine the DH transformation matrices. (c) Determine the equations of motion of the manipulator using Lagrange method. 14. Polar planar manipulator dynamics. A polar planar manipulator with 2 DOF is shown in Figure 5.56. (a) Determine the Newton-Euler equations of motion for the manipulator. (b) Reduce the number of equations to two, for moments at the base joint and force at the P joint. (c) Substitute the vectorial quantities and calculate the action force and moment in terms of geometry and angular variables of the manipulator. 15. F Dynamics of a spherical manipulator. Figure 5.43 illustrates a spherical manipulator attached with a spherical wrist. Analyze the robot and derive the equations of motion for joints action force and moment",
            " (a) Find the equations of motion for the manipulator utilizing the backward recursive Newton-Euler technique. (b) F Find the equations of motion for the manipulator utilizing the forward recursive Newton-Euler technique. 21. A RPR planar redundant manipulator. (a) Figure 12.27 illustrates a 3 DOF planar manipulator with joint variables \u03b81, d2, and \u03b82. Determine the equations of motion of the 720 12. Robot Dynamics manipulator if the links are massless and there are two massive points m1 and m2. 22. Polar planar manipulator recursive dynamics. Figure 5.56 depicts a polar planar manipulator with 2 DOF . (a) Find the equations of motion for the manipulator utilizing the backward recursive Newton-Euler technique. (b) F Find the equations of motion for the manipulator utilizing the forward recursive Newton-Euler technique. 23. F Recursive dynamics of an articulated manipulator. Figure 5.22 illustrates an articulated manipulator R`RkR. Use g = \u2212g 0k\u03020 and find the manipulator\u2019s equations of motion (a) utilizing the backward recursive Newton-Euler technique",
            " (a) Derive the equations of motion for the SRMS utilizing the backward recursive Newton-Euler technique for g = 0. (b) Derive the equations of motion for the SRMS utilizing the forward recursive Newton-Euler technique for g = 0. 26. 3R planar manipulator Lagrange dynamics. Find the equations of motion for the 3R planar manipulator shown in Figure 12.29 utilizing the Lagrange technique. The manipulator is attached to a wall and therefore, g = \u2212g 0 \u0131\u03020. 27. Polar planar manipulator Lagrange dynamics. Find the equations of motion for the polar planar manipulator, shown in Figure 5.56, utilizing the Lagrange technique. 12. Robot Dynamics 721 28. F Lagrange dynamics of an articulated manipulator. Figure 5.22 illustrates an articulated manipulator R`RkR. Use g = \u2212g 0k\u03020 and find the manipulator\u2019s equations of motion utilizing the Lagrange technique. 29. F Lagrange dynamics of a SCARA robot. A SCARA robot RkRkRkP is shown in Figure 5.23. If g = \u2212g 0k\u03020 determine the dynamic equations of motion by applying the Lagrange technique. 30. F Lagrange dynamics of an SRMS manipulator. Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001621_j.procir.2015.08.060-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001621_j.procir.2015.08.060-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of exposure parameters and volume energy density EV in SLM process",
        "texts": [
            " An increase in the freedom of design as well as the degree of innovation and efficiency in production can be achieved. Selective Laser Melting is based on a remelting process in which the compaction of the material is determined only by the flow and wetting behavior of the melt [1]. In order to avoid undesired consequences such as material defects such as pores and cracks, delamination, component warping, uncontrolled changes of chemical and physical component properties, the exposure parameters (Figure 1) must be optimized, taking into account their mutual interactions. The intensity of the laser beam and the specific material parameters determine the absorbed optical energy during the laser material processing. This energy is available as process heat in the material for further phase transformation processes [2]. Figure 2 shows a schematic representation of the three phases in the SLM process. The coupled laser energy primarily leads to local melting of the powder material. However, the powder grains in the outer area of the beam absorb less energy than the grains in the beam center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003492_j.msea.2020.140660-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003492_j.msea.2020.140660-Figure3-1.png",
        "caption": "Fig. 3. Charpy specimens according to their BDs (a) dimensions of the notched specimens in mm; (b) dimensions of the un-notched specimens in mm; (c) vertical notched specimens; (d) horizontal notched specimens; (e) horizontal un-notched specimens.",
        "texts": [
            "1 and 5 Hz, respectively. Force measurements were conducted with a 50 kN load cell mounted on the test rig. A total number of 51 specimens were used to plot the S\u2013N curves as the results. The number of samples used specifically for each build condition can be seen from the curves presented in section 3.7. Finally, Charpy tests were conducted at room temperature to measure the notch fracture toughness of the specimens with different BDs. The specimens were built following ASTM E23 [30], as shown in Fig. 3. The notches were manufactured by additive manufacturing. The fractured surface of each sample was analyzed with a KEYENCE VR-3200 3D macroscope to measure their shear fracture appearances (SFA) accurately. The SFA can be used as a quantitative criterion to compare the fracture mechanisms of the Charpy samples. Un-notched samples having the same effective areas as the standard samples (Fig. 3b and e) were also tested to evaluate the notch effect of the surface inhomogeneities in the as-built specimens, similar to the work of Yasa et al. in Ref. [17]. The un-notched samples were divided into two groups based on their surface qualities, i.e., as-built and machined. Three samples were considered to be tested for each building condition (12 samples in total). It should be noted that by considering the small fluctuations and errors in the achieved data from the tests in this study, the average values of the measured characteristics, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure10.40-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure10.40-1.png",
        "caption": "Fig. 10.40 Comparison between contact patches under (a) large spin slip only and (b) still quite large spin slip with the addition of a little of lateral slip. Case (d) shown for completeness. Values of \u03d5 are in m\u22121",
        "texts": [
            " Again, the goal is to achieve the highest possible value of Fn y . The large effect of even a small amount of \u03c3y on the normalized lateral force Fn y as a function of \u03d5 is shown in Fig. 10.38. However, this is quite an expected result 332 10 Tire Models Fig. 10.38 Normalized lateral force vs spin slip, at different values of lateral slip Fig. 10.39 Vertical moment vs spin slip, at different values of lateral slip after (10.79). Consistently, also the vertical moment MD z changes a lot under the influence of small variations of \u03c3y (Fig. 10.39). Figure 10.40 provides a pictorial representation of the tangential stress in two relevant cases, that is those that yield the highest lateral force. Quite remarkably, a 10 % higher value of Fn y is achieved in case (b) with respect to case (a). In general, a little \u03c3y has a great influence on the stress distribution in the contact patch. Conversely, the same lateral force can be obtained by infinitely many combinations (\u03c3y,\u03d5). This is something most riders know intuitively. Obviously, Fx = 0 in all cases of Fig. 10.40. Under these operating conditions, according to (2.69), the slip angle \u03b1 never exceeds two degrees. Therefore, the wheel has excellent directional capability. It should be observed that the larger value of Fn y of case (b) in Fig. 10.40 is associated with a smaller value of MD z . Basically, it means that the tangential stress distribution in the contact patch is better organized to yield the lateral force, without wasting much in the vertical moment (mainly due to useless longitudinal stress components). The comparison shown in Fig. 10.40(c) confirms this conclusion. A lateral slip in the \u201cwrong\u201d direction, like in Fig. 10.40(d), yields a reduction of the lateral force and an increase of the vertical moment. As reported in Figs. 10.38 and 10.39, there are particular combinations of (\u03c3y,\u03d5) which provide either Fn y = 0 or MD z = 0. The stress distributions in such two cases are shown in Fig. 10.41. The interaction of longitudinal slip \u03c3x and spin slip \u03d5 yields the effects reported in Fig. 10.42 on the longitudinal and lateral forces. A fairly high value \u03c3x = \u22120.15 has been employed. Examples of stress distributions are given in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003887_j.ijmecsci.2019.05.012-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003887_j.ijmecsci.2019.05.012-Figure3-1.png",
        "caption": "Fig. 3. Modeling of a gear tooth with a non-uniform crack distribution. (a) three-dimensional view of the cracked tooth, (b) equivalent model of the mesh stiffness, (c) crack propagation along the tooth width in the crack section A-A.",
        "texts": [
            " w s w t s a F Therefore, when there exists a uniform tooth crack through the hole tooth width on one of the meshing teeth, the equivalent mesh tiffness can be obtained as, 1 \ud835\udc58 \ud835\udc52 = 1 \ud835\udc58 \u210e + 1 \ud835\udc58 \ud835\udc4f 1 ,\ud835\udc50 \ud835\udc5f\ud835\udc4e\ud835\udc50 \ud835\udc58 + 1 \ud835\udc58 \ud835\udc60 1 ,\ud835\udc50 \ud835\udc5f\ud835\udc4e\ud835\udc50 \ud835\udc58 + 1 \ud835\udc58 \ud835\udc4e 1 + 1 \ud835\udc58 \ud835\udc531 + 1 \ud835\udc58 \ud835\udc4f 2 + 1 \ud835\udc58 \ud835\udc60 2 + 1 \ud835\udc58 \ud835\udc4e 2 + 1 \ud835\udc58 \ud835\udc532 (10) here the subscripts 1 and 2 represent the gear 1 and 2 respectively. Then, in order to model the crack propagating non-uniformly along he tooth width, the cracked tooth is divided into finite thin slices, as hown in Fig. 3 . So, the crack depth for each slice could be regarded as constant when the slice width d z is small enough like that shown in ig. 3 (a). Reasonably, the bending and shear stiffness for each slice can b a b \ud835\udc58 \ud835\udc58 e d ( \ud835\udc5e \ud835\udc5e c \ud835\udc5e c r T p b 3 a d e T t g r m a f a r \ud835\udc39 o \ud835\udc3c \ud835\udc3c \ud835\udc5a \ud835\udc5a E \ud835\udc5a \ud835\udc5a \ud835\udc5a w \ud835\udc66 a \ud835\udc5a \ud835\udc39 e calculated with Eqs. (1) and (2) . Then, by integrating the stiffness of ll slices, the total bending and shear stiffness for the cracked tooth can e obtained as, \ud835\udc4f,\ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59 = \u222b \ud835\udc3f 0 \ud835\udc58 \ud835\udc4f,\ud835\udc60\ud835\udc59\ud835\udc56\ud835\udc50\ud835\udc52 ( \ud835\udc67 ) (11) \ud835\udc60,\ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59 = \u222b \ud835\udc3f 0 \ud835\udc58 \ud835\udc60,\ud835\udc60\ud835\udc59\ud835\udc56\ud835\udc50\ud835\udc52 ( \ud835\udc67 ) (12) The distribution of the crack depth along the tooth width can be stimated as a parabolic function in the crack section A-A [15,19] , as epicted in Fig. 3 (c). Thus, for the crack length L c < L , the crack curve solid curve) can be described by, ( \ud835\udc67 ) = \ud835\udc5e 0 \u221a \ud835\udc3f \ud835\udc50 \u2212 \ud835\udc67 \ud835\udc3f \ud835\udc50 , \ud835\udc67 \u2208 [ 0 , \ud835\udc3f \ud835\udc50 ] (13) ( \ud835\udc67 ) = 0 , \ud835\udc67 \u2208 [ \ud835\udc3f \ud835\udc50 , \ud835\udc3f ] (14) While for the crack extending through the entire tooth width, the rack curve (dash curve) can be described by, ( \ud835\udc67 ) = \u221a \ud835\udc5e 2 2 \u2212 \ud835\udc5e 2 0 \ud835\udc3f \ud835\udc67 + \ud835\udc5e 2 0 (15) Thus, the equivalent mesh stiffness of a single tooth pair can be cal- ulated by, 1 \ud835\udc58 \ud835\udc52 = 1 \ud835\udc58 \u210e + 1 \ud835\udc58 \ud835\udc4f 1 ,\ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59 + 1 \ud835\udc58 \ud835\udc60 1 ,\ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc59 + 1 \ud835\udc58 \ud835\udc4e 1 + 1 \ud835\udc58 \ud835\udc531 + 1 \ud835\udc58 \ud835\udc4f 2 + 1 \ud835\udc58 \ud835\udc60 2 + 1 \ud835\udc58 \ud835\udc4e 2 + 1 \ud835\udc58 \ud835\udc532 (16) Finally, the total mesh stiffness for the double-tooth-pair meshing duation can be calculated by the summation of two tooth pairs\u2019 stiffness"
        ],
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    },
    {
        "image_filename": "designv10_1_0001255_tro.2012.2217795-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001255_tro.2012.2217795-Figure3-1.png",
        "caption": "Fig. 3. Examples of one-dimensional solution sets of the IGP with assigned orientation for the 2\u20132 robot. (a) a2x = 4, a2z = 1, r2x = \u2212r1x = 1, r1z = \u22120.5, r2z = 0, and x = 2. (b) a2x = 4, a2z = 1, r1x = 0, r2x = 1.5, r2z = r1z = \u22120.5, and z = 1.5. In both cases, equilibrium configurations are feasible along the entire path.",
        "texts": [
            " Under assumption A, this occurs if either one of the following conditions holds: 1) rix = 0 and x = aix , with i = 1 or 2; 2) a2 \u00d7 r21 \u00b7 j = 0, r21x = 0 and x = \u2212a2x r1x /r21x . In the former case, Ai , Bi , and G lie on a line parallel to k, and the robot operates like a one-dof crane, with the ith cable holding the entire charge. In the latter case, the line segments A1A2 and B1B2 are parallel, and the platform may follow a quasi-static linear path parallel to k, with orientation being constant and the load being sustained by both cables [see Fig. 3(a)]. 2) Orientation and Variable z Are Assigned: If the orientation and z are assigned, (26) provides, in general, two solutions in x. If all coefficients of p1 vanish, the solution set is one-dimensional, and it coincides with a line perpendicular to k. Under assumption A, p1 is identically nought if r1z = r2z , z + r1z = ajz , and rix = 0, with i = j, namely if points B1 , B2 , and Aj lie on a line perpendicular to k, and the segment BiG is parallel to k [see Fig. 3(b)]. In this case, L1 ,L2 , and Le intersect in Bi . 3) Orientation and an Approximate Position of G Are Assigned: If the orientation and an approximate desired location (xd , zd ) of G are assigned, x and z must be found so that (26) is satisfied and the error \u03b5 = (x \u2212 xd )2 + (z \u2212 zd )2 is minimized. Since both \u03b5 and p1 are continuously differentiable in x and z, the global minimum of \u03b5 is a stationary point of the function L\u03b5 = (x \u2212 xd )2 + (z \u2212 zd )2 + 2The constant-orientation statical workspace of the 2\u20132 CDPR is a conic on the xz-plane, as observed in [26]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000378_a:1021153513925-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000378_a:1021153513925-Figure12-1.png",
        "caption": "Figure 12 Distribution of residual stresses during a direct laser metal powder deposition (laser power: 600 W, scanning speed: 10 mm/s): (1) \u03c4 = 42.8 s and (2) \u03c4 = 90 s.",
        "texts": [],
        "surrounding_texts": [
            "The distribution of residual stresses obtained by finite element modeling resulting from the use of 10 mm/s scanning speed and 600 W laser power are shown in Figs 11 and 12. Residual stresses were also investigated with the x-ray diffraction technique. X-ray residual stress calculations were undertaken perpendicular to the direction of the line builds using the sin2 \u03c8 method [18]. The technique is not described here in detail as the theoretical background and basic principles have been recently summarized [19]. The distribution of residual stresses within a single layer obtained by finite element modeling was compared with that obtained by x-ray diffraction technique showing satisfactory agreement (Fig. 13). The figure indicates that there is a strong variation in the level of residual stresses inside the deposited layers. The distribution of residual stresses is tensile within the center of the layers and compressive towards the edges. Moreover, immediately outside the melt-pool the stress in the heat-affected zone is tensile. It can be expected that this will revert to compressive stress as the distance from the melt track increases. However, due to the time-consuming nature of x-ray diffraction technique, this detail was not measured, but is confirmed by the finite element modeling (please see Figs 11 and 12). The effect of subsequent layers deposition on the residual stresses distribution is shown in Fig. 14. The sample was allowed to cool below 50\u25e6C between each subsequent build in order to eliminate any preheating effect. The data presented in Fig. 14 indicate a distribution of stresses within the first layer (left) similar to that plotted in Fig. 13. However, there is a progressive increase in the level of tensile residual stresses as subsequent layers are deposited. In addition, in the case of subsequent layers deposition, transverse cracks (i.e. perpendicular to the direction of laser scan (Fig. 15)) as well as longitudinal cracks (i.e. parallel to the direction of laser scan (Fig. 16)), were detected. This can be explained by a stepwise increase in the residual stresses with each successive, overlapping laser track [19]. We deliberately designed experiments in which each subsequent deposited layer was allowed to cool below 50\u25e6C before carrying out the following pass. This was to avoid the effect of preheating on the residual stresses. However, cracking can be avoided by preheating the specimen, but also reduces the cooling rate. The mechanism that prevents cracking by preheating increases the ductility of the MONEL 400-alloy. The effect of a preheating treatment to 400\u25e6C and post-heat treatment to 600\u25e6C for 1 hour is shown in Figs 17 and 18, respectively. When preheated to 400\u25e6C, the residual stresses are reduced to about +400 MPa. After a stress-relieving treatment at 600\u25e6C, the residual tensile stresses are further reduced to about +200 MPa. These results suggest that shrinkage in the melt-zone produces residual tensile stresses and that stress-relieving could reduce those values."
        ]
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure1-1.png",
        "caption": "Fig. 1. Serial chains generating special 3-DOF motion. (a) PU chain (b) UP chain (c) RPR chain.",
        "texts": [
            " The product consists of a translations parallel to a linearly independent vectors followed by b rotations around b axes passing through one point undergoing the a translations. The motion generated by an RPR open chain belongs to the special 1T2R category and can be decomposed into a product of three factors. There are three special categories of 3-DOF motion that include two rotational DOFs and one translational DOF. The first category is a special 1T2R motion, which can be produced by a serial PU chain, as shown in Fig. 1(a). A new family of PM that has the special 1T2R motion is proposed in [8]. Using Kong\u2019s virtual chain approach [9], we call this family of 3-DOF PMs as PU-equivalent PM, where U denotes a universal joint. The second category is a special 2R1T motion, which can be generated by a serial UP chain, as shown in Fig. 1(b). The UP motion is the kinematic inverse of the PU motion. The UPequivalent PMs were first proposed by Kong and Gosselin [9]. The third category is a special motion, which can be realized by a serial RPR chain, as shown in Fig. 1. A PM that generates such a motion is called an RPR-equivalent PM. The displacement of the moving platform of an RPR-equivalent PM can be represented by a product of a rotation followed by a translation and then a rotation. The two axes of rotation generally do not intersect and remain perpendicular to each other. The RPR-equivalent PMs are suitable for many manipulations along a curved surface when high rigidity and accuracy are 1552-3098 \u00a9 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission",
            " {L1} = {G(u)}{S(F)}, {L2} = {S(Da)}{G(v)}, and {L3} = {S(Db)}{G(v)} Like the 4\u20134\u20134 subcategory, the PM in 5\u20135\u20135 subcategory can be constructed by two combinations, respectively. The first combination is {L1} = {G(u)}{S(F)} and {L2} = {S(Da)}{G(v)}, {L3} = {S(Db)}{G(v)} with Da \u2208 axis(O, u) and Db \u2208 axis(O, u). The second combination is {L1} = {S(D)}{G(v)} and {L2} = {G(u)}{S(Fa)}, {L3} = {G(u)}{S(Fb)} with Fa \u2208 axis(B, v), and Fb \u2208 axis(B,v). The second family results from the kinematic inversion of the first family. Fig. 10 shows a 2-SPR/RPS PM. The realization is obtained by replacing in Fig. 1, the three U joints by S pairs with the same centers. Limbs 2 and 3 are SPR chains, in which the S joint is embodied by three revolute pairs with intersecting axes. Limb 1 is a RPS chain. D1 denotes the center of the spherical joint in limb 1. F2 and F3 denote the centers of the spherical joint in limbs 2 and 3, respectively. Bi denotes the center of the last revolute pair in the ith limb. The kinematic bond of limb 1 is {L1} = {R(A1 , u)}{T(r)}{S(D1)} with r\u22a5u = {G(u)}{S(D1)}, D1 \u2208 (B,v). (15) The kinematic bond of limb 2 is {L2} = {S(F2)}{T(s2)}{R(B2 , v)}with s2\u22a5v = {S(F2)}{G(v)},F2 \u2208 (O,u)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002084_j.cirpj.2010.03.005-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002084_j.cirpj.2010.03.005-Figure7-1.png",
        "caption": "Fig. 7. 3-D CAD volume model of the optical system for high power skin\u2013core SLM applications, upper fibre active.",
        "texts": [],
        "surrounding_texts": [
            "As described above, a top hat beam profile is eligible for additive manufacturing techniques especially for large scan line spacing which are inevitable for an increased build rate. Yet, a uniform intensity distribution requires the superposition of several modes over the running length of the fibre core. Furthermore not all rays that enter the fibre core are allowed to propagate (see Fig. 11) [16]. Considering a free wave the phase of the wave front C0A0 concur in all single points. Hence, only waves whose phases concur in each point on the wave front AC can propagate through the waveguide [16]. Since this wave only consists of the incoming and the reflected wave, this constraint is fulfilled only if the phases of two rays differ in a multiple of 2p. Due to the incident-angle-dependant phase shift V the constraint for constructive interference becomes the following transcendent eigenvalue equation: 2 ncdcos\u00f0\u2019km\u00de l \u00bc m\u00feV p (8) where \u2018\u2018nc\u2019\u2019 is the refractive index of the core, \u2018\u2018d\u2019\u2019 is fibre core diameter, \u2018\u2018d\u2019\u2019 is wavelength and \u2018\u2018m\u2019\u2019 is the mode number. With regard to multi-mode fibres the second summand on the right side of the equation can be neglected since its maximum value is 1. Hence, the maximum number of modes mmax occur for the smallest possible angle \u2013 the critical angle for total reflection wg \u2013 which is calculated according to: \u2019g \u00bc arcsin nc ncl (9) where \u2018\u2018ncl\u2019\u2019 is the refractive index of the fibre cladding. The numerical aperture NA is calculated according to: NA \u00bc nc cos\u00f0\u2019g\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 c n2 cl q (10) The combination of Eqs. (8)\u2013(10) leads to the characteristic Vparameter for optical fibres: V \u00bc pd ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 c n2 cl q l (11) The number of modes for cylindrical fibres, N, is finally calculated according to: N \u00bc 4 p2 V2 (12) The probability to achieve a uniformly top hat shaped beam profile increases with the number of modes overlaying in an optical fibre. With regard to the optical setup used for the described prototype machine tool (NA = 0.11, l = 1030 nm) the mode number of the 50 mm fibre is calculated to 114, whereas the mode number of the 200 mm fibre is calculated to 1825. Although the absolute values do not indicate whether the resulting intensity profile is a top hat one or not, it becomes quite obvious that in the case of the smaller fibre core diameter (50 mm) the resulting intensity profile is more likely to be a Gaussian type than the intensity profile of the 200 mm fibre, whereas for the top hat intensity distribution it is vice versa. In summary it can be estimated that the intensity distribution for the manufacturing of the large volume core (where large build rates needs to be achieved) which is done with the 200 mm fibre, is likely to be a top hat one. In contrast, the outer skin is manufactured with the 50 mm fibre, whose intensity profile is more likely to be in between top hat and Gaussian shaped."
        ]
    },
    {
        "image_filename": "designv10_1_0002463_s11837-020-04260-y-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002463_s11837-020-04260-y-Figure5-1.png",
        "caption": "Fig. 5. Schematic of overall processing steps for screen/stencil 3D printing. A high-viscosity metal powder/binder paste is spread and pushed through a screen layer by layer.",
        "texts": [
            "26 Another unique advantage of the MEAM process is its ability to print internal latticework infill structures, which drastically reduces the processing time as well as resulting in parts that are lightweight (Fig. 4). Some of the disadvantages of this process include the slow nature of the build, which does not lend itself to mass production, and the relatively poor surface finish compared with some other metal AM printing technologies. The third sinter-based AM technique is screen or stencil printing, which uses pastes created by mixing metal or alloy powders with organic or aqueous solvent-based slurries. A schematic of the printing process is shown in Fig. 5. The screen is located slightly above a substrate on which the part is printed. The screens can be fabricated as a negative of the part design, while stencils are typically cut by a laser from sheet metal. Once the floodbar has spread the paste over the screen, a printing squeegee bar pushes on the paste, which then presses on the screen and squeezes material through in places where the screen mesh has openings. The paste used generally exhibits shear thinning during the processing step. The substrate on which the layer of paste is deposited is transported out of the printing chamber and quickly dried to remove the solvents before the next layer can be printed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002458_1.4043983-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002458_1.4043983-Figure6-1.png",
        "caption": "Fig. 6 a) a 3D FGM turbine disk having a ring and blades made of Cu10Sn and 316L respectively, b) an Eiffel tower whose material transited from Cu10Sn at the bottom to 316L at top gradually.",
        "texts": [
            " So the quantity of Cu9NiSn3 and FGM hardness would increase as the percentage of Cu10Sn increasing. 30 40 50 60 70 80 100 vol%Cu10Sn 25 vol% 316L 50 vol% 316L 75 vol% 316L 100 vol% 316L    Cu3.8Ni  Cr0.19Fe0.7Ni0.11  (Fe,Ni) Cu Cu9NiSn3    In te n si ty ( a .u .) 2-Theta (Deg.) 100 vol% 316L 75 vol% 316L 50 vol% 316L 25 vol% 316L 100 vol% Cu10Sn  Cu41Sn11          Fig. 5 XRD result of the SLM processed horizontal FGM sample with material transiting from 316L to Cu10Sn For demonstration purpose, a set of horizontal and 3D FGM models were manufactured, as shown in Fig.6. Fig. 6a shows a turbine disk having a ring and blades made of Cu10Sn and 316L respectively, and the material was gradually Acc ep te d Man us cr ip t N ot C op ye di te d Downloaded From: https://manufacturingscience.asmedigitalcollection.asme.org on 06/19/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use 12 changed from Cu10Sn to 316L at the root of the blades. Fig. 6b presents a 2D Eiffel tower whose material transited from Cu10Sn at the bottom to 316L at top smoothly. The red arrows in these images show the directions of material transiting from Cu10Sn to 316L. This paper has demonstrated a multiple material dispensing based SLM approach to fabricate the horizontal and 3D functional graded material structures and the feasibility to deposit five different metallic powder mixture materials within the same building layer. Macrostructure analysis of the 316L/Cu10Sn square sample presented gradual rainbow-like color change and clear boundaries on the sample top surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000589_0077-7579(64)90001-8-Figure29-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000589_0077-7579(64)90001-8-Figure29-1.png",
        "caption": "Fig. 29. T h e appara tus used in the s tudy of the or ien ta t ion mechan i sm of Daphnia magn~, B = h a ~ - ~ F T = flUorc~gent~tube; G A = g r ~ . ~ t c d a rc ; L = lever mechan i sm to lift the-tu.,~ntable wi th the screen; PB == c i rcular ~ ~ s r i r J a a p inned d a p h n i d ; S : screen; T =~ table ; T T = circular t u rn t ab l e wi th the screen S.",
        "texts": [
            " is dimmed, the number of animals that make somersaults decreases. In the homogeneous A.L.D. of the apparatus described in part 12a, when placed vertically, a number of animals will also somersault. Other animals are temporarily orientated to the contrast in the planes oblique to the illuminated one, but these animals suddenly make loopings when they turn in the illuminated plane. Therefore it was thought possible to study the influence of the absolute light intensity with this apparatus. Five animals were swimming in the flat circular perspex box (P.B. fig. 29) and the number of somersaulting daphnids was counte~ at one minute intervals:The observations were made at different light intensifies, measured with a barrier layer cell with an aperture of 180 \u00b0. In D I U R N A L V E R T I C A L M I G R A T I O N OF D A P H N I A 3 7 9 fig. 28 the percentage of the animals performing somersaults is made a function of the light intensity. Each point is the mean value of at least 40 countings with groups of five animals. The standard error of the mean percentage is indicated by vertical bars",
            " As has been pointed ou~ ~'arlier (RINGELBERG, 1963) this mechanism may work by gravity perception (either through special receptors (BIDDER, 1929) or through the \"attgemeine Lagereflex\" (YON BUDDENBROCK, t914) or it may be :,. passive process as a result of the position of the centre of gravity (EWALD, 1910) ). Obviously this \"night system\" does not function at higher light intensities even when the A.t,.D. is unsuitable for proper photic orientation. 12. T H E O R I E N T A T I O N T O C O N T R A S T S a. M E T H O D S 30 cm) fluorescent tube (fig. 29, FT) was mounted in a hardboard box (B) with circular openings in bot tom and cover. A small watertight circular perspex box (PB) could be fixed on a small table (T) in the centre of the fluorescent tube. A Daphnia magna could be fixed by a small pin through the broodpouch in the centre of the fluorescent tube. The leg of the small table (T) in the centre of the tube could be used as an axis for a circular turntable (TT) on which a screen (S) could be fixed. It was possible to raise the turntable with the screen with a set of levers (L), thereby screening off the light from the fluorescent tube"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003043_j.jmbbm.2015.10.019-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003043_j.jmbbm.2015.10.019-Figure1-1.png",
        "caption": "Fig. 1 \u2013 The schematic diagram of tensile specimen.",
        "texts": [
            " Phase identification was studied by X-ray diffractometer (XRD, D/MAX-2500PC) with CuK\u03b1 radiation. Microstructural observation was observed using optical microscope (Axio Vert.A1, ZEISS) and Scanning Electron Microscope (SEM, SU-8010) on the surface etched by a mixture of 5 mL H2O2 and 20 ml HCl for 10 s at room temperature. Tensile tests were performed on a universal testing machine at room temperature, with an initial strain rate of 2 mm/s. Three specimens were tested for each group. The schematic diagram of tensile specimen is shown in Fig. 1. Fractography were examined by using SEM. The static immersion test was performed in accordance with the ISO 10271 standard. Samples (n\u00bc15) with the dimensions of 30mm 15mm 1.5 mm were fabricated by SLM. Prior to performing this study, the samples were ground with water proof emery paper from 240, 600, 800, 1000 up to 1200 grit under running water, then ultrasonically cleaned in acetone for 15min, rinsed in distilled water and finally dried at room temperature for 3 h. Therewith, the static immersion tests were conducted in 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure5.13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure5.13-1.png",
        "caption": "Fig. 5.13 Helicopter force balance in simple lateral manoeuvre",
        "texts": [
            " PIOs represent a limit to safe flight for both types of aircraft and criteria are needed to ensure that designs are not PIO prone. This issue will be addressed further in Chapter 6. The examples discussed here highlight a conflict between attitude control (or stability) and flight path control (or guidance) for the helicopter pilot. This conflict is most vividly demonstrated by an analysis of constrained flight in the horizontal plane (Ref. 5.15). Lateral Motion We consider a simple model of a helicopter being flown along a prescribed flight path in two-dimensional, horizontal flight (Figure 5.13). The key points can be made with the most elementary simulation of the helicopter flight dynamics (i.e. quasi-steady rotor dynamics). It is assumed that the pilot is maintaining height and balance with collective and pedals, respectively. The equation for the rolling motion is given in terms of the lateral flapping \ud835\udefd1s. Ixx?\u0308? = \u2212M\ud835\udefd\ud835\udefd1s (5.52) where M\ud835\udefd is the rolling moment per unit flapping given by M\ud835\udefd = (NbK\ud835\udefd 2 + hRT ) (5.53) The rotor thrust T varies during the manoeuvre to maintain horizontal flight"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.15-1.png",
        "caption": "Fig. 3.15 Load transfer without suspension roll, but with vehicle raising",
        "texts": [
            " Summing up, a lateral force \u2212Y j at P is totally equivalent to a lateral force \u2212Y1j at Q1 and another lateral force \u2212Y2j at Q2, plus the horizontal moment Y(h \u2212 qb)i (Fig. 3.11) applied to the vehicle body. Figures 3.14 and 3.15 shows how each force Yi at Qi is transferred to the ground by the suspension linkage, without producing any suspension roll. This is the key feature of the roll center Qi . Quite remarkably, this is true whichever the direction of the force there applied, and hence it is correct to speak of a (no-)roll center point (at first, Fig. 3.15 might suggest the idea of a roll center height qi ). The moment Y(h\u2212qb) is the sole responsible of suspension roll. More precisely Y ( h \u2212 qb )= ks \u03c61 \u03c6s 1 + ks \u03c62 \u03c6s 2 = \u0394ZL 1 t1 + \u0394ZL 2 t2 (3.103) exactly like in (3.89). The total lateral load transfer \u0394Zi on each axle is therefore given by \u0394Ziti = (\u0394ZY i + \u0394ZL i ) ti = Yiqi + ks \u03c6i \u03c6s i = k p \u03c6i \u03c6 p i (3.104) that is by the sum of the part due to the suspension linkage and the part due to the suspension springs (Eqs. (3.105) and (3.89)). However, no suspension roll does not mean no other effects at all. Indeed, there are always lateral load transfers (Fig. 3.15) \u0394ZY i ti = Yiqi (3.105) and hence also some rolling of the vehicle body related to the tire vertical deflections. 3.8 Suspension First-Order Analysis 79 Moreover, since the lateral forces exerted by the road on the left and right tires are not equal to each other (they will be equal to Yi/2 \u00b1 \u0394Yi , where \u0394Yi depends on the tire behavior), there is also a small rising zs i of the vehicle body (Fig. 3.15) zs i = \u0394Yi 2bi ks zi ci = \u0394Yi 4qi ks zi ti (3.106) associated with a small track variation \u0394ti \u0394ti = \u22122bi ci zs i = \u22124qi ti zs i = \u2212 ( 4qi ti )2 \u0394Yi ks zi (3.107) and suspension jacking. The stiffness of the tires does not appear in (3.106) and (3.107). All relevant equations for the first-order suspension analysis have been obtained. Solving them provides the relationship between Y and the total roll angle \u03c6 and, more importantly, the relationship between the front and rear load transfers \u0394Z1 and \u0394Z2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001621_j.procir.2015.08.060-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001621_j.procir.2015.08.060-Figure15-1.png",
        "caption": "Fig. 15. Laser molten tool prototypes generated of WC/Co 83/17 powder",
        "texts": [
            " Due to the extremely high cooling gradient, a fine grained acicular solidified structure is formed in the molten beads, which contains only a small weight percentage of cobalt. This results in an enormous material embrittlement. A typical sintered structure is generated between the layers and the melting tracks. It contains approximately the initial amount of cobalt binder. In addition, no changes in the carbide grains are visible in the intermediate areas. 4. Validation of results Within the scope of the validation studies, first special tool prototypes could be laser molten from carbide powder (Figure 15). Special tools are an important subcategory of cutting tools, which are often used in industrial production processes. Additively manufactured inserts or drills with integrated cooling channels have the potential to increase productivity enormously. Through internal and conformal cooling of the tools, dry machining without cooling lubricants is possible. This reduces pollution on the environment as well as on the machine operator. In addition, heat accumulations can be eliminated from the tool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003724_j.jmatprotec.2015.06.002-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003724_j.jmatprotec.2015.06.002-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagrams of thin wall (a) and scanning strategy of cuboid samples (b).",
        "texts": [
            " A 127 mm-focal length ZnSe lens worked at a certain defocused distance to get a 1.0 mm spot size. The 3D model was designed and then transformed into G-code by self-developed software. All the DLF experiments were implemented in an argon gas-filled glove box with O2 concentration controlled below 40 ppm. Gas atomized Rene 104 powders with particle sizes from 50 to 100 m were used as the starting material in DLF experiments, whose chemical composition is listed in Table 1. According to the laser scanning strategies shown in Fig. 2b and processing parameters listed in Table 2, a one-pass thin wall part with 45 mm in length and 40 mm in height and several cuboid samples by multipass deposition were fabricated, respectively. Further, two cuboid samples deposited at a power of 720 W and a hatch spacing of 0.5 and 0.7 mm were hipping treated at a temperature of 1107 \u25e6C, a shielding gas pressure of 1030 bar and a dwelling time of 2 h. In order to avoid the formation of defects during sampling, the DLFed thin wall and cuboid samples were cut from the substrate and divided into small blocks for various positions by the nondestructive sampling method of wire electrical discharge machining",
            " Standard metallographic techniques were used to prepare metallographic specimens of as-DLFed and DLF + hipped samples on cross and vertical sections. Thereafter, microstructure observation was performed by an optical microscope and a Philips XL30 scanning electron microscope respectively. Finally, lengths and counts of the cracks in all samples were measured using image processing software. For the DLF technology, one-pass deposition is the basic step to evaluate the workability of new materials. Fig. 3 reveals the microstructures on the top, middle and bottom sections (shown in Fig. 2a) of the DLFed Rene 104 thin wall. Although a small number of micropores with diameters below 10 m are observed in Fig. 3, no obvious defects such as cracks and bonding errors at the interface between adjacent layers exist on both sections at different heights, implying that Rene 104 superalloy parts with an extremely fine and dense microstructure can be obtained at proper parameters through DLF. During DLF, extreme rapid solidification rate and high temperature gradient (200 \u223c 500 K/mm) at a very small molten pool (roughly 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure5.25-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure5.25-1.png",
        "caption": "Fig. 5.25 Results: see (B) MT =",
        "texts": [
            "24 consists of a circular tube 1 and a solid circular shaft 2 . They are connected with a bolt at point A. Determine the torque MT acting in the system and the angle \u03b2 of the bolt (see the figure) if the ends of the two parts make the angle \u03b1 in the stress-free state (i.e., before the bolt is attached). GIT2 1 2 \u03b1 \u03b2 GIT1 A a b Results: see (A) MT = GIT1 5.5 Supplementary Examples 225 E5.17Example 5.17 Two rigid levers 1 and 2 are attached to the free end of a thin-walled rectangular tube (shear modulus G), see Fig. 5.25. The end points of the levers are at a distance a from the end points of two springs (spring constant c). Determine the torque MT in the tube and the maximum shear stress \u03c4max if the springs are connected to the levers. 4 a c h 1 + 2 c l G h t , \u03c4max = a cG Gh t+ 2 c l . E5.18Example 5.18 The shaft shown in Fig. 5.26 consists of a tube (shear modulus G2) which is bonded to a core (shear modulus G1). It is subjected to a torque MT at its free end. Determine the maximum shear stresses in the core 1 and in the tube 2 and the angle of twist"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003857_j.jmatprotec.2016.12.033-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003857_j.jmatprotec.2016.12.033-Figure9-1.png",
        "caption": "Fig. 9. Average track contact angle and variations as a function of scan speed and laser power.",
        "texts": [
            " Four tracks with a height of more than 35 m ere observed as shown in Fig. 8b. It was found that the track eight was independent of the scan speed. Moreover, at the contant scan speed the tracks in the continuous zone or some of the eep penetration zone (laser power ranges from 60 W to 80 W) tend o have an increased track height. The big variance of track height or some cases (60 W @ 500 mm/min, 65 W @ 2500 mm/min, 80 W 1500 mm/min and etc.) could be contributed to the waviness of he top surface of the tracks. .2.4. Contact angle Fig. 9 shows the average contact angle of the tracks as a function f scan speed and laser power. Due to the fact that no penetration as found in the discontinuous zone, only the tracks with a laser ower higher than 45 W were measured. The contact angles 1 and 2 (Fig. 9) were measured three times at each side of the tracks, nd then the contact angle value for each track was averaged. For ach fixed laser power, there is no obvious trend of contact angle or different scan speeds. However, regardless of scan speed, the ontact angle tends to decrease with the increase of laser power. his could be explained by the fact that the fluid metal has lower iscosity value and lower surface tension at the high temperatures ue to the high heat input of the laser. function of scan speed and laser power"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure6.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure6.1-1.png",
        "caption": "Figure 6.1. All objects have the inherent property of inertia, the resistance to a change in the state of motion. The measure of linear motion inertia is mass. A medicine ball has the same resistance to acceleration (5 kg of mass) in all conditions of motion, assuming it does not travel near the speed of light.",
        "texts": [
            " Newton stated that all objects have the inherent property to resist a change in their state of motion. CHAPTER 6 Linear Kinetics 133 His first law is usually stated something like this: objects tend to stay at rest or in uniform motion unless acted upon by an unbalanced force. A player sitting and \u201cwarming the bench\u201d has just as much inertia as a teammate of equal mass running at a constant velocity on the court. It is vitally important that kinesiology professionals recognize the effect inertia and Newton's first law have on movement technique. The linear measure of inertia (Figure 6.1) is mass and has units of kg in the SI system and slugs in the English system. This section is an initial introduction to the fascinating world of kinetics, and will demonstrate how our first impressions of how things work from casual observation are often incorrect. Understanding kinetics, like Newton's first law, is both simple and difficult: simple because there are only a few physical laws that govern all human movement, and these laws can be easily understood and demonstrated using simple algebra, with only a few variables"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001708_tia.2009.2023393-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001708_tia.2009.2023393-Figure13-1.png",
        "caption": "Fig. 13. Armature and field flux of IPM motor (Ia = 300 A, \u03b2 = 90\u25e6). (a) Total flux. (b) Field flux. (c) Armature flux.",
        "texts": [
            " The third harmonic eddy currents of the surface-mounted type flow in small loops, which correspond to the stator slot openings. On the other hand, the currents of the interior-type motor flow in a large loop that covers the entire magnet. The sixth harmonic eddy-current distributions of each motor are similar. However, the loss in the interior-type motor is very small. The carrier harmonic losses are nearly the same for all the motors. Let us now discuss why the magnet eddy-current distribution of the interior-magnet-type motor is different from those of other motors by using a simple magnetic circuit model. Fig. 13 shows the decomposed components of flux densities produced by the field (magnet) and armature. It can be observed that the field flux linkages of the N and S magnets are almost the same. On the other hand, the armature flux enters into only one magnet at this rotor position. It alternately varies due to the rotation of the rotor. It is caused by the permeance distribution of the rotor along the peripheral direction. Fig. 14 shows the total, field, and armature flux linkages of the magnet (A and B in Fig. 13). It is clarified that the time variation of the magnet flux, which causes the magnet eddy-current loss, is produced mainly by the armature flux. In addition, the time-harmonic order of this variation is third, which caused the major eddy-current loss in the IPM-type motor shown in Fig. 12. The armature flux paths in the rotor can be simplified as shown in Fig. 15: a) path of tooth\u2013bridge\u2013magnet\u2013the other tooth; b) path of tooth\u2013bridge\u2013the other bridge\u2013the other tooth. There is one more path (c), which is at the rotor surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000502_j.mechmachtheory.2012.05.008-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000502_j.mechmachtheory.2012.05.008-Figure6-1.png",
        "caption": "Fig. 6. Geometry of contacting bodies viewing from two orthogonal directions.",
        "texts": [
            " 5, which can be written as, H3 \u00bc H\u2032 3sin 0:25\u03c0=\u0394T1 mod \u03b8dj;2\u03c0 \u03b80 \u03b80\u2264mod \u03b8dj;2\u03c0 \u2264\u03b81 H\u2032 3 \u03b81bmod \u03b8dj;2\u03c0 b\u03b83 H\u2032 3sin 0:25\u03c0=\u0394T3 mod \u03b8dj;2\u03c0 \u03b80 \u03b83\u2264mod \u03b8dj;2\u03c0 \u2264\u03b84 0 otherwise 8>>>< >>>: \u00f07\u00de where \u0394T1 and \u0394T3 are given by, \u0394T1\u00bc \u0394T3\u00bc arcsin 0:5B=Do\u00f0 \u00de defect on the outer race arcsin 0:5B=Di\u00f0 \u00de defect on the inner race \u00f08\u00de The raceway contact angle \u03b8dj is represented by, \u03b8dj \u00bc 2\u03c0 Z j 1\u00f0 \u00de\u00fe \u03c9ct the outer race contact angle 2\u03c0 Z j 1\u00f0 \u00de\u00fe \u03c9c \u03c9\u00f0 \u00det the inner race contact angle 8>< >: \u00f09\u00de The initial angular offset of the defect of the jth ball is, \u03b80\u00bc 2\u03c0 Z j 1\u00f0 \u00de\u00fe \u03c6di defect on the outer race 2\u03c0 Z j 1\u00f0 \u00de\u00fe \u03c6do defect on the inner race 8>< >: \u00f010\u00de where \u03c6di and \u03c6do are the initial angular offsets of the defect of the first ball, j is 1 to Z, and \u03b8e is half of the tangential size of defect. Note that \u03b80 in Eq. (10), which is defined as the initial angular position of the first ball with respect to the localized defect, is assumed to be 0. For the first case, H\u20321 is equal to the height of the defect [6,12], and for others case, H\u20321, H\u20322 and H\u20323 are equal to H\u2032sd. According to the description in Fig. 6, Hd can be written as, Hd\u00bc0:5d 0:5d\u00f0 \u00de2 0:5B\u00f0 \u00de2 0:5 \u00f011\u00de Hence, H\u2032sd can be formulated size as, H\u2032 sd\u00bc H H b Hd Hd H \u2265 Hd \u00f012\u00de Next, the contact deformation at the edge of the defect is calculated and coupled to the impulse function H\u2032sd. In this study, in order to describe the relationship between the contact deformation at the edge and the size of the localized defect, the contact deformation function P(W, L, B, H) is defined as follows: Pi W; L;B;H\u00f0 \u00de\u00bc a1B 2\u00fe b1B\u00fe e1 \u00f013\u00de where Pi(W, L, B, H) is contact deformation at the edge of the localized defect, W the factor of the external load and it is ignored at here, L is the length of the defect, B is the width of the defect, H is the depth of the defect, i denotes the number of the contact point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001404_j.engfailanal.2013.08.008-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001404_j.engfailanal.2013.08.008-Figure4-1.png",
        "caption": "Fig. 4. Tooth thickness changing according to method 2 [3].",
        "texts": [
            " In cases where there are two tooth pairs in contact, the same calculations are repeated for the second tooth pair to find Km2. Then we can obtain the equivalent stiffness for meshing as follows: Km \u00bc Km1 \u00fe Km2 \u00f018\u00de Chaari et al. [1] presented an analytical approach to calculating the reduction in the total gear mesh stiffness due to crack depth propagation, as well as a model using FEM to verify the results obtained analytically. In stiffness calculations the of the coefficients of Eq. (15). authors assumed that the reduction in the tooth thickness concerned the cracked root part only, as shown in Fig. 4. In order to provide a clear comparison of the effects of changing the method for tooth thickness reduction, the same approach as that utilised in method 1 is applied again in method 2, but with the assumption that the reduction in the tooth thickness only concerns the cracked root part. As the crack propagates in the tooth root, the cracked side of the tooth shows relatively low stresses distributed in the area bounded by the tooth flank, see Fig. 5a\u2013c. This means that this area is not strained mechanically enough under the action of the applied load due to the existence of a crack",
            " This method assumes reduction of the effective tooth thickness with a straight line; it works for small crack sizes, for which it provides an approximate fit, but for larger sizes the straight line starts removing an effective area which should be included for the stiffness evaluation. Moreover, this straight line does not demarcate exactly the assumed dead area that should be excluded. Method 2, see Fig. 8, only shows acceptable results for crack levels as small as around 16%. Basically, when applying this method, one assumes that the reduction in the tooth thickness concerns the cracked root part only, as shown in Fig. 4, and depends merely on the inclination of the crack angle. Consequently, we can see in Table 4 that the percentage difference from the FEM result for method 2 for crack case D is 18.29%, which is a significant difference. The amount of the tooth thickness reduction is so small that the stiffness reduction for crack levels larger than 16% could not be described, and with this approach there will be no reduction in the case of a zero crack angle. Method 3, see Fig. 9, shows good agreement for crack levels greater than 30%, with the percentage difference from the FEM result for crack case D being significantly reduced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003937_j.engfailanal.2017.08.028-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003937_j.engfailanal.2017.08.028-Figure2-1.png",
        "caption": "Fig. 2. Geometric parameters of the gear tooth fillet-foundation deflection in presence of tooth root crack.",
        "texts": [
            " They are expressed as [26], = + + + + +X h\u03b8 A \u03b8 B h C h \u03b8 D \u03b8 E h F( )i f i f i i f i f i i 2 2 (2) However, the effective load bearing area of the gear between the gear tooth and the gear body will be reduced when the tooth root crack appears, and thus the contribution of the gear body deformation to the gear tooth displacement will be increased, which thereby results in the reduction of the gear tooth fillet-foundation stiffness. Therefore, in order to put forward the calculation method of the gear tooth fillet-foundation stiffness with tooth root crack and to improve further the accuracy of gear mesh stiffness calculation, two improved models are proposed to calculate the stiffness of gear tooth fillet-foundation in this paper based on the model proposed in [26]. Fig. 2 shows the geometrical parameters of a gear tooth and its gear body when a tooth root crack appears. Appearance of the tooth root crack will cause reduction of the actual load carrying area of the gear body compared with the healthy case. Therefore, a hypothesis is put forward that the reduction of the gear body stiffness is proportional to the percentage of the crack length in the linear range. Thus the stiffness of the gear tooth fillet-foundation with tooth root crack can be expressed as, = \u2212K K x(1 )f (3) where, Kf is the stiffness of healthy gear tooth fillet-foundation; And x is the ratio of the crack length and the total length of the potential crack path, which is calculated as, =x l L 0 (4) where, the symbol l0 is the tooth root crack length; L denotes the total length of the tooth root crack. This model is simple to use for the calculation of gear mesh stiffness with respect to gear tooth root crack. As shown in Fig. 2, geometric parameters of the fillet-foundation deflection will change in the presence of tooth root crack. It is assumed that the stiffness of the gear fillet-foundation is related to the variations of geometric parameters of the fillet-foundation due to the tooth root crack. Compared with the geometric parameters as shown in Fig. 1, the load bearing area is changed from Sf to Sf\u2032, and uf is changed to uf\u2032 due to the presence of the gear tooth root crack. A rectangular coordinate system is established as shown in Fig. 2. Here, Rb is the radius of base circle, and Rg is the radius of dedendum circle; L denotes the total length of the fictitious crack crossing over the whole tooth thickness and l0 is the length of the practical crack; \u03b1m is action angle of the mesh force; The coordinate of point OA is (0, \u2212Rg); While the coordinate of point D is (xD, yD), X is the ratio of the practical crack length to the fictitious crack length. It can be seen that the line of the applied force is through the point H from Fig. 2, and the coordinate of the point H is (0, uf). Therefore, the equation for the action line of the force can be obtained as, = +y x \u03b1 utan m f1 (5) And uf can be derived from the geometric relationship, which can be calculated as, = \u2212u R \u03b1 R cosf b m g (6) Since the line OAD is through the point OA, and the slope of the straight line OAD is tan\u03bb, the equation representing the line OAD can be expressed as, = \u2212 \u2212y x \u03bb R tan g2 (7) where, \u2032= \u2220 \u2212 \u2220 = \u2212 \u03bb EO H EO G S S R2A A f f g (8) Thus, Eq. (7) can be rewritten by substitution of \u03bb in Eq",
            " (5)\u2013(9), which is calculated as, \u23a7 \u23a8 \u23a9 = \u2212 = \u2212 + + + + x y R D \u03bb u R \u03b1 \u03bb D u R \u03b1 \u03bb g tan ( ) tan tan 1 tan tan 1 f g m f g m (10) While the length of the line segment O DA is denoted as, = + +O D x y R| | ( )A D D g 2 2 (11) Consequently, the length of the line segment OAD can be derived further by substitution of Eq. (10) into Eq. (11). It is shown as, = + + O D u R cos\u03bb sin\u03bbtan\u03b1 | |A f g m (12) And uf\u2032 is calculated as, \u2032= \u2212u O D R| |f A g (13) From the Eqs. (12) and (13), uf\u2032 can be deduced as, \u2032= + + \u2212u u R \u03bb \u03bb \u03b1 R cos sin tanf f g m g (14) As shown in Fig. 2, the symbol X is the percentage of the practical crack length over the fictitious crack length through the whole tooth thickness. It can be expressed as, =X l L 0 (15) Here, assuming that the relationship between Sf\u2032 and Sf is, \u2032= \u2212S S X(1 )f f (16) And, \u03b1 can be deduced from the tangent theorem of the circle, which is shown as, = \u2220 =\u03b1 CO D CO O D cos cos A A A (17) Then, from the Eqs. (12), (13), and (17), \u03b1 can be derived as, \u2032 = + \u03b1 R u R cos b f g (18) Thus, when considering the effect of the tooth root crack, the contribution of the gear body to the deformation of the gear teeth can be obtained and calculated as, \u2032 \u2032\u2032 \u2032\u2032= \u23a1 \u23a3 \u23a2 \u23a2 \u23a2 \u23a2 \u239b \u239d \u239c \u239c\u239c \u239e \u23a0 \u239f \u239f\u239f + + + \u23a4 \u23a6 \u23a5 \u23a5 \u23a5 \u23a5 \u03b4 E F b \u03b1 L u S M u S P Q \u03b11 cos [1 tan ]f f f f f 2 2 2 (19) It should be noted that these parameters Sf\u2032, uf\u2032 and \u03b1will equal to Sf, uf and \u03b1m, respectively, when the tooth root crack disappears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure2-5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure2-5-1.png",
        "caption": "Fig. 2-5 rotor circuit represented by three-phase windings.",
        "texts": [
            " 2-3-4 Stator-Inductance Ls due to all three stator currents (not including the flux linkage due to the rotor currents), the total flux linkage of phase-a can be expressed as \u03bb \u03bb \u03bba a a s a m a s a L i L i L i rotor-open leakage magnetizing= + = + = , , , (2-14) where the stator-inductance Ls is L L Ls s m= + . (2-15) EQuIvalENT WINdINgS IN a SQuIrrEl-CagE roTor 13 2-4 EQUIVALENT WINDINGS IN A SQUIRREL-CAGE ROTOR For developing equations for dynamic analysis, we will replace the squirrel cage on the rotor by a set of three sinusoidally distributed phase windings. The number of turns in each phase of these equivalent rotor windings can be selected arbitrarily. However, the simplest, hence an obvious choice, is to assume that each rotor phase has Ns turns (similar to the stator windings), as shown in Fig. 2-5a. The voltages and currents in these windings are defined in Fig. 2-5b, where the dotted connection to the rotor-neutral is redundant for the following reason: In a balanced rotor, all the bar currents sum to zero at any instant of time (equal currents in either direction). Therefore, in Fig. 2-5b, the three rotor phase currents add up to zero at any instant of time i t i t i tA B C( ) ( ) ( ) .+ + = 0 (2-16) Note that similar to the stator windings, a positive current into a rotor winding produces flux lines in the radially outward direction along its magnetic axis. 2-4-1 Rotor-Winding Inductances (Stator Open-Circuited) The magnetizing flux produced by each rotor equivalent winding has the same magnetic path in crossing the air gap and the same number of turns as the stator phase windings",
            " (2-18) 14 INduCTIoN MaCHINE EQuaTIoNS IN PHaSE QuaNTITIES Note that with the choice of the same number of turns in the equivalent three-phase rotor windings as in the stator windings, the rotor leakage inductance L\u2113r in Eq. (2-18) is the same as \u2032L r in the perphase, steady-state equivalent circuit of an induction motor. The same applies to the resistances of these equivalent rotor windings, that is, R Rr r= \u2032. rEvIEW oF SPaCE vECTorS 15 2-5 MUTUAL INDUCTANCES BETWEEN THE STATOR AND THE ROTOR PHASE WINDINGS If \u03b8m\u00a0 =\u00a0 0 in Fig. 2-5a so that the magnetic axes of stator phase-a is aligned with the rotor phase-A, the mutual inductance between the two is at its positive peak and equals Lm,1-phase. at any other position of the rotor (including \u03b8m\u00a0 =\u00a0 0), this mutual inductance between the stator phase-a and the rotor phase-A can be expressed as L LaA m m= \u22c5, cos .1-phase \u03b8 (2-19) Similar expressions can be written for mutual inductances between any of the stator phases and any of the rotor phases (see Problem 2-3). Eq. (2-19) shows that the mutual inductance and hence the flux linkages between the stator and the rotor phases vary with position \u03b8m as the rotor turns",
            " 2-29), which in a compact form include mutual coupling between the six windings: three on the stator and three on the equivalent rotor. In terms of phase quantities of an induction machine, we have developed voltage equations for the rotor and the stator, expressed in a compact space vector form (Eq. 2-31 and Eq. 2-32). These voltage equations include the time derivatives of flux linkages that depend on the rotor position. This dependence can be seen if we examine the flux linkage equations by expressing them with current space vectors defined with respect to their own reference axes in Fig. 2-5 as i t i t er a r A j m( ) ( )= \u03b8 (2-33) and i t i t es A s a j m( ) ( ) .= \u2212 \u03b8 (2-34) using the above two equations in the flux linkage equations (Eq. 2-28 and Eq. 2-29), \u03bb \u03b8 s a s s a m r A jt L i t L i t e m( ) ( ) ( )= + (2-35) and \u03bb \u03b8 r A m s a j r r At L i t e L i tm( ) ( ) ( ).= +\u2212 (2-36) The flux linkage equations in the above form clearly show their dependence on the rotor position \u03b8m for given values of the stator and the rotor currents at any instant of time. For this reason, the voltage equations in phase quantities, expressed in a space vector form by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure6.22-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure6.22-1.png",
        "caption": "Figure 6.22. Simple sagittal plane model of throwing illustrates the Segmental Interaction Principle. Joint forces (FE) from a slowing proximal segment create a segmental interaction to angularly accelerate the more distal segments ( FA).",
        "texts": [
            " This theory originated from observations of the close association between the negative acceleration of the proximal segment (see the activity on Segmental Interaction below) with the positive acceleration of the distal segment (Plagenhoef, 1971; Roberts, 1991). This mechanism is logically appealing because the energy of large muscle groups can be transferred distally and is consistent with the large forces and accelerations of small segments late in baseball pitching (Feltner & Dapena, 1986; Fleisig, Andrews, Dillman, & Escamilla, 1995; Roberts, 1991). Figure 6.22 illustrates a schematic of throwing where the negative angular acceleration of the arm ( A) creates a backward elbow joint force (FE) that accelerates the forearm ( FA). This view of the Segment Interaction Principle states that slowing the larger proximal segment will transfer energy to the distal segment. It is clear that this movement strategy is highly effective in creating high-speed movements of distal segments, but the exact mechanism of the segmental interaction principle is not clear. When you get down to this level of kinetics, you often end up with a chicken-oregg dilemma"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002833_physrevapplied.5.017001-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002833_physrevapplied.5.017001-Figure8-1.png",
        "caption": "FIG. 8. When a bilayer is freed, its top layer contracts, and its bottom layer expands, causing the bilayer to roll up. From Ref. [96], reprinted with permission from AAAS.",
        "texts": [
            " The strain is also asymmetric, with the magnitude of compression at the crest higher than the tension in the valley [Fig. 6(c)]. This phenomenon is exacerbated when using a 325-nm laser, as the neutral plane of the crest is similar to the maximum penetration depth. The wave number at the crest (\u03c92min) becomes much lower than it should be, while the valley wave number (\u03c92max) stays close to \u03c9bulk [Fig. 6(d)] [71]. Strain gradients in a flexible layer can cause bending along the direction with the smallest Young\u2019s modulus, through energy minimization [92,93]. Specifically, as shown in Fig. 8, a strained bilayer is produced with its top layer in-plane compressed and its bottom layer tensilely stressed. When the sacrificial layer is selectively etched away, the strained bilayer becomes detached from the substrate. Its top layer contracts, while its bottom layer expands, which results in rolling [94]. If the shape of the layer is adapted to this rolling direction, micro- or nanotubes can be formed as shown in Fig. 8 [44,94,95]. In previous literature, several approaches have been proposed to introduce the necessary strain gradient or strain difference into flexible layers with a bi- or multilayered structure, which will be discussed in the following. The first method utilizes lattice mismatch in an epitaxial bi- or multilayer structure. The advantage of this method is 017001-7 that the strain gradient can be well controlled and thus the tube diameter is tunable (see the discussion later). If the thickness of the layer is smaller than the critical value, the layer is coherent, and one can easily calculate the strain gradient based on the well-known values of the lattice constants [97,98]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002622_icamechs.2016.7813499-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002622_icamechs.2016.7813499-Figure1-1.png",
        "caption": "Fig. 1 Quadcopter aerial vehicle",
        "texts": [],
        "surrounding_texts": [
            "Keywords\u2014 quadcopter; cascade PID; Newton-Euler method; dynamics\nI. INTRODUCTION The multi-rotor helicopter has experienced a remarkable development over last decade, the most commonly used and studied one is the quadcopter which is also known as a quadrotor. It has drawn a lot attention from engineers and researchers due to its simple mechanical structure and a massive growth in applications. Recently, the quadcopter becomes one of the most popular studied systems in control area. It severs as an excellent test-bed for investigating the behavior of multipleinput multiple-output (MIMO) systems. In general, there are two types of quadcopter configuration, which are the plus and cross structures respectively. In this paper, the dynamics modelling and controller design are based on the latter structure. The quadcopter is seen as an under-actuated system which has six degrees of freedom (three translational and three rotational) [1], but with only four independent inputs (the speed of each motor), this brings the strong coupling of rotational and translational dynamics . Due to the under-actuated properties of quadcopters, maintaining its balancing state or a desired attitude becomes more challenging. Therefore, the control algorithm design is very important and modelling a more realistic dynamic model of a quadcopter is also crucial.\nOver the last decade, various control methodologies have been proposed to investigate the attitude control problem of unmanned aerial vehicles (UAV). Both linear and nonlinear control schemes are involved. In [2] [3] [4]the model-based PD and Linear Quadratic Regulator (LQR) control schemes are applied to an indoor micro quadcopter. The PID algorithm in three structures are considered to formulate the control tasks,\nPID, PI-D and I-PD controllers are compared and examined with respect to the best performance [5]. Optimized PID control method is proposed in [6], two simulations are carried out with respect to optimized PID and Back-step controller. Other kinds of control strategies are also mentioned in such as H infinity [7], linear quadratic optimal control, back-stepping control [8], sliding mode control [9] and so on. Many people have emphasized the merits of PID control method in their papers [10] [11] [12], and it is true that the PID control technique has been widely used in many areas and provides an effective performance in controlling unstable systems. Nonetheless, the drawback of PID control method is when the disturbance results a large error in the system, the transient response of systems in terms of settling time, overshoots and steady-state response will be compromised which presents a weaker robustness [13]. Especially in the quadcopter system, the external disturbances always cause a large tracking error, which raises the difficulty of controller design [14]. Hence, a robust cascade PID algorithm is proposed to improve the stability by lowering the system sensitivity to the external disturbances. In addition, the mathematical models of quadcopter dynamics are usually derived from Euler-Lagrange or Newton-Euler methods [15] [16], the latter is employed and the dynamics of motors are taken into account during the modelling for maximum accuracy and feasibility [17]. In section III, the proposed cascade PID controller is developed based on the linear model of the system. In section IV, the simulations of cascade PID and a parallel structure PID controllers are both performed.\n978-1-5090-5346-9 / 16 / $31.00 \u00a92016 IEEE 498",
            "II. MATHEMATICAL MODELLING\nTo specify the attitude of quadcopters in space, two frames\nhave to be introduced which are inertial frame and body frame . Let the position vector of the quadcopter be defined as , and its orientation vector described by Euler angle in terms of roll, pitch and yaw angles; then, the linear velocity and angular velocity of the quadcopter have the following relationship with position and orientation vectors:\n(1)\n(2)\n(3)\nwhere is a rotational matrix and is an angular velocity transformation matrix which convert attitude and angular speed of the quadcopter from body frame to inertial frame; c and s represent cosine and sine functions respectively. Small angle assumption has been made around hovering condition [18] which results in cos(.) = 1, sin(.)=0, hence, the angular velocities in both frames are equivalent.\nThe dynamics model is obtained based on the following\nassumptions: 1) the body frame of the quadcopter is rigid and\nsymmetric; 2) the center of the body frame coincides with the\ncenter of gravity; 3) the aerodynamics effects are neglected.\nAccording to the aerodynamics, the lifting force and moment are proportional to the square of propeller rotation speed.\n(4)\nwhere and are the aerodynamics force and moment constant. These constants can be determined experimentally.\nThe attitude and altitude are governed by varying the speed of four motors independently, thus, the total thrust and torques generated by rotating propellers can be expressed by:\n(5)\nDefine , by using Newton-Euler method, the rotational motion equations can be described as:\n\u019e \u019e (6)\n(7)\nDue to the symmetrical structure of the quadcopter, the inertial matrix I is a diagonal matrix. By substituting (7) into (6), the following equation can be established:\n(8)\nExpanding each term leads to,\n(9)\nBecause of the dynamics of a quadcopter is directly related to the accelerations of the rotational and translational motions, so Dynamics equations have to be in accelerations form. The translational motion equations can be derived by applying Newton\u2019s Second law:\n(10)\n(11)\nwhere is the total forces acting on the quadcopter in body frame. By substituting (11) into (10), the following equations can be obtained:"
        ]
    },
    {
        "image_filename": "designv10_1_0002798_tec.2020.2964942-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002798_tec.2020.2964942-Figure4-1.png",
        "caption": "Fig. 4. Lightweight rotor/shaft assemblies, a) inner-rotor/shaft with lattice structure for PM motor application (CAD and complete rotor assembly) \u2013 Paderborn University, Karlsruhe Institute for Technology and Leibniz University Hannover [16], b) outer- rotor/shaft for open-frame PM motor \u2013 Newcastle University",
        "texts": [
            " In Fig 3a) the authors report 31% higher total mass flow and 20% improvement in total heat conduction and efficiency of the cooling system as compared with a more conventional design [14]. The authors do not provide details regarding the metal alloy used to fabricate the housing, but considering thermal conductivity of available alloys, it is most likely to be an aluminium alloy, e.g. AlSi10Mg. Reducing the mass of structural parts of the motor assembly is another area where AM has been successfully used. Fig. 4 shows examples of rotor/shaft assemblies designed to be fabricated using AM. Fig. 4a) presents a lightweight innerrotor/shaft assembly: CAD and practical implementation, together with permanent magnet (PM) array and damping coils [16]. The rotor/shaft was manufactured using tool steel (H13). Although the magnetic properties of H13 are relatively poor the authors show that by appropriate heat treatment these can be significantly improved to match properties of the existing soft magnetic composites (SMCs). More importantly by introducing a rotor/shaft with a lattice structure, the overall mass of the rotor was reduced by 25% and the moment of inertia decreased by 23%, compared with a more conventional design. The next example here, Fig. 4b), shows the mechanical parts of an outer-rotor/shaft for an open-frame PM motor. Here, the intention was to provide a sufficient through air flow for removing heat from the motor active parts. The presented mechanical components have been designed and manufactured using titanium alloy (Ti6Al4V) to provide an ultra-lightweight motor assembly. Enabling high-performance and robust rotor designs for high-speed machines is another area, where AM has been showcased. Fig. 5 presents an interesting example of a solid steel rotor design with copper cladding for a high-speed induction machine [17]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure24.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure24.10-1.png",
        "caption": "Fig. 24.10 The second design: \u2018Passion\u2019",
        "texts": [
            " There are two ants heading towards the overflow chocolate. The white colour external surface of the \u2018Mushy\u2019 causes this part to become the highlight of the design. The intention is to make users feel curious and make them investigate what is inside the \u2018Mushy\u2019. The snap-fit lid is easy to open. Besides, there is sweet scent on the external surface of the lid. Users can choose the scent they desire while purchasing \u2018Mushy\u2019. Available sweet scents include caramel, chocolate, vanilla and honey. The second design, \u2018Passion\u2019 (see Fig. 24.10), is an orange-shaped biscuit container with matte surface. The matte surface is to suggest similarity of this biscuit container with real orange. This container comprises a tissue paper chamber and six compartments for users to contain and sort various cookies. The transparent biscuit container lid allows users to see the cookies inside the container without opening it. As the white arrow shows, users can rotate the compartment around the tissue paper chamber to search for cookies they desire. Each of the individual compartments can be taken out easily by simply lifting it upward"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003750_s00170-017-1303-0-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003750_s00170-017-1303-0-Figure4-1.png",
        "caption": "Fig. 4 Dimensions of the designed samples and build plate",
        "texts": [
            " The residual stress distribution among the scanning and build directions has been measured using the XRD method. A correlation between the surface microstructure and residual stress distribution has been made. Simplified airfoil blade geometries were selected for this study. The dimensions of a typical airfoil blade were simplified into inclination angle, center distance, and leading-edge diameter and trailing-edge diameter as shown in Fig. 3. Four groups of samples A\u2013D were designed, and each group consisted of nine samples as shown in Fig. 4. These groups were used for studying the effect of two factors: (i) part dimensions; and (ii) part location on the build plate. Group A to study the inclination angle, group C to study the center distance, and group D to study the thickness (trailing- and leading-edge diameters). Group B consists of identical samples to study the part location on the build plate. Table 1 illustrates the dimensions of the samples in each group. The samples were produced from stainless steel 316L powder (supplied by Renishaw Canada) using a Renishaw AM250 machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003477_s00170-019-03828-6-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003477_s00170-019-03828-6-Figure1-1.png",
        "caption": "Fig. 1 a Schematic diagram of experimental setup and b manufactured product with specimen preparation locations",
        "texts": [
            " Furthermore, the result of this research may facilitate understanding of the mechanical performance of this superalloy under the same heat treatment condition. The following sections of this paper will chronologically explain the experimental procedure, microstructural evolution upon heat treating, and major outcomes of this study in-depth. The WAAM system consists of two six-axis Fanuc ArcMate100iB robots. One of them, which is occupied with a Fronius Advanced 4000MVRColdMetal Transfer (CMT) machine, a VR7000 wire feeder, and a controller (Fanuc R-J3iB), was used for the WAAM process, as shown in Fig. 1a. The CMT process is used due to its characteristics of saving most energy possible by modifying the droplet transfer process to the weld pool. In this process, the wire feeds in a back-and-forth motion. The power supply is interrupted after the short circuit occurs, and the wire is retracted at the same time. This promotes droplet transfer without the help of electromagnetic force. The arc reinitiates after completion of droplet transfer [37]. The subsequent advantages are low heat input, less spatter, and high deposition rate [38]",
            " The welding parameters selected are presented in Table 2. A single layer across the square wall was 374.65 mm long and 6\u20137 mm thick. The substrate, along with 5 mm of material deposited along the bottom, was removed when the as-deposited structure is separated to maintain microstructural homogeneity of the Inconel 625 and avoid the multi-material welding scenario. A band saw was used for separating the structure from the substrate. The square wall was separated into four different walls to be heat treated (Fig. 1b). Three of the separated walls were heat treated in an electric furnace at 980 \u00b0C for 30 min, 1 h, and 2 h and then water quenched. For analysis of the y-z plane microstructure (see the cube of Fig. 1b), a small specimen cut from each of the as-deposited and heat-treated samples was hot mounted with graphite powder. The prepared specimens were then immediately etched with Aqua Regia (9 mL hydrochloric acid and 3 mL nitric acid) after grinding and subsequent manual polishing until the microstructure revealed itself. The optical microscopy on the revealed microstructure was done under several objectives (3\u00d7, 50\u00d7, 100\u00d7, 500\u00d7) using a Nikon Eclipse MA1000 microscope and Nikon SMZ 1500 microscope. The FEI Quanta 200 scanning electron microscope (SEM) was used for higher magnification (2000\u00d7, 2500\u00d7, and 10,000\u00d7) imaging of the microstructures",
            " Specimens were coated with carbon for inspecting the elemental map and SEM images. Xray diffraction (XRD) was conducted with a RigakuUltima IV X-ray diffractometer on all the specimens to support the phase prediction upon viewing the microstructures. A normal line focus CuK\u03b1 radiation tube was used with power settings of (40 kV, 44 mA). The diffraction patterns were recorded using a scan speed of 4.00 deg./min. The low magnification (3\u00d7) optical micrograph denotes different waviness values at the two different sides (inside and outside, Fig. 1b) of a single wall of the built part. The arithmetical mean roughness (Ra) was measured using the equation as follows: Ra \u00bc 1 n \u2211n i\u00bc1jyij; where n is the number of points to measure roughness and yi is the distance measured from peak and depressions corresponding to a mean line drawn on Fig. 2a (AB and CD). The average waviness calculated at the inside and outside regions is 333.29\u03bcm and 287 \u03bcm, respectively. The difference in roughness value at the inside and outside is related to the cooling rate when solidified"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001153_002199837100500314-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001153_002199837100500314-Figure1-1.png",
        "caption": "Figure 1. Bolt bearing test specimen.",
        "texts": [
            " An implied goal in this study is a relative evaluation of the three proposed anisotropic failure criterion: maximum stress, maximum strain, and distortional energy. A constant strain, finite element computer program modified to handle anisotropic composite materials [1] was used for the stress analysis. Only specially orthotropic laminates, i.e. laminates which are mid-plane symmetric and are crossplied, were investigated since the published data on bolt bearing specimens is also limited to this class of laminates. The bolt bearing test specimen contains two lines of specimen symmetry as shown in Figure 1. Thus it was only necessary to include one-fourth of the specimen in the finite element simulation. The grid representation used contains 480 triangular elements and 279 nodes. A cosine distribution of normal stress acting over the upper half of the hole surface was used to simulate the resulting stress distribution caused by the bolt. The interaction was assumed to be frictionless. Bickley [2] shows this to be an excellent approximation for isotropic bolt bearing specimens. Several isotropic bolt bearing test specimens were simulated using the cosine distribution of normal stress and the grid mesh previously described"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000273_tia.2009.2013550-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000273_tia.2009.2013550-Figure7-1.png",
        "caption": "Fig. 7. Eddy-current distribution of magnet (28 magnet divisions, obtained by main calculation considering carrier, 6000 min\u22121).",
        "texts": [
            " Accordingly, their distribution varies due to the slot pitch, and they are concentrated at the sides of the magnet because the slot harmonic flux density is concentrated at the rotor surface [4]. On the other hand, the result considering the carrier shows remarkable difference. In this case, the eddy currents flow through the whole part of the magnet because they are mainly produced by the carrier harmonic flux density, whose distribution varies due to one pole pitch, and it enters into the rotor deeply [4]. Furthermore, the frequency of the major carrier harmonics is higher than the slot harmonics. As a result, the eddy-current density of Fig. 7 is much higher than Fig. 6. C. Variation of Magnet Eddy-Current Loss Due to Divisions Next, let us investigate the effects of the magnet divisions. Fig. 8 shows the eddy-current distribution of model (a), which is without the magnet division, obtained by the main calculation considering the carrier. In this case, the eddy currents concentrate at the edge of the magnet due to the skin effect. The maximum eddy-current density is nearly twice of the case of 28 magnet divisions. On the other hand, it can be seen that the region where the eddy currents flow is restricted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000109_s0007-8506(07)63450-7-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000109_s0007-8506(07)63450-7-Figure7-1.png",
        "caption": "Figure 7 : Top, gripper with disk translator as drive: Bottom, gripper with PicomotorTM as drive [31].",
        "texts": [
            " For instance, in [31] they used 50 pm wide and 10 pm thick tweezers fixed to the arms by use of a resin adhesive. The material for those tweezers can be either titanium or high-quality steel. A Ushaped spring is placed between the two arms and causes the opening of the jaws. The deformation of the spring was made through a force applied exactly in the centre of the \"U\" stripe in order to obtain a symmetrical opening of the jaws. The force is obtained either byTg piezoelectric disk translator or a piezoelectric Picomotor (New Focus) (see figure 7). A - non-magnetic - CuBez alloy was chosen for the jaws. Carrozza et al. [32] and Ando et al. [33] built parallel jaw grippers driven by a piezoelectric element of which the motion is amplified through lever mechanisms with flexible hinges. Breguet et al. [34] cut the whole gripper out of a piezoceramic plate as shown in figure 8. The electrodes are designed to render active only the parts of the piezo which are underneath them. A piezoelectric force sensor can be easily integrated in one of the jaws",
            " The system includes one gripper and a pair of tweezers driven by a single control unit. They are mounted on a three-axial table to perform an XYZ-movement. The ranges are 20 mm in X and Y and 5 mm in Z-direction. The gripper is controlled by one piezo-actuator. The arms of the tweezers are independently controlled by two piezoelements. A similar system was built at IPT, Aachen [31] for use in a large-chamber SEM. Two independent Z-slides are provided with microgrippers driven by piezoactuators (figure 7). An XY-plus-rotation table carries the products to be assembled. This arrangement allows to keep the focus of the LC-SEM system on the gripper jaws all the time. A small gear pump has been assembled as a case study. Hatamura et al. [95] developed a three-dimensional fabrication and assembly system, consisting of three chambers: a shaping, a handling and a buffer chamber. The shaping chamber contains a fast neutral atom beam and optical microscopes. The handling chamber contains several manipulators and a multi-view SEM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002052_0954406213486734-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002052_0954406213486734-Figure3-1.png",
        "caption": "Figure 3. Elastic force on the external gear tooth.15",
        "texts": [
            " For the external gear, the analytical expressions of the bending stiffness kb, shear stiffness ks and axial compressive stiffness ka are derived in Ref.15 as follows: 1 kb \u00bc Z 2 1 3 1\u00fe cos 1 \u00f0 2 \u00desin cos \u00bd 2 \u00f0 2 \u00decos 2EL\u00bdsin \u00fe\u00f0 2 \u00decos 3 d \u00f06\u00de 1 ks \u00bc Z 2 1 1:2\u00f01\u00fe \u00de\u00f0 2 \u00de cos cos 2 1 EL\u00bdsin \u00fe \u00f0 2 \u00de cos d \u00f07\u00de 1 ka \u00bc Z 2 1 \u00f0 2 \u00de cos sin 2 1 2EL\u00bdsin \u00fe \u00f0 2 \u00de cos d \u00f08\u00de where 2 is the half tooth angle on the base circle of the external gear, 1 is the angle between the force component Fb and the acting force F which can be decomposed into two orthogonal component forces: Fa and Fb (see Figure 3). at Purdue University on September 1, 2014pic.sagepub.comDownloaded from It is checked and confirmed that equations (6) to (8) can still be used to evaluate the mesh stiffness of the external gear of a pair of external\u2013internal gears. However, due to the configuration differences of the external\u2013external gears and the external\u2013internal gears, the expression for 1 has changed. The angle 1 is the only variable in equations (6) to (8), which reflects the change in contact position of the meshing gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure2-3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure2-3-1.png",
        "caption": "Fig. 2-3 Single-phase magnetizing inductance Lm,1-phase and leakage inductance L\u2113s.",
        "texts": [
            " Field distributions in the air gap due to currents ib and ic are identical in sinusoidal shape to those due to ia, but they peak along their respective phase-b and phase-c magnetic axes. 2-3 STATOR INDUCTANCES (ROTOR OPEN-CIRCUITED) The stator windings are assumed to be wye-connected as shown in Fig. 2-2b where the neutral is not accessible. Therefore, at any time i t i t i ta b c( ) ( ) ( ) .+ + = 0 (2-5) For defining stator-winding inductances, we will assume that the rotor is present but it is electrically inert, that is \u201csomehow\u201d hypothetically of-course, it is electrically open-circuited. 2-3-1 Stator Single-Phase Magnetizing Inductance Lm,1-phase as shown in Fig. 2-3a, hypothetically exciting only phase-a (made possible only if the neutral is accessible) by a current ia results in two equivalent flux components represented in Fig. 2-3b: (1) magnetizing flux which crosses the air gap and links with other stator phases and the rotor, and (2) the leakage flux which links phase-a only. Therefore, the self-inductance of a stator phase winding is L i i s a a i a a L a a s , , , self only leakage magnetizing = = + \u03bb \u03bb \u03bb ia Lm, - . 1 phase (2-6a) Therefore, L L Ls s m, , .self -phase= + 1 (2-6b) It requires no-load and blocked-rotor tests to estimate the leakage inductance L\u2113s, but the single-phase magnetizing inductance Lm,1-phase 10 INduCTIoN MaCHINE EQuaTIoNS IN PHaSE QuaNTITIES can be easily calculated by equating the energy storage in the air gap to 1 2 2Li : L r N p m o g s , - ,1 2 phase =       \u03c0\u00b5 (2-7) where r is the mean radius at the air gap, \u2113 is the length of the rotor along its shaft axis, Ns equals the number of turns per phase, and p equals the number of poles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure1.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure1.11-1.png",
        "caption": "FIGURE 1.11. Illustration of Stanford arm; an R`R\u22a5P spherical manipulator.",
        "texts": [
            " R`R\u22a5P The spherical configuration is a suitable configuration for small robots. Almost 15% of industrial robots, Stanford arm for instance, are made of this configuration. The R`R\u22a5P configuration is illustrated in Figure 1.10. By replacing the third joint of an articulate manipulator with a prismatic joint, we obtain the spherical manipulator. The term spherical manipulator derives from the fact that the spherical coordinates define the position of the end-effector with respect to its base frame. 10 1. Introduction Figure 1.11 schematically illustrates the Stanford arm, one of the most well-known spherical robots. 4. RkP`P The cylindrical configuration is a suitable configuration for medium load capacity robots. Almost 45% of industrial robots are made of this kind. The RkP`P configuration is illustrated in Figure 1.12. The first joint of a cylindrical manipulator is revolute and produces a rotation about the base, while the second and third joints are prismatic. As the name suggests, the joint variables are the cylindrical coordinates of the end-effector with respect to the base"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003221_j.mechmachtheory.2019.103670-Figure23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003221_j.mechmachtheory.2019.103670-Figure23-1.png",
        "caption": "Fig. 23. The schematic diagram of the rigid-flexible coupled finite element of HPGT.",
        "texts": [
            " FEM Verification Since the model involved in this paper is large, and the contact stress of its transient dynamics is effectively captured, the mesh size should be less than or equal to 0.1 mm. After meshing it, the number of finite-element meshes is large, so it is impossible to calculate its transient dynamics with ANSYS. Therefore, this paper uses the rigid-flexible coupled finite element method of ADAMS to verify the dynamic model of the transmission system. Firstly, the planet gears are meshed and flexible, and the schematic diagram of the rigid-flexible coupled finite element of HPGT is shown in Figure 23 . The meshed planet gears are replaced with the transmission system, and initial conditions such as constraints and boundary conditions are applied to complete the constraint setting of the transmission system. The constraints imposed therein are shown in Table 6 . The simulation duration is set to 0.03s, and the meshing force curves on the inner and outer meshing lines of the transmission system are obtained. Due to the fluctuations and inevitable assembly interference in the simulation process, the meshing force curves fluctuate greatly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure1-1.png",
        "caption": "Fig. 1. (a) A model of spur gears tooth. (b) Geometrical parameters for the fillet-foundation deflection.",
        "texts": [
            " According to material mechanics and elastic mechanical, Uh, Ub, Us and Ua can be expressed as follows: Uh \u00bc F2 2kh where Kh \u00bc \u03c0EL 4 1\u2212v2 \u00f01\u00de Ub \u00bc F2 2kb \u00bc Z d 0 Fb d\u2212x\u00f0 \u00de\u2212Fah\u00bd 2 2EIx dx \u00f02\u00de Us \u00bc F2 2ks \u00bc Z d 0 1:2Fb 2 2GAx dx \u00f03\u00de Ua \u00bc F2 2ka \u00bc Z d 0 Fa 2 2EAx dx \u00f04\u00de Ix \u00bc 1 12 2hx\u00f0 \u00de3L \u00f05\u00de Ax \u00bc 2hx\u00f0 \u00deL \u00f06\u00de where F represents the acting force by the mating tooth in the contact point. Fa, Fb are radial and tangential forces, G, E, L, v represent shearmodulus, Young's modulus, thewidth of tooth and Poisson's ratio, respectively. Ix, Ax are the areamoment of inertia and area of the section where the distance from the dedendum circle is x, the other parameters are shown in Fig. 1(a). When two gears are meshing, the total energy can be obtained by U \u00bc F2 2k \u00bc Uh \u00fe Ub1 \u00fe Us1 \u00fe Ua1 \u00fe Ub2 \u00fe Us2 \u00fe Ua2 \u00bc F2 2 1 kh \u00fe 1 kb1 \u00fe 1 ks1 \u00fe 1 ka1 \u00fe 1 kb2 \u00fe 1 ks2 \u00fe 1 ka2 \u00f07\u00de where k represents the total effective mesh stiffness, subscripts \u201c1\u201d and \u201c2\u201d indicate the driving and driven gear, respectively. Besides the tooth deformation, the fillet-foundation deflection also influences the stiffness of gear tooth [27]. An effective method to calculate gear foundation elasticity was proposed by Sainsot, Velex and Duverger [31]. The fillet-foundation deflection can be calculated by: \u03b4 f \u00bc F kf \u00bc F cos2 \u03b1m EL L \u03bc f S f !2 \u00feM \u03bc f S f ! \u00fe P 1\u00fe Q tan2 \u03b1m ( ) : \u00f08\u00de The coefficients L\u2217, M\u2217, P\u2217, Q\u2217 can be approached by polynomial functions Xi \u00bc Ai=\u03b8 f 2 \u00fe Bih 2 f i \u00fe Cihf i=\u03b8 f \u00fe Eihf i \u00fe Fi; \u00f09\u00de the values of Ai, Bi, Ci, Di, Ei, Fi are given in reference [31]. L is the face width. uf, sf hfi = rf/rint and \u03b8f are defined in Fig. 1(b). In conclusion, for gear teeth in contact, the total effective mesh stiffness can be written as: k \u00bc Xn i\u00bc1 1 1 kh;i \u00fe 1 kb1;i \u00fe 1 ks1;i \u00fe 1 kf1;i \u00fe 1 ka1;i \u00fe 1 kb2;i \u00fe 1 ks2;i \u00fe 1 ka2;i \u00fe 1 kf2;i \u00f010\u00de where subscripts \u201c1\u201d and \u201c2\u201d denote the driving and driven gears respectively, and n represents the number of the gear toothmeshing at the same time. The tooth profiles of spur gears go into and out of contact along thewhole face width at the same time. This will therefore result in a sudden loading and sudden unloading on the teethwhen tooth profiles go into and out of contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002117_j.mechmachtheory.2019.103597-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002117_j.mechmachtheory.2019.103597-Figure4-1.png",
        "caption": "Fig. 4. The positions of the shifted ball center and groove curvature centers for the q th ball.",
        "texts": [
            " 3 , \u03b8 x and \u03b8 y are the angular position coordinates of the inner ring respected to the x and y axises, respectively; the balls are numbered by 1\u2013q; \u03d5 is the angular difference between two adjacent balls; \u03d5q is the azimuth of the q th ball; and the ball distribution and coordinate system definition of the bearing are given in Fig. 3 . When the ACBB is subjected to the combined loads, the inner ring will produce the axial displacement \u03b4a and radial displacement \u03b4rq . The positions of the shifted ball center and groove curvature centers for the q th ball are depicted in Fig. 4 . Here, the ball center will be moved to O b from O b \u2019 ; the curvature center of the groove of the inner ring will be moved to O i from O i \u2019 . The loads applied on the q th ball are depicted in Fig. 5 . The geometry and compatibility equations for the ACBB are represented as ( A 1 q \u2212 X 1 q ) 2 + ( A 2 q \u2212 X 2 q ) 2 \u2212 [ ( f i \u2212 0 . 5) D + \u03b4iq ]2 = 0 (6) X 2 1 q + X 2 2 q \u2212 [ ( f o \u2212 0 . 5) D + \u03b4oq ] 2 = 0 (7) where \u03b4i q and \u03b4o q are the contact deformations of the inner and outer rings, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000113_70.105387-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000113_70.105387-Figure17-1.png",
        "caption": "Fig. 17. Global and local optimal paths",
        "texts": [
            " The branch and bound search explored 714 grid paths, all shown in Fig. 15. The threshold for the upper bound E was selected heuristically to be 20% above the lowest upper bound. This resulted in 96 \u201cgood\u201d paths which after filtering, with Omax = 0.30 m, reduced to the nine paths, all shown in Fig. 16, with the times ranging from 1.166 to 1.281 s. The paths were smoothed by B splines with 4 to 6 control points (8 to 12 parameters). These paths converged in the local optimization to the optimal path A shown in Fig. 17, with the traveling time of 1.10 s. This path is consistent with results obtained by other intuitive methods [ 171. The improvement in motion time from the best grid path to the optimal one was 1.166 - 1.10 = 0.066 s. This is lower than the upper bound on the improvement of 0.09 s suggested by the sensitivity curves in Fig. 11 for a grid size of 0.26 m. This confirms that the E used in this optimization was sufficiently high to guarantee convergence to the global optimum. Fig. 17 shows another local optimal path, marked B , with the time of 1.34 s. No path in this region was selected by the branch and bound search because of their high cost relative to paths in the upper region. Note that the optimization was carried out in the Cartesian space, considering only one kinematic solution and avoiding kinematically singular points. This excluded the global optimal path that was shown to pass through the manipulator base [ 101. Enter End Points Grid Search j \u20187; 1 Branchand Evaluate Paths with Lower Bound Tests The relative effectiveness of the various tests is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure10-1.png",
        "caption": "Fig. 10. (a) Representation of inner race of the bearing which combines the equivalent mass of the rotor disk and the stiffness and damping of the rotor shaft, and (b) bond graph sub-model of the inner race.",
        "texts": [
            " Here, Cdb represents the average depth of entry into the spall. The fault modelling, as has been detailed in Section 3.3, is essentially representation of appearance and disappearance of intermittent clearance between the races and the faulty rolling element under the conditions mentioned above. The model is developed here in a modular manner using the method proposed in [27], where bearing's two races, cage and all balls are modelled as separate sub-models. As in [28], it is assumed that the inner race is fixed to the ground (See Fig. 10(a)) through a pair of spring-dampers in orthogonal directions, which represent the rotor shaft stiffness and damping. A torque or constant angular velocity source may be applied on the rotor shaft. The center of mass is assumed to be at a small distance of e (eccentricity) from the shaft geometric axis, i.e. the spin axis. The instantaneous angular position of the mass center is \u03b8i and shaft angular speed is \u03b8 \u03c9\u0307 =i . In the inertial reference frame, the mass center ( )x , ym m position is given by (refer to Fig. 10(a)) \u03b8 \u03b8= + = + ( )x x e y y ecos and sin 32m mi i i i where ( )x , yi i is the position of the centre of the inner race. Thus, the velocity of the mass center is \u03b8 \u03b8 \u03b8 \u03b8\u0307 = \u0307 \u2212 \u0307 \u0307 = \u0307 + \u0307 ( )x x e y y esin and cos 33m mi i i i i i Since the bond graph model will be developed in the inertial reference frame, it is not required to perform acceleration analysis. Note that the centrifugal forces and the additional polar moment of inertia (me2) are automatically taken care of when the kinematics in Eq. (33) is represented in the bond graph model. The inner race sub-model is shown in Fig. 10(b) where the rotary inertia is modeled by JI: S and the spin resistance is modeled by RR: K. The torsional stiffness and damping of the coupling between the motor and the rotor shaft are modeled by C K: C and R R: C, respectively. The equivalent mass of the rotor disk, shaft and the race are modeled by MI: S in x and y directions, and the synchronous whirl bending stiffness and damping of the rotor shaft which are referred to the bearing end are represented with C K: S and R R: S, respectively. The self-weight \u2212 M gSe: S is modeled at \u03071ym junction",
            " If the motor is assumed to provide a torque then \u03c9Sf: i and coupling model are replaced by an effort source (Se). This sub-model has a multi-bond interface port numbered as 1 (shown within a circle) to connect it with several rolling element sub-models. The outer race (See Fig. 11(a)) is assumed to have no rotation. It is mounted on the bearing pedestal which has some structural stiffness and damping. Its sub-model is similar to that of the inner race and can be obtained from the later removing \u03b8 \u03071 i junction of Fig. 10(b) and all connected parts (eccentricity model, and drive and coupling) and labeling the remaining junctions appropriately, to obtain the sub-model shown in Fig. 11(b). In Fig. 11(b), the equivalent mass, mounting structural stiffness and damping, and the self-weight are represented with MI: p, KC: p, RR: p and \u2212 M gSe: p , respectively. For vibration analysis and bearing condition monitoring, the acceleration or velocity of the pedestal in the vertical direction is measured. Thus, an effort detector De (analogous to accelerometer when mass is constant) and a flow detector Df (analogous to velocity sensor) are implemented at appropriate locations in the model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002934_j.ymssp.2020.107257-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002934_j.ymssp.2020.107257-Figure3-1.png",
        "caption": "Fig. 3. Schematic force diagram of the inner ring.",
        "texts": [
            " The rolling element\u2013raceway friction force is obtained by [24] F ij \u00bc lNij DV ij DV ijj j Foj \u00bc lNoj DVoj DVojj j 8>< >: \u00f010\u00de The formula for calculating the friction coefficient between the rolling element and the races is given as [20,30] l \u00bc 0:4 DVj j DVj j < 0:05 0:02 others \u00f011\u00de where the DV is the relative slip velocity between the rolling elements and the inner\\outer race. The slipping velocity can be given by: DV ij \u00bc xi Ri xoj Ri xsj Rr DVoj \u00bc xoj Ro xsj Rr \u00f012\u00de where thexoj andxsj are the orbit and the self-rotation speed of the jth rolling element. And Ri and Ro denote the radiuses of the inner and the outer raceway, respectively. As shown in Fig. 3, the motion of the inner ring is directly affected by the external radial load, the contact forces between the rolling element and the inner race, and the corresponding friction forces. Vertical motion of the inner ring: mi x W \u00fe XNb j\u00bc1 Nijcoswj F ijsinwj \u00bc 0 \u00f013\u00de Horizontal motion of the inner race: mi y\u00fe XNb j\u00bc1 Nijsinwj \u00fe F ijcoswj \u00bc 0 \u00f014\u00de The schematic forces diagram of the cage mass block is shown in Fig. 4. The dynamic equations of circumferential motion of the cage can be derived as: mcR 2 mwcj Rm Ncfj Ncbj\u00fe1 \u00fe Nccj \u00bc 0 \u00f015\u00de While for the rolling elements of the rolling bearing, their detailed force analysis can be referenced to Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002220_s00170-017-0703-5-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002220_s00170-017-0703-5-Figure11-1.png",
        "caption": "Fig. 11 Illustration of power bed simulation",
        "texts": [
            " Variables \u03b61, \u03b62, \u03b63, and \u03c91 represent the epistemic uncertainty in the EAM potential, T is the sintering temperature, d is the gap between two nanoparticles, and R1 and R2 are the radii of the two nanoparticles. In this example, the distributions are assumed to be Gaussian for the sake of illustration. The method presented in this example is applicable to any kind of distributions. The distributions of the gap between nanoparticles and radii of nanoparticles can be obtained from the powder bed simulation as illustrated in Fig. 8. Figure 11 shows the geometry of two nanoparticles. Figure 12 plots the strain-stress curve obtained from the tensile test model under a given realization of the random Table 2 Random variables of the laser sintering of nanoparticles Variable R1 (\u00c5) R2 (\u00c5) d (\u00c5) T (K) \u03b61 \u03b62 \u03b63 \u03c91 Distribution Gaussian Gaussian Gaussian Gaussian Gaussian Gaussian Gaussian Gaussian Mean 22.25 21.75 0.05 1075 11.675 \u22120.0115 0.475 \u22123.5 \u00d7 10\u22124 Standard deviation 0.005 0.005 0.01 15 0.02 5 \u00d7 10\u22123 0.02 1.75 \u00d7 10\u22125 variables. Based on the LAMMPS simulation runs, surrogate models are built for the stress response using the Kriging surrogate model method as discussed in Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000612_1.323970-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000612_1.323970-Figure1-1.png",
        "caption": "FIG. 1. Sketch of a bent three-layer composite. The radius of curvature R, forces F l , and moments Ml are all drawn in the positive sense. Each layer has a particular thickness t j , elastic modulus E l , length L, and width w.",
        "texts": [
            " In the past decade, much attention has been paid to stress distributions in epitaxial structures1 ,2 and; more re cently, to heterojunction laser structures. 3,4 The pur pose of the present paper is to describe a closed-form solution for the stress distribution within individual layers of a multilayered structure in which known elas tic strains exists, and to discuss in detail applications of the calculation to Alpa1 _.As heterojunction lasers. Consider a multilayered structure having length L, width w, and elas tic moduli E i such as that shown in Fig. 1 in which known elastic strains exist between the layers. In general, this elastic strain will have two effects: (1) a stress a I will be set up in each layer; (2) the composite will bend in response to these stresses and assume some radius of curvature R. The origin of these strains might be differences in lat tice parameter, thermal expansion coeffiCient, or other material properties. SaulS and Reinhart and Logan6 have calculated the stresses in particular regions of one dimensional N-layer composites. The present calcula tion builds upon these methods to derive a general closed-form expression. The solution consists of solv ing for the radius of curvature R and stresses a I in terms of the forces F to moments M i' and strains Eli which exist in the composite. More complete details may be found elsewhere. 7 Equilibrium of forces F; and moments M I yield N L.; F;=O, (1) 1=1 (2) The positive directions of forces and moments are shown in Fig. 1 (i. e., tensile forces are positive). The actual signs are part of the solution. The other (N - 1) equations are obtained by solving for the strains E; at the (N -1) interfaces between each 2543 Journal of Applied Physics, Vol. 48, No.6, June 1977 layer, assuming that atom-by-atom alignment (coherence) is maintained across the interface. ~ ( FI+l ~ 1 ( )~ L.J EI -E i +1 = E wt - E wt - 2R tl +tl+l . 1=1 1+1 1+1 I I (3) At this point a closed-form solution for F I and R is a rather formidable task which is best left to the com puter",
            " This difference could be accounted for if AlAs has a lower elastic constant than GaAs, but it should be con sidered that the combined uncertainty of the other input parameters to the calculation could also cause this error. A five-layer double-heterojunction AlxGa1_xAs/GaAs laser structure is shown in Fig. 2. Using Eqs. (4) and (6), the stress at each interface and radius of curvature were calculated as shown. Positive values of stress are tensile while negative values are compressive. R is measured from the bottom as shown in Fig. 1 and is positive if the structure is concave up (looking from the bottom). An elastic modulus E of 1 xl012 dyn/cm2 was assumed throughout, since exact values for AlAs are unavailable (but should be well within a factor of 2 of E for GaAs 10 based on the data of Table I. TABLE I. Calculated and experimental radii of curvature. Experimental radius % Calculated radius of curvature (cm) (cm) difference Whole crystal right 275 after growth, 255 p.m thick, 0.5 XO.5-cm2 area Whole crystal after 72 lapping to 125-p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003950_j.ymssp.2018.09.027-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003950_j.ymssp.2018.09.027-Figure13-1.png",
        "caption": "Fig. 13. Evaluation of the bolts\u2019 stiffness and damping coefficient based on the Logarithmic decrement method.",
        "texts": [
            " (39) can be achieved via the Non-Linear Least Squares (NLLS) method or some intelligent methods such as the one presented in [51]. During the optimization process, the optimization method changes the value of the bearing stiffness and damping coefficients iteratively. The best combination of the bearing coefficients, which results in the lowest deviation error e, is the final solution. In this study, a test rig was set to evaluate the stiffness and damping properties of the bolt. As is shown in Fig. 13(a), where a cylindrical steel mass block (with diameter 76.2 mm and height 38.2 mm, weight 1.36 kg) was mounted on the base by a hexagon socket bolt with a rubber mat (thickness of 1 mm) between the two contact surfaces. The base is a large solid aluminum block (1200 mm 600 mm 50 mm) with mass properties of about 100 kg. A torque wrench was used to measure the preload of the bolt and a torque angle gauge was used to lock the bolt precisely. Sensors 1 and 2 mounted on the mass block were used to measure the impulse vibration of the mass along the vertical and horizontal directions, respectively",
            " In the test, the applied load of torque wrench was set to 15 ft-lbf and the rotation angle of the torque angle gauge utilized to lock the bolt was set to 60 , which are the same mounting conditions as that of the gearbox casing fixed on the work bench. Due the large mass of the base compared to the mass of the cylindrical block including the mass of the two sensors mounted on it, the base can be assumed as a sturdy ground, and the vibration of the cylindrical mass can be simplified as one degree-of-freedom (DOF) spring-mass-damper systems with stiffness and damping coefficients ky, cy and kx, cx along the vertical and horizontal directions, respectively, see Fig. 13(b). The dynamic model of a one DOF system can be expressed as: m\u20acx\u00fe c _x\u00fe kx \u00bc Fcos Xt\u00f0 \u00de \u00f040\u00de Dividing by the mass m on both side of Eq. (40), one obtains \u20acx\u00fe 2nxn _x\u00fex2 nx \u00bc Fcos Xt\u00f0 \u00de=m \u00f041\u00de where xn \u00bc ffiffiffiffiffiffiffiffiffi k=m p is the natural frequency of the system, n \u00bc c=2mxn \u00bc c=2 ffiffiffiffiffiffiffi mk p is the damping ratio, and X is the frequency of the impulse force. Based on the Logarithmic decrement method, the damping ratio of the vibration can be evaluated by f \u00bc 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe 2p=d\u00f0 \u00de2 p d \u00bc 1 n ln A0 An 8< : ; \u00f042\u00de where f is the damping ratio, A0 is the amplitude of the reference point, An is the amplitude of the positive peak n periods away, and n is an integer, see Fig",
            " xd \u00bc 8800 Hz for the vibration in the vertical direction), the actual natural frequency xn of the mass block can be evaluated by xn \u00bc xd= ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 f2 p . The evaluated natural frequencies can be further used to determine the total stiffness of the bolts via k \u00bc mx2 n, in whichm is the total mass of the block and the sensors mounted on it. With the known mass of the block and the evaluated f and k, the damping coefficient of the bolts can be evaluated by c \u00bc 2f ffiffiffiffiffiffiffi mk p \u00f043\u00de The impact hammer with a steel tip, see Fig. 13(a), can excite a wide range in the frequency band. In this test, the frequency with the highest amplitude was considered as the main damped natural frequency and utilized to calculate the bolt stiffness and damping coefficient. The evaluated total stiffness and damping coefficient of the four bolts mounting the gearbox based on Eq. (31) are shown in Table 1 in the Appendix. In this study, the roughness of the gear tooth surface was directly measured by the Surface Roughness Tester (SRT, phase II SRG-4000), as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001214_j.rcim.2017.02.002-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001214_j.rcim.2017.02.002-Figure1-1.png",
        "caption": "Fig. 1. DHm parameterization of the robot with kinematic parallelogram. (a) Kinematic modeling. (b) Kinematic parameters.",
        "texts": [
            " Section 5 presents detailed robot posture optimization methodology based on the performance maps, which contains three sub-steps. Experiments are conducted in Section 6 to validate the proposed methodology, and discussions about the possible extensions and limitations of the proposed methodology are presented in Section 7. Finally, Section 8 summarizes the main results and contributions. The modified Denavit Hartenberg parameters (DHm) [28] are adopted to parameterize the robot with kinematic parallelogram (labeling of each joint shown in Fig. 1(a)): \u03b8i is the angle of Ji (i=1, 2, 4, 5, 6, A, B, C), and \u03b83 is the angle of the driving motor which is located in J2, not the angle of J3. The analytical expressions of the kinematic Jacobian Matrix elements are displayed in Appendix A. And the robot configuration ranges in the joint space are shown in Table A1. Because of the robot with kinematic parallelogram, the range of \u03b83 is influenced by the value of \u03b82. It means the range of \u03b83 is a function of \u03b82. But J3 has a specific range shown in Table A1, no matter what values \u03b82 and \u03b83 take. According to Fig. 1 and Table 1, it can be seen that the angle of J3 is \u03b8 \u03b8 \u03c0+ + /22 3 . For convenience of calculations, \u03b8 real3 which is the real angle of J3, will replace \u03b83 to plot the following maps. A kinematic performance index of a robotic mechanical system is a scalar quantity that measures how well the system behaves with regard to the force and motion transmission. Nowadays, the reciprocal of the condition number of Jacobian matrix, which can quantify the distance to singularities, is used as a kinematic performance index called kinetostatic conditioning index [13] (KCI), defined as: where Jk( )N is the condition number [29] of homogeneous Jacobian normalized by characteristic length [30], the subscript N and tr(\u2219) denote a normalizing operation and the trace of a matrix [29], respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000484_j.jsv.2005.11.021-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000484_j.jsv.2005.11.021-Figure1-1.png",
        "caption": "Fig. 1. The 6-degree-of-freedom nonlinear model.",
        "texts": [
            " The model includes four inertias, namely load, prime mover, pinion and gear. The torsional compliances of shafts and the transverse compliances of bearings combined with those of shafts are included in the model. Both bearing and shaft dampings are also considered in the model. The transverse vibrations of the gears are considered along the line of action. With this model, the response, including modulations due to transverse and torsional vibration stemming from bearing and shaft compliances, can be calculated. The 6-degree-of-freedom nonlinear model is shown in Fig. 1. It has four angular rotations (of prime mover, pinion, gear and load) and two translations (of pinion and gear) along the line of action. The effects that are included in the mathematical model and thus considered in the dynamic analysis are: time-varying mesh stiffness and mesh damping; torsional compliances of pinion and gear shafts; material damping in shafts (linear viscous); bearing compliances and dampings (linear viscous); transverse compliances of shafts; inertia of prime mover and load; drive and load torques and backlash. The governing equations of motion for the model depicted in Fig. 1 can be written as follows (a list of symbols is given in the Nomenclature): IDy 00 D \u00fe ct1\u00f0y 0 D y01\u00de \u00fe kt1\u00f0yD y1\u00de \u00bc TD, (1) I1y 00 1 \u00fe ct1\u00f0y 0 1 y0D\u00de \u00fe kt1\u00f0y1 yD\u00de \u00bc W 0R1, (2) I2y 00 2 \u00fe ct2\u00f0y 0 2 y0L\u00de \u00fe kt2\u00f0y2 yL\u00de \u00bcW 0R2, (3) ILy 00 L \u00fe ct2\u00f0y 0 L y02\u00de \u00fe kt2\u00f0yL y2\u00de \u00bc TL, (4) m1y 00 1 \u00fe c1y01 \u00fe k1y1 \u00bcW 0, (5) m2y 00 2 \u00fe c2y 0 2 \u00fe k2y2 \u00bc W 0. (6) Here, W0 is the dynamic mesh force given by W 0 \u00bc km\u00f0y1R1 y2R2 \u00fe y2 y1\u00de \u00fe cm\u00f0y 0 1R1 y02R2 \u00fe y02 y01\u00de (7) and 0 denotes differentiation with respect to time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002552_17452759.2020.1832695-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002552_17452759.2020.1832695-Figure4-1.png",
        "caption": "Figure 4. Coordinate transformations among the TCP, sensor, and workpiece frames.",
        "texts": [
            " The standard hand-eye calibration method (Tsai and Lenz 1989) was applied. The detailed implementation of the hand-eye calibration can be found in (Rodr\u00edguez-Ara\u00fajo and Rodr\u00edguez-Andina 2015). Once the transformation from the TCP to the sensor frame (TT S ) is obtained, the sensor\u2019s pose relative to the workpiece (TW S ) can then be calculated using the following relationship: TW S = TW T T T S (1) where TW T is the TCP\u2019s pose relative to the workpiece that can be read from the robot controller. The coordinate frames involved in Equation (1) are illustrated in Figure 4. Using the above relationship, 2D profile data captured by the sensor can be transformed into 3D point clouds, which will be explained in detail in Section 2.2. A software platform dedicated to surface monitoring for LAAM is developed in this research. The proposed multinodal architecture of the software platform is introduced in this section. A computer running a Linux OS (Ubuntu 18.04LS) serves as the central controller for the surface monitoring system, in which the in-house developed software is installed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003381_s11071-019-05301-1-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003381_s11071-019-05301-1-Figure1-1.png",
        "caption": "Fig. 1 Quadrotor UAV architecture",
        "texts": [
            " Section 3 presents the new adaptive robust finite time control strategy for the quadrotor system with unmodeled dynamics, external disturbances, and nonsymmetric input saturation nonlinearity, where the finite time convergence of the entire closed-loop system is proved using finite time Lyapunov stability theory. In Sect. 4, simulation results are provided to demonstrate the effectiveness and robustness of the proposed method. Finally, the conclusions of this paper are drawn in Sect. 5. 2 Problem formulation and preliminaries Consider the quadrotor as a solid body evolving in a 3D space. The mechanical architecture and the coordinate reference frames for establishing the dynamic model are illustrated in Fig. 1, where i represents the angular speed of the i th propeller. Based on the simplified rotor model,we can obtain the total translational force tz \u2208 R and the control torque vector for the rotational motion u\u03c4 = [u\u03c6, u\u03b8 , u\u03c8 ]T using rotational speed vector \u2208 R4 [21]. For the sake of simplicity, we will not repeat it here. Let B = [ BX , BY , BZ ] and E = [ EX , EY , EZ ] denote the body-frame coordinates and the earth-frame coordinates, respectively. OB is the center of mass of the quadrotor aircraft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.43-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.43-1.png",
        "caption": "Fig. 17.43a\u2013c Phasor diagram and torque characteristic of a synchronous machine. (a) Generator operation, overexcited; (b) motor operation, underexcited; (c) torque as a function of polar wheel angle",
        "texts": [
            " It represents the electrical angle between the phasor of the terminal voltage V 1 and the phasor of the magnet wheel voltage V p. This magnet wheel voltage is the fictitious induced voltage that would result only from excitation without considering the armature reaction of the current I1. The polar wheel angle \u03d1 is zero at idle speed. It has a positive value in generator operation and a negative value in motor operation. Constant values of the voltage and excitation and sinusoidal torque M(\u03d1) result in a circular transfer locus of the current (in Fig. 17.43, neglecting the resistance R1). Thereafter the torque characteristic shows a breakover point, which depends on the polar wheel voltage in both generator and motor operation. The quantity Xq/X d is on the order of 0.7 for large generators and synchronous motors. Figure 17.44a shows the static stability limit of a synchronous generator, which restricts the steady operation area under excitation. The V -curves can be used to allocate values of the stator current I1 to the polar wheel voltage Vp (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure24.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure24.9-1.png",
        "caption": "Fig. 24.9 The first design: \u2018Mushy\u2019",
        "texts": [
            " Based on the experiential knowledge gained from the first stage, 15 design concepts were created for the young segment. These concepts were further categorised into five groups and, subsequently, a final design concept was chosen and revised from each group. Thus, five biscuit 716 C.-H. Chen et al. container design concepts in total were generated. In order to conduct a customer survey at the later stage, CAD (Computer Aided Design) models of all 5 designs as well as \u2018Mary Biscuit\u2019 were created using SolidWorks software. The first design, \u2018Mushy\u2019 (see Fig. 24.9), is a marshmallow-shaped biscuit container with matte surface. The internal surface of Mushy is in brown colour, which suggests the container is filled with chocolate and, hence, may increase users\u2019 appetite. There are two ants heading towards the overflow chocolate. The white colour external surface of the \u2018Mushy\u2019 causes this part to become the highlight of the design. The intention is to make users feel curious and make them investigate what is inside the \u2018Mushy\u2019. The snap-fit lid is easy to open"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001574_tac.2009.2026940-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001574_tac.2009.2026940-Figure3-1.png",
        "caption": "Fig. 3. Kinematic car model.",
        "texts": [
            " In this section, we illustrate the behavior of the algorithms proposed in the previous sections, by means of a simulated example. Nonhonolomic car motion planning [39] is a typical application area for testing the performances of HOSM algorithms. We use a benchmark problem [13], [15], [16] that gives us the possibility to test the behavior of our algorithms and obtain a comparison with existing approaches. The system is described by where are the cartesian coordinates of the rear-axle middle point, is the orientation angle, is the steering angle and is the control variable, see Fig. 3. Parameters , represents the longitudinal velocity and the distance between the two axles, respectively. The goal of the control system is to steer the car from a given initial position to the trajectory . Thus, a sliding variable is defined as It is easy to check that the relative degree of this system is 3 Note that, for small angles , , we have Hence, under the assumption of small angles so that , . However, since moderately ample angles can manifest in the transient, we conservatively let , , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000502_j.mechmachtheory.2012.05.008-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000502_j.mechmachtheory.2012.05.008-Figure7-1.png",
        "caption": "Fig. 7. Ball bearing modeled as a lumped spring-mass system.",
        "texts": [
            " For the case 2, P can be described as: P \u00bc P1\u00fe P2 P1\u00f0 \u00desin sin 0:5\u03c0=\u0394T mod \u03b8dj;2\u03c0 \u03b80 \u00f014\u00de The P of the case 3 can be given by: P \u00bc P1\u00fe P4 P1\u00f0 \u00desin sin 0:5\u03c0=\u0394T mod \u03b8dj;2\u03c0 \u03b80 \u00f015\u00de For the case 4, P can be written as: P \u00bc P1\u00fe P3 P1\u00f0 \u00desin 0:25\u03c0=\u0394T1 mod \u03b8dj;2\u03c0 \u03b80 \u03b80\u2264mod \u03b8dj;2\u03c0 \u2264\u03b81 P2 \u03b81bmod \u03b8dj;2\u03c0 b\u03b83 P3\u00fe P1 P3\u00f0 \u00desin 0:25\u03c0=\u0394T3 mod \u03b8dj;2\u03c0 \u03b80 \u03b83\u2264mod \u03b8dj;2\u03c0 \u2264\u03b84 8>>< >>: \u00f016\u00de For the case 5, P can be modeled as: P \u00bc P1 P1sin 0:25\u03c0=\u0394T5 mod \u03b8dj;2\u03c0 \u03b80 \u03b80\u2264mod \u03b8dj;2\u03c0 \u2264\u03b81 0 \u03b81bmod \u03b8dj;2\u03c0 b\u03b83 P1sin 0:25\u03c0=\u0394T5 mod \u03b8dj;2\u03c0 \u03b80 \u03b83\u2264mod \u03b8dj;2\u03c0 \u2264\u03b84 8>>< >>: \u00f017\u00de where \u0394T5 is given by, \u0394T5\u00bc arcsin ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d=2\u00f0 \u00de2 d=2 H\u00f0 \u00de2 q =Do defect on the outer race arcsin ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d=2\u00f0 \u00de2 d=2 H\u00f0 \u00de2 q =Di defect on the inner race 8>< >: \u00f018\u00de The angular position of the jth ball, \u03b8j, which is given by \u03b8j\u00bc 2\u03c0 j 1\u00f0 \u00de Z t \u00fe\u03c9ct \u00fe\u03b80x \u00f019\u00de where \u03b80x is the initial angular position of the first ball with respect to the x-axis, and \u03c9c is the rotational speed of the cage. To analyze the vibrational characteristics of the ball bearing, the contact between the ball and raceway is considered as a lumped spring-mass system as shown in Fig. 7. This model was first proposed by Sunnersjo [1]. However, in the Sunersjo's model, the bearing is only considered as a spring-mass system, the damping effect is ignored, and no defect is assumed. That study is only applied to analyze the vibration response of rolling element bearing system with time-varying compliance. In the present study, to the proposed formulation includes the effects of damping, time-varying compliance property of the bearing system and localized surface defect. Now, the governing equations of dynamic motion for the two-degree of freedom bearing system can be formulated as follows: m\u20acx\u00fe c _x\u00fe K XZ j \u00bc1 \u03bbj\u03b4 1:5 j cos\u03b8j\u00bcwx \u00f020\u00de m\u20acy\u00fe c _y\u00fe K XZ j \u00bc1 \u03bbj\u03b4 1:5 j sin\u03b8j\u00bcwy \u00f021\u00de where m is the mass of the inner race and rotor supported by the bearing, c is the damping factor, wx and wy are the components of radial force acting on the rotor, and K is the overall contact stiffness by using Harris's method [14,15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003089_978-3-319-04867-3-Figure4.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003089_978-3-319-04867-3-Figure4.16-1.png",
        "caption": "Fig. 4.16 a GNPs were illuminated with white light using a darkfield condenser. Only scattered light was detected by the objective lens. The same nanoparticle was imaged before and after coverage with a LC. b Sketch of an electrically controlled light scattering device. GNPs were embedded in a LC cell coated with ITO contact and polyimide alignment layers. Application of an electric field F reorients the LC. The optical anisotropy was indicated by the dotted ellipsoid [108]. Copyright from American Institute of Physics 2002",
        "texts": [
            " To explore novel LC/GNP hybrid materials for a new generation of LC devices, it is important to systematically investigate the structure\u2013property relationships between GNPs and LCs, particularly for alignment and electro-optical responses. LC can organize the dispersed GNPs in various ways depending on the GNP size, shape and how their surface coating interacts with the LC host. For example, an 4 Liquid Crystal-Gold Nanoparticle Hybrid Materials 123 electrically controlled light scattering by GNP in a nematic LC medium was demonstrated (Fig. 4.16) [108]. The idea was to embed GNPs in an electro-optical LC material to induce a spectral shift of the SPR via an electric field. The GNPs become optically spheroidal when covered by an anisotropic LC and the two particle plasmon resonances of the optically spheroidal GNPs can be spectrally shifted by up to 50 meV when 10 kV/cm and higher electric fields were applied. For the LC/GNP hybrid materials, a most attractive potential application probably is metamaterials. Metamaterials obtain their unusual properties which are unachievable with conventional materials based on their specially designed micro/ nano structures, depending on the precise shape, geometry, size, orientation and arrangement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure6-2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure6-2-1.png",
        "caption": "Fig. 6-2 dq windings at t\u00a0>\u00a00; drawn for k\u03c4\u00a0<\u00a01.",
        "texts": [
            " 97 6 Detuning Effects in Induction Motor Vector Control Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink\u00ae, First Edition. Ned Mohan. \u00a9 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. 98 DETuNINg EFFECTS IN INDuCTIoN MoTor VECTor CoNTrol Also initially, i isd sd= * , and \u03b8da\u00a0=\u00a0\u03b8da,est\u00a0=\u00a00. Initially, the torque component of the stator current is assumed to be zero, that is i isq sq * = = 0. At t\u00a0=\u00a00+ and beyond, isd* remains unchanged, but there is a step jump in isq* to produce a step change in torque. The commanded currents are supplied to the estimated dq windings shown in Fig. 6-2, drawn for k\u03c4\u00a0<\u00a01 at some time t. on the basis of discussions later on, we will show that for k\u03c4\u00a0<\u00a01, \u03b8da,est will be less than the actual \u03b8da. The angle \u03b8da is the angle of the actual d-axis along which the rotor flux-linkage vector lies (not the estimated axis, which the EFFECT oF DETuNINg 99 controller considers, incorrectly of course, to be the actual d-axis). Therefore, with the help of Fig. 6-2, we can compute the currents in the dq stator windings (along the correct dq axes in the actual motor) by projecting the dq winding currents along the estimated axes i i e i es dq d s dq d j s dq d jda da _ _ est _ estest err= =\u2212 \u2212 \u2212, ( ) , ( ), ,\u03b8 \u03b8 \u03b8 (6-2) where \u03b8 \u03b8 \u03b8err est= \u2212da da, . (6-3) Note that in this detuned case, we are applying (although mistakenly) the commanded currents to the windings along the estimated d\u2013q axes. Therefore, i i jis dq d sd sq_ est, * * .= + (6-4) using Eq. (6-4) in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000628_j.automatica.2011.01.024-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000628_j.automatica.2011.01.024-Figure7-1.png",
        "caption": "Fig. 7. Obstacle avoidance.",
        "texts": [
            " Our proposed strategy consists in switching between the obstacle avoidance law (4), with d(t) replaced by di(t) := distDi [r(t)] for a properly chosen i, and straight moves to the target: u(t) = 0. (9) As before, the obstacle avoidance maneuver is associated with the safety margin dsafe > 0 and the desired distance d0 > dsafe to the obstacle. The rule for switching between (9) and (4) employs two more parameters \u03f5 > 0 and C > d0 + \u03f5. (10) Here C is the distance to an obstacle at which avoidance is commenced; the maneuver termination is allowed only if the vehicle is close enough to the obstacle: di \u2264 d0 + \u03f5. Specifically, the rule for switching between (9) and (4) is as follows (see Fig. 7, where the initial right turn is caused by the assumed initial dominance of the first addend d\u0307 < 0 in the sum in the curly brackets from (4)): R1 Switching from (9) to (4) with d(t) replaced by di(t) occurs at any time instant \u03c4 when the distance from the vehicle to the obstacle Di reduces to the value C , i.e., di(\u03c4 ) = C , whereas di(t) > C for t < \u03c4, t \u2248 \u03c4 . R2 Switching from (4) with d(t) replaced by di(t) to (9) occurs when di(t) \u2264 d0 + \u03f5 and the vehicle is oriented towards the target. This strategy tacitly assumes that the situation where the rule R1 becomes active simultaneously for several obstacles cannot be encountered: N [C,Di] \u2229 N [C,Dj] = \u2205 \u2200i =\u0338 j"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure1.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure1.3-1.png",
        "caption": "Figure 1.3.3. Acceleration components.",
        "texts": [
            " Handling analysis may be based on the open loop alone, where tests are intended to reveal the vehicle characteristics, or on the closed loop which also involves the performance of the driver. 1.3 Axis Systems and Notation To study the response of a vehicle to control inputs or to disturbances it is necessary to specify one or more coordinate systems to measure the position of the vehicle. The method recommended by SAE will be described here (see SAE J670e in Appendix E). It was originally developed from aeronautical practice. Broadly similar methods are used throughout engineering dynamics analysis. First there is an Earth-fixed axis system XYZ (Figure 1.3.1). Upper-case letters are used to denote Earth-fixed coordinates. For all ground vehicles the Earth may be considered to be stationary. This is not true in an absolute sense \u2013 the Earth spins about its own axis, and also moves around the Sun \u2013 but the associ- 8 Tires, Suspension and Handling ated accelerations are small, so for our purposes the XYZ system is an inertial coordinate system, i.e., it has negligible acceleration. The X-axis is chosen longitudinally forward in the horizontal plane; Y is then 90\u00b0 clockwise from X as viewed from above, and also in the horizontal plane. To form a right-hand coordinate system, the Z-axis is vertically downward, because this is the direction of motion of a right-hand screw turning X to Y. The origin of the XYZ system may be at any convenient point, typically in the ground plane. This is the SAE system. In the International Organization for Standardization (ISO) system, the Y-axis is to the left and the Z-axis is upward. There is also an axis system xyz (lower-case letters) fixed to the vehicle (Figure 1.3.2). The use of upper-case XYZ for the Earth-fixed inertial system and lower-case xyz for the vehicle-fixed system follows widely accepted conventions. The origin of the xyz system is usually placed at the vehicle center of mass. The x-axis is approximately in the central plane, pointing forward, and is horizontal when the vehicle is in its usual pitch attitude; thus the pitch angle is the angle of x to the horizontal plane. The y-axis points to the driver's right, and is horizontal when the vehicle has zero roll angle; thus the roll angle is the angle between the y-axis and the horizontal plane",
            " The three rotations defined as standard by the SAE, starting from a position with xyz aligned with XYZ, are, in sequence: 10 Tires, Suspension and Handling (1) A yaw rotation \u03c8 about the z-axis (2) A pitch rotation \u03b8 about the y-axis (3) A roll rotation \u03a6 about the x-axis Note that the rotations are taken about the vehicle-fixed axes. (A nomenclature list for each chapter appears in Appendix A.) Roll angle \u03a6 is positive for a clockwise rotation seen from the rear. Pitch angle \u03b8 is positive for a nose-up position. The translational velocity of the vehicle is taken as the velocity of its center of mass G, at the origin of xyz, measured in the system XYZ. For convenience the velocity is resolved into components along each of the xyz axes (Figure 1.3.2). There is: (1) A longitudinal velocity u along the x-axis (2) A side velocity v along the y-axis (3) A normal velocity w along the z-axis Because the x and y axes are not generally exactly parallel to the ground plane, other terms are also defined as follows. Forward velocity is the velocity component in the ground plane perpendicular to y; essentially this is the longitudinal velocity resolved into the ground plane. Lateral velocity is the velocity component in the ground plane perpendicular to the x-axis; essentially this is the side velocity resolved into the ground plane",
            " These refer, respectively, to vertical and lateral motions in linear translation without rotation. Because the xyz axes are attached to the vehicle, the position of G is constant and it has zero velocity and acceleration in these axes. The actual acceleration of the vehicle in the XYZ system is again resolved into components parallel to the xyz axes, there being a longitudinal acceleration u along x, a side acceleration v along y, and a normal acceleration w along z. There are also lateral, forward and heave linear accelerations. Figure 1.3.3, with exaggerated attitude angle, shows how the total horizontal acceleration may be resolved into forward and lateral components, or into tangential and centripetal components. The centripetal Introduction 11 acceleration is the component parallel to the road plane and perpendicular to the vehicle path, i.e., directed toward the path center of curvature. The angular velocities of the vehicle are naturally measured relative to the inertial XYZ system, but are resolved about the xyz axes for convenience, to give: (1) The roll angular speed p (2) The pitch angular speed q (3) The yaw angular speed r These are expressed as rad/s or deg/s. In rotation there are roll (p), pitch (q) and yaw (r) angular accelerations. Referring again to Figure 1.3.1, looking down on the horizontal XY plane, we have: (1) The angular position \u03c8 (psi) of the projected x-axis relative to the X-axis, called the heading angle, measured positive clockwise. (2) The angular position \u03b2 (beta) of the forward velocity, relative to the projected x-axis, called the attitude angle (sometimes sideslip angle), again positive clockwise. (3) The angular position of the velocity vector, which is tangential to the path and denoted by v (nu), called the course angle. 12 Tires, Suspension and Handling Consequently The terminology introduced here becomes familiar only with regular use",
            " Fortunately, most practical handling problems arc adequately analyzed by dealing with simplified cases, for example by treating the vehicle as being in approximately plane motion parallel to the ground plane, so that the full generality of the equations is not required. For those readers interested in the general approach, the bibliography at the end of this chapter gives references. Notation for forces on the vehicle follows a similar pattern to kinematic notation, including the use of the various subscripts for axis directions, and terms such as longitudinal force and side force. Notation for forces in the ground plane follows the acceleration notation of Figure 1.3.3. The centripetal force FC gives the centripetal acceleration that causes path curvature. The tangential force FT controls the acceleration along the path. Figure 1.4.1(a) shows the free-body diagram of the vehicle in the ground plane, viewed in the XYZ inertial coordinate axes. The free-body diagram shows the chosen free body with the relevant forces that act on it. As a result of the net forces in Figure 1.4.1(a) the vehicle experiences accelerations AT and AC according to F = mA in the inertial XYZ system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003392_rob.21597-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003392_rob.21597-Figure9-1.png",
        "caption": "Figure 9. 3D Octomap and occupancy grid of an example of a USAR-like scene.",
        "texts": [
            " In the experiments, the initial poses of both robots are defined as the origins of their local coordinate systems. When there is more than one robot in a subscene, the global coordinate frame for each subscene is the same as the local coordinate frame of the wheeled robot. To register the maps of the two robots, it is assumed that the initial poses of the two robots relative to each other are known. The OctoMap was converted into an occupancy grid to be used for robot exploration and local navigation within the Deliberation module. Figure 9 shows an example of an OctoMap and its corresponding occupancy grid. As previously mentioned, in order to classify the occupied cells as climbable or nonclimbable obstacles, we used a rubble profile categorization technique that we developed in Doroodgar et al. (2014). Using the depth profile of an occupied cell, we used the slope and smoothness of a rubble pile by fitting a plane to the depth information using a leastsquares method. The combination of the two parameters can be used to determine if the rubble pile is a climbable or nonclimbable obstacle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure10-8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure10-8-1.png",
        "caption": "Fig. 10-8 Space vector and phasor diagrams.",
        "texts": [
            " 10-3-6 Space Vector Diagram in Steady State In a balanced sinusoidal steady state with \u03c9d\u00a0=\u00a0\u03c9m, the damper winding currents in the rotor are zero, as well as all the time derivatives of SALIENT-POLE SYNChRONOUS MAChINES 155 currents and flux linkages in dq windings. Therefore, in Eq. (10-23) and Eq. (10-24), \u03bbsd sd sd md fdL i L i= + (10-34) and \u03bbsq sq sqL i= . (10-35) From Eq. (10-28) and Eq. (10-29), using Eq. (10-34) and Eq. (10-35) v R i L isd s sd m sq sq= \u2212\u03c9 (10-36) and v R i L i L isq s sq m sd sd m md fd= + +\u03c9 \u03c9 . (10-37) Multiplying Eq. (10-37) by (j) and adding to Eq. (10-36), v jv R i jR i j L i j L i L isd sq s sd s sq m sd sd m md fd m sq sq+ = + + + \u2212\u03c9 \u03c9 \u03c9 , (10-38) which is represented by a space vector diagram in Fig. 10-8a, where v jv vsd sq s+ = 2 3 (10-39) and i ji isd sq s+ = 2 3 . (10-40) The corresponding phasor diagram is shown in Fig. 10-8b. 156 VECTOR CONTROL OF PERMANENT-MAGNET DRIVES 10-4 SUMMARY In this chapter, we have extended the dq-analysis of induction machines to analyze and control synchronous machines. REFERENCES 1. N. Mohan, Electric Machines and Drives: A First Course, Wiley, hoboken, NJ, 2011. http://www.wiley.com/college/mohan. 2. E.W. Kimbark, Power System Stability: Synchronous Machines, IEEE Press, New York, 1995. 3. http://www.baldor.com. PROBLEMS 10-1 In the simulation of Example 10-1, replace the ideal inverter by an appropriate SV-PWM inverter, similar to that described in Chapter 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003818_j.cja.2019.04.018-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003818_j.cja.2019.04.018-Figure6-1.png",
        "caption": "Fig. 6 Experimental test device schematic.",
        "texts": [
            " All experiments were carried out under the same conditions to avoid the impact of changes in the external environment around the gearbox. In the experiment, the sampling rate was set as 20.48 kHz and the sampling time interval was 6 s. Five sets of sample data were collected for each condition and a total of 30 sets of independent sample data. During the experiment, vibrational signals in three directions were collected. In the data processing, only signals from the vertical direction were used. The principle of experimental verification device is shown in Fig. 6. Enough gears were purchased to ensure the smooth running of the experiment. The parameters of the experimental gear are shown in Table 1. Pitting corrosion of six gears as shown in Table 2. The pitting percentage was quantified by identifying the pitting area using the Adobe Photoshop software. The percentage of pitting is the ratio of the area of the pitting of the tooth surface to the total area of the tooth surface. Pitting percentage is an approximation and is primarily used to distinguish the severity of gear pitting fault"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003443_bf02120338-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003443_bf02120338-Figure3-1.png",
        "caption": "Fig. 3. The cross-spring pivot deflected through a small angle.",
        "texts": [
            " The force to be transmitted by the cross-spring pivot can always be resolved into two components N t and N 2 acting along the initial central lines of the (identical) flat springs, as indicated in fig. 2. To .\\, & ,/\" 2 ~ / I I I \\,, Big. 2. The load to be transmitted by the cross-spring pivot consists of the two force components N 1 and N 2, acting along the initial central lines of the springs, and the moment 21r deflect the cross-spring pivot through a given angle 9 a moment M is required with respect to the initial midpoints of the two springs. This angle being small, the springs at their upper ends (see fig. 3) can only be displaced'in a direction perpendicular to their initial central lines. Moreover, at a spring length L and an angle of intersection 2a, the distance between the two spring ends is always equal to L sin a. These conditions can be met only if the displacements of the two THE CROSS-SPRING PIVOT AS A CONSTRUCTIONAL ELEMENT 317 sprilag ends have the same value [ while 2t sin a or [ = 89 L 9. (1) -- L sin a ' This means t ha t for small angles q0 the pivot point coincides with th6 initial point of intersection of the two springs, and tha t the distort ion at the ends is bound by the same condit ion (1) for each flat spring separately"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003041_s11837-015-1298-7-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003041_s11837-015-1298-7-Figure1-1.png",
        "caption": "Fig. 1. Typical designations for determining the orientation dependence of mechanical properties for wrought products based on (a) ASTM E399, (b) ISO 12135.",
        "texts": [
            " The work is part of a larger team effort lead by Case Western Reserve University (CWRU) and Carnegie Mellon University (CMU), and it is funded by America Makes to examine Rapid Qualification Methods for Powder Bed Direct Metal AM Processes. An ARCAM EBM machine at NCSU (model A2; Arcam AB, Mo\u0308lndal Sweden), was used to construct 10 mm 9 20 mm 9 100 mm multilayer pads using ARCAM pedigree Ti-6Al-4V ELI spherical powders with average particle size range of 40\u2013105 lm. The chemistry of powder was measured using MAS-ICP method and reported in Table I. It was found to meet the requirements of ASTM F3001.18 Figure 1a and b shows the typical ASTM/ISO designations for determining the orientation dependence of mechanical properties for wrought products.26,27 In Fig. 1a, RD indicates rolling direction, L designates longitudinal, T designates transverse, and S designates short. This nomenclature creates the possibility of determining the properties in six different orientations (i.e., LS, SL, LT, TL, ST, and TS).26 The first letter designates the direction normal to the crack plane, and the second letter designates the expected direction of crack propagation. ISO standards use an X, Y, Z nomenclature (i.e. X-Y, Y-X, X-Z, Z-X, Y-Z, and Z-Y).27 The letter before the hyphen represents the direction normal to the crack plane and the letter following the hyphen represents the expected direction of crack extension"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure2-2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure2-2-1.png",
        "caption": "Fig. 2-2 Three-phase windings.",
        "texts": [
            " Notice that regardless of the positive or the negative current in phase-a, the flux-density distribution produced by it in the air gap always has its peak (positive or negative) along the phase-a magnetic axis. 2-2-1 Three-Phase, Sinusoidally Distributed Stator Windings In the previous section, we focused only on phase-a, which has its magnetic axis along \u03b8\u00a0=\u00a00\u00b0. There are two more identical sinusoidally distributed windings for phases b and c, with magnetic axes along \u03b8\u00a0=\u00a0120\u00b0 and \u03b8\u00a0 =\u00a0 240\u00b0, respectively, as represented in Fig. 2-2a. These three STaTor INduCTaNCES (roTor oPEN-CIrCuITEd) 9 windings are generally connected in a wye-arrangement by joining terminals a\u2032, b\u2032, and c\u2032 together, as shown in Fig. 2-2b. a positive current into a winding terminal is assumed to produce flux in the radially outward direction. Field distributions in the air gap due to currents ib and ic are identical in sinusoidal shape to those due to ia, but they peak along their respective phase-b and phase-c magnetic axes. 2-3 STATOR INDUCTANCES (ROTOR OPEN-CIRCUITED) The stator windings are assumed to be wye-connected as shown in Fig. 2-2b where the neutral is not accessible. Therefore, at any time i t i t i ta b c( ) ( ) ( ) .+ + = 0 (2-5) For defining stator-winding inductances, we will assume that the rotor is present but it is electrically inert, that is \u201csomehow\u201d hypothetically of-course, it is electrically open-circuited. 2-3-1 Stator Single-Phase Magnetizing Inductance Lm,1-phase as shown in Fig. 2-3a, hypothetically exciting only phase-a (made possible only if the neutral is accessible) by a current ia results in two equivalent flux components represented in Fig",
            "magnetizing due to (2-9b) Therefore, in Eq. (2-8), using Eq. (2-6a) and Eq. (2-9b), L Lmmutual phase= \u2212 1 2 1, - . (2-10) The same mutual inductance exists between phase-a and phase-c, and between phase-b and phase-c. The expression for the mutual inductance can also be derived from energy storage considerations (see Problem 2-2). 12 INduCTIoN MaCHINE EQuaTIoNS IN PHaSE QuaNTITIES 2-3-3 Per-Phase Magnetizing-Inductance Lm under the condition that the rotor is open-circuited, and all three phases are excited in Fig. 2-2b such that the sum of the three phase currents is zero as given by Eq. (2-5), \u03bba i i i m a b c L i, , -magnetizing (rotor open-circuited) phase + + = = 0 1 a b cL i L i+ +mutual mutual . (2-11) using Eq. (2-10) for Lmutual, and from Eq. (2-5) replacing (\u2212ib\u00a0\u2212\u00a0ic) by ia in Eq. (2-11), L i Lm a a i i i m a b c = = + + = \u03bb , , , - .magnetizing rotor open phase 0 1 3 2 (2-12) using Eq. (2-7), L r N p m o g s=       3 2 2 \u03c0\u00b5 . (2-13) Note that the single-phase magnetizing inductance Lm,1-phase does not include the effect of mutual coupling from the other two phases, whereas the per-phase magnetizing-inductance Lm in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001001_1.3453357-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001001_1.3453357-Figure4-1.png",
        "caption": "Fig. 4 Roller-Race contact geometry",
        "texts": [
            " Once <p' is known, rbr may be determined in the inertial frame using equation (9), and it may be referenced in the race azimuth frame as rbr a = [T(<p', 0, O)]rbr i and in the contact frame where the matrix [Tae] has already been defined above. (12) (13) The computation of the roller azimuth if; is quite straightforward once the orbital position, 0, locating the roller mass center is known from prescribed rb '\" (x, r, 0) in cylindrical coordinates. Once the geometric center of the roller is located relative to the race land center, it will be necessary to examine every point on the roller for possible interaction. Hence, the introduction of the roller geometry becomes essential at this point. Fig. 4 shows this geometry for a typical roller in a cylindrical roller bearing. The. interaction between the roller and race will be restricted to the central flat land and the crowned areas at this point. Later in the next section the interaction between the roller end and race flange will be considered. Now a point of the roller surface is best described in the roller frame by the position vector 296 / VOL. 101, JULY 1979 rb = I~R' sin <1\u00bb R' cos <I> (14) where <I> is the angular position about the X axis, I is the length coordinate along the X axis and R' is the effective radius. For the geometry shown in Fig. 4 R' will depend on I. , d L2 L2 R =-'--<1<- d \u00a322 -12 and R'=---,-- 2 4Re 2' 2 - - 2 where Re is the crown radius as shown in Fig. 4. The vector can be expressed in the contact frame as (15) For the point to be in the contact plane the y component of r e must vanish and this condition will determine the relevant <1>. Since the rotation of the roller about the Y and Z axes will be in general small, it will only be necessary to compute <I> for the roller center, hence ( T 23 ) <I> = arctan - T22 (16) where T 23 and T22 are the corresponding elements in a matrix ob tained by the product of matrices shown in equation (15). The deflection at any point on the roller surface is now given as (17) A negative value of 0 will mean no contact",
            " In order to determine the effective contact length, when the rollet is crowned, the length coordinate I in equation (17) will be determined by standard bisection techniques. In other words, the value of I for o = \u00b0 will determine the contact length. Clearly, there will be two such roots and they both have to be determined separately since in general . the roots may not be symmetric. ' For the purpose of computing the total interaction, it will be con venient to divide the contact length into a finite number of elements as shown in Fig. 4 and compute the normal and tractive loads for each element. A proper summation will then give the total required load. Thus, the analysis presented below for the normal and tractive lmid will apply to each element in the contact zone. Normal Contact Load. The load deflection relation for a line contact is not uniquely defined, as in case of point contact. The de flection can be computed only in terms of strains corresponding to finite lengths in the two interacting bodies. In view of this difficulty, Lundberg [4] has determined an empirical equation based on actual load deflection measurements in line con tact",
            " If we assume that both roller and race deform equally, which is quite reasonable, then the required position vector may be written as rpb = /-(R - :/2) sin <pI (R - 0/2) cos <p (21) In order to compute the local slip velocities, let the race have a translation velocity Vr and an angular velocity Wr . Likewise, let the roller have a translational velocity Vb and an angular velocity Wb. Generally, the angular velocities are specified in the body fixed frames while the translational velocities are measured in the inertial frame. Furthermore, the roller velocity is conveniently measured in the cy lindrical coordinate frame in terms of components X, f, and 0. In terms of these components, the local slip velocity Us of the race relative to the roller at point P (see Fig. 4) is given in the contact frame in terms of the race and roller velocities, Ur and Ub respectively, as UsC = r C- ue e (24) where the vector Rp , which locates the center of elementary strip with respect to the race mass center, is computed as (25) The components us, e and US2 e in the contact frame will result in traction, Us 2 e being along the rolling direction and us, e being normal to it. In case of a roller bearing the slip will be primarily in the y direction and, hence, the tractive force will act along the y axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002058_0022-2569(68)90016-5-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002058_0022-2569(68)90016-5-Figure1-1.png",
        "caption": "Figure 1. Generation of a six-bar linkage from two arbitrary four-bars. Joints A and B have the same pitch.",
        "texts": [],
        "surrounding_texts": [
            "K. J. W a l d r o n * Received 8 August 1967 A b s t r a c t This note describes a class of overconstrained linkages which are obtained by combination of other overconstrained linkages. A number of these linkages have apparently not been described before. They are distinguished by having at least one pair of non-adjacent members whose relative screw axis is fixed, with respect to both members, throughout the motion of the linkage. Zusammenfassung--Hybride fibergeschlossene Getriebe. Dieser Aufsatz beschreibt eine Klasse von fibergeschlossenen Getrieben, die dfirch sine Kombinierung von anderen fibergeschlossenen Getrieben erhalten sind. Eine Anzahl von diesen Getrieben sind offenbar noch nicht beschrieben worden. Dieselben sind gekennzeichnet dadurch, dass sis wenigstens sin Paar von nicht benachbarten Gliedern besitzen, deren relative Schraubenachse an beiden Gliedern, w~ihrend der Bewegung des Getriebes, befestigt ist. Pe3mMe--F]~6p~m, Ie c B e p ~ r b l e MexaH]S3M],I--K. YaYIApoH. HaeTomHas pa6oTa OHHCI, IBaeT KIIaO~ cBepx3,aMKHyTI,IX MeXaHH3MOB, KOTOpble HOJI~eH~ KOM6aeuapoaam~eM Rpyrllx cBepx3aMKHyTI, IX MeXaItIt3MOB. HeKoTopoc I\u00a2O3n~'clOCTBO 3THX MexaHII3MOB ~o ~ nop He 6SLrm onKcaH~. OHH O T ~ T C f l TeM, \"qTO HMelOT no Kpa,~e~ MepC OH~:ly napy He COCe,HHHX 3BeHI~B, OTHOCHTeJ'I]bHa~ BHHTOBaf[ OCb KOTOpMX i/pHKpen.rleHa K 3\"rHM 3B~H]b~IM BO BpeM.q ABmKeHHS MeXaHH3Ma. IN THE following, the linkages considered are such that their joints are all simple joints of connectivity one. t Additionally, we restrict ourselves to lower-pair joints, that is, revolutes, prismatic joints and screw joints. The most important linkage joints with higher connectivity, in particular, the lower pairs with higher connectivity, are equivalent to open chains with joints of this type.~ We start by considering a single-loop linkage with mobility one in which two nonadjacent members have a fixed relative axis. We mean by this that the relative screw axis of these two members is fixed with respect to these members, in both position and pitch, throughout the motion of the linkage. The two members could, therefore, be connected by a screw joint having the same axis and pitch as the fixed relative axis. The mobility of the linkage and, indeed, its motion, would be unaffected. The resulting linkage would be a two-loop linkage. Each of the loops would have mobility one if the other parts of the linkage were removed. I f it were to have mobility greater than one, the original linkage would necessarily have mobility greater than one. I f it had no mobility then those joints of the original linkage which are included in the loop would be permanently locked [5]. Conversely, let us take two single-loop linkages such that one joint of each has a given pitch (Fig. la). We arrange the two loops so that these two joints also have the same axis, * Research Assistant, Department of Mechanical Engineering, Stanford University, Stanford, California. t The terminology used throughout this note is that of reference [1]. In particular, to avoid confusion, it should be noted that we will not use the word pair in the sense of kinematic pair, since a kinematic pair falls within the definition of a joint in reference [1]. This fact seems first to have been established by Delassus [2]. Grtibler, to whom it is usually attributed stated it somewhat later [3]. More recently it has been discussed in reference [4]. 73 and we fix the members adjacent to the joints to each other as in Fig. lb. If we remove the joint common to the two loops, the resulting single-loop linkage (Fig. lc) is certainly mobile. If its mobility is one, we have a linkage of the type considered above. This method of deriving overconstrained linkages was ftrst used by Bennett [6]. However, thereis no guarantee that the resulting linkage will not have mobility greater than one. The condition for a single-loop linkage to have mobility one is that the difference between the sum of the connectivities of the simple joints of the linkage, and the order of the equivalent screw system (ESS for brevity) shall be one [1 ]. Now the sum of the connectivities of the simple joints is, in this case, simply the number of joints in the linkage. This number, for the resultant linkage, is two less than the sum of the numbers of joints in the two original linkages. Also, since the ESS of the resultant linkage contains the screw axes of all joints of the linkage, it contains the ESS's of both of the original linkages when they are placed in the position of Fig. lb. Thus the order of the ESS of the resultant linkage is the sum of the orders of the ESS's of the original linkages, less the order of their intersection when placed in the position of Fig. lb. Now the orders of the ESS's of the original linkages are both one less than the number of joints in the respective linkages. Therefore the order of the ESS of the final linkage is equal to the number of joints of that linkage less the order of the intersection of the ESS's of the original linkages. Therefore, if the linkage is to have mobility one, this intersection must have order one. Since the two original ESS's at least intersect in the axis of the common joint, they may intersect only in this screw axis. Thus the condition for the resultant linkage to have mobility one is that the ESS's of the original linkages shall intersect only in the screw axis of the common joint when they are placed as in Fig. lb. Delassus [7, 8] has derived all possible three and four-bar linkages whose joints are lower pairs with connectivity one. Therefore we can, by the above method, derive all four and five-bar linkages which have fixed relative axes, and many of the six-bars. The two three-bars are the differential screw linkage and the linkage which contains three prismatic joints all parallel to the same plane. One of the three screws of the differential-screw linkage may have infinite pitch. It is possible to match this with a prismatic joint from either the three prismatic joint linkage or another differential-screw linkage in which one screw has infinite pitch. We obtain, in this manner, the two four-bars which have fixed relative axes. They are quite trivial. The first consists of two coaxial screws plus two prismatic joints, all parallel to the same plane. The other has two pairs of coaxial screws whose axes are parallel. In a similar manner, we can match and remove joints of three and four-bar linkages to obtain five-bars, but the results are not of much interest. Neither are the six-bar linkages, formed from three and five-bars. I f we use a three-bar linkage the resultant linkage will always contain one of two possible joint combinations. The first is two coaxial screw joints. They are coaxial with the fixed relative axis if it has finite pitch, or parallel to it if it has infinite pitch. I f the fixed relative axis has finite pitch, we could also get a finite-pitch screwjoint coaxial with the fixed axis and a prismatic joint parallel to it. This combination occurs when the three-bar is a differential-screw linkage. The second joint combination is two adjacent prismatic pairs which are parallel to the same plane as the fixed relative axis. The pitch of the fixed relative axis is infinite. This combination results when the three-bar is a three-prismatic-pair linkage. A more interesting case arises when the linkages used are both four-bars. The six-bar linkages which can be formed in this way are tabulated. The four-bar linkages given by Delassus are listed along the vertical axis of the table and numbered 1 to 13. The same linkages are denoted by their numbers along the horizontal axis. The properties of the combination of two linkages are given in the space at the intersection of the respective column and row of the linkages. X denotes a six-bar with mobility one and Y a six-bar whose mobility is greater than one. In some cases more than one pair of joints is available for elimination. The pitch of any screw pair in any of the four-bar linkages which is neither zero nor infinity may, in all cases, take an arbitrary value. There are therefore three different types of elimination which result when the pitch of the screw concerned is respectively of zero, infinite or other pitch. These three cases are denoted, where necessary, by appending in parentheses the symbols 0, ~ , h respectively. Those linkages in the table which have mobility greater than one were identified using the result derived above concerning the intersection of the ESS's of the original linkages. As an example, consider the combination of two Delassus parallelogram linkages. The joints of the parallelogram linkage (8) are screw joints, all parallel, and such that the arithmetic means of the pitches of the two pairs of opposite joints are equal. I f we select two of these linkages which each have a joint of a given pitch, we can eliminate those joints and so obtain a six-bar with six parallel screw pairs. Now, as is shown in reference (5), four parallel screw pairs will, in general, define a screw system which contains all screws, whatever their pitches, parallel to the given screws. Thus the ESS of the six-bar cannot have order greater than four. Since the ESS's of the four-bars were both of order 3, the order of their intersection is at least two, as is the mobility of the six-bar. Many of the overconstrained six-bars given in the table do not appear to have been noticed before. One of these is a combination of two Bennett linkages which is shown in Fig. 2. Several of the other linkages are in common use. In some of those cases in which screw pairs are present, they may be replaced by revolutes without increasing the mobility of the linkage. Most of these are among the linkages discussed in references [9] and [5], as are many of the other linkages. It should also be noted that in none of these cases does the elimination of a screw pair with pitch other than zero or infinity result in a linkage with mobility one. Thus six-bars with fixed relative axes of pitch other than zero or infinity can only be formed by combination of a three-bar with a five-bar. As noted above, they are rather trivial. Using the procedure described above we can also combine either a four-bar with a five-bar or a three-bar with a six-bar to give a seven-bar with a fixed relative axis. An obvious use for linkages with fixed relative axes is in situations in which two members are to be joined with a fixed relative screw axis but, because of obstructions, or for other reasons, it is not convenient to connect them directly. The Sarrus linkage, a special case [5, 6, 9] of the linkage obtained by elimination of the prismatic joints of two screw slider cranks, is used in this manner. The double Hooke's joint [6], which is obtained from two spherical four-bars having different centers, is very widely used as a transmission coupling. This is because of its constant velocity characteristics in certain configurations. However, none of the other linkages would seem to be suited to this function unless a non-steady output is required. The linkage of Fig. 2 does have constant velocity configurations. Acknowledgment Theauthor wishesto acknowledgethe financial assistanceoftheNational Science Foundation (grant NSF GK 660) and the advice and criticism of Professor Bernard Roth of Stanford University during the course of this work. i ~. ~I ~ \u00b0- ~ Q s _ .Q 0 I L ! ! e +.~ ~ ~I \u00b0 ~i~ ~o r- \u00ae ~ o J ~ - ~ '"
        ]
    },
    {
        "image_filename": "designv10_1_0000660_icra.2011.5980244-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000660_icra.2011.5980244-Figure1-1.png",
        "caption": "Fig. 1. The inertial coordinate system O and the vehicle coordinate system V.",
        "texts": [
            " Given that the mass of the pendulum is small compared to the mass of the quadrotor, it is reasonable to assume that the pendulum\u2019s reactive forces on the quadrotor are negligible. The dynamics of the quadrotor, then, do not depend on the pendulum, whereas the dynamics of the pendulum are influenced by the motion of the quadrotor. This assumption is justified by the experimental setup, with the weight of the pendulum being less than 5% of that of the quadrotor vehicle. The quadrotor is described by six degrees of freedom: The translational position (x, y, z) is measured in the inertial coordinate system O as shown in Figure 1. The vehicle attitude V is defined by three Euler angles. From the inertial coordinate system, we first rotate around the z-axis by the yaw angle \u03b1. The coordinate system is then rotated around the new y-axis by the pitch angle \u03b2, and finally rotated about the new x-axis by the roll angle \u03b3: O V R(\u03b1, \u03b2, \u03b3) = Rz (\u03b1)Ry (\u03b2)Rx (\u03b3) , (1) where Rx (\u03b3) =   1 0 0 0 cos \u03b3 \u2212 sin \u03b3 0 sin \u03b3 cos \u03b3   , (2) 978-1-61284-385-8/11/$26.00 \u00a92011 IEEE 763 Ry (\u03b2) =   cos\u03b2 0 sin\u03b2 0 1 0 \u2212 sin\u03b2 0 cos\u03b2   , (3) Rz (\u03b1) =   cos\u03b1 \u2212 sin\u03b1 0 sin\u03b1 cos\u03b1 0 0 0 1   "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000372_027836499801701205-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000372_027836499801701205-Figure2-1.png",
        "caption": "Fig. 2. The DELTA robot. See text for explanation of numbers 1-4.",
        "texts": [
            " Application to the DELTA Parallel Robot In this section, we illustrate the method proposed in Section 3 by an application on the DELTA parallel robot. The robot is first described and its Jacobian matrix is derived. Based on this Jacobian matrix, the mass matrix of the robot is evaluated considering a complete model first. It is then shown that the model can be simplified without substantially affecting its precision. The virtual work principle is finally applied to the DELTA robot, leading to a simple form of its dynamic model. 4.1. The DELTA Robot Description As illustrated in Figure 2, the DELTA robot is made of three parallel kinematic chains linked at the travelling plate (3). Each chain is moved, driven by a motor (4) fixed to the robot base. Motions of the travelling plate are achieved by the combination of arm movements (1) that are transmitted to the plate by the system of parallel rods (2) through a pair of ball-andsocket passive joints. These parallel rods, also called forearms, ensure that the travelling plate always remains parallel to the robot base. 4.2. Geometric Parameters The absolute reference frame { R is chosen as shown in Figure 2, at the center of the triangle drawn by the axes of the three motors, with z pointing upward, and x perpendicular to the axis of motor 1. Owing to the robot\u2019s triple symmetry, each arm can be treated separately. Its geometric parameters are defined in Figure 3. The index i (i = 1, 2, 3) is used to 1329 identify the arm number. Each arm is separated by an angle of 120\u00b0. For each arm, a corresponding frame is chosen that is located at the same place as {7?} but rotated by an angle Oi = 0\u00b0, 120\u00b0, and 240\u00b0, for arms 1, 2, and 3, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000273_tia.2009.2013550-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000273_tia.2009.2013550-Figure2-1.png",
        "caption": "Fig. 2. Three-dimensional meshes.",
        "texts": [
            " In addition, when fc/f (fc is the carrier frequency of the inverter) is not an integer, the orders of the harmonics n are not integers either. In this case, the analysis due to (1)\u2013(3) should be carried out during m time periods to make mfc/f an integer. Table I shows the specifications of the analyzed motor. The motor has one interior magnet per pole. It is a sintered magnet whose remnant flux density is 1.1 T. One magnet is subdivided into 28 pieces along the axial length to prevent the eddy currents. The inverter is IGBT-type PWM inverter whose carrier frequency is 10 kHz. Fig. 2 shows the two kinds of 3-D finite-element meshes, which are models (a) and (b). Model (a) corresponds to the motor without the magnet division. In this case, the half region of the motor along the axis is discretized by the 3-D tetrahedron edge-finite elements with the boundary condition at the symmetrical side, i.e., setting the parallel component of A and \u03c6 as zero. Using this condition, the flux density is fixed as parallel and eddy current as normal to the plane. On the other hand, model (b) corresponds to the measured motor whose magnet is divided into 28 pieces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001100_j.optlastec.2017.05.006-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001100_j.optlastec.2017.05.006-Figure2-1.png",
        "caption": "Fig. 2. Diagram of the basic process parameters of the SLM: (a) process parameters and (b) scanning strategy.",
        "texts": [
            " Typical particle morphology and particle size distribution curve of the starting AlS curve. particle size analyzer (Fritsch Gmbh, Analysette22 MicroTec plus). The results show that the particle size of the AlSi10Mg powder is in the range of 5\u201350 lm (as seen in Fig. 1(b)). The SLM process is carried out by a Renishaw AM-250 powderbed machine. The powders are melted by a diode pumped Nd: YAG laser with the maximum power of 400 W. The adjustable parameters are point distance and exposure time. As illustrated in Fig. 2(a), point distance is the distance between adjacent fusion points along laser scanning direction, and exposure time is the duration time of the laser remaining on each fusion point. In order to minimize part residual stress, a checkerboard scanning strategy was selected for all trials. For one specific powder layer, the checkerboard is scanning in a linear way, and the linear scanning direction rotates with 67 for the next processing powder layer, as shown in Fig. 2(b). Other parameters are set as constants and their effects on part\u2019s properties are not discussed here. Those parameters are listed in Table 2. In the SLM experiments, an aluminum substrate was leveled and fixed on the building platform. The platform temperature was preheated and maintained at 150 C in order to reduce residual stresses and distortion of components. The rectangular specimens with dimensions of 10 mm 10 mm 10 mm were built layer-by-layer until the whole shape completely formed. The LED expressed by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000426_9781118680469-Figure7.28-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000426_9781118680469-Figure7.28-1.png",
        "caption": "FIGURE 7.28 Diverse photodriven motions based on photomechanical LCP materials.",
        "texts": [
            " 260 PHOTOMECHANICAL LIQUID CRYSTALLINE POLYMERS Light, as a material stimulus, can be handled remotely, almost instantly and very precisely. Photomechanical LCP materials take full advantage of this and have been shown to work as main driving parts of light-driven actuators without the aid of batteries, electric wires, or gears. Combining the photomechanical response of LCP materials with the recent progress in materials chemistry allows researchers to design versatile advanced functional materials with controllable photomechanical performance. Thus, diverse photodriven motions as shown in Figure 7.28 can be obtained. Undoubtedly, such novel materials with light-inducedmotion and deformation shown by LCP systems not only reveal their complex photomechanical behavior but also will be relevant to future technologies which build on their photocontrollable response. 1. Li, Q., Ed. Liquid Crystal Beyond Displays: Chemistry, Physics, and Applications; John Wiley & Sons: New Jersey, 2012. 2. Wang, Y.; Li, Q. Light-driven chiral molecular switches or motors in liquid crystals. Adv. Mater. 2012, 24, 1926\u20131945"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure13.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure13.2-1.png",
        "caption": "FIGURE 13.2. Kinematics of a rest-to-rest cubic path.",
        "texts": [
            "15) with the following solutions:\u23a1\u23a2\u23a2\u23a3 a0 a1 a2 a3 \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a3 q0 q00 \u2212 (tf \u2212 t0) \u22122 \u00b3 3q0 \u2212 3qf \u2212 2t0q00 \u2212 t0q 0 f + 2tfq 0 0 + tfq 0 f \u00b4 (tf \u2212 t0) \u22123 \u00b3 2q0 \u2212 2qf \u2212 t0q 0 0 \u2212 t0q 0 f + tfq 0 0 + tfq 0 f \u00b4 \u23a4\u23a5\u23a5\u23a5\u23a5\u23a6 (13.16) A disadvantage of cubic paths is the acceleration jump at boundaries that introduces infinite jerks. Example 348 Rest-to-rest cubic path. Assume q(0) = 10 deg, q(1) = 45 deg, and q\u0307(0) = q\u0307(1) = 0. The coefficients of the cubic path are a0 = 10 a1 = 0 a2 = 105 a3 = \u221270 (13.17) that generate a path for the variable as q(t) = 10 + 105t2 \u2212 70t3 deg . (13.18) 732 13. Path Planning The path information is shown in Figure 13.2. Example 349 To-rest cubic path. Assume the angle of a joint starts from \u03b8(0) = 10 deg, \u03b8\u0307(0) = 12 deg / s and ends at \u03b8(2) = 45 deg, \u03b8\u0307(0) = 0. The coefficients of a cubic path for this motion are: a0 = 10 a1 = 12 a2 = 81 2 a3 = \u221229 2 (13.19) The kinematics of this path are \u03b8(t) = 10 + 12t+ 40.5t2 \u2212 14.5t3 deg (13.20) \u03b8\u0307(t) = 81t\u2212 43.5t2 + 12 deg / s (13.21) \u03b8\u0308(t) = 81\u2212 87t deg / s2 (13.22) and are shown graphically in Figure 13.3. Example 350 Rest-to-rest path with a constant velocity in the middle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure10-6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure10-6-1.png",
        "caption": "Fig. 10-6 Salient-pole machine.",
        "texts": [
            " 10-4 and the Simulink file EX9_1.mdl is included in the accompanying website to this textbook. The simulation results are shown in Fig. 10-5. d-q ANALYSIS 149 F ig . 1 0- 4 Si m ul at io n of E xa m pl e 10 -1 . 150 SALIENT-POLE SYNChRONOUS MAChINES 151 10-3 SALIENT-POLE SYNCHRONOUS MACHINES Synchronous machines with interior permanent magnets result in unequal reluctance along the d- and the q-axis. In this section, we will go a step further and assume a salient-pole rotor structure as shown in Fig. 10-6a with a rotor field excitation and nonidentical damper 152 VECTOR CONTROL OF PERMANENT-MAGNET DRIVES windings along the d- and the q-axis. In such a machine, we have the inductances described in the next section. 10-3-1 Inductances In the stator dq windings, L L Lsd md s= + (10-18) and L L Lsq mq s= + , (10-19) where the magnetizing inductance of the d winding is not equal to that of the q winding (Lmd\u00a0\u2260\u00a0Lmq) due to the nonsalient nature of the rotor. however, both windings have the same leakage inductance L\u2113s, which is not affected by the rotor structure. As shown in Fig. 10-6b, we will replace the actual field winding of Nf turns in the rotor by an equivalent field winding with 3 2/ Ns turns (where Ns equals the number of turns in each phase of the stator windings), supplied by an equivalent field-winding current ifd. This procedure results in the equivalent field winding having the same magnetizing inductance Lmd as the stator d winding, hence the equivalent field winding inductance can be written as L L Lfd md fd= + , (10-20) where L\u2113fd is the leakage inductance of the equivalent field winding. Similarly in Fig. 10-6b, replacing the actual damper windings with equivalent damper windings, each with 3 2/ Ns turns, we can write the following equations for the inductances of the equivalent rotor damper windings (with a subscript \u201cr\u201d): L L Lrd md rd= + (10-21) and L L Lrq mq rq= + , (10-22) where L\u2113rd and L\u2113rq are the leakage inductance of the equivalent rotor damper windings. SALIENT-POLE SYNChRONOUS MAChINES 153 10-3-2 Flux Linkages In terms of these inductances, the flux linkages of the various windings can be expressed as follows: Stator dq Winding Flux Linkages \u03bbsd sd sd md rd md fdL i L i L i= + + (10-23) and \u03bbsq sq sq mq rqL i L i= + "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000655_1.4002333-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000655_1.4002333-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of shaft bearing sys setup, \u201eb\u2026 enlarged view of test bearing, and \u201ec",
        "texts": [
            "org/ on 03/09/2015 Terms paper is to develop a relatively more realistic dynamic model for a deep groove ball bearing, having single and multiple defects on its races. In the present study, experiments have been performed for the validation of a proposed dynamic model. Simulated and experimental results have been compared for single defect and two defects lying on the races of the bearings. Based on the work reported herein, a good correlation between theoretical and experimental results can be seen. The schematic diagram of the shaft bearing system under investigation is provided in Fig. 1 a . Moreover, the deep groove ball bearing designation: SKF BB1B420205 is the study bearing that is mounted at the end of the shaft toward the right hand side. Figure 1 b shows the enlarged view of the study bearing and housing for better visualization. The modeling of the study bearing system is carried out using springs and lumped masses. A free body diagram of a modeled shaft-bearing-housing system under investigation is illustrated in Fig. 1 c . The proposed model incorporates the following realistic assumptions and considerations. \u2022 Balls are positioned equipitched around the shaft and there under study with coordinate: \u201ea\u2026 experimental ee body diagram of modeled components tem is no interaction between them. Transactions of the ASME of Use: http://asme.org/terms J Downloaded Fr \u2022 There is no slipping of the balls during rolling on the surface of races. \u2022 The centrifugal forces acting on the balls are negligible. \u2022 The study bearing operates under isothermal conditions",
            " If 0 is the initial position of the ith ball, the angular position i at any time t is defined by the following relation: i = 2 i Nb + ct + 0 3 where the angular velocity of cage is expressed in term of angular velocity of shaft and is defined as follows: c = 1 \u2212 d D s 2 4 Based on the geometry of the bearing, the normal load on the ball/raceway at position refer Fig. 3 is calculated by the following equation 18 : Q = Qmax 1 \u2212 1 2 1 \u2212 cos 3/2 5 where = 1 /2 1\u2212 Pd /2 r . In Fig. 3, it is clear that the applied radial load W is equal to the sum of the vertical components of the contact reactions. Mathematically, it is expressed as follows: W = =0 = 1 Q cos 6 The deflection of the ith ball in the radial direction is provided by the following expression refer to Fig. 1 c : i = Xs \u2212 Xb cos i + Ys \u2212 Yb sin i \u2212 c 7 nclature: \u201ea\u2026 load distribution in a ball bearing me imulation OCTOBER 2010, Vol. 132 / 041101-3 of Use: http://asme.org/terms w X t B p r s s o e b v t u m t d d w c o p b i w i i u t t f w d 0 Downloaded Fr here radial clearance c = Pd /2 1\u2212cos . Assuming Xh and Yh as the deflections of the housing center in and Y directions, respectively, the total deflection of the ball in he radial direction is written as i = Xs \u2212 Xb cos i + Ys \u2212 Yb sin i + Xb \u2212 Xh cos i + Yb \u2212 Yh sin i \u2212 c 8 2",
            " Moreover, for the stationary outer race the position of defect does not change with respect to the shaft rotation. The deflection of the ith ball varies when it reaches the defective zone of the outer race. Mathematically, the angular position of the ith ball in the defect zone is defined by the following relation: out \u2212 width of defect dout i out + width of defect dout 15 2.4 Equations of Motion. Based on the assumptions made in Sec. 2, the equations of motion for each mass are derived as follows refer to Fig. 1 c : 2.4.1 For Shaft. Equations of motions for shaft in X and Y directions are as follows: MsX\u0308s + KsXs + CsX\u0307s + i=1 Nb Ki inner i inner 3/2 cos i = 0 16 MsY\u0308s + KsYs + CsY\u0307s + i=1 Nb Ki inner i inner 3/2 sin i = 0 17 2.4.2 For Ball. The equations of motions for the ith ball in X and Y directions are as follows: MbiX\u0308bi \u2212 Ki inner i inner 3/2 cos i + Ki outer i outer 3/2 cos i = 0 18 MbiY\u0308bi \u2212 Ki inner i inner 3/2 sin i + Ki outer i outer 3/2 sin i = 0 19 2.4.3 For Housing. The equations of the motion for housing in X and Y directions are written as follows: MhX\u0308h + KhXh + ChX\u0307h \u2212 i=1 Nb Ki outer i outer 3/2 cos i + F = 0 20 MhY\u0308h + KhYh + ChY\u0307h \u2212 i=1 Nb Ki outer i outer 3/2 sin i = 0 21 The expressions for i inner and i outer appearing in Eqs",
            "org/terms t E 1 t i t 4 b s a m d e b m p o a 1 4 k t i G 0 Downloaded Fr ions and X\u0307 and Y\u0307 velocities at time t+ t are calculated using qs. 16 \u2013 21 by the Runge\u2013Kutta method. The time step t of 0\u22127 s has been considered in the present computation. The sysem equations are iteratively solved for specified time period usng MATLAB programming. Flow chart for the numerical compuation is provided in Fig. 6. Results and Discussions A 3DOF model for the vibration studies of deep groove ball earings healthy and defective and shaft system refer to the chematic diagram in Fig. 1 a has been developed. Theoretical nd experimental studies are being presented here considering asses of the shaft, balls, and housing along with single and two efects in bearing races. Figures 1 b and 1 c demonstrate an nlarged view of the test bearing and free body diagram of the earing system modeled using springs, dampers, and lumped asses. The input data related to shaft and bearing systems are rovided in Table 1. In order to validate the proposed model, experiments are carried ut for four different cases, as listed in Table 2",
            " In case of two defects on surface of inner ace of the bearing, vibration pulse comprising of each defect is xpected. In order to access these, vibrations of balls 8 and 1 are nalyzed, as shown in Figs. 11 a and 11 b , respectively. As ilustrated in Fig. 11 a , at t=0 s point A8 , the first defect is in ontact with ball 8, and the angular difference between the second efect and ball 1 is 15 deg 0.26 rad . The time requires to aproach the second defect by ball 1 is 0.26 / s\u2212 c =2.7 10\u22123 s, which is clearly observed in Fig. 11 b point A1 . A requency spectrum for the theoretical results is shown in Fig. 1 c . The BPFI 123 Hz with amplitude modulation of shaft otation frequency is observed. The reciprocal of time difference n pulse occurrence for two defects in the inner race of ball bearng is f i, which is computed using the relation 5 f i = 0 Nb fs \u2212 fc 24 The time delay between two impulses of ball 8 is 0.5235 / s c =5.42 10\u22123 s f i=184.43 Hz . The experimental spectrum for two defects on inner race of test earing is shown in Fig. 12. The BPFI peak is found at 124 Hz, hich is close to calculated value of BPFI 123 Hz "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002367_j.jmbbm.2020.103775-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002367_j.jmbbm.2020.103775-Figure12-1.png",
        "caption": "Fig. 12. Lattice structures for cell biocompatibility test (a) CAD model, (b) as-fabricated sample.",
        "texts": [
            " A similar observation was observed in a study of SLM in-situ alloyed Ti\u2013Nb\u2013Sn (Chen et al., 2018). Nevertheless, such a claim for the mechanism of void formation remains a hypothesis, with the fractography providing only indirect evidence. Further investigation is thus required to study and confirm this void formation mechanism. For the biocompatibility tests, the overall dimensions of the Ti50Ta lattice structures used were 10 mm in diameter and 2 mm in height. The CAD model and the as-fabricated L-PBF sample are shown in Fig. 12. Cell viability was assessed using a dsDNA picogreen assay. The results are shown in Fig. 13. The dsDNA measurements show an increasing trend for all three materials (n \u00bc 5) as shown by the red dotted line in Fig. 13. After 7 days of in vitro culture, the SAOS-2 cells were found to be viable and proliferating on all the scaffolds. On day 1, 3 and 7, the relative cell number on the scaffolds of the three materials were similar. Using ANOVA, it was statistically determined that there was no significant difference between the results for all three materials at all 3 time points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003080_j.phpro.2014.08.099-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003080_j.phpro.2014.08.099-Figure8-1.png",
        "caption": "Fig. 8. Tube supports generated with 3Data Expert.",
        "texts": [
            " The support structures were crated to be easily removed without damaging the test part surface so the supports needed to be as low volume as possible. The web supports (see Fig. 7) are designed to support overhanging down-facing surfaces of bars of the test piece. The webs of the supports are used to reduce the contact area of the part surface and let the unexposed powder to be easily removed. Dimensions of web supports are 1.30 mm (sample 1) and 1.45 mm (sample 2). The design principle of tube supports (see Fig. 8) was to lower the support volume. As the tubes are hollow the contact surface is smaller which reduces the surface damage after the removal of the supports. The diameters of the tube supports are 1.30 mm and 2.00 mm and they were ranged as sample 3 and 4. There were several pieces of web support structures lost or nearly lost before the removal of the part by sawing. The rest of the supports were planned to be removed manually by some simple tools. The supports of side A and the inner supports (bars with 65, 60, 55, 50 degrees) of B, C and D side could not be removed with pliers because all of these supports were based on the main part\u2019s surfaces (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002770_acc.2014.6859328-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002770_acc.2014.6859328-Figure2-1.png",
        "caption": "Fig. 2: Coordinate frames and free body diagram of tilting quadcopter",
        "texts": [
            " At this nominal hover state, the produced force from each propellers must satisfy: Fi = 1 4 (mg) (6) and hence motor speeds are given by: \u03c9i = \u03c9h = \u221a mg 4kf (7) For a tilting rotor quadcopter, four other variables are added representing the angles of quad-rotor arms. Adjustment of these angles results into improved vehicle maneuverability and capability for hovering at a tilted angle. To illustrate the motion of the tilting rotors quadcopter, a schematic diagram showing the forces/moments acting and coordinate frames used in the modeling is provided in Fig 2. As it can be seen from this figure, the propellers are free to tilt along their axes. The planes shown with dashed lines are the original planes of rotation with zero tilt angles for the respective propellers. Similarly, planes shown with the rigid lines are the tilted planes of rotation for respective propellers. \u03b8i, (i = 1, 2, 3, 4)is the tilted angle of corresponding propellers. It may be noted that the forces generated by the propellers are perpendicular to these respective planes of rotations",
            ", F1 = F2 = F3 = F4), the angular speed is given by: \u03c9i = \u03c9h = \u221a\u221a\u221a\u221a mg 4kfc \u03b81 2 (16) Similar to above, considering hovering with \u03b8 and zero roll angle, the Equation (12) gives: cos( \u03b82 2 ) \u2211 Fi = mg (17) Now similar to above, the angular speeds of the rotors are given by: \u03c9i = \u03c9h = \u221a\u221a\u221a\u221a mg 4kfc \u03b82 2 (18) In this section, the control strategy of the tilting rotor quadcopter is presented. The aim of the control strategy is not only control of the position of the vehicle to follow an arbitrary trajectory in 3 dimensions, but also to have control over the orientation of the vehicle in hovering as well as during trajectory tracking. The controller inputs are four independent speeds of propellers and their rotations about the axes of quadcopter arms. Referring to Fig. 2 and the two Theorems, it is assumed that \u03b81 = \u2212\u03b83 and \u03b82 = \u2212\u03b84. It may be noted that these constraints, in fact, make the over-actuated system into fully actuated system (two inputs to tilt the rotors another four inputs for their rotational speeds make total number of independent control inputs to be six). For 6 DoF quadcopter, this results into complete control over its position and orientation. The dynamic model of the tilting rotor quadcopter, described in (8) and (9), is used to design the PD controllers for orientation adjustment and trajectory tracking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure1.15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure1.15-1.png",
        "caption": "FIGURE 1.15. A planar 3R manipulator and position vector of the tip point P in global coordinate G(X, Y).",
        "texts": [
            " As such, a vector consists of a magnitude, a direction, and an origin of a reference point. We must explicitly denote these elements of the vector. If either the magnitude of a vector r and/or the direction of r in a reference frame B depends on a scalar variable, say \u03b8, then r is called a vector function of \u03b8 in B. A vector r may be a function of a variable in one reference frame, but be independent of this variable in another reference frame. Example 2 Reference frame and parameter dependency. In Figure 1.15, P represents a point that is free to move on and in a circle, made by three revolute jointed links. \u03b8, \u03d5, and \u03c8 are the angles shown, then r is a vector function of \u03b8, \u03d5, and \u03c8 in the reference frame G(X,Y ). The length and direction of r depend on \u03b8, \u03d5, and \u03c8. If G(X,Y ), and B(x, y) designate reference frames attached to the ground and link (2), and P is the tip point of link (3) as shown in Figure 1.16, then the position vector r of point P in reference frame B is a function of \u03d5 and \u03c8, but is independent of \u03b8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure8.41-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure8.41-1.png",
        "caption": "Fig. 8.41 Sequence of events following high-pitch tail rotor failure in cruise",
        "texts": [
            " Accompanying the yaw will be roll and pitch motions, driven by the increasing sideslip. In the flight trials, several different techniques were explored to recover the aircraft to a stable and controllable flight condition. For failures in high-speed cruise, attempts to decelerate through the power bucket to a safe-landing speed were unsuccessful; the right sideslip (left yaw) built up to limiting values, and controlling heading with cyclic demanded a very high workload. A successful strategy was developed as illustrated in Figure 8.41. A high-power climbing turn to the left gave a sufficiently stable flight condition so that deceleration could be accomplished without the aircraft diverging in yaw. The aircraft could then be levelled out at about 40 knots and a slow decelerating descent initiated. Gentle turns to both right and left (left preferred) were possible in this condition. The landing was accomplished by lining the aircraft up with the nose well to port and applying collective, and levelling the aircraft, just before touchdown to arrest the rate of descent and 516 Helicopter and Tiltrotor Flight Dynamics align the aircraft with the flight path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000717_j.conengprac.2010.06.007-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000717_j.conengprac.2010.06.007-Figure1-1.png",
        "caption": "Fig. 1. DP system block diagram.",
        "texts": [
            " Several offshore operations use DPSs, such as drilling, underwater pipelaying, offloading, and diving support (Fossen, 1994). A DPS is a complex system composed of several sensors, control and filtering algorithms, and propellers. The sensors are used to measure the position of the floating vessel, while the algorithms are responsible for calculating the forces to be delivered by each propeller to counteract environmental forces, such as wind, waves, and current loads. A simplified block diagram of a DPS is presented in Fig. 1, in which the connections between the wave filter, wind filter, controller, thruster allocation algorithm, propeller, and vessel are shown. It is a normal feedback control system with wind feed-forward action with two additional blocks: the first is a wave filter that suppresses the high-frequency motion from the measurements, and the second is a thrust allocation algorithm that is necessary to distribute the forces among the propellers as a DPS vessel is generally overactuated. The number of vessels with DPSs has increased in recent years due to increased oil and gas exploration at sea"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002261_tcst.2017.2709274-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002261_tcst.2017.2709274-Figure1-1.png",
        "caption": "Fig. 1. Roll rig experimental setup.",
        "texts": [
            " The variation of the airspeed will have a significant impact on the closed-loop stability and performance, meaning that a PID controller designed for a given airspeed Va may become unstable if the airspeed changes. Therefore, the airspeed Va is selected as the operating condition identifier. In the design and implementation of the gain scheduled control system, the parameter used to identify the operating conditions of the system is required to be measured in real time. In this application, an aircraft equipped with airspeed sensors is used, as shown in Fig. 1. Although only one of the sensors is used, another sensor is installed for increased redundancy. The differential pressure sensors and pitot static tubes are used to measure the airspeed in advance, because they are positioned ahead of the aircraft. The advanced measurement of the airspeed is advantageous in providing phase-advanced information relating to the changes in operating conditions, leading to smoother transitions from one operating condition to another. For the roll axis control, the primary control surface used to influence the angular rate, p, is the aileron deflection, \u03b4a , which is the control variable in this case",
            " This antiwindup mechanism has been validated on PID control of electrical drives and power converters [30]. To evaluate the proposed algorithm, experimental results are presented in this section. First, the experimental setup is described, followed by a feedback relay experiment on the inner and outer loop systems at different operating conditions to obtain the appropriate controller gains. The fixed-wing aircraft chosen for this paper is the Slick 360 airframe, and its operational speed is between 7 and 15 m/s (see Fig. 1) [36]. The aircraft\u2019s physical specifications are described in Table I [37]. In order to individually isolate the roll axis, the aircraft is fixed along its thrust line on the roll test rig. The roll axis is allowed to rotate freely with minimal friction, while the pitch and yaw axes are fixed and cannot be rotated. This ensures that the roll axis will not be affected by the changes in other axes. The aircraft was installed on the rig at 0\u00b0 angle-of-attack. For this experimental study, a custom developed flight controller is used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000603_j.mechmachtheory.2010.11.016-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000603_j.mechmachtheory.2010.11.016-Figure3-1.png",
        "caption": "Fig. 3. Six degrees of freedom nonlinear models of the geared bearing system. Bearings are modeled by equivalent elements with viscous damping coefficients cjk (j=p,g,k=x,y)and linear springs kjk(j=p,g,k=x,y).",
        "texts": [
            " (2), one can obtain the backlash due to dynamic changing of axle center distance as, 2\u0394b = 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a cos an + x2\u2212x1\u00f0 \u00de2 + y2\u2212a sin an\u2212y1\u00f0 \u00de2 q \u2212a tan an \u00f04\u00de and th The new dynamic half backlash b\u2032 with the effect of the center distance error can be defined as, b\u2032 = b + \u0394b \u00f05\u00de e backlash function in the nonlinear dynamic system can be rewritten as, f x\u00f0 \u00de = x\u2212b\u2032 x N b\u2032 0 xj j\u2264 b\u2032 x + b\u2032 x b b\u2032 8< : \u00f06\u00de Here it considers the effect of the dynamical motion on the changing of backlash, which is the motive of the paper. The nonlinear model of the geared bearing systemwith gear inertias Ip and Ig, gear massesmp andmg, and base circle radius Rp and Rg as shown in Fig. 3, is considered here. The gear mesh is described by a nonlinear stiffness km and viscous damping cm. Note that the nonlinear meshing stiffness km is deduced from a curve fitted tooth stiffness equation in Ref. [31] and developed using the method proposed in Ref. [30] to adapt the friction force in gear transmission system. Then themeshing stiffness can be represented as, km = k0 1 + k t\u00f0 \u00de\u00bd \u00f07\u00de 0 is the averaged tooth stiffness, k(t) is the variant part of the stiffness, in general it can be expanded in Fourier series",
            " [30]. The friction arms spi\u3001sgi of tooth on any point of the actual line of contact relative to the drive pinion and driven gears can be expressed as spi t\u00f0 \u00de = Rg + Rp tan an\u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 ap\u2212R2 g q + Rp\u03c9ht sgi t\u00f0 \u00de = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 ap\u2212R2 g q \u2212Rp\u03c9ht \u00f011\u00de Here, Rap is the addendum circle radius of pinion. Then equations of the coupled transverse torsional motion of the nonlinear geared bearing system, as shown in Fig. 3, are Ip \u0308\u03b8p + Rp\u2211 \u03b5\u00bd i=1 Fpi + Tp\u2212\u2211 \u03b5\u00bd i=1 \u03bbi\u03bciFpispi = 0 Ig \u03b8\u0308g\u2212Rg\u2211 \u03b5\u00bd i=1 Fpi\u2212Tg + \u2211 \u03b5\u00bd i=1 \u03bbi\u03bciFpisgi = 0 mp \u0308xp + cpx x\u0307p + kpxxp + \u2211 \u03b5\u00bd i=1 \u03bbi\u03bciFpi = 0 mp \u0308yp + cpy y\u0307p + kpyyp\u2212\u2211 \u03b5\u00bd i=1 Fpi = 0 mg \u0308xg + cgx x\u0307g + kgxxg\u2212\u2211 \u03b5\u00bd i=1 \u03bbi\u03bciFpi = 0 mg y\u0308g + cgy y\u0307g + kgyyg + \u2211 \u03b5\u00bd i=1 Fpi = 0 8>>>>>>>>>>>>>>< >>>>>>>>>>>>>>: \u00f012\u00de Here the dot on each variable means derivative with respect to time t. To proceed with our analysis, two assumptions could be made: (i) the viscous damping acting on the mating gear teeth is constant, i.e. cm1=cm2=cm. (ii) the two gears with the same base radius are selected, and the support stiffness and damping are the same in the X- and Y-direction as shown in Fig. 3, namely, kix=kiy=kp, i=p,g. The first two functions of Eq. (12) can be simplified further by defining a new variable x = Rp\u03b8p\u2212Rg\u03b8g\u2212e t\u00f0 \u00de \u00f013\u00de dimensionless form of Eq. (12) is obtained by letting Tg/m2Rg+Tp/m1Rp=F\uff0cIp/Rp2=m1\uff0cIg/Rg2=m2\uff0cm2m1/(m1+m2)=me, and a x=x1bn\uff0cxp=x2bn\uff0cyp=x3bn\uff0cxg=x4bn\uff0cyg=x5bn\uff0c\u03c4=\u03d6t\uff0ccm1= cm2= cm\uff0c\u03c9h /\u03d6=\u03c9\uff0ccm/2\u03d6me=\u03c21\uff0c\u03d62=k0 /me\uff0c F /\u03d6 2 = F 1\uff0c\u03c9 2e 0 /\u03d6 2b n = F 2\uff0cme =mp = m\u03031\uff0ckpx = k0 = k\u03031 cpx = cm = c\u03031\uff0ckpy = k0 = k\u03032\uff0c cpy = cm = c\u03032\uff0cme =mg = m\u03032\uff0c kgx = k0 = k\u03033\uff0ccgx = cm = c\u03033\uff0c kgy = k0 = k\u03034\uff0ccgy = cm = c\u03034\uff0c\u03c9h/\u03d6=\u03c9\uff0ccm/2\u03d6me=\u03c21"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000450_physrevlett.100.088103-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000450_physrevlett.100.088103-Figure1-1.png",
        "caption": "FIG. 1. A sketch of the arrangement of a bottom-heavy squirmer. Gravity acts in the g direction, while the squirmer has orientation vector e. G is the center of gravity. Gray arrows schematically show the squirming velocity on the surface.",
        "texts": [
            " Our former studies [1,12] revealed, however, that near-field fluid dynamics play an important role in the orientational change of microorganisms. Thus, in this Letter, we solve both far- and near-field fluid dynamics precisely and perform Stokesian-dynamics simulation of swimming particles for the first time. A swimming microorganism is modeled as a squirming sphere with prescribed tangential surface velocity, which will be referred to as a squirmer [12,13]. The squirmer is assumed to be neutrally buoyant, but the center of gravity of the spherical cell may not coincide with its geometric center (bottom-heaviness), as shown in Fig. 1. We assume that the flow field around the microorganisms is Stokes flow, and Brownian motion is not taken into account. The surface of the spherical squirmer is assumed to move purely tangentially and these tangential motions are assumed to be axisymmetric, time independent, and invariant during the interactions. The surface velocity of a squirmer us was analyzed by Blake [14] and is given by u s X2 n 1 2 n n 1 Bn e r r r r e P0n e r=r ; (1) where e is the orientation vector of the squirmer, Bn is the nth mode of the surface squirming velocity, Pn is the nth Legendre polynomial, r is the position vector, and r jrj"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure13-1.png",
        "caption": "Fig. 13. Strain gauge positions.",
        "texts": [
            " 9, a removable support is used to give AE to the shaft of Gear 1 by changing the position of this support. Fig. 10 is tooth-contact pattern measured. Fig. 11 is the tooth-contact pattern calculated under the same conditions. In Fig. 11, A is the areas of double pair toothcontact and B is the area of single pair tooth-contact. It is found that calculated contact pattern is agreement with the measured one well. Root strains are also measured. Fig. 12 is comparisons between the measured root strains and the calculated ones at measurement positions of stain gauges 1\u20134 as shown in Fig. 13. It is also found that calculated root strains are agreement with the measured ones. Tooth-contact lengths and contact stresses of a pair of spur gears with lead crowning were also calculated by the special FEM software and compared with measurement results in Ref. [17]. It was also found that the calculated results were agreement with the measured ones well. Gears used as research objects are given in Table 1. In Table 1, the wheel is cut by a hob under accuracy requirement of JIS 5th grade. Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001447_j.isatra.2013.09.023-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001447_j.isatra.2013.09.023-Figure4-1.png",
        "caption": "Fig. 4. Furuta pendulum system prototype.",
        "texts": [
            " Notice that the coefficients of the controller should be chosen in accordance with the fact that, asymptotically, the tracking error is being approximately governed by the differential equation: e\u00f04\u00de1 \u00fek3e \u00f03\u00de 1 \u00fek2 \u20ace1\u00fek1 _e1\u00fek0e1 \u00bc \u03be\u00f0t\u00de z\u03021 \u00f024\u00de the set of design coefficients, fk3;\u2026; k1; k0g should render Hurwitz the underlying characteristic polynomial: p\u00f0s\u00de \u00bc s\u00f04\u00de \u00fek3s\u00f03\u00de \u00fek2s2\u00fek1s\u00fek0 We propose k3 \u00bc 4\u03b6c\u03c9c , k2 \u00bc 2\u03c92 c \u00fe4\u03b62c\u03c9 2 c , k1 \u00bc 4\u03b6c\u03c93 c , k0 \u00bc\u03c94 c . Please cite this article as: Ram\u00edrez-Neria M, et al. Linear active disturbance rejection control of underactuated systems: The case of the Furuta pendulum. ISA Transactions (2013), http://dx.doi.org/10.1016/j.isatra.2013.09.023i Fig. 3 shows a diagram of the experimental platform used for the Furuta Pendulum. The experimental device (Fig. 4) consists of a Brushed servomotor from Moog, model C34L80W40, which drives the horizontal arm through a synchronous belt with a 4.5:1 ratio. The angles of the pendulum and arm (motor) can be measured with Incremental optical encoders of 2500 CPR. A Copley Controls digital amplifier model Junus 90, working in current mode, is in charge of driving the motor. The Data acquisition is carried out through a data card from Quanser consulting, model QPIDe terminal board. This card reads signals from the optical incremental encoders and supplies control voltages to the power amplifiers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure10-1.png",
        "caption": "Fig. 10. Free-body diagrams of a metal V-belt CVT system: (a) band pack forces; (b) belt element forces; (c) forces on the pulley sheave; (d) torques on the driver pulley [61].",
        "texts": [
            " It is evident from their work that not only the configuration and loading conditions, but also the inertial forces, influence the dynamic performance of a CVT, especially the slip behavior and torque capacity. The authors also reported that the inactive arc region of a band pack is different from that of a belt element. This consequently led to the formation of shock sections at the element\u2013band interface separating the inactive region of pulley wrap from the active region. However, the results reported were valid for one cycle i.e. till the belt moved past the exit of either of the two pulleys. Fig. 10 [61] depicts the free-body diagrams of the metal V-belt CVT drive reported by the authors to capture the various transient dynamic performance indices of the CVT system. Srivastava et al. [59,62] also highlighted the significance of a feasible set of initial operating conditions required to initiate torque transmission in a CVT system. The authors proposed that a CVT, being a highly nonlinear system, needs a specific set of operating conditions, which can be found using an efficient search mechanism, in order to successfully meet the load requirements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001398_jestpe.2018.2811538-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001398_jestpe.2018.2811538-Figure6-1.png",
        "caption": "Fig. 6. Flux density distribution at no-load for a) healthy and b) faulty conditions with 3.75% fault intensity.",
        "texts": [
            " At high rotational speeds \ud835\udc5f\ud835\udc4e\ud835\udc53 \u226a \ud835\udf14\ud835\udc3f\ud835\udc4e\ud835\udc53 , influence of the resistance can be ignored and the contribution of the induced back-emf saturates (first term). In this situation, short circuit current is only and indirectly affected by the rotational speed due to the changes in the faulty phase current iah. Magnetic field distribution is expected to be affected in case of ITSC fault. According to the faraday law, the flux generated by short circuit current varies in a direction against the rotor and stator flux depending on the operating point. This causes a reduction in the flux inside the stator core. Fig. 6 shows the reduction of flux density inside the stator core due to ITSC fault, in which 3.75% of the coils of a phase is short-circuited. In order to clarify the effect of ITSC fault on the flux density distribution, the flux densities at two points, inside the stator core and around the shorted turns, are shown in Fig. 7. Amplitude of flux density at point B is affected more than that of point A, since point B is located on the main flux path. To explore the influence of the operating point and fault intensity on the machine variables, the following fault cases are analyzed by applying a balanced 3-phase voltage to phase terminals"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure10.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure10.10-1.png",
        "caption": "Fig. 10.10 Historical HVDC test system 250 kV for oil-paper-insulated cable systems made by Koch and Sterzel 1936",
        "texts": [
            "6 Withstand voltage of XLPE cable models and test frequency (1) without artificial defects and (2) with artificial defects 10.2 Test Voltages Applied on Site 425 where the frequency-tuned circuits have a much better weight-to-test power ratio than the inductance-tuned systems (Table 3.2; Fig. 10.9). The design of the transformers and reactors depends strongly on the test objects and will be discussed in Sect. 10.3. DC voltage (see Chap. 6) can be applied for on-site testing of HVDC components. For historic reasons and based on long experience (Fig. 10.10), it is also still applied for field tests on oil-paper-insulated AC cable systems and for the insulation of some rotating machines as well. A DC generator can charge such a capacitive test object even with a very low current if sufficient time is available. The DC testing of other AC equipment cannot be recommended. IEC 60060-3: 2006 requires the following parameters of DC voltages for on-site tests: For the generation of DC voltages, usually modular HVDC test systems are applied. They can be air-insulated or\u2014for higher current\u2014oil-insulated, see Figs",
            "3 delivers an overview on the available voltages for on-site testing, before some examples are explained more in detail. The insulation resistance of an oil-paperinsulation is much lower than that of an extruded insulation. Therefore, the voltage distribution inside such a cable for AC and DC has similarities, even in the vicinity of defects. Furthermore, LIP insulation is quite resistant against partial discharges. Additionally, decades ago, only mobile DC voltage test systems were available (see Fig. 10.10). Therefore, if AC cable systems had to be tested, DC test voltages were applied. The high DC 10.4 Examples for On-Site Tests 443 T ab le 10 .3 C ha ra ct er is ti cs or di ff er en t te st vo lt ag es fo r on -s it e te st in g of ca bl e sy st em s T es t vo lt ag e IE C 60 06 0- 3; IE E E 40 0 D C A C 50 /6 0 H z A C R F 20 \u2026 30 0 H z V L F 0. 01 \u2026 1 H z D A C D C ra m p; 20 \u2026 50 0 H z; da m pi ng \\ 40 % C ha ra ct er is ti c R ep re se nt at io n of st re ss es in se rv ic e Id en ti ca l fo r D C ca bl es , ve ry di ff er en t fo r A C ca bl es Id en ti ca l fo r A C ca bl es C lo se to A C vo lt ag e M uc h di ff er en t fr om th e A C 50 /6 0 H z st re ss Im pu ls e vo lt ag e, m uc h di ff er en t fr om A C 50 / 60 H z st re ss D es cr ip ti on of vo lt ag e U ni po la r an d co nt in uo us vo lt ag e (r ef er en ce fo r al l D C ca bl es ) A lt er na ti ng vo lt ag e (r ef er en ce fo r al l A C ca bl es ) A lt er na ti ng ; in th e ra ng e of th e re fe re nc e fr eq ue nc y V er y sl ow ly al te rn at in g; fa r fr om re fe re nc e fr eq ue nc y D ir ec t vo lt ag e ra m p fo ll ow ed by da m pe d os ci ll at io n D is ch ar ge an d br ea kd ow n pr oc es s S lo w an d de te rm in ed by sp ac e ch ar ge s T yp ic al fo r A C of po w er fr eq ue nc y V er y si m il ar to A C of po w er fr eq ue nc y D if fe re nt , hi gh er te st vo lt ag e va lu es ne ce ss ar y D if fe re nt , ch ar ge ac cu m ul at io n du ri ng ra m p, th en po la ri ty re ve rs al R ep ro du ci bi li ty at di ff er en t ca bl e sy st em s P er fe ct P er fe ct A cc ep ta bl e, fr eq ue nc y m ai nl y w it hi n 30 \u2026 10 0 H z G oo d P oo r, ch an ge in \u2022 ra m p du ra ti on , \u2022 fr eq ue nc y, \u2022 da m pi ng G en er at io n in th e fi el d E as y F or H V /E H V : im po ss ib le , M V : fe w se co nd s G oo d fo r M V ca bl es , ac ce pt ab le fo r H V / E H V ca bl es G oo d fo r M V ca bl es , qu es ti on ab le fo r H V ca bl es G oo d fo r M V ca bl es R ec om m en de d fo r ac ce pt an ce te st in g A ll D C ca bl es ; (A C ca bl es w it h L IP in su la ti on tr ad it io na ll y) O nl y fo r A C m ed iu m - vo lt ag e ca bl es A ll A C ca bl es fr om M V to E H V P ar tl y ap pl ie d fo r M V ca bl es , no t fo r H V ca bl es P ar tl y ap pl ie d fo r M V ca bl es , no t fo r H V ca bl es R ec om m en de d fo r di ag no st ic te st in g A ll D C ca bl es M V A C ca bl es A ll A C ca bl es fr om M V to E H V M V ca bl es M V A C ca bl es 444 10 High-Voltage (HV) Testing on Site withstand voltage test levels up to 4U0 are related to the limited sensitivity of defects at DC voltage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002854_j.engfailanal.2013.07.005-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002854_j.engfailanal.2013.07.005-Figure1-1.png",
        "caption": "Fig. 1. Contact positions on a spur gear tooth profile with crack.",
        "texts": [
            " A tooth pair comprised of a pinion tooth and a gear tooth in contact and the total effective mesh stiffness consists of pinion and gear tooth mesh stiffness. In the single tooth pair contact, the load is transmitted through the tooth pair results in an equal loading for both the pinion and gear tooth. Consequently, the instantaneous tooth pair mesh stiffness is a series combination and can be given by [18,27,28,33,34] as, kt\u00f0stpc\u00de \u00bc 1 1 kcp \u00fe 1 kg \u00f01\u00de where kcp is the tooth stiffness of the cracked pinion and kg is the stiffness of gear tooth with no crack. Considering a spur gear tooth with face width \u2018B\u2019 and crack of length \u2018a\u2019 as shown in Fig. 1, let the \u2018F1 = F2 = F3 = F\u2019 represents the applied load at three distinct points and \u2018W\u2019 represents the applied load per unit length of face width as W = F/B. The displacement in the direction of load \u2018F\u2019 is \u2018d\u2019. The introduction of crack of length \u2018a\u2019 will cause a change in the elastic strain energy \u2018dU\u2019 [18]. The change in elastic strain energy \u2018dU\u2019 in the cracked tooth is defined by [18] as, dU \u00bc Z a 0 @U @a da \u00f02\u00de And the strain energy release rate \u2018G\u2019 for a linear elastic structure under fixed loading is defined by [18] as, G \u00bc 1 B @U @a \u00f03\u00de @U \u00bc B Z a 0 Gda \u00f04\u00de The strain energy release rate \u2018G\u2019 can be written as a function of mode-I and mode-II stress intensity factors KI and KII for plane stress by [18] as follows: G \u00bc 1 E K2 I \u00fe K2 II \u00f05\u00de where \u2018E\u2019 represents young\u2019s modulus of elasticity",
            " Fillet foundation deformation is not considered here for simplicity.The potential energy stored in the gear tooth is given by [32\u201334], Ub \u00bc M2 2EI \u00bc \u00bdFa\u00f0h\u00de FbC 2 2EI \u00f018\u00de Us \u00bc 1:2F2 a 2GA \u00bc \u00bd1:2F cos / 2 2GA \u00f019\u00de Ua \u00bc F2 b 2EA \u00bc \u00bdF sin / 2 2EA \u00f020\u00de where \u2018h\u2019 and \u2018C\u2019 can be measured using the gear tooth profile. The value of these parameters vary (namely h1, h2, h3 and C1, C2, C3) with change in contact position from highest point of single tooth contact \u20181\u2019 (HPSTC) and pitch point \u20182\u2019 to lowest point of single tooth contact \u20183\u2019 (LPSTC) as indicated in Fig. 1. The symbol \u2018/\u2019 represents the pressure angle. Referring to Fig. 2, S and B represents tooth thickness and face width. \u2018Fa\u2018 provide bending and shear effect while \u2018Fb\u2019 provides compressive effect and can be expressed for the pressure angle \u2018/\u2018 (20 in the present study) as, Fa \u00bc F cos a \u00f021\u00de Fb \u00bc F sina \u00f022\u00de I and A represents the area moment of inertia and area of cross section at tooth root and \u2018G\u2019 represents shear modulus. They can be obtained by [32\u201334] as, I \u00bc 1 12 S3 B \u00f023\u00de A \u00bc S B \u00f024\u00de G \u00bc E 2\u00f01\u00fe v\u00de \u00f025\u00de Hence, the stiffness of uncracked gear tooth kg is given by [32\u201334] as, kg \u00bc 1 1 kh \u00fe 1 kb \u00fe 1 ks \u00fe 1 ka \u00f026\u00de The total effective mesh stiffness (kt) of a single tooth pair in contact comprises of a cracked pinion tooth and an uncracked gear tooth can be given by previous Eq",
            "4, comes under the category of narrow gears and permits the calculation of shape factor (Y) for obtaining SIF using Eq. (30) given in [15]. The deflection (d) of the cracked tooth along the line of contact has been calculated using mode-I SIF (KI) using the equation given in Section 2.1. The stiffness of uncracked gear tooth is calculated using expressions given in Section 2.2. The aim of the experiment is, to calculate the applied or nominal stresses, to obtain SIF by counting the fringe order (N) at three single tooth pair contact positions, as shown in Fig. 1 at starting, pitch point and end of single tooth contact on line of contact as shown in Fig. 8b1\u2013b3), which is otherwise calculated using Eq. (28). Three different crack length of 1 mm, 2 mm and 4 mm has been introduced at the tooth fillet region for the study of fringe order in the test specimen as shown in Fig. 4c\u2013 e. For this a typical plane polarizer setup is used as shown in Fig. 5a\u2013c and it is evident that, the fringe pattern starts to appear from three distinct locations, one is at the point of load application or the contact point and the other two are at the points of largest stress that is at tooth fillets as long as there is no other geometrical discontinuity, profile complexity and stress raisers in the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003492_j.msea.2020.140660-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003492_j.msea.2020.140660-Figure2-1.png",
        "caption": "Fig. 2. Schematic of the HCF specimens showing their BDs and loading directions during the fatigue test: (a) dimensions in mm; (b) horizontal samples; (c) vertical samples.",
        "texts": [
            " Samples from the second set were manufactured as cylinders, and the final specimens were machined out of the bulk metal by removing 2.5 mm of material; these are referred to as \u201cheavily machined\u201d in the results and discussion. Three samples were considered to be tested for each building condition; however, if the result of the first two runs were a complete match, the third run was omitted. High-cycle fatigue (HCF) tests were performed at room temperature under constant load amplitudes using a force-controlled 100 kN test rig. The specimens were manufactured per ASTM E466 [29], as shown in Fig. 2. In this study, fatigue lives in excess of 1.1 \u00d7 106 cycles were considered to be run-outs. However, to ensure the consistency of the results, some samples were tested up to 3.0 \u00d7 106 cycles. The loading ratio (R) and frequency (f) were 0.1 and 5 Hz, respectively. Force measurements were conducted with a 50 kN load cell mounted on the test rig. A total number of 51 specimens were used to plot the S\u2013N curves as the results. The number of samples used specifically for each build condition can be seen from the curves presented in section 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000214_robot.1993.291970-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000214_robot.1993.291970-Figure5-1.png",
        "caption": "Figure 5: Rotational constraints on a U-joint.",
        "texts": [
            " The solution is obtained by solving the inverse kinematic problem for each joint-liilk train, treated as a 2R-P-3R serial robot with two additional homogeneous transformations. For most industrial robots, analytical solutions for the nominal inverse kinematic problem exist but are not necessarily unique. For the joint-link train of this Stewart platform the analytical solution for the nominal model exists and is unique. The uniqueness of the solution is due to the physical constraints introduced by the ball and the Ujoints. For example, the U-joint angle 9, (Figure 5) , between X, and X,, is limited to the range of 0\" <9,<180\" . Similar constraint are inherent to e,, 9, and 8,. However, there is no angle limitation for 8, (rotational angle of the ball-joint about the asis Zo). Although a unique analytical solution for the nominal kinematic problem exists, it may be impossible to obtain an analytical solution for the general inverse kinematic problem and therefore numerical solution is inevitable. The model-based Newton-Raphson method [ 111 is employed to solve this problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure5.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure5.1-1.png",
        "caption": "Fig. 5.1",
        "texts": [
            " This type of loading is associated with a torque acting on the cross section of the member. In general, combinations of all these different types of loading will occur. For example, an eccentric load in the longitudinal direction causes a normal force and a bending moment (cf. Section 4.8). Let us consider a second example in order to demonstrate the possible coupling between the different types of stressing. For this purpose, we consider a cantilever with a rectangular cross sec- tion. At point P of the free end it is subjected to a load F that acts in an arbitrary direction (Fig. 5.1a). First, we decompose the load into its Cartesian components Fx, Fy and Fz (Fig. 5.1b). Then we move the action lines of the components without changing their directions until they pass through the centroid of the cross section at the free end. To avoid changing the effect of the force components on the cantilever, the respective moments of the forces have to be taken into account in addition to the force components (cf. Volume 1, Section 3.1.2). Therefore, the single eccentric force F is equivalent to the three force components acting at the centroid of the cross section and the three moments, see Fig. 5.1c. Here the individual forces and moments have been separated according to their different mechanical meanings: 1) The transverse load Fz and the external moment My = h 2Fx lead to symmetric bending (cf. Section 4.3). 2) If, in addition, the transverse load Fy and the external moment Mz = \u2212 b 2Fx are acting, we have unsymmetric bending (cf. Section 4.7). 3) The longitudinal load Fx causes tension in the bar (cf. Chapter 1). The external moment Mx = b 2Fz \u2212 h 2Fy causes torsion of the member. This example shows how a single force simultaneously can lead to the three typical loadings of a bar: tension, bending and torsion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000337_1.1555660-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000337_1.1555660-Figure10-1.png",
        "caption": "Fig. 10 Three-dof nonlinear model of the geared rotor system ~from Kahraman and Singh @10#!",
        "texts": [
            "org/terms Downloaded From of undamped motion equations of a multi-degree-of-freedom system with three coupled nonlinear oscillators. They presented general formulations for the determination of both the existence and the stability of solutions for primary resonance and a harmonic excitation. Furthermore, these general formulations can also be used to discuss a number of modal spacing and modal coupling issues. Later, Kahraman and Singh @10# further extended the above researches and developed a 3-dof dynamic model of a geared rotor-bearing system, and examined its nonlinear frequency response characteristics, as shown in Fig. 10. This model includes the nonlinearity associated with radial clearance in the radial rolling element bearing and backlash in a spur pair. It assumed linear time-invariant gear meshing stiffness and used both an analytical solution and a numerical technique to investigate the non-linear frequency characteristics. Several key issues, such as non-linear modal interactions, differences between internal static transmission error excitation and external torque excitation, were discussed. And the investigation of system parameters, such as the ratio between bearing stiffness and gear mesh stiffness, alternating and mean forces, and radial bearing preload and mean force, on the non-linear vibration behavior was performed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002986_tie.2015.2450714-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002986_tie.2015.2450714-Figure1-1.png",
        "caption": "Fig. 1. The configuration of the X-33 near space vehicle [26].",
        "texts": [
            " The attitude kinematics of a NSV is described by \u03b3\u0307 = R(\u03b3)\u03c9 (3) The rotational matrix R(\u03b3) \u2208 {R1(\u03b3),R2(\u03b3)} is given by R1(\u03b3) =    1 tan \u03b8 sin\u03d5b tan \u03b8 cos\u03d5b 0 cos\u03d5b sin\u03d5b 0 sin\u03d5b/ cos \u03b8 cos\u03d5b/ cos \u03b8    , \u03b3 =    \u03d5b \u03b8 \u03c8    R2(\u03b3) =    cos\u03b1 0 sin\u03b1 sin\u03b1 0 \u2212 cos\u03b1 0 1 0    , \u03b3 =    \u03d5 \u03b2 \u03b1    where R1(\u03b3) is used in the ascent phase and R2(\u03b3) is used in the reentry phase (In this paper, we choose R2 as R ). \u03b3 represents the attitude angle of NSV. \u03d5b, \u03b8, \u03c8 are the roll angle, the pitch angle and the yaw angle, respectively; \u03d5, \u03b1, \u03b2 are the bank angle, the angle of attack, and the sideslip angle, respectively. It is well known that the command torque T is related to the deflection command vector \u03b4, namely, T = B(t)\u03b4 where B(t) \u2208 R3\u00d7m, m is the number of the control-surface deflection variables. In this paper, we choose the X-33 NSV as the operation plant. Fig. 1 shows the configuration of the X-33 NSV. X-33 has four sets of control surfaces: rudders, body flaps, inboard and outboard elevons, with left and right sides for each set. Each control surface can independently be actuated with one actuator for each surface. The controlsurface deflection variables, collectively known as the effector vector, are given by \u03b4 = [\u03b41, \u00b7 \u00b7 \u00b7 , \u03b48], where \u03b41 and \u03b42 are the right and left inboard elevons, \u03b43 and \u03b44 are the right and left body flaps, \u03b45 and \u03b46 are the right and left rudders, \u03b47 and \u03b48 are the right and left outboard elevons",
            " Then the time derivative of Lyapunov function V5 is described as V\u03075 =\u2212K1 \u2225 \u2225E\u03041 \u2225 \u2225 2 \u2212K2 \u2016E2\u2016 2 \u2212 E\u0304T 1 G1(x1)x\u03032 \u2212 ET 2 8 \u2211 i=1 g2i(x)\u03c6 T i \u031fi (43) From Corollary 1, Theorem 2, and the Barbalat lemma [31], together with the equality in (43), it follows that limt\u2192\u221e V5(t) = 0, which in turn implies that limt\u2192\u221e E\u03041 = 0 and limt\u2192\u221eE2 = 0. Thus we can obtain the conclusion as limt\u2192\u221e(x2 \u2212 xc2) = 0. In this section, we present and discuss simulation results for a case study regarding the reentry vehicle model considered in [3,11]. All aerodynamic parameters of the X-33 are selected from [33-34]. The X-33 vehicle model considered here is equipped with four sets of control surfaces: rudders, body flaps, inboard and outboard elevons, with left and right sides for each set. Fig. 1 shows the configuration of the X-33. Each of the eight surfaces can be independently actuated with one actuator for each surface. Each actuator is assumed to behave as a first-order system: ui(s) uci(s) = 30 s+ 30 Let u = \u03b4 = [\u03b4rei, \u03b4lei, \u03b4rfl, \u03b4lfl, \u03b4rvr, \u03b4lvr, \u03b4reo, \u03b4leo] T be the control surface perturbations from the trim values, where \u03b4rei, \u03b4lei are the right and left inboard elevons, \u03b4rfl, \u03b4lfl the right and left body flaps, \u03b4rvr, \u03b4lvr the right and left rudders, and \u03b4reo, \u03b4leo the right and left outboard elevons"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002308_j.jallcom.2017.06.251-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002308_j.jallcom.2017.06.251-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the SHPB test.",
        "texts": [
            " The microhardness, wear resistance and corrosion resistance had been investigated and published [30]. Eventually, the test specimen was manufactured with 42mm 2 mm by Wire Electric Discharge Machining (WEDM). The end faces of the specimen were polished and treated with MoS2 lubricant to reduce barreling as a result of friction at the interface with the pressure bars. The dynamic impact tests were performed using a compressive Split Hopkinson Pressure Bar (SHPB) apparatus at strain rates of 1000 s 1, 5000 s 1, 8000 s 1 and temperatures of 20 C, 200 C, 400 C, 600 C, 800 C. Fig. 1 presents a schematic illustration of the SHPB apparatus and the measuring procedures. It can be found that SHPB system basically comprises an incident bar, a transmitted bar and a strike bar, which are made of high strength alloy steel. The incident bar and transmitted bar is supported on the base bymeans of the cylindrical surface bearing, and the bars are coaxial. The diameter of incident bar, transmitted bar and strike bar are 5 mm, and the length is 450 mm, 450 mm and 100 mm, respectively. During compression testing, the specimenwas positioned between the incident bar and the transmitted bar"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure7.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure7.6-1.png",
        "caption": "Figure 7.6.1. Vehicle free-body diagram in Earth-fixed axes.",
        "texts": [
            ", to find the amplitude of path oscillations in response to an oscillatory steer input, then the equations of motion should be expressed in Earth-fixed axes. The equations of motion in Earth-fixed axes are The slip angles expressed in the variables of the Earth-fixed axis system are: where is the yaw angular speed. The actual values of the angles are, of course, the same in the two systems. Compared with the slip angle expressions of the last section, the use of u instead of v results in the appearance of \u03c8 in the expressions. Figure 7.6.1, shows the free-body diagram in the Earth-fixed axes XYZ. These are inertial axes, so compensation forces are not required. From the free-body diagram, the equations of motion in Earth-fixed axes are: Substituting, as in the last section, collecting terms and using the D operator notation gives: Unsteady-State Handling 449 This may also be expressed in other forms, e.g., by using u = DY, r = D\u03c8 or u = vV. Using the last substitution gives: The above equations can be contrasted with the equivalent formulation, in \u03b2 and \u03c8, for vehicle-fixed axes from the last section, which were 450 Tires, Suspension and Handling Elimination of v or \u03c8 from the Earth-fixed axes formulation, after cancellation of terms and dividing by VD, gives the following characteristic equation: which multiplies out to Despite the different starting equations for the Earth-fixed axes, this is the same characteristic equation as was found for the vehicle-fixed axes; physically this is correct because the natural frequency and damping ratio must be the same in both coordinate systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000474_s0005-1098(01)00184-4-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000474_s0005-1098(01)00184-4-Figure1-1.png",
        "caption": "Fig. 1. Forces acting on the aircraft.",
        "texts": [
            " Appendix A contains a sketch of the proofs of the stability results in Section 4. The purpose of this paper is the design of a feedback law for autonomous (vertical) landing of a VTOL aircraft on a oscillating deck. As in Hauser et al. (1992), Martin et al. (1994) and Lin et al. (1999) a simpli\"ed model describing the motion of this aircraft in the verticallateral plane is the following one. Let x, y and denote, respectively, the horizontal and vertical position of the center of mass C and the roll angle of the aircraft with respect to the horizon, as in Fig. 1. The control inputs are the thrust \u00b9 directed out the bottom of the aircraft and the rolling moment produced by a couple of equal forces F acting at the wingtips. Their direction is not perpendicular to the horizontal body axis, but tilted by some \"xed angle . IfM denotes the mass of the aircraft, J the moment of inertia about the center of mass, l the distance between the wingtips and g the gravitational acceleration, the motion of the aircraft on the lateral-vertical plane is modeled by the equations MxK\""
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure12.8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure12.8-1.png",
        "caption": "Fig. 12.8 A scheme of a typical optical scanner, where the 3D positions of the sampled points are computed by triangulation given the sampled point projection B(C) on the sensor plane and the known relative position/orientation of the emitter and the sensor [17]",
        "texts": [
            " There is a remarkable variety of 3D optical techniques, and their classification, as given in Fig. 12.5, is not unique. In this section, some of the more prominent approaches are briefly explained and compared (Table 12.3). Active optical devices are based on an emitter, which produces some sort of structured illumination on the object to be scanned, and a sensor, which is typically a CCD camera and acquires images of the distorted pattern reflected by the object surface [17]. In most cases the depth information is reconstructed by triangulation (Fig. 12.8), given the known relative positions of the emitter-sensor pair. The emitter can produce coherent light (e.g. a laser-beam) or incoherent light; in both cases, a given light pattern (point-wise, stripe-wise or a more complex pattern) is projected on the object surface. Different technologies have been adopted to 12 Reverse Engineering 331 produce the structured light pattern: laser emitters, custom white light projectors (which can filter light by means of a glass slide with a stripe pattern engraved via photo-lithography), low cost photographic slide projectors and finally digital video projectors",
            " Passive methods reconstruct a 3D model of an object by analysing the images to determine coordinate data [3]. It is similar to (active) structured-light methods in its use of imaging frames for 3D reconstruction; however, in passive methods, there is no projection of light sources onto the object for data acquisition. The typical passive methods are shape from shading and shape from stereo. Laser triangulation method is a technique which uses the law of sine to find the coordinates and distance of an unknown point by forming a triangle with it and two known reference points [2]. In Fig. 12.8, A and B are the two reference locations given by the camera and the sensor locations, and C is the location of the object point of interest. The distance from A to B can be measured as c, and the angles \u03b1 and \u03b2 can also be measured. Following the law of sine the distances a and b can be calculated. The coordinates of A and B are known, then the coordinate of C can also be calculated. The same principle is employed in various other scanning methods. Time-Of-Flight (TOF) method uses the radar time-of-flight principle [8]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure22.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure22.10-1.png",
        "caption": "Figure 22.10 Example of network with an adaptive diffusion strategy.",
        "texts": [
            " Consider a set of coefficients bk that add up to one when node k is excluded. These coefficients could be obtained from the coefficients ak as follows: bk = \u23a7\u23a8\u23a9 ak \u2211 \u2208Nk\u2212{k} ak if k = are linked, 0 otherwise. Now, we combine the local estimates at the neighbors of node k, say as before, but excluding node k itself. This step results in an intermediate estimate: \u03c8 (i\u22121) k = \u2211 \u2208Nk\u2212{k} bk \u03c8 (i\u22121) . Then this aggregate estimate is combined adaptively with the local estimate at node k to provide the desired combination (compare with (22.40) and see Fig. 22.10): \u03c6 (i\u22121) k = \u03b3k(i)\u03c8 (i\u22121) k + [1 \u2212 \u03b3k(i) ] \u03c8 (i\u22121) k , where the coefficient {\u03b3k(i)} is adapted in order to improve performance (such as reducing the mean-square error further whenever possible) [10, 12]. The idea is that the selection of \u03b3k will give more or less weight to the local weight as opposed to the combination from the neighbors depending on which source of information is more reliable (or less noisy); we forgo the details of adapting the coefficient \u03b3k . Once this is done, we may continue to the adaptation step: \u03c8 (i) k = \u03c6 (i\u22121) k + \u03bc u\u2217 k,i [ dk(i) \u2212 uk,i\u03c6 (i\u22121) k ] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure23.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure23.16-1.png",
        "caption": "Fig. 23.16 Design information generated along with the concurrent design process",
        "texts": [
            " During the detailed design process, quality and quantity of design information within an early design stage can reduce time and costs for design more than the effort of resolving design conflicts downstream. The quality of the concurrent process can be improved by prediction; using 3D models and simulation techniques will play a key role [39]. For example, if there might be plans to build block divisions for production, the trade-off of each plan can be shown with quantitative data and the best plan can be chosen based on costs, schedule and other limitations. Time history of design information will change as shown in Fig. 23.16. Much more design information will be created within an early stage of the design process. As for designing simple bulk carriers, more than 20,000 h are spent on the design work and the efficiency varies according to the quality of work in the design process. The concept of CE was introduced to shipbuilding industry years ago and has delivered improvement; however, barriers for implementing fully concurrent and front-loaded design, such as local optimization and data conversion, still exist [18, 20, 39]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.22-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.22-1.png",
        "caption": "Fig. 3.22 Rotor blade lag motion",
        "texts": [],
        "surrounding_texts": [
            "parachute. We return to the modelling of vortex ring state in the context of tiltrotor aircraft Chapter 10. Modelling Helicopter Flight Dynamics: Building a Simulation Model 101 Momentum Theory in Forward Flight In high-speed flight, the downwash field of a rotor is like that of a fixed-wing aircraft with circular planform and the momentum approximations for deriving the induced flow at the wing apply (Ref. 3.13). Figure 3.14 illustrates the flow streamtube, with freestream velocity V at angle of incidence \ud835\udefc to the disc, and the actuator disc inducing a velocity vi at the rotor. The induced flow in the far wake is again twice the flow at the rotor (wing) and the conservation laws give the mass flux as m\u0307 = \ud835\udf0cAdVres (3.136) and hence the rotor thrust (or wing lift) as T = m\u03072vi = 2\ud835\udf0cAdVresvi (3.137) where the resultant velocity at the rotor is given by V2 res = (V cos \ud835\udefcd)2 + (V sin \ud835\udefcd + vi)2 (3.138) Normalizing velocities and rotor thrust in the usual way gives the general expression 102 Helicopter and Tiltrotor Flight Dynamics where \ud835\udf07 = V cos \ud835\udefcd \u03a9R , \ud835\udf07z = \u2212 V sin \ud835\udefcd \u03a9R (3.140) and where \ud835\udefcd is the disc incidence, shown in Figure 3.14. Strictly, Eq. (3.139) applies to high-speed flight, where the downwash velocities are much smaller than in hover, but the solution also reduces to the cases of hover and axial motion in the limit when \ud835\udf07= 0. In fact, this general equation is a reasonable approximation to the mean value of rotor inflow across a wide range of flight conditions, including steep descent, and provides an estimate of the induced power required. Summarizing, we see that the rotor inflow can be approximated in hover and high-speed flight by the formulae V = 0, vi = \u221a( T 2Ad\ud835\udf0c ) (3.141) V \u226b vi, vi = T 2VAd\ud835\udf0c (3.142) showing the dependence on the square root of disc loading in hover, and proportional to disc loading in forward flight. Between hover and \ud835\udf07 values of about 0.1 (about 40 knots for Lynx), the mean normal component of the rotor wake velocities is still high, but now gives rise to strong nonuniformities along the longitudinal, or, more generally, the flight axis of the disc. Several approximations to this nonuniformity were derived in the early developments of rotor aerodynamic theory using the vortex form of actuator disc theory (Refs. 3.14\u20133.16). It was shown that a good approximation to the inflow could be achieved with a first harmonic with a linear variation along the disc determined by the wake angle relative to the disc, given by \ud835\udf06i = \ud835\udf060 + rb R \ud835\udf061cw cos\ud835\udf13w (3.143) where \ud835\udf061cw = \ud835\udf060 tan ( \ud835\udf12 2 ) , \ud835\udf12 < \ud835\udf0b 2 \ud835\udf061cw = \ud835\udf060 cot ( \ud835\udf12 2 ) , \ud835\udf12 > \ud835\udf0b 2 (3.144) and the wake angle, \ud835\udf12 , is given by \ud835\udf12 = tan\u22121 ( \ud835\udf07 \ud835\udf060 \u2212 \ud835\udf07z ) (3.145) where \ud835\udf060 is the uniform component of inflow as given by Eq. (3.139). The solution of Eq. (3.144) can be combined with that of Eq. (3.139) to give the results shown in Figure 3.15 where, again, \ud835\udefcd is the disc incidence and V is the resultant velocity of the free stream relative to the rotor. The solution curves for the (nonphysical) vertical descent cases are included. The nonuniform component is approximately equal to the uniform component in high-speed straight and level flight, i.e. the inflow is zero at the front of the disc. In low-speed steep descent, the nonuniform component varies strongly with speed and is also of similar magnitude to the uniform component. Longitudinal variations in blade incidence lead to first harmonic lateral flapping and hence rolling moments. Flight in steep descent is often characterised by high vibration, strong and erratic rolling moments and, as the vortex-ring region is entered, loss of vertical control power and high rates of descent (Ref. 3.17). The simple uniform/nonuniform inflow model given above begins to account for some of these effects (e.g. power settling, Ref. 3.18) but cannot be regarded as a proper representation of either the causal physics or flight dynamics effects; in particular, the dramatic loss of control power caused by the build-up of the toroidal vortex ring is not captured by the simple model, and recourse to empiricism is required to model this effect. Modelling Helicopter Flight Dynamics: Building a Simulation Model 103 An effective analysis to predict the boundaries of the vortex-ring state, using momentum theory, was conducted in the early 1970s (Ref. 3.19) and extended in the 1990s using classical vortex theory (Ref. 3.20). Wolkovitch\u2019s results are summarised in Figure 3.16, showing the predicted upper and lower boundaries as a function of normalised horizontal velocity; the so-called region of roughness measured previously by Drees (Ref. 3.21) is also shown. The parameter k shown on Figure 3.16 is an empirical constant scaling the downward velocity of the wake vorticity. The lower boundary is set at a value of k< 2, i.e. before the wake is fully contracted, indicating breakdown of the protective tube of vorticity a finite distance below the rotor. Knowledge of the boundary locations is valuable for including appropriate flags in simulation models (e.g. Helisim). Once again, though, the simple momentum and vortex theories are inadequate at modelling the flow and predicting flight dynamics within the vortex-ring region. We shall return to this topic in Chapters 4 and 5 when discussing trim and control response, and later in Chapter 10 relating to tiltrotor aircraft. The momentum theory used to formulate the expressions for the rotor inflow is strictly applicable only in steady flight when the rotor is trimmed and in slowly varying conditions. We can, however, gain an appreciation of the effects of inflow on rotor thrust during manoeuvres through the concept of the lift deficiency function (Ref. 3.7). When the rotor thrust changes, the inflow changes in sympathy, increasing for increasing thrust and decreasing for decreasing thrust. Considering the thrust changes as perturbations on the mean component, we can write \ud835\udeffCT = \ud835\udeffCTQS + ( \ud835\udf15CT \ud835\udf15\ud835\udf06i ) QS \ud835\udeff\ud835\udf06i (3.146) where, from the thrust equation (Eq. (3.91))( \ud835\udf15CT \ud835\udf15\ud835\udf06i ) QS = \u2212 a0s 4 (3.147) 104 Helicopter and Tiltrotor Flight Dynamics and where the quasi-steady thrust coefficient changes without change in the inflow. If the inflow changes are due entirely to thrust changes, we can write \ud835\udeff\ud835\udf06i = \ud835\udf15\ud835\udf06i \ud835\udf15CT \ud835\udeff CT (3.148) The derivatives of inflow with thrust have simple approximate forms at hover and in forward flight \ud835\udf15\ud835\udf06i \ud835\udf15CT = 1 4\ud835\udf06 , \ud835\udf07 = 0 (3.149) \ud835\udf15\ud835\udf06i \ud835\udf15CT \u2248 1 2\ud835\udf07 , \ud835\udf07 > 0.2 (3.150) Combining these relationships, we can write the thrust changes as the product of a deficiency function and the quasi-steady thrust change, i.e. \ud835\udeffCT = C\u2032\ud835\udeffCTQS (3.151) where C\u2032 = 1 1 + a0s 16\ud835\udf06i , \ud835\udf07 = 0 (3.152) and C\u2032 = 1 1 + a0s 8\ud835\udf07 , \ud835\udf07 > 0.2 (3.153) Rotor thrust changes are therefore reduced to about 60\u201370% in hover and 80% in the mid-speed range, by the effects of inflow. This would apply, for example, to the thrust changes due to control inputs. It is important to note that these deficiency functions do not apply to the thrust changes from changes in rotor velocities. In particular, when the vertical velocity component changes, there are additional inflow perturbations that lead to even further lift reductions. In hover, the deficiency function for vertical velocity changes is half that due to collective pitch changes, i.e. C\u2032 \ud835\udf07z = C\u2032 2 , \ud835\udf07 = 0 (3.154) Modelling Helicopter Flight Dynamics: Building a Simulation Model 105 In forward flight, the lift loss is recovered and Eq. (3.151) also applies to the vertical velocity perturbations. This simple analysis demonstrates how the gust sensitivity of rotors increases strongly from hover to mid-speed, but levels out to the constant quasi-steady value at high speed (see discussion on vertical gust response in Chapter 2). Because the inflow depends on the thrust and the thrust depends on the inflow, an iterative solution is required. Defining the zero function g0 as g0 = \ud835\udf060 \u2212 ( CT 2\u039b1\u22152 ) (3.155) where \u039b = \ud835\udf072 + (\ud835\udf060 \u2212 \ud835\udf07z)2 (3.156) and recalling that the thrust coefficient can be written as (Eq. (3.91)) CT = a0s 2 ( \ud835\udf030 ( 1 3 + \ud835\udf072 2 ) + \ud835\udf07 2 ( \ud835\udf031sw + pw 2 ) + ( \ud835\udf07z \u2212 \ud835\udf060 2 ) + 1 4 (1 + \ud835\udf072)\ud835\udf03tw ) (3.157) Newton\u2019s iterative scheme gives \ud835\udf060j+1 = \ud835\udf060j + fjhj(\ud835\udf060j ) (3.158) where hj = \u2212 ( g0 dg0\u2215d\ud835\udf060 ) \ud835\udf06=\ud835\udf060j (3.159) i.e. hj = \u2212 (2\ud835\udf060j \u039b1\u22152 \u2212 CT )\u039b 2\u039b3\u22152 + a0s 4 \u039b \u2212 CT (\ud835\udf07z \u2212 \ud835\udf060j ) (3.160) For most flight conditions, the above scheme should provide rapid estimates of the inflow at time tj+1 from a knowledge of conditions at time tj. The stability of the algorithm is determined by the variation of the function g0 and the initial value of \ud835\udf060. However, in certain flight conditions near the hover, the iteration can diverge, and the damping constant f is included to stabilise the calculation; a value of 0.6 for f appears to be a reasonable compromise between achieving stability and rapid convergence (Ref. 3.4). A further approximation involved in the above inflow formulation is the assumption that the freestream velocity component normal to the disc (i.e. V sin \ud835\udefcd) is the same as \ud835\udf07z. This is a reasonable approximation for small flapping angles, and even for the larger angles typical of low-speed manoeuvres the errors are small because of the insensitivity of the inflow to disc incidence (see Figure 3.15). The approximation is convenient because there is no requirement to know the disc tilt or rotor flapping relative to the shaft to compute the inflow, hence leading to a further simplification in the iteration procedure. The simple momentum inflow derived above is effective in predicting the gross and slowly varying uniform and rectangular, wake-induced, inflow components. In practice, the inflow distribution varies with flight condition and unsteady rotor loading (e.g. in manoeuvres) in a much more complex manner. Intuitively, we can imagine the inflow varying around the disc and along the blades, continuously satisfying local flow balance conditions and conservation principles. Locally, the flow must respond to local changes in blade loading, so if, for example, there are one-per-rev rotor forces and moments, we might expect the inflow to be related to these. We can also expect the inflow to take a finite time to develop as the air mass is accelerated to its new velocity. Also, the rotor wake is far more complex and discrete than the uniform flow in a streamtube assumption of momentum theory. It is known that local blade\u2013vortex interactions can cause very large local perturbations in blade inflow and hence incidence. These can be sufficient to stall the blade in certain conditions and are important for predicting rotor stall boundaries and the resulting flight dynamics at the flight envelope limits. We shall return to this last topic later in the discussion on advanced, high-fidelity modelling. Before leaving inflow, however, we shall examine the theoretical developments needed to improve the prediction of the nonuniform and unsteady components. 106 Helicopter and Tiltrotor Flight Dynamics Local-Differential Momentum Theory and Dynamic Inflow We begin by considering the simple momentum theory applied to the rotor disc element shown in Figure 3.17. We make the gross assumption that the relationship between the change in momentum and the work done by the load across the element applies locally as well as globally, giving the equations for the mass flow through the element and the thrust differential as shown in Eqs. (3.161) and (3.162). dm\u0307 = \ud835\udf0cVrbdrb d\ud835\udf13 (3.161) dT = dm\u03072vi (3.162) Using the two-dimensional blade element theory, these can be combined into the form Nb 2\ud835\udf0b (1 2 \ud835\udf0ca0c(\ud835\udf03U 2 T + UTUp)drb d\ud835\udf13 ) = 2\ud835\udf0crb(\ud835\udf072 + (\ud835\udf06i \u2212 \ud835\udf07z)2)1\u22152\ud835\udf06i drb d\ud835\udf13 (3.163) Integrating around the disc and along the blades leads to the solution for the mean uniform component of inflow derived earlier. If, instead of averaging the load around the disc, we apply the momentum balance to the one-per-rev components of the load, and inflow, then expressions for the nonuniform inflow can be derived. Writing the first harmonic inflow in the form \ud835\udf06i = \ud835\udf060 + rb(\ud835\udf061c cos\ud835\udf13 + \ud835\udf061s sin\ud835\udf13) (3.164) Eq. (3.163) can be expanded to give a first harmonic balance, which, in hover, results in the expressions \ud835\udf061c = 3a0s 16 1 \ud835\udf060 F(1) 1c (3.165) and \ud835\udf061s = 3a0s 16 1 \ud835\udf060 F(1) 1s (3.166) where the F loadings are given by Eqs. (3.92) and (3.93). These one-per-rev lift forces are closely related to the aerodynamic moments at the hub in the nonrotating fuselage frame \u2013 the pitching moment CMa and the rolling moment CLa, i.e. 2CLa a0s = \u22123 8 F(1) 1s (3.167) 2CMa a0S = \u22123 8 F(1) 1c (3.168) These hub moments are already functions of the nonuniform inflow distributions; hence, just as with the rotor thrust and the uniform inflow, we find that the moments are reduced by a similar moment deficiency Modelling Helicopter Flight Dynamics: Building a Simulation Model 107 factor CLa = C\u2032 1CLaQS (3.169) CMa = C\u2032 1CMaQS (3.170) where, as before, the deficiency factors are given by C\u2032 1 = 1 1 + a0s 16\ud835\udf060 (3.171) in hover, with typical value 0.6, and C\u2032 1 = 1 1 + a0s 8\ud835\udf07 (3.172) in forward flight, with typical value of 0.8 when \ud835\udf07= 0.3. In hover, the first harmonic inflow components given by Eqs. (3.165) and (3.166) can be expanded as \ud835\udf061c = C\u2032 1 a0s 16\ud835\udf060 (\ud835\udf031c \u2212 \ud835\udefd1s + q) (3.173) \ud835\udf061s = C\u2032 1 a0s 16\ud835\udf060 (\ud835\udf031s + \ud835\udefd1c + p) (3.174) As the rotor blade develops an aerodynamic moment, the flowfield responds with the linear, harmonic distributions derived above. The associated deficiency factors have often been cited as the cause of mismatches between theory and test (Refs. 3.9, 3.22\u20133.29), and there is no doubt that the resulting overall effects on flight dynamics can be significant. The assumptions are fragile, however, and the theory can, at best, be regarded as providing a very approximate solution to a complex problem. Developments with more detailed spatial and temporal inflow distributions are likely to offer even higher fidelity in rotor modelling (see Pitt and Peters, Ref 3.26, and articles by Peters et al., Refs. 3.27\u20133.29). The inflow analysis outlined above has ignored any time dependency other than the quasi-steady effects and harmonic variations. In reality, there will always be a transient lag in the build-up or decay of the inflow field; in effect, the flow is a dynamic element in its own right. An extension of momentum theory has also been made to include the dynamics of an apparent mass of fluid, first by Carpenter and Fridovitch in 1953 (Ref. 3.30). To introduce this theory, we return to axial flight; Carpenter and Fridovitch suggested that the transient inflow could be taken into account by including an accelerated mass of air occupying 63.7% of the air mass of the circumscribed sphere of the rotor. Thus, we write the thrust balancing the mass flow through the rotor to include an apparent mass term T = 0.637\ud835\udf0c 4 3 \ud835\udf0bR3vi + 2Ad\ud835\udf0cvi(Vc + vi) (3.175) To understand how this additional effect contributes to the motion, we can linearise Eq. (3.175) about a steady hover trim; writing \ud835\udf06i = \ud835\udf06itrim + \ud835\udeff\ud835\udf06i (3.176) and CT = CTtrim + \ud835\udeffCT (3.177) the perturbation equation takes the form \ud835\udf0f\ud835\udf06?\u0307?i + \ud835\udeff\ud835\udf06i = \ud835\udf06CT \ud835\udeffCT (3.178) where the time constant and the steady-state inflow gain are given by \ud835\udf0f\ud835\udf06 = 0.849 4\ud835\udf06itrim \u03a9 , \ud835\udf06CT = 1 4\ud835\udf06itrim (3.179) 108 Helicopter and Tiltrotor Flight Dynamics For typical rotors, moderately loaded in the hover, the time constant for the uniform inflow works out at about 0.1 s. The time taken for small adjustments in uniform inflow is therefore very rapid, according to simple momentum considerations, but this estimate is clearly a linear function of the apparent mass. Since this early work, the concept of dynamic inflow has been developed by several researchers, but it is the work of Peters, stemming from the early Ref. 3.23 and continuing through to Ref. 3.29, that has provided the most coherent perspective on the subject from a fluid mechanics standpoint. The general formulation of a 3-DoF dynamic inflow model can be written in the form [M] \u23a7\u23aa\u23a8\u23aa\u23a9 ?\u0307?0 ?\u0307?1s ?\u0307?1c \u23ab\u23aa\u23ac\u23aa\u23ad + \u23a1\u23a2\u23a2\u23a3L \u23a4\u23a5\u23a5\u23a6 \u22121 \u23a7\u23aa\u23a8\u23aa\u23a9 \ud835\udf060 \ud835\udf061s \ud835\udf061c \u23ab\u23aa\u23ac\u23aa\u23ad = \u23a7\u23aa\u23a8\u23aa\u23a9 CT CL CM \u23ab\u23aa\u23ac\u23aa\u23ad (3.180) The matrices M and L are the apparent mass and gain functions, respectively; CT, CL, and CM are the thrust, rolling, and pitching aerodynamic moment perturbations inducing the uniform and first harmonic inflow changes. The mass and gain matrices can be derived from several different theories (e.g. actuator disc, vortex theory). Peters has extended the modelling to an unsteady three-dimensional finite-state wake (Ref. 3.29), which embraces the traditional theories of Theordorsen and Lowey (Ref. 3.31). Dynamic inflow will be discussed again in the context of stability and control derivatives in Chapter 4, and the reader is referred to Refs. 3.28 and 3.29 for full details of the aerodynamic theory.1 Before discussing additional rotor dynamic DoFs and progressing on to other helicopter components, we return to the centre-spring model for a further examination of its merits as a general approximation. Rotor Flapping\u2013Further Considerations of the Centre-Spring Approximation The centre-spring equivalent rotor (CSER), a rigid blade analogue for modelling all types of blade flap retention systems, was originally proposed by Sissingh (Ref. 3.32) and has considerable appeal because of the relatively simple expressions, particularly for hub moments, that result. However, even for moderately stiff hingeless rotors like those on the Lynx and Bo105, the blade shape is rather a gross approximation to the elastic deformation, and a more common approximation used to model such blades is the offset-hinge and spring analogue originally introduced by Young (Ref. 3.33). Figure 3.18 illustrates the comparison between the centre-spring, offset-hinge and spring and a typical first elastic mode shape. Young proposed a method for determining the values of offset-hinge and spring strength, the latter from the nonrotating natural flap frequency, which is then made up with the offset to match the rotating frequency. The ratio of offset to spring strength is not unique and other methods for establishing the mix have been proposed; for example, Bramwell 1Readers can also refer to David Peters review paper \u2019How Dynamic Inflow Survives in the Competitive World of Rotorcraft Aerodynamics, JOURNAL OF THE AMERICAN HELICOPTER SOCIETY 54, 011001 (2009) Modelling Helicopter Flight Dynamics: Building a Simulation Model 109 (Ref. 3.34) derives an expression for the offset e in terms of the first elastic mode frequency ratio \ud835\udf061 in the form e = \ud835\udf062 1 \u2212 1 \ud835\udf061 (3.181) with the spring strength in this case being zero. In Reichert\u2019s method (Ref. 3.35), the offset hinge is located by extending the first mode tip tangent to meet the undeformed reference line. The first elastic mode frequency is then made up with the addition of a spring, which can have a negative stiffness. Approximate modelling options therefore range from the centre spring out to Bramwell\u2019s limit with no spring. The questions that naturally arise are, first, whether these different options are equivalent or what are the important differences in the modelling of flapping motion and hub moments, and second, which is the most appropriate model for flight dynamics applications? We will try to address these questions in the following discussion. We refer to the analysis of elastic blade flapping at the beginning of Chapter 3 and the series of equations from (3.8) to (3.16), developing the approximate expression for the hub flap moment due to rotor stiffness in the form M(r) h (0, t) \u2248 \u03a92(\ud835\udf062 1 \u2212 1)P1(t) R \u222b 0 mrS1dr (3.182) where S1 is the first elastic mode shape and P1 is the time-dependent blade tip deflection. The \u2018mode shape\u2019 of the offset-hinge model, with flap hinge at eR, can be written in the form S1(r) = 0 0 \u2264 r \u2264 eR S1(r) = r \u2212 eR R(1 \u2212 e) eR \u2264 r \u2264 R (3.183) If we substitute Eq. (3.183) into Eq. (3.182), we obtain the hub flap moment M(r) h (0, t) = \u03a92I\ud835\udefd(\ud835\udf062 \ud835\udefd \u2212 1)\ud835\udefd(t) ( 1 + eRM\ud835\udefd I\ud835\udefd ) (3.184) where I\ud835\udefd = R \u222b eR m(r \u2212 eR)2 dr, M\ud835\udefd = R \u222b eR m(r \u2212 eR)dr (3.185) and the tip deflection is approximately related to the flapping angles by the linear expression P1(t) \u2248 R\ud835\udefd1(t) \u2248 R(1 \u2212 e)\ud835\udefd(t) (3.186) The expression for the flap frequency ratio \ud835\udf06\ud835\udefd can be derived from the same method of analysis used for the centre-spring model. Thus, the equation for the flapping motion can be written in the form \ud835\udefd\u2032\u2032 + \ud835\udf062 \ud835\udefd \ud835\udefd = ( 1 + eRM\ud835\udefd I\ud835\udefd ) \ud835\udf0ex + \ud835\udefe 2 R \u222b eR (U 2 T\ud835\udf03 + UT UP)(rb \u2212 e)drb (3.187) where, as before \ud835\udefd\u2032 = d\ud835\udefd d\ud835\udf13 and the Lock number is given by \ud835\udefe = \ud835\udf0cca0R4 I\ud835\udefd (3.188) 110 Helicopter and Tiltrotor Flight Dynamics The in-plane and normal velocity components at the disc are given by (cf. Eqs. (3.24) and (3.25)) UT = rb(1 + \ud835\udf14x\ud835\udefd) + \ud835\udf07 sin\ud835\udf13 UP = \ud835\udf07z \u2212 \ud835\udf060 \u2212 \ud835\udf07\ud835\udefd cos\ud835\udf13 + rb(\ud835\udf14y \u2212 \ud835\udf061) \u2212 (rb \u2212 e)\ud835\udefd\u2032 (3.189) and the combined inertial acceleration function is given by the expression \ud835\udf0ex = (p\u2032 \u2212 2q) sin\ud835\udf13 + (q\u2032 + 2p) cos\ud835\udf13 (3.190) Finally, the flap frequency ratio is made up of a contribution from the spring stiffness and another from the offset hinge, given by \ud835\udf062 \ud835\udefd = 1 + K\ud835\udefd I\ud835\udefd\u03a92 + eRM\ud835\udefd I\ud835\udefd (3.191) The hub moment given by Eq. (3.184) is clearly in phase with the blade tip deflection. However, a more detailed analysis of the dynamics of the offset-hinge model developed by Bramwell (Ref. 3.34) reveals that this simple phase relationship is not strictly true for the offset-hinge model. Referring to Figure 3.19, the hub flap moment can be written as the sum of three components, i.e. M(r)(0, t) = K\ud835\udefd\ud835\udefd \u2212 eRSz + eR \u222b 0 F(r, t)rdr (3.192) The shear force at the flap hinge is given by the balance of integrated aerodynamic (F(r, t)) and inertial loads on the blade; thus Sz = \u2212 R \u222b eR [F(r, t) \u2212 m(r \u2212 eR)\ud835\udefd]dr (3.193) If we assume a first harmonic flap response so that \ud835\udefd = \u2212\u03a92\ud835\udefd (3.194) then the flap moment about the hub centre takes the form M(r)(0, t) = \u03a92I\ud835\udefd(\ud835\udf062 \ud835\udefd \u2212 1)\ud835\udefd(t) + eR R \u222b eR F(r, t)dr + eR \u222b 0 rF(r, t)dr (3.195) Modelling Helicopter Flight Dynamics: Building a Simulation Model 111 The third component due to the lift on the flap arm is O(e3) in the hover and will be neglected. The result given by Eq. (3.195) indicates that the hub moment will be out of phase with blade flapping to the extent that any first harmonic aerodynamic load is out of phase with flap. Before examining this phase relationship in a little more detail, we need to explain the inconsistency between Young\u2019s result above in Eq. (3.184) and the correct expression given by Eq. (3.195). To uncover the anomaly, it is necessary to return to the primitive expression for the hub flap moment derived from bending theory (cf. Eq. (3.13)): M(r) h (0, t) = R \u222b 0 [ F(r, t) \u2212 m ( \ud835\udf152w \ud835\udf15t2 + \u03a92w )] rdr (3.196) Using Eqs. (3.9) and (3.10), the hub moment can then be written in the form M(r)(0, t) = R \u222b 0 F(r, t)rdr \u2212 \u221e\u2211 n=1 \u222b R 0 mrSn dr \u222b R 0 mS2 n dr R \u222b 0 F(r, t)Sn dr +\u03a92 \u221e\u2211 n=1 (\ud835\udf062 n \u2212 1)Pn R \u222b 0 mrSn dr (3.197) If an infinite set of modes is included in the hub moment expression, then the first two terms in Eq. (3.197) cancel, leaving each modal moment in phase with its corresponding blade tip deflection. With only a finite number of modes included, this is no longer the case (Bramwell, Ref. 3.34). In particular, if only the first elastic mode is retained, then the hub flap moment has a residual M(r)(0, t) = R \u222b 0 F(r, t) \u239b\u239c\u239c\u239c\u239c\u239d r \u2212 \u222b R 0 mrS1 dr \u222b R 0 mS2 1 dr S1 \u239e\u239f\u239f\u239f\u239f\u23a0 dr + \u03a92(\ud835\udf062 1 \u2212 1)P1 \u222b R 0 mrS1 dr (3.198) When the aerodynamic loading has the same shape as the first mode, i.e. F(r, t) \u221d mS1 (3.199) then the first term in Eq. (3.198) vanishes and the hub moment expression reduces to that given by Young (Ref. 3.33). These conditions will not, in general, be satisfied since, even in hover, there are r2 terms in the aerodynamic loading. Substituting the mode shape for the offset hinge, given by Eq. (3.183), into Eq. (3.198), leads to the correct hub moment with the out-of-phase aerodynamic component as given by Eq. (3.195). Neglecting the effect of the in-plane loads, we see that the roll-and-pitch hub flap moments applied to the fuselage from a single blade in nonrotating coordinates, are given by the transformation Lh = \u2212M(r) sin\ud835\udf13 (3.200) Mh = \u2212M(r) cos\ud835\udf13 (3.201) Substituting for the aerodynamic loads in Eqs. (3.200) and (3.201) and expanding to give the quasi-steady (zeroth harmonic) components, leads to the hover result 2Lh I\ud835\udefd\u03a92 = \u2212(\ud835\udf062 \ud835\udefd \u2212 1)\ud835\udefd1s \u2212 eRM\ud835\udefd I\ud835\udefd ( 1 + eRM\ud835\udefd0 M\ud835\udefd ) ( p\u2032 \u2212 2q) \u2212e \ud835\udefe 2 \u239b\u239c\u239c\u239c\u239d p + \ud835\udefd1c ( 1 \u2212 3 2 e ) + \ud835\udf031s 3 \u239e\u239f\u239f\u239f\u23a0 (3.202) 112 Helicopter and Tiltrotor Flight Dynamics 2Mh I\ud835\udefd\u03a92 = \u2212(\ud835\udf062 \ud835\udefd \u2212 1)\ud835\udefd1c \u2212 eRM\ud835\udefd I\ud835\udefd ( 1 + eRM\ud835\udefd0 M\ud835\udefd ) (q\u2032 + 2p) \u2212e \ud835\udefe 2 \u239b\u239c\u239c\u239c\u239d q + \ud835\udefd1s ( 1 \u2212 3 2 e ) + \ud835\udf031c 3 \u239e\u239f\u239f\u239f\u23a0 (3.203) The blade mass coefficient is given by M\ud835\udefd0 = R \u222b eR mdrb (3.204) The inertial and aerodynamic components proportional to the offset e in the above are clearly absent in the centre-spring model when the hub moment is always in phase with the flapping. The extent to which the additional terms are out of phase with the flapping can be estimated by examining the hub moment derivatives. By far the most significant variations with offset appear in the control coupling derivatives. Expressions for the flapping derivatives can be derived from the harmonic solutions to the flapping equations; hence \ud835\udf15\ud835\udefd1c \ud835\udf15\ud835\udf031c = \ud835\udefd1c\ud835\udf031c = \ud835\udefd1s\ud835\udf031s = S\ud835\udefd d\ud835\udefd ( 1 \u2212 4 3 e ) (3.205) \ud835\udf15\ud835\udefd1c \ud835\udf15\ud835\udf031s = \ud835\udefd1c\ud835\udf031s = \u2212\ud835\udefd1s\ud835\udf031c = \u2212 1 d\ud835\udefd ( 1 \u2212 8 3 e )( 1 \u2212 4 3 e ) (3.206) where d\ud835\udefd = S2 \ud835\udefd + ( 1 \u2212 8 3 e )2 (3.207) The hub roll moment control derivatives can therefore be written to an accuracy of O(e2) in the form 2Lh\ud835\udf031c I\ud835\udefd\u03a92 ( 8 \ud835\udefe ) = \u2212S\ud835\udefd\ud835\udefd1s\ud835\udf031c \u2212 eR 4 3 \ud835\udefd1c\ud835\udf031c ( 1 \u2212 3 2 e ) (3.208) 2Lh\ud835\udf031s I\ud835\udefd\u03a92 ( 8 \ud835\udefe ) = \u2212S\ud835\udefd\ud835\udefd1s\ud835\udf031s \u2212 eR 4 3 [ 1 + \ud835\udefd1c\ud835\udf031s ( 1 \u2212 3 2 e )] (3.209) To compare numerical values for the roll control derivatives with various combinations of offset and spring stiffness, it is assumed that the flap frequency ratio \ud835\udf06\ud835\udefd and the blade Lock number remain constant throughout. These would normally be set using the corresponding values for the first elastic flap mode frequency and the modal inertia given by Eq. (3.11). The values selected are otherwise arbitrary and uses of the offset-spring model in the literature are not consistent in this regard. We chose to draw our comparison for a moderately stiff rotor, with \ud835\udefe2 \ud835\udefd = 1.2 and S\ud835\udefd = 0.2. Figure 3.20 shows a cross-plot of the flap control derivatives for values of offset e extending out to 0.15. With e= 0, the flap frequency ratio is augmented entirely with the centre spring; at e= 0.15, the offset alone determines the augmented frequency ratio. The result shows that the rotor flapping changes in character as hinge offset is increased, with the flap/control phase angle decreasing from about 80\u2218 for the centre-spring configuration to about 70\u2218 with 15% offset. The corresponding roll and pitch hub moment derivatives are illustrated in Figure 3.21 for the same case. Figure 3.21 shows that over the range of offset-hinge values considered, the primary control derivative increases by 50% while the cross-coupling derivative increases by over 100%. The second curve in Figure 3.21 shows the variation of the hub moment in phase with the flapping. More than 50% of the change in the primary roll moment derivative is due to the aerodynamic moment from disc flapping in the longitudinal direction. These moments could not be developed from just the first mode of an elastic blade and are a special feature of large offset-hinge rotors. Modelling Helicopter Flight Dynamics: Building a Simulation Model 113 Fig. 3.21 Cross-plot of roll control derivatives as a function of flap hinge offset The results indicate that there is no simple equivalence between the centre-spring model and the offset-hinge model. Even with Young\u2019s approximation, where the aerodynamic shear force at the hinge is neglected, the flapping is amplified as shown above. A degree of equivalence, at least for control moments, can be achieved by varying the blade inertia as the offset hinge is increased, hence increasing the effective Lock number, but the relationship is not obvious. Even so, the noticeable decrease in control phasing, coupled with the out-of-phase moments, gives rise to a dynamic behaviour which is not representative of the first elastic flap mode. On the other hand, the appeal of the centre-spring model is its simplicity, coupled with the preservation of the correct phasing between control and flapping and between flapping and hub moment. The major weakness of the centre-spring model is the crude approximation to the blade shape and corresponding tip deflection and velocity, aspects where the offset-hinge model is more representative. The selection of parameters for the centre-spring model is relatively straightforward. In the case of hingeless or bearingless rotors, the spring strength and blade inertia are chosen to match the first elastic mode frequency ratio and modal inertia, respectively. For articulated rotors, the spring strength is again selected to give the correct flap frequency ratio, but now the inertia is changed to match the rotor blade Lock number about the real offset flap hinge. It needs to be remembered that the rigid blade models discussed above are only approximations to the motion of an elastic blade and specifically to the first cantilever flap mode. The blade responds by deforming 114 Helicopter and Tiltrotor Flight Dynamics in all its modes, although the contribution of higher bending modes to the quasi-steady hub moments is usually assumed to be small enough to be neglected. As part of a study of hingeless rotors, Shupe (Refs. 3.36 and 3.37) examined the effects of the second flap bending mode on flight dynamics. Because this mode often has a frequency close to three-per-rev, it can have a significant forced response, even at one-per-rev, and Shupe has argued that the inclusion of this effect is important at high speed. This brings us to the domain of aeroelasticity and we defer further discussion until Section 3.4, where we shall explore higher fidelity modelling issues in more detail. Rotor blades need to lag and twist in addition to flap, and here we discuss briefly the potential contributions of these DoFs to helicopter flight dynamics. Rotor in-Plane Motion: Lead\u2013Lag Rigid or elastic lead\u2013lag blade motion attenuates the in-plane forces on the rotor. On articulated rotors, the rigid-blade lead\u2013lag motion revolves about an offset hinge, necessary to enable the applied torque to rotate the rotor. On hingeless rotors, lead\u2013lag takes the form of in-plane bending. Because the in-plane aerodynamic damping forces are low, it is usual to find mechanical dampers attached to the lead\u2013lag hinge. Additional mechanical in-plane damping is even found on some hingeless rotors. A comprehensive discussion on the significance of lead\u2013lag on blade stability and loads is provided by Johnson in Ref. 3.7. For most flight mechanics analysis, the presence of lead\u2013lag motion contributes little to the overall response and stability of the helicopter. However, there is one aspect that is relevant and needs to be referred to. To aid the discussion, the coupled equations of flap/lead\u2013lag motion are required; for the present purposes, we assume that the flap and lag blade inertias are equal and describe the coupled motion in the simplified form: \ud835\udefd\u2032\u2032 + \ud835\udf062 \ud835\udefd \ud835\udefd \u2212 2\ud835\udefd\ud835\udf01 \u2032 = MF (3.210) \ud835\udf01 \u2032\u2032 + C\ud835\udf01 \ud835\udf01 \u2032 + \ud835\udf062 \ud835\udf01 \ud835\udf01 + 2\ud835\udefd\ud835\udefd\u2032 = ML (3.211) We assume that both the flap (\ud835\udefd) and lead\u2013lag (\ud835\udf01) motion can be approximated by the centre-spring equivalent model as illustrated in Figures 3.6 and 3.22. The direct inertial forces are balanced by restoring moments; in the case of the lag motion, the centrifugal stiffening works only with an offset lag hinge (or centre-spring emulation of centrifugal stiffness). If the lag hinge offset is e\ud835\udf01 , then the frequency is given by \ud835\udf062 \ud835\udf01 = 3 2 ( e\ud835\udf01 1 \u2212 e\ud835\udf01 ) (3.212) The natural lag frequency \ud835\udf06\ud835\udf01 is typically about 0.25 \u03a9 for articulated rotors; hingeless rotors can have subcritical (<\u03a9, e.g. Lynx, Bo105) or supercritical (>\u03a9, e.g. propellers) lag frequencies, but \ud835\udf06\ud835\udf01 should be far removed from \u03a9 to reduce the amount of in-plane lag response to excitation. The flap and lag equations above have a similar form. We have included a mechanical viscous lag damper C\ud835\udf01 for completeness. MF and ML are Modelling Helicopter Flight Dynamics: Building a Simulation Model 115 the aerodynamic flap and lag moments. Flap and lag motions are coupled, dynamically through the Coriolis forces in Eqs. (3.210) and (3.211), and aerodynamically from the variations in rotor blade lift and drag forces. The Coriolis effects are caused by blade elements moving towards and from the axis of rotation as the rotor flaps and lags. Because of the lower inherent damping in lag, the Coriolis moment tends to be more significant in the lag equation due to flap motion. In addition, the lag aerodynamic moment ML will be strongly influenced by in-plane lift forces caused by application of blade pitch and variations in induced inflow. The impact of these effects will be felt in the frequency range associated with the coupled rotor/fuselage motions. In terms of MBCs, the regressing and advancing lag modes will be located at (1\u2212 \ud835\udf06\ud835\udf01 ) and (1+ \ud835\udf06\ud835\udf01 ), respectively. A typical layout of the uncoupled flap and lag modes is shown on the complex eigenvalue plane in Figure 3.23. The flap modes are well damped and located far into the left plane. In contrast, the lag modes are often weakly damped, even with mechanical dampers, and are more susceptible to being driven unstable. The most common form of stability problem associated with the lag DoF is ground resonance, whereby the coupled rotor/fuselage/undercarriage system develops a form of flutter; the in-plane rotation of the rotor centre of mass resonates with the fuselage/undercarriage system. Another potential problem, seemingly less well understood, arises through the coupling of rotor and fuselage motions in flight. Several references examined this topic in the early days of hingeless rotor development (Refs. 3.38, 3.39), when the emphasis was on avoiding any hinges or bearings at the rotor hub to simplify the design and maintenance procedures. Control of rotor in-plane motion and loads through feedback of roll motion to cyclic pitch was postulated. This design feature has never been exploited, but the sensitivity of lag motion to attitude feedback control has emerged as a major consideration in the design of autostabilisation systems. The problem is discussed in Ref. 3.6 and can be attributed to the combination of aerodynamic effects due to cyclic pitch and the powerful Coriolis moment in Eq. 3.211. Both the regressing and advancing lag modes are at risk here. In Ref. 3.40, Curtiss discusses the physical origin of the couplings and shows an example of where the regressing lag mode goes unstable at a relatively low value of gain in a roll rate to lateral cyclic feedback control system (\u22120.2%/s). In contrast, the roll-regressing mode can be driven unstable at higher values of roll attitude feedback gain. The results of Ref. 3.40 and the later Bo105 study by Tischler (Ref. 3.41) give clear messages to the designers of autostabilisers and, particularly, high gain active control systems for helicopters. Designs will need to be evaluated with models that include the lead\u2013lag dynamics before implementation on an aircraft. However, the modelling requirements for specific applications are likely to be considerably more complex than is implied by the simple analysis outlined above. Pitch\u2013flap\u2013lag couplings, nonlinear mechanical lag damping and pre-cone are examples of features of relatively small importance in themselves, but which can have a powerful effect on the form of the coupled rotor/fuselage modes. 116 Helicopter and Tiltrotor Flight Dynamics Of course, one of the key driving mechanisms in the coupling process is the development of in-plane aerodynamic loads caused by blade pitch; any additional dynamic blade twist and pitch effects will also contribute to the overall coupled motion, but blade pitch effects have such a profound first-order effect on flapping itself that it is in this context that they are now discussed. Rotor Blade Pitch In previous analysis in this chapter the blade pitch angle was assumed to be prescribed at the pitch bearing in terms of the cyclic and collective applied through the swash plate. Later, in Section 3.4, the effects of blade elastic torsion are referred to, but there are aspects of rigid blade pitch motion that can be addressed prior to this. Consider a centrally hinged blade with a torsional spring to simulate control system stiffness, K\ud835\udf03 , as shown in Figure 3.24. For simplicity, we assume coincident hinges and centre of mass and elastic axis so that pitch\u2013flap coupling is absent. The equation of motion for rigid blade pitch takes the form \ud835\udf03\u2032\u2032 + \ud835\udf062 \ud835\udf03 \ud835\udf03 = Mp + \ud835\udf142 \ud835\udf03 \ud835\udf03i (3.213) where the pitch natural frequency is given by \ud835\udf062 \ud835\udf03 = 1 + \ud835\udf142 \ud835\udf03 (3.214) where MP is the normalised applied moment and \ud835\udf03i is the applied blade pitch. The natural frequency for free pitch motion (i.e. with zero control system stiffness) is one-per-rev; because the so-called propeller moment contribution to the restoring moment. This effect is illustrated in Figure 3.25 where mass elements along the chord line experience in-plane inertial moments due to small components of the large centrifugal force field. For rigid control systems, \ud835\udf03 = \ud835\udf03i. The control system stiffness is usually relatively high, giving values of \ud835\udf14\ud835\udf03 between 2 and 6 \u03a9. In this range, we usually find the first elastic torsion mode frequency, the response of which can dominate that of the rigid blade component. A similar form to Eq. 3.213 will apply to the first elastic mode, which will have a nearly linear variation along the blade radius. This aspect will be considered later in Section 3.4, but there are two aspects that are relevant to both rigid and elastic blade torsion, which will be addressed here. First, we consider the gyroscopic contribution to the applied moment MP. Just as we found with flap motion earlier in this chapter, as the rotor shaft rotates under the action of pitch and roll moments, so the Modelling Helicopter Flight Dynamics: Building a Simulation Model 117 rotor blade will experience nose-up gyroscopic pitching moments of magnitude given by the expression MP(gyro) = \u22122(p sin\ud835\udf13 + q cos\ud835\udf13) (3.215) The induced cyclic pitch response can then be written as \ud835\udeff\ud835\udf031s = \u22122p \ud835\udf062 \ud835\udf03 \u2212 1 , \ud835\udeff\ud835\udf031c = \u22122q \ud835\udf062 \ud835\udf03 \u2212 1 (3.216) where p and q are the helicopter roll and pitch rates, with the bar signifying normalization by\u03a9. For low blade torsional or swash plate stiffness, the magnitude of the gyroscopic pitch effects can therefore be significant. More than a degree of induced cyclic can occur with a soft torsional rotor rolling rapidly (Ref. 3.42). The second aspect concerns the location of the pitch bearing relative to the flap and lag hinges. If the pitch application takes place outboard of the flap and lag hinges, then there is no kinematic coupling from pitch into the other rotor DoFs. However, with an inboard pitch bearing, the application of pitch causes in-plane motion with a flapped blade and out-of-plane motion for a lagged blade. The additional motion also results in an increased effective pitch inertia and hence reduced torsional frequency. These effects are most significant with hingeless rotors that have large effective hinge offsets. On the Lynx, the sequence of rotations is essentially flap/lag followed by pitch, while the reverse is the case for the Bo105 helicopter (Figures 3.26a and b). The arrangement of the flap and lag real or virtual hinges is also important for coupling of these motions into pitch. Reference 3.7 describes the various structural mechanisms that contribute to these couplings, noting that the case of matched flap and lag stiffness close to the blade root minimises the induced torsional moments (e.g. Westland Lynx). As already noted, any discussion of blade torsion would be deficient without consideration of blade elastic effects and we shall return to these briefly later. However, the number of parameters governing the dynamics is large and includes the location of the elastic axis relative to the mass axis and aerodynamic centre, the stiffness distribution and any pre-cone and twist. Introducing this degree of complexity into the structural dynamics also calls for a consistent approach to the blade section aerodynamics, including chordwise pitching moments and unsteady aerodynamics. These are all topics for further discussion in Section 3.4. Before we proceed with detailing the modelling of the other rotorcraft components, there is one final rotor-related aerodynamic effect to be considered \u2013 ground effect. Ground Effect on Inflow and Induced Power Operating helicopters close to the ground introduces a range of special characteristics in the flight dynamic behaviour. The most significant is the effect on the induced velocity at the rotor and hence the rotor thrust and power required. A succinct analysis of the principal effects from momentum considerations was reported in Ref. 3.43, where, in addition, comparison with test data provided useful validation for a relatively simple theory. Close to the ground, the rotor downwash field is strongly influenced by the surface as shown in Figure 3.27. In Ref. 3.43, Cheeseman and Bennett modelled the ground plane influence with a rotor of equal and opposite strength, in momentum terms, at an equidistance below the ground (Figure 3.27). This mirror image was achieved with a simple fluid source that, according to potential flow theory, served to reduce the inflow vi at the rotor disc in hover by an amount given by \ud835\udeffvi = Advi 16\ud835\udf0bz2 g (3.217) where zg is the distance of the ground below the rotor disc and Ad is the rotor disc area. The rotor thrust, at constant power, can be written as the ratio of the induced velocity out-of-ground effect (oge) to the induced velocity in-ground effect (ige). Reference 3.43 goes on to derive an approximation for the equivalent thrust change in forward flight with velocity V, the approximation reducing to the correct expression in hover, given by Eq. 3.218. Tige Toge = 1[ 1 \u2212 1 16 ( R zg )2/( 1 + ( V vi )2 )] (3.218) 118 Helicopter and Tiltrotor Flight Dynamics (a) (b) Modelling Helicopter Flight Dynamics: Building a Simulation Model 119 120 Helicopter and Tiltrotor Flight Dynamics Figure 3.28 illustrates the variation in normalised thrust as a function of rotor height above ground and forward velocity. Ground effect is most significant in hover, and, below heights of the order of a rotor radius, thrust increments of 5\u201315% are predicted. In forward flight, ground effect becomes insignificant above normalised speeds of 2. Simple momentum considerations are unable to predict any influence of blade loading on ground effect. By combining momentum theory with blade element theory, it can be shown that increasing blade loading typically reduces ground effect such that a 10% increase in blade loading reduces the ige thrust increment by about 10% (Ref. 3.43). Another interesting result from these predictions is that the increase in power required as a helicopter transitions oge is greater than the decrease in power due to the reduction in induced velocity. Figure 3.29, from Ref. 3.43, illustrates the point, showing the variation in power required as a function of forward speed, and reflects practical observations that a power increase is required as a helicopter flies off the ground cushion (Ref. 3.44). Further discussion of ground effect, particularly the effects on nonuniform inflow and hub moments, can be found in Ref. 3.45."
        ]
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure6.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure6.2-1.png",
        "caption": "Figure 6.2. Force and motion do not always act in the same direction. This free-body diagram of the forces and resultant force (FR) on a basketball before release illustrates how a skilled player applies a force to an object (Fh) that combines with the force of gravity (Fg) to create the desired effect. The motion of the ball will be in the direction of FR.",
        "texts": [
            " So casual observation can often lead to incorrect assumptions about the laws of mechanics. We equate forces with objects in contact or a collision between two objects. Yet we live our lives exercising our muscles against the consistent force of gravity, a force that acts at quite a distance whether we are touching the ground or not. We also tend to equate the velocity (speed and direction) of an object with the force that made it. In this chapter we will see that the forces that act on an object do not have to be acting in the direction of the resultant motion of the object (Figure 6.2). It is the skilled person that creates muscle forces to precisely combine with external forces to balance a bike or throw the ball in the correct direction. Casual visual observation also has many examples of perceptual illusions about the physical realities of our world. Our brains work with our eyes to give us a mental image of physical objects in the world, so that most people routinely mistake this constructed mental image for the actual object. The color of objects is also an illusion based on the wavelengths of light that are reflected from an object's surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003406_s00170-015-8329-y-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003406_s00170-015-8329-y-Figure4-1.png",
        "caption": "Fig. 4 Sample melt pool geometry for 2-D FEM simulation of SLM in XYview",
        "texts": [
            " These model has been implemented in Matlab\u2122 and results are presented in later sections. Temperature solutions in the XY plane will be utilized in determining the melt pool geometry. The goal of this work is to utilize predicted and validated temperature distributions to determine the regions of solid, liquid + solid, and liquid phases in order to identify melt pool shape and size. During the SLM process, the laser beam melts the material which then extends to the trailing section of the scanning direction (see Fig. 4). This molten area that follows the laser is referred to as the melt pool, similar to the weld pool observed in welding processes. As the laser beam moves, the melt pool changes in size and shape due to various laser and material properties such as the non-homogeneous laser power output andmaterial porosity. Thematerial outside this melt pool region has either both melted and re-solidified, or is still in powder form. Material can still be in powder form because it has been thermally unaffected or because of incomplete fusion after heating has occurred"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003126_j.jsv.2015.08.002-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003126_j.jsv.2015.08.002-Figure6-1.png",
        "caption": "Fig. 6. Ball/defect interactions. (a) Interaction shown in plane xkzk , (b) interaction shown in plane ykzk , (c) contact force, and (d) defect size (wd and hd correspond to the width and the depth, respectively). This schematic is shown for the interaction between a ball and a defect located in outer raceway. The interaction between a ball and a defect located in inner raceway is similar to that shown in this figure.",
        "texts": [
            " The determination of \u03b4d is important for the calculation of the contact force between the ball and the defect, and correspondingly the vibration responses of the bearing. In most of the available literature [30\u201332,34,35,37,40,42], the ball is modeled as a point mass, and this results in overestimated contact force between a roller and a defect [33]. A proper way to deal with this problem is to take account of the finite size of the ball as it rolls through the defect [33]. In this paper, the model proposed in Ref. [42] is improved by considering the effect of the finite size of a ball on the basis of Ref. [33]. As shown in Fig. 6, defect frame Odxdydzd is established to determine the position of the defect center. The contacting point between a ball and a raceway under normal conditions is Ok, and a frame called contact frame Okxkykzk is established at this point. The zk axis is along the direction of vector rbc, and the yk axis is along the opposite direction of the orbital speed of the ball. Moreover, as shown in Fig. 6(a), vector rbc intersects with the raceway axis of rotation at point m, and the position vector locating the raceway groove center c relative to point m is rmc. Based on the geometry property of the bearing, vector rmc can be described in contact frame Okxkykzk as rmc \u00bc 0 0 rcr3 cos \u03b1 n oT (15) where rc r3 is the third component of vector rcr . In Eq. (15), vector rcr should be described in azimuth frame Oaxayaza, as shown in Fig. 6(a). For any point (such as point p in Fig. 6(b)) on the surface of a ball, the position vector locating this point relative to ball center b can be described in contact frame Okxkykzk as rp \u00bc 0 d 2 sin \u03c6 d 2 cos \u03c6 n oT (16) where \u03c6 is the angle between vector rp and axis zk. Moreover, the position of point p relative to point m can be given as rmp \u00bc rmc7rbc\u00ferp (17) where signs \u201c\u00fe\u201d and \u201c \u201d refer to outer raceway and inner raceway respectively. In Fig. 6(b), vector rmp intersects with the raceway at point q. The geometrical interaction between the ball and the raceway at point p, \u03b4bd, can be determined based on the length of vector rmp and the geometry property of the raceway: \u03b4bd \u00bc rmp R \u03b8R (18) where rmp is the length of vector rmp, and R \u03b8R is the length of vector rmq as a function of the angle between vector rmp and axis zd (i.e., \u03b8R, as shown in Fig. 6(b)). Eq. (18) should be calculated for every point on the ball in plane ykzk, and the maximum positive \u03b4bd (\u03b4bd\u00fe ) is adopted as the geometrical interaction between the ball and the defect: \u03b4d \u00bc max \u03b4bd\u00fe (19) The contact force between the ball and the defect can be obtained by Hertzian contact theory: Qbd \u00bc Kbd\u03b4 1:5 d (20) where Kbd is the Hertzian contact stiffness coefficient. Here, we assume that Kbd is the same as that under normal conditions. Indeed, non-Hertzian contact occurs between the ball and the defect due to the geometrical singularity of the defect",
            " (19), the corresponding contact force between the ball and the defect, Qbd, can be calculated based on Hertzian point contact theory. However, when the ball interacts with the defect, the direction of contact force Qbd is not coincident with the line which connects the ball center b and the original raceway groove curvature center c, and an additional force Qbd1 along axis xk can be decomposed from Qbd. In other words, contact force Qbd can be decomposed into two components, i.e., tangential and normal components (Qbd1 and Qbd2 in Fig. 6(c)) with respect to the original normal raceway. These effects should be considered in the dynamic model to accurately model the behaviors of actual defective ball bearings. Therefore, the contact force is transformed to the original contact frame: Q k bd \u00bc 0 Qbd sin \u03c6 Qbd cos \u03c6 n oT (21) where angle \u03c6 should satisfy Eq. (19). It will be shown in Section 3 that the second component of Q k bd largely influences the orbital speed of a ball and the BPFs. The defect model discussed in Section 2.2 is integrated into the bearing model provided in Section 2",
            "1, the reasonability of the dynamic model for the prediction of the behaviors of actual defective ball bearings and for the calculation of BPFs is discussed. In Section 3.2, parametric studies are carried out to investigate the influences of operating conditions, lubrication characteristics, bearing parameters, and defect sizes on BPFO and BPFI. These factors include shaft speed \u03a9 i, axial load Fa, radial load Fr , friction coefficient \u03bc1 (refer to Fig. 2), ball/cage pocket clearance \u03b4bp, raceway groove curvature factors of inner raceway (f i) and outer raceway (f o), initial contact angle \u03b10, and defect width wd (refer to Fig. 6(d)). The other geometrical parameters of the simulated bearing are listed in Table 1. In Table 1, the ball number, and ball and pitch diameters are the same as those in Ref. [26] for investigating general dynamic motions of rolling ball bearings. As mentioned above, compared with available models for defective ball bearings, cage effects and relative slippage at contacting surfaces are considered in the proposed model. Moreover, the effect of the defect on changes of directions of contact force when a ball rolls through the defect is also taken into account",
            " However, under large radial load conditions (such as Fr\u00bc2000 N) where the skidding is slight, \u0394f varies from 0.077% to 0.56% for BPFO, and changes from 0.015% to 0.4% for BPFI when \u03b10 changes from 10 degree to 30 degree. As discussed in Section 3.1, when a ball rolls through a defect, the orbital speed of the ball varies due to the impacts with the defect. Therefore, the defect size, which influences the orbital speed of a ball, plays an important role in the BPFs calculated by using dynamic models. In this section, the effects of defect width wd (Fig. 6(d)) on BPFs are discussed. As the defect mainly affects the orbital speed of a ball, the bearing investigated in this section is operated at different shaft speeds. Moreover, the bearing is loaded by an axial load of 1000 N. The depth of the maximum orthogonal shear stress, which is the main cause of subsurface fatigue failure [43], is about 0.07 mm when this bearing is loaded by an axial load of 1000 N. Therefore, the defect depth is sect as 0.1 mm to take account of the damage growth after a spall is generated on the raceway [35]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002271_tfuzz.2019.2952832-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002271_tfuzz.2019.2952832-Figure8-1.png",
        "caption": "Fig. 8. The experimental environment of 3-DOF helicopter system",
        "texts": [
            " The distance from the center of 3-DOF helicopter system body to elevation axis is la and lh is the distance from pitch axis to either motor. Vf and Vb are the voltages applied to the front and back motor, respectively. V1 = Vf +Vb represents the sum of the voltages, and V2 = Vf \u2212 Vb denotes the difference between the two voltages. m = mh \u2212 mwlw/la is the effective mass of the 3-DOF helicopter system, g is the gravitational acceleration constant. It should be noted that the pitch and elevation angles are limited to [\u221245\u25e6 + 45\u25e6] and [\u221227.5\u25e6,+30\u25e6], respectively. Furthermore, the experimental environment is given in the following Fig. 8. The external disturbance is generated by utilizing the electric fan that operates at the first gear speed as show in Fig. 8 . Then, by denoting X1 = [x1, x3] T = [\u03b1, \u03b2]T and X2 = [x2, x4] T = [\u03b1\u0307, \u03b2\u0307]T , we have the following 3-DOF helicopter system model  X\u03071 = X2 X\u03072 = F (X) +G(x)U Y = X1 (45) 1063-6706 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. where the expressions of F (x), G(x) and U are given as F (X) = [f1, f2] T = [\u2212mgla cos(x1), 0] T , (46) G(X) = [g1 g2 ] = [ Kf la Je cos(x3) 0 0 Kf lh Jp ] , (47) U = [Vf + Vb Vf \u2212 Vb ] (48) For the simulation example 2, the parameters for the system model are given as Kf = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001708_tia.2009.2023393-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001708_tia.2009.2023393-Figure10-1.png",
        "caption": "Fig. 10. Three kinds of motors with concentrated windings. (a) IPM. (b) Inset. (c) SPM.",
        "texts": [
            " In the concentrated winding motor, the slot harmonic field is very large, and it deeply enters into the rotor because of the wide slot pitch. It must cause large eddy-current loss of the magnet. On the other hand, in the distributed winding motor, this harmonic field exists only at the surface of the rotor because of the short slot pitch. This must be the reason why the eddy-current loss caused by the slot harmonics is very small in the distributed winding motor. Next, the loss variation due to the rotor shape is investigated. Three kinds of rotors are considered as shown in Fig. 10. Fig. 10(b) shows the inset type, and Fig. 10(c) shows the surface permanent magnet (SPM) type. The volume, width, and number of divisions of the magnets are identical. The stator cores and windings are also identical. Fig. 11 shows the classified losses due to their origins. The losses due to the slot harmonics show large differences among themselves, while the other losses are nearly the same. The rotor core loss decreases as the magnet is located near the rotor surface. The magnet eddy-current loss of the inset-type motor is the largest among the three motors",
            " However, it is clarified that the main part of the magnet eddy-current loss in the IPM motor is caused by the variation of the total magnetic path with the rotation, which is expressed by the magnetic circuit. On the other hand, in the case of the SPM motor, this effect is small because the permeance distribution of the rotor along the peripheral direction is almost uniform. In this case, the magnet eddy-current loss must be mainly produced by the regional variation of the flux density due to the stator slot opening. The loss in the inset-type motor shown in Fig. 10(b) is caused by both of these effects. Losses in permanent-magnet synchronous motors with concentrated windings were investigated using the 3-D finiteelement method, considering carrier harmonics of PWM inverters and a simple linear magnetic circuit. The eddy-current loss of the permanent magnet in the concentrated winding motor is much larger than that in the distributed winding motor. Furthermore, it increases when the magnet is located on the rotor surface. In this case, the magnet eddy-current loss is mainly produced by regional variation in the flux density due to the stator slot opening"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003546_tmag.2015.2446951-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003546_tmag.2015.2446951-Figure2-1.png",
        "caption": "Fig. 2. DC and PM flux paths in a simplified model with linear material characteristics. (a) Idc = 0A. (b) No PM, Idc > 0A. (c) PM, Idc > 0A.",
        "texts": [
            " the slot area is divided into four equal parts. The DC winding is excited to produce alternate north and south poles. Permanent magnets, magnetized in a direction parallel to the magnet circumferential edge, are placed in all the slot openings between two adjacent stator poles with alternate magnetization directions such that their flux path is in opposite direction to that of the DC excitation flux of the same stator pole. The basic operating principle can be explained using the simplified model in Fig. 2, assuming a linear magnetic circuit. On open-circuit, Fig. 2 (a), no flux-linkage variation with rotor position will be observed in the coil since the magnet flux will not link with the rotor. The constant magnet flux links the coil only on the salient stator pole and consequently no electromotive force (EMF) is induced in the coil. If the magnets are removed and the core is excited by a coil, its flux will link both the rotor and stator via the air-gap, EMF will be induced in the coil and theoretically electromagnetic energy conversion can occur, Fig. 2 (b). When both coil current and PM are present, Fig. 2 (c), flux from both sources will link both the rotor and stator and thus contribute to the induced EMF in the coil. The PM flux now links the stator and rotor via the air-gap because of the magnetic pull between both excitation fields. This same principle applies to the three phase machine under the influence of DC and armature currents. It is worth mentioning that the amount of the PM flux that links both stator and rotor will depend on the magnitude of the currents and also on the saturation of the magnetic circuit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.48-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.48-1.png",
        "caption": "Fig. 4.48",
        "texts": [
            " The bending moments cause the deflections w(x) and v(x), whereas the normal force causes only a displacement u(x) in the direction of the beam axis. These deformations may be superimposed. Note that the deformation due to the normal force is usually much smaller than the deformation caused by the bending moments. Consequently the change in length of the beam may be neglected and the beam may be considered to be rigid with respect to tension/compression. As an example let us consider a column with a circular cross section (radius r) that is subjected to an eccentrically acting force F (Fig. 4.48a). This is statically equivalent to the system of the same force F with the action line equal to the x-axis and the moment MB = r F (Fig. 4.48b). If we neglect the weight of the column, then the stress resultants N and My = MB are independent of x: N = \u2212 F, M = MB = r F. The bending moment about the z-axis is equal to zero: Mz = 0 (ordinary bending). With A = \u03c0 r2 and I = \u03c0 r4/4 (see Table 4.1), the normal stress follows from (4.54b): \u03c3 = \u2212 F \u03c0 r2 + r F 4 \u03c0 r4 z = F \u03c0 r2 [ \u2212 1 + 4 z r ] . It is shown in Fig. 4.48c. The maximum stress is found at z = \u2212r: |\u03c3|max = 5F \u03c0 r2 . 4.8 Bending and Tension/Compression 173 According to (1.18), the change of length \u0394l of the beam due to the compressive force F is given by \u0394l = \u2212 F l EA . The deflection of point B due to the moment M0 = r F can be taken from Table 4.3: wB = \u2212 M0 l 2 2EI = \u2212 r F l2 2EI . Inserting A and I, the ratio between \u0394l and wB is found to be \u0394l wB = r 2 l . As a numerical example, we choose l/r = 20 which yields \u0394l/wB = 1/40. Hence, the shortening of the beam is small as compared with the deflection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002882_j.commatsci.2018.06.019-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002882_j.commatsci.2018.06.019-Figure8-1.png",
        "caption": "Fig. 8. Single-pass grain structure during the building process without bulk nucleation. (a) and (b): the IPFOMs with respect to the building direction; (a): center plane and (b): cross-section. (c): the (1 0 0) PF calculated from (a).",
        "texts": [
            " The IPFOMs and PFs are all generated using the Matlab toolbox MTEX. The color key of the IPFOMs throughout this work is shown in Fig. 7. We will first discuss a simulation without any bulk nucleation (by setting the N0 to be zero) to verify the epitaxial nucleation and competitive growth mechanism captured by the CA method; then the more complicated cases with the bulk nucleation will be discussed. The grain structure examined at the center plane of the built track and a cross section during the building process are shown in Fig. 8a and b. The fusion line (black dotted line) is defined as the partition line between un-melted and melted metal when examining a 2D section. As can be seen in Fig. 8a and b, the epitaxial nucleation initiates at the fusion line and the grains grow across the fusion line. In Fig. 8a, it is observed that the columnar grains dominate the grain structure and tend to grow perpendicular to the moving solidification front (orange dashed line). At the cross-section, although many grains seem to be equiaxed, they are actually the columnar grains growing into the crosssection plane. The competitive growth mechanism can be observed in Fig. 8a; some grains (e.g., grain B) are outgrown by more \u201cfavored\u201d grains (e.g., grain A) whose \u23291 0 0\u232a directions is better aligned the local temperature gradient direction (the local moving direction of the solidification front). To demonstrate this, the (1 0 0) PF calculated from the IPFOM in Fig. 8a is plotted in Fig. 8c along with the individual orientations of grain A and B. A fiber texture is observed in Fig. 8c where the grains have one of their \u23291 0 0\u232a axes aligned with the white dashed line (referred as the fiber) in the BD-SD plane, while the other two \u23291 0 0\u232a axes are free, forming a band across the pole figure. Similar fiber texture is also reported by the experimental work of [35]. The fiber texture is due to the competitive growth which results in the preference of the \u23291 0 0\u232a directions towards the local moving direction of the solidification front. It can be observed in Fig. 8c that a typical dominating grain (grain A) has its orientation aligned with the fiber, while a typical grain being outgrown (grain B) has its orientation deviating from the fiber. The effects of bulk nucleation parameters (Fig. 4), N0 and T\u0394 c, on the grain structure are investigated; T\u0394 \u03c3 is fixed as a small number in the following discussion because we find its effects on the grain structure are relatively insignificant. Before the discussion of the effects of bulk nucleation, we use Hunt\u2019s CET model [15] to predict the grain morphology according to the \u201cG-V condition\u201d of the simulated thermal history"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002022_s11661-015-2864-x-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002022_s11661-015-2864-x-Figure1-1.png",
        "caption": "Fig. 1\u2014Specimen geometry used for load increase tests.",
        "texts": [
            " For preparation of process parameters, SLM AutoFab software (Marcam Engineering GmbH) was used. During processing, the substrate platform was heated to a constant temperature of 473 K (200 C) to minimize the evolution of residual stresses. All samples used for fatigue tests were fabricated with a layer thickness of 30 lm in z-direction, thus the build-direction was parallel to the loading axis. The specimen geometry used for the CT-scans and the subsequently load increase tests is depicted in Figure 1. These samples were taken from cuboids with dimensions of 8 9 28 9 12 mm3 using electro-discharge machining. For the experimental investigations focusing on the internal defects, four different conditions have been considered as listed in Table I. In order to obtain a precise picture regarding the porosity, five samples per condition have been characterized by computed tomography. The first condition was Ti-6-4 directly from SLM processing without any heat treatment, in the remainder of the text referred to as \u2018\u2018as-built\u2019\u2019"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.2-1.png",
        "caption": "Fig. 3.2 Global kinematics of a vehicle in planar motion",
        "texts": [
            "1007/978-94-017-8533-4_3, \u00a9 Springer Science+Business Media Dordrecht 2014 47 48 3 Vehicle Model for Handling and Performance underlying hypotheses impose some restrictions on its applicability, which a vehicle engineer should be well aware of. Basically, a vehicle model (like most physical models) is made of three separate sets of equations \u2022 congruence (kinematic) equations; \u2022 equilibrium equations; \u2022 constitutive (tire) equations. It may be convenient to consider first the whole vehicle and then the suspensions. The analysis of the vehicle kinematics is based on Fig. 3.2. It is good common practice to define the body-fixed reference system S = (x, y, z;G), with unit vectors (i, j,k). It has origin in the center of mass G and axes fixed relative to the vehicle. The x-axis marks the forward direction, while the y-axis indicates the lateral direction. The z-axis is vertical, that is perpendicular to the road, with positive direction upward. The motion of the vehicle body may be completely described by its angular speed and by the velocity VG of G, although any other point would do as well",
            "2 Vehicle Congruence (Kinematic) Equations 49 to the assumed planarity of the vehicle motion, VG is horizontal and is vertical. More precisely VG = ui + vj (3.1) and = rk (3.2) The component u is called vehicle forward velocity, while v is the lateral velocity. The quantity r is the vehicle yaw rate. Like in (2.1), the velocity of any point P of the vehicle body is given by the well known formula VP = VG + \u00d7 GP (3.3) Therefore, the kinematics of the vehicle body is completely described by, e.g., the three state variables u(t), v(t) and r(t), as shown in Fig. 3.2. Under normal operating conditions u > 0 and u |v| and u |r|l (3.4) Let S0 = (x0, y0, z0;O0) be a ground-fixed reference system, as shown in Fig. 3.3, with unit vectors (i0, j0,k0). Therefore i0 \u00b7 i = cos\u03c8 and j0 \u00b7 i = \u2212 sin\u03c8 (3.5) 50 3 Vehicle Model for Handling and Performance Fig. 3.3 Ground-fixed coordinate system and yaw angle \u03c8 where \u03c8 is the vehicle yaw angle. Accordingly VG = x\u03070i0 + y\u03070j0 = ui + vj (3.6) with x\u03070 = u cos\u03c8 \u2212 v sin\u03c8 y\u03070 = u sin\u03c8 + v cos\u03c8 \u03c8\u0307 = r (3.7) The yaw angle \u03c8 of the vehicle, at any time t = t\u0302 , is given by \u03c8(t\u0302 ) = \u03c8(0) + \u222b t\u0302 0 r(t)dt (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003815_s102745101901004x-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003815_s102745101901004x-Figure1-1.png",
        "caption": "Fig. 1. FANUC robot operating system of WAAM-CMT and three-dimensional schematic diagram.",
        "texts": [
            " In this regard, a large number of researchers have shown interest and a lot of research on process parameters, process patterns; and consequently translate into rapid development of equipment technology [7\u201213]. Based on the principle of cold metal process (CMT) and milling machine path conversion of CNC machine tools, a set of WAAM system was established. With the help of the off-line 3D route simulation software in the system, the 3D model path was constructed; supported with high precision and flexibility FANUC robot operating system, different shaped models of aluminum alloy through WAAM were prepared to study the stability of WAAM-CMT system. Figure 1 presents the FANUC robot operating system of WAAM-CMT and three-dimensional schematic diagram. Its main components include 6-axis FANUC robot, robot control unit, CMT welder, single-axis positioner, heating station, air compressor and computer, etc. JOURNAL OF SURFACE INVESTIGATION: X-RAY, SYNCHRO The working radius of FANUC robot is 1035mm, welding torch is attached at the end of sixth axis of FANUC robot and keeps coaxial with it. In addition, the wire feed system of CMT welder can maneuver the welding torch so as to deposit liquid metal layer along the 3D profile based on the shape of the field parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure16-1.png",
        "caption": "Fig. 16. CAD model of (a) outer race, (b) inner race and (c) cage and (d) inner race with cage and balls.",
        "texts": [
            " The flexible coupling is designed in the model by attaching a bushing between the rotor and motor shafts. A small parallel misalignment of 1 mm is introduced in the model by shifting the axis of rotor and axis of connecting shaft of the motor. The rotor shaft is supported by two deep groove ball bearings which are mounted on two pedestals. Like the experimental setup, a good bearing is installed in the near end and the faulty/test bearing is mounted at the far end of the motor. The inner races of the bearings (Fig. 16(b)) are constrained to move with the rotor shaft by attaching a fixed joint (ADAMS nomenclature for the constraint) between the rotor shaft and the inner race. A loader is attached near the test bearing to impart radial load. The motion of the loader is constrained by fixed connection/ joint between the rotor shaft and loader. The outer races (Fig. 16(a)) are connected to spring damper systems in horizontal and vertical directions in order to model structural stiffness and damping of bearing mounts. To resist the axial forces andmoments on the outer race, a bushing with high stiffness and damping in the three mutually perpendicular directions to both bearings is used between the outer races and the corresponding pedestals. These bushings are not shown in Fig. 16(a) to maintain clarity of the figure. The cage (Fig. 16(c)) is modelled as a floating body which accommodates balls at constant angular spacing. The cage does not contact with the inner as well as outer races. The bearing model permits slip between the ball and races, and ball and cage. It is modelled by giving suitable parameters in definition of contact force between the connecting bodies. The calculations of contact and friction forces are given in the next section. The balls (Fig. 16(d)) are modelled as rigid bodies which are held inside the cage. Contact constraints are defined between each ball and the cage which permits a small play (clearance) between each ball and the cage groove. Likewise, contact constraints are defined between each ball and both the inner and outer races. The contacts between the balls and races and ball and cage are considered to be of solid to solid type. The contact stiffness and damping are determined using Hertzian contact theory, in which the load deflection factor is dependent on the curvatures of the mating surfaces and the material parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002277_j.jmapro.2020.08.060-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002277_j.jmapro.2020.08.060-Figure1-1.png",
        "caption": "Fig. 1. 3 + 2-axis Addilan machine [18].",
        "texts": [
            " In this paper, all the parameters that can influence the obtained properties or the productivity have been considered. The WAAM technique, based on GMAW, was used to manufacture walls with different strategies in ER70S-6 mild steel (EN ISO 14341-A - G 42 3 M21 3Si1). Commercially produced ER70S-6 wire with a diameter of 1.2 mm was employed as the deposited material (the elemental composition of the wire, as provided by the supplier, is given in Table 1). Furthermore, 8 mm S235JR steel (DIN ST37-2) plates were used as a substrate. To carry out the experiments, an automatic welding system was utilized. Fig. 1 shows the used 3 + 2-axis Addilan WAAM machine [18] with a GMAW welding system, composed of a Titan XQ 400 AC puls generator and an M drive 4 Rob5 XR RE wire feeder from the EWM welding manufacturer. This machine has high versatility due to its particular architecture and the open CNC software. In addition, it offers the opportunity to manufacture parts utilizing additional AM technologies, such as WAAM-based Gas Tungsten Arc Welding (GTAW) or WAAM-based Plasma Arc Welding (PAW). This machine is also equipped with a close chamber which allows for the manufacturing of parts in reactive materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure2-1.png",
        "caption": "Fig. 2. A three-dimensional model of helical gears.",
        "texts": [
            " The tooth profiles of spur gears go into and out of contact along thewhole face width at the same time. This will therefore result in a sudden loading and sudden unloading on the teethwhen tooth profiles go into and out of contact. As a result, vibration and noise are produced. However, the tooth surfaces of two engaging helical gears contact on a straight line inclined to the axes of the gears. The length of the contact line changes gradually from zero to maximum and then changes from maximum to zero (see in Fig. 2). This makes the vibration characteristics of helical gears different from those of spur gears. Obviously, the mesh stiffness of helical gears cannot be calculated as same as spur gears due to the existence of helix angle. However, if helical gears are divided into some independent thin pieces whose thickness is dy (see in Fig. 3), the helical gears can be considered as a series of staggered spur gears with no elastic coupling since they are usually negligible for narrow-faced gears with low helix angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000842_robot.2006.1641979-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000842_robot.2006.1641979-Figure7-1.png",
        "caption": "Fig. 7. Grasping a spherical object",
        "texts": [
            " These terms typically consist of the dot-product of one or more of the coordinate system axes xH , yH , zH and a vector v to which it should be aligned either parallel or vertical, within a tolerance specified by the weight w1 of the term: w1 \u00b7 \u2223\u2223|xH \u00b7 v| \u2212 1 \u2223\u2223 One common special penalty term aligns the vector G \u2212 H to xH , thus causing the end-effector to point towards the center of the target object. Another possibility is to make G\u2212 H vertical to one of the axes of the target object coordinate system xG, yG, zG, thus causing the end-effector to be aligned parallel to one of the coordinate planes: w2 \u00b7 (\u2223\u2223(G \u2212 H) \u00b7 xH \u2223\u2223 \u2212 1 ) w3 \u00b7 \u2223\u2223(G \u2212 H) \u00b7 yG \u2223\u2223 Using these components, goal function templates for a variety of target objects, such as cylindrical, box-shaped, spherical and planar shapes, have been defined. For example, a goal function for a spherical object as depicted in Figure 7 might be defined as follows: \u03c6sphere = \u2016G \u2212 H\u2016 + 50 \u2223\u2223(G \u2212 H) \u00b7 xH \u2212 1 \u2223\u2223 To model the goal region, a threshold value g needs to be defined for the goal function. A value below g implies that the given configuration is a part of the goal region. While goal functions following the scheme presented above are easily defined and produced good results in our experiments, careful tuning of the penalty weights is necessary to ensure that the resulting function is largely free of local minima. Determining alternative methods for modeling the goal region that are local-minima free is likely to improve the planning algorithm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.74-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.74-1.png",
        "caption": "Fig. 17.74a,b Starting examples for induction machines: (a) star delta starting and (b) starting with the help of a start-up transformer",
        "texts": [
            " In the star circuit the voltage is 1/ \u221a 3 times the voltage in the delta circuit. Therefore, the current flowing through the branches is also 1/ \u221a 3 times the current flowing in delta circuit. As a result the values of the consumed power, the line currents, and the torque of the machine are reduced by 1/3 compared to the delta connection. In M 1 2 3 4 \u03a9 a) M 1 2 3 \u03a9 b) some cases, the machine can be started with the help of a starting transformer, which allows the voltage level to be increased until the machine has run up completely (Fig. 17.74). For low-power electric machines the so-called softstart techniques are used. These methods are applied in order to protect shafts and gears from torque surges. For three-phase rotating machines a converter that generates a linearly variable magnitude and frequency of the voltage at the clamps of the drive is used. A soft start can also be realized by the parallel connection of several resistance levels with the rotor of the machine. Changes in the resistance levels cause the machine to start-up stepwise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003274_j.optlastec.2020.106477-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003274_j.optlastec.2020.106477-Figure4-1.png",
        "caption": "Fig. 4. Laser scanning strategies for SLM simulation, (a) stripe scanning strategy, (b) chessboard (island) scanning strategy.",
        "texts": [
            "7, and the scanning speed is 600 mm/s. Two laser powers at 160 W and 200 W are considered. Also, two laser scanning strategies are adopted, and they are chessboard (or island) scanning trajectory and stripe scanning trajectory. As such, a total of 4 cases are simulated, and they are: Case 1, 160 W laser power + chessboard scanning; Case 2, 160 W laser power + stripe scanning; Case 3, 200 W laser power + chessboard scanning; and Case 4, 200 W laser power + stripe scanning. Detailed scanning trajectories are illustrated in Fig. 4, with the stripe scanning patterns shown in Fig. 4(a) and the chessboard scanning patterns shown in Fig. 4(b). It can be seen from Fig. 4(a) that four adjacent layers of stripe scanning are shown, and they are labeled as 0\u00b0, 30\u00b0, 60\u00b0, and 90\u00b0 receptively. For each additional layer deposited on top of the 90\u00b0 layer, the angle increases by 30\u00b0. Meanwhile, the chessboard scanning patterns in Fig. 4(b) indicates that each layer is divided into small rectangular regions (2.5 \u00d7 1.5 mm), and stripe scanning is applied to each small rectangular region. Fig. 5 shows the stress distributions of the deposited material under the combination of 200 W laser power and stripe scanning strategy (i.e., Case 4). As indicated in Fig. 3, the length and the width of the simulation area are 5 mm and 3 mm, respectively. The height of simulation area varies from 0.4 mm to 2 mm at different time moment of the SLM process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002748_j.triboint.2015.07.021-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002748_j.triboint.2015.07.021-Figure1-1.png",
        "caption": "Fig. 1. Coordinate systems used.",
        "texts": [
            " Considering the geometric relationship and interaction between raceways, balls, cage and lubricant, differential equations governing the motions of bearing elements are established. In this model, the motion of each ball is considered with six degrees of freedom, the inner race motion with three degrees of freedom, and the cage has one rotational degree of freedom. The frictional forces at contact interfaces are calculated based on EHD lubrication theory. The skidding behaviors of angular contact ball bearing under different operating conditions are investigated. In order to describe the motion of the rolling element, three coordinate systems are established as shown in Fig. 1. The first coordinate system (O-xyz) is fixed at the bearing center with z axis coinciding with the bearing axis; the second coordinate system (O-x0y0z0) is a moving coordinate system axis z0 axis parallel with bearing axis and the coordinate origin attached to the center of rolling element, rotating around z axis with speed \u03c9c. In this coordinate, the ball has three angular velocity components \u03c9x0 , \u03c9y0 , \u03c9z0 around x0, y0 and z0 axis, respectively. The third one is also a moving coordinate system x\u2033y\u2033z\u2033 with x\u2033-axis and y\u2033-axis lying in the plane of the contact patch between ball and raceways and z\u2033-axis perpendicular to the contact patch",
            "y\u2033 o \u00bc \u03c9x0 \u00f0r2o x\u20332o \u00de1=2 \u00f0r2o a2o\u00de1=2\u00fe \u00f00:5d\u00de2 a2o h i1=2 8>>>>< >>>>: \u00f07\u00de Similarly, at any point (x\u2033i, y\u2033i) in the ball/inner-raceway contact elliptical spot, the sliding speed due to translational speed differential is given by: \u0394V !x\u2033 i \u00bc 0:5dm\u00f0\u03c9i \u03c9c\u00de \u03c9y0 sin \u03b1i\u00fe\u03c9z0 cos \u03b1i\u00fe\u00f0\u03c9i \u03c9c\u00de cos \u03b1i \u00f0r2i x\u203321 \u00de1=2 \u00f0r2i a2i \u00de1=2\u00fe \u00f00:5d\u00de2 a2i h i1=2 \u0394V !y\u2033 i \u00bc \u03c9x0 \u00f0r2i x\u203321 \u00de1=2 \u00f0r2i a2i \u00de1=2\u00fe \u00f00:5d\u00de2 a2i h i1=2 8>>>>< >>>>: \u00f08\u00de Besides, due to the rotational speed differential, the balls also spin on the raceways as shown in Fig. 4. On the ball/outer raceway contact elliptical area, the spinning velocity can be deduced from Fig. 1 as follows, \u03c9!o s \u00bc \u00f0\u03c9y0 cos \u03b1o \u03c9z0 sin \u03b1o\u00de \u03c9c sin \u03b1o \u00f09\u00de Similarly, on the ball/inner raceway contact elliptical area, the spinning velocity is obtained as follows, \u03c9!i s \u00bc \u00f0\u03c9y0 cos \u03b1i \u03c9z0 sin \u03b1i\u00de\u00fe\u00f0\u03c9i \u03c9c\u00de sin \u03b1i \u00f010\u00de Finally, we can get the skidding velocity vector resultant from sliding and spinning velocities as shown in Fig. 4: \u0394V ! i=o\u00f0x\u2033; y\u2033\u00de \u00bc \u00f0\u0394Vx\u2033 i=o \u03c9i=o s y\u2033\u00de i!\u2033\u00fe\u00f0\u0394Vy\u2033 i=o\u00fe\u03c9i=o s x\u2033\u00de j!\u2033 \u00f011\u00de The calculation of traction forces is done in the moving coordinate system x\u2033y\u2033z\u2033 as shown in Fig. 1. The friction forces and moments for elliptical contact are calculated based on EHD lubrication model. The traction forces in a lubricant film results from shearing action of lubricant. As the oil film thickness is extremely small between the contact surfaces, the assumption is made that the sliding velocity across film thickness changes linearly. The shear stress in the lubricant film can be determined as: \u03c4\u00f0x\u2033; y\u2033\u00de \u00bc \u03b7\u00f0x\u2033; y\u2033\u00de\u0394Vi=o\u00f0x\u2033; y\u2033\u00de h \u00f012\u00de Owing to high pressure in contact areas and temperature variation resulting from the frictional heat, the lubricant viscosity changes greatly",
            " 5b the contact force acted on the ball by cage pillar can be expressed as: Fjc \u00bc kcage\u00f0\u03b8cage \u03b8jc\u00de dm 2 \u00f019\u00de The total contact force acted on the cage by all the balls can be formulated as: Fcage \u00bc XN j \u00bc 1 kcage\u00f0\u03b8jc \u03b8cage\u00de dm 2 \u00f020\u00de where, \u03b8jc is the position angle of the jth ball at time t, and \u03b8cage is the angle that the cage has rotated at time t. So \u00f0\u03b8jc \u03b8cage\u00de dm=2 is the relative displacement of the jth ball with respect to cage. Each ball must overcome a viscous drag force imposed by the lubricant-air mixture within the bearing cavity owing to its orbital rotation. The viscous drag force acting on the ball can be calculated as follow [33], Fd \u00bc \u03c0 32 Cd\u03c1e\u00f0Dmd\u03c9jc\u00de2 \u00f021\u00de where \u03c1e is the equivalent density of the lubricant\u2013air mixture in bearing cavity; Cd is the drag coefficient, which can be determined referring to [34]. As shown in Fig. 1, each ball rotates not only about the bearing axis (z-axis in the xyz-frame) with speed \u03c9c, but also about the three axes in the moving coordinate system (x0y0z0). The differential equations of motion describing the ball rotation around x0, y0 and z0 axes can be derived by using Euler\u2019s equations as follows, Mx0 \u00bc I\u00f0 _\u03c9jx0 \u03c9jc\u03c9jy0 \u00de \u00f022\u00de My0 \u00bc I\u00f0 _\u03c9jy0 \u00fe\u03c9jc\u03c9jx0 \u00de \u00f023\u00de Mz0 \u00bc I _\u03c9jz0 \u00f024\u00de where I\u00bc2mr2/5 is the rotational inertia of a ball. The friction moment terms Mx', My' and Mz' in the differential equations can be calculated in terms of traction forces and moments given in Section 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000378_a:1021153513925-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000378_a:1021153513925-Figure11-1.png",
        "caption": "Figure 11 Distribution of residual stresses during direct laser metal powder deposition (laser power: 600 W, scanning speed: 10 mm/s): (1) \u03c4 = 12.2 s and (2) \u03c4 = 28.4 s.",
        "texts": [],
        "surrounding_texts": [
            "The distribution of residual stresses obtained by finite element modeling resulting from the use of 10 mm/s scanning speed and 600 W laser power are shown in Figs 11 and 12. Residual stresses were also investigated with the x-ray diffraction technique. X-ray residual stress calculations were undertaken perpendicular to the direction of the line builds using the sin2 \u03c8 method [18]. The technique is not described here in detail as the theoretical background and basic principles have been recently summarized [19]. The distribution of residual stresses within a single layer obtained by finite element modeling was compared with that obtained by x-ray diffraction technique showing satisfactory agreement (Fig. 13). The figure indicates that there is a strong variation in the level of residual stresses inside the deposited layers. The distribution of residual stresses is tensile within the center of the layers and compressive towards the edges. Moreover, immediately outside the melt-pool the stress in the heat-affected zone is tensile. It can be expected that this will revert to compressive stress as the distance from the melt track increases. However, due to the time-consuming nature of x-ray diffraction technique, this detail was not measured, but is confirmed by the finite element modeling (please see Figs 11 and 12). The effect of subsequent layers deposition on the residual stresses distribution is shown in Fig. 14. The sample was allowed to cool below 50\u25e6C between each subsequent build in order to eliminate any preheating effect. The data presented in Fig. 14 indicate a distribution of stresses within the first layer (left) similar to that plotted in Fig. 13. However, there is a progressive increase in the level of tensile residual stresses as subsequent layers are deposited. In addition, in the case of subsequent layers deposition, transverse cracks (i.e. perpendicular to the direction of laser scan (Fig. 15)) as well as longitudinal cracks (i.e. parallel to the direction of laser scan (Fig. 16)), were detected. This can be explained by a stepwise increase in the residual stresses with each successive, overlapping laser track [19]. We deliberately designed experiments in which each subsequent deposited layer was allowed to cool below 50\u25e6C before carrying out the following pass. This was to avoid the effect of preheating on the residual stresses. However, cracking can be avoided by preheating the specimen, but also reduces the cooling rate. The mechanism that prevents cracking by preheating increases the ductility of the MONEL 400-alloy. The effect of a preheating treatment to 400\u25e6C and post-heat treatment to 600\u25e6C for 1 hour is shown in Figs 17 and 18, respectively. When preheated to 400\u25e6C, the residual stresses are reduced to about +400 MPa. After a stress-relieving treatment at 600\u25e6C, the residual tensile stresses are further reduced to about +200 MPa. These results suggest that shrinkage in the melt-zone produces residual tensile stresses and that stress-relieving could reduce those values."
        ]
    },
    {
        "image_filename": "designv10_1_0000506_0954405981515590-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000506_0954405981515590-Figure1-1.png",
        "caption": "Fig. 1 Residual stress distribution in welds. (a) Cross-section of a single bead on plate. (b) Graphical representation of the stress distribution through the weld and substrate (A\u2013A) showing that compressive stresses are at their maximum in the top of the weld (maximum heat input). This changes to tensile stress further from the point of heating, reaching a maximum at the base of the weld. (c) Distribution of stresses in the plate surface (x\u2013x) range from compressive (+) stress in and about the weld to balancing tensile (\u00b9) stress away from the weld",
        "texts": [
            " The weld, and material in the immediate vicinity of the weld, having been subjected to greater heating, undergo greater thermal expansion than regions more remote from the heat source; hence contraction is greater once heat is removed. As shrinkage occurs, so tensile stresses are exerted in regions in and about the weld. Further from the weld, these tensile forces tend to be compressive in the region where plastic yielding has occurred, caused by thermal stress and a softening of the material (10) (Fig. 1). Temperature variations within a part, and the degree of cooling experienced, will also be influential in the generation of internal stresses and the resulting strength of the structure. Where a greater variation in temperature exists between the weld and the substrate, cooling will be more rapid and may influence the formation of the internal grain structure of the deposited weld bead. The severity of cooling may be influential in the degree of plastic/elastic deformation that is achieved. Rapid cooling may result in the formation of a brittle structure which, when subjected to tensile forces caused by cooling contraction, may generate cracking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003921_j.actamat.2015.01.063-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003921_j.actamat.2015.01.063-Figure8-1.png",
        "caption": "Fig. 8. Movement of intersection points of different dendrite domains with orientation for (a) the x-, (b) y-, and (c) z-axis rotations.",
        "texts": [
            " Bearing the variation in the values of cosw in mind, one can see that the intersections of the dendrite domains have some connections with the results we presented in Figs. 4 and 5. Therefore, to show the underlying mechanism on the distributions of Vd and Gd under different rotation manners, the change in the number and location of the intersection should be checked. By using the geometric model of Rappaz et al. [24\u201326], the movements of intersection points of different dendrite domains with n when the sample is rotated around the x-, y-, and z-axis were calculated and shown schematically in Fig. 8, respectively. At the initial orientation angle n = 0 , the boundaries of different dendrite domains are illustrated by the dash-dotted lines. There are two intersections locating at the center positions on the two sides of the weld pool, as the solid triangles present. With the increase of n from 0 to 45 by every 15 increment, the variations in the position of the intersection points for the three kinds of rotation are different. For the x-axis rotation, Fig. 8(a), the left intersection point, at which the \u00bd0 10 ; [100], and [001] dendrite domains meet, moves to upper left side and finally leaves the pool, while the right one shifts to the lower left and stops at the centerline. When nx reaches 45 , only this intersection exists. For the z-axis rotation, Fig. 8(c), both of the intersections move nearly horizontally to the right side with the increase of n and only the left one exists finally at the centerline when nz reaches 45 . The situation for the y-axis rotation, however, is quite different. The two intersection points shift upwards or downwards with ny when the rotation is performed clockwise or counterclockwise and disappear when ny reaches 45 or 45 . The most obvious feature of this rotation manner that differs from the other two is that the intersection points can be removed entirely when ny is either 45 or 45 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000509_tcst.2002.804120-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000509_tcst.2002.804120-Figure1-1.png",
        "caption": "Fig. 1. Planar vertical takeoff and landing aircraft.",
        "texts": [
            " A vertical takeoff and landing (VTOL) aircraft, such as the Harrier (YAV-8B), is a highly maneuverable jet aircraft. This aircraft has two modes of operations: forward flight mode as a fixed-wing jet aircraft and maneuvering (hovering) mode using reaction jets. In addition to these two modes of operation, the Harrier has a transition mode between hovering flight and forward flight. We are interested in controlling the VTOL aircraft in the hovering mode (lateral motion control). Therefore, we consider a prototype PVTOL aircraft model. The PVTOL aircraft shown in Fig. 1, has a minimum number of states and inputs but retains many of the features that must be considered when designing control laws for a real aircraft such as the Harrier. The aircraft state is simply the position , of the aircraft center of mass, the roll angle of the aircraft, and the corresponding velocities , , . The control inputs and are, respectively, the thrust (directed out the bottom of the aircraft) and the rolling moment about the aircraft center of mass. In a PVTOL aircraft, the roll moment reaction jets in the wingtips create a force that is not perpendicular to the -body axis. Thus, the production of a positive rolling moment will also produce a slight acceleration of the aircraft to the right. As will be demonstrated, this phenomenon makes the aircraft nonmin- imum phase. From Fig. 1, and by using Newton\u2019s law, the dynamic model of the PVTOL aircraft can be obtained as (22) (23) (24) where is a small coefficient that characterizes the coupling between the rolling moment and the lateral force, , on the aircraft. For simplicity, we scale this model by dividing (22), (23) by , and (24) by . Let us define , , , and . Then, the rescaled dynamics becomes (25) (26) (27) where is an inertia parameter with nominal value . The control objective is to find a control law for the PVTOL aircraft such that the aircraft tracks a given path in the inertial frame with closed-loop stability"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure4.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure4.6-1.png",
        "caption": "Figure 4.6.1. Axle location systems.",
        "texts": [
            " (2) The live axle \u2013 has driven wheels and carries the differential in an integrated unit. (3) The de Dion axle \u2013 has driven wheels but does not carry the differential. Live and de Dion axles have more stringent location requirements, particularly for rigidity to avoid large displacements or large-amplitude axle vibrations when tractive forces are applied. The axle must have freedom to heave and roll relative to the body, hence requiring two degrees of freedom, i.e., a four degrees-of-freedom constraint. This can therefore be achieved by four radius rods (Figure 4.6.1(a)). It is common practice to introduce an extra link to provide two links above the axle (Figure 4.6.1(b)). Although this is geometrically redundant, it affects the stiffness and hence the response to forces. The Panhard rod lateral location of Figures 4.6.1 (a), (b) and (c) can, of course, be replaced in any of these examples by an alternative such as a lateral Watt linkage. The upper longitudinal links can be turned around to also give the Watt type linkages (Figure 4.6.1(c)). Alternatively the two top links can be angled to provide lateral location, thus eliminating the need for the Panhard rod and reducing the number of links back to four (Figure 4.6.1(d)). This upper link pair is sometimes formed into a single wishbone, or a T-bar. The lower links may also be inclined inward (Figure 4.6.1(e)). There are several systems using a single front ball-joint (three degrees of constraint), plus a lateral location. These may be wide-based at the rear (Figure 4.6.1(f)), or the so-called \"torque tube\" (Figure 4.6.1(g)), a singularly unfortunate name since it does not resist significant engine torque except on those rare cases where it is mounted rigidly to the engine unit, but does oppose axle pitch. 200 Tires, Suspension and Handling Suspension Components 201 As these examples show, the lateral location of an axle may be achieved as part of the function of a convergent link pair (or pivot arm), or by a dedicated system such as a Panhard rod. The sliding block and channel gives an accurate straight-line path, but there are large lateral forces so it has substantial friction and consequently also wears, although a roller-bearing system might resolve this",
            " The resultant of the two forces at A and B acts through a point somewhere on AB. However, the cornering force acts in the vertical transverse plane of the wheel centers, neglecting pneumatic trail, so the roll center is where AB intersects this plane. The torque due to trail can be dealt with separately. Suitable points A and B can be found for other axle link layouts. For example, if the lower links are parallel then the point B is at infinity, so AB is parallel to the bottom links. If the bottom link pair is replaced by a torque tube or similar system (Figure 4.6.1(f)), then point B is the front ball-joint. If transverse location is by a Panhard rod, then point A is the point at which the rod intersects the vertical central plane. A characteristic of the Panhard rod is that the roll center rises for roll in one direction, and falls for the other because of vertical motion of the point of connection to the body. For other axle lateral location systems it is similarly necessary to find point A where the line of action of the force intersects the Suspension Characteristics 253 central plane",
            "5, find the mean load transfer factor and the mean incremental roll center height for this increment of acceleration. Q 5.7.1 Explain with diagrams how to find roll centers for rigid link located axles. Q 5.7.2 In an axle roll center analysis, with track 1.44 m, point A is found 1.20 m behind the suspension plane at a height of 420 mm, and point B is 2.15 m in front at height 220 mm. What are the roll center height, net link load transfer factor and net link load transfer at 3200 N sprung mass side force? Q 5.7.3 Analyze the effect of vertical load on roll center height for the axles of Figure 4.6.1. Q 5.7.4 \"A solid axle is not subject to the link force jacking effect of independent suspensions.\" Discuss, with diagrams. Q 5.7.5 For a four link solid axle (Figure 5.7.1) explain how changes to the lateral spacing of the front ends of the bottom links will affect the roll center height. Q 5.8.1 Explain the roll center position of a leaf-spring mounted solid axle. Q 5.8.2 Explain the roll center position of a trailing twist axle. Q 5.9.1 Discuss various methods of experimental roll center measurement",
            "6 Explain how the link geometry of an axle leads to roll steer, and how this may depend on the vehicle load in a favorable way. Q 5.16.7 Discuss roll steer of leaf-spring rear axles. Q 5.16.8 Discuss the extra complications of roll steer on leaf-spring axles at the front rather than the rear. Q 5.16.9 Explain roll steer of the trailing twist axle. Q 5.16.10 Discuss the desirability of, and limitations on, deliberate static toein and toe-out. Q 5.16.11 Analyze qualitatively the effect of load on the roll steer coefficient of the axles of Figure 4.6.1. Q 5.16.12 Is it possible to arrange for no bump steer of a slider (pillar) suspension? Q 5.16.13 For a rack forward of the steering axis by 120 mm, higher than the steering arm ball-joints by 8 mm, and with tie-rods of length 290 mm against a geometric ideal of 306 mm, calculate the linear and quadratic bump steer coefficients, and draw the bump steer graph. Q 5.16.14 Explain the relationship between bump steer and roll steer. Q 5.17.1 Define and explain compliance steer coefficients and compliance camber coefficients"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure7-2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure7-2-1.png",
        "caption": "Fig. 7-2 Cross-section of DFIG.",
        "texts": [
            " 6-2 repeat the calculations in Example 6-2 and compare results with Problem 6-1 in steady state for k\u03c4: 0.75, 1.0, and 1.5. Doubly fed induction generators (DFIGs) are used in harnessing wind energy. The principle of operation of doubly wound induction machines was described in steady state in Reference [1]. In this chapter, we will mathematically describe doubly wound induction machines in order to apply vector control. As an introduction, Fig. 7-1 shows a doubly fed induction generator. The cross-section of a DFIG is shown in Fig. 7-2. It consists of a stator, similar to the squirrel-cage induction machines, with a three-phase winding, each having Ns turns per phase that are assumed to be distributed sinusoidally in space. The rotor consists of a wye-connected threephase windings, each having Nr turns per phase that are assumed to be distributed sinusoidally in space. Its terminals, A, B, and C, are supplied appropriate currents through slip-rings and brushes, as shown in Fig. 7-1b. The benefits of using a DFIG in wind applications are as follows: 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000927_0094-114x(82)90042-8-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000927_0094-114x(82)90042-8-Figure3-1.png",
        "caption": "Figure 3. Displacement functions.",
        "texts": [
            " The rank of the matrix of the screws expressed in Pliicker coordinates is 5, and, therefore, all the 6 \u00d7 6 determinants of the 7 \u00d7 6 matrix of the Pliicker coordinates are instantaneously zero. The mechanism has mobility two instantaneously. Also (see[l]) since the pitches of the screws representing revolute joints are zero ~ef i r~ tan A~ = r3 tan A3 = r5 tan ,~5 = h (8) where h is the pitch of ~ (Note, the Pliicker coordinates of a C pair are expressed in terms of the Plucker coordinates of co-axial R and P pairs[I,3]. It follows that the C pair axes and the ~ axis are mutually perpendicular.) Figure 3(a-f) illustrate the displacement functions of a spatial 5-1ink RCRCR mechanism with dimensions au = lO/~(3)m 0/12 = 150 o S l ! = lOm a23 = 10.0 a23 = 315 \u00b0 $33 = 5/V'(2) a34 = 5/X/(2) 0/34 = 2700 $55 = 20 a45 = 0.0 0/45 = 90 \u00b0 aSl = 20/~/(3) 0/51 = 300 \u00b0 All the 6 \u00d7 6 determinants were zero at 05 = 90% and the determinant of the screws of the C2 - R3 - C4 - R5 pairs plotted against 0s is superimposed on the input-output function 01 VS 05 in Fig. 3(a). The mechanism has an uncertainty configuration as illustrated by Fig. 4, and all the, displacement functions Figs. 3(a-f) exhibit a double root at 05 = 90 \u00b0. Consider now that a 6 x 6 determinant Di = 0 (i denotes the 6 \u00d76 determinant which excludes the ith screw) of the 7 x 6 matrix of the Pliicker coordinates. It follows that all the screws except the ith screw are linearly dependent and, therefore, the ith joint cannot move instantaneously. Figure 5 illustrates the input--output function 01 vs 05 of an RCRCR mechanism with the following dimensions al2 = 25 m 0~12 = 60 \u00b0 S "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001456_s00170-015-8289-2-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001456_s00170-015-8289-2-Figure1-1.png",
        "caption": "Fig. 1 Schematic illustrating the SLM process and some of the parameters that influence the properties of a part",
        "texts": [
            " Three-dimensional computer simulations to understand the relationship between processing parameters and the thermal behavior of the material as it is melted by the laser, for example, see [9, 11, 17, 19, 22], can be quite expensive to run, even on high-performance computer systems, especially if they include various aspects of the physics underlying SLM. Exploring the design space using experiments can also be challenging as there are a large number of parameters, more than 130 by some estimates [31], that influence the process and thus the final quality of the part. Figure 1 shows some of the parameters related to the laser and the powder bed. These include: \u2013 The laser parameters such as (i) the laser power, ranging from 50 to 400 W, though higher-powered lasers are also available; (ii) the laser beam profile, usually Gaussian, though flat-top is also used; (iii) the laser scan speed, ranging from 100 mm/s to over 5000 mm/s; (iv) the scan-line overlap, which is the distance between adjacent scan lines and must be chosen to ensure no unmelted powder remains between scan lines; and (v) the scan strategy, which is the path taken by the laser to melt the powder in appropriate places in a slice"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002203_j.ymssp.2013.06.040-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002203_j.ymssp.2013.06.040-Figure9-1.png",
        "caption": "Fig. 9. Dynamic model of a reduction gear system with six DOF.",
        "texts": [
            " 1a, and the time-varying mesh stiffnesses for all the studied cases are shown in Fig. 8b. A high backup ratio with a crack angle of 701 is considered here. The dynamic response of a gear system can be extracted using dynamic lumped parameters modelling to study the effect of tooth crack propagation on the obtained vibration response from a fault detection point of view. A dynamic simulation of a six DOF model has been performed based on the time-varying mesh stiffness model which was explained earlier. Fig. 9 shows the dynamic model which was used in the present research study and which was adopted in [4,38,39]. This model represents six DOF and is explained in the equations below by introducing the friction force caused by sliding between the mating teeth. The parameters of the dynamic model are explained in Table 7. The gear system works under a torque of 60 N m applied on the driven gear. It is assumed that the radial stiffness and damping in the bearings of the pinion and gear have the same values as those given in Table 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.42-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.42-1.png",
        "caption": "FIGURE 5.42. Simplification of the coordinate frames for an assembled of a spherical hand and arm.",
        "texts": [
            " The forward kinematics of the robot for tool frame B9 can be found by a matrix multiplication. 0T9 = 0T1 1T2 2T3 3T4 4T5 5T6 6T7 7T8 8T9 (5.149) The matrices i\u22121Ti are given in Examples 161 and 167. We can eliminate the coordinate frames B3, and B4 to reduce the total number of frames, and simplify the matrix calculations. However, we may prefer to keep them and simplify the assembling process of changing the wrist with a new one. If this assembled robot is supposed to work for a while, we may do the elimination and simplify the robot to the one in Figure 5.42. We should mathematically substitute the eliminated frames B3 and B4 by a transformation matrix 2T5. 2T5 = 2T3 3T4 4T5 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d6 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.150) d6 = d3 + d4 + d5 (5.151) Now the forward kinematics of the tool frame B9 becomes: 0T9 = 0T1 1T2 2T5 5T6 6T7 7T8 8T9 (5.152) Example 169 Spherical robot forward kinematics. Figure 5.43 illustrates a spherical manipulator attached with a spherical wrist to make an R`R`P robot. The associated DH parameter is shown in Table 5.12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure5.15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure5.15-1.png",
        "caption": "Fig. 5.15",
        "texts": [
            " Evaluating the force equilibrium condition in z-direction and the equilibrium of moments about the x- and the y-axis yield the support reactions at A (Fig. 5.14d): Az \u2212B = 0 \u2192 Az = 54 91 MD l , MAx \u2212MD + bB = 0 \u2192 MAx = 73 91 MD , MAy + l B = 0 \u2192 MAy = \u2212 54 91 MD . 5.5 5.5 Supplementary Examples Detailed solutions to the following examples are given in (A) D. Gross et al. Formeln und Aufgaben zur Technischen Mechanik 2, Springer, Berlin 2010, or (B) W. Hauger et al. Aufgaben zur Technischen Mechanik 1-3, Springer, Berlin 2008. E5.7 Example 5.7 The solid circular shaft in Fig. 5.15 consists of three segments. The radii of the segments 1 and 3 are constant; segment 2 has a linear taper. The shaft is subjected to a torque M0. Determine the angle of twist \u03d1E at the free end. Result: see (B) \u03d1E = 62M0 l \u03c0 G r40 . E5.8 Example 5.8 A thin-walled tube (Fig. 5.16) is subjected to a torque MT . Given: a = 20 cm, t = 2 mm, \u03c4allow = 40 MPa, l = 5m, G = 0.8 \u00b7 105 MPa. Determine the allowable magnitude MTallow of the torque and the corresponding angle of twist \u03d1 for a) a closed cross section and b) an open cross section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002342_j.jsv.2011.03.031-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002342_j.jsv.2011.03.031-Figure8-1.png",
        "caption": "Fig. 8. Dent geometry on different bearing components. (a) Inner race. (b) Outer race. (c) Ball.",
        "texts": [
            " From the radius of the inner and outer races it is clear that the radial clearance in the bearing is c\u00bc 5 mm. The contact angle of the bearing is calculated from an equation in Ref. [18] as a0 \u00bc cos 1 1 c 2A , (34) where A is given by A\u00bc rII1i\u00ferII10 rb: (35) The initial contact angle for the analysed bearing is a\u00bc 12:23. The outer ring, the inner ring and the shaft are made from steel. The dynamic response of the bearing will be taken from point P1, which is on the top of the aluminium ring, Fig. 7(b). The geometrical properties of the local faults are shown in Fig. 8. The faults on the inner race and the ball will rotate and their position will move in and out of the loading zone in the bearing. The fault on the outer race is stationary, and the position of the dent on outer race is very important. Analyses will be made for the dent in the middle of the loading zone, at the bottom of the outer race. For the numerical solution the initial conditions and the step size are very important for a successful and economical computational solution. The larger the time step, the faster the computation",
            " The conclusion can be made that the bearing has no fault, although in the spectra there are detectable characteristic fault frequencies. If the bearing was faulty, there would also be a second harmonic of the characteristic fault frequency. Fig. 11(a) shows the system response at point P1 with one outer race defect, located in the centre of the loading zone. Every roller will hit the fault while going through the loading zone, which should result in an overwhelmingly dominant Fr eq ue nc y [H z] Fr eq ue nc y [H z] frequency at the roller passing frequency. The size and the shape of the defect is shown in Fig. 8(a). The vibration at point P1 increases dramatically when the ball hits the dent, Fig. 11(a), and the peak amplitude is more than two orders higher than in a healthy bearing. In the envelope analysis spectrum, Fig. 11(b), there is the presence of the bearing\u2019s instantaneous shaft rotation frequency fSi\u00bc21 Hz, and two frequencies that correspond to the characteristic frequency of the outer race fault foD \u00bc 2:589 21\u00bc 54:37 55 Hz and its second harmonic 2 foD \u00bc 108:7 111 Hz. The small difference in the frequency is due to the changing shaft rotation frequency from 21 to 22 Hz in the analysed signal",
            " The response will be very high when the defect hits its mating surface in the loading zone. On the other hand, when the defect will be on top of the inner race, the balls will mostly miss the point defect, and thus this shifts the dominant faulty frequency to lower bands. For this reason the detection of a fault on the inner race is more challenging than on a fixed race. Fig. 13(a) shows the vibration response of the outer ring to the inner race defect. The size and the shape of the inner race defect are shown in Fig. 8(b). The envelope spectrum shows a shaft frequency peak at 22 Hz, which is the shaft\u2019s rotating frequency. The characteristic frequency of the inner race defect fiD\u00bc4.411 22\u00bc97 Hz and its second harmonic 2 fiD\u00bc194 Hz can be clearly identified in the envelope spectrum, Fig. 13(b). The small difference in the frequencies is due to the changing speed of the shaft. Fr eq ue nc y [H z] From the time\u2013frequency plot of the CWT, Fig. 14, the existence of high-frequency components is detected and their occurrence is repetitive, which indicates the presence of the fault",
            " These two frequencies correlate very well with the characteristic frequencies of the outer race defect at the instantaneous shaft speeds fSi1\u00bc20.7 Hz at t1\u00bc2.27 s and fSi2\u00bc22.5 Hz at t2\u00bc2.45 s. It is clear that each technique can detect the presence of this bearing fault, where the time interval in the CWT has to be taken carefully, since only in the loading zone is there the high-frequency vibration. To investigate the vibration response of the bearing to the ball fault, it is assumed that the dent is on the first ball. The size and the geometry of the flattened ball are shown in Fig. 8(c). The vibration response at point P1 is shown in Fig. 15(a). The vibration signal is highly modulated, since the high impulsive response is noticed only when the damaged ball is in the loading zone. For this reason the signal taken for the envelope analysis has to be taken carefully. For the spectrum of the envelope analysis the vibration signal is taken from 2.3 to 2.45 s. With the shorter signal the characteristic defect frequency it is hard to identify, but due to a larger change of the shaft\u2019s rotation frequency in this time interval, the shaft\u2019s rotation frequency is not present in the frequency spectrum of the envelope analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure33-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure33-1.png",
        "caption": "Fig. 33 a Archetype of the proposed cooling system; b geometric parameters of the jet impingement model [54]",
        "texts": [
            " Proper clamping forms can effectively reduce distortions and defects in the manufacture of wire and arc additives. The results show that the edge clamping form has better performance than the angular clamping form. In the edge clamping form, the transverse clamping dominates the longitudinal clamping to ensure dimensional accuracy. Based on the analysis of the residual stress distribution, the minimum residual stress distribution can be obtained using only the clamping form of the transverse clamping. Filippo simulated a workpiece cooling system (shown in Fig. 33) based on impinging air jets to the WAAM forming system in order to reduce the heat input, and reduce the residual stress and deformation of the workpiece [54]. This research proposes to solve this problem by introducing a workpiece cooling system based on impinging air jets (the simulation results are shown in Fig. 34). The numerical model of jet impingement cooling is applied to the finite element thermal model of the WAAM process in order to evaluate its effectiveness, and the proposed technique can be considered a useful method to prevent heat accumulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure8-3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure8-3-1.png",
        "caption": "Fig. 8-3 Voltage vector in sector 1.",
        "texts": [
            " The above conditions are generally met if the average voltage vector is synthesized by means of the two instantaneous basic nonzero voltage vectors that form the sector (in which the average voltage vector to be synthesized lies) and both the zero voltage vectors, such that each transition causes change of only one switch status to minimize the inverter switching loss. In the following analysis, we will focus on the average voltage vector in sector 1 with the aim of generalizing the discussion to all sectors. To synthesize an average voltage vector v V es a s j s( )= \u02c6 \u03b8 over a time period Ts in Fig. 8-3, the adjoining basic vectors v1 and v3 are applied for intervals xTs and yTs, respectively, and the zero vectors v0 and v7 are applied for a total duration of zTs. In terms of the basic voltage vectors, the average voltage vector can be expressed as v T xT v yT v zTs a s s s s= + + \u22c5 1 01 3[ ] (8-7) or v xv yvs a = +1 3, (8-8) where x y z+ + = 1. (8-9) In Eq. (8-8), expressing voltage vectors in terms of their amplitude and phase angles results in \u02c6 ./V e xV e yV es j d j d js\u03b8 \u03c0= +0 3 (8-10) By equating real and imaginary terms on both sides of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001308_j.jbiomech.2010.01.031-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001308_j.jbiomech.2010.01.031-Figure1-1.png",
        "caption": "Fig. 1. We attached an inertial measurement unit to the lateral-aspect of each subject\u2019s shank. The normal and tangential accelerations were measured along the n and t axes, respectively. The gyroscope axis is orthogonal to the plane defined by the tangential and normal axes. We defined the world coordinate as xoy, with the vertical axis y parallel to gravity. Shank angle, y, is defined as the angle between the normal axis of the accelerometer and the vertical axis of the world coordinate system. As per the right hand rule, positive angular velocities correspond to a counterclockwise rotation of the shank. Arrows indicate positive directions for each axis.",
        "texts": [
            " Our approach took advantage of the inverted pendulum-like behavior of the stance leg during walking to identify a new method for segmenting the gait cycle and estimating the initial conditions for integration. Shank linear accelerations and angular velocity were measured using a bi-axial accelerometer (Analog Devices ADXL320) and a gyroscope (Analog Devices ADXRS300), respectively. To compute the displacements along the horizontal and vertical world coordinate axes, an\u00f0t\u00de and at\u00f0t\u00de at time t into component accelerations ax\u00f0t\u00de and ay\u00f0t\u00de in the world coordinate system (Fig. 1) according to ax\u00f0t\u00de ay\u00f0t\u00de \" # \u00bc cosy\u00f0t\u00de siny\u00f0t\u00de siny\u00f0t\u00de cosy\u00f0t\u00de \" # at \u00f0t\u00de an\u00f0t\u00de \" # 0 g \" # ; \u00f01\u00de where g is the acceleration due to the gravity and y\u00f0t\u00de is the shank angle which was computed by integrating the measured angular velocity o\u00f0t\u00de, y\u00f0t\u00de \u00bc Z t 0 o\u00f0t\u00dedt\u00fey\u00f00\u00de; \u00f02\u00de where y\u00f00\u00de is the initial shank angle before integration. We segmented the continuous walking motion into a series of stride cycles before computing the displacements. Mid-stance shank vertical events\u2014the time in the stance phase when the shank is parallel to the direction of gravity\u2014defined each new stride cycle (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000112_j.robot.2003.10.003-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000112_j.robot.2003.10.003-Figure2-1.png",
        "caption": "Fig. 2. Geometry of the omnidirectional vehicle.",
        "texts": [
            " The paper ends with some concluding remarks in Section 6. The omnidirectional drive consists of three sets of wheel assemblies equally spaced at 120 degrees from one another (see Fig. 1). Each of the wheel assembly consists of a pair of \u2018orthogonal wheels\u2019 [16] with an active (the propelling direction of the actuator) and a passive (free-wheeling) direction which are orthogonal to each other. The point of symmetry is assumed to be co-incident with the center of mass (CM) of the robot. The schematic arrangement of the wheel assemblies is shown in Fig. 2. The positions (P0i) of these units are easily given (in the frame which is fixed to the center of mass of the robot) with the help of the rotation matrix (\u03b8 is the angle of counterclockwise rotation) R(\u03b8) = ( cos \u03b8 \u2212 sin \u03b8 sin \u03b8 cos \u03b8 ) , (1) as P01 = L ( 1 0 ) , P02 = R ( 2\u03c0 3 ) P01 = L 2 ( \u22121\u221a 3 ) , P03 = R ( 4\u03c0 3 ) P01 = \u2212L 2 ( 1\u221a 3 ) , (2) where L is the distance of the drive units from the CM. The unit vectors Di that specify the drive direction the ith motor (also relative to the CM) are given by Di = 1 L R (\u03c0 2 ) P0i, D1 = ( 0 1 ) , D2 = \u22121 2 (\u221a 3 1 ) , D3 = 1 2 (\u221a 3 \u22121 ) ",
            " The salient feature of this model is that the amount of torque available for acceleration is a function of the speed of the motor. With the no-slip condition, the force generated by a DC motor driven wheel is simply f = \u03b1U \u2212 \u03b2v, (5) where f (N) is the magnitude of the force generated by a wheel attached to the motor, and v (m/s) is the velocity of the wheel. The constants \u03b1 (N/V) and \u03b2 (kg/s) can readily be determined from \u03b1\u0304, \u03b2\u0304, and the geometry of the vehicle. The vector P0 = ( x y )T is the position of the CM in a Newtonian frame as shown in Fig. 2. The drive positions and velocities are given by ri = P0 + R(\u03b8)P0i, (6) vi = P\u03070 + R\u0307(\u03b8)P0i, (7) while the individual wheel velocities are vi = vT i (R(\u03b8)Di). (8) Substituting Eq. (7) into Eq. (8) results in vi = P\u0307T 0 R(\u03b8)Di + PT 0iR\u0307 T(\u03b8)R(\u03b8)Di. (9) The second term of the right hand side is just the tangential velocity PT 0iR\u0307 T(\u03b8)R(\u03b8)Di = L\u03b8\u0307. (10) The drive velocities are thus linear functions of the velocity and the angular velocity of the robot   v1 v2 v3   =   \u2212 sin \u03b8 cos \u03b8 L \u2212 sin (\u03c0 3 \u2212 \u03b8 ) \u2212 cos (\u03c0 3 \u2212 \u03b8 ) L sin (\u03c0 3 + \u03b8 ) \u2212 cos (\u03c0 3 + \u03b8 ) L     x\u0307 y\u0307 \u03b8\u0307   "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002621_rob.21673-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002621_rob.21673-Figure2-1.png",
        "caption": "Figure 2. DRC-HUBO+ robot platform. (a) Modular design of the robot. Each joint of the robot is easily changeable. (b) Air cooling design and conduction of motor heat to the frame.",
        "texts": [
            " SYSTEM OF DRC-HUBO+ The humanoid robot platform, DRC-HUBO+, was developed for the DRC Finals by Rainbow Robotics and the HuboLab. It contains all the technologies developed since the first generation of HUBO, KHR-1, was developed (J. H. Kim, Park, Park, & Oh, 2002; Park, Kim, Park, & Oh, 2005). It especially was designed based on what Team KAIST learned and experienced at the previous competition, the DRC Trials (Lim & Oh, 2015; Oh & Oh, 2015). In the following subsections, the key features of DRC-HUBO+\u2019s hardware are briefly described. 2.1.1. DRC-HUBO+ robot platform As can be seen in Figure 2, DRC-HUBO+ has been designed as a humanoid because the given tasks are all concerned with human environments and, consequently, human morphology will bring an advantage to the tasks. At the DRC Trials, it was found that a wheel based robot had an advantage in conducting indoor tasks on flat ground. To take advantage of this situation, DRC-HUBO+ can select two types of mobility mode by transforming the posture of its legs (see Subsection 4.1.1). It can travel on flat land using wheels attached to the knees; it can also walk and traverse rubble and stairs using its two legs. As can be seen in Figure 2(b), this robot has an air-cooled heat dissipation system of actuators at pelvis pitch, knee pitch, and ankle pitch that can generate enough power for the robot to walk or change mobility mode. This system can endure 1.7 times the maximum continuous current. To secure enough rigidity to protect against deflection due to the robot\u2019s weight, the DRC-HUBO+ designers used an exoskeletal structure and tried to avoid cantilever forms. This design strategy also reduced the thickness and weight of each limb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure12.29-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure12.29-1.png",
        "caption": "FIGURE 12.29. A 3R planar manipulator attached to a wall.",
        "texts": [
            " Eliminate the joints\u2019 constraint force and moment to derive the equations for the actuators\u2019 force or moment. 9. A planar Cartesian manipulator. Determine the equations of motion of the planar Cartesian manipulator shown in Figure 12.24. Hint : The coordinate frames are not based on DH rules. 10. F Global differential of a link momentum. In recursive Newton-Euler equations of motion, why we do not use the following Newton equation? iF = Gd dt iF = Gd dt m iv = m iv\u0307 + i 0\u03c9i \u00d7m iv 11. 3R planar manipulator dynamics. A 3R planar manipulator is shown in Figure 12.29. The manipulator is attached to a wall and therefore, g = g 0\u0131\u03020. (a) Find the Newton-Euler equations of motion for the manipulator. Do your calculations in the global frame and derive the dynamic force and moment at each joint. (b) Reduce the number of equations to three for moments at joints. (c) Substitute the vectorial quantities and calculate the moments in terms of geometry and angular variables of the manipulator. 12. A planar Cartesian manipulator dynamics. Determine the Newton-Euler equations of motion for the planar Cartesian manipulator shown in Figure 5",
            " (b) Derive the equations of motion for the SRMS and calculate the joints\u2019 force system for g = \u2212g 0k\u03020. (c) Eliminate the constraint forces and reduce the number of equations equal to the number of action moments. (d) Assume the links are made of a uniform cylinder with radius r = .25m and m = 12 kg/m. Use the characteristics indicated in Table 5.10 and find the equations of motion when the endeffector is holding a 24 kg mass. 20. 3R planar manipulator recursive dynamics. The manipulator shown in Figure 12.29 is a 3R planar manipulator attached to a wall and therefore, g = \u2212g 0 \u0131\u03020. (a) Find the equations of motion for the manipulator utilizing the backward recursive Newton-Euler technique. (b) F Find the equations of motion for the manipulator utilizing the forward recursive Newton-Euler technique. 21. A RPR planar redundant manipulator. (a) Figure 12.27 illustrates a 3 DOF planar manipulator with joint variables \u03b81, d2, and \u03b82. Determine the equations of motion of the 720 12. Robot Dynamics manipulator if the links are massless and there are two massive points m1 and m2",
            " (b) utilizing the forward recursive Newton-Euler technique. 25. F Recursive dynamics of an SRMS manipulator. Figure 5.24 shows a model of the Shuttle remote manipulator system (SRMS). (a) Derive the equations of motion for the SRMS utilizing the backward recursive Newton-Euler technique for g = 0. (b) Derive the equations of motion for the SRMS utilizing the forward recursive Newton-Euler technique for g = 0. 26. 3R planar manipulator Lagrange dynamics. Find the equations of motion for the 3R planar manipulator shown in Figure 12.29 utilizing the Lagrange technique. The manipulator is attached to a wall and therefore, g = \u2212g 0 \u0131\u03020. 27. Polar planar manipulator Lagrange dynamics. Find the equations of motion for the polar planar manipulator, shown in Figure 5.56, utilizing the Lagrange technique. 12. Robot Dynamics 721 28. F Lagrange dynamics of an articulated manipulator. Figure 5.22 illustrates an articulated manipulator R`RkR. Use g = \u2212g 0k\u03020 and find the manipulator\u2019s equations of motion utilizing the Lagrange technique",
            " There is a load Fe = \u221214g 0j\u03020N at the endpoint. Calculate the static moments Q1 and Q2 for \u03b81 = 30deg and \u03b82 = 45deg. 33. Statics of a 2R planar manipulator at a different base angle. In Exercise 32 keep \u03b82 = 45deg and calculate the static moments Q1 and Q2 as functions of \u03b81. Plot Q1 and Q2 versus \u03b81 and find the configuration that minimizes Q1, Q2, Q1+Q2, and the potential energy V . 722 12. Robot Dynamics l2 x2 y2 Y y1 x1 X m1 m2 Q1 Q2 l1 2\u03b8 1\u03b8 12. Robot Dynamics 723 34. Statics of a 3R planar manipulator. Figure 12.29 illustrates a 3R planar manipulator attached to a wall. Derive the static force and moment at each joint to keep the configuration of the manipulator if g = \u2212g 0\u0131\u03020. 35. F Statics of an articulated manipulator. An articulated manipulator R`RkR is shown in Figure 5.22. Find the static force and moment at joints for g = g 0k\u03020. The end-effector is carrying a 20 kg mass. Calculate the maximum base force moment. 36. F Statics of a SCARA robot. Calculate the static joints\u2019 force system for the SCARA robot RkRkRkP shown in Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure8.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure8.19-1.png",
        "caption": "Fig. 8.19 Interconnected suspensions activated when bouncing",
        "texts": [
            " As anticipated, the scheme of Fig. 8.13 is not as general as it may seem at first. We need a suspension layout with three springs, although we still have only two axles. Interconnected suspensions are the solution to this apparent paradox. A very basic scheme of interconnected suspensions is shown in Fig. 8.18. Its goal is to explain the concept, not to be a solution to be adopted in real cars (although, it was actually employed many years ago). To understand how it works, first suppose the car bounces, as in Fig. 8.19. The springs contained in the floating device F get compressed, thus stiffening both axles. On the other hand, if the car pitches, as in Fig. 8.20, the floating device F just translates longitudinally, without affecting the suspension stiffnesses. This way we have introduced the third independent spring k3 in our vehicle. Obviously, hydraulic interconnections are much more effective, but the principle is the same. We have an additional parameter to tune the vehicle oscillatory behavior. 268 8 Ride Comfort and Road Holding Although only a few cars have longitudinal interconnection, almost all cars are equipped with torsion (anti-roll) bars, and hence they have transversal interconnection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001530_978-3-642-81857-8-Figure1.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001530_978-3-642-81857-8-Figure1.10-1.png",
        "caption": "Fig. 1.10. Reactions of the i-th member",
        "texts": [],
        "surrounding_texts": [
            "Let the kinematic chain be fictively ruptured at the i-th joint and consider the equilibrium of the mechanism free end (Fig. 1.9). The action of the rejected mechanism part is substituted by forces and re+e +N ->-e ->-N action moments Mi , pqi' Ri , Ri \u2022 The driving torque in the \"ruptured\" ~joint is divided into the collinear and perpendicular component to the jOint axis: M~ and tl!. The force components are collinear Rie and per~ , ~ . pendicu1ar R~ to the joint axis ~i. When considering the kinetostatic equilibrium the external forces and moments of inertial forces of the rejected chain members are reduced to the center of the i-th (\"rup tured\") jOint. According to D'A1ambert's principle, the force and mo ment after the reduction are balanced by the reactions. The resulting force and moment of the j-th member are given by where Gj is the external force and ~ the external moment. Introducing (1.1.18) and (1.1.25) one obtains j ~ ->- \u2022. k ->-0 ->- ->- t. a'kq + a J, - mJ'wo + GJ\" k=l J 49 To obtain the reactions, it is appropriate to establish the recursive relations between the reactions of two adjacent joints. From Fig. 1.lOa, where one mechanism member is illustrated, it is evident that + + +, Ri Ri +l - r i , (1.1.27) M. + + + + + r; i,; Mi +l + (rii -ri , i+l) x Ri + l - r ii x ~ J, ~ Circling the chain from the last to the first member according to (1.1.27), all reactions can be determined. The chain is \"ruptured\" gradually, progressing from the last to the first (basic) member. The +.... d +,... corresponding forces rj an moments Lj are therefore reduced to the jOints illustrated~in Fig. 1.9. Reducing r: and i,: to the center of ) J the i-th joint and to their components parallel and perpendicular to + e i , one determines the values of reactions (Fig. 1.lOb) n +, j + _k -I r. = -I ( l a. q + ao). - m.w + GJ.) j=i J (j) k=l Jk ) 0 n + .... -+ +, - L (L. +r .. x r . ) j=i J )~ J Ri - R1 -I [~ (bjk+~jiXajk)qk + ~ji x aj (j) k=l (1.1.28) T~ese expressions enable us to determine the drives in the i-th joint. Here, the normal components cannot produce mechanism motion. Forces and di:;iving torques depend on the collinear components. If the i-th joint 50 is rotational, +M Me + M+ P. e i Piei , ~ i (1.1. 29) and for the linear kinematic pair, +F Re + F+ P. e i Piei \u00b7 ~ i The block-scheme for determining reactions is given in Fig. 1.11. The algorithm calculates the reactions at all joints in terms of two compo nents (parallel and perpendicular to the axis of the kinematic pair) \u2022 The algorithm is based on relations (1.1.27) and (1.1.28). The value of the cycle counter i corresponds to the jOint number and circling of all joints starts from the chain end. The preceding expression for the equilibrium of moments in the i-th , jOint represents a differential equation of motion; Writing this equation for all mechanism jOints, one finds that where H (1.1.30) [ .. 1 .. n]T q \u2022\u2022\u2022 q -+ :+ --+ -+ F M H = -e (b +r xa) where P~ denotes either P~ or P~, ikj i ,jk ji jk'. \u2022\u2022 51 52 The motion equations can be differently derived in a slightly modified form. Using the virtual displacement principle, one obtains the analo gous equations n \\' (r ~~. . + L ~~. . -+--+ L + P;q;J.J i=l ~ ~J ~ ~J ~ ~ 0, (1.1. 31) . -7 -7 -7 where tne index j of the variables vi' wi an~ qi indicates that they have been produced by the virtual velocity qJ. Equation (1.1. 31) holds both .for an open and closed kinematic chain. For the open chain, relative motion is realized in the i-th joint only and the preceding member stays fixed. Taking qi=l for simplicity, one finds that for the open kinematic chain n \\' (-7 ~-7 + -7 ~-7 ) L r.v.. L;WiJ\u00b7 i=l ~ ~J ~ (j=l,2, \u2022\u2022. ,n) \u2022 (1.1.32) Substituting expressions (1.1.27) and (1.1.23) into (1.1.31) and col lecting the terms containing q, the matrix differential equation (1.1.33) is obtained, where H, Hl , H2 , H3 are nxn, nxn,nx3andnx3matrices, re spectively. The elements of these matrices are: -qij (the virtual velocity in direction of ej ), n . Im.vkJ \u00b7 k=l.K ~ (1.1. 34) where index j ind~cates that the j-th component of these vectors is taken into account. The components of vector s from (1.1.33) are n s\u00b7 = - I (~k'~k + ~k\u00b7bk)' ~ k=l ~ ~ (1.1. 35) where b~ +~. Hl is a diagonal matrix with components equal to the virtual velocities. 53 If the virtual velocities are equal to unity, HI becomes a unit matrix, so (1.1.33) becomes Hq P + H2wo + H3Eo + i;; , i.e., (1.1. 36) q AP + Bwo + CEO + 0, where A=H- l , -1 B=H H2 , -1 C=H H3 , -1 D=H i;;. Fig. 1.12. illustrates the block-scheme of the. algorithm for mechanism modelling on a digital computer. Here it is supposed that the motion + + + + + . law (vo ' wo ' wo , EO' Rl ) of the basic mechanism members is k~own. I! the chain is connected to the base, the first four vectors (vO, ... ,E O) are equal to zero. The block-scheme illustrated contains two algorithms previous considered for \"assembling\" the chain and forming differential equations of motion."
        ]
    },
    {
        "image_filename": "designv10_1_0002888_j.ymssp.2019.106379-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002888_j.ymssp.2019.106379-Figure15-1.png",
        "caption": "Fig. 15. Schematic representation of the robotic system.",
        "texts": [
            " [20] also assure a satisfactory tracking and the modified continuous Fixed TSMC achieves a much faster transient over the FTSMC of Ref. [20]. The numerical simulations clearly demonstrate that the proposed robust control offers a much improved control design for faster transient and higher steady-state tracking of robot manipulators in the presences of parametric uncertainties and bounded disturbances. The proposed Fixed TSMC is further validated experimental on an industrial robot manipulator. The diagram of the robotic system is shown in Fig. 14 and is drawn schematically in Fig. 15. It consists of a motor, a dSPACE (DS1103) control board, and a multilink robot. The servo is operated in torque mode, so the motor acts as torque source and it accepts an analog voltage as a reference of torque signal. The feedback position is measured by an incremental encoder. The controller executes programs at a sampling frequency 1kHz. According to the used motors, the supply torques are limited within smax \u00bc 30; 30\u00bd T Nm. The desired positions are set as qd \u00bc p=4sin 0:5t\u00f0 \u00de 1 exp 0:05t3 ; 1 exp 0:1t\u00f0 \u00de T rad\u00f0 \u00de and illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure5.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure5.18-1.png",
        "caption": "Figure 5.18.1 Body, wheel and road positions.",
        "texts": [
            " Hence, for passenger cars it is convenient to measure the ride height at the highest point of the wheel arch opening, the so-called eyebrow level. For ground-effect racing cars, the rules frequently specify a flat, or partially flat, underbody, in which case this flat plane is often used to define the ride heights. Alternatively, measurements may be made to the inner axis of the bottom suspension arm. Under running conditions, the ride heights or vertical positions of the body (sprang mass), of the wheel and of the local road position are measured from the mean road plane; Figure 5.18.1 shows this for one suspension unit. Hence there are vertical positions ZB to some reference point on the body, ZW to the wheel center and ZR to the road height. Each of these has four values, one at each wheel specified by appropriate subscripts, normally either: 316 Tires, Suspension and Handling (1) f and r for front and rear, with L and R for left and right, or i and o for inner and outer. The static positions are ZB1, ZW1, and ZR1, the last of these being zero by definition. The increase of these in dynamic, running condition compared with the static condition, represented by lower case z, becomes The static tire deflection is then so Suspension Characteristics 317 The static loaded radius is In running conditions, the loaded radius is The running tire deflection is which becomes The increase of tire deflection is simply Frequently in handling analysis, the road is deemed to be smooth and level, in which case zR = 0, giving The suspension deflection (bump) is The basic body height is measured at the center of mass, giving a single value for ZB"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000753_j.eswa.2008.05.052-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000753_j.eswa.2008.05.052-Figure2-1.png",
        "caption": "Fig. 2. (A) Experimental set-up, (B) slight-worn gear, (C) broken-tooth gear, (D) acceler mechanism.",
        "texts": [
            " For each configuration, three different fault conditions were tested that were slight-worn, medium-worn, broken-tooth of gear. For evaluating the meticulousness of the technique, two very similar models of worn gear have been taken into account with partial difference. The rotational speed of the system was measured by tachometer used as a measure to compensate the fluctuations owing to uncertainties of the load mechanism which was a constant static load. Moreover, the signals were also sampled at 16384 Hz lasting eight seconds. Fig. 2 clearly shows all parts of fault simulator and related components in detail. It is important to pre-process any raw data before use since it contains redundant information. The pre-processing of vibration signals was involved in synchronization of the signals and computation of standard deviation of wavelet packet coefficients per- formed in the following two steps to extract the feature vector. Accurate pre-processing of the data to feed neural network can make ANN training more efficient because of a considerable reduction of the dimensionality of the input data and therefore improving the network performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000403_j.actamat.2011.03.033-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000403_j.actamat.2011.03.033-Figure4-1.png",
        "caption": "Fig. 4. Arcam A2 EBM system schematic rendering. Numbered components and machine functions are described in the text.",
        "texts": [
            " Particles were encapsulated in mounting epoxy, which was ground, polished and etched to reveal the interior microstructures by EBM. (a) Small cylinder, (b) quarter section from 5 cm (25 cm2) block, of the particles as illustrated in Fig. 3, where the grain size averages 6 lm, a relatively small size that gives rise to an instrumental Vickers microindentation hardness of 72, as indicated in Fig. 3a. The magnified view shown in Fig. 3b illustrates the selective etching of precipitates within the grain boundaries forming regular, often square or rectangular, pits. Fig. 4 shows the Arcam A2 EBM system schematic. In this system the Cu precursor powder (Fig. 1) was contained in cassettes indicated at (4), where it was gravity fed to the build table to be raked (5) into successive layers roughly 100 lm thick. The electron beam is generated in the electron gun (1) at an accelerating voltage of 60 kV, focused by magnetic lenses at (2) and scanned by scan coils at (3) to preheat and selectively melt the powder layer using a computer-aided design (CAD) program. As the component (6) was fabricated, the build table (7) drops down"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002224_j.ymssp.2018.02.028-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002224_j.ymssp.2018.02.028-Figure2-1.png",
        "caption": "Fig. 2. FEA model of gears in contact.",
        "texts": [
            " Since the gears are not rigid, the gears undergo deformation, which results in the transmission error (TE), which is the angular difference between the ideal and actual position of the output gear: TE \u00bc hideal2 h2 \u00bc R1 R2 h1 h2 \u00f01\u00de where h1 and h2 are the angular displacements and R1 and R2 are the radii of input and output gears, respectively. It can be transformed to the following equation TE \u00bc Tout KgR 2 2 \u00f02\u00de where Tout is the torque applied at the output shaft and Kg is the linear gear meshing stiffness (GMS) representing the rigidity of the gears in contact. The faulty gear may undergo more deformation, which leads to the higher TE, and this is the basic idea that constitutes the signal for the diagnosis. Finite element model is created by FEA software ANSYS as shown in Fig. 2 for the gears in contact, of which the material is stainless steel with elastic modulus 204 GPa and Poisson ratio 0.3, module is 4 mm, and the input and output pitch diameters are 140 and 280 mm respectively. Five teeth are generated for the both gears as shown in the figure, which are meshed with finer element size of 0.25 mm. Torque is applied to the input gear while the hub of the output gear is constrained. FEA is carried out over the range of five teeth distance to obtain the TE profile. Spall with the length and depth being 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002706_tmag.2014.2364988-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002706_tmag.2014.2364988-Figure1-1.png",
        "caption": "Fig. 1. Winding arrangement for a 12-slot/10-pole geometry. (a) Three-phase winding. (b) Dual three-phase winding.",
        "texts": [
            " Although no experimental verification is given, the finite element simulation is expected to give a fair judgment, as it is difficult to separate the rotor loss component from the total machine losses to assess the improvement in rotor loss reduction experimentally. II. PROPOSED WINDING CONNECTION FOR 12-SLOT/10- POLE THREE-PHASE MACHINE Among different slot-pole combinations of a three-phase PM machine with FSCW, the 12-slot/10-pole combination and its multiples have shown promise in different applications [20]. Since the proposed winding is based on a dual threephase winding, a double layer winding layout is selected. A 12-slot/10-pole machine with a conventional double layer winding is shown in Fig. 1a. Each phase comprises four coils with a total of twelve coils for a three-phase winding. Each two nonadjacent series coils are represented using one coil in Fig. 2a. For this slot number, , the angle between any two successive slots is 30 0 . Hence, the winding configuration can be modified to a dual three-phase configuration as shown in Fig. 1b allowing for a mechanical angular shift of 30 0 between the two winding sets. In the literature, the dual threephase windings are fed by two three-phase current groups supplied from two separate three-phase inverters with a time shift between the two current groups of 30 0 . Alternatively, the required 30 0 between the two current groups can be simply obtained using the combined star-delta connection [16], by connecting one of the winding sets as a delta, while the other winding is connected between the threephase inverter and the delta connected winding terminals, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000372_027836499801701205-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000372_027836499801701205-Figure3-1.png",
        "caption": "Fig. 3. The geometric parameters of a revolute-actuated DELTA robot.",
        "texts": [
            " Motions of the travelling plate are achieved by the combination of arm movements (1) that are transmitted to the plate by the system of parallel rods (2) through a pair of ball-andsocket passive joints. These parallel rods, also called forearms, ensure that the travelling plate always remains parallel to the robot base. 4.2. Geometric Parameters The absolute reference frame { R is chosen as shown in Figure 2, at the center of the triangle drawn by the axes of the three motors, with z pointing upward, and x perpendicular to the axis of motor 1. Owing to the robot\u2019s triple symmetry, each arm can be treated separately. Its geometric parameters are defined in Figure 3. The index i (i = 1, 2, 3) is used to 1329 identify the arm number. Each arm is separated by an angle of 120\u00b0. For each arm, a corresponding frame is chosen that is located at the same place as {7?} but rotated by an angle Oi = 0\u00b0, 120\u00b0, and 240\u00b0, for arms 1, 2, and 3, respectively. The transformation matrix between frames { Ri and { R is given by As the travelling plate can only be translated, a frame attached to it will always keep the same orientation as {R}. This fact allows us to consider the distance from the reference frame {R} to the motor as being R = RA - RB, and thus P = BI = B2 = B3; that is, the travelling plate is reduced to a single point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002042_adem.201900617-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002042_adem.201900617-Figure6-1.png",
        "caption": "Figure 6. Microtrusses made of IN718 using the EOS powder bed AM system. Reproduced with permission.[79] Copyright 2016, Elsevier.",
        "texts": [
            " For the powder bed-based approach, a 3D model is first created and converted to a stereolithography (STL) file. It is then sliced into 2D slices. A layer of powder material is spread and a laser beam scans the powder based on the 2D cross section and sinters\u2019 or melts\u2019 selected locations, as shown in Figure 5. The process repeats itself until the part is built.[78] The PBF process is governed by ASTM F2792-12. Although a more matured technology and having the ability to produce an intricate structure (e.g., microtrussed shown in Figure 6), it has inherent problems with powder balling during melting and spatter formation as well. It also requires large amounts of powder material to fill the powder bed, even if a small part is being built. This process also makes the change to a different material a lengthy process. The direct powder feed AM process is considered to have the greater potential for aerospace applications considering that material is only deposited where it is needed and most engineering metals and ceramics already exist in powder form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000289_s0021-9290(02)00183-5-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000289_s0021-9290(02)00183-5-Figure1-1.png",
        "caption": "Fig. 1. Scheme of the experimental setup, the analysed system (right leg), and the coordinate system. White circles show the digitised markers, hatched circles the modelled tissue masses attached to shank and thigh. Segment angles (not depicted) are measured with respect to the x-axis. Their differences evaluate to the shown joint angles. Segment lengths are labelled in parenthesis, a denotes the angle of attack, the grey line symbolises the leg length.",
        "texts": [
            " High-speed video data and ground reaction force were sampled with 500 Hz: The complete analytical method including the estimation of joint torques by an inverse dynamics process taking soft tissue dynamics into account is described elsewhere (G .unther et al., 2002b). Essentially this analysis process determines the bone motion of the stance leg from corrected skin marker data of the ankle, knee, and hip assuming constant segment lengths. The centre of mass kinematics of the soft tissue masses is estimated by integrating the dynamics of point masses in parallel to the bone motion which are coupled visco-elastically to the shank and thigh bone, respectively. Fig. 1 depicts the used experimental setup, the coordinate system (horizontal: x; vertical: y; each angle j measured with respect to the inertial system), and the biomechanical model from the viewpoint of the video camera. A numerical index denotes a segment number, a double index refers to a linkage between two segments, and omitting a numerical index refers to a leg variable. E.g. l1 means the foot length, whereas j12 denotes the ankle joint angle as the difference between the foot angle j1 and the shank angle j2: The subjects\u2019 anthropometric data are listed in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure5.29-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure5.29-1.png",
        "caption": "Fig. 5.29",
        "texts": [],
        "surrounding_texts": [
            "E5.19 Example 5.19 The assembly shown in Fig. 5.27 consists of a thinwalled elastic tube (shear modulus G) and a rigid lever. The lever is subjected to a couple. Given the allowable shear stress \u03c4allow, calculate the allowable forces and the corresponding angles of twist for the cross sections 1 and 2 . Results: see (A) Fallow1 = \u03c0 2 a2t b \u03c4allow, Fallow2 = a2t b \u03c4allow, \u0394\u03d11 = 2 + \u03c0 \u03c0 l \u03c4allow aG , \u0394\u03d12 = (1+ \u221a 2) l \u03c4allow aG . E5.20 Example 5.20 A solid circular shaft has a linear taper from 4a at the left end to 2a at the right end (Fig. 5.28). A torque MT is applied at its free end. Determine the angle of twist \u03d1 and the maximum shear stress \u03c4max in the shaft at a location x along the shaft\u2019s axis. Results: see (A) \u03d1(x) = MT l 12 \u03c0Ga4 \u23a7\u23aa\u23a8 \u23aa\u23a9 1( 1\u2212 x 2l )3 \u2212 1 \u23ab\u23aa\u23ac \u23aa\u23ad , \u03c4max(x) = MT WT = 2MT \u03c0 a3 ( 2\u2212 x l )3 . 5.5 Supplementary Examples 227 E5.21Example 5.21 Determine the torsion constant IT and the section modulus of torsion WT for each of the depicted thin-walled cross sections (t b). Calculate the ratio \u03c4max,o/\u03c4max,c of the maximum shear stresses for the open cross sections (o) and the closed cross sections (c) assuming that the sections are subjected to a torque MT . Results: see (B) a,b,c) IT = 17 3 bt3 , WT = 17 6 bt2 , d) IT = 3 8 b3t , WT = \u221a 3 2 b2t ; \u03c4max,o \u03c4max,c = 3 \u221a 3b 17 t ."
        ]
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure12.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure12.10-1.png",
        "caption": "Fig. 12.10 Different light patterns used in structured-light techniques [3]",
        "texts": [
            " Additionally, time-of-flight sensors face difficulties with shiny surfaces, which reflect little back-scattered light energy except when oriented perpendicularly to the line of sight. 332 G. \u0160agi et al. Structured-light systems project a predetermined pattern of light onto the object, at a known angle. An image of the resulting pattern, reflected by the surface, is captured, analysed and the coordinates of the data point on the surface are calculated by using a triangulation method. The light pattern can be (i) a single point; (ii) a sheet of light (line); and (iii) a strip, grid, or more complex coded light (Fig. 12.10). The CCD camera, the object and the light source form the triangulation geometry (Fig. 12.11). The accuracy of these methods is primarily a function of the camera resolution and secondarily of geometric dimensions and illumination precision. System geometry and illumination are not as critical. Thus, structuredlight systems offer a more practical solution than passive stereographic systems in achieving the accuracy necessary for an RE system. The most commonly used pattern is a sheet of light, generated by fanning out a light beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000084_physrevlett.96.058102-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000084_physrevlett.96.058102-Figure3-1.png",
        "caption": "FIG. 3. (a) Top view of the arrangement of two elliptical trajectories which represent two beating cilia. The distance r and the angle are indicated. (b) The state diagram as a function of the distance vector x x0 2 x 0 1, y y0 2 y 0 1, determined from the numerical solution of the full model equations. Three different regions are indicated. In the region of asynchronous beat, two frequencies occur. Two synchronous states can be distinguished with equal (Sync ) and opposite (Sync ) phases of both cilia in the limit of large separation r.",
        "texts": [
            " The problem of two coupled phase oscillators is equivalent to the Kuramoto model [10], a classical model for describing synchronization phenomena [11]. Performing numerical solutions to these dynamic equations, we find that, for certain parameter values, after long times the motion of both spheres becomes periodic with the same frequency and the oscillations thus synchronize. A synchronized state is characterized by the phase lag h 2 1i, where the brackets denote a time average over one period. Regions of synchronous states and a region of asynchronous states are indicated in the state 05810 diagram of Fig. 3(b). The two regions of synchronous states correspond to equal and opposite phases in the limit of infinite separation r. The values of are displayed in Fig. 4 as a function of the angle for different distances r jx0 1 x0 2j between the two cilia. For some intervals of , no synchronized solution occurs and the spheres rotate in an asynchronous manner with two different frequencies. Note that even if both cilia have identical properties, the arrangement shown in Fig. 3(a) breaks the symmetry and both cilia can have different preferred frequencies when they interact. The existence and stability of synchronous states can be studied analytically. First, using Eq. (12), we find for large r a f0 t\u03021 $ x1 I $ v1 t\u03021 $ x1 G $ x2;x1 $ x2 v2 O f0a2D4 r6 : (13) Here, we have used the fact that for large r a the interactions decay as G / r 3, while the friction terms scale with the sphere size, / a. Using this relation between the tangential velocities, we can study synchronization",
            " The variation T of the oscillation period T of sphere 1 can then be written as T Z 2 0 1 _ 1 1 _ 0 d Z T0 0 v0 v1 v0 dt 1 f0 Z T0 0 t\u03021 $ x1 G $ x2;x1 $ x2 t\u03022v2dt; (14) where the last expression becomes correct in the limit of large r=a. In this limit, the variation T can be calculated using the Ansatz x1 x0 1 x 0 !t and x2 x0 2 x 0 !t resulting in a function T r; ; . A synchronized steady state exists if the change in period due to interactions is the same for both spheres, i.e., T r; ; T r; ; , where we have taken into account that exchanging both spheres corresponds to ! and ! ; see Fig. 3(a). Furthermore, a synchronized steady state is locally stable if @=@ T r; ; T r; ; <0. In order to find explicit expressions for T, we perform a systematic expansion in the small parameter K. In the limit of vanishing radius a, the friction matrix $ becomes independent of the height z. The velocity of a single sphere then becomes constant along the trajectory (K 0). As a consequence, the corresponding variation T0 of the period, resulting from Eq. (14), becomes symmetric with respect to ! as well as with respect to "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000787_systol.2010.5675979-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000787_systol.2010.5675979-Figure1-1.png",
        "caption": "Fig. 1. The structure of quadrotor and its frames",
        "texts": [
            " Nonlinear model In this section, the general dynamic model of a quadrotor UAV has been studied. In lightweight flying systems, the dynamic model ideally includes the gyroscopic effects resulting from both the rigid body rotation in space, and the four propeller\u2019s rotation. The dynamic model is derived using Euler-Lagrange formalism. A body-fixed frame B and the earth-fixed frame E are assumed to be at the center of gravity of the quadrotor UAV, where the z-axis is pointing upwards, as seen in Figure 1. The position of the quadrotor UAV in earth frame U 978-1-4244-8154-5/10/$26.00 \u00a92010 IEEE 239 is given by a vector ( , , )x y z . The orientation of quadrotor UAV that referred to as roll, pitch, and yaw is given by a vector ( , , ) which measured with respect to the earth coordinate frame E. The transformation of vectors from the body-fixed frame to the earth-fixed frame can be obtained based on Euler angles and the rotation matrix EBR . EB C C S C C S S S S C S C R S C C C S S S C S S S C S C S C C (1) where the abbreviations ( )S and ( )C have been used for sin( ) and cos( ) , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure10.24-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure10.24-1.png",
        "caption": "Figure 10.24 (a) Far-field model; (b) definition of source direction.",
        "texts": [
            "1 Initial Values for k-Means Clustering The k-means algorithm is sensitive to the initial values of the centroids especially when the number of sources N is large and the reverberation time is long. Therefore, 336 UNDERDETERMINED BLIND SOURCE SEPARATION USING ACOUSTIC ARRAYS we designed the initial centroids by using the far-field model, where the frequency response hjk(f ) is given as hjk(f ) \u2248 exp [\u2212j2\u03c0f c\u22121dT j qk], and using the same normalization as each feature. Here, c is the propagation velocity of the signals, and the three-dimensional vectors dj and qk represent the location of sensor j and the direction of source k, respectively (see Fig. 10.24 and [80]). When designing the initial centroids, the sensor locations dj (j = 1, . . . ,M) were on almost the same scale in each setup, and the initial directions qk were set so that they were as scattered as possible. Concretely, in the experiments, we utilized the sensor vector qk = [cos \u03b8k cos \u03c6k, sin \u03b8k cos \u03c6k, sin \u03c6k]T (see Fig. 10.24). The azimuth of the kth source was set at \u03b8k = 2\u03c0/N \u00d7 k (k = 1, . . . , N ) for M \u2265 3, and \u03b8k = \u03c0/N \u00d7 k (k = 1, . . . , N ) for M = 2. The elevation \u03c6k = 0 for all sources k. Note that these initial values of dj and qk were not exactly the same in each setup. The separation performance is evaluated in terms of signal-to-interference ratio (SIR) improvement and signal-to-distortion ratio (SDR). A larger number represents a better result for both criteria. To calculate these numbers, we need the individual source observations xJk defined by xJk(t) = \u2211 l hJk(l)sk(t \u2212 l), which are not available with the BSS procedure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure7.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure7.3-1.png",
        "caption": "Figure 7.3.1. Single-degree-of-freedom sideslip model.",
        "texts": [
            " Particularly notable is the resonant response for \u03c9f close to the natural frequency \u03c9. For road vehicles the yaw damping ratio is generally in the range 0.2 to 1.0, and the yaw natural frequency is typically about 6 rad/s (1 Hz), so there may be observable resonance in yaw behavior. 7.3 1-dof Sideslip In the one-degree-of-freedom sideslip model the vehicle is considered inca- pable of yaw; this is of course unrealistic and is investigated here only in order to throw light on the more complex two- and three-degrees-of-freedom models considered later. Figure 7.3.1 shows the bicycle model vehicle with side force F(t) positioned to give zero yaw, with resultant lateral velocity component y giving attitude angle \u03b2. It is apparent from the figure that a steady F(t) will cause the development of a steady y such that \u03b2 gives adequate tire forces to oppose F(t). Also, because there is a damping force but no stiffness force, there will not be a natural frequency. where C0 is the zeroth moment vehicle cornering stiffness: 438 Tires, Suspension and Handling The characteristic equation of the free motion is This confirms that the natural response is exponential rather than oscillatory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.41-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.41-1.png",
        "caption": "FIGURE 5.41. Assembling of a spherical hand and arm.",
        "texts": [
            "40 respectively. Assembling of a hand to a manipulator is kinematic surgery in which during an operation we attach a multibody to the other. In this example we attach a spherical hand to a spherical manipulator to make a spherical arm-hand robot. The takht coordinate frame B4 of the manipulator and the neshin coordinate frame B4 of the wrist are exactly the same. Therefore, we may assemble the manipulator and wrist by matching these two frames and make a combined manipulator-wrist robot as is shown in Figure 5.41. However, 288 5. Forward Kinematics in general case the takht and neshin coordinate frames may have different labels and there be a constant transformation matrix between them. The forward kinematics of the robot for tool frame B9 can be found by a matrix multiplication. 0T9 = 0T1 1T2 2T3 3T4 4T5 5T6 6T7 7T8 8T9 (5.149) The matrices i\u22121Ti are given in Examples 161 and 167. We can eliminate the coordinate frames B3, and B4 to reduce the total number of frames, and simplify the matrix calculations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001836_jestpe.2014.2299765-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001836_jestpe.2014.2299765-Figure14-1.png",
        "caption": "Fig. 14. Layout of a three-phase power module mounted on a heat sink.",
        "texts": [
            "70e\u22124 (23) EOFF(i) = \u22121.96e\u22127 \u00b7 i2 + 1.20e\u22124 \u00b7 |i | + 6.68e\u22124 (24) Err(i) = \u22122.33e\u22127 \u00b7 i2 + 1.26e\u22124 \u00b7 |i | + 2.90e\u22124. (25) With these polynomials, switching and reverse recovery loss in IGBT\u2013FWDI pair 1 can be calculated by (26) and (27). It should be noted that these equations are only valid if the current through the considered device is different from zero. If not, switching loss falls to zero Psw,igbt,1 = 1 Ts \u00b7 ( EON(iigbt,1) + EOFF(iigbt,1) ) \u00b7 Udc Uref (26) Prr,fwdi,1 = 1 Ts \u00b7 Err(ifwdi,1) \u00b7 Udc Uref . (27) Fig. 14 shows the internal layout of the three-phase power module. It consists of six IGBT\u2013FWDI pairs soldered to a DBC substrate. The substrate is soldered to a copper base plate, which is mounted on a heat sink. To estimate the junction temperatures, the device losses are supplied to a lumped-parameter thermal network. Fig. 15 shows the thermal model which is split into 12 separate Cauer (ladder type) equivalent circuits representing the junction-case transient thermal impedance of each FWDI and IGBT"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.47-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.47-1.png",
        "caption": "Fig. 17.47 DC motor (SIEMENS)",
        "texts": [
            " They are used as machine tools, hoisting devices, and machines in the basic material and paper industries. Every DC machine has an armature winding A and, except for machines with permanent magnets, one excitation winding. This excitation winding can be implemented as a separate excitation winding F, as a shunt excitation E, or a series excitation D (Fig. 17.46). The armature current flows through the interpole winding B, which is responsible for the commutation process. Machines that place high demands on the dynamic system also have a compensation winding Fig. 17.47, which compensates the field of the armature. In this case a current slew rate of (diA/dt)/IN of up to 300 s\u22121 can be reached. Machines for variable-speed drives are produced with laminated iron sheet to suppress the flux delays in the armature as well as in the stator. Steady-State Operating Characteristics The characteristic operation behavior of a DC machine is illustrated by the rotational speed and armature current as a function of torque. If constant losses are neglected the following relations apply \u03a9 = V/c\u03a6 \u2212 RA/(c\u03a6)2 M , IA = 1/(c\u03a6)M "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000599_tro.2004.842341-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000599_tro.2004.842341-Figure2-1.png",
        "caption": "Fig. 2. Planar 4RRR manipulator with a goal EE path.",
        "texts": [
            ", the widespread computed-torque PD control law [21] becomes where respectively and is the desired and measured trajectory, is the error vector and and are gain matrices. The PM is controlled by . The presented approach was implemented in a MBS dynamics simulation tool. A variety of planar and spatial manipulators were investigated aiming to minimize the overall control forces. The first example is a 4RRR PM [32]. As its name suggests, the manipulator has 4 identical legs each consisting of a chain of three revolute joints connecting the base to the platform (Fig. 2). Since all joint axes are parallel the platform can only perform planar motions. The 4RRR PM originates from the 3RRR PM that has attracted much interest due its simple construction, but also due to the hazardous distribution of singularities in its workspace [6]. Most of the singularities of the 3RRR are removed by redundant actuation [32]. Thus the effort for the additional fourth chain is justified by the enlarged singularity free workspace and the ability to allow for components with joint clearing when controlling internal preload. Since closed-loop control is not the subject of this paper the model is assumed to be perfect and the manipulator is controlled by the inverse dynamics solution. The 4RRR PM has three kinematic loops. The loops are opened by removing three revolute joints connecting the respective limb to the platform, as indicated in Fig. 2. The remaining joint variables of the resulting kinematic tree structure constitute the generalized coordinates of the constrained MBS. Each of the three cut joints delivers two constraints constituting a system of 6 independent closure constraints. The DOF of the PM is . The joints at the base are actuated. The vector of active joint variables is of which are considered as independent. The configuration of the PM is uniquely determined by . That is the system is full-actuated with simple actuator redundancy . Fig. 2 depicts the position of the EE-tip for a desired motion. In this example the EE has to remain in its initial orientation. The EE-trajectory is determined according to velocity, acceleration and jerk limits. The corresponding time evolution of the joint variables, velocities and accelerations are found from the inverse kinematics (Fig. 3). Because of the four identical drives the weighting is . An actuator preload of Nm is required. Upper bounds are not considered. The task duration of 6 s is discretized in 5 ms steps and (19) is solved with a local one-dimensional search"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002350_j.snb.2017.04.052-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002350_j.snb.2017.04.052-Figure1-1.png",
        "caption": "Fig. 1. The schematic illustration of (a) the synthesis process and (b) structure of the composite film and its application in glucose detection.",
        "texts": [
            " Therefore, it is essential to find a more facile way o fabricate novel CuxO nanostructures with high active surface on u foils for enzyme-free glucose sensing. In our work, the novel thin film assembled by CuO/Cu2O anosheets on a Cu foil is synthesized by a facile and template-free ay involving only H2O2 solution. The obtained heterostructure is ade up by assembled ultrathin CuO nanosheets, ultrathin Cu2O lm and Cu substrate. As an electrochemical glucose sensor, the uO/Cu2O nanosheets film works as the active materials for the etection of glucose, and Cu foil substrate serves as the electronic ransport medium (Fig. 1). The as-prepared electrode shows high ensitivity, low detection limit, good stability, high selectivity and owerful reliability for analyzing human serum samples, indicating hat it is promising to be used as an enzyme-free glucose sensor. . Experimental .1. Chemicals Cu foil of thickness about 0.3 mm (99.96%) was purchased from ian Jinwei Co.td (Shenzhen, China). Sodium hydroxide (NaOH), ydrogen peroxide (30%), glucose, ascorbic acid (AA), uric acid (UA), odium chloride (NaCl), fructose, lactose and sucrose were obtained rom Aladdin Reagents",
            " First, Cu foils were burnished with abrasive paper n an orderly manner, then were used after ultrasound cleaning in M HCl, acetone, ethanol and deionized water. Cu substrate (10 m \u00d7 10 mm) with CuO/Cu2O nanosheets on it can be acquired y oxidizing Cu foil at 180 \u25e6C for 12 h in a reaction kettle (25 ml) rs B 248 (2017) 630\u2013638 631 containing 5 ml hydrogen peroxide (5%) which was diluted from 30% hydrogen peroxide solution. What is more, non-reaction proportion was sealed by Teflon tape to avoid oxidation. The whole process as shown in Fig. 1(a). 2.3. Instruments The X-ray diffractometer (Bruker-AXS D8 ADVANCE) equipped with Cu k radiation source ( = 1.54 \u00c5) was used to characterize the crystal phase of the as-prepared integrated CuO/Cu2O/Cu. The Raman spectrum of the sample was obtained by using an HR800 Raman spectrometer (HORIBA JOBIN YVON) attached with a CCD detector and He-Ne laser (514 nm). Kratos Axis Ultra DLD spectrometer using an Al mono K X-ray source was applied to measure X-ray photoelectron spectroscopy. The morphology of the products was observed by JSM-7000F field-emission scanning electron microscope (FE-SEM, JEOL, Japan)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003041_s11837-015-1298-7-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003041_s11837-015-1298-7-Figure2-1.png",
        "caption": "Fig. 2. Specimen orientations illustrating crack growth directions with respect to the build direction based on (a) ASTM, (b) ISO nomenclature. Five different sample orientations were evaluated in the present work.",
        "texts": [
            "26 The first letter designates the direction normal to the crack plane, and the second letter designates the expected direction of crack propagation. ISO standards use an X, Y, Z nomenclature (i.e. X-Y, Y-X, X-Z, Z-X, Y-Z, and Z-Y).27 The letter before the hyphen represents the direction normal to the crack plane and the letter following the hyphen represents the expected direction of crack extension. X always denotes the direction of principal deformation. However, there is no current ASTM/ISO designation for AM test orientations, and Fig. 2a and b is provided to begin the discussion for a similar nomenclature. One potential way to begin such discussions is to identify the START versus END of the build, as shown in Fig. 2a and b. The raster direction (RD) can be designated as shown, but it must be realized that AM processes often vary the raster direction from the START to END of the build, and thus Fig. 2a and b designates a final RD with the recognition that the AM community may also need to specify the type of raster profile during the build (e.g., same direction, orthogonal, etc.). The longitudinal (L/X), transverse (T/Y), and short (S/Z) directions are also shown in Fig. 2a and b. With the nomenclature shown in Fig. 2a and b, it is now possible to define at least eight different orientations for AM parts. For example in Fig. 2a, LS-END indicates that the crack growth direction occurs from the END to the START of the build, in the LS plane. In contrast, LS-START indicates that the crack growth direction occurs from the START to the END of build in the LS plane. A similar situation is observed with the TS-END and TSSTART samples where the crack again grows either to the START or to the END of the build, but in a different plane (i.e., TS). As indicated in Fig. 2a, for thin builds, the LT and TL orientations capture BOTH the start and end of the build during crack growth and are thus designated BOTH while the plane of fracture is also designated (e.g., TL and LT). Much thicker (and/or wider) builds may require other designations because the test sample may be removed closer to the START, MIDDLE, or END of the build. SL and ST orientations can also be evaluated at different locations depending on the height of the build. Figure 2a illustrates SL and ST specimens designed to fracture at the midplane of the build (i.e., SL-MIDDLE and ST-MIDDLE). Similar designations are possible for the evolving ISO standard as shown in Fig. 2b. Although ASTM F42 is beginning to address standards for mechanical testing of AM materials, Fig. 2a and b is provided to begin the discussion and provide some clarity to the orientations examined in the current work. With Fig. 2a provided as a guideline, Fig. 3 illustrates the schematics of an ARCAM EBM machine and orientation of specimens with regard to both the build and raster directions (RDs). LSEND, LS-START, LT-BOTH, TL-BOTH, and SLMIDDLE were evaluated in this preliminary study. As indicated earlier, thicker builds could require Seifi, Dahar, Aman, Harrysson, Beuth, and Lewandowski additional designations depending on how and where the test specimen is removed from the build. In the current study, the whole build comprised the test sample",
            " The fracture toughness experiments were conducted to failure at a displacement rate of 0.25 mm/min. Fracture Technology Associates (Bethlehem, PA) software was used to continuously monitor crack growth in both the fatigue and fracture toughness tests to comply with existing ASTM requirements. In all cases, 1\u20131.5 amp current input was used with voltage drop amplified by 10 K gain. Fatigue crack growth tests were performed in room-temperature air with a relative humidity of 40% in accordance with ASTM29 on various orientations shown in Fig. 2a. A cyclic frequency of 20 Hz was used in all cases. Again, the DCPD technique was used to monitor and control crack growth. Fatigue crack growth tests were first started at an intermediate DK using R values of 0.1, 0.3, and 0.7, followed by load shedding to establish the true fatigue threshold, DKth, as required by ASTM E647. The fatigue test was then stopped and restarted at a 5% lower DK than that used initially (to obtain enough overlap), and the test was run under rising DK conditions until catastrophic fracture. The Paris law slope and fatigue overload, Kc, was calculated for multiple tests conducted in this manner. As indicated earlier, the specimen orientation was varied in order to determine the presence of any anisotropy in properties. Five different distinguishable crack growth directions according to Fig. 2a were examined in this work: LS-END, LS-START, LT-BOTH, TL-BOTH, and SL-MIDDLE. To improve the efficiency of fatigue precracking and fatigue crack growth testing, the investigators at CWRU have developed both remote monitoring and controlling of the closed-loop computer-controlled test systems. This provides real-time remote access and/or remote control of the testing from various devices, including handheld phones, tablets, etc. This is particularly useful in fatigue crack growth testing where each experiment may require up to 1 week of machine time due to the need to achieve fatigue threshold at the ASTM E647 prescribed rate of crack growth",
            " 6 along with Rockwell C hardness values for the top (END) surface. The hardness values for wrought materials30 are also included. Fracture toughness results for all orientations tested are provided in Table II. The sample thickness requirement (i.e., 11\u201316 mm) for valid KIC measurements was nearly met, thus requiring the present fatigue-precracked fracture toughness data to be reported as Kq. Representative fatigue crack growth results at load ratios of 0.1, 0.3, and 0.7 for some of the orientations shown in Fig. 2a are provided in Table III. Fatigue overload values, KC, reported in Table III were all obtained at very high a/W (e.g., 0.7\u20130.8) and are presented only for completeness. Planar crack fronts were exhibited for all toughness and fatigue samples, suggesting minimal residual stress in the as-deposited builds. Table II indicates some level of anisotropy in the limited number of orientations tested to date, with the SL-MIDDLE producing the lowest toughness values. The fatigue crack growth tests summarized Evaluation of Orientation Dependence of Fracture Toughness and Fatigue Crack Propagation Behavior of As-Deposited ARCAM EBM Ti-6Al-4V Seifi, Dahar, Aman, Harrysson, Beuth, and Lewandowski in Table III also reveal anisotropy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure4-12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure4-12-1.png",
        "caption": "Fig. 4-12 Vector-controlled condition with the rotor speed \u03c9 \u03c9m p=( )( / )2 mech electrical rad/s.",
        "texts": [
            " For the relative distribution and hence the torque produced to remain the same as at t\u00a0=\u00a00+, the two windings must rotate at an exact \u03c9slip, which depends linearly on both the rotor resistance \u2032Rr and isq (slightly less by the factor Lm/Lr due to the rotor leakage flux), and inversely on B\u0302r \u03c9slip ( / ) ,= \u2032 k R L L i B r m r sq r 2 \u02c6 (4-21) where k2 is a constant. Now we can remove the restriction of \u03c9mech\u00a0=\u00a00. If we need to produce a step change in torque while the rotor is turning at some speed \u03c9mech, then the d-axis and the q-axis windings should be equivalently rotated at the appropriate slip speed \u03c9slip relative to the rotor speed \u03c9 \u03c9m p=( )( / )2 mech in electrical rad/s, that is, at the synchronous speed \u03c9yn\u00a0=\u00a0\u03c9m\u00a0+\u00a0\u03c9slip, as shown in Fig. 4-12. VECTOR CONTROL WITH d-AXIS ALIGNED WITH ROTOR FLUX 71 72 VECTOR CONTROL OF INDUCTION-MOTOR DRIVES 4-6 TORQUE, SPEED, AND POSITION CONTROL In vector control of induction-motor drives, the stator phase currents ia(t), ib(t), and ic(t) are controlled in such a manner that isq(t) delivers the desired electromagnetic torque while isd(t) maintains the peak rotor-flux density at its rated value. The reference values i tsq * ( ) and i tsd * ( ) are generated by the torque, speed, and position control loops, as discussed in the following section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure29-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure29-1.png",
        "caption": "Fig. 29. Contour lines of tooth contact stress (MPa).",
        "texts": [
            " It is found that machining errors have greater effects on tooth contact pattern and contact stress distribution by comparing Fig. 27 with Fig. 21. Fig. 28 is contour lines of SCS calculated in Case 5. It is found that tooth contact pattern is changed from a uniform contact into a center heavy contact for the effect of lead crowning. The maximum contact stress also has a bigger change from 1650 into 2064 MPa. But position of the maximum stress distribution line almost has no change by comparing Fig. 28 with Fig. 21. Fig. 29 is contour lines of SCS calculated in Case 6. It is found that tooth contact pattern and the maximum contact stress have the greatest changes in six cases for the effects of AE, ME and TM. For gears having contact ratios in the range 1 < e < 2, the maximum tensile root stress happens at the position of outer limit contact of the gears. This tooth engagement position is often called \u2018\u2018worst load position\u2019\u2019 and this position is used to do LTCA and RBS calculation for tooth bending strength design of gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003992_1350650117711595-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003992_1350650117711595-Figure7-1.png",
        "caption": "Figure 7. Schematic illustration of a plastic pinion tooth (Source: Kim48).",
        "texts": [
            " Modification techniques employed to the tooth of polymer gears Various techniques have been used by researchers to modify the tooth of polymer gears for enhancing the performance of these gears. These techniques are listed in Table 1. Brief discussions of these techniques are given below. Inserting a steel pin in the internal hole of the gear tooth A steel-pin was inserted into a drilled hole in the tooth of plastic pinion.48 The hole was drilled at the intersection of the tooth centerline and the base circle of the pinion as shown in Figure 7. The pinions made of nylon and acetal was tested on a power-circulating type gear test machine under different speed and torque combinations. The specific wear rate was calculated using the following expression49 Ws \u00bc Wv 2zmbNT \u00f01\u00de Test results indicated a decrease in tooth surface temperature that led to a reduced wear rate. Thus, the service life of plastic pinions improved significantly by introducing a steel-pin in the drilled hole of the tooth. Applying different fillet radius on gear tooth In this study, polymer gears with different tooth fillet radius of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure3-3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure3-3-1.png",
        "caption": "Fig. 3-3 Stator and rotor representation by equivalent dq winding currents. The dq winding voltages are defined as positive at the dotted terminals. Note that the relative positions of the stator and the rotor current space vectors are not actual, rather only for definition purposes.",
        "texts": [
            ") Similar to the stator case, each of the dq windings on the rotor has 3 2/ Ns turns, and a magnetizing inductance of Lm, which is the same as that for the stator dq windings because of the same number of turns (by choice) and the same magnetic path for flux lines. Each of these rotor equivalent windings has a resistance Rr and a leakage inductance L\u2113r (equal to \u2032Rr and \u2032L r , respectively, in the perphase equivalent circuit of induction machines in the previous course). The mutual inductance between these two orthogonal windings is zero. 3-2-3 Mutual Inductance between dq Windings on the Stator and the Rotor The equivalent dq windings for the stator and the rotor are shown in Fig. 3-3. The mutual inductance between the stator and the rotor d-axis windings is equal to Lm due to the magnetizing flux crossing the air gap. Similarly, the mutual inductance between the stator and the rotor q-axis MATHEMATICAL RELATIONSHIPS OF THE dq WINDINGS 33 windings equals Lm. Out of four dq windings, the mutual inductance between any d-axis winding with any q-axis winding is zero because of their orthogonal orientation, which results in zero mutual magnetic coupling of flux. 3-3 MATHEMATICAL RELATIONSHIPS OF THE dq WINDINGS (AT AN ARBITRARY SPEED \u03c9d) Next, we will describe relationships between the stator and the rotor quantities and their equivalent dq winding components in Fig. 3-3, which in combination produce the same mmf as the actual three phase windings. It is worth repeating that the space vectors at some arbitrary time t in Fig. 3-3 are expressed without a superscript \u201ca\u201d or \u201cA.\u201d The reason is that a reference axis is needed only to express them mathematically by means of complex numbers. In other words, these space vectors in Fig. 3-3 would be in the same position, independent of the choice of the reference axis to express them. We should note that the relative position of is and ir is shown arbitrarily here just for definition purposes (in an induction machine, the angle between is and ir is very large\u2014 more than 145\u00b0). 34 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS Hereafter, we will drop the superscript to any space vector expressed using d-axis as the reference. From Fig. 3-3, we note that at time t, the d-axis is shown at an angle \u03b8da with respect to the stator a-axis. Therefore, i t i t es s a j tda( ) ( ) .( )= \u2212 \u03b8 (3-10) Substituting for isa from Eq. (3-1), i t i e i e i es a j b j c jda da da( ) .( / ) ( / )= + +\u2212 \u2212 \u2212 \u2212 \u2212\u03b8 \u03b8 \u03c0 \u03b8 \u03c02 3 4 3 (3-11) Equating the real and imaginary components on the right side of Eq. (3-11) to isd and isq in Eq. (3-4) i t i t sd sq da da da( ) ( ) cos( ) cos cos         = \u2212       \u2212 2 3 2 3 \u03b8 \u03b8 \u03c0 \u03b8 4 3 2 3 4 3 \u03c0 \u03b8 \u03b8 \u03c0 \u03b8 \u03c0       \u2212 \u2212 \u2212       \u2212 \u2212   sin( ) sin sinda da da                  \u2192[ ]Ts abc dq i t i t i t a b c ( ) ( ) ( ) ,             (3-12) where [Ts]abc\u2192dq is the transformation matrix to transform stator a-b-c phase winding currents to the corresponding dq winding currents. This transformation procedure is illustrated by the block diagram in Fig. 3-4a. The same transformation matrix relates the stator flux linkages and the stator voltages in phase windings to those in the equivalent stator dq windings. From Fig. 3-3, we note that at time t, d-axis is at an angle \u03b8dA with respect to the rotor A-axis. Therefore, i t i t er r A j tdA( ) ( ) .( )= \u2212 \u03b8 (3-14) The currents in the dq rotor windings must be ird and irq, where these two current components are 2 3/ times the projections of i tr ( ) vector along the d- and q-axis, as shown in Fig. 3-3 i i t drd r= \u00d72 3/ ( )projection of along the -axis (3-15) and i i t qrq r= \u00d72 3/ ( ) .projection of along the -axis (3-16) Similar to Eq. (3-12), replacing \u03b8da by \u03b8dA i t i t rd rq dA dA dA( ) ( ) cos( ) cos cos         = \u2212       \u2212 2 3 2 3 \u03b8 \u03b8 \u03c0 \u03b8 4 3 2 3 4 3 \u03c0 \u03b8 \u03b8 \u03c0 \u03b8 \u03c0       \u2212 \u2212 \u2212       \u2212 \u2212   sin( ) sin sindA dA dA                  [ ] \u2192Tr ABC dq i t i t i t A B C ( ) ( ) ( ) ,             (3-17) where [Tr]ABC\u2192dq is the transformation matrix for the rotor. This transformation procedure is illustrated by the block diagram in Fig",
            " Inverting the resulting matrix and discarding the last column whose contribution is zero, we obtain the desired relationship MATHEMATICAL RELATIONSHIPS OF THE dq WINDINGS 35 36 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS i t i t i t a b c da da da ( ) ( ) ( ) cos( ) sin( ) cos             = \u2212 + 2 3 4 3 \u03b8 \u03b8 \u03b8 \u03c0      \u2212 +       +       \u2212 sin cos sin \u03b8 \u03c0 \u03b8 \u03c0 \u03b8 da da da 4 3 2 3 +                             [ ] \u2192 2 3 \u03c0 Ts dq abc i i sd sq         , (3-18) where [Ts]dq\u2192abc is the transformation matrix in the reverse direction (dq to abc). A similar transformation matrix [Tr]dq\u2192ABC for the rotor can be written by replacing \u03b8da in Eq. (3-18) by \u03b8dA. 3-3-2 Flux Linkages of dq Windings in Terms of Their Currents We have a set of four dq windings as shown in Fig. 3-3. There is no mutual coupling between the windings on the d-axis and those on the q-axis. The flux linking any winding is due to its own current and that due to the other winding on the same axis. Let us select the stator d-winding as an example. Due to isd, both the magnetizing flux as well as the leakage flux link this winding. However, due to ird, only the magnetizing flux (leakage flux does not cross the air gap) links this stator winding. Using this logic, we can write the following flux expressions for all four windings: Stator Windings \u03bbsd s sd m rdL i L i= + (3-19) and \u03bbsq s sq m rqL i L i= + , (3-20) where in Eq",
            " 3-5, the current, voltage, and flux linkage space vectors with respect to the \u03b1axis are related to those with respect to the d-axis as follows: v v es s dq j da _ _\u03b1\u03b2 \u03b1 \u03b8= \u22c5 (3-26a) i i es s dq j da _ _\u03b1\u03b2 \u03b1 \u03b8= \u22c5 (3-26b) MATHEMATICAL RELATIONSHIPS OF THE dq WINDINGS 37 38 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS and \u03bb \u03bb\u03b1\u03b2 \u03b1 \u03b8 s s dq je da _ _= \u22c5 , (3-26c) where v v jvs dq sd sq_ = + and so on. Substituting expressions from Eq. (3-26a through c) into Eq. (3-25), v e R i e d dt es dq j s s dq j s dq jda da da _ _ _\u22c5 = \u22c5 + \u22c5\u03b8 \u03b8 \u03b8\u03bb( ) or v e R i e d dt e j d dt s dq j s s dq j s dq j da s da da da d _ _ _\u22c5 = \u22c5 + \u22c5 + \u22c5\u03b8 \u03b8 \u03b8 \u03c9 \u03bb \u03b8 \u03bb _dq je da\u22c5 \u03b8 . Hence, v R i d dt js dq s s dq s dq d s dq_ _ _ _= + +\u03bb \u03c9 \u03bb , (3-27) where ( / )d dt da d\u03b8 \u03c9= is the instantaneous speed (in electrical radians per second) of the dq winding set in the air gap, as shown in Fig. 3-3 and Fig. 3-5. Separating the real and imaginary components in Eq. (3- 27), we obtain v R i d dt sd s sd sd d sq= + \u2212\u03bb \u03c9 \u03bb (3-28) and v R i d dt sq s sq sq d sd= + +\u03bb \u03c9 \u03bb . (3-29) In Eq. (3-28) and Eq. (3-29), the speed terms are the components that are proportional to \u03c9d (the speed of the dq reference frame relative to the actual physical stator winding speed) and to the flux linkage of the orthogonal winding. Equation (3-28) and Equation (3-29) can be written as follows in a vector form, where each vector contains a pair of variables\u2014the first entry corresponds to the d-winding and the second to the q-winding: v v R i i d dt sd sq s sd sq sd sq d         =         +         + \u2212\u03bb \u03bb \u03c9 0 1 1 0               [ ] ",
            " 3-9 COMPUTER SIMULATION In dq windings, the flux linkages and voltage equations are derived earlier. We will use \u03bbsd, \u03bbsq, \u03bbrd, and \u03bbrq as state variables, and express isd, isq, ird, and irq in terms of these state variables. The reason for choosing flux linkages as state variables has to do with the fact that these quantities change slowly compared with currents, which can change almost instantaneously. We can calculate dq-winding currents from the stator and the rotor flux linkages of the respective windings as follows: Referring to Fig. 3-3, the stator and the rotor d-winding flux linkages are related to their winding currents (rewriting Eq. 3-19 and Eq. 3-21 in a matrix form) as \u03bb \u03bb sd rd s m m r L sd rd L L L L i i         =                 [ ] . (3-59) 48 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS Similarly, in the q-axis windings, from Eq. (3-20) and Eq. (3-22), the matrix [L] of the above equation relates flux linkages to respective currents \u03bb \u03bb sq rq s m m r L sq rq L L L L i i         =                 [ ] . (3-60) Combining matrix Eq",
            " To accomplish this, we will make use of the phasor analysis in the initial steady state as follows: Phasor Analysis In the sinusoidal steady state, we can calculate current phasors Ia and \u2032 = \u2212I Ira A( ) in Fig. 3-11 for a given Va. All the space vectors and the dq-winding variables at t\u00a0=\u00a00 can be calculated. The phasor current for phase-a allows the stator current space vector at t\u00a0=\u00a00 to be calculated as follows: I I i I ea a i s a I j s i= \u2220 \u21d2 =\u02c6 ( ) \u02c6 . \u02c6 \u03b8 \u03b8 0 3 2 (3-63) Assuming the initial value of \u03b8da to be zero (i.e., the d-axis along the stator a-axis), and using Fig. 3-3 and Eq. (3-5) and Eq. (3-6) i i d Isd s Is ( ) projection of ( ) on -axis0 2 3 0 2 3 3 2 = \u00d7 =       \u02c6 \u02c6 cos( )\u03b8i (3-64) 50 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS and i i q Isq s Is ( ) projection of ( ) on -axis0 2 3 0 2 3 3 2 = \u00d7 =       \u02c6 \u02c6 sin( ).\u03b8i (3-65) Similarly, we can calculate \u03bdsd(0) and \u03bdsq(0). The phasor I IA ra( )= \u2212 \u2032 allows ird(0) and ir (0) to be calculated. Knowing the currents in the dq windings at t\u00a0 =\u00a0 0 allows the initial values of the flux linkages to be calculated from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002682_j.ijheatmasstransfer.2019.06.038-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002682_j.ijheatmasstransfer.2019.06.038-Figure17-1.png",
        "caption": "Fig. 17. Three dimensional snapshots showing velocity and temperature field (a) and the flow rate of Y-Z section towards the X direction near the lowest point over time from 146.28 ls to 390.08 ls (b).",
        "texts": [
            " Lateral snapshots showing temporal evolution of the melt pool on the X-Z cross The red and blue arrows represent the lowest point of the molten pool in each case. Th time in the \u2018\u2018necking\u201d area. By comparison, the molten pool was stable with a spoon-like shape throughout the process when a relatively sufficient packing density was applied. The difference in surface undulation indicated that the velocity profiles were dissimilar. Thus, the temporal velocity field and temperature at 146.28 ls with different packing densities were captured, as shown in Fig. 17a. As indicated by the arrows, the obvious backward flow caused by the Marangoni effect and recoil pressure could always be observed under both conditions, and it seemed independent of powder quantity. Further, the flow rate near the bottom of the molten pool of different Y-Z sections along the X axis (towards X direction) at different times are illustrated in Fig. 17b. It was apparently found that the flow rate basically followed a parabolic trend, and the maximum flow rate was located right at the bottom of the molten pool, as indicated by the red and blue arrows. It was worth noting that the flow rate behind the bottom decreased sharply with the increase of the distance away from the bottom and kept this state through the entire process when the powder packing density was 3.183 kg/m3. Under this situation, the continuous high backward input flow at the bottom and the low output flow at the rear resulted in an increased amount of liquid behind the bottom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000736_0278364904047392-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000736_0278364904047392-Figure3-1.png",
        "caption": "Fig. 3. Free-body diagram of rigid wheel on deformable terrain.",
        "texts": [
            " Thus, the terrain strength constraint can be written for deformable terrain as( Ti / Ai ) \u03c4max i \u2200 i, i = {1 . . . n} . (12) A priori estimates of c and \u03c6 an be used if the terrain properties are known in advance. If the parameters are unknown or variable, estimation techniques can be employed. A method for on-line estimation of c and \u03c6 has been developed (Iagnemma, Shibley, and Dubowsky 2002). The algorithm relies on a simplified form of classical terramechanics equations, derived from quasi-static analysis of wheel\u2013 terrain interaction (see Figure 3). The method uses a linear least-squares estimator to compute c and \u03c6 in real time. This allows a rover to optimize its wheel traction to locally changing terrain conditions. In this paper, however, we assume a priori knowledge of c and \u03c6 for simplicity. To solve the optimization problem discussed above, the local wheel\u2013terrain contact angles must be known. Here, we present a method for estimating wheel\u2013terrain contact angles from simple on-board rover sensors. Consider a planar two-wheeled system on uneven terrain (see Figure 4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003493_j.matchar.2020.110842-Figure21-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003493_j.matchar.2020.110842-Figure21-1.png",
        "caption": "Fig. 21. Strut end-fitting for space technology produced by hybrid SLM and DED technology.",
        "texts": [
            " The elimination of defects such as pores during AM and a higher annealing temperature (prevention of \u03b4-phase precipitation) could decrease the gap in the mechanical properties between the DED and SLM parts. During the investigation, the interface between the SLM and DED part was rarely the weak point. The reason for this strong bond was the higher rate of the solidification due to heat transfer into the SLM part. This is also the reason for the lesser extent of \u03b4-phase in the DED area near the SLM/DED interface, resulting in the strong bond (Fig. 6c). The technology demonstrator considered in this study was the strut end-fitting shown in Fig. 21, with a 20% mass reduction and the same strength characteristics as the same conventional end-fitting design. Our study showed that in spite of all the drawbacks, combining the 2 AM technologies is feasible and exhibits great potential for further M. Godec et al. Materials Characterization 172 (2021) 110842 implementation in the space industry in the form of different structural parts for space vehicles and the assembly elements of different propulsion systems. We investigated samples of a hybrid SLM/DED AM-processed Inconel 718"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000416_027836498200100204-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000416_027836498200100204-Figure1-1.png",
        "caption": "Fig. 1. Link and joint numbering and other conventions for open-loop kinematic chains.",
        "texts": [
            " In order to interpret the result and compare it to the Newton-Euler formulation, however, it is finally necessary to make some of these definitions. Such details are not the point of this paper and will be kept to a minimum. The links of the manipulator are numbered consecutively from the base to the tip, as are the joints that connect them. The base is considered to be link 0, while the terminal link is numbered link n. The joints are numbered 1 through n, joint 1 connecting link I to the base. Thus, joint i connects links i - 1 and i; link i is bounded by joints i and i + 1, as shown in Fig. 1. If joint i is rotational, the joint variable qi mea- sures the angle of rotation from some (arbitrary for the present discussion) reference point; if it is translational, q; measures the sliding distance. The unit vector ~i is attached to joint i and points along the axis of rotation for rotary joints or along the sliding axis for sliding joints. Note that for rotary joints, qt must be measured in a right-hand sense about 2i. Finally, let Pj be a position vector that points from anywhere along the axis of joint j to the center of mass of link i",
            " Acknowledgments I would like to thank John Hollerbach, Mike Brady, and Berthold Horn for many useful discussions and comments, and Frank Morgan for teaching me tensor algebra. Appendix: Details for the Lagrangian Formulation . In this Appendix are the details that were omitted from the derivation of the generalized forces presented earlier. For (Eq. 18): For (Eq. 23): Since the inertia tensor 1 is not velocity-dependent, it can be shown that Thus, we have Therefore, The final (and trickiest) proof is for (Eq. 19): We will need (Eqs. 27 and 29) and the conventions of Fig. 1, except that for convenience we will take zk to be 0 if joint k is translational. First note that if joint j is translational or if j > i, mj is independent of both q; and q;, so both sides of the equation are identically zero. Now fort *5 i, since 2j is attached to joint j and therefore link j, we may write By considering the rotation of a vector by some angle about a given axis, we can see that Now we have everything we need for the proof. Starting with (Eq. 30), REFERENCES Armstrong, W. W. 1979"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000214_robot.1993.291970-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000214_robot.1993.291970-Figure2-1.png",
        "caption": "Figure 2: U-joint and its coordinate frames.",
        "texts": [
            " As a result, both U-joints and ball joints are not perfect - their axes neither intersect nor are perpendicular to each other. As such, joint centers in actuality do not exist. Consequently, the axes of the actuators are skew to joint axes. A kinematic model, which accommodates these errors, is needed in order to analyze their effect on the platform accuracy. 3.1 Modeling of multi-axis joints As mentioned above, U-joints and ball-joints are used in the construction of the Stewart platform, and therefore there is a need to model these multi-axis joints. A U-joint can rotate about two ases Z, and Z, (Figure 2) while ball joint can rotate about three ases Z, , Z, and 2, (Figure 3). The D-H convention [lo] is used to model the joints so that the above errors can be included. By the D-H convention, Ti represents homogeneous transformation from frame {i-1) to frame {i} and is defined by: Ri Q i T = [ o 1 1 where cos 0, - sin 8, cos a, sin 0, sin a, RI = sine, cos 8, cosa, -cos e, sina, [ 0 sina, cos a, and yi=[aicosei , aisinei , di ] T (4) For an imperfect U-joint the parameters al and d, the twist define the distance between its ases and a, anglc between them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000620_41.481408-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000620_41.481408-Figure5-1.png",
        "caption": "Fig. 5. 3-mass system. (a) 3-mass system model. (b) Block diagram of 3-mass system.",
        "texts": [
            " The results of the proposed controller when R = fi and R = are illustrated in Fig. 4(c) and (d), respectively. The proposed method is superior to the II 1 Td 11 0*01 q2 [Ndrad] (1 1.2938 *1: when R=n. *2: when R = conventional P&I method both in its command response and disturbance rejection. V. APPLICATION TO 3-MASS SYSTEM As a 3-mass system has two resonant frequencies, we need the higher order system model to represent it than in the 2- mass system. The model of 3-mass system is illustrated in Fig. 5(a) consisting of three rigid masses connected with two flexible shafts. Its block diagram is shown in Fig. 5(b). 60 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 43, NO. 1, FEBRUARY 1996 The state equations of the 3-mass system are given in (12) where J1 represents the inertia moment of the motor, and J 2 and J 3 represent inertia moments of the loads. and K 2 3 are the stiffnesses of the shaft. There are five state variables: x = ( w 1 e12 w2 1923 ~ 3 ) ~ . T,, the motor torque, is the control input and TL is the disturbance input. w 1 is the measurable motor speed, and w 3 is the load speed to be controlled but is not measurable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.20-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.20-1.png",
        "caption": "FIGURE 5.20. The position of the final frame in the base frame.",
        "texts": [
            " This problem can be solved by determining transformation matrices 0Ti to describe the kinematic information of link (i) in the base link coordinate frame. The traditional way of producing forward kinematic equations for robotic manipulators is to proceed link by link using the Denavit-Hartenberg notations and frames. Hence, the forward kinematics is basically transformation matrix manipulation. For a six DOF robot, six DH transformation matrices, one for each link, are required to transform the final coordinates to the base coordinates. The last frame attached to the final frame is usually set at the center of the gripper as shown in Figure 5.20. For a given set of joint variables, the transformation matrices i\u22121Ti are uniquely determined. Therefore, the position and orientation of the end-effector is also a unique function of the joint variables. The kinematic information includes: position, velocity, acceleration, and jerk. However, forward kinematics generally refers to the position analysis. So the forward position kinematics is equivalent to a determination of a combined transformation matrix 0Tn = 0T1(q1) 1T2(q2) 2T3(q3) 3T4(q4) \u00b7 \u00b7 \u00b7 n\u22121Tn(qn) (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003503_j.measurement.2016.03.001-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003503_j.measurement.2016.03.001-Figure5-1.png",
        "caption": "Fig. 5. Bending stress distribution within the cross section of gear tooth.",
        "texts": [
            " Maximum bending stress at differe sections along the tooth length to the number of cross sections along the tooth length. Kav is constant for a particular load position of given gear specification. As the load moves on the profile the average factor will be changed and calculated corresponding bending stress distribution. The variation in Kav from engagement to disengagement is plotted in Fig. 4. The bending stress varies linearly along the cross section from neutral axis to top or bottom edge of the cross section of tooth as shown in Fig. 5. So the average stress within the top or bottom portion of the tooth cross section from the neutral axis will be the half of the maximum stress at the top or bottom edge of the rectangular cross section. The total average bending stress rav in the top or bottom portion of the tooth from the neutral axis along the tooth length as well as along the cross section can be written in the terms of maximum bending stress at the tooth root rmax as; rav \u00bc rmax 2kav \u00f07\u00de By using Eqs. (7), and (5) can be written as; U \u00bc Z vol r2 max 4K2 avE dV \u00f08\u00de By using Hooke\u2019s law r \u00bc Ee, the Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002277_j.jmapro.2020.08.060-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002277_j.jmapro.2020.08.060-Figure2-1.png",
        "caption": "Fig. 2. The welding torch.",
        "texts": [
            " In addition, it offers the opportunity to manufacture parts utilizing additional AM technologies, such as WAAM-based Gas Tungsten Arc Welding (GTAW) or WAAM-based Plasma Arc Welding (PAW). This machine is also equipped with a close chamber which allows for the manufacturing of parts in reactive materials. In the GMAW process, the electric arc melts the wire to deposit it on the top of the substrate obtaining the desired geometry. Furthermore, to control the process, a geometrical laser scanner (Laser Scanner Q4 Series) and a pyrometer (Optris CT) were placed in the welding torch (Fig. 2). For the measurement of the surface temperature, an emissivity of 0.5 was considered for mild steel following the recommendations provided by the supplier. The laser scanned the geometry of the walls every two layers, obtaining a cloud of points that represented the transversal geometrical shapes of the deposited layers and, thanks to this cloud of points, the operator can decide the Z position for the following layer. For more detail, this laser measures 244 points per profile and the profiles are given every 2 mm in the longitudinal direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.24-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.24-1.png",
        "caption": "Fig. 17.24a,b Single-phase transformer construction: (a) UI transformer; (b) EI transformer",
        "texts": [
            " Aluminum produced by electrodeposition involves the additional materials of bauxite and cryolite in fluid state. Electroplating is the production of metallic coatings using an electrolysis procedure (for example, nickel plating). Working Principle and Equivalent Circuit Diagram A simple transformer device has two magnetically coupled windings [17.9]. One side of the transformer is called the primary winding and the other side is the secondary winding. The transformer consists of copper windings and an iron core carrying flux which produces magnetic coupling between the two windings of the transformer (Fig. 17.24). Depending on construction principles, usage, power rating, and other factors we can distinguish between the following groups and subgroups: \u2022 Usage: power, regulating, generator, and transmission transformers\u2022 Power rating: small, medium, and large power transformers, and high-performance transformers \u2022 Type of cooling: oil-immersed and dry-type transformers\u2022 Core type: core- and shell-type transformers\u2022 Transformation ratio: step-up and step-down transformers\u2022 Arrangement of windings: separate winding transformers and auto-transformers\u2022 Number of phases: single- and three-phase transformers, grouped into three- and five-limb cores The transformer can be mathematically analyzed as a reverse two-port network"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.5-1.png",
        "caption": "Fig. 3.5 Out-of-plane bending of a rotor blade",
        "texts": [
            " One of the key features of the Helisim model family is the use of a common analogue model for all three types \u2013 the so-called centre-spring equivalent rotor (CSER). We need to examine the elastic motion of blade flapping to establish the fidelity of this general approximation. The effects of blade lag and torsion dynamics are considered later in this section. Fig. 3.4 Three flap arrangements: (a) teetering; (b) articulated; (c) hingeless Blade Flapping Dynamics \u2013 Introduction We begin with a closer examination of the hingeless rotor. Figure 3.5 illustrates the out-of-plane bending, or flapping, of a typical rotating blade cantilevered to the rotor hub. Using the commonly accepted engineer\u2019s bending theory, the linearised equation of motion for the out-of-plane deflexion w(r, t) takes the form of a partial differential equation in space radius r and time t, and can be written (Ref. 3.5) as \ud835\udf152 \ud835\udf15r2 ( EI \ud835\udf152w \ud835\udf15r2 ) + m \ud835\udf152w \ud835\udf15t2 + \u03a92 \u23a1\u23a2\u23a2\u23a3mr \ud835\udf15w \ud835\udf15r \u2212 \ud835\udf152w \ud835\udf15r2 R \u222b r mrdr \u23a4\u23a5\u23a5\u23a6 = F(r, t) (3.8) 80 Helicopter and Tiltrotor Flight Dynamics where EI(r) and m(r) are the blade radial stiffness and mass distribution functions and \u03a9 is the rotorspeed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002211_j.ijfatigue.2016.03.012-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002211_j.ijfatigue.2016.03.012-Figure2-1.png",
        "caption": "Fig. 2 Orientation of CT specimen and main planes with respect to the build direction",
        "texts": [
            " The lateral separation between consecutive scan lines has been set at 180 \u03bcm whereas the layer thickness has been fixed at 50 \u03bcm. The selective layer-by-layer melting of the powder by the laser beam induces an inherent texture in the SLM material. Consequently, the parts have some degree of anisotropy. The CT specimens with characteristic size w = 30 mm and thickness t = 6 mm according to the geometry specified in ASTM E 647-08 have been fabricated by the SLM process. The crack propagation direction has been identical with the build direction, see Fig. 2. The as-produced CT specimen is shown in Fig. 3. It is pointed out that the pin holes and the starter notch have been obtained directly. The pin holes have then been reamed to the final tolerance. Specimens for metallographic analysis have been cut out from as-produced CT specimen after fatigue testing in such a way that the microstructure in the three main planes defined in Fig. 2 could be visualized. Specimens have been hot-pressed into Duroplast using CitoPress-1 device. Surfaces for observation have been prepared using an automatic grinding and polishing system TegraPol-15. Grinding was conducted using SiC paper (220 grit) and fine sanding on the MD Largo discs with the addition of DiaProAlegro Largo emulsion. Polishing has been conducted using MD Dac canvas with the addition of DiaProDac emulsion, followed by a final chemical polishing on the MD Chem polishing wheel with the addition of OP-S suspension",
            " The fracture surface is very similar to that reported for conventionally manufactured alloy [16, 19]. The SLM produced components are characterized by high residual stresses, see for example [24] in the case of Ti-6Al-4V. Strong differences in the crack propagation rate in the as-built and after stress relief were found and were attributed to the modified residual stress systems. In the present case, the SLM IN718 specimens are in the as-produced state. Considering that the crack growth direction is parallel to the build direction, Fig. 2, and that the material around the starter notch is selectively melted last, a system of tensile residual stresses is expected to affect the notch root and favor closure-free crack growth. If that were the case, the present SLM IN718 alloy near threshold FCG data could be compared to the surely crack closure free data (at R = 0.8) of wrought Inconel 718, [20]: such a comparison shows a coincident value of Kth equal to about 3 MPam 1/2 . Therefore, residual stresses may have a key role in the interpretation of the FCG behavior of SLM materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001097_j.jsv.2015.10.015-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001097_j.jsv.2015.10.015-Figure2-1.png",
        "caption": "Fig. 2. Spall definition on the outer race.",
        "texts": [
            " From Hertz contact theory, the contact force between the jth ball and the raceway is given by f j \u00bc kb\u03b4 1:5 j (6) According to the equations above, the total nonlinear contact forces of the bearing in the x- and y-directions are, respectively, f x \u00bc kb X \u03b3j\u03b4 1:5 j cos \u0278j (7) f y \u00bc kb X \u03b3j\u03b4 1:5 j sin \u0278j (8) where kb is the stiffness of the load contact. When the local fault occurs on the outer race, the depth of the local fault is defined as cd, angle spanned by the fault \u0394\u0278d, the width of the fault L and angular position of the fault \u0278d. Fig. 2 shows a diagram of the model of the outer race fault and some of the geometric relations. L\u00bcD sin \u0394\u03a6d 2 (9) Please cite this article as: L. Cui, et al., Vibration response mechanism of faulty outer race rolling element bearings for quantitative analysis, Journal of Sound and Vibration (2015), http://dx.doi.org/10.1016/j.jsv.2015.10.015i When the ball moves over the site of the local fault, the ball releases deformation. At this time, the deformation from the jth rolling element entering the site of the fault is expressed as \u03b4j \u00bc xs xp cos \u0278j\u00fe ys yp sin \u0278j c \u03b2jcd (10) Switch function value \u03b2j in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000513_s11661-008-9566-6-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000513_s11661-008-9566-6-Figure1-1.png",
        "caption": "Fig. 1\u2014Schematic of real time MPS and ZHC system applied to the LENS process.",
        "texts": [
            " Accordingly, it is necessary to provide proper thermal management of the melt pool during deposition. This can be achieved by two means: one is proper choice of process parameters; another is via the implementation of external sensor and control strategies to ensure that the melt pool size and deposited thickness are stable during the course of deposition.[24] Therefore, a real time melt pool sensor (MPS) and a Z-height control (ZHC) subsystems have been developed and applied to our LENS experiments, as shown in Figure 1. The developed MPS subsystem is designed to automatically adjust the laser input power level to maintain a constant surface area of the molten pool, which is useful for the deposition of variable materials as well as for eliminating melt pool size variations that can occur due to geometrical changes in the component. The developed ZHC subsystem is designed to automatically retain the same deposition distance by changing the laser travel speed. The challenge of controlling microstructure and component dimensions requires a quantitative understanding of the relationship between process parameters (such as laser output power and travel speed), dimension, cooling rate, microstructure, and properties by developing a fundamental understandingof the associated transport phenomena"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003546_tmag.2015.2446951-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003546_tmag.2015.2446951-Figure1-1.png",
        "caption": "Fig. 1. Doubly salient machines having 12/10 stator/rotor poles. (a) Proposed hybrid-excited machine. (b) Variable flux machine.",
        "texts": [
            " This will have the advantages that (a) the DC and magnet flux paths are in parallel thus maintaining good flux regulation capability, and (b) the risk of demagnetization may be less since the magnets are not placed in the main magnet circuit of the stator or rotor. The concept of inserting PM between salient stator poles has been experimentally validated in a single phase doubly salient selfexcited generator [13, 14], switched reluctance machine [20] and hybrid reluctance machine with magnetically isolated stator phases [21]. This paper applies the concepts of: (a) inserting PM between adjacent salient stator poles and (b) using the PM flux to counteract the DC excitation flux to propose a new threephase stator hybrid-excited machine, Fig. 1. This machine is driven by three phase sinusoidal currents and it is developed by inserting PM in the stator slot of the electrically excited I \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014 I. A. A. Afinowi, Z. Q. Zhu, and Y. Guan are with Department of Electronic and Electrical Engineering, University of Sheffield, S1 3JD, UK (E-mail: {ibrahim.afinowi, z.q.zhu, elp10yg}@sheffield.ac.uk, iafinowi@gmail.com,) J. C. Mipo and P. Farah are with Valeo Powertrain Electric Systems, 94017 Cr\u00e9teil Cedex, France (E-mail:{jean-claude.mipo, Philippe.farah} @valeo.com, philippe.farah@valeo.com) 0018-9464 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 2 12/10 stator/rotor pole variable flux machine (VFM), having both its armature and DC windings in the stator slot [4], Fig. 1. The VFM is a modification of the three phase unipolar excited switched reluctance machine (SRM) by employing an additional DC-excited winding and exciting the armature windings with sinusoidal bipolar currents. Although the VFM maintains the robustness and low cost of conventional SRMs [22, 23], the conventional SRMs\u2019 characteristics are considerably influenced by different excitation techniques and coil connections [24-26]. In VFM, the torque production mechanism is more dependent on the DC-armature winding mutual inductance variation with rotor position and not the variation of armature self-inductance with rotor position, which is the case in unipolar excited SRMs",
            " back-EMF, flux-linkage, cogging torque, electromagnetic torque, PM demagnetization, iron- and PM losses are investigated. In addition, the electromagnetic torque and machine losses are compared for the proposed hybrid-excited machine (HSSPM) and the electrically-excited variable flux machine (VFM). Finally, the electromagnetic performance of the HSSPM machine is experimentally validated. II. MACHINE STRUCTURE AND BASIC OPERATION PRINCIPLE The proposed three phase hybrid-excited machine with doubly salient 12/10 stator/rotor poles is shown in Fig. 1. The machine is characterised by the following constraints: \u2022 Number of phases m = 3. \u2022 Stator poles Ns = 12. \u2022 Rotor poles Nr = Ns - 2. \u2022 The machine has a balanced double layer, concentrated windings with a fractional slot per pole per phase q < 1. \u2022 The coil span/coil throw equals one slot pitch. Each stator pole of the HSSPM machine has a pair of coils in the stator slot: one for the armature winding (A/B/C 1-4) and the other for the DC winding (DC). Each phase winding consists of four armature coils connected in series"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000933_s0022112086001131-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000933_s0022112086001131-Figure1-1.png",
        "caption": "FIGURE 1 . Orientation of the swimming velocity V , of an algal cell idealized as a sphere. L is the rearward displacement of the centre of mass (*) relative to the geometrical centre (+). As in (2), the gravitational torque Tg = mgL sin 0 is balanced by the viscous torque Tp = 4xpa3(V x u ) ~ , where (V x u ) ~ is the horizontal component of vorticity. The cells swim in the direction - ( L / L ) , propelled by their flagella F.",
        "texts": [],
        "surrounding_texts": [
            "Physics Department, University of Arizona, Tucson, AZ 85721, USA (Received 22 May 1986) Gravitational and viscous torques acting on swimming micro-organisms orient their trajectories. The horizontal component of the swimming velocity of individuals of the many algal genera having a centre of mass displaced toward the rear of the cell is therefore in the direction g x (V x u) , where g is the acceleration due to gravity. This phenomenon, called gyrotaxis, results in the cells swimming toward downwardflowing regions of their environment. Since the cells\u2019 density is greater than that of water, regions of high (low) cell concentration sink (rise). The horizontal component of gyrotaxis reinforces this type of buoyant convection, whilst the vertical one maintains it. Gyrotactic buoyant convection results in the spontaneous generation of descending plumes containing high cell concentration, in spatially regular concentration/convection patterns, and in the perturbation of initially4 well-defined flow fields. This paper presents a height- and azimuth-independent steady-state solution of the Navier-Stokes and cell conservation equations. This solution, and the growth rate of a concentration fluctuation, are shown to be governed by a parameter similar to a Rayleigh number."
        ]
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure7.66-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure7.66-1.png",
        "caption": "Fig. 7.66 Design principles of low-inductive shunts",
        "texts": [
            "5 kA/ls, the peak voltage of the inductive component becomes (40 nH) (0.5 kA/ls) = 20 V. This is approx. 200 % of the peak voltage measurable across an \u2018\u2018ideal\u2019\u2019 shunt after the instant t 3sc \u00bc 6 ls given by (1 kA) (10 mX) = 10 V. 358 7 Tests with High Lightning and Switching Impulse Voltages To minimize the measuring error due to the induced voltage, the area of the measuring loop must be as small as possible. This is usually realized using either coaxial shunts or even disc-shaped shunts as illustrated in Fig. 7.66. The simplest way to eliminate the voltage induced in the measuring loop is to apply a pure inductive converting device. As illustrated in Fig. 7.67, this may consist either of only a single turn or even numerous turns known as Rogowski coil (Rogowski 1913). Based on the inductance law, the voltage detectable at the output of the coil without load (i.e. open loop) can be approximated by: 7.5 Measurement of High Currents in LI Voltage Tests 359 vl t\u00f0 \u00de \u00bc M di dt \u00bc l0 n b 8 ln 2a\u00fe b 2a b di dt ; \u00f07:43\u00de with M mutual inductance l0 permeability of air n number of turns a distance between conductor and Rogowski coil b diameter of turns As the voltage v(t) induced in the Rogowski coil is proportional to the derivate of the current, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure4.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure4.9-1.png",
        "caption": "FIGURE 4.9. Rotation about an axis not going through origin.",
        "texts": [
            " The coordinates of P in the global frame G(OXY Z) can be found by using the homogeneous transformation matrices. The position of P in frame B2 (x2y2z2) is indicated by 2rP . Therefore, its position in frame B1 (x1y1z1) is \u23a1\u23a2\u23a2\u23a3 x1 y1 z1 1 \u23a4\u23a5\u23a5\u23a6 = \u2219 1R2 1d2 0 1 \u00b8\u23a1\u23a2\u23a2\u23a3 x2 y2 z2 1 \u23a4\u23a5\u23a5\u23a6 (4.116) 170 4. Motion Kinematics X Y Z x1 y1 z1 r x2 y2 z2 d1 P G B1 B2 d2 Example 93 F Rotation about an axis not going through origin. The homogeneous transformation matrix can represent rotations about an axis going through a point different from the origin. Figure 4.9 indicates an angle of rotation, \u03c6, around the axis u\u0302, passing through a point P apart from the origin. We set a local frame B at point P parallel to the global frame G. Then, a rotation around u\u0302 can be expressed as a translation along \u2212d, to bring the body fame B to the global frame G, followed by a rotation about u\u0302 and a reverse translation along d GTB = Dd\u0302,dRu\u0302,\u03c6Dd\u0302,\u2212d = \u2219 I d 0 1 \u00b8 \u2219 Ru\u0302,\u03c6 0 0 1 \u00b8 \u2219 I \u2212d 0 1 \u00b8 = \u2219 Ru\u0302,\u03c6 d\u2212Ru\u0302,\u03c6d 0 1 \u00b8 (4.118) where, Ru\u0302,\u03c6 = \u23a1\u23a3 u21 vers\u03c6+ c\u03c6 u1u2 vers\u03c6\u2212 u3s\u03c6 u1u3 vers\u03c6+ u2s\u03c6 u1u2 vers\u03c6+ u3s\u03c6 u22 vers\u03c6+ c\u03c6 u2u3 vers\u03c6\u2212 u1s\u03c6 u1u3 vers\u03c6\u2212 u2s\u03c6 u2u3 vers\u03c6+ u1s\u03c6 u23 vers\u03c6+ c\u03c6 \u23a4\u23a6 (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure4.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure4.4-1.png",
        "caption": "FIGURE 4.4. Representation of a point P in coordinate frames B and G.",
        "texts": [
            "13) indicates the rigid motion of body B2 with respect to frame G. The composition defines a third rigid motion, which can be described by substituting the expression for 2r into the equation for Gr. Gr = GR2 \u00a1 2R1 1r+ 2d1 \u00a2 + Gd2 = GR2 2R1 1r+GR2 2d1 + Gd2 = GR1 1r+ Gd1 (4.14) Therefore, GR1 = GR2 2R1 (4.15) Gd1 = GR2 2d1 + Gd2 (4.16) which shows that the transformation from frame B1 to frame G can be done by rotation GR1 and translation Gd1. 154 4. Motion Kinematics 4.2 Homogeneous Transformation As shown in Figure 4.4, an arbitrary point P of a rigid body attached to the local frame B is denoted by BrP and GrP in different frames. The vector Gd indicates the position of origin o of the body frame in the global frame. Therefore, a general motion of a rigid body B (oxyz) in the global frame G (OXY Z) is a combination of rotation GRB and translation Gd. Gr = GRB Br+ Gd (4.17) Using a rotation matrix plus a vector leads us to the use of homogeneous coordinates. Introducing a new 4 \u00d7 4 homogeneous transformation matrix GTB, helps us show a rigid motion by a single matrix transformation Gr = GTB Br (4",
            " GTB = DX,a = \u23a1\u23a2\u23a2\u23a3 1 0 0 a 0 1 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (4.49) GTB = RX,\u03b3 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 cos \u03b3 \u2212 sin \u03b3 0 0 sin \u03b3 cos \u03b3 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (4.50) GTB = DY,b = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 b 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (4.51) GTB = RY,\u03b2 = \u23a1\u23a2\u23a2\u23a3 cos\u03b2 0 sin\u03b2 0 0 1 0 0 \u2212 sin\u03b2 0 cos\u03b2 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (4.52) GTB = DZ,c = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 c 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (4.53) GTB = RZ,\u03b1 = \u23a1\u23a2\u23a2\u23a3 cos\u03b1 \u2212 sin\u03b1 0 0 sin\u03b1 cos\u03b1 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (4.54) 4. Motion Kinematics 161 Example 85 Homogeneous transformation as a vector addition. It is seen in Figure 4.4 that the position of point P can be described by a vector addition GrP = Gd+ BrP . (4.55) Since a vector equation is meaningful when all the vectors are described in the same coordinate frame, we need to transform either BrP to G orGd to B. Therefore, the applied vector equation is GrP = GRB BrP + Gd (4.56) or BRG GrP = BRG Gd+ BrP . (4.57) The first one defines a homogenous transformation from B to G, GrP = GTB BrP (4.58) GTB = \u2219 GRB Gd 0 1 \u00b8 (4.59) and the second one defines a transformation from G to B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003372_j.ijrmhm.2018.10.004-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003372_j.ijrmhm.2018.10.004-Figure1-1.png",
        "caption": "Fig. 1. (a) Powder morphology, (b) powder particle distribution for tungsten, (c) illustration of the spatial reference system including the \u2018meander\u2019 scan strategy used and (d) CAD illustration of the test specimens manufactured.",
        "texts": [
            " The overall aim of the work was to use \u2018process maps\u2019 as a basis to more systematically evaluate the relationships between the process variables and part quality. The results have been quantified in terms of the part density and nature of the defects produced, as well as their microstructure and crystallographic texture. Plasma-spheroidised commercial purity tungsten powder supplied by Tekna Advanced Materials (Macon, France) was used for producing the test pieces in a Renishaw AM125 LPBF system (Stone, UK). Fig. 1 (a) shows a scanning electron microscope (SEM) image of the highly spherical morphology of the powder and Fig. 1 (b) shows the powder particle size distribution (PSD). SEM analysis was carried out using a Jeol 6610 (Akishima, Japan) scanning electron microscope at 20 kV. Table 2 shows the chemical composition of the powders, as documented in the supplier's powder certification. It can be seen from Table 2 that the initial levels of oxygen in the powder are low at 0.009 wt%. and the powder has high purity with>99.9 wt% comprising of tungsten. The tungsten powder was melted in an argon atmosphere with an initial residual oxygen content of< 1800 ppm (0",
            " Careful consideration, as shown is previous studies [26], is needed when selecting the substrate material as its thermal properties have been reported to significantly affect the LPBF process, particularly through influencing the size of the melt pool and the solidification rate [26]. The laser-based melting of the tungsten powder was carried out by fabricating two types of tungsten specimens. Several square section blocks measuring L=10mm, W=10mm and H=5mm, and L=5mm, W=5mm and H=10mm were manufactured for density, microstructural and XCT measurements, as shown in Fig. 1 (d). A \u2018snaking\u2019, also often referred to as the meander, scan strategy was used for each build where the angle of the laser was rotated by 67\u00b0 between each layer, as illustrated in Fig. 1 (c). Table 3 provides a summary of the six sets of processing parameters used to manufacture the different tungsten LPBF test samples using a constant laser power of 200W, exposure time of 200 \u03bcs and layer thickness of 50 \u03bcm. The controlled processing parameters investigated were hatch distance (or spacing) and point distance. The specimens were subsequently named S1HD1 to S2HD3, where S is the scanning speed and HD is the hatch distance. The input laser energy was calculated and derived from the 3 dimensional (3D) specific energy input [27\u201330]: = P S t \u2107 \u03bd "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001434_0094-114x(80)90021-x-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001434_0094-114x(80)90021-x-Figure10-1.png",
        "caption": "Figure 10.",
        "texts": [
            " 9 which also, coincidentally, points up the duality between an octahedron and a hexahedron. For all the octahedral linkages, aii+ I = 0, al l i. In order to relate the skew angles between adjacent joints directly to the appropriate angles of the triangular plates, shown in the models to be illustrated later, we adopt a special sign convention. We make the joint offsets alternately positive and negative so that, at every point of intersection, either both offsets are directed towards the point or both directed away from it, as illustrated in Fig. 10. Since each common normal is of zero length, we are free to choose a convenient direction for it. At every point of intersection of offsets, then, we choose its direction so that the usual right-hand screw convention makes the skew angle equal to the angle in the triangle which supports the relevant joint axes. This procedure is also evident in Fig. 10. In measuring joint angles on the models, it is consequently necessary to take some care to observe the appropriate convention, since the common normals will be manifested only as directions. The line-symmetric octahedral case Two views of a line-symmetric octahedral linkage model are shown in Figs. 11 and 12. Two views of another model, illustrating an alternative loop from the same octahedron are depicted in Figs. 13 and 14. Figure 15 shows a model due to Goldberg[2] which illustrates a special case of this linkage type, although Goldberg seems, erroneously, to regard it as a trihedral linkage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001031_pime_proc_1988_202_127_02-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001031_pime_proc_1988_202_127_02-Figure5-1.png",
        "caption": "Fig. 5 (a) Outer ring waviness (b) Ball and inner ring waviness",
        "texts": [
            " The negative sign indicates that a reduction in internal clearance produces an increase in spring compression and hence spring force. Substitution Proc Instn Mech E n p Vol 202 No C5 at UQ Library on June 19, 2014pic.sagepub.comDownloaded from of equation (7) into equations ( 5 ) and (6) enable firstand second-order approximations to spring force to be determined. In general thrust loaded ball bearings may produce radial and axial components of vibration force and a vibration moment. These are determined by resolving spring forces in the appropriate directions. Figure 5a and b shows the frames of reference used in the analysis. O X Y Z is a fixed reference frame with 0 at the bearing\u2019s geometric centre and OZ coincident with the bearing\u2019s axis. O x y z is a rotating frame, again with Oz coincident with the bearing\u2019s axis but spinning with angular velocity w, so that axes Ox and Oy rotate with the ball set. Relative to the rotating frame resultant axial and radial components of force are given by FA = 1 Qjsin a N - 1 j = O N - 1 FK,= 1 Qjcosacos dj (8) j = O N - 1 FRY = 1 Qj cos a sin + j The resultant moments about Ox and Oy are M,, = 1 Qj f sin a sin (bj j = o where 4j is measured relative to Ox",
            " For brevity only the case of a bearing with a stationary outer and a rotating inner ring is considered. For small amplitude waviness spring loads and deflections in the dynamic model are described by equation (5). Combining this equation with equations (7), (8) and (9) and simplifying enables the bearing vibration forces and moment to be expressed in terms of bearing parameters and the time-dependent component of radial internal clearance PD[(b(t)] : N - l F A = -$~6/ \u2019 tan CI 1 P,{+,(t)} i = O 7.1 Outer race waviness Outer race waviness is shown in Fig. 5a and is described by a=aosinmyo, r n = l , 2 , 3 ,... where m is the number of waves per circumference and yo is measured from the stationary axis OX. The corresponding time-varying component of radial internal Cp IMcchE 1988 at UQ Library on June 19, 2014pic.sagepub.comDownloaded from clearance is given by VIBRATION FORCES OF THRUST LOADED BALL BEARINGS: PART I of internal clearance is given by 309 P D - {4(t)} = a. sin m(4 + w, t ) 2 where yo = 4 + w, t. Note that P , is defined with respect to the moving reference frame O x y z (Fig. 5a) so that putting 4 = &j gives the time-varying component of deflection of spring j . Substituting for P,, in equation (10) (for axial force) and simplifying the summation term using reference (6) gives x sin mw,t +- m,), m = 1,2 ,3 , . . . (11) { N The term (sin mlr/N)/(sin - z/N) in equation (1 1) takes the value N when m is an integer multiple of N and zero for all other values of m. Equation (11) may thus be further simplified to F A - = -$c8'12N tan a sin i(No, t + (N - 1)n) a0 m N i = - , m = N, 2N, 3N, ",
            " Not all orders of waviness produce vibration. Axial vibration is produced when the number of waves per circumference is an integer multiple of the number of balls in the bearing and radial and moment vibration is produced by waviness of the order iN f 1. For all other orders of waviness the time-dependent components of ball load sum to zero. 7.2 Inner race waviness Theranalysis for simple harmonic waviness on the inner race follows that of the preceding section but takes into account ring rotation. Waviness amplitude is given by (Fig. 5b) : a=a,sinmy,, m = l , 2 , 3 ,... where yI is measured with respect to a point on the inner ring. The corresponding time-varying component Q IMechE 1988 P D - [&(t)] = a, sin m(4 + (0, - q ) t } 2 where yI = 4 + (0, + w,)t and PD is defined with respect to the moving reference frame Oxyz. Substituting for PD in equations (10) and simplifying yields the required expression for vibration forces and moments : - F A = -$,&/2N a1 x tan a[sin i{N(wc - w,)t + (N - l ) ~ } ] (15) m=iN, i = l , 2 , 3 ,.",
            " Axial vibration is produced when the number of waves per circumference is an integer multiple of the number of balls, whereas radial and moment vibration is only produced by waviness of the order m = iN f 1. 7.3 Ball waviness Unlike the raceways the balls are free to spin about any axis and this axis may even change during the course of bearing operation. For simplicity only the case of waviness on one ball is considered and this ball is assumed to remain rotating about an axis normal to the plane containing the centres of the inner and outer race contacts. For these conditions waviness is described by Fig. 5b: a=a,sinmy,, m = l , 2 , 3 ,... Proc Instn Mech Engrs Vol 202 No C5 at UQ Library on June 19, 2014pic.sagepub.comDownloaded from where yB is measured with respect to a point on the ball surface. Variation in ball load and hence spring force in the dynamic model of Fig. 2 is produced by changes in the ball diameter through inner and outer contacts, given by DB(t) = 2aB sin myB, m = 2, 4, 6, ... This results in a time-varying component internal clearance given by P D - { &)} = 2aB sin(mwB t + 4J, m = 2, 4, 6, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000599_tro.2004.842341-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000599_tro.2004.842341-Figure8-1.png",
        "caption": "Fig. 8. 4RRR PM moving with EE orthogonally aligned to an ellipsoidal path.",
        "texts": [
            " Fig. 5 shows results for a cubic spline with segments. The problem (21) is solved for the 23 independent coefficient with a standard method for constrained optimization [4], [28]. The applied algorithm converges rapidly but the necessary computation time makes a real time solution impossible. The admissible sign vector yields smaller control torques as shown in Figs. 6 and 7. The second task consists in following the surface of a cylindrical object with the EE orthogonally aligned to the surface (Fig. 8). For this task the required preload of nm can only be achieved with . Results are shown in Fig. 9. The heptapod (a hexapod with one additional strut) in Fig. 10 serves as second example. It is closely related to the Falcon [9], a PM equipped with seven cable drives. The seven prismatic joints are actuated. For this spatial RFA PM the task was to draw a circle on a spherical surface with orthogonally aligned EE and without rotation about the longitudinal axis. The ask must be accomplishes in 10 s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002535_j.jsv.2017.04.010-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002535_j.jsv.2017.04.010-Figure8-1.png",
        "caption": "Fig. 8. The contact and traction forces at the interface between the ball and the races.",
        "texts": [
            " The locations of instantaneous centers of cage, inner race, rolling elements and outer race are decided by dynamics of system. The model considers constrained motion of rolling element within the cage. Fig. 7 shows the rolling element bearing as a spring-mass-damper system and free body diagram (FBD) of its different parts. The full model would include several rolling elements. The positions of all rigid bodies in the model are defined in the inertial reference frame ( \u2212x y frame). The contact of a rolling element with the races, say that of j-th rolling element, is represented in Fig. 8. The positions of centre of inner race, outer race, and ball with respect to inertial frame are designated as ( )A x y,i i , ( )B x y,o o and ( )C x y,b b , respectively. It may be noted that the normal forces at the inner and outer race contact points are not collinear when points A and B are not coincident. The contact between inner race and j-th ball is at ( )P x y,P P , and contact between outer race and ball is at ( )Q x y,q q . The radius of inner race, outer race and ball are ri, ro and rb, respectively, and the angular orientation of ball center with respect to inner and outer race centers are \u03b1 and \u03b2 , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000799_scitranslmed.3001148-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000799_scitranslmed.3001148-Figure1-1.png",
        "caption": "Fig. 1. Sensor array with integrated telemetry system before implantation. The implant is 3.4 cm in diameter and 1.5 cm thick. The top surface of the implant includes two polyester velour patches for tissue adhesion. Cross-sectional schematic view shows electronics modules (A), telemetry transmission portal (B), battery (C), and sensor array (D).",
        "texts": [
            " Eight 300-mm platinum working electrodes, with associated platinum counterelectrodes and Ag/AgCl potential reference electrodes, are arranged as four sensor pairs on the surface of a 1.2-cm-diameter alumina disc (11). The electrodes are covered by a thin electrolyte layer, a protective layer of medical-grade polydimethylsiloxane (PDMS), and a membrane of PDMS with wells for the immobilized enzymes located over certain electrodes. The enzymes are immobilized in the wells by cross-linking with albumin using glutaraldehyde, and the resulting gel is rinsed extensively to remove unbound material. The alumina disc is fused into a hermetically sealed titanium housing (Fig. 1) containing a potentiostat and signal-conditioning circuitry for each sensor, a wireless telemetry system, and a battery having a minimum 1-year lifetime. The implant is sterilized with a chemical sterilant by a procedure that has been validated according to standard methods (12). The telemetry system samples the currents from individual sensors, encodes the samples into multiplexed signal segments, and transmits the segments as a train of radio-frequency signals at regular 2-min intervals to an external receiver, where the signals are decoded and recorded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure6.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure6.9-1.png",
        "caption": "Fig. 6.9 Steady state behavior: (a) nose-out, (b) nose-in",
        "texts": [
            "57) that is, the totality of steady-state conditions as function of the forward speed u and of the steering wheel angle \u03b4v . This is quite obvious: given and kept constant the forward speed u and the steering wheel angle \u03b4v , after a while (a few seconds at most) the vehicle reaches the corresponding steady-state condition, characterized by a constant lateral speed vp and a constant yaw rate rp . While the yaw rate rp has necessarily the same sign as \u03b4v , the same does not apply to the lateral speed vp . As shown in Fig. 6.9, in a left turn the vehicle slip angle \u03b2p = vp/u can either be positive or negative. As a rule of thumb, at low forward speed the vehicle moves \u201cnose-out\u201d, whereas at high speed the vehicle goes round \u201cnose-in\u201d. It is common practice to employ (a\u0303y, \u03b4v), instead of (u, \u03b4v), as parameters to characterize a steady-state condition. This is possible because a\u0303y = urp(u, \u03b4v) which can be solved to get u = u(a\u0303y, \u03b4v) (6.58) At first it may look a bit odd to employ (a\u0303y, \u03b4v) instead of (u, \u03b4v), but it is not, since it happens that some steady-state quantities are functions of a\u0303y only",
            "184) Once we have obtained vp and rp , we can easily compute all other relevant quantities, like the vehicle slip angle \u03b2p and the Ackermann angle \u03b3p = l/Rp \u03b2p = vp u = a2 + a1\u03c7 l \u03c41\u03b4v \u2212 a\u0303y m l2 ( C1a 2 1 + C2a 2 2 C1C2 ) = Sp Rp \u03b3p = lrp u = (1 \u2212 \u03c7)\u03c41\u03b4v \u2212 a\u0303y m l ( C2a2 \u2212 C1a1 C1C2 ) = l Rp (6.185) According to (6.148), we can compute the steady-state front and rear slip angles \u03b11p = \u03c41\u03b4v \u2212 vp + rpa1 u = ma2 lC1 a\u0303y \u03b12p = \u03c7\u03c41\u03b4v \u2212 vp \u2212 rpa2 u = ma1 lC2 a\u0303y (6.186) A non-zero lateral speed vp at steady state may look a bit strange, at first sight. It simply means that the trajectory of G is not tangent to the vehicle longitudinal axis. As shown in Fig. 6.9(a), at low lateral acceleration we have very small slip angles \u03b11p and \u03b12p and, as a consequence, \u03b2p has the same sign as \u03b4v . At high lateral acceleration, the large slip angles cause \u03b2p to become of opposite sign with respect to \u03b4v , as shown in Fig. 6.9(b). The speed u\u03b2 that makes \u03b2p = vp = 0 is given by (6.184) and is equal to (if \u03c7 = 0) u\u03b2 = \u221a C2a2l a1m (6.187) It is called tangent speed. It is of some practical interest to study the behavior of a vehicle (albeit a very linear one) when suddenly subjected to a lateral force, like the force due to a lateral wind gust hitting the car when, e.g., exiting a tunnel. Actually, the same mathematical problem also covers the case of a car going straight along a banked road. 6.17 Linear Single Track Model 195 We have only to modify the equilibrium equations (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002430_taes.2014.120705-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002430_taes.2014.120705-Figure1-1.png",
        "caption": "Fig. 1. Quad-rotor aircraft concept.",
        "texts": [
            " Throughout this paper, unless otherwise stated, In and 0n indicate the identity and zero matrix of dimension n \u00d7 n, respectively, \u2016H (s)\u2016L1 denotes the L1 gain of H (s), \u2016x(t)\u2016L\u221e , the L\u221e norm of x(t), \u2016x\u20162 and \u2016A\u2016F , the two and Frobenius norms of the vector x and the matrix A, respectively. The basic flight mechanism of a quad-rotor UAV is depicted as follows: vertical motion is created by collectively increasing and decreasing the speed of all four rotors; pitch or roll motion is achieved by the differential speed of the front-rear set or the left-right set of rotors, coupled with lateral motion; yaw motion is realized by the different reaction torques between the (1, 3) and (2, 4) rotors, as shown in Fig. 1. Let I = {Oexeyeze} denote an earth-fixed inertial frame and B = {Oxyz} denote a body-fixed frame whose origin O is located at the center of mass of the quad-rotor. Let p \u2208 R 3 denote the position vector of the center of mass in the frame I, = (\u03c6, \u03b8, \u03c8)T \u2208 R 3 the Euler angles (i.e., roll, pitch, yaw), and the corresponding rotation matrix R \u2208 SO(3) to orient the quad-rotor can be expressed as R = \u23a1 \u23a2\u23a3 C\u03b8C\u03c8 S\u03b8C\u03c8S\u03c6 \u2212 S\u03c8C\u03c6 S\u03b8C\u03c8C\u03c6 + S\u03c8S\u03c6 C\u03b8S\u03c8 S\u03b8S\u03c8S\u03c6 + C\u03c8C\u03c6 S\u03b8S\u03c8C\u03c6 \u2212 C\u03c8S\u03c6 \u2212S\u03b8 C\u03b8S\u03c6 C\u03b8C\u03c6 \u23a4 \u23a5\u23a6 , where S(\u00b7) = sin(\u00b7), C(\u00b7) = cos(\u00b7)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001193_tmech.2017.2766279-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001193_tmech.2017.2766279-Figure1-1.png",
        "caption": "Fig. 1. Experimental facility for linear-motor-based motion control system.",
        "texts": [
            " In Section III, we first introduce the AFOTSM controller, where the systematical analysis for the stability and the control performance is conducted, and then an SMDO scheme with super-twisting technique is introduced in details. Experimental studies are presented in Section IV to validate the effectiveness by comparing with other existing controllers for LM-based motion. Section V summarizes all the work. The experimental facility (by Akribis System Company) used for verifying the effectiveness of the designed LM-based motion control system is shown in Fig. 1. An absolute position encoder is equipped on the moving stage, which is driven directly by the rotor of linear motor and has a 50 cm travel range along the linear guide. The plant model of liner motor can be given by [16] mp\u0308 = (1 \u2212 km )(kf u\u2212 f \u2212 d) (1) f = kc sgn (p\u0307) + kv p\u0307 (2) where m denotes the mass of the moving stage, p means the absolute position, km represents the gain of the variable load, kf is the voltage-to-force amplifier gain, and d stands for the bounded lumped uncertainty including disturbance and measurement noise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003705_j.msea.2019.138361-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003705_j.msea.2019.138361-Figure1-1.png",
        "caption": "Fig. 1. Schematic of Inconel 625 alloy tubes (TD\u2014transverse direction, ND\u2014normal direction, RD\u2014rolling direction).",
        "texts": [
            " The hot extrusion samples were solution treated at 1150 \u00b0C for 60min followed by air cooling to room temperature, subsequent the cold rolling tests was carried on the twin-roll cold rolling mill, and the cold rolling reduction was about 62%. Finally, the cold rolling sample was followed by annealing at 1120 \u00b0C for holding 20min. The bulk specimens with the in height 2mm and 10mm in length and 5mm in width were cut from the TD-RD cross-section of the hot extruded, solution treated, cold rolled and annealing treated in the Inconel 625 alloy tubes, respectively. The bulk specimen schematic of Inconel 625 alloy tube is shown in Fig. 1. The examined TD-RD crosssection of the bulk specimens were firstly mechanically polished by follow standard metallographic procedure to obtain mirror finished surface. Subsequently for Eelectron backscatter diffraction (EBSD) analysis, the bulk specimens are electropolished in a solution with 80% methanol and 20% H2SO4 at 20 V for 30 s at room temperature. The EBSD investigation was carried out using a fully automated EBSD system (Oxford Instruments, UK) attached to a FEG-SEM (Carl-Zeiss, Model: Quanta 450)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003706_j.oceaneng.2019.106329-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003706_j.oceaneng.2019.106329-Figure2-1.png",
        "caption": "Fig. 2. The schematics of the spatial trajectory-tracking guidance based on the virtual vehicle method.",
        "texts": [
            " Then, the desired sway velocity vR of the virtual vehicle is equal as following vR\u00bc \ufffd ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u03bd2 P u2 R w2 R q (42) Taking the derivative of Eq. (42) with respect to time, we can obtain the acceleration (27) and jerk (28) of the virtual vehicle. Combined with the underactuated dynamics of the virtual vehicle, the surge acceleration and jerk are calculated as Eqs. (29) and (30). Similarly, the heave acceleration and jerk are obtained as Eqs. (31) and (32). Step 3. From Fig. 2, by definitions of the float and course angle, we can obtain the expressions (33) and (34) of the desired float and course angle of the virtual vehicle. According to Assumption 5, the desired pitch and yaw angle of the virtual vehicle are as following: \u03b8R \u00bc \u03c7P and \u03c8R \u00bc \u03b3P. Taking the derivative of the desired pitch angle, the pitch angular velocity and acceleration are as following (37) and (38). Similarly, the yaw angular velocity and acceleration are obtained as following (39) and (40). The introduction of auxiliary speed \u03bdt is to simplify the calculation of the angular velocity and acceleration of the virtual vehicle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.7-1.png",
        "caption": "Fig. 3.7 Road-tire friction forces",
        "texts": [
            "5 Forces Acting on the Vehicle 61 where Cz1 and Cz2 have been introduced. In other words, in straight running, the aerodynamic force Fa is given as two vertical loads Za 1 and Za 2 acting directly on the front and rear tires, respectively, plus the aerodynamic drag Xa acting at road level. The road-tire friction forces Ftij are the resultant of the tangential stress in each footprint, as shown in (2.15). Typically, for each tire, the tangential force Ftij is split into a longitudinal component Fxij and a lateral component Fyij , as shown in Fig. 3.7. It is very important to note that these two components refer to the wheel reference system shown in Fig. 2.2, not to the vehicle frame. If \u03b4ij is the steering angle of a wheel, the components of the tangential force in the vehicle frame S are given by Ftij = Xij i + Yij j where Xij = Fxij cos(\u03b4ij ) \u2212 Fyij sin(\u03b4ij ) Yij = Fxij sin(\u03b4ij ) + Fyij cos(\u03b4ij ) (3.58) with obvious simplifications if \u03b4ij is very small. To deal with shorter expressions, it is convenient to define X1 = X11 + X12, X2 = X21 + X22 Y1 = Y11 + Y12, Y2 = Y21 + Y22 \u0394X1 = X12 \u2212 X11 2 , \u0394X2 = X22 \u2212 X21 2 \u0394Y1 = Y12 \u2212 Y11 2 , \u0394Y2 = Y22 \u2212 Y21 2 (3",
            " After quite a bit of work, we are now (almost) ready to set up our first-order vehicle model for handling and performance analyses. Essentially, setting up a model means collecting all relevant equations, their order being not important. Of course, a twoaxle vehicle is considered. We have three in-plane equilibrium equations (3.64) max = m(u\u0307 \u2212 vr) = X = X1 + X2 \u2212 1 2 \u03c1SCxu 2 may = m(v\u0307 + ur) = Y = Y1 + Y2 Jzr\u0307 = N = Y1a1 \u2212 Y2a2 + \u0394X1t1 + \u0394X2t2 (3.64\u2032) where the tangential (grip) forces are defined in (3.59) with respect to the vehicle frame (Fig. 3.7) X1 = X11 + X12, X2 = X21 + X22 Y1 = Y11 + Y12, Y2 = Y21 + Y22 \u0394X1 = X12 \u2212 X11 2 , \u0394X2 = X22 \u2212 X21 2 \u0394Y1 = Y12 \u2212 Y11 2 , \u0394Y2 = Y22 \u2212 Y21 2 (3.59\u2032) and in (3.58) to exploit the contribution of each single tire Ftij = Xij i + Yij j where Xij = Fxij cos(\u03b4ij ) \u2212 Fyij sin(\u03b4ij ) Yij = Fxij sin(\u03b4ij ) + Fyij cos(\u03b4ij ) (3.58\u2032) We also have other four out-of-plane equilibrium equations (3.79), which link the vertical loads acting on each tire to the vehicle motion 3.11 Vehicle Model for Handling and Performance 87 Z11 = Fz11 = 1 2 [ mga2 l \u2212 1 2 \u03c1aSaCz1u 2 \u2212 maxh \u2212 Jzxr 2 l ] \u2212 \u0394Z1 Z12 = Fz12 = 1 2 [ mga2 l \u2212 1 2 \u03c1aSaCz1u 2 \u2212 maxh \u2212 Jzxr 2 l ] + \u0394Z1 Z21 = Fz21 = 1 2 [ mga1 l \u2212 1 2 \u03c1aSaCz2u 2 + maxh \u2212 Jzxr 2 l ] \u2212 \u0394Z2 Z22 = Fz22 = 1 2 [ mga1 l \u2212 1 2 \u03c1aSaCz2u 2 + maxh \u2212 Jzxr 2 l ] + \u0394Z2 (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000337_1.1555660-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000337_1.1555660-Figure1-1.png",
        "caption": "Fig. 1 Simplified purely torsional mechanical model of a gear pair",
        "texts": [
            " Finally, several critical issues for further research needed in the area of nonlinear vibration of gear transmission systems are discussed. Appl Mech Rev vol 56, no 3, May 2003 30 : http://appliedmechanicsreviews.asmedigitalcollection.asme.org/ on 03/01/2 Transmitted by Associate Editor RA Ibrahim \u00a9 2003 American Society of Mechanical Engineers9 015 Terms of Use: http://asme.org/terms Downl A simplified purely torsional mechanical model of a gear pair supported by rigid mounts with backlash and time-varying mesh stiffness, as shown in Fig. 1 @3#, was used to obtain the governing equations without losing generality. In Fig. 1, u i(t) and u j(t) are the rotational vibratory components of gears i and j due to the mesh action, t represents real time, and ri and r j are the base radii. If the relative displacement across the mesh action line is expressed by x(t)5riu i(t) 1r ju j(t), then the vibration model can be reduced to a single degree of freedom with the coordinate x(t), and the corresponding equation of motion can be obtained as follows: m d2x dt2 1c dx dt 1k~ t !g~x~ t !!5 f ~ t ! (1a) where g~x~ t !!5H x~ t !2b x~ t "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001386_ijma.2012.046583-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001386_ijma.2012.046583-Figure4-1.png",
        "caption": "Figure 4 Mechanism of slave system (see online version for colours)",
        "texts": [
            " The operating information from the handle is transmitted to the slave side, where the catheter clamp inserts and rotates the actual catheter as commanded from the master side. If the catheter contacts a blood vessel wall, the load cell detects it and the information is transmitted to the surgeon\u2019s hand. Force feedback is realised by the master-slave robotic catheter operating system. The surgeon feels the contact, and no X-rays are required during intravascular neurosurgery. The slave side mechanism shown in Figure 4 is similar to the master side, it also has two DOFs, one is axial motion along the frame, and the other one is radial motion, two graspers are placed at this part. The operator can drive the catheter to move along both axial and radial when the catheter is clamped by grasper 1. The catheter keeps its position and the catheter driven part can move smoothly when the catheter is clamped by grasper 2. The slave side consists of a catheter clamping device, two DC motors, a slide platform, step motor, maxon motor, load cell, torque sensor, and support frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002145_20100901-3-it-2016.00302-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002145_20100901-3-it-2016.00302-Figure6-1.png",
        "caption": "Fig. 6. A five-link 3D biped with point feet that is 0.55 m at the hip and has a total mass of 7.25 Kg. (a) shows the coordinates for single support on leg-1 and (b) shows the coordinates for single support on leg-2.",
        "texts": [
            " The feedback controller is not necessarily synthesized with the same virtual constraints used to find the periodic orbit, though it often is; for details, see Westervelt et al. [2007] and Chevallereau et al. [2009b]. The design of a stabilizing controller for a simple 3D bipedal robot is illustrated here. The influence of the frontal (coronal) plane dynamics on the overall motion of the robot will be emphasized as this is the major new element when passing from 2D to 3D. With this in mind, the simplest mechanical structure that highlights this aspect of the gait design and stabilization problem will be used. Biped: The 3D-biped depicted in Fig. 6 is taken from Chevallereau et al. [2009b]. It consists of five links: a torso and two legs with revolute one DOF knees that are independently actuated and terminated with \u201cpoint-feet\u201d. Each hip consists of a revolute joint with two DOF and each DOF is independently actuated. The width of the hips is nonzero. The stance leg is assumed to act as a passive pivot in the sagittal and frontal planes, with no rotation about the z-axis (i.e., no yaw motion). Indeed, the small link in the diagram that appears to form a foot has zero length and no mass",
            " This section will illustrate this technique and the utility of reduction on a nontrivial 3D biped consisting of multiple discrete phases corresponding to different phases of walking. In particular, we will consider a 3D biped with feet, locking knees, and a hip as in Sinnet and Ames [2010]; this will result in a hybrid model with four phases, two of which are single-support and two of which are double-support. On the single-support phases, functional Routhian reduction will be implemented through the general procedure illustrated in Fig. 6; in fact, this is the procedure that has been utilized on a wide variety of bipedal models implementing this form of control Ames et al. [2006], Ames and Gregg [2007], Sinnet and Ames [2009b], Ames et al. [2007, 2009]. On the double-support phases, local control laws will be used to effect the appropriate phase transitions. We begin by considering the sagittal restriction of the 3D biped\u2014this model will be a 2D model operating in the sagittal plane obtained by applying a sagittal-restriction to the 3D model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure3-11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure3-11-1.png",
        "caption": "Fig. 3-11 Per-phase equivalent circuit in steady state.",
        "texts": [
            " (3-54) results in v R i j L i j L i is dq s s dq s s dq m s dq r dq_ _ syn _ syn _ _= + + +\u03c9 \u03c9 ( ) (3-55) and 0 = + + + R s i j L i j L i ir r dq r r dq m s dq r dq _ syn _ syn _ _\u03c9 \u03c9 ( ). (3-56) The above space vector equations in a balanced sinusoidal steady state correspond to the following phasor equations for phase a: V R I j L I j L I Ia s a s a m a A= + + +\u03c9 \u03c9syn syn ( ) (3-57) COMPUTER SIMULATION 47 and 0 = + + + R s I j L I j L I Ir A r A m a A\u03c9 \u03c9syn syn ( ). (3-58) The above two equations combined correspond to the per-phase equivalent circuit of Fig. 3-11 that was derived in the previous course [1] under a balanced sinusoidal steady-state condition. Note that in Fig. 3-11, I IA ra= \u2212 \u2032 . 3-9 COMPUTER SIMULATION In dq windings, the flux linkages and voltage equations are derived earlier. We will use \u03bbsd, \u03bbsq, \u03bbrd, and \u03bbrq as state variables, and express isd, isq, ird, and irq in terms of these state variables. The reason for choosing flux linkages as state variables has to do with the fact that these quantities change slowly compared with currents, which can change almost instantaneously. We can calculate dq-winding currents from the stator and the rotor flux linkages of the respective windings as follows: Referring to Fig",
            " 3-9-1 Calculation of Initial Conditions In order to carry out computer simulations, we need to calculate initial values of the state variables, that is, of the flux linkages of the dq windings. These can be calculated in terms of the initial values of the dq winding currents. These currents allow us to compute the electromagnetic torque in steady state, thus the initial loading of the induction COMPUTER SIMULATION 49 machine. To accomplish this, we will make use of the phasor analysis in the initial steady state as follows: Phasor Analysis In the sinusoidal steady state, we can calculate current phasors Ia and \u2032 = \u2212I Ira A( ) in Fig. 3-11 for a given Va. All the space vectors and the dq-winding variables at t\u00a0=\u00a00 can be calculated. The phasor current for phase-a allows the stator current space vector at t\u00a0=\u00a00 to be calculated as follows: I I i I ea a i s a I j s i= \u2220 \u21d2 =\u02c6 ( ) \u02c6 . \u02c6 \u03b8 \u03b8 0 3 2 (3-63) Assuming the initial value of \u03b8da to be zero (i.e., the d-axis along the stator a-axis), and using Fig. 3-3 and Eq. (3-5) and Eq. (3-6) i i d Isd s Is ( ) projection of ( ) on -axis0 2 3 0 2 3 3 2 = \u00d7 =       \u02c6 \u02c6 cos( )\u03b8i (3-64) 50 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS and i i q Isq s Is ( ) projection of ( ) on -axis0 2 3 0 2 3 3 2 = \u00d7 =       \u02c6 \u02c6 sin( )",
            " 3-6 The \u201ctest\u201d motor described in Chapter 1 is operating at its rated conditions. Calculate \u03bdsd(t) and \u03bdsq(t) as functions of time, (a) if \u03c9d\u00a0=\u00a0\u03c9syn, and (b) if \u03c9d\u00a0=\u00a00. 3-7 Under a balanced sinusoidal steady state, calculate the input power factor of operation based on the d- and the q-axis equivalent circuits of Fig. 3-10 in the \u201ctest\u201d motor described in Chapter 1. 3-8 Show that the equations for the dq windings in a balanced sinusoidal steady state result in the per-phase equivalent circuit of Fig. 3-11 for \u03c9d\u00a0=\u00a00 and \u03c9d\u00a0=\u00a0\u03c9m. 3-9 Using Eq. (3-46) and Eq. (3-47), derive the torque expressions in terms of (1) stator dq winding flux linkages and currents, and (2) stator dq winding currents and rotor dq winding flux linkages. 3-10 Show that for the transformation matrix in Eq. (3-12), 58 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS [ ] [ ] [ ].T T Iabc dq dq abc\u2192 \u00d7 \u2192 \u00d7 \u00d7 = 2 3 3 2 2 2 3-11 Derive the voltage equations in the dq stator windings (Eq. 3-28 and Eq. 3-29) using the transformation matrix of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000150_j.jmatprotec.2007.10.051-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000150_j.jmatprotec.2007.10.051-Figure1-1.png",
        "caption": "Fig. 1 \u2013 Single stringer/multiple layer depositions.",
        "texts": [
            " The interpass cooling regime was a balance based on the build parameters requiring a consistent cooling rate for microstructure and side-wall profile against the induced stresses from the sharp temperature differential. High rate deposition can otherwise allow a significant build up in thermal mass, which can risk an adverse precipitation response. Clearly, the ability to perform this interpass interval when producing larger SMD structures would be highly dependent on the speed of positional control offered by the robotic welding/deposition facility. A schematic example of single string/multiple layer weld deposition geometry is illustrated in Fig. 1. In order to increase the overall width of any deposited structure, parallel, multiple stringer welds are often required. However, from the point of view of metallurgical control, it is preferable to fabricate such structures from repeatable \u201cbuilding blocks\u201d of consistent geometry and associated microstructural detail. Therefore, during the present study, emphasis was placed on the validation of a specific \u201cvoxel\u201d section (Degarmo et al., 2003). Hence, a voxel parameter set was developed, which produced a consistent, crosssectional profile and internal microstructure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.80-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.80-1.png",
        "caption": "Fig. 10.80 Artist\u2019s impression of NASA\u2019s Large Civil Tiltrotor2 (LCTR, second generation, image NASA)",
        "texts": [
            " Flying Qualities of Large Civil Tiltrotor Aircraft Flying qualities of large civil tiltrotor aircraft have been the topic of research at NASA Ames during the last decade, and Refs. 10.80\u201310.86 record the progress and outputs achieved. The concept has evolved to the LCTR2 (Large Civil Tiltrotor, second generation), designed to carry 90 passengers at 300 knots with a range of 1000 nm (Ref. 10.86); the LCTR2 concept weighs more than 100 000 lbs, with a wingspan of 107 ft, and features two tilting nacelles supporting 65 ft diameter rotors (Figure 10.80). Ref. 10.87 describes the various design trades and compromises required to achieve the operational capability of LCTR2 in helicopter and airplane modes. At 45 tonnes, the LCTR2 is much larger and heavier than the V-22 (24 tonnes) and the largest of the three configurations in the Liverpool study (EUROFAR, 15 tonnes); so, what kind of MTEs could such an aircraft be expected to fly in helicopter mode? What temporal and spatial performance standards could be achieved with satisfactory, Level 1, flying qualities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure6.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure6.16-1.png",
        "caption": "Figure 6.16.1. Reduced moment arm of steered-wheel forces.",
        "texts": [
            " in addition there may be effects because of cambering of the wheels at large steer angles, but this is hard to quantify because of lack of tire data. The attitude angles at the center of mass G and at the rear axle differ by the rear kinematic steer angle 406 Tires, Suspension and Handling This reduces the attitude angle at G caused by the rear slip angle, which has already been dealt with in Section 6.12. It gives a longitudinal load transfer Adapting the equation derived for slip attitude effects (Section 6.12), which is an oversteer effect. Figure 6.16.1 shows a four-wheeled vehicle with steer and slip angles and traction at the rear. The front vertical force lateral transfer factor eVf results in a front side force transfer factor eSf. The parameter eSf is zero for equal side forces Steady-State Handling 407 and unity for all side force on the outer wheel. The moment arm of the front side force is This causes The total radius effect including longitudinal load transfer is therefore 6.17 Banking Road slopes can be divided into two main types: longitudinal and lateral"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002294_j.ymssp.2014.09.001-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002294_j.ymssp.2014.09.001-Figure3-1.png",
        "caption": "Fig. 3. Dynamic model of a reduction gear system with 12 DOF.",
        "texts": [
            " Accordingly, the xp and xg displacements are then excluded. The 8 DOF are then reduced to 6 DOF, and this model is referred to as having \u20188 DOF reduced to 6 DOF\u2019. This model (with 6 DOF) was used previously in [2,4]. A one-stage gear dynamic model including a gyroscopic effect has been developed in this study. This model consists of 12 DOF and has 5 DOF (three rotational and two translational) for each gear disc, as well as 1 DOF for each motor disc and load disc to describe the rotation. A schematic diagram of the 12 DOF model is shown in Fig. 3. The equations of motion for this model can be explained as follows. The equations of motion in the \u2018x\u2019 direction for the pinion and gear are mp \u20acxp \u00bc KxpT xp CxpT _xp\u00feFp KxpC \u03c8p CxpC _\u03c8p \u00f015\u00de mg \u20acxg \u00bc KxgT xg CxgT _xg\u00feFg KxgC \u03c8 g CxgC _\u03c8 g \u00f016\u00de The equations of motion in the \u2018y\u2019 direction for the pinion and gear are mp \u20acyp \u00bc KypT yp CypT _yp N\u00feKypC \u03c6p\u00feCypC _\u03c6p \u00f017\u00de mg \u20acyg \u00bc KygT yg CygT _yg\u00feN\u00feKygC \u03c6g\u00feCygC _\u03c6g \u00f018\u00de The equations of motion in the \u2018\u03b8\u2019 direction for the pinion and gear are Ip \u20ac\u03b8p \u00bc rp N\u00feMp kt \u03b8p \u03b8m ct _\u03b8p _\u03b8m \u00f019\u00de Ig \u20ac\u03b8g \u00bc rg N\u00feMg kt \u03b8g \u03b8b ct _\u03b8g _\u03b8b \u00f020\u00de The equations of motion in the \u2018\u03c6\u2019 direction for the pinion and gear are Idp \u20ac\u03c6p \u00bc Ipwp _\u03c8p\u00feKypC yp KypR \u03c6p\u00feCypC _yp CypR _\u03c6p \u00f021\u00de Idg \u20ac\u03c6g \u00bc Igwg _\u03c8 g\u00feKygC yg KygR \u03c6g\u00feCygC _yg CygR _\u03c6g \u00f022\u00de The equations of motion in the \u2018\u03c8 \u2019 direction for the pinion and gear are Idp \u20ac\u03c8p \u00bc Ipwp _\u03c6p KxpC xp KxpR \u03c8p CxpC _xp CxpR _\u03c8p \u00f023\u00de Idg \u20ac\u03c8 g \u00bc Igwg _\u03c6g KxgC xg KxgR \u03c8 g CxgC _xg CxgR _\u03c8 g \u00f024\u00de The equations of motion in the \u2018\u03b8\u2019 direction for the motor and load are Im \u20ac\u03b8m \u00bc kt \u03b8m \u03b8p ct _\u03b8m _\u03b8p \u00feTm \u00f025\u00de Please cite this article as: O"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure12.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure12.19-1.png",
        "caption": "Fig. 12.19 Camera-based triangulation system in the back, the casting in the front (left), coloured dots indicating the deviation from the CAD file of the casting (middle), a colour plot of the casting scan compared with the CAD file of the machined part (right) [25]",
        "texts": [
            " 12 Reverse Engineering 341 According to [24], this time is required to apply the reference points, mark the characteristic features, place the scale bars, record about fifty images and transfer them to a laptop, carry out an automatic evaluation (the definition of the marker lines, the alignment of the measurement data with the nominal data, the calculation of the deviations) and to prepare and print out a measurement report. The case presented in [25] covers the measurement of a large iron casting for a wind turbine gearbox with an optical LED-based triangulation system (Fig. 12.19). As the castings undergo a final machining process, it is important to know the amount of excess material. The presence of sufficient excess material will be precisely 342 G. \u0160agi et al. determined by the alignment of the part on the machine. By measuring the castings before machining, it is possible to determine in advance the best suited alignment and detect the castings that deviate too much to fabricate good parts, so that at least the machining costs can be saved. The results show that a systematic inspection of castings is an added value of the production process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002306_tie.2017.2681975-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002306_tie.2017.2681975-Figure9-1.png",
        "caption": "Figure 9. Temperatures in the stator laminations at steady state 60 kW operation at 1500 min-1 for direct oil cooling (on the left) and direct water cooling (on the right) in \u00baC.",
        "texts": [
            " Finally, table V shows the mean temperatures of the active parts for both cases. The results really reveal the effectiveness of the direct stator cooling. This machine, unfortunately suffers from unintentional extra losses in the rotor which limits the performance of the machine via hot PM temperatures. However, the cool stator in case of water cooling also helps keeping the rotor magnets at acceptable temperatures. In addition, temperatures in the stator laminations for both cases are presented in Fig. 9 and the rotor temperatures are depicted in Fig. 10. Temperature distribution in the windings from 3D CFD analyses are presented for direct water cooling in Fig. 11 a) and direct oil cooling in Fig. 11 b). IV. MEASUREMENT ANALYSIS The previous results of the axial-flux machine measurements with indirect cooling are repeated here for the readers\u2019 convenience. The three scenarios A, B, and C defined in Section III are compared. A single load point was selected for comparison of the cooling methods A, B, and C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002378_055605-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002378_055605-Figure3-1.png",
        "caption": "Figure 3. Damaged sun gears: (a) having a cracked tooth and (b) having a pitted tooth.",
        "texts": [
            " Since the crack is usually initiated at the point of greatest stress of gear teeth and occurs along the normal line of the tooth\u2019s root curve, it was introduced along the normal line of the tooth\u2019s root curve using machine tools. The pitted tooth was created by running the gear for a long time and with a large torque. Because the gear just has hardness around HB190 and is soft, it is easy to create pits on the gear tooth. In the first stage of the planetary gearbox, there are three planet gears and 20, 40 and 100 teeth on the sun gear, planet gears and ring gear respectively. Pictures of the damaged sun gears are displayed in figure 3. Since vibration-based analysis is one of the principal tools for diagnosing mechanical faults [20, 21], the vibration is measured under each of the three gear health conditions using a tri-axial accelerometer, which is mounted on the planetary gearbox casing. An NI data acquisition system and a laptop with the data acquisition software are used to collect the vibration data for further processing. The speed of the driving motor and the load of the magnetic brake are varied to simulate the general planetary gearbox working conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003017_j.jmapro.2019.05.001-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003017_j.jmapro.2019.05.001-Figure3-1.png",
        "caption": "Fig. 3. Selective laser melting: (a) illustration of the machine; and (b) working principle of the system [59], [60].",
        "texts": [
            " High energy density in fact enables the powder to fully melt which offer high density (\u02dc99%) parts [56]. After heating, melting, and solidifying the one layer of powder, the powder bed is lowered down by an amount equal to the layer thickness of the solidified layer which usually ranges within 30\u201370 \u03bcm [57]. Thus, after each cycle a fresh layer of thickness 30\u201370 \u03bcm is deposited and spread over the entire surface by a coated blade. Rest of the powder which remains inside the build chamber and acts like a support structure can be recycled and used for next part production [58]. Fig. 3 shows the SLM system developed at Osaka University. An Nd:YAG laser of highest peak power of 3 kW and maximum average power of 50W is used. The laser light is directed via optical fibre. Laser beam of 0.8mm diameter is focused onto the powder bed. The laser head is attached to the xy-table controlled by a computer. A steel substrate is attached to the piston which moves down one layer thickness of 0.05 or 0.1mm along z direction [59,60]. The main machines in the market that use SLM are Trumaform LM 250, MCP Realizer and LUMEX 25C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.6-1.png",
        "caption": "Fig. 3.6 Aerodynamic forces",
        "texts": [
            " It is quite usual to provide directly the product SaCx as a more effective way to compare the aerodynamic efficiency of cars. For instance, a Formula One car has SaCx of about 1.2 m2, while a commercial one may have it below 0.6 m2. Formula 1 cars have Cz with very high negative values to achieve a very high aerodynamic downforce. Typically, SaCz \u22125.2 m2. In general, the aerodynamic force Fa in not applied at G (why should it be?) and therefore it contributes to MG with an aerodynamic moment Ma = Max i + May j + Mazk, the biggest component being May (pitch moment). It is common practice to do like in Fig. 3.6, thus defining the front and rear aerodynamic vertical forces (positive upward) according to Za 1 = 1 l [Zaa2 \u2212 May + Xah] = 1 2 \u03c1aV 2 a Cz1Sa Za 2 = 1 l [Zaa1 + May \u2212 Xah] = 1 2 \u03c1aV 2 a Cz2Sa (3.57) 3.5 Forces Acting on the Vehicle 61 where Cz1 and Cz2 have been introduced. In other words, in straight running, the aerodynamic force Fa is given as two vertical loads Za 1 and Za 2 acting directly on the front and rear tires, respectively, plus the aerodynamic drag Xa acting at road level. The road-tire friction forces Ftij are the resultant of the tangential stress in each footprint, as shown in (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure8-1.png",
        "caption": "Fig. 8. A crack tooth model.",
        "texts": [
            " Then, the tooth crack can be described as a function of crack length and crack depth: q u\u00f0 \u00de \u00bc q\u2212 q Lc u Lcb L q\u2212 q\u2212q0 L u Lc \u00bc L 8>< >: \u00f025\u00de where q is the crack depth on the front face, Lc is crack length, L is facewidth, and q0 is the crack depth on the back facewhen the crack propagates through the whole face width. The dash line in Fig. 7(b) indicates the case when the crack doesn't propagate through the whole face width, the solid line indicates the case when the crack propagates through the whole face width. As shown in Fig. 8, the gear tooth with crack is divided into many thin pieces. One of the pieces is used to explain the method to calculate themesh stiffness of helical with tooth crack. Since the curve of the tooth profile remains perfect, the Hertzian contact stiffness kh and axial compressive stiffness kawill not change. However, the bending and shear stiffnesswill change due to the influence of the crack.When the crack exists, the effective areamoment of inertia and area of the cross section at a distance of x from the tooth root will be calculated according to Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002571_s0022112071002027-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002571_s0022112071002027-Figure1-1.png",
        "caption": "FIGURE 1. Diagram illustrates envelope over cilia. Co-ordinates (q,, yo) represent envelope, (2, a) mean position. Velocity a t infinity, u = c- U .",
        "texts": [
            " Blake As the organisms are very small, and velocities (both wave and propulsive) small also, the Reynolds numbers are extremely low, thus enabling us to use the creeping flow equations of motion. Taylor (1951) was the first to show that propulsion of a microscopic organism can occur when the viscous stresses are dominant. Through the use of axisymmetric potential theory (Weinstein 1953) we formulate two problems together, (i) the two-dimensional waving sheet, and (ii) axisymmetric waving cylinder, with the waving bodies propelling themselves through the infinite liquid domain (see figure 1). Burns & Parkes (1967) considered the flow in the interior of the \u2018tubes\u2019 (i.e. general term used for both (i) and (ii)), whereas in this problem the flow field outside the \u2018tubes\u2019 is of interest. However, in this paper we will also consider longitudinal movements as well as the transverse oscillations considered by Burns & Parkes. Otherwise, the actual mathematics is obtained by simply replacing the modified Bessel functions of the first kind In(z), by those of the third kind K,(z) (Watson 1966)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002306_tie.2017.2681975-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002306_tie.2017.2681975-Figure10-1.png",
        "caption": "Figure 10. Rotor temperatures with oil cooling (on the left) and water cooling (on the right) in \u00baC.",
        "texts": [
            " Finally, table V shows the mean temperatures of the active parts for both cases. The results really reveal the effectiveness of the direct stator cooling. This machine, unfortunately suffers from unintentional extra losses in the rotor which limits the performance of the machine via hot PM temperatures. However, the cool stator in case of water cooling also helps keeping the rotor magnets at acceptable temperatures. In addition, temperatures in the stator laminations for both cases are presented in Fig. 9 and the rotor temperatures are depicted in Fig. 10. Temperature distribution in the windings from 3D CFD analyses are presented for direct water cooling in Fig. 11 a) and direct oil cooling in Fig. 11 b). IV. MEASUREMENT ANALYSIS The previous results of the axial-flux machine measurements with indirect cooling are repeated here for the readers\u2019 convenience. The three scenarios A, B, and C defined in Section III are compared. A single load point was selected for comparison of the cooling methods A, B, and C. Each machine was warmed until the temperatures stabilized"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002833_physrevapplied.5.017001-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002833_physrevapplied.5.017001-Figure1-1.png",
        "caption": "FIG. 1. Schematics of a (a) released bilayer, (b) bent bilayer with inner radius R, and (c) wrinkled structure with deflection profile \u03b6\u00f0x; y\u00de, amplitude A, and wavelength \u03bb. (d) Ew (solid line) and energy of planar relaxation (dashed line) as a function of h. (e) Wavelength \u03bb (solid line, left axis) and amplitude A (dashed line, right axis) as a function of length h, in the case of wrinkled structure. The vertical dotted-dashed line marks the hcw. Reprinted with permission from Ref. [52] (\u00a9 2009 by the American Physical Society).",
        "texts": [
            " Normally, a small strain gradient produces wrinkles, while a large strain gradient makes the layer bend or roll into a curved structure [52]. Real materials are more complicated, as competition between bending and stretching energy can cause transitions between wrinkling and rolling states after the flexible layer is set free in one end and fixed in the other end. Theoretical analyses have been carried out on both the wrinkling and rolling cases [29,42,52\u201360]. A simple analysis can be done by using an isotropically strained bilayer structure. Shown in Fig. 1 [52], the bilayer with thicknesses d1 and d2 is subjected to biaxial strain \u03b51 and \u03b52, respectively. The bilayer is free hanging over a distance h and is initially in a strained state over the length L. The released portion is free to elastically relax, constrained only by the fixed boundary [see the dashed line in Fig. 1(a)] [52]. The average strain and strain gradient of the bilayer are defined as \u03b5\u0304 \u00bc \u00f0\u03b51d1 \u00fe \u03b52d2\u00de=\u00f0d1 \u00fe d2\u00de and \u0394\u03b5 \u00bc \u03b51 \u2212 \u03b52, respectively, and \u0394\u03b5 > 0. The initial elastic energy (given per unit area) of the bilayer is E0 \u00bc Y\u00f0d1\u03b521 \u00fe d2\u03b522\u00de= \u00f01 \u2212 \u03bd\u00de, where Y and v are the Young\u2019s modulus and Poisson\u2019s ratio, respectively. In the bending case, the fixed boundary limits relaxation in the x direction, and the strain is relaxed via bending in the y direction to form a curved structure with inner radius R [Fig. 1(b)]. Since the layers are thin, the stress component in the radial direction (through the thickness direction) must be zero at equilibrium [61]. The total elastic energy of the bent film Ebent is calculated by integrating the elastic strain energy density from the outer to the inner film surface [52]. The equilibrium elastic energy of the rolled structure Ebent can be obtained by minimizing the energy and is normalized to E0 and then compared with the wrinkle energy Ew [52]. In the wrinkling case [Fig. 1(c)], the deflection of the bilayer can be written as a function \u03b6 \u00bc Af\u00f0y\u00de cos\u00f0kx\u00de, where A is the maximum amplitude of the wrinkle at the free end, k is the wrinkle wave number in the x direction, and f\u00f0y\u00de \u00bc \u00bd1 \u2212 cos\u00f0\u03c0y=h\u00de =2. In the calculation of the wrinkle energy, Ew is averaged over one wavelength, L \u00bc \u03bb, and L is numerically minimized with respect to A, \u03bb, and \u03b3 (where \u03bb is the wavelength of the wrinkle and \u03b3 is the magnitude of relaxation in the y direction). The wrinkle energy as a function of the wrinkle length is given in Fig. 1(d), and it is found that there is a minimum critical wrinkle length hcw, for wrinkle formation. The value of hcw is hcw \u2248 2.57d2 ffiffiffiffiffiffi\u2212\u03b5\u0304p [52]. For h < hcw, energy minimization provides only a trivial minimum of the wrinkle energy with A \u00bc 0 and \u03bb \u2192 \u221e [62], corresponding to a planar relaxation in the y direction [dashed line in Fig. 1(d)]. For h > hcw, wrinkling can occur, and both \u03bb and A increase with h, as demonstrated in Fig. 1(e). The preferred equilibrium shape of a free-hanging film could be found by comparing these two normalized energies, Ebent 017001-2 and Ew. h > hcw does not guarantee wrinkle formation. Large h also allows the bilayer to roll if the strain gradient (or \u0394\u03b5) is also large. A wrinkled structure is formed only when the strain gradient is small enough, even if h > hcw [29,52]. For a typical bilayer consisting of 10 nm In0.1Ga0.9As and 10 nm GaAs, Young\u2019s modulus Y \u00bc 80 GPa, and Poisson ratio \u03c5 \u00bc 0.31, the \u03b51 and \u03b52 are systematically changed to calculate the favorable shape as a function of h and \u0394\u03b5, and the obtained phase diagram is shown in Fig",
            " 2) and the wrinkling region is enlarged [52]. Figure 2 shows that for a wrinkled structure the wavelength \u03bb increases with h, while for a bent structure the equilibrium radius Req decreases with increasing \u0394\u03b5. One should note that, at small length scales, the continuum theory may not always be accurate, as misfit dislocations in the boundary, surface properties, and size effects play an increasing large role. For an anisotropically strained flexible layer, the situation is simpler. The coordinate system is the same as in Fig. 1(a). If the y direction is the most compliant direction, the layer bends or rolls in this direction [29]. If the x direction is the most compliant direction, deformation is dependent on hcw. When h < hcw the boundary [dashed line in Fig. 1(a)] does not allow the strain to relax along the x direction and the strain is retained, but when h > hcw the released layer attempts to bend in the x direction and the constraint thus causes the wrinkles [29,42]. In the above investigation, only pure bending and pure wrinkling are considered, and the favorable shapes are decided by the energy minimization. However, experimental results sometimes show an obvious deviation from these theoretical predictions, and the parameters during release can considerably influence the final geometry [63]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000472_tsmc.1981.4308713-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000472_tsmc.1981.4308713-Figure2-1.png",
        "caption": "Fig. 2. Link parameters 0, d, a, a.",
        "texts": [
            " Link 1 is connected to the base link by joint 1. There is no joint at the end of the final link. The only significance of links is that they maintain a fixed relationship between the manipulator joints at each end of the link (7). Any link can be characterized by two dimensions: the common normal distance a, and an the angle between the axes in a plane perpendicular to an. It is customary to call an \"the length\" and a,n \"the twist\" of the link (see Fig. 1). Generally, two links are connected at each joint axis (see Fig. 2). The axis will have two normals connected to it, one for each link. The relative position of two such connected links is given by d,, the distance between the normals along the joint n axis, and 0On the angle between the normals measured in a plane normal to the axis. dn and 0,n are called 'the distance\" and \"the angle\" between the links, respectively. In order to describe the relationship between links, we will assign coordinate frames to each link. We will first consider revolute joints in which 0,, is the joint variable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003733_0954405416640181-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003733_0954405416640181-Figure7-1.png",
        "caption": "Figure 7. Deposition process using 3D TIG method.",
        "texts": [
            " In the work the first step was to develop a basic understanding of the process characteristics of the used system, regarding deposition stability and formation of defects. Control strategies were developed such that they enable automatic control of the deposition process with process stability and good geometrical fit of the production parts. WAAM technique can be sub-grouped into three major processes based on the type of electric arc torch used to melt the wire: (1) 3D TIG welding (TIG or gas tungsten arc welding (GTAW)+wire feedstock) as shown in Figure 7, (2) 3D metal inert gas (MIG) welding (MIG or gas metal arc welding (GMAW)+wire feedstock), and (3) 3D plasma welding (plasma+wire feedstock). The roots of wire-added AM processes went back to 1920s patented by Baker,69 which stated a new method for producing 3D metallic parts in successive layers using manual arc welding. In the work by Shockey,70 a WAAM technique was investigated in facing and cladding applications for improving the lifetime of components subjected to abrasive wear. White71 used wire+arc welding method to repair worn surfaces of large metal pressure rollers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001868_s00158-010-0496-8-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001868_s00158-010-0496-8-Figure3-1.png",
        "caption": "Fig. 3 Angular-momentum-inducing inverted pendulum model",
        "texts": [
            " The proposed method was used to simulate 3D walking motion for a biped robot. The generated gait pattern consisted of single support and double support phases. The leg supporting exchange conditions and step length and walking velocities were all predicted by 3D-LIPM, which was also able to control walking directions. Kudoh and Komura (2003) presented C2 continuous gait motion for biped robots using an enhanced IPM, named the angular-momentum-inducing inverted pendulum model (AMIPM), which considered angular momentum around the COG as shown in Fig. 3. The gait motion consisted of single support and double support phases. The proposed method was used to control walking motion in the sagittal and frontal planes separately. Park and Kim (1998) proposed a method called the gravity-compensated inverted pendulum model (GCIPM) to design the gait pattern. This method extended the IPM by including the effect of the free motion leg dynamics as shown in Fig. 4. The 7-DOF mechanical system was simplified into two different masses instead of a single mass in the IPM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003706_j.oceaneng.2019.106329-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003706_j.oceaneng.2019.106329-Figure1-1.png",
        "caption": "Fig. 1. The inertial coordinate frame fng, the body-fixed coordinate frame fbg and the six DOF motion states of an underactuated UUV.",
        "texts": [
            " In this work, the spatial trajectory-tracking problem of an underactuated UUV is considered. Such underactuated UUV is only equipped with three independent actuators located at the aft of UUV, namely a pair of the identical stern thrusters, sternplanes and rudder to provide the forward force, the pitch moment and the yaw moment. This type of UUV lacks independent control input in the sway, heave and roll. To analyze the spatial motion of an UUV, it is necessary that two coordinate frames are defined as indicated in Fig. 1, namely the inertial coordinate frame fng and the body-fixed coordinate frame fbg. The frame fng is familiarly chosen the North-East-Down (NED) coordinate system, and its origin is defined relative to the Earth\u2019s reference ellipsoid. For the NED, the x-axis points towards Due North, the y-axis points towards Positive East while the z-axis points downwards normal to the Earth\u2019s surface. The frame fbg is fixed to the vehicle. Its origin is usually chosen to coincide with the midpoint of the connection between the center of gravity and the center of buoyancy. For UUVs, the body axes xb, yb and zb are chosen to coincide with the principal axis of inertia, and they are generally defined as (see Fig. 1): 1) xb - longitudinal axis (directed from aft to fore); 2) yb - transversal axis (directed to starboard); 3) zb - normal axis (directed from top to bottom). For the spatial motion of UUVs, it is usually necessary that six independent coordinates are defined to determine its position and orientation. However, the roll motion of UUVs is neglected, because it can\u2019t be directly controlled by any actuators and is usually self-stabilizing. That is, the spatial motion of UUVs can be described by five independent coordinates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002037_j.promfg.2016.08.067-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002037_j.promfg.2016.08.067-Figure4-1.png",
        "caption": "Figure 4: (a) Schematic of an injection mold sample with internal cooling channels and (b) the mold sample fabricated by the A/SM hybrid process and heat treatment.",
        "texts": [
            " The working chamber had a 290 290 260 mm workspace, and was vacuumed and then filled with nitrogen gas at a pressure of 10 mbar to protect a part being fabricated. The protective atmosphere allowed preventing the oxidation during the fabrication process by maintaining the oxygen content below 0.2%. 3.1 Hybrid process parameters This study used 18Ni (C300) maraging steel powders that were supplied by Sodick Co. Ltd. The powders followed the Gaussian distribution in terms of the particle size with a mean value of 35 \u03bcm. Figure 4 (a) shows a schematic of an injection mold sample with multiple internal flow channels. Similar to the process shown in Figure 1, the internal channels were machined by the milling process during the laser additive process. The microstructure evolution of an A/SM part mainly depended on the local heat transfer condition which was influenced by laser energy, scanning speed, heat conductivity of the powder bed, etc. The additive process parameters were determined based on the considerations of the mold sample quality",
            " Rockwell hardness tests were performed by using an automated CLEMEX\u00ae hardness tester. The tests were conducted on the surface of the sample in different directions and locations. Before the tests, the sample was polished in order to remove the oxide layer in the surface generated during the heat treatment. For each location, 10 measurements were conducted and the mean value of the measurements were calculated. The relative density was measured by the Archimedes method in a deionized water according to the ASTM B311-13 standard. 4 Results and discussion Figure 4 (b) shows the mold sample with the cooling channels produced by the A/SM and heat treatment processes. The chemical compositions (wt%) of the A/SM sample are given in Table 1 and compared with the nominal maraging steel, grade 300. The results of the Archimedes method show that the sample was highly consolidated with a relative density of 99.2%. As shown in Figure 6, significantly fewer internal defects, such as porosities and voids, can be found in the A/SM sample than in the one fabricated by AIM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure6.60-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure6.60-1.png",
        "caption": "Fig. 6.60 Puma sideslip and sideways flight limits: (a) sideslip envelope in forward flight and (b) pedal margin for hover in wind",
        "texts": [
            " Specific flying qualities criteria for the response characteristics in flight at steep descent angles do not exist, but perhaps the emphasis should be on deriving methods to assist the pilot in respecting the very real limits to safe flight that exist in this flight regime, conferring carefree handling, a topic returned to in Chapter 7. The unique VRS characteristics with tiltrotor aircraft are discussed in Chapter 10. 6.6 Yaw Axis Response Criteria As we turn our attention to the fourth and final axis of control, the reader may find it useful to reflect on the fact that of all the \u2018control\u2019 axes available to the pilot, yaw is, arguably, the most complex and the one that defines the greatest extent of the flight envelope boundary, both directly or indirectly. Figure 6.60a,b, for example, 396 Helicopter and Tiltrotor Flight Dynamics show the SA330 Puma control limits for the forward flight sideslip envelope, bounding the envelope at higher speeds, and for hovering in a wind from the starboard side, bounding the low-speed envelope. Excursions beyond these boundaries can lead to loss of control or structural damage. Within these constraints, the pilot may feel able to command yaw motion in a relatively carefree manner. However, the pilot is not provided with a cue as to the magnitude of the loads in the tail rotor critical components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003694_aae10e-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003694_aae10e-Figure4-1.png",
        "caption": "Figure 4. Layout of the tensile andC(T) specimen blocks on the build platformwith the standard AMaxis system [41].",
        "texts": [
            " Edwards et al [38] evaluated the Paris region life of electron beam melted Ti-6Al-4V components and obtained crack growth rates lower than thewroughtmaterial. Similarly, SLMTi-6Al-4V samples at a load ratio of 0.1 showed slower crack growth rates compared to thewrought material [39]. The as-built SLMTi-6Al-4V samples tested byHooreweder et al [40] showed faster crack growth rates for the lower\u0394K (15\u201330MPa\u221am) and slower crack growth rates in the higher\u0394K region (30\u201380MPa\u221am). Jiao et al [41] compared the fatigue crack growth resistance of SLMTi-6Al-4Vmanufactured in different orientations (figure 4) at two different temperature levels, i.e. room temperature (RT) and 400 \u00b0C,with conventionallymanufactured Ti-6Al-4V. They reported the fatigue crack growth (FCG) resistance to be dependent on the specimen orientation only in the near threshold region not in the steady growth stage at RT. This dependencywas not observed at 400 \u00b0C. In the lower\u0394K region, the steady stage FCG rate at higher temperature is higher than that at RT,whereas this relationship is inversed in the higher\u0394K region. Figure 5 shows the fatigue strength of SLMTi-6Al-4V specimens on a spectrum as reported by different authors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001080_s00170-016-9429-z-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001080_s00170-016-9429-z-Figure1-1.png",
        "caption": "Fig. 1 Laser processing of stripes with hatching in laser powder bed fusion [11]",
        "texts": [
            " The desired three-dimensional (3D) part geometry is realized where the L-PBF machine builds the solidified structure layer-by-layer using 2D sliced geometry by adding a new powder layer on top of the previously processed and solidified layer. In order to minimize the oxidation, an inert gas such as Argon or Nitrogen is pumped into the chamber and the platform is heated up to a temperature on the order of 80 \u00b0C prior to laying and processing of the first powder metal layer. Once the process is completed, the excess powder metal is vacuumed and filtered to be reused. The laser beam is scanned over the powder surface, often in a hatched stripe pattern, using numerically controlled mirrors until a layer is processed as shown in Fig. 1 where both a graphical representation of the laser scanning of hatches and an actual image captured while solidified stripes are created in the powder metal bed. The L-PBF process works by melting desired locations of the powder bed on a layer. The area to be processed is first divided into stripes. Each stripe consists of multiple tracks, separated by a hatch distance. Each track is processed with the laser beam at a constant scan velocity. After a track is completed by the movement of laser in one direction, the laser turns off and shifts towards the next unprocessed track where it turns back on and starts moving in the opposite direction of the previous track as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002143_celc.201402141-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002143_celc.201402141-Figure5-1.png",
        "caption": "Figure 5. Electron-transfer mechanisms utilised in biofuel cell technology: a) direct electron transfer, b) electron transfer performed by a redox mediator species, and c) electron transfer by nanoparticles.",
        "texts": [
            "[3, 67] In an original work, Dutton and co-workers[67] demonstrated that by favouring proteins with redox centres placed within 14 of each other, natural selection fosters robust electron-transfer designs. In Figure 4, it can be observed that within the 14 tunnelling boundary, the calculated ~G-optimised tunnelling rates are very high\u2014in the 1013\u2013107 s 1 range. For distances greater than 14 , the values of reorganisation energy (l) and ~G, which sustain tunnelling rates that are faster than typical catalytic rates, decrease sharply.[67] ET reactions can occur in two ways. The first is based on the utilisation of redox mediators (Figure 5 a). In this case, the enzyme catalyses the oxidation or reduction of the mediator that is regenerated on the electrode surface.[68] The mediator must be capable of efficiently promoting electron transfer at a particular potential, that is, it must be capable of transferring electrons rapidly with the application of a small driving force. The mediator reduction potential is important because it usually dictates the potential at which the electrode will operate.[3] The other way is based on direct electron transfer (DET), for which the electron is transferred directly from the electrode to the substrate molecule (or vice versa) by the active site of the enzyme (Figure 5 b).[10d] The direct transfer pathway can be established by strongly linking the enzyme on the electrode in the correct position, either by directed covalent or strong noncovalent bonding. A third way in which ET has been commonly observed in recent years is the use of nanomaterials at the enzyme/electrode interface (Figure 5 c). In this case, although the ET occurs through the nanomaterial located between the enzyme and the electrode surface, many authors have considered this to be DET.[69] Besides, in some cases, the immobilised nanomaterials are considered to be an extension of the electrode surface. This strategy can be used to provide an increased surface area to be covered and may lead to enhanced stability of the enzymatic electrode. The first works on the DET of adsorbed redox proteins were published in 1977 independently by Eddowes and Hill[70] and Yeh and Kuwana"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000426_9781118680469-Figure9.25-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000426_9781118680469-Figure9.25-1.png",
        "caption": "FIGURE 9.25 Scheme of the assembly and permeability test for microcapsules embedded with Co@gold nanoparticles under an oscillating magnetic field. Reproduced with permission from [187]. Copyright 2005 American Chemical Society.",
        "texts": [
            " For example, microcapsules containing both gold and magnetic nanoparticles can be made to accumulate in a given site by SYSTEMS OF METAL NANOPARTICLES WITH SMART ORGANIC MATERIALS 319 320 STIMULI-RESPONSIVE SMART ORGANIC HYBRID METAL NANOPARTICLES a static magnetic field, and triggered by NIR irradiation [184]. Polymer materials, including temperature-sensitive PEM [185] or block copolymer [186], incorporating iron oxide nanoparticles either in the interior or on the surface can be used to trigger release under magnetic fields. Besides most frequently used iron oxide nanoparticles, other magnetic nanomaterials such as gold-coated cobalt have also been used to trigger the release (Fig. 9.25) [187]. There are a variety of other smart systems. For example, magnetic-core gold-shell structures have been synthesized that bring the properties of magnetic Fe2O3 and gold together [188]. In addition, metabolite can be used as a new stimulus source. For example, both the nanoparticle and liposome cargos were released, in such a system a DNA aptamer can bind to adenosine. AMP and ATP were used as a linker to attach either DNA functionalized gold nanoparticles or liposomes to DNA functionalized hydrogels [189]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002404_tcst.2017.2670522-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002404_tcst.2017.2670522-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor model in \u201cX\u201d configuration.",
        "texts": [
            " The remainder of this brief is organized as follows. Section II briefly describes the quadrotor dynamics, and the problem of quadrotor actuator FTC is formulated in Section III. In Section IV, we present the detailed design and analysis of the altitude and attitude nonlinear adaptive faulttolerant controller. Section V describes the algorithm implementation using a real-time indoor flight test environment and experimental results, illustrating the effectiveness of the proposed method. Finally, some concluding remarks are given in Section VI. Fig. 1 shows a simplified model of the quadrotor along with the assumed body frame, inertial frame, and angular rates direction of rotation using the right-hand rule. As can be seen, the quadrotor motors and propellers are configured, such that rotors M1 and M3 rotate counterclockwise, and rotors M2 and M4 rotate clockwise. Each rotor is located at a distance d from the quadrotor center of mass and produces a force Fs (s = 1, . . . , 4) along the negative z-direction relative to the body frame. In addition, due to the spinning of the rotors, a reaction torque \u03c4s is generated on the quadrotor body by each rotor",
            " 3 shows the altitude and attitude tracking performance of the quadrotor for the case with two simultaneous actuator faults. As can be seen, the quadrotor altitude and attitude tracking performance is recovered shortly after the occurrence of two simultaneous actuator faults. Note that only the pitch angle and quadrotor altitude are significantly affected over a short duration of time by the LOE in the two rotors. This can intuitively be explained by considering the quadrotor configuration shown in Fig. 1. A sudden LOE by the thrust produced by the two forward rotors (i.e., rotors M1 and M2) would result in an LOE in the pitching torque and a loss of total thrust, which coincides with the pitch angle and altitude errors shown in Fig. 3. In addition, note that rotors M1 and M2 are configured to have opposing spinning direction. Thus, due to their symmetrical location on the quadrotor frame, a loss of equal magnitude in rotors M1 and M2 would have canceling effects on the rolling and yawing torque produced by the two rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure5.40-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure5.40-1.png",
        "caption": "Fig. 5.40 Elemental ramp gust used in the statistical discrete gust approach",
        "texts": [
            " to shear layers exhibiting sharp velocity gradients, are clearly important for helicopter applications in the wake of hills and structures, and a different form of modelling is required in these cases. The statistical discrete gust (SDG) approach to turbulence modelling was developed by Jones at the RAE for fixed-wing applications (Refs 5.52\u20135.55), essentially to cater for more structured disturbances, and appears to be ideally suited for low-level helicopter applications. In Ref. 5.49, the SDG method is recommended for the assessment of helicopter response to, and recovery from, large disturbances. The basis of the SDG approach is an elemental ramp gust (Figure 5.40) with gradient distance (scale) H and gust amplitude (intensity) wg. A non-Gaussian turbulence record can be reconstituted as an aggregate of discrete gusts of different shapes and sizes; different elemental shapes, with self-similar characteristics (Ref. 5.54), can Modelling Helicopter Flight Dynamics: Stability Under Constraint and Response Analysis 311 be used for different forms of turbulence. One of the properties of turbulence, correctly modelled by the PSD approach, and that the SDG method must preserve, is the shape of the PSD itself, which appears to fit measured data well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001406_j.proeng.2014.12.139-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001406_j.proeng.2014.12.139-Figure1-1.png",
        "caption": "Fig. 1. Inertial and body-fixed frame of quadrotor.",
        "texts": [
            " Each propeller rotates at the angular velocity \u03c9i producing the corresponding force Fi directed upwards and the counteracting torque directed opposite to the direction of the rotation. Propellers with the angular speed \u03c91 and \u03c93 spin counter-clockwise and the other two spin clockwise. The alteration of the position and the orientation is reached by varying the thrust of a specific rotor. Angular velocities corresponding to the inertial frame EI ( \u03b6 ) and the bodyfixed frame EB (\u019e) are presented in Fig. 1. The rotation matrix from EB to EI is an orthogonal matrix given by equation (1), where Cangle and Sangle designate cos(angle) and sin(angle) respectively [13, 14]. CCSCS SCCSSCCSSSCS SSCSCCSSSCCC MR (1) Angular velocities with respect to the inertial frame EI can be converted to angular velocities with respect to body-fixed frame EB using the transformation matrix R\u03b6 [13, 14, 15]. coscossin0 sincoscos0 sin01 \u03b6R\u03b7 \u03b6 (2) The reverse transformation of angular velocities can be obtained by the inverse of the transformation matrix R\u03b6-1 [13, 14]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001708_tia.2009.2023393-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001708_tia.2009.2023393-Figure4-1.png",
        "caption": "Fig. 4. Calculated loss density and eddy-current distributions of motors with concentrated and distributed windings (Ia = 300 A, \u03b2 = 60\u25e6, 6000 min\u22121). (a) Concentrated. (b) Distributed.",
        "texts": [
            " The underestimation of the analysis may have been caused by the neglect of the strain of the core due to the manufacturing process. From these results, the validity of the finite element analysis is confirmed. III. INVESTIGATION OF LOSS VARIATION DUE TO SHAPE To understand the loss characteristics of the motor with concentrated windings, the same analysis of the motor with distributed windings is carried out. In the motor, the number of the stator slots is 96. The total magnetomotive force and current are set as identical to those of the concentrated winding motor. The rotors of the two motors are also identical. Fig. 4 shows the loss and magnet eddy-current distributions of the motors with concentrated and distributed windings. Figs. 5 and 6 show the calculated iron losses and torques due to the current phase angle. It can be seen that the magnet eddy currents in the concentrated winding motor are much larger than those in the distributed winding motor. The rotor core loss also increases, while the stator core loss and torque decrease. To understand these characteristics, the losses are decomposed into harmonic components and classified due to their origins [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002203_j.ymssp.2013.06.040-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002203_j.ymssp.2013.06.040-Figure2-1.png",
        "caption": "Fig. 2. Geometrical parameters for the fillet foundation deflection [3].",
        "texts": [
            " When the crack length extends through the whole tooth width: q\u00f0z\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2o q22 W z\u00feq22 s \u00f08\u00de where q2 is shown in Fig. 1c. Sainsot et al. [31] studied the effect of fillet foundation deflection on the gear mesh stiffness, derived this deflection, and applied it for a gear body. The fillet foundation deflection can be calculated as follows [31]: \u03b4f \u00bc F U cos 2\u00f0\u03b1m\u00de W UE Ln uf Sf 2 \u00feMn uf Sf \u00fePn\u00f01\u00feQn tan 2\u00f0\u03b1m\u00de\u00de ( ) \u00f09\u00de where the following notation is used: \u03b1m is the pressure angle. uf and Sf are illustrated in Fig. 2. Ln; Mn; Pn; and Qn can be approximated using polynomial functions as follows [31]: Xn i \u00f0hf i; \u03b8f \u00de \u00bc Ai=\u03b8 2 f \u00feBih 2 f i\u00feCihf i=\u03b8f \u00feDi=\u03b8f \u00feEihf i\u00feFi \u00f010\u00de Xn i represents the coefficients Ln; Mn; Pn; and Qn. hf i \u00bc rf =rint. rf ; rint; and \u03b8f are illustrated in Fig. 2. Tab Val Ln M P Q The coefficients Ai; Bi; Ci; Di; Ei and Fi are given in Table 1. Then the stiffness due to fillet foundation deflection can be obtained as follows: 1 Kf \u00bc \u03b4f F \u00f011\u00de For a pinion it could be denoted as Kfp. Yang and Sun [32] ascertained that the stiffness of the Hertzian contact of two gears in mesh is constant during the whole contact period, and therefore, has the same value at all the contact positions along the path of contact. The Hertzian contact stiffness Kh can be calculated as follows: 1 Kh \u00bc 4\u00f01 \u03bd2\u00de \u03c0 UEUW \u00f012\u00de After calculating the stiffness of a cracked pinion tooth, Ktp, due to bending, shear, and axial compression and then calculating the stiffness due to the fillet foundation deflection, Kfp, we can perform the same calculations for an uncracked mating gear tooth to find Ktg and Kfg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure12-1.png",
        "caption": "Fig. 12. 5\u20135\u20135 RPR-equivalent PMs in the first family. (a) 2-DSvPR/uRPFS. (b) 2-DSvRR/uRPFS. (c) 2-DSvPR/uRRFS. (d) 2-DSvRR/uRRFS",
        "texts": [
            " For the same reason, in the ijUvRRR limb, the unit vectors i, j,v are linearly independent, and generally i and j can belong to the vector plane orthogonal to v without being u and w. However, for example, one can set i = v and j = w for a uRPRijU limb and i = w and j = u or a ijUvRRR or a ijUvRPR limb. A 2- uRPRvwU/wuUvRRR and a 2-uRPRvwU/wuUvRPR PM is, thus, obtained as shown in Fig. 11. We can readily verify that the wR pairs in vwU and wuU are idle, and the 2-uRPRvwU/wuUvRRR works like an overconstrained 2-uRPRvR/uRvRRR PM. Table VII enumerates 49 RPR-equivalent PMs in this category Fig. 12 shows four RPR-equivalent PMs belonging to the first family in 5\u20135\u20135 category. For the readers\u2019 sake, Fig. 13 shows four RPR-equivalent PMs belonging to the second family in the 5\u20135\u20135 category. B. {L1} = {X(u)}{X(v)} and {L2} = {G(u)}{S(F )} With F (B,v) and {L3} = {S(D)}{G(v)} With D \u2208 axis(O, u) When {L1} = {X(u)}{X(v)} and {L2} = {G(u)}{S (F)}, the intersection of {L1} and {L2} is given by {L1} \u2229 {L2} = {X(u)}{X(v)} \u2229 {G(u)}{S (F) } = {G(u)}{R(B, v)}{T(u)} \u2229 {G(u)}{R(B,v)} \u00d7{R(F, i)}{R(F, j)} = {G(u)}{R(B,v)}({T(u)} \u2229 {R(F, i)}{R(F, j)}) = {G(u)}{R(B,v)}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003217_j.msea.2019.01.024-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003217_j.msea.2019.01.024-Figure4-1.png",
        "caption": "Fig. 4. Schematic diagram of the overlap area melt.",
        "texts": [
            " As a result, the pores can be formed more easily, and it is more difficult for the entrapped gas to escape because of the increase in depth of melt pools. Therefore, it is easy to generate pores at the beginning/end of the scan vector. This is similar to a previous report [15]. Similarly, the side surface of the isolated sample is also the location where the laser turns on or off, as shown in Fig. 3(a). Therefore, there are also some pores in the isolated sample boundary. Secondly, two lasers irradiate the overlap area, as shown in Fig. 4, inducing high laser energy input and large pores. The beginning/end of the scan vector is on the side of the samples. As for isolated area, the side surface of the sample is adjacent to the powders. The thermal conductivity of the powders is much lower than that of the bulk. Therefore, it induces the high temperature and long lifetime of melt pools. During the process, large bubbles can escape before solidification. Thus, the small bubbles leave in the sample after solidification. As for the overlap area, the melt pool lifetime is shorter than that of the isolated sample because of the high thermal conductivity of the bulk, and the depth of the melt pool increases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003314_j.ymssp.2018.01.005-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003314_j.ymssp.2018.01.005-Figure10-1.png",
        "caption": "Fig. 10. Modeling of pitting in four damage degrees: (a) no pitting, (b) slight pitting, (c) moderate pitting and (d) severe pitting.",
        "texts": [
            " Since the pinion and wheel gear are assumed as linearly elastic in the modeling, the deformation of the meshing point is proportional to the displacement of the hub node of the pinion. In this way, the deformation of the meshing point in the direction of the action line is able to be acquired. Considering the linear relationship between the deformation and torque, we can obtain the TVMS by the ratio of the torque to the deformation. The same four pitting degrees are simulated as those in Section 3, which are shown in Fig. 10. The TVMS of four degrees obtained from FEM is given in Fig. 11. Taking the results of FEM as reference, we choose the stiffness at moment M (h1 \u00bc 15:5 , during the singletooth engagement) and N (h1 \u00bc 19:8 , during the double-tooth engagement) to illustrate the comparison results between the proposed model and the FEM, listed in Table 4. When the gears are healthy, the results obtained from the proposed method and FEM are quite close. For example, in Fig. 12(a), the stiffness obtained from the potential energy method has a small difference of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure5.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure5.11-1.png",
        "caption": "Figure 5.11.1. Vehicle load transfer model, vehicle-fixed axes.",
        "texts": [
            " The roll moment produced by the stiffness elements in roll depends on the body roll relative to the axle, i.e., relative to a line joining the wheel centers. This is the suspension roll angle. Because of load transfer on the tire vertical stiffness, typically 250 N/mm, the axle itself, solid or independent, has a small roll angle called the axle roll angle. The body roll is the suspension roll plus the axle roll. Axle roll is typically one-eighth of suspension roll, reaching 1\u20132\u00b0. Suspension Characteristics 263 5.11 Vehicle Load Transfer Figure 5.11.1 shows a two-axle vehicle model. This distinguishes the sprung mass mS from the front and rear unsprung masses mUf and mUr, each with its own center of mass. There are different front and rear roll center heights, tracks, etc. The vehicle is in steady-state left-hand cornering. It is convenient to perform this analysis in the accelerating coordinate system xyz attached to the vehicle (vehicle-fixed axes), so the centrifugal compensation forces are included at each mass center. In this coordinate system there are no linear or angular accelerations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001277_j.procir.2016.11.009-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001277_j.procir.2016.11.009-Figure10-1.png",
        "caption": "Fig. 10. Final design \u2013 Modal analysis Eigen modes.",
        "texts": [
            " The second cycle focused on the definition of the design specifications based on the prerequisites defined in the first cycle. The feedback that the students received from the machine shop during the first two cycles was used for drafting an initial design within the third cycle of the pilot. The fourth cycle was focused on the detailed dynamic and thermal analysis of the selected design. Finally, during the fifth cycle the students presented their final solution as a result of this collaborative design process (Fig. 10). The modular nature of the Teaching Factory may suit the needs and limitations of both the academia and industry. Not all manufacturing problems can have their solution worked out via methods selected for the pilot cases of this study. This is the reason why the Teaching Factory asks for a high-degree of modularity when adopted for academic and industrial practice. New ICT technologies may help the concept to be implemented. There is room for the ICT technologies of the Teaching Factory to be improved in terms of didactic content"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001011_tmech.2016.2614672-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001011_tmech.2016.2614672-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor model",
        "texts": [
            " Additionally, this real-time implementation shows the efficiency and efficacy of T2FNNs for the first time to control highly nonlinear, underactuated and relatively fast dynamic aerial vehicles. Paper organization: This paper is organized as follows: Section II starts with the kinematic and dynamical model of a quadrotor. In Section III, adaptive T1FNN and T2FNN with elliptic MFs are discussed. In section IV, we present the experiments and results. Lastly, some conclusions are drawn from this study in Section V. The schematic diagram of a quadrotor with its two sets of rotors (1, 3) and (2, 4) is illustrated in Fig. 1. Whereas rotor 1 and rotor 3 rotate clockwise, rotor 2 and rotor 4 rotate anticlockwise direction. This configuration is necessary to eliminate net torque around z axis such that zero reaction torques at hover can be achieved. By manipulating the angular speeds of each individual rotors, one can control six degreesof-freedom (DOF) motion of the quadrotor through four inputs (roll, pitch, yaw, thrust). Specifically, in order to roll, a difference in angular speeds of rotor 2 and rotor 4 results in reaction torque along the x axis",
            " Moreover, yawing motion is resulted from the balance torque of the counter-clockwise rotating rotors against the clockwise rotating rotors. Unlike a conventional helicopter, a quadrotor has fixed pitch propeller hardware design. Therefore, the resulting thrust Fz of the rotors only points along the z axis of frame B which determines motion (X\u0308 ,Y\u0308 , Z\u0308) in frame E. 1083-4435 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The two reference frames are shown in Fig. 1: the Earth inertial frame E and the body-fixed frame B. In the bodyfixed frame B, we assign (o,x,y,z) with o as the center of mass, x points towards the rotor 1, y points towards the rotor 4 and z points upwards. The linear position about the frame E is represented by (O,X ,Y,Z) and the three Euler angles roll-pitch-yaw (\u03c6 ,\u03b8 ,\u03c8) are described as the orientation of the frame B with respect to the frame E. The linear velocities (U,V,W ) and the body angular rates (p,q,r) are defined with respect to the B",
            " Applying the Newton\u2019s translational motion equation and Euler\u2019s rotational motion equation to vehicle dynamics, we can obtain six equations as follows: X\u0308 = (sin\u03c8 sin\u03c6 + cos\u03c8 sin\u03b8 cos\u03c6) Fz m + Dx m (3) Y\u0308 = (\u2212cos\u03c8 sin\u03c6 + sin\u03c8 sin\u03b8 cos\u03c6) Fz m + Dy m Z\u0308 = \u2212g+(cos\u03b8 cos\u03c6) Fz m + Dz m \u03c6\u0308 = (Iyy\u2212 Izz)\u03b8\u0307 \u03c8\u0307\u2212 Jr\u03b8\u0307\u03c9r + \u03c4x Ixx \u03b8\u0308 = (Izz\u2212 Ixx)\u03c6\u0307 \u03c8\u0307 + Jr\u03c6\u0307\u03c9r + \u03c4y Iyy \u03c8\u0308 = (Ixx\u2212 Iyy)\u03c6\u0307 \u03b8\u0307 + \u03c4z Izz where m is the mass of the quadrotor and Ixx, Iyy and Izz are the inertial components along the x, y and z directions in the frame B. The term Fz represents the vertical thrust along the z axis. The terms \u03c4x, \u03c4y and \u03c4z represent the torques associated to the thrust difference of each rotor pairs. The terms Dx, Dy and Dz are the drag forces for the velocities in X , Y and Z directions, Jr is the rotor inertia, and \u03c9r is the overall speed of the rotor as defined below: \u03c9r =\u2212\u03c91 +\u03c92\u2212\u03c93 +\u03c94 (4) The relations between Fz,\u03c4x,\u03c4y, \u03c4z and each rotor\u2019s angular speeds can be obtained by analyzing the free body diagram of the model in Fig. 1. The terms \u03c91, \u03c92, \u03c93 and \u03c94 represent the angular speeds of the four rotors, b represents thrust factor, d represents drag factor, and l represents the length of each quadrotor\u2019s arm. The following matrix shows the relationships between Fz,\u03c4x,\u03c4y, \u03c4z and the angular velocities of the four propellers:  Fz \u03c4x \u03c4y \u03c4z  =  b b b b 0 \u2212lb 0 lb \u2212lb 0 lb 0 d \u2212d d \u2212d  .  \u03c92 1 \u03c92 2 \u03c92 3 \u03c92 4  (5) Since the aerodynamical effects are negligible and complicated to model in low velocities in which the quadrotor operates, they are ignored in the model in this study"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure16.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure16.5-1.png",
        "caption": "Fig. 16.5 Migration with temporary co-existence",
        "texts": [
            " To reduce the risk associated with the migration or to split the overall effort in manageable sub tasks a step-by-step approach is more appropriate. The steps shall be derived from business drivers like products, programs, or subdivision. It needs to consider basic preparatory work, common data like standard parts or libraries, and will handle structural data separately from mass CAD data. Depending on the requirements of the processes based on the source system and the chosen splitting approach a partial re-synchronization may be necessary (Fig. 16.5). This involves an additional data flow back from target to source. The data flow back asks for an automated solution which tends to increase the complexity of the uni-directional migration to a bi-directional integration scenario. 478 L. L\u00e4mmer and M. Theiss A PLM integration platform provides a common, easily available access mechanism to all necessary PLM information for collaborative engineering in a heterogeneous system world. Standardized interfaces to the majority of the required PDM functionality allow short set-up times for establishing working partnerships"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003206_tte.2016.2528505-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003206_tte.2016.2528505-Figure1-1.png",
        "caption": "Fig. 1. The geometry of the investigated machine, implemented in Maxwell. The windings are presented in dark orange, the iron in gray and the magnets are shown violet colour.",
        "texts": [
            " In Section IV, a procedure is introduced in order to compare several different MTPA methods for the entire operating region of the PMSM. In Section V, the proposed MTPA in this paper is explained and in Section VI is compared with several other control strategies. Finally, in Sections VII and VIII, the performance and energy efficiency consequence of using the proposed algorithm is compared with a recent MTPA algorithm. In order to properly compare different control algorithms, the PMSM presented in [20] and is shown in Fig. 1 is modeled, using a FEA software (Ansys Maxwell). The parameters of the machine are presented in Table I. 2332-7782 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. An inverter fed PMSM has some constraints due to the limitations of the inverter and the supplying dc source that have to be respected by the controllers. The key limitations are the maximum current and voltage of the machine [21], [22]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure64-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure64-1.png",
        "caption": "Fig. 64 Implementation process flow of the ANN-based geometric compensation approach [95]",
        "texts": [
            " Therefore, the WAAM-molded workpiece has a large deviation from the original three-dimensional model. The important measure to improve this deviation is to compensate by the model design. Chowdhury [95] proposed a neural network algorithm to directly compensate the geometric design of the workpiece to offset the heat shrinkage and deformation. A well-trained network is implemented into the STL file to perform the required geometric corrections to produce parts with modified geometry for dimensionally accurate finished products; the whole process is shown in Fig. 64. After obtaining the monitoring data of the molding process, the most important thing is to obtain valuable information from the data. The advantage of machine learning is to use the existing data to train the model to achieve the purpose of prediction and classification. At present, the data obtained by the monitoring system generally has many pictures, and many studies use convolutional neural networks (CNNs) to achieve the purpose of classification of forming features. Zhang [96] established a visual monitoring system with a high-speed camera to capture the molten pool image during the forming process at high speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000050_tpel.2004.839785-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000050_tpel.2004.839785-Figure10-1.png",
        "caption": "Fig. 10. Increased maximum rotor current, i , for Method I, when the leakage inductance is underestimated, ~L = 0:5L , due to a symmetrical voltage sag as a function of the sag size, V , and the current control bandwidth, .",
        "texts": [
            " It is, thus, not only necessary to design the converter according to the desired variable-speed range, but also according to a certain voltage sag to withstand. A. Influence of Erroneous Parameters As mentioned earlier, the methods are mostly sensitive to an underestimated , mainly since the bandwidth of the current control loop then becomes lower than the desired. Simulations with shows that Method I is very sensitive to an underestimated during voltage sags, especially for low bandwidths of the current control loop, see Fig. 10. By using Method IV, the influence of an erroneous value of is, in principle, removed. If the current control loop bandwidth is below 2 p.u., the difference in the maximum rotor current is below 0.02 p.u. For Method IV and variations in , , and with , the difference in maximum rotor current is insignificant; while for Method I, and have small impacts for smaller . However, for higher values of this impact is also insignificant. As an example of this, Fig. 11 shows the minimum remaining grid voltage that can be handled without triggering the crowbar as a function of the power"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001834_j.proeng.2015.08.007-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001834_j.proeng.2015.08.007-Figure4-1.png",
        "caption": "Fig. 4. EBM samples preparation: (a) near-net-shaped rectangular and round samples; (b) extraction of fatigue and tensile specimens.",
        "texts": [
            " Post-LENS annealing was also performed to generate comparison with the asdeposited cases. The annealing treatment used was: 760\u00b0C +/- 4\u00b0C for 1 hour in vacuum, followed by air cooling. EBM samples were fabricated at Oak Ridge National Laboratory (ORNL) in two batches, B1 and B2, representing two different machine models A2 and Q10. The processing parameters were defined by the internal algorithm of the ARCAM machines. Similarly, near-net-shaped cylindrical and rectangular samples were designed for tensile and fatigue crack growth studies respectively, Fig. 4(a, b). The effects of solutionizing, annealing temperature and time, and aging temperature and time have been systematically evaluated for EBM fabricated Ti6Al-4V [14], and the optimum heat treatment was used in this study: solutionizing at 950\u00b0C for 1 hour, water quenching to room temperature; aging at 500\u00b0C for 7 hours, and air cooling. Metallographic samples were mounted in Bakelite and polished using diamond suspension down to 0.05\u03bcm. Samples were then etched by Kroll\u2019s reagent (2% HF, 6% HNO3 and 92% DI H2O)",
            " Comparing between LENS fabrications, LP as-deposited Ti-6Al-4V yieled higher strength, but significantly lower ductility due to the presence of \u03b1' martensite. After annealing, significant increase in ductility was observed as a result of \u03b1' decomposition into \u03b1 + \u03b2 lamellae. Similar heat treating effect was also found in HP fabricated Ti-6Al-4V alloys, as the elongation increased from 7% to 10% after annealing. 3.2.2. EBM fabricated Ti-6Al-4V For EBM fabrication, tensile tests were conducted at both horizontal and vertical orientations, Fig. 4(b). Tensile data for EBM fabricated Ti-6Al-4V are given in Table 3. Similar tensile properties were found in as-deposited B1 and B2 batches at two diffrernt orientations. Comparing these results with the as-deposited cases in LENS fabrication, EBM and LENS yielded comparable tensile strength, but EBM fabrication achieved much better ductility than LENS fabrication due to the powder bed heating, which prevents the formation of martensitic \u03b1' phases. The optimum post-EBM heat treatment was found to be able to further increase the tensile strength while maintaining a moderate ductility"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000307_0278364908098447-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000307_0278364908098447-Figure1-1.png",
        "caption": "Fig. 1. The ATHLETE Lunar vehicle (Wilcox et al. 2007).",
        "texts": [
            "comDownloaded from reason is the lack of an adequate motion planner capable of computing sequences of footsteps and postural adjustments specifically adapted to the local geometric and physical properties of the terrain. In this paper we describe the design and implementation of a motion planner that enables legged robots with many degrees of freedom (DOFs) to navigate safely across varied terrain. Although most of this planner is general, our presentation focuses on its application to two robots: the six-legged Lunar vehicle ATHLETE (Wilcox et al. 2007) and the humanoid HRP-2 (Kaneko et al. 2004). ATHLETE (shown in Figure 1) is large and highly mobile. A half-scale Earth test model has a diameter of 2.75 m and mass of 850 kg. It can roll at up to 10 km h 1 on rotating wheels over flat smooth terrain and walk carefully on fixed wheels over irregular and steep terrain. With its six articulated legs, ATHLETE is designed to scramble across terrain so rough that a fixed gait (for example, an alternating tripod gait) may prove insufficient. Such terrain is abundant on the Moon, most of which is rough, mountainous and heavily cratered\u2014 particularly in the polar regions, a likely target for future surface operations",
            " First, we create a nominal position and orientation of the chassis: (i) we fit a plane to the footfalls in in a least-squares sense (ii) we place the chassis in this plane, minimizing the distance from each hip to its corresponding footfall and (iii) we translate the chassis a nominal distance perpendicular to the plane-fit and away at UNIV OF MICHIGAN on March 8, 2015ijr.sagepub.comDownloaded from from the terrain. Then, we sample a position and orientation of the chassis in a Gaussian distribution about this nominal placement. Finally, we compute the set of joint angles that cause each foot to either reach or come closest to reaching its corresponding footfall. Note that here a footfall fixes the intersection of the ankle pitch and ankle roll joints relative to the chassis (Figure 1). The hip yaw, hip pitch and knee pitch joints determine this position. There are up to four inverse kinematic solutions for these joints or, if no solutions exist, there are two configurations that are closest (straight knee and completely bent knee). The knee roll, ankle roll and ankle pitch determine the orientation of the foot, for which there are two inverse kinematic solutions. We select a configuration that satisfies joint-limit constraints if none exist, we reject the sample and repeat. HRP-2: Each contact in the stance corresponds to the placement of a robot link on the terrain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000951_adem.201100233-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000951_adem.201100233-Figure2-1.png",
        "caption": "Fig. 2. Bi-directional scanning strategy.",
        "texts": [
            " Leuvenwas used to produce different cubical (5 5 5mm3) blocks using different values for the laser power P (100, 200, 250W), scan speed v (63\u20131600mm s 1), track distance h (53\u2013145mm), and layer thickness t (30, 60, 90mm) while maintaining the same energy density E. This last parameter gives an indication of the energy supply during SLM and can be calculated using the previous parameters, E\u00bcP/vht in J mm 3. A bidirectional scanning strategy was used for all the specimens. After scanning the contour, the first layer is scanned in zigzag and each successive layer is rotated by 908 as indicated in Figure 2. The relative density of the different blocks was measured using the Archimedes principle leading to a maximal value of 99.7% and a set of optimal scan parameters as indicated in Table 1. 2. Experimental All experiments are performed using CT-specimens with geometry as shown in Figure 3. The specimens of the reference material were extracted from a solid block according to the T-L A, Weinheim http://www.aem-journal.com 93 C O M M U N IC A T IO N Table 1. Optimal scan parameters. Laser power P [W] Scan speed v [mm s 1] Track distance h [mm] Layer thickness t [mm] 250 1600 60 30 Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001315_978-1-4419-1117-9-Figure5.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001315_978-1-4419-1117-9-Figure5.1-1.png",
        "caption": "Fig. 5.1 CAD model of the spatial 6-dof parallel mechanism with prismatic actuators (Figure by Thierry Laliberte\u0301 and Gabriel Cote\u0301)",
        "texts": [],
        "surrounding_texts": [
            "Chapter 5 Spatial Parallel Robotic Machines with Prismatic Actuators\nIn this chapter, we first introduce a fully six degrees of freedom fully-parallel robotic machine with prismatic actuators. Then several new types of parallel mechanisms with prismatic actuators whose degree of freedom is dependent on a constraining passive leg connecting the base and the platform is analyzed. The mechanisms are a series of n-dof parallel mechanisms which consist of n identical actuated legs with six degrees of freedom and one passive leg with n degrees of freedom connecting the platform and the base. This series of mechanisms has the characteristics of reproduction since they have identical actuated legs, thus, the entire mechanism essentially consists of repeated parts, offering price benefits for manufacturing, assembling, and maintenance.\nA simple method for the stiffness analysis of spatial parallel mechanisms is presented using a lumped parameter model. Although it is essentially general, the method is specifically applied to spatial parallel mechanisms. A general kinematic model is established for the analysis of the structural rigidity and accuracy of this family of mechanisms. One can improve the rigidity of this type of mechanism through optimization of the link rigidities and geometric dimensions to reach the maximized global stiffness and precision. In what follows, the geometric model of this class of mechanisms is first introduced. The virtual joint concepts are employed to account for the compliance of the links. A general kinematic model of the family of parallel mechanisms is then established and analyzed using the lumped-parameter model. Equations allowing the computation of the equivalent joint stiffnesses are developed. Additionally, the inverse kinematics and velocity equations are given for both rigid-link and flexible-link mechanisms. Finally, examples for 3-dof, 4-dof, 5-dof, and 6-dof are given in detail to illustrate the results.\nD. Zhang, Parallel Robotic Machine Tools, DOI 10.1007/978-1-4419-1117-9 5, c Springer Science+Business Media, LLC 2010\n69",
            "A 6-dof parallel mechanism and its joint distributions both on the base and on the platform are shown in Figs. 5.1\u20135.3. This mechanism consists of six identical variable length links, connecting the fixed base to a moving platform. The kinematic chains associated with the six legs, from base to platform, consist of a fixed Hooke joint, a moving link, an actuated prismatic joint, a second moving link, and a spherical joint attached to the platform. It is also assumed that the vertices on the base and on the platform are located on circles of radii Rb and Rp, respectively.\nA fixed reference frame O xyz is connected to the base of the mechanism and a moving coordinate frame P x0y0z0 is connected to the platform. In Fig. 5.2, the points of attachment of the actuated legs to the base are represented with Bi and the points of attachment of all legs to the platform are represented with Pi , with i D 1; : : : ; 6, while point P is located at the center of the platform with the coordinate of P.x; y; z/.\nThe Cartesian coordinates of the platform are given by the position of point P with respect to the fixed frame, and the orientation of the platform (orientation of frame P x0y0z0 with respect to the fixed frame), represented by three Euler angles ; , and or by the rotation matrix Q.",
            "Fig. 5.2 Schematic representation of the spatial 6-dof parallel mechanism with prismatic actuators\nX\u2019\nB1\nB6\nB2\nB3\nB4 B5\nP1P2\nP3\nP4 P5\nP6\nZ\nX\nY O\nP Y\u2019\nZ\u2019\nIf the coordinates of point Bi in the fixed frame are represented by vector bi , then we have\npi D 2 4 xi yi zi 3 5 ; r 0 i D 2 4 Rp cos pi Rp sin pi 0 3 5 ; p D 2 4 x y z 3 5 ; bi D 2 4 Rb cos bi Rb sin bi 0 3 5 ; (5.1)"
        ]
    },
    {
        "image_filename": "designv10_1_0001315_978-1-4419-1117-9-Figure5.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001315_978-1-4419-1117-9-Figure5.10-1.png",
        "caption": "Fig. 5.10 The passive constraining leg with flexible links",
        "texts": [
            " Matrices A and B are the Jacobian matrices of the structure without the special leg. Similarly, the stiffness matrix for the mechanism with flexible links can be written as K D \u0152.J04/ TK4.J04/ 1 C ATB TKJB 1A ; (5.65) where K4 D diag\u0152k41; k42; k43; 0; 0; 0 ; (5.66) where k41; k42, and k43 are the stiffnesses of the virtual joints introduced to account for the flexibility of the links in the constraining leg. The architecture of the constraining leg including the virtual joints is represented in Fig. 5.10, and J04 is the Jacobian matrix of the constraining leg in this 3-dof case, while A and B are the Jacobian matrices of the structure without the constraining leg. The comparison between the mechanism with rigid links (without virtual joints) and the mechanism with flexible links (with virtual joints) is given in Table 5.6. The Cartesian compliance in each of the directions is given for a reference configuration of the mechanism, for progressively increasing values of the link stiffnesses. From Table 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003117_s00466-019-01748-6-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003117_s00466-019-01748-6-Figure6-1.png",
        "caption": "Fig. 6 A complex canonical part utilized to validate the proposed method: Geometry profile and meshed model including the substrate using all tetrahedral elements",
        "texts": [
            " In general, if better accuracy is needed, we only need to increase the number of the equivalent layers. However, more equivalent layers will definitely lead to longer computational time of the nonlinear layer-by-layer mechanical analysis. As a result, it is highly necessary to find a compromise between model accuracy and the computational cost with consideration of the requirement in practical applications. Residual deformation of a DMLS-processed canonical component containing curved thin walls shown in Fig.\u00a06 has been investigated. For the outer section of the component, the length and width are 81.6\u00a0mm and the wall thickness is 2.91\u00a0mm. For the inner section of the component, the length and width are 29.8\u00a0mm, and the thickness of the wall is 1.05\u00a0mm. The height of the entire component is 64.35\u00a0mm, indicating around 2100 thin layers in the large part. It took around 20\u00a0h to finish the DMLS printing of the component, as shown in Fig.\u00a07b. This canonical part is made of Ti64 and all the involved elastoplastic material properties are the same with the first example. Since the geometry of the canonical part is very complex, a fine mesh has to be used to discretize the model for FEA. To simulate the constraint of the big plate, a substrate with a size of 200 \u00d7 200 \u00d7 10\u00a0mm3 is included in the analysis as shown in Fig.\u00a06. The meshed model of the canonical part containing 346,420 tetrahedral elements is shown in Figs.\u00a06 and 7a. For convenience of discussion, the X-axis is defined as the longitudinal direction and Y-axis is defined as the transverse direction, while Z-axis denotes the build direction. The bottom surface of the substrate is fixed in displacement as the mechanical boundary condition. In the solution process, the inherent strain is applied to the canonical part with 60 equivalent layers employed, each having 36 physical layers merged together"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000788_1.334797-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000788_1.334797-Figure7-1.png",
        "caption": "FIG. 7. Schematic diagram of the fonnation of an n-layer composite plate.",
        "texts": [
            ", CII' C12' and C44\u2022 Further more, the shear strains and nonnal stresses are decoupled and vice versa. For simple tension (or compression) and pure bending involved in this study, no shear strain will be creat ed. The situation, therefore, reduces to isotropic, which ex plains the good agreement between the observed and calcu lated lattice curvature based upon isotropic elasticity. GENERALIZATION TO n-LA YER-SUBSTRATE COMPOSITE The previous calculation is generalized to include n layers on top of the substrate. Consider the situation shown in Fig. 7. Let Pi be the misfit dislocation density associated with the interface between ith and (i - l)th layers and bl be the component of the Burgers vector parallel to the interface. The matching of the boundary conditions of the n interfaces require 00 -AoFo + (BoI2R) = 01 - aoPlbl -AIFI - (BI/2R), 01 - A IFI + (B 1/2R ) = a2 - a l P2b2 - A,.F2 - (B2/2R ), (26) aN_I -AN_IFN_ 1 + (BN_ I /2R) = aN - aN_I PNbN - ANFN - (BNI2R), where aN(I - v) AN = andBN =ONtN' ENtN10 Solving for the forces FI in tenns of Fo, we obtain F j = i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000516_s0022112079001051-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000516_s0022112079001051-Figure2-1.png",
        "caption": "FIGURE 2. Wave form and co-ordinate system for locomotion by helical waves.",
        "texts": [
            " To obtain a co-ordinate system ( X , Y , Z ) consistent with the analysis of I, the origin is placed a t the centre of the sphere with the X axis along the helical axis. The Y and Z axes are chosen such that the sphere does not rotate with respect to this frame. Call this co-ordinate system the body frame. (x, y, z ) = (x, E(z) a cos (kx - wt) , E(x) a sin (kx- wt) ) In the body frame, the flagellum is attached to the cell body a t the point: x, = (X,,O,O), and the helical wave is expressed: X(X, t ) = ( X , E ( X - X,) 01 cos (k (X - X,) - wt) , E ( X - X,) asin ( k ( X - X,) - w t ) ) ( i i ) (see figure 2). Flagellar propulsion : helical wavds 335 When the position of a point on an inextensible flagellum is given by X(s, t ) where (12) 8 is the arclength measured from X,, the velocity of the point is given by a u(s , t ) = - X(s, t ) . at The arclength s as a function of X and t is expressed as Substituting from ( 1 l), we obtain: X xo s = / [ 1 + (akE(X))' + ( o I E ' ( X ) ) ~ ] * d X . (14) Note from this expression that s is a function of X only and is independent oft. Therefore, a a - X(s, t ) = - X(X, t ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002730_j.jmatprotec.2018.06.019-Figure16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002730_j.jmatprotec.2018.06.019-Figure16-1.png",
        "caption": "Fig. 16. (a) The sample with a concave surface and (b) the geometric model for laser polishing.",
        "texts": [
            " However, constant changing of the defocusing distance is unavoidable when polishing nonplanar surfaces using a 2D laser device. The rate of the change depends on the curvature of the complex surface geometry. Thus, the most important thing is to discover the relationship between the laser focus position and the surface to be polished. This observation allows us to develop a simple and effective geometric polishing model to analyze the relationship. In this study, the geometric model was built based on the samples with the concave surface to illustrate the relationship (Fig. 16(a)). The first step is to develop an equation that matches the sample with the concave surface. As it involves surface treatment, only an equation of the graphical outline is needed when developing the geometric model. The equation of the graphical contour of the spherical concave surface is shown below in Eq. (3). \u2212 + \u2212 + \u2212 =x a y b z c r( ) ( ) ( )2 2 2 2 (3) In this equation, r represents the spherical radius and z< r, (a, b, c) represents the spherical coordinates. The next step is to set up the model coordinate system, which is fairly important to facilitate the calculation in the following work",
            " + + \u2212 =x y z zr2 02 2 2 (4) In order to precisely control the defocusing distance during the polishing each time, the concave surface was divided into a number of layers. The thickness of each layer (ti) should not be larger than the focal depth of the laser (ti < focal depth). In this study, the thickness of each layer ti = 0.2 mm. Different heights on the concave surface correspond to the modified area to be polished. For each time, the laser height and layer to be polished need to be adjusted (Fig. 16(b)). Only in this way, can the defocusing distance remain constant, and the energy radiating on the surface remain stable. In the geometric model, a different value of z corresponds to a different curved surface. Specifically, when the height of the right defocusing point is hi (z= hi), the corresponding area to be polished can be calculated by the Eq. (5), which is + = \u2212x y h r h2 i i 2 2 2 (5) The radius of the corresponding circle ri is (2hir\u2212 hi2)1/2, and the area to be polished is \u03c0(2hir\u2212 hi2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure27.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure27.2-1.png",
        "caption": "Fig. 27.2 Simplification of the car development process",
        "texts": [
            " Components and systems are integrated into the whole car to verify that the requirements are fulfilled. For this purpose, real prototypes (preseries and series vehicles) are built. Doing so provides a first impression of the suitability of the planned processes and prototype tools. The start of production (SOP) follows a positive evaluation of first pre-series vehicles. After that milestone, the series support strives for performing short-term optimization (e.g., quality) as well as fulfilling short-term requirements [28]. Figure 27.2 shows a representation of a simplified car modeling process, in which the stages of product development, which are to be investigated in the frame of the battery module project, are highlighted. The battery module is an example of sustainable engineering for mobility, that will be detailed in the next chapter as case study. Similar case studies have been addressed in the past [31, 32]. Dhameja has presented an approach for simulating and validating the development of batteries for hybrid and electric vehicle applications",
            " However, a detailed excursion in that direction would exceed the scope of this chapter. A survey over Systems Engineering is presented in Chap. 9 of this book. 27 Sustainable Mobility 789 The main objective of the project \u201cprocess battery module\u201d is contributing to sustainability through the use of an alternative, green power supply for vehicles. The first step consists of the preparation of the EDAG Light Car Model to pilot the stages of the car development process, which have been presented in Fig. 27.2. Necessary interfaces and adapters for information exchange between the disciplines involved are to be identified and processes as well as methods which enable an integrated process from the requirements definition to the stage \u201cCAD and Simulation Body\u201d (see Fig. 27.2) are to be defined. In most cases, the different disciplines involved in the product development use tools that are not connected to each other. This situation is due to the fact that the different tools are proprietary and sometimes there is no standard specification that can be implemented as software interfaces or adapters to support the transmission of information from one System to another. The consequence of this fact often is the isolation of product development stages (see Fig. 27.3), which normally should be connected for tracking purposes and, therefore, managing complexity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000388_ac951094b-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000388_ac951094b-Figure3-1.png",
        "caption": "Figure 3. Cyclic voltammograms of CCEs in phosphate buffer, pH 5.7; scan rate, 10 mV/s; geometric area, 0.07 cm2. (I) Type A electrodes, (a) GOx/CCE and (b) Pd-GOx/CCE, (i) in the absence of glucose and (ii) with 6 mM glucose. (II) Type B electrode, Pd-GOx/ CCE, in the absence of glucose. (III) Type B electrode, PEG/PdGOx/CCE, in the absence of glucose.",
        "texts": [
            " PEG/Pd-GOx/CCE electrode contains 125 mg of PEG/g of graphite. b nd, not amenable for nitrogen adsorption analysis. Analytical Chemistry, Vol. 68, No. 13, July 1, 1996 2017 electrolyte, thereby increasing the wetted section inside the matrix. A typical example is the use of poly(ethylene glycol). The poly(ethylene glycol)-containing CCE matrix (type B, PEG/PdGOx/CCE) showed an observed capacitance of 10.6 mF/cm2, which is approximately twice as large as those of electrodes not containing PEG (type B, Pd-GOx/CCE) (Figure 3). The impact of increased wetting on the sensor response is demonstrated and discussed later. Response of Pd Metal-Modified GOx/CCE. Figure 3 shows the cyclic voltammograms of the bulk-modified GOx/CCE and Pd-GOx/CCE in the presence and in the absence of glucose in the solution. A delay time of 5 min was used between successive cycles to accumulate a substantial quantity of hydrogen peroxide in the porous network. The anodic wave, corresponding to the oxidation of hydrogen peroxide, was shifted by \u223c0.4 V by the Pd electrocatalysis. In all cases, the response dropped down to the base value when the electrolyte was changed to phosphate buffer without glucose"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000802_s0021-9258(17)44495-4-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000802_s0021-9258(17)44495-4-Figure4-1.png",
        "caption": "FIG. 4. Effect of the membrane potential of the cell on the swimming speed of YN-1 cells. Experimental conditions were the same as in Fig. 3, except that the cell concentration was 5 X lo7 cells/ ml. The values of the membrane potential at various external K+ were obtained from the data of Fig. 3.",
        "texts": [
            "2 mM was about -170 mV and was quite close to that of the cells without valinomycin. Under the condition where K' concentrations in the medium were higher than 1 mM, the measured values of the membrane potential of the cell were well fit with the theoretical values of the membrane potential which were simply calculated as a K+ diffusion potential from intracellular and extracellular K+ concentrations. These results show that the use of valinomycin offers a reliable method to quantitatively vary the membrane potential of YN-1 cells. Fig. 4 shows the relationship between the swimming speed of valinomycin-treated YN-1 cells and the membrane potential of the cells. The swimming speed was linearly decreased with decreasing the membrane potential of the cells, and at about -90 mV, almost all the cells showed no motility. In these experiments, Na' concentration in the medium was fixed at 50 mM, and the intracellular Na+ concentration was found to be almost constant regardless of different membrane potential of the cells (Table 111). Therefore, the chemical potential of Na+ in YN-1 cells was constant throughout the experiments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001001_1.3453357-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001001_1.3453357-Figure1-1.png",
        "caption": "Fig. 1 Coordinate frames for roller motion",
        "texts": [
            " Finally, algorithm for the numerical integration of the differential equations of motion is presented. Generalized Equations of Roller Motion The motion of a roller in a generalized simulation of the dynamic performance of a roller bearing can be considered in two parts: (1) Motion of the roller mass center in an inertial reference frame. (2) Rotational motion of the roller about its mass center. A formulation of both the above parts of roller motion and a definition of the relevant coordinate frames will be the basic objective of this section. Motion of Roller Mass Center. As shown in Fig. 1, the translational motion of the roller center is best considered in a cylindrical coordinate frame which is fixed in space and it, therefore, represents the inertial frame of reference. The classical differential equations of motion are written as Journal of Lubrication Technology JULY 1979, VOL. 101 / 293 Copyright \u00a9 1979 by ASME l . Y. . : lytical rmulationIor e r tion lindrical l r i g prese s f sical fferential ations f tion. ller-race teraction a ed tail d ulting r al o (~ d ent t rs termined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001054_iros.2007.4399139-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001054_iros.2007.4399139-Figure4-1.png",
        "caption": "Fig. 4. Two tire types for the robot.",
        "texts": [
            " As a result, constant kinematic parameters can be optimized off-line for a specific robotic task, according to typical path motions, particular soil types, and speed ranges. The P3-AT has a 4-wheel drive skid-steer platform. It measures approximately 0.5 m in length and is 0.25 m tall. Tread length (i.e., the distance between the front and rear wheels) is 0.27 m. Two different wheels sets are provided by the manufacturer: Solid rubber tires of 19 cm diameter (intended mainly for indoor use), and pneumatic tires of 22 cm diameter (see Fig. 4). The distance between longitudinal tread centerlines is L = 0.4 m for both tire types. The drive systems use reversible-DC motors equipped with an optical quadrature shaft encoder. It has a maximum speed of 1 wheel revolution per second. The robot weights 23.6 kg and can carry a 35 kg payload. It can run over two hours on three 12 V DC batteries. The robot receives orders from a PC and sends operational information under a built-in client-server architecture. Odometric estimations are calculated from an implicit symmetric kinematic model, which can be adjusted by the user through a pair of integer parameters, namely Ticksmm and Revcount"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001515_j.jclepro.2010.12.010-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001515_j.jclepro.2010.12.010-Figure4-1.png",
        "caption": "Fig. 4. Illustration of CLAD process.",
        "texts": [
            " the elaboration process, as well as the stages which take place before (extraction of raw materials, production of powder, transport, etc.) and after (recycling). CLAD process allows the direct manufacturing of mechanical parts and complex profiles layer by layer, with a low power fiber laser device (P < 200 W). This process is based on the principle of the laser cladding of metallic powders by a patented coaxial nozzle (Freneaux et al., 1995). The powder travels precisely in fluidized bed through the laser beam axis in order to optimize the laser/powder interaction (Fig. 4). With this coaxial configuration, the laser beam energy is used to melt both particles and a thin layer of substrate. Thus, a fully dense deposit and a clad/substrate metallurgical bonding are obtained. Some examples are given in Fig. 5. A special nozzle development allows the use of a small powder stream diameter (from 500 to 1000 mm) in order to optimize the powder catchment efficiency (PCE) up to 90%. Owing to this PCE, which take powder recycling rate into account, both surface roughness andprocessing time are improved andproductionvelocity reaches values ranging from 2 to 10 cm3 h 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000688_j.jmatprotec.2010.11.002-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000688_j.jmatprotec.2010.11.002-Figure1-1.png",
        "caption": "Fig. 1. Weld-based rapid prototyping schematic diagram.",
        "texts": [
            " However, in rapid prototyping process there are many depositing path probabilities and path combinations. Different depositing sequences will result in different thermal cycling curves, leading to different microstructure characters and mechanical performances. In the paper, the effects of different depositing directions on the thermal process of single-pass multi-layer weld-based rapid prototyping are investigated in details. 3. Weld-based rapid prototyping experiments The schematic diagram of single-pass multi-layer weld-based rapid prototyping is illustrated in Fig. 1. Mild steel plates S235JR (200 mm \u00d7 120 mm \u00d7 10 mm) as shown, and weld material F t H r i i 1 i i 2 e 3 s i F 4 u p s h c a p i r 8 a p w t d n e d t C m m e e o d d r t i 5.1. Comparison of calculated and experimental results After simulating the ten-layer depositing process, the calculated thermal cycling curves and the experimental thermal cycling ig. 2. 3D finite element model of single-pass multi-layer weld-based rapid protoyping. 08Mn2Si were used to deposit under the heat source of direct curent gas metal arc welding (GMAW)",
            " Results and analysis In this section, after the comparison of calculated and experimental results of the single-pass multi-layer rapid prototyping, the temperature field evolution, thermal cycling character, temperature gradient and the effects of depositing directions on thermal process of single-pass multi-layer rapid prototyping are investigated in details. c d r s m fi a m t k e c 5 a t ( h a t A i w h p h a t f h t t o c s urves of points A and B are compared, as shown in Fig. 5. The ashed lines are the simulated thermal cycling curves, while the eal lines are the experimental results measured by thermocouples hown in Fig. 1. Both the simulated thermal cycling and actually easured thermal cycling are ten-peak curves. As shown in the gure, the variation trend of thermal cycling results in numerical nalysis is in agreement with the experimental results within noral operating conditions. And there exist some error includes the emperature measuring error, the simulation error and so on, due to inds of influence factors. Therefore it is confirmed that the paramters used in proposed model are appropriate to predict the thermal ycling of weld-based rapid prototyping"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001708_tia.2009.2023393-Figure18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001708_tia.2009.2023393-Figure18-1.png",
        "caption": "Fig. 18. Magnetic circuit model for field flux.",
        "texts": [
            " Although this neglect may cause a relatively large error in the case of high flux density, it will be acceptable in the case of the field weakening control at high rotational speeds. Solving the equation of this magnetic circuit, we can obtain the time variation of the armature flux in each part. On the other hand, the torque \u03c4 of the motor can be calculated as \u03c4 = 1 T T\u222b 0 ( niU d\u03a6U d\u03b8 + niV d\u03a6V d\u03b8 + niW d\u03a6W d\u03b8 ) dt (14) where niU , niV , and niW are the magnetomotive forces of each tooth, and \u03a6U , \u03a6V , and \u03a6W are the total flux linkages of armature coils, which are the sum of the armature and field fluxes. The field flux can be obtained by solving the circuit shown in Fig. 18. In this case, the magnetomotive force is given by the magnetization of the permanent magnets M , for example, V f V = kM\u03b1 V FM \u2212 kM\u03b2 V FM (15) where FM = M \u03bc0 HM . (16) Fig. 19 shows the measured and calculated torques, which are in good agreement. The slight underestimation of the calculated result must have been caused by the neglect of the path (c) in Fig. 15. Fig. 20 shows the calculated ac flux linkage of the magnet. The result obtained by the magnetic circuit is almost identical to that of the finite element method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001949_13552541211218216-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001949_13552541211218216-Figure2-1.png",
        "caption": "Figure 2 Schematic layouts of parts regarding the gas direction",
        "texts": [
            " The schematic pattern of the mentioned scanning strategy has been shown in Figure 1. Argon gas was pumped into the chamber and across the build platform in order to keep O2 level below 0.9 per cent. The gas flowed from the right hand side of the chamber to the left hand side at a height just above the bed surface. Two sets of cylindrical specimens (with a diameter of 14mm and a length of 120mm) were produced parallel and perpendicular to the gas flow. In each set, four specimens were placed on the bed, as shown in Figure 2. These sets were designed in order to investigate the outcome of different layouts of the SLM bed. The laser beam spot size was 180mm. A laser power of 87W, scan speed of 150mm/s, scan line spacing of 130mm, and layer thickness of 75mm was used to produce both sets of parts. These parameters were in the range of parameters suggested by machine manufacturer. The temperature distribution at the end of SLM process was revealed using a Fluke Ti40FT thermal imager infrared camera. The manufactured cylindrical parts were cross-sectioned to be prepared as tensile, compression, and shear-punch specimens, as seen from Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000263_robot.1988.12075-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000263_robot.1988.12075-Figure2-1.png",
        "caption": "Figure 2 . Desired Velocity Trajectory f o r Joint 2",
        "texts": [],
        "surrounding_texts": [
            "If we assign as cost function\nthen (5.10.9) gives\n2Ru' + p * = B = 0 j U* = - - R - ' P * ~ B 1 2\nTherefore. minimum energy problem given in4 was treated in the n-th space. Notice the fact that the above formulation does not include jo int angles constraints because it would introduce n more state variables complicating the solution more. This is suggested for further research.\n6. ON-LINE RESULTS Since numerical solutions for the Cartesian space problem have not been obtained yet. in this section only the jo int unconstrained space is considered in order t o validate the assumption for the negative effect of jerk on the performance of a manipulator.\nIn order t o plot the trajectories resulting from the previous analysis and validate the claims made, consider the following motion of the end effector of the PUMA-600. which was actually tested on the P U M A 4 0 0 robotic manipulator of the Robotics and Automation Labs of Rensselaer Polytechnic Institute.\nInitial Condition i\np ; = [ 0 0.4 0.21'\nn , = [ ~ o -11'\n0, = [ -1 0 01'\na; = [ O 1 01'\nFinal Condition f\np j = I 0.4 0.4 -0.2IT\nn, = I O o -11'\n0, = [ - 1 0 01'\na j = [ O 1 01'\nThe minimum execution time for the case of minimum energy problem i s found from (4.8). T2 = 1.375 sec. while for the case of minmax problem i s found from (3.15). 7'2 = 1.4667 sec. Therefore, we selected T = 1.8 sec.\nThe trajectories and the errors of jo int 2 were considered a s representative and were plotted in Figures 1-5.\nIn order t o compare the resulting \"optimal\" trajectories, two more trajectories were considered. The first plotted under the label \"Cartesian triangular acceleration profile\", follows a straight line between the init ial and final point, wi th a Cartesian acceleration having a triangular profile, starting and finishing with zero Cartesian velocity and acceleration, which for a configuration with nonsingular Jacobian are translated to zero jo int velocity and acceleration for all joints: something desirable for the actuators. The second. plotted under the label \"simple Cartesian straight line\", is a constant Cartesian velocity straight line trajectory having. a s a matter of fact, large jerk a t the beginning and the end of the trajectory.\nThe trajectories were tested using a computed torque/PID controller and the position errors can be found in Figure 5. The superiority of the \"optimal\" trajectories is obvious, especially for the intervals where the other have large jerk. However, the performance of the trajectory with \"Cartesian triangular acceleration profile\" is considered very satisfactory.\n7. CONCLUSIONS The error analysis of Section 6 demonstrated the significance of jerk and the optimality of our results. Jerk affects adversely the performance of the actuators and has t o be minimum. The mathematical analysis and solution for the unconstrained jo int space problem was given to given an insight of the problem and also to verify the assumptions on the significance of jerk.\nHowever, due to the fact that in a realistic environment the robot has t o follow an arbitrary Cartesian trajectory, in order t o satisfy the obstacle avoidance specifications, this problem was stated and theoretically solved. In this case of a general Cartesian trajectory the optimal control problem was reduced to a two-point boundary value problem as\nexpected. Further research could be directed towards the numerical solution of the resulting equations and a more detailed solution including the jo int angles constraints which have not been considered here, using a formulation involving the complete bounded state variable approach developed in2'.\nAdditionally, other cost functions, as minimum time or functions of jerk should be considered for minimization. ACKNOWLEDGEMENTS\nThe authors would like to express their gratitude to Steve Murphy for his assistance. This work was supported under the NSF Grant DMC-\nREFERENCES\n83-12179.\n[l] A. Bazerghi. A. A. Goldenberg. and J. Apkarian. \"An Exact Kinematic Model of P U M A 4 0 0 Manipulator\". IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-14. No. 3. May/June 1984.\n[2] J. E. Bobrow. S. Dubowsky and J. S. Gibson, \"On the Optimal Control of Robotic Manipulators With Actuator Constraints\", Proceedings of American Control Conference, pp. 782-787. June 1983.\n[3] M . Brady. \"Trajectory Planning and Robot Motion: Planning and Control\", Cambridge. MA: M I T Press, 1982.\n[4] Hollerbach. J. M.. \"The Minimum Energy Movement for a Spring Muscle Model\", Artificial Intelligence Laboratory, M.I.T.. AIM-424, 1977.\n[ 5 ] R. Horowitz and M . Tomizuka. \"Discrete Time Model Reference Adaptive Control of Mechanical Manipulators\". Computers in Engineering, 1982. Vol. 2. Robots and Robotics. ASME. pp. 107-112.\n[GI 0. Khatib. \"Real-Time Obstacle Avoidance for Manipulators and Mobile Robots\". Proceedings 1985 IEEE International Conference on Robotics and Automation pp. 5OC-505.\n[7] P. K . Khosla. \"Real-Time Control and Identification or Direct-Drive Manipulators\". Ph.D. Thesis, Department of Electrical and Computer Engineering, Carnegie Mellon University, August 1986.\n[ 8 ] M . B . Leahy and G. N. Saridis. \"Compensation of Unmodeled PUMA Manipulator Dynamics\". Proceedings 1987 IEEE International Conference on Robotics and Automation, pp. 151-156.\n[9] M . B . Leahy. \"Development and Application of a Hierarchical Robotic Evaluation Environment\". Ph.D. Dissertation, Robotics and Automation Labs, RPI. August 1986.\n[ l o ] J. Y. S. Luh and C. S. Lin. \"Optimal Path Planning for Mechanical Manipulators\". ASME Journal of Dynamic Systems. Measurement and Control, Vol. 102. pp. 142-151. June 1981.\n[ll] G. L. Luo and G. N. Saridis. \"L-Q Design of PID Controllers for Robot Arms\". IEEE Journal of Robotics and Automation. Vol. RA1. No. 3. September 1985\n1121 B. R . Markiewicz. \"Analysis of the Computed Torque Drive Method and Comparison with Conventional Position Servo for a Computed Controlled Manipulator\". Technical Memo 33-601. JPL. March 1973.\n1131 R. P. Paul, \"Robot Manipulators: Mathematics, Programming and Control\". Cambridge, MA: M I T Press, 1981.\n[14] R. Paul, \"Manipulator Cartesian Path Control\". IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-9. No. 11. Nov.\n[15 ] P. P. Paul, B . Shimano and G. E. Mayer. \"Kinematic Control Equations for Simple Manipulators\". IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-11. pp. 449-455. June 1981.\n[16] F. Pfeiffer and R. Johanni. \"A Concept for Manipulator Trajectory Planning\", IEEE Journal of Robotics and Automation, Vol. RA-3, No. 2. April 1987. pp. 115-123.\n[17] L . S. Pontryagin. V . Boltyanskii. R. Gamkrelidze and E. Mishehenko. The hfathematical Theory of Optimal Processes. lnterscience Publishers. Inc.. New York, 1962.\n[18] G. Saridis and Z. V . Rekasius. \"Investigation of Worst-case Errors When Inputs and Their Rate of Change Are Bounded\", IEEE Transactions on Automatic Control, Vol. AC-11. No. 2. April 1966. pp.\n[19] G. Saridis, \"Algorithms for Worst Error in Linesr Systems with Bounded Input and i t s Rate of Change\". IEEE Transactions on Autotnatic Control, Vol. AC-12. No. 2. April 1967. pp. 203-207.\n1979. pp. 702-711.\n296-300.",
            "(201 G. N. Saridis and Z. V. Rekasius, \"Design of Approximately Opt imal Feedback Controllers for Systems of Bounded States\". IEEE Transactions on Automatic Control. Vol. AC-12. No. 4. August\n[21] K. G. Shin and N. D. McKay. \"Automatic Generation o f Trajectory Planners for Industrial Robots\", Proc. 1986. IEEE Conference on Robotics and Automation, pp. 260-266. April 1986.\n[22] K . G. Shin and N. D. McKay. \"Minimum-Time Trajectory Planning for Industrial Robots with General Torque Constraints\", Proc. 1986. IEEE Conference on Robotics and Automation, pp. 412-417. April 1986.\n[23] S . E. Thomson. R. V. Patel. \"Formulation of Joint Trajectories for Industrial Robots Using B-Splines\" , IEEE Transactions on Industrial Electronics, Vol. IE-34. No. 2. May 1987. pp. 192-199.\n1967. pp. 373-379.\nP o s i t i o n T r a j e c t o r y 0 rlrplc cart ItT 11\u00b0C 0 c l 1 trlang ~ C C i i r o f l l e 0 hy nlnlllilng narlul - P by ainlmlzlnQ Tu2'dt -\n13\nFigure 1. Differential Desired Position Trajectory wrt to Initial Angles for Joint 2\n' o oa 0 53 I 3 7 1.60 TlmelSec)\nFigure 3. Desired Acceleration Trajectory for Joint 2\nJ e r k T r a j e c t o r y , 0 by .Inlmlilng ju\"\"dt Q r isr ic c a r 1 sir l i n e Q i r t tr lanp acc profile\n13\nFigure 4. Resulting Jerk Trajectory for Joint 2"
        ]
    },
    {
        "image_filename": "designv10_1_0002854_j.engfailanal.2013.07.005-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002854_j.engfailanal.2013.07.005-Figure2-1.png",
        "caption": "Fig. 2. Applied forces on gear tooth.",
        "texts": [
            "The potential energy stored in the gear tooth is given by [32\u201334], Ub \u00bc M2 2EI \u00bc \u00bdFa\u00f0h\u00de FbC 2 2EI \u00f018\u00de Us \u00bc 1:2F2 a 2GA \u00bc \u00bd1:2F cos / 2 2GA \u00f019\u00de Ua \u00bc F2 b 2EA \u00bc \u00bdF sin / 2 2EA \u00f020\u00de where \u2018h\u2019 and \u2018C\u2019 can be measured using the gear tooth profile. The value of these parameters vary (namely h1, h2, h3 and C1, C2, C3) with change in contact position from highest point of single tooth contact \u20181\u2019 (HPSTC) and pitch point \u20182\u2019 to lowest point of single tooth contact \u20183\u2019 (LPSTC) as indicated in Fig. 1. The symbol \u2018/\u2019 represents the pressure angle. Referring to Fig. 2, S and B represents tooth thickness and face width. \u2018Fa\u2018 provide bending and shear effect while \u2018Fb\u2019 provides compressive effect and can be expressed for the pressure angle \u2018/\u2018 (20 in the present study) as, Fa \u00bc F cos a \u00f021\u00de Fb \u00bc F sina \u00f022\u00de I and A represents the area moment of inertia and area of cross section at tooth root and \u2018G\u2019 represents shear modulus. They can be obtained by [32\u201334] as, I \u00bc 1 12 S3 B \u00f023\u00de A \u00bc S B \u00f024\u00de G \u00bc E 2\u00f01\u00fe v\u00de \u00f025\u00de Hence, the stiffness of uncracked gear tooth kg is given by [32\u201334] as, kg \u00bc 1 1 kh \u00fe 1 kb \u00fe 1 ks \u00fe 1 ka \u00f026\u00de The total effective mesh stiffness (kt) of a single tooth pair in contact comprises of a cracked pinion tooth and an uncracked gear tooth can be given by previous Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003272_tvt.2020.2993725-Figure18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003272_tvt.2020.2993725-Figure18-1.png",
        "caption": "Fig. 18. Exploded CAD view of 12/16 e-Bike SRM components [55]",
        "texts": [
            " The commercial e-bike motor was a surface permanent magnet motor with an active diameter of 220 mm and axial length of 52.5 mm. The maximum speed of the motor is 400 rpm at 36 V DC link voltage. The motor is claimed to deliver its peak torque at 55 A rms. In the design process of the e-bike SRM, several pole configurations have been evaluated. It was concluded that 12/16 SRM provides the best balance between average torque, torque ripple, and efficiency. Fig. 17 shows the prototype 12/16 e-bike SRM next to the commercial permanent magnet e-bike motor. Fig. 18 shows the internal structure of the e-bike SRM. Since this is an exterior rotor design, the phase conductors leave the motor through shaft and the larger bearing (Bearing B). For the lamination material, Cogent (Sura) M470-50A electrical steel was Authorized licensed use limited to: Newcastle University. Downloaded on May 17,2020 at 23:19:28 UTC from IEEE Xplore. Restrictions apply. 0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure2-8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure2-8-1.png",
        "caption": "Fig. 2-8 relationship between space vector and phasor in sinusoidal steady state.",
        "texts": [
            " The earlier physical explanation not only permits the stator current space vector to be visualized, but it also simplifies the derivation of the electromagnetic torque, which can now be calculated on just this single hypothetic winding, rather than having to calculate torques separately on each of the phase windings and then summing them. Similar space vector equations can be written in the rotor circuit with the rotor axis-A as the reference. 2-6-1 Relationship between Phasors and Space Vectors in Sinusoidal Steady State under a balanced sinusoidal steady-state condition, the voltage and current phasors in phase-a have the same orientation as the stator voltage and current space vectors at time t\u00a0=\u00a00, as shown for the current in Fig. 2-8; the amplitudes are related by a factor of 3/2: 18 INduCTIoN MaCHINE EQuaTIoNS IN PHaSE QuaNTITIES This relationship is very useful because in our dynamic analyses, we often begin with the induction machine initially operating in a balanced, sinusoidal steady state. (See Problem 2-5.) 2-7 FLUX LINKAGES In this section, we will develop equations for stator and rotor flux linkages in terms of currents. We will begin by assuming the stator and the rotor to be open-circuited, one at a time. Then, by superposition, based on the assumption of magnetic material in its linear range, we will be able to obtain flux linkages when the stator and the rotor currents are simultaneously present"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure8.20-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure8.20-1.png",
        "caption": "Fig. 8.20 Interconnected suspensions not activated when pitching",
        "texts": [
            " We need a suspension layout with three springs, although we still have only two axles. Interconnected suspensions are the solution to this apparent paradox. A very basic scheme of interconnected suspensions is shown in Fig. 8.18. Its goal is to explain the concept, not to be a solution to be adopted in real cars (although, it was actually employed many years ago). To understand how it works, first suppose the car bounces, as in Fig. 8.19. The springs contained in the floating device F get compressed, thus stiffening both axles. On the other hand, if the car pitches, as in Fig. 8.20, the floating device F just translates longitudinally, without affecting the suspension stiffnesses. This way we have introduced the third independent spring k3 in our vehicle. Obviously, hydraulic interconnections are much more effective, but the principle is the same. We have an additional parameter to tune the vehicle oscillatory behavior. 268 8 Ride Comfort and Road Holding Although only a few cars have longitudinal interconnection, almost all cars are equipped with torsion (anti-roll) bars, and hence they have transversal interconnection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001503_j.matchar.2015.06.027-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001503_j.matchar.2015.06.027-Figure9-1.png",
        "caption": "Fig. 9",
        "texts": [
            " During DLF process, a higher laser scanning velocity and a lower single-track cladding overlap rate will lead to less heat accumulation (lower energy input) and thus a faster cooling rate of the molten pool, so a more refined microstructure usually can be obtained, which will logically benefit the microhardnees of the samples [29]. In our study, a wide range of Ev from 176 J/mm 3 to 600 J/mm 3 is considered for the AC C EP TE D M AN U SC R IP T - 19 - fabrication of IN718 samples, so the samples may have distinct different relative densities with the change of Ev. Therefore, the relative density of all the samples was measured and Fig. 9 gives the relative density of the samples at different Ev. In the area A of Fig. 9, a lower Ev of less than 220 J/mm 3 may cause a lack of fusion of the powders in DLF process, so the samples have the relative density of less than 99.4%. In the area B of Fig. 9, when Ev increases from 220 J/mm 3 to 550 J/mm 3 , the relative density of the samples also increases from 99.4% to 99.9%. Further, in the area C of Fig. 9, where Ev is more than 550 J/mm 3 , the relative density of the samples has been more than the level of 99.9%. Based on the above discussion, it is interesting to note that, on the one hand, a lower energy input will generally result in the increase of porosity in the as-DLFed samples, and thus lead to an inferior mechanical properties of IN718 alloy due to these building defects [23,24]. On the other hand, it has been concluded that a lower energy input will lead to more refined microstructure, less amount of Laves and more precipitated phases of \u03b3\" and \u03b3' in the matrix for the as-DLFed IN718 samples, which are all beneficial for the mechanical properties of IN718 alloy on the contrary [17,18]",
            " EDS analysis results for the position P1, (a) and P2, (b) of Fig. 4 (c). Fig. 6. SEM micrographs of the as-DLFed samples on horizontal section, showing the precipitated \u03b3\" and \u03b3' phases in matrix at the Ev of (a) 176 J/mm 3 , (b) 248 J/mm 3 , (c) 350 J/mm 3 and (d) 600 J/mm 3 . AC C EP TE D M AN U SC R IP T - 27 - Fig. 7. XRD spectra of the as-DLFed samples on horizontal section at different Ev. Fig. 8. Vickers microhardness of the as-DLFed IN718 samples as a function of Ev at different laser power and overlap rate in this study. Fig. 9. Relative density of the as-DLFed IN718 samples deposited at different Ev. AC C EP TE - 28 - AC C EP TE D M AN U SC R IP T - 39 - Highlights 1) The columnar grain is no longer continuous and uniform at a higher energy input. 2) There is a dendrites to cells transition with increasing energy input. 3) The volume fraction of Laves phase increases with increasing energy input. 4) The volume fraction of hardening phase decreases with increasing energy input. 5) The microhardness increases by decreasing energy input at a given parameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003364_j.mechmachtheory.2017.11.011-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003364_j.mechmachtheory.2017.11.011-Figure2-1.png",
        "caption": "Fig. 2. Translational-rotational model of a fixed-shaft gear set.",
        "texts": [
            " Afterwards, the effect of torsional vibration of the gearbox on the electric machine is studied, and the spectrum characteristics of the mechanical vibration signals of the gearbox and the electrical signals of the electric machine are compared at normal and resonance speed. The objectives of this study are twofold: (1) develop a detailed dynamic model that is suitable for general gearboxes, involving all combinations of fixed-shaft and planetary gears, operating in stationary or nonstationary conditions; and (2) provide theoretical guidance for the dynamics design, speed adjustment, and state monitoring of electric drive gear systems. The translational-rotational motion model of a fixed-shaft gear set is illustrated in Fig. 2 . \u03b8 i , highlighted in Eq. (1) , is the total rotation angle of gear i ( i = 1, 2); r i is the base radius of gear i ; and k 12 , c 12 , e 12 , and \u03b112 are the mesh stiffness, in-mesh damping, mesh error, and pressure angle, respectively, of the gear pair. k bi and c bi are the radial bearing stiffness and damping, respectively, of gear i. T i is the torsional torque applied to gear i . \u03b8i (t) = \u222b \u03c9 i (t) dt + \u03c6i (t) (1) where \u03c9 i is the rigid angular velocity of gear i which is determined by the operating speed of the electric machine , and \u03c6i is the elastic torsional-vibration angle superimposed on the rigid-body rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002781_j.msea.2016.11.047-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002781_j.msea.2016.11.047-Figure3-1.png",
        "caption": "Fig. 3. Temperature contour plots in top view (a) and comparisons of simulated (left) and experimental (right) melt pool profiles on cross-section at different \u03b7: (b) 322.92 J/ mm3; (c) 215.28 J/mm3; (d) 161.46 J/mm3 (hatching space 50 \u00b5m).",
        "texts": [
            "28 J/mm3 were chosen to study the homogeneity of microstructure and mechanical property of SLMprocessed tool steel. High accuracy blades were successfully fabricated from 5CrNi4Mo steel powders for applications in aerospace and automobile industries, showing a good surface finish without macroscopic balling phenomenon and dimensional distortion (Fig. 2b). 4.2. Verification of accuracy of simulated results by experimental investigations The temperature distribution plot of the top surface of melt pool, as the \u03b7 is settled at 215.28 J/mm3, is shown in Fig. 3a. It could be found that the melt pool and heat-affected zone (HAZ) had an elongated shape in the scanning direction. The ellipse shape instead of circular shape was believed to be caused by the movement of heat source, which was also discussed by Wang et al. [17]. In order to verify the accuracy of simulated results, the cross-sections of melt pools of simulation predicted and experimentally obtained under different \u03b7 are given in Fig. 3b\u2013d. The results showed that the melt pool shapes obtained by simulation calculation and experiments were observed similar and there were few distinctions in width and depth. The calculated maximum temperature Tm of the melt pool varied from 2765 K at 161.46 J/mm3 to 2847 K at 322.92 J/mm3, which was close to the Tm of 316 L stainless steel about 2740 K [18]. Fig. 4 demonstrates a high degree of consistency of the simulated and experimentally measured melt pool dimensions under various \u03b7, which further validates the accuracy of the simulation models"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002925_1.4040615-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002925_1.4040615-Figure1-1.png",
        "caption": "Fig. 1 The schematic diagram of the LPBF process",
        "texts": [
            " Subsequently, these features were linked to the process parameters using machine learning approaches. Through these image-based features, process conditions under which the parts were built were identified with the statistical fidelity over 80% (F-score). [DOI: 10.1115/1.4040615] Keywords: laser powder bed fusion, porosity, in-process monitoring, image analysis, spectral graph theory, multifractal analysis 1.1 Background. Powder bed fusion (PBF) refers to a family of additive manufacturing (AM) processes in which thermal energy selectively fuses regions of a powder bed [1]. Figure 1 shows the schematic of the PBF process. A layer of powder material is spread across a build plate. Certain areas of this layer of powder are then selectively melted (fused) with an energy source, such as a laser or electron beam. The bed is lowered and another layer of powder is spread over it and melted [2]. This cycle continues until the part is built. The PBF process embodied in Fig. 1 depicts a laser power source for melting the material; accordingly, the convention is to refer to the process as laser powder bed fusion (LPBF). A galvanic mirror scans the laser across the powder bed. The laser is focused on the bed with a spot size on the order of 50\u2013100 lm in diameter, the laser power is typically maintained in the range of 200\u2013400 W, the linear scan velocity of the laser is varied in the 200\u20132000 mm/s range, and the distance between each stripe of the laser, called the hatch spacing, is maintained in the range of 100\u2013200 lm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001530_978-3-642-81857-8-Figure1.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001530_978-3-642-81857-8-Figure1.1-1.png",
        "caption": "Fig. 1.1. Kinematic pair of the fifth class",
        "texts": [
            " These coordinates and velocities can be regarded as initial condi tions in the time instant t 2 . Using these initial conditions the construction of the differential equations for time t2 can be per*) formed and the process repeated . Each calculation therefore consists of two parts: the formulation of the differential motion equations and their integration. This procedure can be illustrated by the general algorithm block-scheme in Fig. 1.12. active spatial mechanisms, the complex kinematic pairs must be reduced to simple fifth c,lass pairs using equivalent kinematic chains (Fig. 1.1). For example, a kinematic pair of the third class (spherical) can be presented in the form of a three-joint chain, connected by zero length members (Fig. 1.2). Hence, the method always can consider mem bers with simple joints, always supposing that for joints of other the substitution has already been performed. The simplest kinematic pair is illustrated in Fig. 1.1. Here two members of an anthropomorphic me chanism (i-l and i) are connected by a rotational joint, the axis of ->- ->- ->- which is determined by means of the unit vector e .. By r. 1 . and r .. ~ 1 1- ,1 1,1 we denote the vectors from some point on the joint axis (conditionally, the axis is taken to pass through the center of the jOint) to the cen ter of gravity of the (i-l)st and i-th member, respectively. Fig. 1.1. illustrates one pair of that type. The joint center is marked by a *) This concerns Euler~s integration method. 35 black circle and the centers of gravity by empty circles which con tain the member numbers. A generalized coordinate qi is chosen for the angle of relative rotation for a rotational kinematic pair. This angle -+ is defined as the angle between the projections of the vectors -ri-l,i' ~ .. onto the plane perpendicular to the joint axis ~i (Fig. 1.1). The l,l -+ positive direction is counterclockwise for an observer from the e i end. -+ The angle is calculated from -ri - l i. A special case can arise when one of the vectors ~ .. defining the an~le is parallel to the ~. joint axis. lJ J Then its projection onto the plane, perpendicular to the joint axis co incides with the projection of this axis onto that plane, so determin- 36 ing the angle by means of the method described becomes impossible. Some unit vector -;; ... 1-;;. is therefore positioned at the i-th member"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002303_j.engfailanal.2016.09.003-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002303_j.engfailanal.2016.09.003-Figure2-1.png",
        "caption": "Figure 2 Schematic diagram for spalled gear tooth",
        "texts": [
            " b b s R d k E I                   (4) In equations (1)-(4) Ls, As and Is are the length of contact, area of tooth cross section and are moment of inertia respectively and their values will vary according to equations (5) \u2013 (7). for healthy region for spalled region s s L L L l     (5) 2.h .L for healthy region (2.h .L) ( . ) for spalled region x s x s s A h l     (6) 3 3 3 2 .h .L for healthy region 3 1 [(2.h ) .L ( . ) for spalled region 12 x s x s s I h l        (7) where 2[( )cos sin ]x bh R       and L, ls, hs are shown in Fig. 2. The definition of remaining parameters can be obtained in Ref. [16] and are shown in Figs. 1 and 2. AC C EP TE D M AN Besides the tooth deformation, the fillet-foundation deflection also influences the stiffness of the gear tooth. Sainsot et al. [22] derived the fillet-foundation deflection of the gear based on the theory of Muskhelishvili [23]. The stiffness with consideration of gear filletfoundation deflection can be obtained by [21], 2 2 * * * * 21 1 cos1 (1 tan ) , f f f f f u u L M P Q k EL S S                          (8) where, L is the tooth width and \u03b11is acting pressure angle of gear tooth",
            "2(1 )(cos sin ) ( )cos [sin ( )cos ] s d EL k d EL                                        2 1 (17)             2 2 1 1 2 2 2 1 1 2 2 1 (18) ( ) cos (sin cos ) , 2 [sin ( )cos ] 1 ( )cos (sin cos ) 2 [sin ( )cos ] ak d EL d EL                                    2 1 (19)           AC C EP TE D M AN U SC R IP T Various parameters of spalling which influences the TVMS are discussed in this section The length of the spall is considered as a parameter responsible for mesh stiffness variation since tooth contact does not take place in this region. In the literature [5-7] the effect of spall length on TVMS is studied but the use of potential energy methods to demonstrate this phenomenon is not used in any previous work. For a rectangular spall of length \u2018ls\u2019 as shown in Fig. 2, it is assumed that no tooth contact occurs in the spalled area which will directly affect Hertzian contact stiffness and has a slight effect on other stiffness components. Using equations (1) \u2013 (11) the effect of spall length on TVMS can be studied. 4.2Spall symmetry about vertical axis Spalling may develop either symmetrically or asymmetrically about the vertical plane of symmetry. Fig. 4(a) shows a symmetrical spall and the resultant distribution of forces. Fig. 4 (b) shows an unsymmetrical spall and the resultant distribution of forces",
            " In this section the effect of rectangular, circular and V-shaped spalls is studied. In all the cases, the spall is assumed to be present about the pitch point of the pinion and is in the single point contact region only. Also, the spall is assumed to be symmetric. AC C EP TE D M AN U SC R IP T 4.3.1Modeling of rectangular spall To model a rectangular spall, a spall is assumed near the pitch line to be as a rectangular indentation as done in Ref. [5-7] having dimensions ls x ws x hs as shown in Fig. 2. Modeling of rectangular spall has already been explained in section 2 in equations (1) \u2013 (11). Figure 5 Schematic diagram to represent circular spall To model a circular spall, a 2 mm radius spall is assumed whose centre coincides with the pitch line of the gear tooth as shown in Fig. 5 (a). Using the equation of a circle, 2 2 2 ,x y r  (21) and assuming the centre of the circle is at the origin as shown in Fig. 5(b), gives, 2 2 x r y  (22) where, r = radius of the circular spalland y varies from -r to +r"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003003_tmech.2017.2651057-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003003_tmech.2017.2651057-Figure4-1.png",
        "caption": "Fig. 4: Navigation device; a) original device, b) remodeled device, c) schematic depiction",
        "texts": [
            " To validate the proposed algorithm, several experiments were conducted with the USV as shown in Fig. 1. The USV is a remodeled fishing boat produced by the Smartliner boat company [46]. The size of the ship is 5.00m(length) \u00d7 2.25m(beam) \u00d7 0.38m(draft) and its weight is 600kg. Since the boat in Fig. 1 is originally designed for the human driving, it should be reformed appropriately to be utilized in the experiments, i.e., the driving system composed of a steering handle and throttle stick should be revised to be able to be controlled by two BLDC motors. As shown in Fig. 4, the human-based driving system was revised using two belt-pulley and BLDC motors to control the boat automatically. To control the overall USV system, an single-board computer produced by the ADLINK Technology Inc.[47] was equipped on the USV. The SBC is composed of the Intel i72710QE (Quad-Core) processor and 4GB DDR3 memory. To measure the motion and position of the USV, a inertial measurement (IMU) sensor and GPS antenna/receiver produced by the NovAtel Inc.[48] were furnished on the USV as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002863_j.msea.2015.10.045-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002863_j.msea.2015.10.045-Figure7-1.png",
        "caption": "Fig. 7. Schematics of the building defects and the impact fractures in (a) V and (b) H specimens.",
        "texts": [
            " 5 and 6 indicates that the fracture surfaces of the V and H specimens belonged to the xy and yz planes, respectively, and that the building defects in the fracture surfaces of the V and H specimens were also nearly spherical and linear, respectively. These observations clearly demonstrate that these SLM building defects were disc-shaped and that the appearances of these defects in the xy and yz planes were thus divergent. 3.4. The effect of building defect To further clarify the role of the disc-shaped building defects in the anisotropy of toughness, the schematics of V and H specimens under impact loading are presented in Fig. 7. Due to the geometries of these defects, the projections of the disc-shaped pores in the fracture surfaces of V specimens (xy plane) and H specimens (yz plane) were approximately spherical and linear, as mentioned previously. The reduction in the load-bearing cross-section was obviously larger in the xy plane than in the yz plane. The building defects in the V specimens sufficiently decreased the load-bearing cross-section and reduced the impact energy. In contrast, the loadbearing cross-section of the H specimens was less affected by the presence of disc-shaped pores, resulting in the greater resistance to the impact loading"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002188_smll.201704374-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002188_smll.201704374-Figure2-1.png",
        "caption": "Figure 2. From cells to bioinspired microswimmers. Cells can be modified to become biohybrids, from very simple ones, where the synthetic part consists of small cargos as liposomes or internalized nanoparticles, to more complex ones with synthetic external cargos. Bioinspired synthetic swimmers lack all the biological components.",
        "texts": [
            "[23] Magnetically controlled biohybrids or magnetically powered bioinspired microswimmers can be externally controlled, obviate fuel requirements, and hold the potential for online biomedical imaging.[24,25] The latter feature is crucial for application scenarios where microswimmers shall be controlled inside the human body since control implies the existence of a feedback signal.[26] To present an understanding of magnetic biohybrid and bioinspired microswimmers, we pursue the following structure: we start with the fundamentals of microswimming and magnetism and then move gradually from microorganisms over functionalized biohybrids toward purely synthetic swimmers, as depicted in Figure 2. Thereby, we shed light on possible application scenarios for the individual systems. Many motile microorganisms swim and navigate in chemically and mechanically complex environments. These organisms can be functionalized and directly used for applications (biohybrid approach), but also inspire designs for fully synthetic microbots. The most promising designs of biohybrids and bioinspired microswimmers include one or several magnetic components, which lead to sustainable propulsion mechanisms and external controllability"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.18-1.png",
        "caption": "FIGURE 5.18. A planar slider-crank linkage, making a closed loop or parallel mechanism.",
        "texts": [
            " Therefore, we can change the order of D and R about and along the same axis and obtain the same DH transformation matrix 5.11. Therefore, i\u22121Ti = Dzi,di Rzi,\u03b8i Dxi,ai Rxi,\u03b1i = Rzi,\u03b8i Dzi,di Dxi,ai Rxi,\u03b1i = Dzi,di Rzi,\u03b8i Rxi,\u03b1i Dxi,ai = Rzi,\u03b8i Dzi,di Rxi,\u03b1i Dxi,ai . (5.54) Example 152 F DH application for a slider-crank planar linkage. For a closed loop robot or mechanism there would also be a connection between the first and last links. So, the DH convention will not be satisfied by this connection. Figure 5.18 depicts a planar slider-crank linkage R\u22a5P`RkRkR and DH coordinate frames installed on each link. 5. Forward Kinematics 257 Applying a loop transformation leads to [T ] = 1T2 2T3 3T4 4T1 = I4 (5.55) where the transformation matrix [T ] contains elements that are functions of a2, d, a3, \u03b83, a4, \u03b84, and \u03b81. The parameters a2, a3, and a4 are constant while d, \u03b83, \u03b84, and \u03b81 are variable. Assuming \u03b81 is input and specified, we may solve for other unknown variables \u03b83, \u03b84, and d by equating corresponding elements of [T ] and I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001563_j.jmatprotec.2010.07.036-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001563_j.jmatprotec.2010.07.036-Figure3-1.png",
        "caption": "Fig. 3. Digitalization process for coaxial nozzle. From real part (left) to mesh (right) through CAD digitalization (centre).",
        "texts": [
            " The studied nozzle geometry is ighly complex and the accuracy requirements are also extremely igh, otherwise the final result will diverge from the real one if the eometry definition in the model is not accurate. Therefore, it has een necessary to measure all the nozzle elements to obtain the xact geometry of each one. A coordinate measurement machine CMM) Zeiss MC-850 has been used to obtain the complete geomtry. This CMM presents a measuring uncertainty below 5 m. A D CAD model of the complete assembly for the coaxial nozzle has een obtained from the measured data, as can be observed in Fig. 3. he nozzle geometry was exported to the pre-processor format and he mesh was built following the 3D geometry. sing Technology 210 (2010) 2125\u20132134 4.2. Numerical simulation The simulation step solves the numeric model presented in Section 2 using the nozzle geometry and process parameters of Table 1. Due to the problem complexity, the model is solved by a finite volume method, i.e. a volume control is defined. The volume is meshed using the pre-processor and taking into account the mesh density on the different areas"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002543_s00521-018-3520-3-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002543_s00521-018-3520-3-Figure4-1.png",
        "caption": "Fig. 4 Model of three-joint IRMs",
        "texts": [
            " Furthermore, integrating _V t\u00f0 \u00de with respect to time, we have: Z t 0 _V t\u00f0 \u00dedv Z t 0 sTKsdv or Z t 0 sTKsdv Z t 0 _V t\u00f0 \u00dedv \u00bc V 0\u00f0 \u00de V t\u00f0 \u00de V 0\u00f0 \u00de 1 Thus, by Barbalat\u2019s lemma can prove that limt!0 s t\u00f0 \u00de \u00bc 0. Therefore, both the global stability of the system and the tracking errors are guaranteed, and converged to zero when the time tends to infinite by the adapting control law (18). In this section, a three-link IRM is applied to verify the validity of the proposed control scheme for illustrative purposes. The detailed system parameters of three-link IRMs model (Fig. 4) are given as follows: M \u00bc M11 M12 M13 M21 M22 M23 M31 M32 M33 2 4 3 5 C \u00bc C11 C12 C13 C21 C22 C23 C31 C32 C33 2 4 3 5; G \u00bc g1 g2 g3 2 4 3 5 M11 \u00bc l21 p1 \u00fe p2\u00f0 \u00de \u00fe p2l 2 2 \u00fe 2p1p2 cos q2\u00f0 \u00de M12 \u00bc p2l 2 2 \u00fe p2l1l2 cos q2\u00f0 \u00de; M13 \u00bc M23 \u00bc M31 \u00bc M32 \u00bc 0; M21 \u00bc M12 M22 \u00bc p2l 2 2; M33 \u00bc p3 C11 \u00bc p2l1l2 2 _q1 _q2 \u00fe _q22 sin q2\u00f0 \u00de; C21 \u00bc p2l1l2 _q 2 1 sin q2\u00f0 \u00de; C12 \u00bc C13 \u00bc C22 \u00bc C23 \u00bc C31 \u00bc C32 \u00bc C33 \u00bc 0 g1 \u00bc p1 \u00fe p2\u00f0 \u00degl1 cos q1\u00f0 \u00de \u00fe p2gl2 cos q1 \u00fe q2\u00f0 \u00de g2 \u00bc p2gl2 cos q1 \u00fe q2\u00f0 \u00de; g3 \u00bc p3g where p1; p2; p3 are links masses; l1; l2; l3 are links lengths; g \u00bc 10 m=s2\u00f0 \u00de is acceleration of gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000535_978-1-4020-8482-9-Figure3.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000535_978-1-4020-8482-9-Figure3.3-1.png",
        "caption": "Fig. 3.3 Different types of f (\u03c3 ): (a) F[0,k] and F(0,k); (b) F[k1,,k2]; and (c) F\u221e",
        "texts": [
            "2) 40 3 Sufficient Conditions of Absolute Stability: Classical Methods where x \u2208 Rn is the state variable, b, c \u2208 Rn are known constant vectors, \u03c3 is the feedback control variable, f (\u03c3) is a nonlinear function. System (3.2) is shown in Fig. 3.2. The form of f is not specified, but it is known that it belongs to some type of functions F[0,k], F[0,k), F[k1,k2) or F\u221e. Here, F[0,k] := { f | f (0) = 0, 0 < \u03c3 f (\u03c3) \u2264 k \u03c32, \u03c3 = 0, f continues } ; F[0,k) := { f | f (0) = 0, 0 < \u03c3 f (\u03c3) < k \u03c32, \u03c3 = 0, f continues } ; F[k1,k2] := { f | f (0) = 0, k1 \u03c32 \u2264 \u03c3 f (\u03c3) \u2264 k2 \u03c32, \u03c3 = 0, f continues } ; F\u221e := { f | f (0) = 0, \u03c3 f (\u03c3) > 0, \u03c3 = 0, f continues} . The above functions are demonstrated in Fig. 3.3. Many practical nonlinear feedback control problems can be described by system (3.2), but the form of f is usually not known. Partial information about f may be obtained from experiments. However, experiments can only be carried out under specific loads, and thus f depends upon the leads. Usually one only knows that f belongs to F[0,k], F[0,k], or F[k1,k2). Any other information is not available in practice. For example, for the above centrifugal governor, the control signal \u03c3 of the governor is proportional to the change of the sliding valve\u2019s position, \u2206s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003126_j.jsv.2015.08.002-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003126_j.jsv.2015.08.002-Figure4-1.png",
        "caption": "Fig. 4. Ball/Cage pocket interaction. This figure is a simplified version of the figure which was originally provided in Ref. [39] for investigating the interaction between a roller and a cage pocket.",
        "texts": [
            " According to the rolling direction of the ball, some friction forces will lead the ball to accelerate (these forces can be recognized as traction forces), while other opposite friction forces will lead the ball to decelerate. The cage investigated in this paper is assumed to be cylindrical. Similar to the approach used in ball/raceway interaction calculations, the interaction between a cage pocket and a ball is determined by the relative position between the cage pocket center and the ball center. Fig. 4 is a simplified version of the figure which was originally provided in Ref. [39] for investigating the interaction between a roller and a cage pocket. In Fig. 4, cage frame Ocaxcaycazca is established to determine the azimuth and the radial position of the cage in inertial frame Oixiyizi. As shown in Fig. 4, position vectors rb, rca, and rcp are the position vectors locating the center of the ball in inertial frame Oixiyizi, the center of the cage in inertial frame Oixiyizi, and the center of the cage pocket in cage frame Ocaxcaycazca, respectively. The relative position between the ball center and the cage pocket center can be given as rbcp \u00bc rb rca rcp (11) It should be noted that the vectors on the right side of Eq. (11) should be transformed to proper frames before calculating. More details can be found in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003657_j.measurement.2020.108855-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003657_j.measurement.2020.108855-Figure9-1.png",
        "caption": "Fig. 9. FE mesh for pitch bearing [34].",
        "texts": [
            " Based on geometric interaction model, Aguirrebeitia [3132] established the theoretical model to predict the static load capacity of pitch-and yaw bearings by considering the influence of preloading, as shown in Fig. 8. Based on Hertz Formula, Yu [33] investigated the load distribution of yaw bearing. Compared with theoretical prediction, Finite element analysis can X. Jin et al. Measurement 172 (2021) 108855 carry out further researches on fatigue life analysis. Through finite element analysis, HERAS [34] obtained the stiffness curves of WTGS slewing bearings, shown in Fig. 9. Herewith, an effective tool was developed to estimating the stiffness. Plaza [35] introduced super elements into finite element model to significantly reduce the calculation cost when the accuracy can be guaranteed meantime. He [36] obtained the contact stress distribution in ABAQUS, which were imported into FESAFE for fatigue analysis combined with Morrow mean stress correction and Brown Miller criterion, shown in Fig. 10.He [37] also used nonlinear spring elements to model rolling elements in yaw bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000587_ac00001a009-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000587_ac00001a009-Figure7-1.png",
        "caption": "Figure 7. Changes in the fluorescence spectra of 1 X 10 -3 mol dm-3 HQS caused by addition of GOx (a) and plots of In ( I , , / I ) as a function of the concentration of GOx (b). Amount of GOx added: (1) none, (2) 1, (3) 3, (4) 5 g dm-3. Excitation: 240 nm.",
        "texts": [
            " cRelative ratio to the initial value of current response and amount of electroactive HQS. Figure 6 shows a calibration curve for glucose obtained a t a GOx/HQS/PPy electrode that was prepared with a deposition charge of polypyrrole of 25 mC cm-2. Although the calibration curve is not linear but curves, glucose concentrations from 0.5 to 50 mmol dm-3 can be detected a t this electrode. Anyway, the GOx/HQS/PPy electrodes prepared in this study can be said to have a wide dynamic range. By use of the results shown in Figure 7, the apparent MichaelisMenten constant K , was determined to be 9.0 mmol dm-3, which was a little higher than the value of 3.3 mmol dm-3 reported by Jonsson and Gordon, who used covalently immobilized glucose oxidase on graphite onto which Nmethylphenazinium ions was adsorbed as a mediator (7). However, the obtained K , value was smaller than the value obtained by Foulds and Lowe (30.7 mmol dm-3) at polypyrrole films immobilized by GOx alone (14 ) . Table I shows the results obtained by stability tests of a GOx/HQS/PPy electrode prepared with a deposition charge of 25 mC cm-2",
            " Accordingly, GOx and HQS must be incorporated into polypyrrole films in such a way as to allow easy electrical communications between the two. Electronic interaction of GOx with HQS in the deposition bath of polypyrrole was evidenced by changes in the absorption spectra of GOx on addition of either HQS or pyrrole. I t is well-known that several kinds of anions easily adsorb on proteins, causing changes in optical properties such as fluorescence and absorption spectra of both protein and anions (25). Fluorescence spectra of HQS taken by the excitation at 240 nm in the presence of GOx are given in Figure 7a, from which it is noticed that the fluorescence of HQS was greatly quenched by the addition of GOx and simultaneously the wavelength giving the fluorescence maximum was shifted toward shorter wavelengths. The results seem to suggest that HQS has electronic interaction with GOx possibly by making adsorption. Though GOx shows absorption at 240 nm, its absorbance is much lower than that of HQS, giving a negligible effect on the fluorescence spectra measurements. If the ratios of the fluorescence intensity of HQS obtained in the absence of GOx, which is denoted here as I,,, to that obtained in the presence of GOx, I , was plotted as a function of the concentration of GOx, a linear relationship was obtained between In (Io/T) and the concentration, as shown in Figure 7b, indicating that the quenching was static (26) and HQS was adsorbed on GOx. I t may be thought that the quenching of the fluorescence of HQS is due to the absorption of GOx. We cannot rule out this possibility, but this interpretation seems to fail to explain the shift of the fluorescence peak of HQS with the increase of GOx. The observed fluorescence peak shift gives indirect evidence of the presence of electronic interaction between GOx and HQS. Parts a and b of Figure 8 show the absorption spectra of GOx in the presence of HQS and pyrrole, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure5-1.png",
        "caption": "Fig. 5 4\u20134\u20134 RPR-equivalent PMs that are kinematic inversions of the first family. (a) 2-uPRuvU/uvUvPR. (b) 2-uPRuvU/uRvPRR. (c) 2-uRPuvU/uvUvPR. (d) 2-uRPuvU/uRvPRR. (e) 2-uRRuvU/uvUvPR. (f) 2-uRRuvU/uRvPRR.",
        "texts": [
            " Hence, the displacement set of the moving platform is given by {L1} \u2229 {L2} = {G(u)}{R(B1 , v)} \u2229 {R(O, u)}{G(v)} = {R(O, u)}({G(u)} \u2229 {G(v)}){R(B1 , v)} = {R(O, u)}{T(w)}{R(B1 , v)} = {R(O, u)}{T(w)}{R(B,v)} B \u2208 axis(B1 , v). (14) It is shown in (14) that the two axes of rotation are axis (O, u) and axis (B, v). The 2-UPR/RPU PM is an RPR-equivalent PM. Its kinematic inversion is a 2-RPU/UPR PM that is also an RPR-equivalent PM. For conciseness, Table IV only enumerates 49 RPRequivalent PMs belonging to the first family in 4\u20134\u20134 category. Figs. 3 and 4 illustrate 12 architectures that have potentials in practice. Although kinematic inversions are neglected in Table IV, Fig. 5 shows six kinematic inversions for reader\u2019s better understanding. In our view, the 4\u20134\u20134 RPR-equivalent PMs with identical limbs, such as the 2-UPR/RPU, 2-URR/RRU, and their kinematic inversions, are of particularly important interest for practical application. For example, compared with the 2-UPR-SPR PM in Exechon robot, the 2-UPR/RPU PM has a simpler structure because the one spherical joint is replaced by a universal joint. Another advantage is the two specified axes of rotation that will simplify the control and calibration of the PKM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003442_s00170-015-7112-4-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003442_s00170-015-7112-4-Figure9-1.png",
        "caption": "Fig. 9 Schematic diagram of deposited MLSP",
        "texts": [
            " Droplets are transferred to the molten pool with a certain speed under the effect of the arc force, resulting in a digging action and a weld penetration. As deposition with a large current, the plasma flow force is increased significantly, and the spray transfer mode always occurs. The droplets are transferred to the molten pool with a high speed and a strong impact, inducing a strong distortion and a worse instability of the pool surface. The schematic diagram of a deposited MLSP in GMAWbased AM is shown in Fig. 9. The first layer is deposited on the substrate with best heat emission conditions; the heat is conducted to the substrate quickly. During the subsequent depositions, both sides of the layer are directly in contact with the air. Thus, the heat conducting area is small, and the heat can only be conducted from previously deposited layers, then to the substrate. As the number of layers increases, the path of the heat flow conducted from the nth layer to the substrate increases. Therefore, more heats will accumulate at the nth layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001995_tvt.2010.2041260-Figure19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001995_tvt.2010.2041260-Figure19-1.png",
        "caption": "Fig. 19. EV prototype with two in-wheel SRM drives.",
        "texts": [
            " In other words, the proposed optimal control method can improve the dynamic and steady-state performances of EVs and extend the service life of the battery in EVs. In summary, the experimental results demonstrate that the proposed optimal control method can achieve the best motoring operation of SRM drives for EVs. The proposed control method for the best motoring operation of SRM drives has been applied to an EV prototype, in which two in-wheel SRMs are integrated with two rear rims and, hence, drive two rear wheels directly, respectively, as shown in Fig. 19. The EV prototype has run successfully. For SRM drives in EVs, the typical optimization methods published include the maximization of torque and the maximization of torque per ampere. Figs. 20 and 21 show the comparisons between the proposed method and published methods at a current reference of 10 A. Fig. 20 illustrates the comparisons between the proposed method and the reported method to maximize torque. It can be seen that the torque and torque smoothness factor from the proposed method are approximately consistent with the torque and torque smoothness factor from the reported method, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000806_j.optlaseng.2011.06.016-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000806_j.optlaseng.2011.06.016-Figure4-1.png",
        "caption": "Fig. 4. Scanning pattern used to produce dense blocks. Indicated are the first, second and third contours and the fill vectors. The horizontal cross-sections of the cubes are 10 mm 10 mm.",
        "texts": [
            " In a second step, which runs in parallel processing loops at the FPGA, the image moments [25, Chapter 4] are calculated in order to determine the melt pool area, length and width. This is done since image moments allow to determine the long and short axis of an ellipse which has the same area as the melt pool (see [25, Chapter 4] for more details), thus allowing to identify the melt pool length and width. The maximal processing delay is about 1 ms. In the experiments presented in this paper using the high speed camera, images were captured and processed in real-time at 10 kHz. Dense blocks have been build to investigate the effect of adjacent scan vectors in LLM. Fig. 4 shows the scanning pattern used to produce those blocks. All vectors are scanned with identical process parameters (laser power, scan velocity, laser spot size). The first scan lines (indicated as \u2018first contour\u2019) are scanning a material layer that fully consists of loose powder (no powder is yet consolidated into solid material within this newly deposited layer). The second scan lines (indicated as \u2018second contour\u2019) are always adjacent to the first scan lines. Next, the fill vectors are scanned to fill up the contour lines and consolidate the powder inside the layer contour",
            " 6 shows histograms of the signals measured during the first, second and third contour and the fill vectors. It can be seen that the first vector yields a significantly higher signal than the second contour and fill vectors, which have statistically equal processing behavior. The last remelting contour yields a significantly lower signal than the other two groups. The physical reason behind this observation is sketched in Fig. 7, which schematically reflects the situation when the laser beam passes the cross-section A\u2013A from Fig. 4. Fig. 7(a) shows the situation when scanning the first contour. The melt pool is then on both left and right side surrounded by (heat-insulating) powder material. The main heat flux is to the substrate (i.e. the already solidified material from the previous layers). Moreover, powder particles from left and right side are drawn into the melt pool, yielding a relatively large melt pool. During scanning of the second contour and the fill vectors, the situation as shown in Fig. 7(b) is valid. Since in that situation there is an overlap between the melt pool and already solidified material, the heat can flow away more easy, yielding a smaller melt pool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000023_joe.2003.823312-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000023_joe.2003.823312-Figure11-1.png",
        "caption": "Fig. 11. The JHUROV, a 140-kg 1000-m vehicle.",
        "texts": [
            " The velocity error norm was calculated as mean , where and are the desired/reference and simulated velocity of the JHUROV in DOF . Fig. 10 displays a bar chart containing both the position and velocity tracking error for each controller in the DOF for the reference trajectories listed in Table IV. The corresponding plots of the simulated vehicle position and velocity and the reference position and velocity versus time are presented in Figs. 1\u20139. Some plots are shortened with respect to time (y-axis) to zoom in for detail. The JHUROV, shown in Fig. 11, is a tethered remotely operated underwater robot. The JHUROV is powered by an isolated 10-kW dc power supply. The dry mass of the vehicle is 140 kg and its dimensions are 1.5 m long 1 m wide 0.6 m high. The position and heading of the vehicle are actively controlled and the vehicle is passively stable in roll and pitch. Actuation is provided by five dc brushless electric thrusters. A complete description of the JHUROV is reported in [54] and [55]. The JHUROV is equipped for full six-DOF position measurement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003417_j.asej.2017.08.001-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003417_j.asej.2017.08.001-Figure2-1.png",
        "caption": "Fig. 2. Five degrees of freedom robot arm model.",
        "texts": [
            " Section 6 presents the result of an experimental study on a real 5 DOF robot arm. Finally section 7 concludes the paper. Robotic arm is constructed by connecting different joints using links. The robotic arm can be modeled as an open-loop chain with many links connected in series by joints that are driven by stepper motors. Robot kinematics is related to the study of the geometry of the motion of a robot. Being more complex, difficult to solve, more common to be exist in research papers, the author choose the 5 DOF to be the testbed for simulation and implementation. Fig. 2 shows a five link robot which will be used to study the Soft-Computing based tool methods for solving the IK problem, its simulation results and experimental study. Fig. 3 shows link frame assignment for robot arm. Table 1 shows the DH parameters for the robot arm. Where ai-1 is the length of the common normal, ai-1 is the angle about common normal, from old Z-axis to new Z-axis, di is the offset along previous Z-axis to the common normal and bi is the angle about previous Z-axis from old X-axis to new X-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000706_j.triboint.2012.10.009-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000706_j.triboint.2012.10.009-Figure1-1.png",
        "caption": "Fig. 1. A schematic of the test rig.",
        "texts": [
            " To validate the model, experiments are carried out on a bearing test rig for different values of rotational speed and external radial loads. Further simulations are carried out in order to investigate the importance of different parameters on the thermal response of the ball bearing assembly. To investigate the thermal behavior of a roller bearing, a test rig was designed and constructed. The rig is designed for installing a 75-mm (2.953 in.) bore bearing to operate at variable speeds up to 5600 rpm ; see Fig. 1. It is capable of testing different bearing materials such as stainless steel balls in a brass cage as well as ceramic balls in a polyamide cage. Heavy duty roller bearings with DN number (the mean diameter of the bearing in millimeter times the rotational speed of the shaft in RPM) as high as 574,000 can be safely tested on this test rig. Equipped with a variety of sensors such as temperature, torque, vibration and acoustic signals, this test rig can be used for failure prognosis in roller bearing systems. Fig. 1 shows a schematic view of the test rig. The speed of motor could be set independently by a variable frequency drive. Installed between the motor and the shaft are two couplings. The coupling closer to the support bearing is of torque limiting type whereas the other one is a standard coupling. To protect the motor, VFD, and instrumentation, the torque limiting coupling was chosen to act as a safety mechanism at the failure. This coupling is connected to the support bearings and the test bearing by means of a 76"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000273_tia.2009.2013550-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000273_tia.2009.2013550-Figure6-1.png",
        "caption": "Fig. 6. Eddy-current distribution of magnet (28 magnet divisions, obtained by precalculation neglecting carrier, 6000 min\u22121).",
        "texts": [
            " Accordingly, their distribution varies due to the slot pitch, and they are concentrated at the sides of the magnet because the slot harmonic flux density is concentrated at the rotor surface [4]. On the other hand, the result considering the carrier shows remarkable difference. In this case, the eddy currents flow through the whole part of the magnet because they are mainly produced by the carrier harmonic flux density, whose distribution varies due to one pole pitch, and it enters into the rotor deeply [4]. Furthermore, the frequency of the major carrier harmonics is higher than the slot harmonics. As a result, the eddy-current density of Fig. 7 is much higher than Fig. 6. C. Variation of Magnet Eddy-Current Loss Due to Divisions Next, let us investigate the effects of the magnet divisions. Fig. 8 shows the eddy-current distribution of model (a), which is without the magnet division, obtained by the main calculation considering the carrier. In this case, the eddy currents concentrate at the edge of the magnet due to the skin effect. The maximum eddy-current density is nearly twice of the case of 28 magnet divisions. On the other hand, it can be seen that the region where the eddy currents flow is restricted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002187_acssuschemeng.7b03314-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002187_acssuschemeng.7b03314-Figure3-1.png",
        "caption": "Figure 3. Schematic illustration of the Cu\u2212Co/rGO dendrite formation mechanism.",
        "texts": [
            " The subsequent growth of nanofeelers on both of its sides enables the formation of a highly branched 3D dendrite structure. Under the high voltage electrodeposition process, vigorous hydrogen bubbles evolved over the PGE surface. With the formation and growth of these hydrogen bubbles, the simultaneous electrochemical reduction of Cu2+\u2212Co2+ ions and GOwas achieved in the interval spaces of hydrogen bubbles,19 yielding the 3D Cu\u2212Co/rGO dendrite architectures, and the corresponding growth mechanism is schematically illustrated in Figure 3. The HR-TEM image of Cu\u2212Co/rGO (Figure 2d) exhibits the orderly arranged lattice fringes for Cu\u2212Co nanostructures with d spacing of 0.209 nm, matching with the (111) plane of cubic structure. The corresponding selected area electron diffraction (SAED) pattern (inset Figure 2d) reveals rings and clear spots with random arrangement, specifying the polycrystalline structure of Cu\u2212Co/ rGO. The EDAX pattern of PGE reveals the presence of C (96.4 at %) and O (3.6 at %) elements (Figure S2a). The EDAX pattern of Cu/PGE shows the existence of Cu (95"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002214_j.engfailanal.2016.04.025-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002214_j.engfailanal.2016.04.025-Figure2-1.png",
        "caption": "Fig. 2 Nonuniform cantilever beam model of tooth with spalling",
        "texts": [
            " Section 3 verifies the model by comparing the TVMS obtained from the proposed method with that obtained from FE method. Conclusions are presented in Section 4. In this paper, the shape of spalling is simulated by a rectangle groove [19] (see Fig. 1), and the groove is symmetrical about the mid-face of tooth. The spalling has the dimensions: ws (spalling width)\u00d7ls (spalling length a)\u00d7hs (spalling depth). When the tooth contact occurs in the scope of the spalling, the cross-section Si will change from a rectangle to a gib. [Fig. 1] The gear tooth is modeled as a nonuniform cantilever beam, as shown in Fig. 2. In the figure, rb denotes the radius of base circle, \u03b1s denotes the pressure angle of the spalling starting position and \u03b2 is the operating pressure angle. The mesh stiffness of single-tooth pair with spalling at meshing position j is written as follow [9]: AC C EP TE D M AN U SC R IP T 2f2t1f1th 11111 1 )( kkkkk k j   , (1) where kti and kfi (i=1,2) are the stiffness of tooth and fillet-foundation, respectively, here, subscripts 1 and 2 denote the driving gear and driven gear; kh denotes the local contact stiffness. [Fig. 2] The stiffness of tooth kti can be expressed as:               )2,1,( 111 1 )2,1,( 111 1 asssb s asb t iGDj kkk iGDj kkk k iii iii i , (2) where GD is the scope of the spalling on tooth surface (see Fig. 2), j denotes meshing position, i (i=1, 2) represents the driving gear and driven gear. The healthy tooth stiffness consists of the bending stiffness kbi, shear stiffness ksi and axial compressive stiffness kai. For the spalled tooth, kbsi, kssi and kasi denote the bending stiffness, shear stiffness and axial compressive stiffness, respectively. Based on elastic mechanics, when spalling appears, the relationships between the bending stiffness kbsi, axial compressive stiffness kasi, shear stiffness kssi and bending energy Ubsi, axial compressive energy Uasi, and shear energy Ussi are obtained, which can be written as: si si k F U b 2 b 2  , a si a si k F U 2 2  , si si k F U s 2 s 2  , (3) where F is the total force applied on the contact tooth with spalling",
            "1 1 D 4 4 2 3 3 2 2 2 2 1 2 \u03c0 1 2 DG 3 3 2 2 2 2 1 2 \u03c0 1 2 GJ 2 2 2 1 2 \u03c0 1 2 ss 0 0 0                                           y GA y GA y GA y GA y GA y GA y GA y GA y GA k D D G G J G G J J yyyy yyy yy i ,(9)                  )( d d dsin d d dsin d d dsin d d dsin )( d d dsin d d dsin d d dsin )( d d dsin d d dsin 1 D 4 4 2 3 3 2 2 2 2 1 2 \u03c0 1 2 DG 3 3 2 2 2 2 1 2 \u03c0 1 2 GJ 2 2 2 1 2 \u03c0 1 2 as 0 0 0                                           y EA y EA y EA y EA y EA y EA y EA y EA y EA k D D G G J G G J J yyyy yyy yy i . (10) The calculation methods of J , G , D  , B  , \u03b3,  d d and d d d d d d 4321 yyyy \uff0c\uff0c can be found in Ref. [9]. The local contact stiffness in the healthy and spalling scopes can be expressed as Refs. [11, 24, 25]: mm ms m lsrFF GDj FwWE GDj FWE k             , )( 275.1 )( )( 275.1 1.08.09.0 1.08.09.0 h , (11) where GD is the scope of the spalling on the tooth surface (see Fig. 2). Fm denotes the meshing force of the mth tooth pair. lsrm is the load sharing ratio. 2.2 TVMS calculation of spalled gears considering revised fillet-foundation stiffness, nonlinear contact stiffness and ETC AC C EP TE D M AN U SC R IP T Generally, two meshing teeth on driven or driving gears share one gear body [16], however, the total mesh stiffness of gear pairs in traditional methods is the direct summation of the mesh stiffness of tooth pairs, which can lead to the mesh stiffness of double-tooth engagement larger than the actual value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002032_j.jmatprotec.2016.04.006-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002032_j.jmatprotec.2016.04.006-Figure5-1.png",
        "caption": "Fig. 5. Fixed type of the substrate in the fixture.",
        "texts": [
            " The stable current is approximately 300 A, and the heating power is approximately 2.1 kW. The filler wire is made of H13 steel. The diameter of the wire is 1 mm and the wire feed speed is 157 mm per second. Under such a speed, the laser hot\u2010wire system offers a high deposition rate of 3.46 kg per hour. The experiment was conducted by Schwam et al . (2014) and Udvardy et al. (2014). The dimensions of the workpiece are listed in Fig 4.. The substrate is made of H13 steel in a tempering state (46.5 HRC). The substrate was sunk into a fixture and fastened tightly by two tips Fig 5. The substrate cannot undergo free\u2010form deformation due to the existence of fixture constraints. Four thermocouples were installed on the underside of the substrate F i g 6 . A l l f ou r thermocouples were built inside the substrate. The depth of thermocouples 1, 2, and 3 is 17.5 mm, and that of thermocouple 4 is 10.2 mm. As shown in Fig 7., the whole deposited block is cladded layer by layer from the bottom to the top. Each layer consists of between 23 and 28 passes. All the passes are parallel with the same motion directions from point A to point B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001525_tia.2009.2036507-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001525_tia.2009.2036507-Figure12-1.png",
        "caption": "Fig. 12. Dual-stage harmonic gear.",
        "texts": [
            " 11, such that the gear is akin to a magnetic version of the mechanical cycloid gear and may exhibit higher level of mechanically and magnetically generated acoustic noise. However, since the low-speed rotor is mounted eccentrically to the high-speed rotor, a mechanical system is required to connect the low-speed eccentric rotor to an external concentric shaft [10]. The requirement for a coupling between the flexible structure and an output shaft can be overcome if a dual-stage harmonic gear is employed, as shown in Fig. 12 [11]. This configuration consists of a first stage, which is implemented as discussed previously, and a second stage, in which the outer concentric magnet array is allowed to rotate and constitutes the output rotor. The high-speed and flexible rotors are common to both stages, although the flexible rotor carries a different number of magnet poles in each of the two stages. As discussed previously, the rotation of the high-speed rotor results in a geared rotation of the flexible rotor in the first stage, which, in turn, results in a geared rotation of the output rotor in the second stage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000806_j.optlaseng.2011.06.016-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000806_j.optlaseng.2011.06.016-Figure1-1.png",
        "caption": "Fig. 1. Schematic overview of a typical LLM machine.",
        "texts": [
            " Data processing rates up to 10 kHz and real-time process monitoring are achieved using image and signal processing on a Field Programmable Gate Array (FPGA). Several case studies will be presented showing that the geometric influencing factors can be studied and quantified by analyzing the melt pool sensor output. & 2011 Elsevier Ltd. All rights reserved. Layerwise Laser Melting (LLM)1 is a layerwise production technique enabling the production of complex metallic parts. A schematic overview of a typical LLM machine is shown in Fig. 1. In the LLM process, a thin layer of metal powder is first deposited on a build platform by means of a powder coating system. After depositing, the powder is melted selectively according to a predefined scanning pattern, by means of a laser source [1]. A scanning pattern typically consists of a set of subsequent linear scan vectors. After scanning a layer, the build platform moves down over a fixed distance equal to the thickness of one layer (in LLM typically 20240 mm) and a new layer is deposited and scanned"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure2.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure2.12-1.png",
        "caption": "Fig. 2.12",
        "texts": [
            " From the circle the orientation of the unknown x, y-system can be obtained: the counterclockwise angle 2\u03d5 (from point \u03c31 to point P ) in Mohr\u2019s circle corresponds to the clockwise angle \u03d5 between the 1-axis and the x-axis. The angle and the stresses are found as 2\u03d5 = 110\u25e6 \u2192 \u03d5 = 55\u25e6 , \u03c3y = 20 MPa , \u03c4xy = 28 MPa . The stresses and the coordinate systems are shown in Fig. 2.11b. As an important application of plane stress we first consider a thinwalled cylindrical vessel with radius r and wall thickness t r (Fig. 2.12a). The vessel is subjected to an internal gage pressure p that causes stresses in its wall which need to be determined (Fig. 2.12b). At a sufficient distance from the end caps of the vessel, the stress state is independent of the location (homogeneous stress state). Given that t r, the stresses in radial directions can be neglected. Thus, within a good approximation a plane stress state acts locally in the wall of the vessel (note: although the element in Fig. 2.12b is curved, it is replaced by a plane element in the tangent plane). The stress state can be described by the stresses in two sections perpendicular to each other. First, the vessel is cut perpendicularly to its longitudinal axis (Fig. 2.12c). Since the gas or fluid pressure is independent of the location, the pressure on the section area \u03c0r2 (of the gas or fluid) has the constant value p. Assuming that the longitudinal stress \u03c3x is constant across the wall thickness because of t r, the equilibrium condition yields (Fig. 2.12c) 2.2 Plane Stress 69 \u03c3x2 \u03c0 r t\u2212 p \u03c0 r2 = 0 \u2192 \u03c3x = 1 2 p r t . (2.18) As illustrated in Fig. 2.12d we now separate a half-circular part of length\u0394l from the vessel. The horizontal sections of the wall are subjected to the circumferential stress \u03c3\u03d5, also called hoop stress, which again is constant across the thickness. These stresses will counteract the force p 2 r\u0394l, exerted from the gas onto the halfcircular part of the vessel. Equilibrium in the vertical direction yields 2 \u03c3\u03d5 t\u0394 l \u2212 p 2 r\u0394l = 0 \u2192 \u03c3\u03d5 = p r t . (2.19) We notice that the hoop stress is twice the longitudinal stress. This is why a cylindrical vessel under internal pressure usually fails by cracking in the longitudinal direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000339_tie.2011.2157278-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000339_tie.2011.2157278-Figure2-1.png",
        "caption": "Fig. 2. Control of stator flux (proposed TPC).",
        "texts": [
            " (12) Substituting (12) into (10) gets \u0394Te = pn L \u03c8r\u00d7usTk+ ( \u2212Rs L Te\u2212 pn L \u03c8s\u00d7 d dt \u03c8r ) Ts. (13) The calculation of \u0394Te in (13) is simplified, compared with (10). By knowing the magnitude of voltage vector us, the new voltage control angle \u03bb can be derived as follows: \u03bb = arcsin ( \u0394Te + ( Rs L Te + pn L \u03c8s \u00d7 d dt\u03c8r ) Ts pn L |\u03c8r| |Tkus| ) . (14) The purpose of angle \u03bb is to decide the proper direction of voltage vector us for driving the torque error \u0394Te to zero. This angle \u03bb is the phase difference between inverter voltage us and rotor flux \u03c8r (see Fig. 2). Here, there is a need to point out that an angle with the value \u03c0 \u2212 \u03bb also satisfies (13). This result is utilized in the control of the stator flux, as described in the next section. A schematic of PMSM TPC system is shown in Fig. 3. There are two control loops that focus on the performance of the motor torque and flux, respectively. In the proposed control strategy, the motor torque and the stator flux are compared to their reference values. The differences are then sent to the predictive control block to calculate the control angle of voltage vector us according to (14). Finally, the control voltage us is generated from a two-level voltage source inverter to drive the PM motor, where the SVPWM method is used to control the switching of the inverter. The calculation of the control strategy is not complicated and can be carried out within one control cycle Ts, which is 0.1 ms in the simulation and the experiment. Angle \u03bb of voltage vector us in (14) ensures an accurate control of the motor torque. Fig. 2 shows the vector relationship of us, \u03c8s, and \u03c8r. As shown in this figure, \u03c8s is leading phase angle \u03d5 before \u03c8r so that a positive electromagnetic torque is generated. Angle \u03d5 becomes less than zero if negative torque is need. Additionally, the voltage vector us will change the magnitude of the stator flux. Once the phase difference between vectors us and \u03c8s is within \u00b190\u25e6, the magnitude of the stator flux will increase. Otherwise, the magnitude of the stator flux decreases. In most cases, the phase difference between \u03c8s and \u03c8r is small; therefore, when considering the control of the stator flux, the following voltage control angle \u03bb\u2032 is used: 1) magnitude of the stator flux increases, let \u03bb\u2032 = \u03bb; 2) magnitude of the stator flux decreases, let \u03bb\u2032=\u03c0\u2212\u03bb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000318_70.313105-FigureI-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000318_70.313105-FigureI-1.png",
        "caption": "Fig. I . Geometry of a robotic system.",
        "texts": [
            " FLANGE. TOOL (2) The nominal values of transformations A l . . . . , A,, - I and FLANGE can be obtained from the design specifications of the robot. Their actual values can be estimated using a complete robot CalibI'dtion process. It is assumed in this paper that these transformations are known with sufficient precision. The BASE and TOOL transformations are application-dependent, and should be recalibrated more frequently. Since a homogeneous transformation i h always invertible. let (Refer to Fig. I ) A T,, ( 3 ) B E Ai. . . .4 , , - I 'FLANGE (4) x = TOOL-' ( 5 ) Y = BASE ( 6 ) Then by (2), AX = YB (7) 1042-296X/94$04.00 0 1994 IEEE 550 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 10, NO. 4, AUGUST 1994 The homogeneous transformation A is known from end-effector pose measurements, B is computed using the calibrated manipulator internal-link forward kinematics, X is the inverse unknown TOOL transformation, and Y is the unknown BASE transformation. The problem is now reduced to that of solving a system of matrix equations of the type (7)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003126_j.jsv.2015.08.002-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003126_j.jsv.2015.08.002-Figure7-1.png",
        "caption": "Fig. 7. Orbital positions of a ball and a defect. In this figure, the origin of the inertial frame is assumed at the bearing center. The relationship between the orbital positions can be clearly shown in plane yizi.",
        "texts": [
            " In this paper, the variables are not non-dimensionalized. In the current investigation, the computer program has been coded in FORTRAN 95 language. All of the variables in the program are double-precision floating-point. The authors think that the numerical precision can be satisfied by the above programming scheme. Moreover, in the numerical integration procedure, the relative orbital position between a ball and the defect is checked to determine whether the ball rolls into the defect or not. As shown in Fig. 7, the orbital positions of the ball and the defect center are \u03b8b and \u03b8d, respectively. Moreover, in Fig. 7, \u03b8e is half the angle of the defect in the circumference of the raceway. It can be found that when the difference between \u03b8b and \u03b8d (i.e., \u03b8bd in Fig. 7) is smaller than \u03b8e, the ball rolls into the defect. Detailed simulation procedure is given in Fig. 8. Moreover, the descriptions of \u03b8bd and \u03b8e can be found in Ref. [42]. Then, envelope analysis is carried out on the simulated vibration responses to calculate BPFs. In this paper, the frequency resolution is less than 0.1 Hz. As the time step size is step-changing in the numerical integration, the vibration response is re-sampled before the envelope analysis. Moreover, the simulation results obtained by the dynamic model are compared with those obtained by Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure4-8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure4-8-1.png",
        "caption": "Fig. 4-8 Currents and flux at t\u2212.",
        "texts": [
            " In order to keep the mmf and the flux-density distributions the same as in the actual machine with three-phase windings, the currents in these two windings would have to be isd and isq, where, as shown VECTOR CONTROL WITH d-AXIS ALIGNED WITH ROTOR FLUX 67 in Fig. 4-7, these two current components are 2 3/ times the projections of the i ts( ) vector along the d-axis and q-axis. 4-5 VECTOR CONTROL WITH d-AXIS ALIGNED WITH THE ROTOR FLUX In the following analysis, we will assume that the d-axis is always aligned with the rotor flux-linkage space vector, that is, also aligned with B tr( ). 4-5-1 Initial Flux Buildup Prior to t\u00a0=\u00a00\u2212 We will apply the information of the last section to vector control of induction machines. As shown in Fig. 4-8, prior to t\u00a0=\u00a00\u2212, the magnetizing currents are built up in three phases such that i I i i Ia m b c m( ) and ( ) ( ) .,rated ,rated0 0 0 1 2 \u2212 \u2212 \u2212= = = \u2212\u02c6 \u02c6 (4-16) The current buildup prior to t\u00a0 =\u00a0 0\u2212 may occur slowly over a long period of time and represents the buildup of the flux in the induction machine up to its rated value. These currents represent the rated magnetizing currents to bring the air gap flux density to its rated value. Note 68 VECTOR CONTROL OF INDUCTION-MOTOR DRIVES that there will be no rotor currents at t\u00a0=\u00a00\u2212 (they decay out prior to t\u00a0=\u00a00\u2212)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure2.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure2.1-1.png",
        "caption": "Fig. 2.1",
        "texts": [
            " The students will learn how to analyse the plane stress state and how to determine the stresses in different sections. D. Gross et al., Engineering Mechanics 2, DOI 10.1007/978-3-642-12886-8_2, \u00a9 Springer-Verlag Berlin Heidelberg 2011 2.1 Stress Vector and Stress Tensor 49 So far, stresses have been calculated only in bars. To be able to determine stresses also in other structures we must generalize the concept of stress. For this purpose let us consider a body which is loaded arbitrarily, e.g. by single forces Fi and area forces p (Fig. 2.1a). The external load generates internal forces. In an imaginary section s \u2013 s through the body the internal area forces (stresses) are distributed over the entire area A. In contrast to the bar where these stresses are constant over the cross section (see Section 1.1) they now generally vary throughout the section. Since the stress is no longer the same everywhere in the section, it must be defined at an arbitrary point P of the cross section (Fig. 2.1b). The area element \u0394A containing P is subjected to the resultant internal force \u0394F (note: according to the law of action and reaction the same force acts in the opposite cross section with opposite direction). The average stress in the area element is defined as the ratio \u0394F /\u0394A (force per area). We assume that the ratio \u0394F /\u0394A in the limit \u0394A\u2192 0 tends to a finite value: t = lim \u0394A\u21920 \u0394F \u0394A = dF dA . (2.1) This limit value is called stress vector t. The stress vector can be decomposed into a component normal to the cross section at point P and a component tangential to the cross section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003410_adem.201600078-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003410_adem.201600078-Figure7-1.png",
        "caption": "Fig. 7. Scheme to show the difference in the electrical current measuring direction for eddy-current and laser flash measurement. Also depicted is an anisotropic distribution of the residual porosity.",
        "texts": [
            " The columnar microstructure along the building direction might reduce the electrical conductivity slightly, but only a minor influence in the region of 1\u20132% is expected.[28] However, for the highporosity region, not only spherical gas pores occur but the porosity is predominantly determined by layered lack-offusion defects. In that case, a very likely explanation for the deviation in conductivities is the different current direction during measurement with eddy-current (circular in plane of the surface of the slices) and heat current at laser flash analysis (through the slices), see Figure 7. Since the eddy current measurement direction is perpendicular to the pores and not parallel, the electrical conductivity is lower than the thermal conductivity. Here, even more than for the low-porosity samples, no crucial effect of grain orientation is expected.[28] 4.2. Porosity versus Conductivity To discuss the conductivity of SEBM copper at high relative density, only the electrical conductivity is used due to the above discussed, very good correlation between electrical and & Co. KGaA, Weinheim DOI: 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003221_j.mechmachtheory.2019.103670-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003221_j.mechmachtheory.2019.103670-Figure13-1.png",
        "caption": "Fig. 13. 6 types of natural vibration modes of HPGT.",
        "texts": [
            " When the sun gear is floating, the trajectory of these gears is changed. Hence, Figure 10 shows the floating path of sun gear, Figure 11 shows the floating path of planet gears and Figure 12 shows the floating path of ring gear. 5.1. Modal analysis under initial supported conditions Based on the modal calculation theory, the Eq. (26) has been solved. According to the models of vibration characteristic in \u03d5i , the model of vibration of HPGT can be summarized as 6 types modes and the 6 types modes are shown in Figure 13 . That is, no vibration mode, sun gear\u2019s torsional-axial vibration mode, planet gears\u2019 vibration mode, ring gear\u2019s transverse vibration mode, ring gear\u2019s torsional-axial vibration mode, sun gear\u2019s transverse vibration mode and no vibration mode. Shown in Figure 13 , these 6 types of natural vibration modes of HPGT are not only suitable for 3 planet gears, but also universal for different number of planet gears. Table 4 shows the undamped natural frequency of the 3 planet gears HPGT system when the sun gear is normally supported. Moreover, Table 5 shows the undamped natural frequency of the 3 planet gears HPGT system when the sun gear is floating. In summary, the 6 types typical vibration modes of the HPGT are summarized, and the undamped natural frequencies are calculated when the sun gear is normally supported and the sun gear is floating"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure11-1.png",
        "caption": "Fig. 11. Tooth-contact pattern calculated.",
        "texts": [
            "04 , XE = 2.1 mm and ZE = 0.2 mm are given to the gear shaft A0B0 as shown in Fig. 1(b). These gears are ground under the accuracy requirement of JIS 1st grade. A so-called power- circulating form gear test rig is used to do the tests at a very load speed (1.65 rpm) under torque T = 294 N m. Fig. 9 is the test gearbox used in the test rig. In Fig. 9, a removable support is used to give AE to the shaft of Gear 1 by changing the position of this support. Fig. 10 is tooth-contact pattern measured. Fig. 11 is the tooth-contact pattern calculated under the same conditions. In Fig. 11, A is the areas of double pair toothcontact and B is the area of single pair tooth-contact. It is found that calculated contact pattern is agreement with the measured one well. Root strains are also measured. Fig. 12 is comparisons between the measured root strains and the calculated ones at measurement positions of stain gauges 1\u20134 as shown in Fig. 13. It is also found that calculated root strains are agreement with the measured ones. Tooth-contact lengths and contact stresses of a pair of spur gears with lead crowning were also calculated by the special FEM software and compared with measurement results in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure7.14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure7.14-1.png",
        "caption": "Fig. 7.14 Chopped lightning impulse generation. a Chopped lightning impulse (LIC) voltage. b Circuit of two modules of a multiple chopping gap. c Multiple chopping gap for 1200 kV (six single gaps)",
        "texts": [
            " Chopped lightning impulse (LIC) voltagesand chopping gap: An external overvoltage in the power system is limited to the protection level by a lightning arrester. This means the over-voltage is chopped and collapses to this protection level. The duration of the voltage collapse is very short, its steepness very high. Such steepness causes very non-linear stresses in equipment with windings (power, distribution and instrument transformers, reactors, rotating machines). The mainly stressed insulation at the HV terminals of the equipment must be designed accordingly and verified by a test with chopped lightning impulse (LIC; Fig. 7.14a) voltages. An LIC test voltage is generated as an LI test voltage described above and then chopped by a separate chopping gap. For LIC voltages up to about 600 kV, a usual sphere-to-sphere gap can be used; for higher voltages, multiple chopping gaps become technically mandatory (Fig. 7.14b and c). The voltage collapse of a multiple spark gap is much faster than that of a single large sphere gap. The chopping gap consists of in-series-connected sphere-to-sphere gaps, usually one gap for one stage of the generator. One sphere of each gap is fixed and arranged at a fixed insulating column. The other one\u2014on suitable insulating support\u2014is 298 7 Tests with High Lightning and Switching Impulse Voltages moveable by a motor drive and can be adjusted for the relevant voltage value. The parallel capacitor column controls the voltage distribution linearly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000834_jmr.2014.192-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000834_jmr.2014.192-Figure1-1.png",
        "caption": "FIG. 1. Experimental setup for the IN718 test specimens. (a) Top surface view, (b) schematic illustrating hatching procedure. Specimens for microstructure evaluation were cut according to the plane shown in gray, i.e., with the plane of observation lying parallel to the BD and perpendicular to the hatching direction of the last layer.",
        "texts": [
            " The material was supplied by a commercial vendor, TLS Technik GmbH, Bitterfeld. The nominal chemical composition is listed in Table I. Particle size analysis performed on a Malvern Mastersizer 3000 (Malvern, Worcestershire, U.K.) shows a particle size distribution mostly between 45 and 105 lmwith volume median diameter dV50 of 68.8 lm. As starter plate, a 10 mm-thick polycrystalline IN718 disk was used with a composition within the specification according to AMS 5662. In the SEBM experiments, 9 cube-shaped samples (15 15 10mm\u00b3) were built in one run, see Fig. 1. In the present investigation, beam parameters, i.e., deflection speed v and beam power P were varied while scanning parameters, i.e., hatching pattern and line offset were held constant. In particular, a variety of beam power and deflection speed parameter sets were investigated to define a process window for fully dense parts (relative density .99.5%) with the top surfaces free from projections or unevenness. This was done for two beam geometries \u2013 for a more focused beam (spot size ;400 lm) and for a less focused beam (spot size ;500 lm). The hatching pattern defines the way the beam moves over the melting area. In this study, a back and forth hatching method was applied, which is indicated by the black scan vectors in Fig. 1(b). Additionally, the hatching direction was rotated by 90\u00b0 after every layer. The distance between beam lines, i.e., the line distance was set to 0.2 mm. The preheating parameters were held constant over all build processes and lead to a build temperature of ;900 \u00b0C. After removal from the starter plate, the samples were cut with the cutting plane as indicated in gray in Fig. 1(b), i.e., parallel to the building direction (BD) and perpendicular to the hatching direction of the last layer. Themounted specimens were prepared with standard metallographic technique by grinding with SiC-paper with sizes ranging from 80 to 2400 grit, polishing with 3 lm and 1 lm diamond suspensions and polishing with an oxide polishing suspension on soft cloths. The porosity of the polished samples was measured with a constant threshold on a light optical microscope by image analysis software Image C",
            ", the total height of the P-profile, was measured on the polished samples on a stereomicroscope by image analysis software. A profile depth of,200 lm was defined as even and .200 lm as uneven. The grain width in cubes that were dense and had smooth top surfaces was analyzed. The grain width was measured using an optical microscope on the longitudinally cut samples etched electrolytically with oxalic acid. Due to strongly elongated grains in all samples, the grain width rather than the grain diameter was investigated with the intercept method in a total area of 4.83 mm\u00b2, plane of observation as explained above (Fig. 1). The measurements were taken at the same building height of the samples, i.e., 1 mm below the top surface, to assure the same degree of grain selection in every sample. In addition, the influence of the build height on the grain structure was investigated by measuring the mean grain width for one sample at five different build heights. Since samples were built directly on the starter plate, the microstructural evolution is influenced by the grain microstructure of the chosen substrate material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure7.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure7.12-1.png",
        "caption": "Figure 7.12. Calculating the horizontal position of the whole body center of gravity of a high jumper using the segmental method and a three-segment model of the body. Most sport biomechanical models use more segments, but the principle for calculating the center of gravity is the same.",
        "texts": [
            "8 feet in height, his center of gravity in this position would be 47% of his or her height. In the segmental method, the body is mathematically broken up into segments. The weight of each segment is then estimated from mean anthropometric data. For example, according to Plagenhoef, Evans, & Abdelnour (1983), the weight of the forearm and hand is 2.52 and 2.07% for a man and a woman, respectively. Mean anthro- pometric data are also used to locate the segmental centers of gravity (percentages of segment length) from either the proximal or distal point of the segment. Figure 7.12 depicts calculation of the center of gravity of a high jumper clearing the bar using a three-segment biomechanical model. This simple model (head+arms+trunk, thighs, legs+feet) illustrates the segmental method of calculating the center of gravity of a linked biomechanical system. Points on the feet, knee, hip, and shoulder are located and combined with anthropometric data to 182 FUNDAMENTALS OF BIOMECHANICS calculate the positions of the centers of gravity of the various segments of the model. Most biomechanical studies use rigidbody models with more segments to more accurately calculate the whole-body center of gravity and other biomechanical variables",
            " Finding the height of the center of gravity is identical, except that the y coordinates of the segmental centers of gravity are used as the moment arms. Students can then imagine the segment weight forces acting to the left, and the height of the center of gravity is the y coordinate that, multiplied by the whole bodyweight acting to the right, would cancel out the segmental torques toward the left. Based on the subject's body position and the weights of the three segments, guess the height in centimeters of the center of gravity. Did the center of gravity pass over the bar? Finish the calculation in Figure 7.12 to check your guess. The segmental method can be applied using any number of segments, and in all three dimensions during 3D kinematic analysis. There are errors associated with the segmental method, and more complex calculations are done in situations where errors (e.g., trunk flexion/extension, abdominal obesity) are likely (Kingma, Toussaint, Commissaris, Hoozemans, & Ober, 1995). We have seen than angular kinetics provides mathematical tools for understanding rotation, center of gravity, and rotational equilibrium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure5-1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure5-1-1.png",
        "caption": "Fig. 5-1 Stator and rotor mmf representation by equivalend dq winding currents. The d-axis is aligned with \u03bb\u0302r .",
        "texts": [
            " As the last step in this chapter, we will use an idealized space vector pulse width-modulated inverter (discussed in detail in Chapter 7) to supply motor voltages that result in the desired currents calculated by the controller. 5-1 MOTOR MODEL WITH THE d-AXIS ALIGNED ALONG THE ROTOR FLUX LINKAGE \u03bbr -AXIS As noted in the qualitative description of vector control, we will align the d-axis (common to both the stator and the rotor) to be along the rotor flux linkage \u03bb \u03bbr r je( )= \u02c6 0 , as shown in Fig. 5-1. Therefore, 79 5 Mathematical Description of Vector Control in Induction Machines Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink\u00ae, First Edition. Ned Mohan. \u00a9 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. 80 MATHEMATICAL DESCRIPTION OF VECTOR CONTROL \u03bbrq t( ) .= 0 (5-1) Equating \u03bbrq in Eq. (3-22) to zero, i L L irq m r sq= \u2212 . (5-2) The condition that the d-axis is always aligned with \u03bbr such that \u03bbrq\u00a0=\u00a00 also results in d\u03bbrq/dt to be zero",
            "= +1 (5-10) In time domain, the rotor flux linkage dynamics expressed by Eq. (5-10) is as follows: d dt L ird rd r m r sd\u03bb \u03bb \u03c4 \u03c4 + = . (5-11) 5-1-4 Motor Model Based on above equations, a block diagram of an induction-motor model, where the d-axis is aligned with the rotor flux linkage, is shown in Fig. 5-4. The currents isd and isq are the inputs, and \u03bbrd, \u03b8da, and Tem are the outputs. Note that \u03c9d (=\u00a0\u03c9dA\u00a0+\u00a0\u03c9m) is the speed of the rotor field, and therefore, the rotor-field angle with respect to the stator a-axis (see Fig. 5-1) is \u03b8 \u03c9 \u03c4 \u03c4da d t t d( ) ( ) ,= +\u222b0 0 (5-12) where \u03c4 is the variable of integration, and the initial value of \u03b8da is assumed to be zero at t\u00a0=\u00a00. (Continued) EXAMPLE 5-1 The motor model developed earlier, with the d-axis aligned with \u03bbr, can be used to model induction machines where vector control is not the objective. To illustrate this, we will repeat the simulation of Example 3-3 of a line-fed motor using this new motor model (which is much simpler) and compare simulation results of these two examples"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000698_s00170-011-3443-y-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000698_s00170-011-3443-y-Figure5-1.png",
        "caption": "Fig. 5 The relationship between scanning space and overlapping rate",
        "texts": [
            " Due to the above two reasons, the distribution of track shape shift to the lower right in Fig. 3, that is to say lower laser power or higher scanning speed will be fine when producing regular or continuous tracks. In order to obtain dense and smooth surface, appropriate overlapping rate between tracks should be considered (not use the concept of scanning space, as the scanning space varies with the track width). The formula f \u00bc d s d 100% is mostly used to calculate overlapping rate during multi-track fabrication, just as Fig. 5a shows, s is scanning space, d is spot diameter. However, the formula above does not consider practical track width, which varies with laser processing parameters (laser power, scanning speed). Therefore, it is necessary to replace spot diameter d with practical track width dm, and the formula can be changed to f \u00bc dm s dm 100%, as Fig. 5b shows, scanning space s is preset, and practical track width dm can be got according to Fig. 4. According to single-track analysis, the regular- and thick-shape and regular- and thin-shaped tracks were suitable for SLM fabrication. During multi-track fabrication, regular- and thick-shaped track had a larger range of powder-free zone, making the next track not to have enough material and the volume become smaller. Therefore, large scanning spacing (low overlapping rate) should be adopted for the regular- and thick-shaped track"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000477_0079-6425(63)90037-9-Figure53-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000477_0079-6425(63)90037-9-Figure53-1.png",
        "caption": "Fig. 53. Hypothetical growth rate anisotropy required for the formation of a spiral cone eutectic structure. (Alter Fullman and Wood. ~9~ Courtesy of",
        "texts": [
            " Continued growth of the two phases could lead to the formation of a spiral structure if the loop did not completely close. If we now consider the growth rate as a function of direction in the plane of the originally planar interphase boundary of Fig. 52(a) we can imagine that in some directions the growth rate of the ~ phase is larger than the growth rate of the ~ phase, and vice versa in other directions. The hypothetical growth rate plot of the two crystals as a function of orientation is then as shown in Fig. 53. From ~ = 91 to q~ = 90 \u00b0, the 0t phase will tend to surround the [5 phase, and from 9 ~--0 to q~----cp 1 the [5 phase grows faster than the 0t phase. As the [5 phase grows around the ~ phase, the direction of the growing edge changes from 9 ----- 0 to a larger value of ~. When 178 PROGRESS IN MATERIALS SCIENCE the growth direction of the edge reaches ?~, the growth rates of the two phases are equal, and the two phases grow as a cone with half angle ~?l- The cone axis in the direction ~\u00a2 ---- 0 \u00b0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000927_0094-114x(82)90042-8-Figure14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000927_0094-114x(82)90042-8-Figure14-1.png",
        "caption": "Figure 14.",
        "texts": [
            " When the six screws representing the instantaneous motions of the the joints of the robot arm belong to a five system and the screw ~ representing the instantaneous motion of the end effector does not belong to the five system then the robot arm has a stationary configuration. Consider the infinitesimal motion of a robot hand, AR along and A0 about an axis R, which is connected to a fixed frame by g screws. Suppose that any screw ~s has rotational motion A0j 131 about and translation motion hjAO t along its axis is illustrated in Fig. 14. The components of the motion along and about the axis _R due to ~t are given by A0 \u00b0) = cos Aj A0 t (10) AR (~) = hjAO~ cos aj. - A0 i r/sin Aj. (11) The total instant motion is thus g g AO = ~ AO ~j), AR = ~ AR \u2022). (12) 1 I When all j screws are reciprocal to the screw with axis R, then AR - hR. (13) A0 Therefore, the hand cannot have free instantaneous translational movement along this axis because the linear velocity dR/dt and the angular velocity dO/dt must satisfy the relationship (dR/dt) (dO/dt) = -hR"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002810_j.engfailanal.2012.08.015-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002810_j.engfailanal.2012.08.015-Figure4-1.png",
        "caption": "Fig. 4. Proposed variable crack intersection angle (v) approach at the cracked pinion tooth root level.",
        "texts": [
            " 3a in steps until the crack reaches other end of the tooth. The crack propagation path shows a curve extending from tooth root as shown in Fig. 3b. The crack changes direction almost symmetrically around tooth\u2019s central line. Based on the simulation results, a curved path approximation is proposed. It is assumed that the variable crack intersection angle (t) is the angle measured between the line joining the crack initiation point to the end point of the curved path and tooth central line for different crack lengths as shown in Fig. 4 against the straight line path assumed in the past. The crack path is predicted through simulation and the crack intersection angle (t), as shown in Fig. 5a\u2013d for different crack length viz. 20%, 40%, 60% and 80% of fully developed straight line crack assuming at constant angle of 45 and simulated crack for the pinion of gear pair with contact ratio <2 and for different crack length viz. 15%, 20%, 30% 40% and 50% of fully developed crack as shown in Fig. 6a\u2013e for the pinion of gear pair having contact ratio >2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure2.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure2.9-1.png",
        "caption": "Fig. 2.9 Pure rolling: Fx = 0 and T = Fzex",
        "texts": [
            " However, it is more common to assume that five parameters suffice, like in (2.22) (as already discussed, it is less general, but simpler) F\u0303x ( h,\u03b3, Vox \u03c9c , Voy \u03c9c , \u03a9z \u03c9c ) = 0 (2.26) F\u0303y ( h,\u03b3, Vox \u03c9c , Voy \u03c9c , \u03a9z \u03c9c ) = 0 (2.27) M\u0303z ( h,\u03b3, Vox \u03c9c , Voy \u03c9c , \u03a9z \u03c9c ) = 0 (2.28) It is worth noting that pure rolling and free rolling are not the same concept [14, p. 65]. They provide different ways to balance the rolling resistance moment My = \u2212Fzex . According to (2.12), we have pure rolling if Fx = 0 (Fig. 2.9), while free rolling means T = 0 (Fig. 2.10). However, the ratio f = ex/h, called the rolling resistance coefficient, is typically less than 0.015 for car tires and hence there is not much quantitative difference between pure and free rolling. First, let us consider Eq. (2.26) alone F\u0303x ( h,\u03b3, Vox \u03c9c , Voy \u03c9c , \u03a9z \u03c9c ) = 0 (2.29) 7We have basically a steady-state behavior even if the operating conditions do not change \u201ctoo fast\u201d. 2.6 Tire Global Mechanical Behavior 23 which means that Fx = 0 if Vox \u03c9c = fx ( h,\u03b3, Voy \u03c9c , \u03a9z \u03c9c ) (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002645_1.4032168-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002645_1.4032168-Figure1-1.png",
        "caption": "Fig. 1 CAD model of coupon showing overall dimensions and channel shape detail for the teardrop design",
        "texts": [
            " To the best of our knowledge, there have been no studies published that investigate internal feature quality of DMLS parts, especially for minichannels. Therefore, the goal of this study is to investigate the effect of build direction on the quality of internal minichannels. Specifically, metrics useful to a gas turbine designer, such as friction factor and heat transfer, will be used to evaluate build direction effects. To examine the build direction effects on surface roughness, geometric tolerance, and ultimately the pressure loss and heat transfer, different test coupons were designed and manufactured in-house. As shown in Fig. 1, the overall size of the coupons was 25.4 mm long 25.4 mm wide 3.048 mm high. Each coupon had 15 channels spaced 2.5 diameters apart, with a designed hydraulic diameter of Dh\u00bc 508 lm. The material used for manufacturing the coupons was Inconel 718. The three different build directions studied are shown in Figs. 2(a)\u20132(c) including horizontal, diagonal, and vertical. Each build orientation was defined by the position of the channel axes relative to the build plate. The channel axes were parallel to the build plate in the horizontal build direction, 45 deg to the build plate in the diagonal build direction, and perpendicular to the build plate in the vertical build direction",
            " Cylindrical-shaped channels were chosen as the baseline to investigate build direction effects since it is a common design. In addition to the cylindrical channels, channels with diamond and teardrop shapes were also investigated. The design intent for the diamond and teardrop shapes was to create a channel shape that would not collapse when built in the horizontal build direction. These alternate channel shapes were designed to match the cylindrical channel Dh\u00bc 508 lm. A computer-aided design (CAD) model of the teardrop coupon can be seen in Fig. 1, while all of the designed channel shapes are shown in Fig. 3. Building these coupons required support structures to be generated. Most AM methods require structures to support overhanging features. Specific to the DMLS process with Inconel 718, the minimum recommended unsupported angle is 40 deg. Therefore, any feature of the test coupons that was less than 40 deg to horizontal required supports. Using this criteria, the upper surface of the horizontal cylindrical channels required supports; however, it would be difficult to remove these supports after the build was completed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure4.13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure4.13-1.png",
        "caption": "Fig. 4.13 Derivative calculation by backward-forward differencing: (a) small perturbation; (b) large perturbation",
        "texts": [
            " The coefficients in the A and B matrices represent the slope of the forces and moments at the trim point reflecting the strict definition of the stability and control derivatives. Analytic differentiation of the force and moment expressions is required to deliver the exact values of the derivatives. In practice, two other methods for derivative calculation are more commonly used, leading to equivalent linearizations for finite amplitude motion. The first method is simply the numerical differencing equivalent to analytic differentiation. The forces and moments are perturbed by each of the states in turn, either one-sided or two-sided, as illustrated conceptually in Figure 4.13; the effect of increasing the perturbation size is illustrated in the hypothetical case shown in Figure 4.13b, where the strong nonlinearity gives rise to a significant difference with the small perturbation case in Figure 4.13a. The numerical derivatives will converge to the analytic, true, values as the perturbation size reduces to zero. If there is any significant nonlinearity at small amplitude, then the slope at the trim may not give the best fit to the force over the amplitude range of interest. Often, larger perturbation values are used to ensure the best overall linearization over the range of motion amplitude of interest in a particular application, e.g. order 1 m/s for velocities and 0.1 rad for controls, attitudes, and rates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001525_tia.2009.2036507-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001525_tia.2009.2036507-Figure15-1.png",
        "caption": "Fig. 15. (a) Intermediate rotor of prototype. (b) Concentric output rotor of prototype.",
        "texts": [
            " A prototype dual-stage magnetic harmonic gear was built with pw = 1, p1 = 18, p2 = 19, and an overall gear ratio of \u2212360 : 1. The gear has an outside diameter of 140 mm, backiron thicknesses of 5 mm, an inner magnet thickness of 6 mm, an outer magnet thickness of 5 mm, and an active length of 50 mm per stage. Fig. 14 shows a cross-sectional view of the prototype, where it can be seen that the gear is constructed with a rigid intermediate rotor which can rotate around an axis that is eccentric to the high-speed input rotor. Fig. 15(a) shows the intermediate rotor, on which the two stages of the gear can be recognized. The low-speed output rotor of the gear is shown in Fig. 15(b). The measured gear ratio is consistent with the gear ratio given by (10), while at room temperature, the measured pull-out torque of the gear is 115 N \u00b7 m, which occurs at a load angle of 4.5\u25e6 (mechanical), and compares favorably with the predicted peak torque of 122 N \u00b7 m. Furthermore, since the pullout torque is proportional to the square of the remanence of the permanent magnets, its dependence on temperature would be more significant than the torque produced by permanentmagnet brushless machines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001981_s11249-014-0396-y-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001981_s11249-014-0396-y-Figure8-1.png",
        "caption": "Fig. 8 Elementary flow process, a flow unit of area l1l2 moves distance l into an available hole due to an applied shear force; from [68]",
        "texts": [],
        "surrounding_texts": [
            "It became clear in the 1960s that progress in elastohydrodynamic lubrication required knowledge of the properties of lubricants at a combination of high pressure and high strain rate, and this led researchers at Georgia Institute of Technology to build a succession of high-pressure rheometers aimed at measuring liquid properties under these conditions. In 1968, Novak and Winer developed a capillary viscometer able to reach a pressure of 0.7 GPa with an applied shear stress of 0.1 MPa and employed this to study the viscosity of several lubricants [53]. For the polymer solutions tested, they found shear thinning behaviour, but all of the base oils tested showed Newtonian response at all test conditions. This approach was extended in 1975 by using shorter capillaries to reach shear stresses as high as 4 MPa, but again base oils behaved only in a Newtonian fashion once heating effects were taken into account [54]. These two studies failed to reach a sufficiently high shear stress for shear thinning of low MWt base oils to occur, but in 1979, Bair and Winer developed three new high-pressure rheometers based on shear of fluid between a moving piston and stator [55]. They used these to explore both the elastic (stress vs. strain) and viscous (stress vs. strain rate) behaviour of three base fluids. At high pressures and low temperatures up to about 50 C above the glass transition temperature, all three lubricants behaved as elastic solids upon initial application of stress, with an apparent yield stress that increased with pressure and temperature. This yield stress also increased with strain rate. One of the three rheometers was able to reach a combination of high shear stress (up to 50 MPa) with quite high strain rate (up to 500 s-1). This showed that at lower pressures and higher temperatures, all three fluids showed shear thinning behaviour above a shear stress of about 10 MPa, tending towards a limiting shear stress value, sL, that increased linearly with pressure and decreased with temperature. Bair and Winer proposed an equation based on an asymptotic shear thinning expression combined with a viscoelastic term [56]; _c \u00bc 1 Gp ds dt sL gp loge 1 s sL \u00f016\u00de This can be rearranged in terms of shear stress as; s \u00bc sL 1 e gp sL _c 1 Gp ds dt ! \u00f017\u00de In 1982, Bair and Winer developed a new piston-based rheometer to address a problem of pressure drop during test measurement, and shear stress versus strain rate curves were measured for a range of lubricants, including polymer solutions, up to 1.1 GPa and a shear stress of 80 MPa [57]. Shear thinning occurred for both base fluids and polymer solutions and shear stress levelled out as strain rate increased, in a fashion consistent with Eq. 17. A very different method for studying lubricant rheology at high shear stresses was developed by Ramesh and Clifton in 1987 [58]. They measured the compression and shear waves transmitted from the impact of two flat plates separated by a very thin film of lubricant and from these were able to monitor the shear stress and strain of the film over a time scale of less than a millisecond. The approach could not directly study the variation of shear stress with strain rate and applied only very small amounts of shear, but did show that the lubricants tested had an apparent limiting shear stress that increased linearly with pressure over the pressure range of 1\u20135 GPa. In 1990, Bair and Winer developed a new high-pressure viscometer based on a rotating cylinder configuration in order to reach controlled, high strain rates [43]. A key barrier in such development is heating of the test fluid during shear and consequent reduction in effective viscosity. The new design addressed this by using a very short duration of shear to avoid unacceptable cylinder temperature increases, combined with a very narrow film gap down to almost one micron to minimise oil film temperature rise. This enabled combinations of shear stress and strain rate, up to 10 MPa and 104 s-1, respectively, to be reached without significant shear heating. Two fluids were studied, and the same pattern of shear stress versus strain rate behaviour was found as noted at higher pressures and lower strain rates, i.e, linear increase on a log/log plot at low strain rates followed by levelling out towards a limiting value as strain rate was increased. In a subsequent paper in 1992, Bair and Winer combined this data with some taken at very high pressures and low strain rates to suggest that the transition from Newtonian to plastic behaviour described by Eq. 17 broadened as pressure was increased [59]. They proposed a modification of this equation to accommodate this. Further thermal analysis showed that there was a significant flash temperature effect in the cylinder walls even during short duration tests and this led Bair and Winer in 1993 to develop another, \u2018\u2018isothermal\u2019\u2019 concentric cylinder viscometer with a shorter time of operation of 3 ms, so as to prevent significant temperature increase of the cylinders [60]. Again, as shown in Fig. 7, they found levelling-out of shear stress/strain rate curves at high strain rates, in support of the existence of a limiting shear stress, sL. The high-pressure capability of this viscometer was increased by Bair to 600 MPa in 1995 [61] and to almost 1 GPa in 2002 [62]. In 1995, Bair also suggested the use of the reduced Carreau\u2013Yasuda equation; s \u00bc gp _c 1\u00fe gp _c so a 1 n\u00f0 \u00de=a \u00f018\u00de where a and n are constants and n \\ 1 [61]. so is a modulus or stress at which shear thinning becomes significant. Initially Bair used sL in place of so but it is clear that so does not represent a limiting shear stress. For a = 2 and n = 0.5, it is the stress at which the effective viscosity has fallen 21 % below its Newtonian value and it typically has a value between 4 to 10 MPa for simple molecular fluids, but a much smaller one for polymeric liquids. More recently, Bair has tended to use the term sC [44] or G [63], but in this review, so is preferred to avoid confusion with the elastic shear modulus used in the viscoelastic term. In 2002, Bair added a pressure-dependent, limiting shear stress to the Carreau Yasuda model [44] to give, omitting the Maxwell viscoelastic term, s \u00bc min _cgp 1\u00fe gp _c so a n 1\u00f0 \u00de=a ;Kcp \" # \u00f019\u00de Since 2002, there appears to have been relatively little further development of high shear stress viscometry. Bair and his colleagues at Georgia Institute of Technology remain the only group to construct and employ short duration, high-stress/high-strain viscometers, perhaps because of the formidable problems involved in their design, in particular to limit their response time. Bair has used the Carreau\u2013Yasuda equation for modelling EHD lubrication, accompanied by criticism of the Eyring equation [44, 45, 64]. The relative suitability of these equations in EHD contact conditions will be discussed later in this paper, but first their origins are briefly outlined. 5 EHL Rheology Models 5.1 Eyring Eyring\u2019s model of viscosity, introduced in 1936, treats liquid flow as a unimolecular, \u2018\u2018chemical\u2019\u2019 reaction in which the elementary process is a molecule (or flow unit) passing from one equilibrium position to another over a potential energy barrier [65]. It was based on the newly developed partition state chemical reaction rate theory [66, 67]. Figures 8 and 9 show the process schematically. A molecule moves approximately one molecular distance, k, into a neighbouring hole in the liquid. If no external force is applied, the number of times per second that molecules passes over the energy barrier and hence moves in either direction, i.e, their diffusion rate, is given by: kD \u00bc Be Ea=kT \u00f020\u00de where Ea is the activation energy for flow and B contains the ratio of the partition functions of the activated and initial state, which includes a free-volume term. However, when a shear force is applied, this has the effect of reducing the activation energy for a flow process in the direction of applied force and increasing it in the reverse direction, as shown in Fig. 9. The activation energy is assumed to be raised and lowered by the value sk2k3k/2, where s is the applied shear force per unit area, k2 is the length of the molecule in the direction of the applied force, k3 is its length in the transverse direction (so sk2k3 is the shear force on the individual molecule) and k/2 the distance it has to move to reach the top of the energy barrier. The specific flow rates in the forward and backward directions, kf and kb, are therefore given by: kf \u00bc Be Ea sk2k3k=2\u00f0 \u00de=kT \u00bc kDesk2k3k=2kT \u00f021\u00de kb \u00bc Be Ea\u00fesk2k3k=2\u00f0 \u00de=kT \u00bc kDe sk2k3k=2kT \u00f022\u00de Since each time a molecule passes over a potential barrier, it moves a distance k, the rate of motion of the layer relative to its neighbour is given by: Du \u00bc kDk kf kb \u00bc kDk esk2k3k=2kT e sk2k3k=2kT \u00f023\u00de or, from the definition of the sinh() function, Du \u00bc 2kDk sinh sk2k3k 2kT : \u00f024\u00de The shear rate is given by the difference in velocity divided by the spacing between layers, k1 _c \u00bc Du k1 \u00bc 2kDk k1 sinh sk2k3k 2kT \u00f025\u00de while the effective viscosity is the shear stress divided by the strain rate: ge \u00bc s _c \u00bc sk1 2kDk sinh sk2k3k 2kT : \u00f026\u00de At low shear stresses when s 2kT/k2k3k, sinh sk2k3k 2kT \u00bc sk2k3k 2kT , so under these conditions, the (Newtonian) viscosity is given by; g \u00bc sk1 2kDk sk2k3k 2kT \u00bc 2kTk1 2kDk2k3k 2 \u00f027\u00de or kD \u00bc kTk1 gk2k3k 2 : \u00f028\u00de Substituting Eq. 28 into Eq. 25 gives _c \u00bc 2kT gk2k3k sinh sk2k3k 2kT \u00f029\u00de If we set se = 2kT=k2k3k, this becomes Eq. 5, the Eyring equation adopted by many EHD researchers. The product k2k3k is called the \u2018\u2018activation volume.\u2019\u2019 Eyring found that for simple molecular liquids, Eq. 27 predicted the actual Newtonian viscosity when this activation volume was approximately the size of the molecule, but that for larger molecules, the activation volume required to predict the measured viscosity was less that the molecular size [68]. He suggested that this was because the flow unit was not the whole molecule but that the molecule moved in a segmental fashion. In 1941, Eyring included the effect of applied pressure on activation energy to obtain a relationship between viscosity and pressure [69]. It should be noted that in 1936, Eyring\u2019s goal was to develop a priori model of the viscosity of simple liquids which was able to explain how Newtonian viscosity varied with temperature, free-volume and molecular properties. The shear thinning equation via which this was derived was essentially a by-product, and he initially gave it little attention. However, other scientists working on shear thinning of polymer solutions and dispersions very soon started to apply Eyring\u2019s equation to model their findings, with variable degrees of success. In 1955, since the original model failed to model complex fluids and multiphase systems, Ree and Eyring extended Eyring\u2019s model to allow for multiple flow units, for example of dispersed particles in a fluid medium [70, 71]. Their equation was s \u00bc X i aixi sinh 1 bi _c\u00f0 \u00de \u00f030\u00de where xi is the fraction of a shearing layer occupied by flow unit type i, ai = kT k2k3k i is this unit\u2019s se and bi = ki 2kDk is its relaxation time. The complexity of Eq. 30 means that the Ree\u2013Eyring model has not generally found favour, and it is unfortunate that the earliest EHD publications cited these later Ree and Eyring papers while actually used the original simpler Eyring equation [17, 72], with the result that Eyring\u2019s model is often, incorrectly, termed the Ree\u2013Eyring model in the EHD literature. Eyring\u2019s model has also recently been referred to as the Prantl\u2013Eyring model [73], since Prantl, in 1928, developed a similar thermally activated shear model to describe the plastic flow of solids and also dry friction [74, 75]. 5.2 Carreau and Yasuda By the 1960s, several shear thinning models had been developed specifically to describe complex fluids [76]. In 1965, Cross derived a viscosity model for polymer solutions and colloidal dispersions based on equilibrium between the formation and rupture of linkages between dispersed or dissolved particles [77]. This took the form: ge \u00bc g1p \u00fe gp g1p 1 1\u00fe a _c\u00f0 \u00de2=3 ! \u00f031\u00de where a is a constant associated the rupture of linkages, gp is the low shear rate Newtonian viscosity and g?p is its viscosity at infinite shear rate, i.e, when the fluid has shear thinned fully to reach a \u2018\u2018second Newtonian.\u2019\u2019 Note that in the above and the following equations, the suffix p has been included to remind readers that these are limiting Newtonian values at the prevailing pressure. Although Cross derived the value 2/3 as the power of the strain rate term, nowadays, this is often generalised to become a constant m, with value less than 1. This form of shear thinning equation, with limiting values of a first and second Newtonian, is appropriate to fluids where the shear thinning component is dispersed in a Newtonian continuous phase such as a polymer in solvent, and is widely used to describe shear thinning of lubricants containing viscosity modifier polymers. If g?p is set to zero, as might be appropriate for a polymer melt, or simply when it much lower than gp and not reached in experiments [78], then the Cross equation becomes: ge \u00bc gp 1\u00fe a _c\u00f0 \u00de2=3 \u00f032\u00de In principle, all shear thinning equations can include a second Newtonian, and Eyring and Powell extended the Eyring equation in this fashion in 1944 [79]. By the 1960s, a model of polymer rheology was taking shape based on molecular network theory in which randomly arranged polymer chains are linked together by temporary junctions which are lost and created as the liquid flows [80]. In 1972, Carreau showed that one mathematical solution to this type of model was ge \u00bc gp 1\u00fe k _c\u00f0 \u00de2 1 n 2 \u00f033\u00de where k is a time constant and n \\ 1 [81]. He notes that this solution is not unique, stating \u2018\u2018unfortunately the modified network theory does not shed any light on the actual forms of the functions fp(II) and gp(II). In this section, we select arbitrarily plausible forms which will permit good fit of the experimental data for various flow situations.\u2019\u2019 At very high shear rates when k _c 1, Carreau\u2019s equation reduces to ge \u00bc gp k _c\u00f0 \u00den 1 \u00f034\u00de so that a plot of log(effective viscosity) versus log(shear rate) should give a straight line of gradient (n - 1). In 1981, Yasuda carried out an extensive study of the shear thinning of polystyrene polymer solutions and suggested a modification to the Carreau equation to improve its fit in the transition region between Newtonian and strong shear thinning [82]. This has the form; ge \u00bc gp 1\u00fe k _c\u00f0 \u00dea\u00f0 \u00de 1 n\u00f0 \u00de a \u00f035\u00de where a and n are constants. a usually has a value close to 2, as in the Carreau equation. This equation has become known as the Carreau\u2013Yasuda equation and widely used to describe polymer shear thinning, both in the above form and with a second Newtonian term; ge \u00bc g1p \u00fe gp g1p 1 1\u00fe k _c\u00f0 \u00dea\u00f0 \u00de 1 n\u00f0 \u00de=a ! \u00f036\u00de Like the Carreau equation, Eq. 35 reduces to Eq. 34 at high strain rates. The Carreau and Carreau\u2013Yasuda equations can be expressed in terms of shear stress simply by multiplying through by the strain rate, e.g., s \u00bc gp _c 1\u00fe k _c\u00f0 \u00dea\u00f0 \u00de 1 n\u00f0 \u00de=a \u00f037\u00de When the time constant, k, is replaced by gp/so, this results in the form of the Carreau\u2013Yasuda equation advocated by Bair and coworkers and shown in Eq. 18. According to Bair, from thermodynamic arguments, so can be equated to NvkT where Nv is the number of molecules per unit volume [83]. Interestingly, this is very closely related to the expression for se = kT/k1k2k in the Eyring equation, where k1k2k is the activation volume. Indeed, if we set the volume of a molecule equal to the activation volume, se and so become identical. Bair estimated the value of so for various liquids and found that for simple liquids, 1/Nv corresponds quite closely to the volume of a molecule but that for polymers, it becomes much smaller than this [83], just as was found by Kauzmann and Eyring for simple fluids versus ones with larger molecules [68]."
        ]
    },
    {
        "image_filename": "designv10_1_0000052_1.3629602-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000052_1.3629602-Figure2-1.png",
        "caption": "Fig. 2 3C, R mechanism",
        "texts": [
            " At this point the mechanism has been completely solved (the 0,- are known) for only the first position of the input link. To solve the mechanism for a new position, di majr be incremented by a small amount., Adi, and the previously calculated di can be used as initial estimates for the 0,- of the next position. After a few iterations by the same method, these values should converge to the proper values of 0f for the new position. This assumes that the increments in 8i are taken sufficiently small. Extension of Results If, as indicated in the example, Fig. 2, the translational freedoms of a mechanism are described by prismatic pairs, it will be necessary to extend the foregoing derivation. 3 Proof is given in [4], pp. 44\u201446. Condensing and rearranging this information shows that A,(s,-) S a + Q,dSi)AI (47) The only effect which the prismatic pair has on the matrix equation of approximation, therefore, is to change the definition of the corresponding term, the B,-matrix for that pair: Bi = (AiI2 li-iQji . . . AJdst (48) The inclusion of a prismatic pair produces no other changes in the method of attack",
            " 5 Output curves of 3C, R mechanism 360 of mechanisms, planar and spatial, and produced very satisfactory results. I t was found that most mechanisms coulcl be analyzed throughout an entire cycle in increments of 5 deg with a total calculation time of about 2 min, a total cost of about 310.00. The program will give the motion of all joints of the mechanism to an accuracy of six significant figures. Copies of tliis program are available upon request from the authors. The computer program was used to perform the analysis on the 3C, R mechanism of Fig. 2, equation (3) . The total calculation time was 1.92 min. Although space does not permit a detailed listing of the numerical data involved, the curves of the two output motions, 06 and s7, are shown in Fig. 5. T h e data used to draw these curves were accurate to within 0.0001 deg and 0.0001 in. T o achieve tliis accuracy it was necessary to make only four iterations at each position. The rate of convergence of the iteration process can be seen from the data in Table 1. I t lists the correction factors, the ddi and ds;, for each of the four iterations made in position one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.19-1.png",
        "caption": "Fig. 4.19",
        "texts": [
            " The four constants of integration are calculated from geometrical and/or statical boundary conditions. We will now show with the aid of several examples how the differential equations (4.31) or (4.34) can be used to obtain the deflection curve. In this section we restrict ourselves to beams where the integration can be performed in one region, i.e., we assume that each of the quantities q(x), V (x), M(x), w\u2032(x) and w(x) is given by one function for the entire length of the beam. Let us first consider a cantilever beam (flexural rigidity EI) subjected to a concentrated force F (Fig. 4.19a). Since the system is statically determinate, the bending moment can be calculated from the equilibrium conditions (compare Volume 1, Section 7.2). With the coordinate system as shown in Fig. 4.19b, we obtain M = \u2212F (l \u2212 x). Introducing into (4.31) and integrating yields EI w \u2032\u2032 = F (\u2212 x+ l) , EI w \u2032 = F ( \u2212 x2 2 + l x ) + C1 , EI w = F ( \u2212 x3 6 + l x2 2 ) + C1 x+ C2 . The geometrical boundary conditions w \u2032(0) = 0, w(0) = 0 lead to the constants of integration: C1 = 0, C2 = 0 . Hence, the slope and the deflection are obtained as w \u2032(x) = F l2 2EI ( \u2212 x2 l2 + 2 x l ) , w(x) = F l3 6EI ( \u2212 x3 l3 + 3 x2 l2 ) . The maximum slope and the maximum deflection (at x = l, see Fig. 4.19b) are w \u2032 max = F l2 2EI , wmax = F l3 3EI . Let us now consider three beams (bending stiffness EI) subjected to a constant line load q0 (Figs. 4.20a-c). The supports in the three cases are different; the systems in the Figs. 4.20a and b are statically determinate, the system in Fig. 4.20c is statically indeterminate. Since in the latter case the bending moment can not be calculated from equilibrium conditions, we will use the differential equation (4.34b) in all three cases. We introduce a coordinate system and integrate (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.10-1.png",
        "caption": "Fig. 10.10 XV-15 control functions in helicopter and airplane modes",
        "texts": [
            " At 100kts with a nacelle tilt angle of 60 deg, the wing is carrying about half the weight of the aircraft. Increasing load factor, for example in a turn, brings the aircraft closer to the lower corridor, stall, limit. Effectively, the corridor shrinks when manoeuvring at constant speed so pilots need to be aware of the nacelle-angle dependent manoeuvre capability within the corridor. The control functions of a tiltrotor are a mix of helicopter and airplane surfaces as illustrated for the XV-15 in Figure 10.10. In helicopter mode, longitudinal cyclic controls aircraft pitch through fore\u2212aft proprotor disc tilt, while proprotor differential collective pitch (DCP) controls aircraft roll. Asymmetric lateral cyclic is also available for trimming purposes and side-force control. This lateral translation mode (LTM, Tiltrotor Aircraft: Modelling and Flying Qualities 603 Fig. 10.9 Rotor and wing lift sharing as a function of airspeed for different V-22 nacelle angles (Ref. 10.9) Ref. 10.10) was implemented on the XV-15 to allow the pilot to control rotor disc tilt for nacelle angles between 85 and 95 deg",
            " \u03a9s is the IC angular velocity and Qs is the total torque applied to the shaft. Qs = QE + QA + 2\u2211 R=1 QR (10.33) Here, QE is the engine torque after gearing, QA is the engine accessory system torque, QR is the torque load from the two torque-producing proprotor components. At any instant of time, the IC angular velocity is the same as the left and the right rotor rotational speeds (due to the assumed unity gearing), and this value is passed to the collective governor system. Flight Control System Family The basic control functions of the XV-15 were shown in Figure 10.10. The gearing ratios between the pilot inputs and the control surface displacements, for both helicopter and fixed-wing surfaces, are given in Appendix 10B. The helicopter control surfaces (functions) are combined collective (heave), differential collective (roll), combined longitudinal cyclic (pitch), differential longitudinal cyclic (yaw), and combined lateral cyclic (roll trim). A positive input of differential collective decreases the collective of the right rotor and increases collective on the left rotor, generating a positive rolling moment about the body x-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure4.15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure4.15-1.png",
        "caption": "FIGURE 4.15. A screw motion is translation along a line combined with a rotation about the line.",
        "texts": [
            " Motion Kinematics As an example, consider a point P at (2, \u03c03 , \u03c0 3 ) in a spherical coordinate frame. Then, the Cartesian coordinates of P would be\u23a1\u23a2\u23a2\u23a3 c\u03c03 c \u03c0 3 \u2212s\u03c03 c\u03c03 s \u03c0 3 2c\u03c03 s \u03c0 3 c\u03c03 s \u03c0 3 c\u03c03 s\u03c03 s \u03c0 3 2s\u03c03 s \u03c0 3 \u2212s\u03c03 0 c\u03c03 2c\u03c03 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u23a1\u23a2\u23a2\u23a3 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a3 0.866 1.5 1.0 1.0 \u23a4\u23a5\u23a5\u23a6 . (4.140) 4.5 F Screw Coordinates Any rigid body motion can be produced by a single translation along an axis combined with a unique rotation about that axis. This is called Chasles theorem. Such a motion is called screw. Consider the screw motion illustrated in Figure 4.15. Point P rotates about the screw axis indicated by u\u0302 and simultaneously translates along the same axis. Hence, any point on the screw axis moves along the axis, while any point off the axis moves along a helix. The angular rotation of the rigid body about the screw is called twist. Pitch of a screw, p, is the ratio of translation, h, to rotation, \u03c6. p = h \u03c6 (4.141) In other words, the rectilinear distance through which the rigid body translates parallel to the axis of screw for a unit rotation is called pitch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure8.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure8.3-1.png",
        "caption": "Fig. 8.3 Projected differential velocities (optical flow-field) on the ground in a helicopter vertical landing",
        "texts": [
            "11: Speaking in terms of visual sensations, there might be said to exist two distinct characteristics of flow in the visual field, one being the gradients of \u2018amount\u2019 of flow and the other being the radial patterns of \u2018directions\u2019 of flow. The former may be considered a cue for the perception of distance and the latter a cue for the perception of direction of locomotion relative to the surface. Gibson focused mainly on fixed-wing landings but he also presented an example of the optical flow-field generated by motion perspective for the case of a helicopter landing vertically, as shown in Figure 8.3. \u2018For the case of a helicopter landing, the apparent velocity of points in the plane below first increases to a maximum and then decreases again\u2019. The optical flow-field concept clearly has relevance to a helicopter landing at a heliport, on a moving deck or in a clearing, and raises questions as to how pilots reconstruct a sufficiently coherent motion picture from within the confines of a closed-in cockpit to allow efficient use of such cues. Gibson\u2019s ecological approach (Ref. 8.13) is a \u2018direct\u2019 theory of visual perception, in contrast with the \u2018indirect\u2019 theories that deal more with the reconstruction and organization of components in the visual scene by the visual system and associated mental processes (Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000970_tpel.2015.2388493-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000970_tpel.2015.2388493-Figure6-1.png",
        "caption": "Fig. 6. Schematic diagram of stator shorted-circuit winding taps in the experimental PMSM-2. (a) Wye-connection. (b) Delta-connection.",
        "texts": [
            " The outer-loop speed PI controller tracks the optimal shaft speed reference expressed in (42) to generate the maximum power point tracking from WT. R vwopt r   * (42) where opt is the optimal tip speed ratio, vw is the wind speed, R is the blade radius of WT. id=0 control strategy employing current hysteresis controller is commonly adopted to control the PMSM-2 due to its simplicity and effectiveness [33]. In this experiment, the inter-turn fault in the PMSM-2 is made artificially by connecting winding taps with a wire. The short-circuited turn ratio u=0.05, 0.1 and 0.15 is made in each phase, as shown in Fig. 5(a) and Fig. 6. The resistance box with the 3.3  is connected in series with shorted circuit to (a) limit the short current, avoiding a permanent damage to the windings. The parameters of WT and PMSMs used for experimental tests are listed in Table I. (1) Steady-state Condition 0885-8993 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Fig. 7 shows the experimental time-domain waveforms of the ZSVC V0,m together with the fault diagnosis information (fault indicator and angle differences), where the inter-turn fault occurs in the phase c of the wye-connected PMSM-2, and wind speed is 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001609_jas.2017.7510820-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001609_jas.2017.7510820-Figure1-1.png",
        "caption": "Fig. 1. Schematic of CMD system.",
        "texts": [
            " Thus, the closed-loop system is proven uniformly ultimately bounded. The inequality (24) indicates that the tracking error e(t) converges to a small residual set \u03a6 for all time, then the state x in system (1) will follow the desired trajectory xd. The tracking error e(t) can be made arbitrarily small by appropriately choosing the parameters \u03b5, \u03b7 and \u03b3. The increases in \u03b3 and \u03b7, or decrease in \u03b5 will make the tracking performance better. \u00a5 In order to prove the effectiveness of the control scheme, we take a CMD system for simulation. Its schematic is shown in Fig. 1, and the linearized dynamics in the presence of external disturbance could be written as follows [23]: Jl\u03b8\u03082 + c12\u03b8\u03072 + k ( \u03b82 \u2212 g\u22121 r \u03b81 ) = 0 Jd\u03b8\u03081 + c11\u03b8\u03071 + kg\u22121 r ( g\u22121 r \u03b81 \u2212 \u03b82 ) = Td + d (t) (25) where \u03b81 is the drive angle position; \u03b82 is the load angle position; Jl is the total inertias reflected at the load; Jd is the total inertias reflected at the drive; gr = (rlrpl)/(rp2rd) is the gear ratio; Td is control torque input; c11 is the drive rotary damping (modeled as viscous); c12 is the load rotary damping (modeled as viscous); d(t) is the external disturbance, and k = 2klr 2 l is torsional spring constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003262_j.optlastec.2018.09.054-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003262_j.optlastec.2018.09.054-Figure3-1.png",
        "caption": "Fig. 3. (a) 3D Temperature distribution and flow field for moving, single track, (b) the magnified view of the velocity field and the melt pool, (c) the cross-sectional view.",
        "texts": [
            " Based on the grid independence test results, 13,610 elements are finally chosen in the single scan computational domain and 33,056 total elements for the multiple scans, which correspond to the minimum element size of 7.6\u00d7 10\u00d712 \u00b5m. Time step of 2 \u00b5s was used in all simulations. The mathematical model is solved using a commercial finite element package COMSOL MultiPhysics\u00ae. Using the numerical model described, simulations were carried out. The process parameters for simulations are listed in Table 2. 3.1. Temperature distribution and velocity field Temperature distribution and melt pool velocity field results for moving single scan simulations at 100W laser power and 500mm s\u22121 scan speed are presented in Fig. 3a when a quasi-steady state has been achieved. The color scheme illustrates the temperature distribution, while the arrows show the flow vectors. The magnified view of the melt pool is shown (Fig. 3b) for a more detailed insight of the thermo-fluidic transport. An elongated melt pool (Fig. 3b) has been formed as a result of the moving laser beam, with a short front and much longer rear. The melt pool characteristics are symmetric about the xz-plane containing the scan path. Very high temperature (Tmax\u223c 3700 K) and flow velocity magnitude (|\u2192u |max\u223c 4m/s) is observed in the melt pool. The flow velocity magnitude is very small in the center of the melt pool as well as near the boundary, while the flow accelerates and decelerates in the intermediate region. The velocity field at the free surface in the melt pool is directed outwards, which is consistent with a negative temperature coefficient of surface tension (\u2202\u03b3/\u2202T). However, looking closely, a weaker counter-rotating flow is observed deep inside the melt pool (melt pool cross-section view, Fig. 3c). Its origin can be attributed to the viscous effects working in the melt pool. The flow field is symmetric about the plane of symmetry (Fig. 3c). Along the x-direction, however, the flow is not symmetric and the flow loops in the rear part get stretched while those in the front get shrunk. This transports the thermal energy to the distant locations in the melt pool. Another contributing fact in elongating the melt pool is the solidified material behind the melt pool that has thermal conductivity and diffusivity much larger than the powder layer and facilitates quicker heat diffusion towards the rear. The temperature distribution and velocity field in the melt pool are directly proportional to the laser power and inversely proportional to the scan speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002739_j.optlastec.2019.105725-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002739_j.optlastec.2019.105725-Figure15-1.png",
        "caption": "Fig. 15. SLM-manufactured mold with cooling channels: (a) CAD framework; (b) as-fabricated component; (c) surface roughness; and (d, e) top surface morphology.",
        "texts": [
            " As mentioned previously, the decrease in microhardness was attributed to grain growth and residual stress release during solution treatment. In addition, aging treatment played a notable role in the improvement of the hardness. The sample reached the peak hardness value of 543 HV0.5 on the side surface and 532 HV0.5 on the top surface upon solution treatment at 840 \u00b0C for 2 h and aging at 490 \u00b0C for 2 h. As mentioned, the occurrence of the increase in microhardness was due to the formation of intermetallic precipitations after aging treatment. Fig. 15a and b shows the application case of a mold with cooling channels manufactured using the SLM system and optimum process parameters discussed in Section 3.1. From a macroscopic perspective, the scanning strategy adopted in this study resulted in no obvious warp of the part that was induced by residual thermal stress during SLM. The top surface of the as-built mold was associated with a smooth surface and limited defects (Fig. 15d and e). However, the defects were detrimental to the surface roughness. Fig. 15c shows the surface roughness measurements of the as-built mold. The average roughness Ra on the top surface and side surface were measured to be 6.59 \u03bcm and 8.13 \u03bcm, respectively. The as-built part should be further processed by conventional methods for the requirement of high surface accuracy in the automotive domain. Moreover, the average microhardness on the top surface and side surface of the as-built component was 348.83 HV0.5 and 344.18 HV0.5 under a 500 g load for 8 s dwell time, respectively, while the microhardness increased to 577"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure8.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure8.5-1.png",
        "caption": "FIGURE 8.5. Link (i) and associated coordinate frames.",
        "texts": [
            " Velocity Kinematics 453 To calculate the ith column of the Jacobian matrix, we need to find two vectors 0 i\u22121dn and 0k\u0302i\u22121. These vectors are position of origin and the joint axis unit vector of the frame attached to link (i\u2212 1), both expressed in the base frame. Calculating J, based on the Jacobian generating vectors, shows that forward velocity kinematics is a consequence of the forward kinematics of robots. Proof. Let 0di and 0di\u22121 be the global position vector of the frames Bi and Bi\u22121, while i\u22121di is the position vector of the frame Bi in Bi\u22121 as shown in Figure 8.5. These three position vectors are related according to a vector addition 0di = 0di\u22121 + 0Ri\u22121 i\u22121di = 0di\u22121 + di 0k\u0302i\u22121 + ai 0\u0131\u0302i. (8.120) in which we have used Equation (8.6). Taking a time derivative, 0d\u0307i = 0d\u0307i\u22121 + 0R\u0307i\u22121 i\u22121di + 0Ri\u22121 i\u22121d\u0307i = 0d\u0307i\u22121 + 0R\u0307i\u22121 \u00b3 di i\u22121k\u0302i\u22121 + ai i\u22121 \u0131\u0302i \u00b4 + 0Ri\u22121 d\u0307i i\u22121k\u0302i\u22121 (8.121) shows that the global velocity of the origin of Bi is a function of the translational and angular velocities of link Bi\u22121. However, 0 i\u22121d\u0307i = 0d\u0307i \u2212 0d\u0307i\u22121 (8.122) 0R\u0307i\u22121 i\u22121di = 0\u03c9i\u22121 \u00d7 0Ri\u22121 i\u22121di = 0\u03c9i\u22121 \u00d7 0 i\u22121di = \u03b8\u0307i 0k\u0302i\u22121 \u00d7 0 i\u22121di (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure2.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure2.7-1.png",
        "caption": "Figure 2.7.1. Alternative representations of rolling resistance with vertical force.",
        "texts": [
            "7 Rolling Resistance Considering a notional isolated wheel rolling at constant speed down a ramp in a vacuum, forces and moments on the wheel must be in equilibrium. This determines the nature and value of the rolling resistance force and moment. There must be zero moment about the wheel axis (center of mass) to maintain zero angular acceleration, so the total rolling resistance must act through that axis. At the footprint it must comprise a drag force plus a moment, or a drag plus a forward shift of the normal force, which actually arises from changes in the footprint pressure distribution. Figure 2.7.1 shows some possible representations. The rolling resistance is a relatively small force and not of decisive importance in most handling problems; it will be treated as acting at the axis if it is included at all. Its main effect in the context of handling is on steering feel; effects arise from lateral load transfer in steady cornering, or from vertical force variation due to bumps. Practical measurements of rolling resistance show it to be reasonably constant with speed, possibly increasing slightly, up to a Turner number of about 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure5.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure5.11-1.png",
        "caption": "Fig. 5.11 Centrodes of a turning vehicle with handling misbehavior in the final part of the curve (the car goes into a spin)",
        "texts": [
            "10 Vehicle exiting a curve: moving centrode rolling on the fixed centrode a straight line, while the fixed centrode \u03c3f is made of two distinct parts, as is the kinematics of turning: entering the curve and exiting the curve. The velocity center C is the point of rolling contact of the two centrodes. By definition, the vehicle belongs precisely to the same rigid plane of the moving centrode. They move together. Actually, the centrodes shown in Figs. 5.9 and 5.10 are typical of a vehicle making a curve the good way. The centrodes changes abruptly if the vehicle does not make the curve properly. This may happen, e.g., if the speed is too high. An example of \u201cbad\u201d centrodes, and hence of bad performance, is shown in Fig. 5.11. We 5.2 The Kinematics of a Turning Vehicle 121 122 5 The Kinematics of Cornering Fig. 5.12 Centrodes of a Formula car making Turn 5 of the Barcelona circuit (the inflection circle is also shown) see that the centrodes for the exiting phase (Fig. 5.11(c)) are totally different with respect to Fig. 5.10. The vehicle goes into a spin. Quite interestingly, as shown in Fig. 5.11(b), the two centrodes start having a bad shape although the vehicle still has an apparent good behavior. Therefore, the two centrodes could be used as a warning of handling misbehavior. They depart from the proper shape a little before the vehicle shows unwanted behavior. To confirm that this is real stuff, we show in Fig. 5.12 the centrodes of a Formula car making Turn 5 of the Barcelona circuit. In this case everything was fine, as confirmed by the \u201cgood\u201d shape of both centrodes. Also shown are the trajectory of G and the inflection circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure4.26-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure4.26-1.png",
        "caption": "Fig. 4.26 Simple representation of unstable pitch phugoid in hover",
        "texts": [
            "129) or in expanded form as the quadratic equation \ud835\udf062 \u2212 ( Xu + g Mu M2 q ) \ud835\udf06 \u2212 g Mu Mq = 0 (4.130) The approximate phugoid frequency and damping are therefore given by the simple expressions \ud835\udf142 p \u2248 \u2212g Mu Mq (4.131) 2\ud835\udf01p\ud835\udf14p = \u2212 ( Xu + g Mu M2 q ) (4.132) The ratio of the pitching moments due to speed (speed stability) and pitch rate (damping) play an important role in both the frequency and damping of the oscillation. This mode can be visualised in the form of a helicopter rotating like a pendulum about a virtual hinge (Figure 4.26). The frequency of the pendulum is given by \ud835\udf142 = g \ud835\udcc1 (4.133) where \ud835\udcc1 is the length of the pendulum (i.e. distance of helicopter centre of mass below the virtual hinge). This length determines the ratio of u to q in the eigenvector for this mode (cf. Eq. (4.131)). Comparison of the approximations given above with the \u2018exact\u2019 uncoupled phugoid roots is given in Table 4.4. Modelling Helicopter Flight Dynamics: Trim and Stability Analysis 211 There is good agreement, particularly for the Lynx and Bo105"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002229_j.matchar.2019.110016-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002229_j.matchar.2019.110016-Figure1-1.png",
        "caption": "Fig. 1. Schematic image of the tensile samples with the dimensions (in mm) and build orientation. The dashed lines illustrate the as-built shape.",
        "texts": [
            " In this study, a gas-atomized 316L powder was used as feedstock material, having a size distribution of 25\u201353 \u03bcm. The chemical composition of the powder is 0.009 wt% C, 17.4 wt% Cr, 1.6 wt% Mn, 0.005 wt% N, 13.4 wt% Ni, 0.04 wt% O, 0.006 wt% P, 0.005 wt% S, 0.3 wt% Si, and Fe was balanced. The samples were fabricated in an EOS M290 machine (Electro Optical Systems GmbH, Germany). The build was conducted in an Ar environment, where the oxygen content was kept below 0.1%. A standard pre-defined scan strategy known as stripe scanning developed by Electro Optical Systems GmbH was utilized. Fig. 1 illustrates the final dimensions of the samples used for both, mechanical testing and microstructural characterization. The samples were fabricated as rectangular plates (72 \u00d7 12 \u00d7 2.5 mm) and waterjet cutting was used to create the final dimensions as presented in Fig. 1. To evaluate the effect of scan speed and hatch distance, three to five bars for each process parameter set, given in Table 1, were produced. These parameters were selected to examine the influence of energy density on microstructure and mechanical properties. The samples for metallographic examination were cut, mounted, ground and polished following Struers preparation recommendation for austenitic stainless steel. The samples were chemically etched with Glyceregia (10 ml HNO3, 20 ml HCl, 30 ml glycerol) to reveal the microstructure",
            " With respect to the cross section, a hexagonal pattern or elongated cellular structure can be observed, that is illustrated schematically in Fig. 4a. The in-situ formation of nano-sized inclusions are another special characteristic of L-PBF 316L that does not occur in conventionally produced 316 L. These oxide particles (10 nm to several hundred nanometer in size) are rich in silicon and chromium and may contribute to the strength of the material via dislocation pinning [5,17]. All EBSD orientation maps presented in this study were collected from the center of the vertically built samples (as shown in Fig. 1). Supplementary analyses were conducted at different build heights and similar results were obtained across the whole sample. In Fig. 5, EBSD orientation maps of the samples produced with the highest energy density (203.1 J/mm3) are provided in inverse pole figure (IPF) coloring (transverse direction (TD), building direction (BD), normal direction (ND)) with corresponding inverse pole figures and micrograph. The microstructure is consisting of several large elongated grains which have grown along the building direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure1.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure1.4-1.png",
        "caption": "Figure 1.4.2. Rear-view free-body diagram for a right-hand turn: (a) in XYZ, (b) in xyz.",
        "texts": [
            " For those readers interested in the general approach, the bibliography at the end of this chapter gives references. Notation for forces on the vehicle follows a similar pattern to kinematic notation, including the use of the various subscripts for axis directions, and terms such as longitudinal force and side force. Notation for forces in the ground plane follows the acceleration notation of Figure 1.3.3. The centripetal force FC gives the centripetal acceleration that causes path curvature. The tangential force FT controls the acceleration along the path. Figure 1.4.1(a) shows the free-body diagram of the vehicle in the ground plane, viewed in the XYZ inertial coordinate axes. The free-body diagram shows the chosen free body with the relevant forces that act on it. As a result of the net forces in Figure 1.4.1(a) the vehicle experiences accelerations AT and AC according to F = mA in the inertial XYZ system. For example, the equation of motion perpendicular to the path is If we now view the vehicle in a non-inertial coordinate system, having an acceleration relative to XYZ, the measured vehicle acceleration in this system will be different. Thus the acceleration calculated from F = mA will be wrong \u2013 Newton's second law fails in an accelerating coordinate system. This difficulty may be overcome by \"adjusting\" the free-body diagram, by adding compensation forces, or fictitious forces or d'Alembert forces as they are sometimes known, to bring the value of F into agreement with the measured mA in the accelerating coordinate system. The value of the compensation force 14 Tires, Suspension and Handling needed equals the mass of the body times the acceleration of the coordinate system seen in non-accelerating coordinate axes. The compensation force must be added to the free-body diagram acting in the opposite direction to the true acceleration of the free body. This method is shown applied in Figure 1.4.1(b) for the special case of the body-fixed axes. The true centripetal acceleration requires that we add the force mAC opposing the true acceleration. Similarly mAT is added. Because xyz is a body-fixed system, the vehicle has no acceleration in this system. From this freebody diagram the equation of motion perpendicular to the path is because there is no acceleration of the vehicle in the vehicle-fixed axes. Comparing this with the equation from the XYZ system free body, we see it to be correct: the acceleration in inertial axes is AC = FC/m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure2.25-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure2.25-1.png",
        "caption": "Fig. 2.25 Incidence perturbation on advancing and retreating blades during encounter with vertical gust",
        "texts": [
            " Prior to the deliberate design of fixed-wing aircraft with negative static margins to improve performance, fundamental configuration, and layout parameters were defined to achieve a positive static margin. Most helicopters are inherently unstable in pitch, and very little can be achieved with layout and configuration parameters to change this, other than through the stabilizing effect of a large tailplane at high speed (e.g. UH-60). When the rotor is subjected to a positive incidence change in forward flight, the advancing blade experiences a greater lift increment than does the retreating blade (see Figure 2.25). The 90\u2218 phase shift in response means that the rotor disc flaps back and cones up and hence applies a positive pitching moment to the aircraft. The rotor contribution to Mw will tend to increase with forward speed; the contributions from the fuselage and horizontal stabiliser will also increase with airspeed but tend to cancel each other, leaving the rotor contribution as the primary contribution. Figure 2.26 illustrates the variation in Mw for the three baseline aircraft in forward flight. The effect of the hingeless rotors on Mw is quite striking, leading to large destabilizing moments at high speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001001_1.3453357-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001001_1.3453357-Figure3-1.png",
        "caption": "Fig. 3 Exaggerated view of roller-race interaction",
        "texts": [
            " This geo metrical interaction will define the elastic deflection, if a contact exists, which in turn will give the.normal contact load, using a given load-deflection relationship. Once the contact geometry and load are determined, the local slip velocities in the contact zone may be de termined from the prescribed velocities of the roller and race. A suitable traction model for a given lubricant and operating conditions is then used to compute the tractive force. A discussion of all these factors is the objective of this section. Geometrical Considerations. Fig. 3 schematically described an exaggerated view of the geometrical interactions between the roller and a race. For simplicity, the diagram is drawn in the x-z plane and Y axis is normal to the plane of the diagram. The position vector rr locates the mass center of the race, RM, relative to the inertial frame (X, Y, Z). Vector rrg locates the race geometric center, Ra, relative to the mass center and vector rge locates the center of race land RI, relative to the race geometric center, Ra. Similarly the mass center of the roller EM is located by rb relative to the inertial frame and rbg locates the roller relative to the mass center",
            " The vectors rrg and rbg will generally be prescribed, respectively, in the race fixed frame (x, y, z) and the roller fixed frame (x, ;y, z). Also, the relevant transfor mations will be: Transformation from inertial to race frame: [Tir(l1r, (Jr, 'Yr)] Transformation from inertial to roller frame: [Tib(l1b, (Jb, 'Yb)] In addition to the above it will be convenient to define an azimuth frame (xa, Ya, za) such that Za is parallel to the radial component of Journal of lubrication Technology rb, Xa is parallel to the inertial X axis and Ya is determined by the right-hand screw rule. Since the diagram in Fig. 3 is drawn in the x-z plane, this coordinate frame is not shown in the figure. However, the transformation will depend only on the race azimuth angle \\{t, and it may be defined as Transformation from inertial to roller azimuth frame: [Tia(\\{t, 0, 0)] In order to make the entire analysis applicable to both the outer and inner race contacts, it will be convenient to introduce a trans formation from the azimuth to contact frame. Transformation from azimuth to contact frame: [Tae (0, IX, 0)] where IX = 0 for outer race and 1r for inner race",
            " For cylindrical rollers this locus will be a circle and the position vector locating 0, with respect to the roller geometric center in roller frame, is given as It will be necessary to write re in the race frame, and ultimately in the flange frame, and, hence, we recall the transformation from the roller to race frame from the preceding section. (30) Also, a vector rbrg locating the roller geometric center with respect to the race geometric center can be written in terms of the various vectors introduced in Fig. 3 in the preceding section. Now for any selected value of </> in (29), the race azimuth angle>/; is defined such that the vector when written in the race azimuth frame has only X and Z components. (29) Hence, where </> is just angular coordinate about the X axis in the roller\u00b7 fixed frame. OUTER RACE /(]) \u00ae\\ \\@ 0/ 'NNER RACE z. x' z. z\u00b7 xa4-____ -,~~----__ x' 298 / VOL.101,JULY 1979 and (32) where It should be remembered the r er locates the roller corner curvature center with respect to the race geometric center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003401_j.oceaneng.2015.10.038-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003401_j.oceaneng.2015.10.038-Figure1-1.png",
        "caption": "Fig. 1. Definition of coordinates.",
        "texts": [
            " Then, the mathematical model of an underactuated ship moving in a horizontal plane can be described as (Fossen, 2011) _x \u00bc u cos \u00f0\u03c8 \u00de v sin \u00f0\u03c8 \u00de; _y \u00bc u sin \u00f0\u03c8 \u00de\u00fev cos \u00f0\u03c8 \u00de; _\u03c8 \u00bc r; _u \u00bcm22 m11 vr\u00fe f 1\u00f0u\u00de\u00fe 1 m11 \u03c4u\u00fe 1 m11 \u00f0 cos \u00f0\u03c8 \u00def d1\u00fe sin \u00f0\u03c8 \u00def d2\u00de; _v \u00bc m11 m22 ur\u00fe f 2\u00f0v\u00de\u00fe 1 m22 \u00f0 sin \u00f0\u03c8 \u00def d1\u00fe cos \u00f0\u03c8 \u00def d2\u00de; _r \u00bcm11 m22 m33 uv\u00fe f 3\u00f0r\u00de\u00fe 1 m33 \u03c4r\u00fe 1 m33 \u03c4d3; \u00f04\u00de where (x,y) denote the (surge, sway) displacements of the center of mass, and \u03c8 denotes the yaw angle of the ship coordinated in the earth-fixed frame OEXEYE , see Fig. 1; \u00f0u; v; r\u00de denote the surge, sway, and yaw velocities of the ship coordinated in the body-fixed frame ObXbYb; \u00f0m11;m22\u00de denote the masses including added masses in the surge and sway axes; m33 denotes the inertia including added inertia in the yaw axis; the damping functions f 1\u00f0u\u00de, f 2\u00f0v\u00de and f 3\u00f0r\u00de are f 1\u00f0u\u00de \u00bc du1u m11 1 m11 Xn i \u00bc 1 du;2iu2i tanh u \u03f50 \u00fedu;2i\u00fe1u2i\u00fe1 ; f 2\u00f0v\u00de \u00bc dv1 m22 v 1 m22 Xn i \u00bc 1 dv;2iv 2i tanh v \u03f50 \u00fedv;2i\u00fe1v 2i\u00fe1 ; f 3\u00f0r\u00de \u00bc dr1 m33 r 1 m33 Xn i \u00bc 2 dr;2ir2itanh r \u03f50 \u00fedr;2i\u00fe1r2i\u00fe1 ; \u00f05\u00de where nZ1 is an integer, dui, dvi and dri with i\u00bc 1;\u2026 denote the damping coefficients in the surge, sway, and yaw axes, we use tanh\u00f0 =\u03f50\u00de with \u03f50 being a small positive constant to smoothly approximate j j ",
            " globally asymptotically stable in probability if for all \u03f540 there exists a class KL function \u03b2\u00f0 ; \u00de such that PfJx\u00f0t\u00deJr\u03b2\u00f0Jx\u00f0t0\u00deJ ; t t0\u00degZ1 \u03f5; \u00f019\u00de for all tZt0Z0 and x\u00f0t0\u00deARn\u29f9f0g. Theorem 3.1 (Krstic and Deng, 1998). If there exist a C2 function V\u00f0x\u00de, and class K1 functions \u03b31 and \u03b32 such that \u03b31\u00f0JxJ \u00derV\u00f0x\u00der\u03b32\u00f0JxJ \u00de; LV\u00f0x\u00de \u00bc \u2202V \u00f0x\u00de \u2202x f \u00f0x; t\u00de\u00fe1 2 Tr \u0394T \u00f0t\u00deGT \u00f0x; t\u00de\u2202 2V\u00f0x\u00de \u2202x2 G\u00f0x; t\u00de\u0394\u00f0t\u00de r W\u00f0x\u00de; \u00f020\u00de where W : Rn-R is continuous and nonnegative, then there exists a unique strong solution of (14), and the equilibrium x 0 is globally stable in probability and Pflimt-1W\u00f0x\u00f0t\u00de\u00de \u00bc 0g \u00bc 1 8x\u00f0t0\u00deARn. Referring to Fig. 1 where the coordinate frame OdXdYd is attached to the path with the OdXd-axis being tangent to the path, we can see that the ship will be on the path if the errors \u00f0xe; ye\u00de are zero (to be guaranteed by the controls \u03c4u and \u03c4r to be designed later). As such, the errors \u00f0xe; ye\u00de are given by xe ye \" # \u00bc cos \u00f0\u03c8d\u00de sin \u00f0\u03c8d\u00de sin \u00f0\u03c8d\u00de cos \u00f0\u03c8d\u00de \" # x xd y yd \" # ; \u00f021\u00de where \u03c8d is the angle between OdXd and OEXe axes, i.e., \u03c8d \u00bc arctan\u00f0y0d=x0d\u00de: \u00f022\u00de Applying It\u00f4's formula (15) to (21) along the solutions of (8) results in dxe \u00bc \u00f0u cos \u00f0\u03c8 \u03c8d\u00de v sin \u00f0\u03c8 \u03c8d\u00de un d _s\u00feyer n d _s\u00de dt; dye \u00bc \u00f0u sin \u00f0\u03c8 \u03c8d\u00de\u00fev cos \u00f0\u03c8 \u03c8d\u00de xer n d _s\u00de dt; d\u03c8 \u00bc r dt; du\u00bc m22 m11 vr\u00fe f 1\u00f0u\u00de\u00fe \u03c4u m11 \u00fe 1 m11 \u00f0 cos \u00f0\u03c8 \u00de\u03b81\u00fe sin \u00f0\u03c8 \u00de\u03b82\u00de dt \u00fe 1 m11 \u00f0 cos \u00f0\u03c8 \u00de\u03941 dw1\u00fe sin \u00f0\u03c8 \u00de\u03942 dw2\u00de; dv\u00bc m11 m22 ur\u00fe f 2\u00f0v\u00de\u00fe 1 m22 \u00f0 sin \u00f0\u03c8 \u00de\u03b81\u00fe cos \u00f0\u03c8 \u00de\u03b82\u00de dt \u00fe 1 m22 \u00f0 sin \u00f0\u03c8 \u00de\u03941 dw1\u00fe cos \u00f0\u03c8 \u00de\u03942 dw2\u00de; dr\u00bc m11 m22 m33 uv\u00fe f 3\u00f0r\u00de\u00fe \u03c4r m33 \u00fe \u03b83 m33 dt\u00fe \u03943 m33 dw3; \u00f023\u00de where un d \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x02d \u00fey02d q ; rnd \u00bc x0dy \u2033 d x\u2033dy 0 d x02d \u00fey02d : \u00f024\u00de It can be now seen that the error system (23) is of a cascade structure, which suggests that we design the controls \u03c4u and \u03c4r in three steps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure4.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure4.2-1.png",
        "caption": "Figure 4.2.1. Kennedy\u2013Arronhold theorem of co-linear centros.",
        "texts": [
            " They are said to meet at infinity (at either side), and this is where the centro is located. This does not cause any practical analytic problems because lines constructed from the centro are simply parallel to the locating radii. In many practical cases of connected components, the centro location is obvious without formal construction of radii. This is the case, for example, for a radius rod where the rod pivot itself defines the centro for the rod motion relative to the base member. A property that we shall require in the investigation of roll centers is illustrated in Figure 4.2.1; the centros for the three possible pairs of a group of three objects lie on a straight line. This is known as the Kennedy\u2013Arronhold theorem. In this example AB is pivoted on BC, which is pivoted on CDE. Therefore B is the centro for AB with BC, and C is the centro for BC with CDE. Considering motion relative to link AB, evidently C can move only perpendicularly to the radial line BC. Considering the motion of CDE relative to C, the point E must be moving perpendicularly to the radial line CE",
            " In two-dimensions, the connection of a pair of objects can be classified as either a sliding joint or a rotating joint. In practice a sliding joint is usually straight. Relative to a fixed member, a slider has one degree of freedom, i.e., its relative position can be specified by a single parameter. The pivoting link also has one degree of freedom (1-dof), but in rotation the relative position is speci- Suspension Components 185 fied by a single angle. These elements can be joined serially to allow two degrees of freedom relative to the base member (Figure 4.2.2) where the trunnion (c or d) corresponds closely to the function of a typical suspension strut. The links with two degrees of freedom (2-dof) require two parameters to specify their positions relative to the hatched members; e.g., in (b) two angles, in (d) one angle plus the extension. 4.3 Straight-Line Mechanisms It is often desirable to provide a straight motion path for some point of a suspension member, e.g., for lateral location of an axle, and there are several practical ways to achieve this"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002143_celc.201402141-Figure22-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002143_celc.201402141-Figure22-1.png",
        "caption": "Figure 22. Scheme of Y-based fuel cell operating under a co-laminar parallel stream of fuel and oxidant electrolytes. The cathode is parallel to the oxidant stream and the anode is parallel to the fuel stream. This scheme shows the diffusion zone in which the redox reaction occurs. Reprinted from Ref. [197] with permission from InTech.",
        "texts": [
            "[193] Microfluidic FCs are also called laminar-flow-based FCs or membrane-less FCs that work on a microfluidic chip. These devices show promise in the power sources field[194] and can provide an improvement in power density, which increases with reactant flow rate and a decreasing separating electrolyte flow rate.[155] Another important characteristic of microfluidic FCs in terms of improvements in power density is the surface-tovolume ratio, which is inversely proportional to its length, because the electrochemical reactions are surface based.[195] Figure 22 shows a schematic of a microfluidic FC Y-shaped microchannel that operates by the microscale co-laminar parallel streaming of fuel and oxidant electrolytes.[29, 196] Microfluidic BFCs utilise both laminar flow characteristics and biological enzyme strategies. Very few microfluidic BFCs have been reported because of the difficulties in appropriately immobilising the enzyme in the microchannel; furthermore, enzymes are not compatible with lithography processes.[198] Three methods have been reported for microfluidic BFC development: enzymes in solution,[199] enzymes immobilised by electrostatic interactions[200] and the newest method that utilises covalently bound enzymes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.6-1.png",
        "caption": "FIGURE 2.6. Corner P and the slab at first, second, third, and final positions.",
        "texts": [
            "5 after 30 deg rotation about the Z-axis, followed by 30 deg about the Xaxis, and then 90 deg about the Y -axis can be found by first multiplying QZ,30 by [5, 30, 10]T to get the new global position after first rotation\u23a1\u23a3 X2 Y2 Z2 \u23a4\u23a6 = \u23a1\u23a3 cos 30 \u2212 sin 30 0 sin 30 cos 30 0 0 0 1 \u23a4\u23a6\u23a1\u23a3 5 30 10 \u23a4\u23a6 = \u23a1\u23a3 \u221210.6828.48 10.0 \u23a4\u23a6 (2.23) and then multiplying QX,30 and [\u221210.68, 28.48, 10.0]T to get the position of P after the second rotation\u23a1\u23a3 X3 Y3 Z3 \u23a4\u23a6 = \u23a1\u23a3 1 0 0 0 cos 30 \u2212 sin 30 0 sin 30 cos 30 \u23a4\u23a6\u23a1\u23a3 \u221210.6828.48 10.0 \u23a4\u23a6 = \u23a1\u23a3 \u221210.6819.66 22.9 \u23a4\u23a6 (2.24) and finally multiplying QY,90 and [\u221210.68, 19.66, 22.9]T to get the final position of P after the third rotation. The slab and the point P in first, second, 38 2. Rotation Kinematics third, and fourth positions are shown in Figure 2.6.\u23a1\u23a3 X4 Y4 Z4 \u23a4\u23a6 = \u23a1\u23a3 cos 90 0 sin 90 0 1 0 \u2212 sin 90 0 cos 90 \u23a4\u23a6\u23a1\u23a3 \u221210.6819.66 22.9 \u23a4\u23a6 = \u23a1\u23a3 22.90 19.66 10.68 \u23a4\u23a6 (2.25) Example 4 Time dependent global rotation. Consider a rigid body B that is continuously turning about the Y -axis of G at a rate of 0.3 rad/ s. The rotation transformation matrix of the body is: GQB = \u23a1\u23a3 cos 0.3t 0 sin 0.3t 0 1 0 \u2212 sin 0.3t 0 cos 0.3t \u23a4\u23a6 (2.26) Any point of B will move on a circle with radius R = \u221a X2 + Z2 parallel to (X,Z)-plane.\u23a1\u23a3 X Y Z \u23a4\u23a6 = \u23a1\u23a3 cos 0.3t 0 sin 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002364_s11370-020-00311-0-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002364_s11370-020-00311-0-Figure1-1.png",
        "caption": "Fig. 1 Net magnetic forces and torques exerted on the magnetized objects under a uniform and b gradient external magnetic fields. Reproduced with permission [60]. Copyright 2012, Pearson Education",
        "texts": [
            " In addition, the internal magnetization of the material, which slightly varies across the body in reality, can bemodeled to be constant throughout themagnetized object, and the above force and torque equations can be simplified in terms of the net magnetic momentM (A m2) of the body, which is the product of the average internal magnetization and the volume of the body as below: Fm (M \u00b7 \u2207)B (4) The governing equations clearly indicate that the magnetic force is directly proportional to the gradient of the external magnetic field, and the magnetic torque is the crossproduct of the two vectors: net magnetic moment vector and the magnetic flux density vector of the magnetized object. The magnetic force carries the object toward the region of stronger field strength. Rotational torques are developed between the external magnetic field and the magnetized object when the magnetic moment and the external field direction are misaligned. The magnetic torques tend to align the magnetic moment vectors of the object in the direction of the magnetic field (Fig. 1) [60]. Applying this principle, magnetic catheters and guidewires can be steered by an external magnetic field generated from a set of electromagnets or permanents magnets (Fig. 2). Although they often experience both the magnetic force Fm and torque Tm from Eqs. (1) and (2) when placed in a magnetic field as the gradients of the magnetic field are rarely zero, it is the magnetic torque that plays the greater role in steering due to its ability to align the direction of the magnetic moment of the magnetic component with the direction of the applied field"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003454_tnnls.2016.2529843-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003454_tnnls.2016.2529843-Figure1-1.png",
        "caption": "Fig. 1. Pendulum.",
        "texts": [
            " For this situation, using the tracking controller proposed in this paper, the transient tracking error can be bounded by an explicit function of design parameters and input saturation error. Therefore, while the tracking error may not converge to an arbitrarily small neighborhood of zero, our proposed control scheme allows designers to obtain the closed-loop behavior by tuning design parameters in an explicit way. V. SIMULATION STUDY In this section, to illustrate the above methodology on the following example, we consider a pendulum shown in Fig. 1 similar to [35, Ch. 1]. The equation of its motion can be written in the tangential direction as ml \u03b8\u0308 = \u2212mg sin \u03b8 \u2212 kl \u03b8\u0307 + T l + d (61) where \u03b8 denotes the angle subtended by the rod and the vertical axis through the pivot point, m is the mass of the bob, k is the coefficient of friction, g is the acceleration due to gravity, l is the length of the rod, T is a torque applied to the pendulum, and d = sin(\u03b8\u0307 ) is the disturbance to the pendulum dynamic. To obtain a state model for the pendulum, we take the state variables as x1 = \u03b8 and x2 = \u03b8\u0307 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002342_j.jsv.2011.03.031-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002342_j.jsv.2011.03.031-Figure2-1.png",
        "caption": "Fig. 2. Positions of race and balls centres and deflection of the j-th ball race contact.",
        "texts": [
            " The outer ring of the bearing is supported by a flexible housing. The housing can have asymmetric stiffness properties. This effect can be described by springs with different stiffness that are connecting nodes of curved beam elements to the supporting structure or with a finite-element model of the housing. In the mathematical modelling, the ball bearing is considered as a spring-mass system, where the rolling elements act as nonlinear contact springs and the outer race is a deformable body, as shown in Fig. 2. Lagrange equations are applied to derive the equations of motion of the bearing model. Using the Lagrange equations it is necessary to calculate the total potential and kinetic energy of the system. In order to calculate the potential energy of the contact deformation, first the contact deformation of the j-th ball at the inner and outer races has to be calculated. Since the outer race is not fixed and is deformable in the radial direction, the inner and outer contact deformations are expressed as [14] di,j \u00bc r\u00ferb wj, (1) do,j \u00bc \u00f0rj\u00ferb\u00de R\u00f0yj\u00de: (2) The variable yj defines the angular position of the j-th ball centre with respect to the centre of the outer race xo and yo, r is the radius of the inner race, rj is the radial position of the j-th ball, rb is the radius of the ball, xi and yi are the positions of the inner race, and the position of the centre of the ball from the inner race wj is obtained from xi\u00fewjcosywj \u00bc xo\u00ferjcosyj, (3) yi\u00fewjsinywj \u00bc yo\u00ferjsinyj (4) thus, wj \u00bc \u00f0\u00f0xo xi\u00de 2 \u00fer2 j \u00fe2rj\u00f0xo xi\u00decos\u00f0yj\u00de\u00fe2rj\u00f0yo yi\u00desin\u00f0yj\u00de\u00fe\u00f0yo yi\u00de 2 \u00de 2: (5) Since the outer ring in the proposed model is deformable, the local radius of the outer race is R\u00f0yj\u00de \u00bc R0\u00feNe j d e, (6) where R0 is the radius of the nondeformed outer race, Nj e is the vector of the interpolation functions evaluated at the position in the element where the contact occurs and de is the vector of the nodal displacements for the element"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003221_j.mechmachtheory.2019.103670-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003221_j.mechmachtheory.2019.103670-Figure2-1.png",
        "caption": "Fig. 2. 3D model of herringbone gear reducer.",
        "texts": [
            " Transmission theory of gear train Figure 1 shows the structure diagram of the HPGT, where the torque is transmitting from sun gear to carrier through planet gears. The HPGT is mainly composed of an input shaft connected to the motor, a herringbone sun gear, N herringbone planet gears, a carrier, a herringbone ring gear and an output shaft connected to the load. The herringbone sun gear can float radially and the herringbone planet gears are supported by a plain bearing mounted on the carrier. Figure 2 shows the 3D model of HPGT, where carrier is omitted in order to show the inner structure of reducer better. All components of the system are regarded as rigid bodies, Figure 3 shows the schematic diagram of the planetary gear transmission dynamics model where considering the time-varying meshing stiffness, meshing damping and support stiffness. In addition, it is assumed that the tooth meshing deformation is represented by an equivalent spring and bearing along the meshing line, and these identical planet gears are evenly distributed around the sun gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure23.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure23.7-1.png",
        "caption": "Figure 23.7 Cut edges of a set S separating the set of processors and fusion center.",
        "texts": [
            "21) and ensuring that at least one processor is selected,\u2211 j\u2282c z(j, c) \u2265 1, \u2200c \u2208 C. We now need a constraint on the aggregation subgraph to ensure that the sum of the potential functions is delivered to the fusion center, and, hence, the constraint in (23.17) is satisfied. To this end, we define that A separates B if A \u2229 B = \u2205 and A \u2229 B = B. We consider all sets S \u2282 V separating the union of the set of processors and the fusion center. A cut edge of set S is one that has exactly one endpoint in S. As illustrated in Figure 23.7, since all the values at the processors contained within S can be summed up to a single packet, for the information to flow out of S (or into S), at least one cut edge of S is needed. Hence, we write the constraint that \u2211 i\u2208S,j /\u2208S y(i, j) \u2265 1, \u2200S \u2282 V separating {\u22c3 c\u2208C Proc(c) \u22c3 v0 } . We now have the integer program (IP) 1 2 min y,z \u2211 i,j\u2208V [ I (\u2211 c:i\u2282c z(j, c) \u2265 1 ) + y(i, j) ] C(i, j) (IP-1), (23.20) s.t. \u2211 j\u2282c z(j, c) \u2265 1, \u2200c \u2208 C, let Proc(c):={j : z(j, c) = 1}, (23.21)\u2211 i\u2208S,j /\u2208S y(i, j) \u2265 1, \u2200S \u2282 V separating {\u22c3 c\u2208C Proc(c) \u22c3 v0 } , (23",
            " Given a set L \u2282 V of terminals, a Steiner tree (ST) is the tree T \u2282 G of minimum total edge weight such that T includes all vertices in L. Finding the Steiner tree is NP-hard, and there has been extensive work on finding approximation algorithms. A 0\u20131 integer program to find the Steiner tree can be written as min y 1 2 \u2211 i,j\u2208V y(i, j)C(i, j), (23.26) s.t. \u2211 i\u2208S,j /\u2208S y(i, j) \u2265 1,\u2200S \u2282 V separating L, y(i, j) \u2208 {0, 1}, (23.27) where we say that A separates B if A \u2229 B = \u2205 and A \u2229 B = B. This condition ensures that all the terminals are connected, as illustrated in Figure 23.7. 738 ROUTING FOR STATISTICAL INFERENCE IN SENSOR NETWORKS Require: V = {v0, . . . , v|V |\u22121}, v0: Fusion center, C = {c0, . . . , c|C|\u22121}: maximal cliques of MRF, 1: Gc = Metric closure of comm. graph, C = Link costs in Gc, 2: ST(G,L) = \u03b4-approx. Steiner tree on G, terminal set L 3: G\u2032, Vc \u2190 Map(Gc; C, C) A simple MST heuristic approximates the Steiner tree over G and terminal set L with the minimum spanning tree spanning the set L, over the metric closure of G. The MST heuristic has an approximation bound of 2 [39]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001079_9780470487068-Figure23.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001079_9780470487068-Figure23.4-1.png",
        "caption": "Figure 23.4 Routing to designated fusion center is represented through a digraph. Each arc represents the routing path of one packet, carrying one real number.",
        "texts": [
            "12) It is easily seen that the LLR can be expressed as the sum of potentials of an \u201ceffective\u201d Markov random field \u03d2 = {Gd, C, \u03c6} specified as follows: The effective dependency graph Gd = (V , Ed), has the edge set Ed = E0 \u222a E1; the effective clique set is C = C0 \u222a C1, with only the resulting maximal cliques retained; the effective potential functions \u03c6c are given by \u03c6c(Yc):= \u2211 a\u2208C1,a\u2282c \u03c81(Ya) \u2212 \u2211 b\u2208C0,b\u2282c \u03c80(Yb), \u2200 c \u2208 C. (23.13) Therefore, the LLR has a succinct form, which will be used in the rest of this chapter: LLR(YV ;\u03d2) = \u2211 c\u2208C \u03c6c(Yc). (23.14) By optimal routing for inference, we mean the fusion scheme that minimizes the total costs of routing under the constraint that the likelihood function in (23.14) is delivered to the fusion center (Fig. 23.4). Such a scheme involves computing the likelihood function consisting of clique potential functions, each depending only on the measurements in the clique. Hence, these clique potential functions can be computed independently at various nodes. To exploit the Markovian structure of the underlying hypotheses, we consider a class of data fusion schemes that perform local processing within the cliques of the MRF. Specifically, an aggregation scheme involves the following considerations, 732 ROUTING FOR STATISTICAL INFERENCE IN SENSOR NETWORKS namely each clique potential is assigned a computation site or a processor; measurements of the clique members are then transported to its processor to enable computation of the clique potentials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure1.13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure1.13-1.png",
        "caption": "Fig. 1.13",
        "texts": [
            " In this section we will restrict ourselves to statically determinate systems where we can first calculate the forces in the bars with the aid of the equilibrium conditions. Subsequently, the stresses in the bars and the elongations are determined. Finally, the displacements of arbitrary points of the structure can be found. Since it is assumed that the elongations are small as compared with the lengths of the bars, we can apply the equilibrium conditions to the undeformed system. As an illustrative example let us consider the truss in Fig. 1.13a. Both bars have the axial rigidity EA. We want to determine the displacement of pin C due to the applied force F . First we calculate the forces S1 and S2 in the bars. The equilibrium conditions, applied to the free-body diagram (Fig. 1.13b), yield \u2191 : S2 sin\u03b1\u2212 F = 0 \u2190 : S1 + S2 cos\u03b1 = 0 \u2192 S1 = \u2212 F tan\u03b1 , S2 = F sin\u03b1 . According to (1.17) the elongations \u0394li of the bars are given by \u0394l1 = S1 l1 EA = \u2212 F l EA 1 tan\u03b1 , \u0394l2 = S2 l2 EA = F l EA 1 sin\u03b1 cos\u03b1 . Bar 1 becomes shorter (compression) and bar 2 becomes longer (tension). The new position C\u2032 of pin C can be found as follows. We consider the bars to be disconnected at C. Then the system becomes movable: bar 1 can rotate about point A; bar 2 can rotate about point B. The free end points of the bars then move along circular paths with radii l1 +\u0394l1 and l2 +\u0394l2, respectively. Point C\u2032 is located at the point of intersection of these arcs of circles (Fig. 1.13c). The elongations are small as compared with the lengths of the bars. Therefore, within a good approximation the arcs of the circles can be replaced by their tangents. This leads to the displacement diagram as shown in Fig. 1.13d. If this diagram is drawn to scale, the displacement of pin C can directly be taken from it. We want to apply a \u201cgraphic-analytical\u201d solution. It suffices then to draw a sketch of the diagram. Applying trigonometric relations we obtain the horizontal and the vertical components of the 1.5 Statically Determinate Systems of Bars 31 displacement: u = |\u0394l1| = F l EA 1 tan\u03b1 , v = \u0394l2 sin\u03b1 + u tan\u03b1 = F l EA 1 + cos3 \u03b1 sin2 \u03b1 cos\u03b1 . (1.21) To determine the displacement of a pin of a truss with the aid of a displacement diagram is usually quite cumbersome and can be recommended only if the truss has very few members"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002322_j.oceaneng.2020.108179-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002322_j.oceaneng.2020.108179-Figure1-1.png",
        "caption": "Fig. 1. Fully actuated AUV with both inertial and body-fixed reference frames.",
        "texts": [
            " (6) The above differential inequality has the same structure as in (1) of Proposition 1 and the settling time can be obtained as \ud835\udc47 \u2264 (\ud835\udefd \u2212 \ud835\udf032) (\ud835\udefc \u2212 \ud835\udf031)2(\ud835\udc5d1 \u2212 \ud835\udc5d2) ln ( \ud835\udefd \u2212 \ud835\udf032 (\ud835\udefc \u2212 \ud835\udf031)\ud835\udc490\ud835\udc5d1\u2212\ud835\udc5d2 + (\ud835\udefd \u2212 \ud835\udf032) ) + \ud835\udc49 \ud835\udc5d1\u2212\ud835\udc5d2 0 (\ud835\udefc \u2212 \ud835\udf031)(\ud835\udc5d1 \u2212 \ud835\udc5d2) . (7) We can conclude that for all the subsequent time the states \ud835\udc65(\ud835\udc61) of the ystem (1) do not escape the stable region \ud835\udc44, which completes the roof. . AUV modeling and problem formulation .1. AUV kinematics The Omni Directional Intelligent Navigator (ODIN) is a spherical UV, as illustrated in Fig. 1, which is equipped with eight thrusters nd can perform the 3D spatial movement. The motion of AUV in threeimensional space can be described in the inertial frame for navigation nd body-fixed frame. The velocity transformation relating the two oordinate systems can be expressed as (Fossen, 2011) ?\u0307? = \ud835\udc45(\ud835\udf02)\ud835\udf08, (8) here \ud835\udf02 = [\ud835\udc65, \ud835\udc66, \ud835\udc67, \ud835\udf19, \ud835\udf03, \ud835\udf13]\ud835\udc47 represents position and orientation of ehicle in inertial frame and \ud835\udf08 = [\ud835\udc62, \ud835\udc63,\ud835\udc64, \ud835\udc5d, \ud835\udc5e, \ud835\udc5f]\ud835\udc47 represent linear and ngular velocities in body-fixed frame. The rotation matrix \ud835\udc45(\ud835\udf02) that escribes the transformation between the inertial frame and body-fixed rame which is related through the functions of Euler angles is defined s (\ud835\udf02) = [ \ud835\udc451(\ud835\udf02) 03 03 \ud835\udc452(\ud835\udf02) ] , (9) here \ud835\udc451(\ud835\udf02) and \ud835\udc452(\ud835\udf02) are defined as follows: \ud835\udc451(\ud835\udf02) = \u23a1 \u23a2 \u23a2 \u23a3 \ud835\udc50\ud835\udf13\ud835\udc50\ud835\udf03 \u2212\ud835\udc60\ud835\udf13\ud835\udc50\ud835\udf19 + \ud835\udc50\ud835\udf13\ud835\udc60\ud835\udf03\ud835\udc60\ud835\udf19 \ud835\udc60\ud835\udf13\ud835\udc60\ud835\udf19 + \ud835\udc50\ud835\udf13\ud835\udc50\ud835\udf19\ud835\udc60\ud835\udf03 \ud835\udc60\ud835\udf13\ud835\udc50\ud835\udf03 \ud835\udc50\ud835\udf13\ud835\udc50\ud835\udf19 + \ud835\udc60\ud835\udf13\ud835\udc60\ud835\udf03\ud835\udc60\ud835\udf19 \u2212\ud835\udc50\ud835\udf13\ud835\udc60\ud835\udf19 + \ud835\udc60\ud835\udf13\ud835\udc50\ud835\udf19\ud835\udc60\ud835\udf03 \u2212\ud835\udc60\ud835\udf03 \ud835\udc50\ud835\udf03\ud835\udc60\ud835\udf19 \ud835\udc50\ud835\udf03\ud835\udc50\ud835\udf19 \u23a4 \u23a5 \u23a5 \u23a6 , \ud835\udc452(\ud835\udf02) = \u23a1 \u23a2 \u23a2 \u23a3 1 \ud835\udc60\ud835\udf19\ud835\udc61\ud835\udf03 \ud835\udc50\ud835\udf19\ud835\udc61\ud835\udf03 0 \ud835\udc50\ud835\udf19 \u2212\ud835\udc60\ud835\udf19 0 \ud835\udc60\ud835\udf19\u2215\ud835\udc50\ud835\udf03 \ud835\udc50\ud835\udf19\u2215\ud835\udc50\ud835\udf03 \u23a4 \u23a5 \u23a5 \u23a6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002262_j.optlastec.2017.07.034-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002262_j.optlastec.2017.07.034-Figure5-1.png",
        "caption": "Fig. 5. Temperature contour plots during the single-track & multi-layer depositing process when laser irradiates the points P1, P2 and P3. Top view (a, c, e) and longitudinal view (b, d, f).",
        "texts": [
            " When temperature is lower than the solidus temperature TS, the effective thermal conductivity ke can be calculated by the Sih model [27], as the temperature fall into the range of TS to TM (melting temperature), the ke can be calculated by an empirical formula [28]; when the temperature exceeds the TM, the ke is assigned to a constant of 80 W/m K, which takes the fluid flow within the molten pool into account [29], that is: Fig. 4 shows the calculated temperature-dependent thermal conductivity and enthalpy of the material up to the melting temperature. Fig. 5 shows the transient temperature distribution on the top view (Fig. 5a, c, e) and longitudinal view (Fig. 5b, d, f) of the molten pool as laser beam reaches the points P1, P2 and P3 (X = 0.45, Y = 0.195, Z = 0.34, 0.38, 0.42 mm) respectively. The dash line represents the melting temperature (Tm) of 316L stainless steel (1380 C), within which is the molten pool. The isotherm curves of the molten pool are symmetrical in the perpendicular to scanning direction, and the shape looks like an \u2018\u2018egg\u201d, the fore-part of \u2018\u2018egg\u201d are more intense than the rear-part, indicating that temperature gradient in fore-part is much larger than that in rear-part. This can be explained by the change of thermal conductivity as powder transforms from loose to dense state. As the thermal conductivity of powder is much lower than that of the corresponding solid material [30,31], heat in the fore-part of molten pool can not easily conduct to the surrounding materials, resulting in a larger temperature gradient in the fore-part. Besides, Fig. 5a, c, and e also show that the center of molten pool slightly shifts toward back of the laser beam, and the trend becomes more conspicuous as the number of layer increases, this phenomenon can be attributed to the interaction time between laser beam and powder. At a higher scanning speed (100 mm/s), the interaction time can be as short as 0.1 ms, heat can not conduct to the surrounding material sufficiently during this interaction time [32]. When laser irradiates the point P1, the dimensions of molten pool are 134.4 114.8 50.5 lm3 (length width height, see Fig. 5a and b). At point P2, they are 162.3 126.3 56.8 lm3 (see Fig. 5c and d), while at point P3, they become 178.6 134.5 64.2 lm3 (see Fig. 5e and f). Comparing to the point P1, the dimensions of molten pool at point P2 increase by 20.8%, 10% and 12.5%, while at point P3, they increase by 32.9%, 17.2% and 27.2%, respectively. Fig. 6a shows the micrograph of single-track & triple-layer sample, Fig. 6b shows that widths of the three layers from bottom to top are 103, 125 and 140 lm respectively, which agree well with the simulation results. The discrepancy in the width of melting tracks can be attributed to the thermal process during SLM",
            " The slope of curves represents the temperature gradient of the material, and a steep slope means a relatively high temperature gradient. The Tmelting represents the melting temperature of 316L stainless steel (1380 C), it divides the curves into three parts: the melted region, molten pool and unmelted region. The temperature gradient in the melted region L stainless steel as a function of temperature [13]. is much lower than that in the molten pool as it is experiencing the cooling/solidification process. Lengths of the molten pool are 134.4, 162.3 and 178.6 lm, it confirms to the results shown in Fig. 5. In the unmelted region, the temperature almost remains a stable state (almost at room temperature of 25, 46, 57 C). After the laser beam moves away from a specified point on the powder bed, the temperature will drop rapidly. When laser irradiates the point P1, P2 and P3, The temperature at the onset of the scan path are 358, 536 and 646 C, respectively. The DT shown in Fig. 7a indicates that cooling process of the third layer is much slower than that of the first layer. This result also confirms to the increasing dimensions of molten pool",
            " The general trend is that the liquid lifetime and maximum temperature increase with the increasing number of layers, which is consistent with the FE results reported by I.A. Roberts et al. [21]. However, the enhancement tendency are alleviated. Between the 1st and 2nd layers, the increments of liquid time and maximum temperature are 0.49 ms (increasing by 34.3%) and 38 C, while between the 2nd and 3rd layers, they are just 0.23 ms (increasing by 12%) and 27 C. This is because the dimension of molten pool increases as the temperature increases (see Fig. 5), larger dimension means more liquid phase exist in the molten pool. The liquid phase is helpful to improve the metal liquid wetting effect between neighbor layers and thus fills pores effectively [36], thereby reducing the amount of pores in the SLMed parts. Fig. 11 shows the micrographs of cross-section of the samples A and B (Fig. 11a and b are in lower magnification, Fig. 11c\u2013f are in higher magnification). Fig. 12 shows the grain size measured from Fig. 11c\u2013f. It shows that averaged grain size of sample A is 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001759_j.msec.2015.01.023-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001759_j.msec.2015.01.023-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of tensile specimen.",
        "texts": [
            " Microstructural observation was carried out using optical microscope (Axio Vert.A1, ZEISS) and scanning electron microscope (SEM, JSM-6700F). Phase identification was studied by X-ray diffractometer (XRD, D/MAX-2500PC) with CuK\u03b1 radiation. Specimen preparation was firstly mechanically polished, and then etched in HCl for 7 h [14]. Tensile tests were performed on a universal testing machine (MTS E45.105) at room temperature, with an initial strain rate of 2 mm/s. The schematic diagram of tensile specimen is shown in Fig. 2. Fractography were examined by using SEM (SEM, JSM-6700F). Vickers hardness (HV) of the specimenswas also carried out using the hardness tester (HX-1000TM), with a load of 100 gf and a dwell time of 12 s. The density of the samples with the dimension of 10 \u00d7 10 \u00d7 10 mm was measured by applying Archimedes' principle. Electrochemical test was conducted to evaluate the corrosion resistance in the PBS and Hanks solution at 37 \u00b0C. A three-electrode cell was used for the electrochemical measurements. The counter electrode was made of platinum and a saturated calomel electrode (SCE) was used as the reference electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003095_978-3-319-26378-6_15-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003095_978-3-319-26378-6_15-Figure1-1.png",
        "caption": "Fig. 1 Mobile in situ fabrication entails that instead of bringing the work piece to the fixed robotic work cell and referencing the work piece in relation to the robot (left), the robot travels to the worksite and needs to localize itself in relation to the working environment (right)",
        "texts": [
            " 2002) because they are gradually evolving and continuously changing shape during construction, floors are not necessarily flat and there is no guarantee for regular structures in the surroundings, as opposed to prevalent constant conditions in industrial production. Additionally, robots for pre-fabrication are commonly employed at an anchored position within a work cell and work pieces are brought to the stationary unit. Yet, to enable the fabrication of large-scale building structure that exceed the workspace of a fixed robot, the employment of robots on constructions sites requires them to bemobile (Fig. 1). Robots need to be able to travel to the place of production and to move during construction, while still being able to localize themselves with respect to the working environment and fabricate structures accurately in space (Seward 2002; Feng et al. 2014). To take on these challenges, the two ETH Zurich groups Gramazio Kohler Research2 and the Agile & Dexterous Robotics Lab3 are developing an autonomous area-aware mobile robot, called the \u2018In situ Fabricator\u2019 (IF). 1Within this paper, the term \u2018unstructured\u2019 is used to describe the environment of building sites, although, in most cases they can be defined as \u2018semi-structured\u2019, due to partially con-strained and defined conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000123_70.88024-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000123_70.88024-Figure5-1.png",
        "caption": "Fig. 5. The procedure to get the limit curve and wperpo>ition of thc m y - imum velocity curvz.",
        "texts": [
            " t l 1) Using the methods evplained in Section& 111-A -B ,incl C IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 5, NO. 1, FEBRUARY 1989 5 10. 8 . 123 i - 10. e. 12. 5 10. e. r S 45. 1 -45. U:& ' u:3 ' U.\" ' r. (d) S Fig. 7. Simulation resuits. (a) The limiting curves. (b) The limiting curves with superposition of the maximum velocity curve. (c) The complete optimal trajectory. (d) The corresponding optimal torque history. Then, the admissible region for the phase-plane trajectory is under resulting limit curves. The procedure is described graphically in Fig. 5 . The maximum velocity curve is also shown, in order to help understand how the new algorithm differs from the earlier methods. Note that the shaded region in Fig. 5 is inadmissible. This means that once the phase-plane trajectory gets into the shaded region, then later in the trajectory it cannot get out of the region without hitting the maximum velocity curve other than tangentially (in other words, without violating at least one of the actuator bounds). Therefore, the admissible region is under these limit curves, and not merely under the maximum velocity curve used in the earlier methods. 3) The characteristic switching points (points c and e in Fig. 6) have been found in steps 1) and 2 ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003740_tfuzz.2016.2612697-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003740_tfuzz.2016.2612697-Figure2-1.png",
        "caption": "Fig. 2. The underactuated AUV model in plane motion. Body-fixed and Earthfixed reference frames.",
        "texts": [
            "- Implement the neuro-fuzzy identifier using the weights W [i,j] (t) and identification error \u2206id. 4.- Compute the neuro-fuzzy control law using the weights W [i,j] (t), the identification error \u2206id and the tracking error \u2206tr. In this section, the dynamic equations of motion of an AUV equipped with five propellers: port, starboard, 2x horizontal and vertical thrusters are described. The forces and moments of the AUV in three dimensions and two reference frames: Earth-fixed (XE , YE , ZE), and Body-fixed (XB , YB , ZB) are presented in Fig. 2. Considering the motion of the AUV in 6-DOF, the following vector is defined [10]: \u03c5 = [ u, v, w, p, q, r ]> , \u03c4 =[ X, Y, Z, K, M, N ]> where \u03c5 is the velocity vector in the Body-fixed frame; u, v and w denote linear velocities of the AUV; p, q, r are angular velocities; \u03c4 is the vector of forces and moments acting on the AUV in the Body-fixed frame. X , Y , Z are forces in surge, sway and heave direction, respectively; additionally K, M , N denote torsion moments of roll, pitch and yaw, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure15-1.png",
        "caption": "Fig. 15. Test gearbox in power-circulating form gear test rig.",
        "texts": [
            " 12 is FEM results of the maximum surface contact stresses obtained at the same time when FEM calculations are performed. Tooth contact pattern and root strains of a pair of spur gears as shown in Fig. 14 are measured when assembly errors h = 0.42 , / = 0.04 , XE = 2.1 mm and ZE = 0.2 mm are given to the gear shaft A0B0 in Fig. 1. These gears are ground under the accuracy requirement of JIS 1st grade. A so-called power-circulating form gear test rig is used to do the tests at a very low speed (1.65 rpm) under torque T = 294 N m. Fig. 15 is the test gearbox used in the test rig. In Fig. 15, a removable support is used to give AE to the shaft of Gear 1 by changing the position of this support. Fig. 16 is tooth contact pattern measured. Fig. 17 is the tooth contact pattern calculated under the same conditions. In Fig. 17, A is the areas of double pair tooth contact and B is the area of single pair tooth contact. It is found that calculated contact pattern is agreement with the measured one well. Root strains at the compressive side of tooth root are also measured (though tensile strains at the tooth root are more meaningful than the compressive strains for gear bending strength calculation, tensile strains are easily affected by tooth surface friction when lubricant is not enough in the measurement)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.36-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.36-1.png",
        "caption": "Fig. 4.36",
        "texts": [
            " This relative sliding may be prevented if the beams are bonded together by welding, gluing or riveting. This will generate shear stresses in the contact area which have to be supported by the bonding (e.g. the weld seam). F We will now determine the shear stresses in beams with thinwalled cross sections, restricting ourselves to open cross sections. We assume that the shear stresses \u03c4 at a position s of the cross section are constant across the thickness t and that they are parallel to the boundary (Fig. 4.36a). The magnitude and the direction of the shear stresses and the thickness may depend on the coordinate (arc length) s. As in the case of a solid cross section we apply the equilibrium condition to an isolated element of the beam (Fig. 4.36b): \u03c4(s) t(s) dx = \u222b A\u2217 \u2202\u03c3 \u2202x dxdA. With (4.35) we obtain 156 4 Bending of Beams \u03c4(s) = V S(s) I t(s) . (4.39) Here, S(s) = \u222b A\u2217 \u03b6 dA is the first moment of the area A\u2217 with respect to the y-axis. As an example we determine the shear stresses due to a shear force V in the thin-walled cross section shown in Fig. 4.37a. The moment of inertia of the entire cross section (note that t a) is obtained as I = t(2 a)3 12 + 2[a2(a t)] = 8 3 t a3. The first moments of the areas A\u2217 (green areas in the Figs. 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002621_rob.21673-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002621_rob.21673-Figure3-1.png",
        "caption": "Figure 3. Vision system configuration for DRC-HUBO+ and an example of its movement. DRC-HUBO+ has two cameras and one 2D LIDAR sensor installed on its head, allowing it to obtain color images and depth information.",
        "texts": [
            " In SSP, controlling the angle and the angular velocity of the Journal of Field Robotics DOI 10.1002/rob base frame is a more effective method of steadying the robot than controlling the ZMP because the supporting polygon is very narrow relative to the double support phase (DSP), and the measured ZMP rapidly saturates to the edge of the foot when a large disturbance is applied to robot. The performance of the SSP upright controller is represented in Figure 19; ZMP tracks better with the SSP upright controller. As described in Subsection 2.1.2 (Figure 3(a)), the main camera and the LIDAR are mounted together on the same rig, which is rotated by a single motor and enables the sensor system to acquire 3D point data. Through the rotation speed and scope of the motor control, it is possible to adjust the vertical density of the 3D points by trading off the capturing time. The streaming camera is set up on the top-left side of the head guard. This camera, which is different from the rotating camera, is tilted at a fixed 10 degrees. The main purpose of this camera is to deliver the scene of the field to the operators at 10 frames per second (fps)",
            " This image is transmitted first while the LIDAR is scanning, so that the operators can recognize the surrounding environments and reduce the time needed to set the operator guided ROI. When the burst mode is activated, the captured image data is resized to half and compressed to JPEG format with a percentage factor of 95%. Calibration of the sensor system is essential to make the point cloud useful for robot operations. A coordinate system was assigned to each sensor \u2013 three coordinate systems for the camera, laser sensor, and motor \u2013 and the relative pose among them was estimated (see Figure 3). Without loss of generality, the motor\u2019s rotating axis was set as the x-axis of the motor coordinate system and the scanning plane of the 2D laser sensor was set as the x-z plane of the laser coordinate system; these decisions were made so that the laser sensor would scan from \u221245 degrees to 225 degrees (total 270 degrees) of the x-z plane. The intrinsic parameters of the camera are calibrated by a conventional method (Zhang, 2000). To achieve a wide field-of-view, a lens with a short focal length is used with a fish-eye distortion model (Shim et al., 2015); or, other methods (Bouguet, 2004; Kannala & Brandt, 2006; Scaramuzza, Martinelli, & Siegwart, 2006) can also be used to provide precise results. Figure 3(b) shows the coordinate setup of our sensor system. The vision system\u2013centric coordinate is set to a coordinate of the motor, Pm. Calibration between the camera and motor is done by capturing a series of images with various poses of a checkerboard pattern in the motor coordinate system. For each pose of the pattern, 12 images are captured at various motor angles, from \u221230 degrees to 80 degrees, at intervals of 10 degrees. The motor-to-camera transformation, Hmc, and all of the pattern-to-motor transformations, Hn, are optimized using the squared sum of the projection errors of the checkerboard corners, pi , as a cost function: fc(Hmc, H1 \u223c HN, A\u221230 \u223c A80) = \u2211 n \u2211 \u03b8 \u2211 i \u2225\u2225qi \u2212 proj (HmcR\u03b8Hnpi) \u2225\u22252 , where R\u03b8 denotes the rotation of the motor (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001434_0094-114x(80)90021-x-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001434_0094-114x(80)90021-x-Figure6-1.png",
        "caption": "Figure 6.",
        "texts": [
            "2) We have thereby chosen joint axes 1 and 4 to lie in the linkage's plane of symmetry. 271 Rather than attempt to simplify the general 6-bar equations to determine the remaining independent ones for this loop, we consider 'half' of the linkage by replacing joints 5 and 6 by a single revolute, joint 5', which is directed at rightangles to the plane of symmetry and passes through the point of intersection of joints 1 and 4. In order for the substitute 5-bar loop to be mobile, joints 1 and 4 are made cylindric and renamed 1' and 4', respectively. As is clear from Fig. 6, the new linkage will be subject to the dimensional constraints a4,5, = Rs, = as,i, = 0 7r 3~r O/4, 5, ----- - ~ O~5' l ' = - ~ - - . We may now use the 5-bar closure equations for this special C-R-R-C-R- loop to establish relations among 01 - 04 for the original linkage. We clearly must avoid involving r4,, 05,, rv in any equations and, from Fig. 6, we see that ~'+04 z;+Oi 04, - 2 01, = 2 272 Advancing the subscripts in (A5.9) by 4 and 2 yields, respectively, the two following equations. cOvs0/z2 = sO3sO4,s0/23 - c03c04,sa23c0/34 - c04,c0/23sct34 c04,s0/34 = SOvSOS0/23 - CO],CO2Sa23C0/j2- COvC0/23S0/~ 2 Advancing the subscripts in (A5.12) by 2 yields the result - a23(s01,cO2 + cOvsO:0/~2) + RcOt,sat2 - a l : O v + a34sO4, - R3cO4,s0 /34 = O. Alternative equations are available, but the above three are obviously independent of each other and of (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001371_0278364916683443-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001371_0278364916683443-Figure3-1.png",
        "caption": "Fig. 3. Magnetic catheter comprising four flexible, non-magnetic and four rigid, permanent-magnetic segments. The internal states x are parametrized by the station s along the arc length.",
        "texts": [
            " The control inputs for this system are the rate of change of electric current in the electromagnets, which will be stacked into a column vector I\u0307c, and the catheter advancement speed L\u0307c. The output for this system is the position p of the distal end of the catheter. A block diagram overview of the proposed control system is shown in Figure 2. The catheter is modeled as a flexible rod with M magnets along its length, which is parametrized by the station s along the arc length referenced to the proximal end of the catheter. A schematic of the catheter is shown in Figure 3. At any station s, the full local state of the rod is defined by the pose P, which is composed of the position p and orientation quaternion Q, and the internal wrench w, which is composed of the internal force f and internal torque \u03c4 . This state is packed into the 13 \u00d7 1 vector x (s) = \u23a1 \u23a2\u23a2\u23a3 p (s) Q (s) f (s) \u03c4 (s) \u23a4 \u23a5\u23a5\u23a6 (1) with the state at the proximal end identified by x0. By convention, we take the wrench to be positive on the distal side of a cross-section and negative on the proximal side of a cross-section, as shown in Figure 3. The catheter is assumed to be in static equilibrium, and the only external forces and torques acting on the catheter are assumed to arise from gravity, magnetic interactions, and distal and proximal loadings. Since the NdFeB permanent magnets used in the magnetic segments are orders of magnitude stiffer than the material used in the rest of the catheter, we model the catheter as a sequence of flexible and rigid segments. Let there be N segments composing the rod. For any segment i there exists a function Ti( ) that maps this segment\u2019s proximal state xi\u22121 to its distal state xi, given the segment length and the external wrench acting on the segment xi = Ti ( xi\u22121, Li, wext,i ) ",
            " The Jacobian for multiple flexible and rigid segments is obtained by multiplying the segments\u2019 Jacobians together. By convention, we take J1 to denote the Jacobian mapping changes in segment one\u2019s proximal state to changes in segment one\u2019s distal state; we take J1 (\u03c3 ) to be the Jacobian that maps changes in segment one\u2019s proximal state to changes in segment one\u2019s state at inter-segment station \u03c3 ; and we take J, with no subscript, to represent the proximal to distal Jacobian for the entire catheter. For example, the rod depicted in Figure 3 is composed of eight segments that alternate between being flexible or rigid. The resulting Jacobian that maps changes in proximal state to the distal state is given by J = J8J7 \u00b7 \u00b7 \u00b7 J2J1 (27) and the Jacobian that maps changes in the proximal state to some position s along segment four is given by J (s) = J4 (\u03c3 (s)) J3J2J1. (28) Due to the quaternion constraint equation, any resulting Jacobian has a maximum rank of 12. Thus, inversion must be performed with a least-squares method such as the Moore\u2013Penrose pseudoinverse (Horn and Johnson, 1985)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002084_j.cirpj.2010.03.005-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002084_j.cirpj.2010.03.005-Figure8-1.png",
        "caption": "Fig. 8. 3-D CAD volume model of the optical system for high power skin\u2013core SLM applications, lower fibre active, beam deflector cubes visible.",
        "texts": [],
        "surrounding_texts": [
            "As described above, a top hat beam profile is eligible for additive manufacturing techniques especially for large scan line spacing which are inevitable for an increased build rate. Yet, a uniform intensity distribution requires the superposition of several modes over the running length of the fibre core. Furthermore not all rays that enter the fibre core are allowed to propagate (see Fig. 11) [16]. Considering a free wave the phase of the wave front C0A0 concur in all single points. Hence, only waves whose phases concur in each point on the wave front AC can propagate through the waveguide [16]. Since this wave only consists of the incoming and the reflected wave, this constraint is fulfilled only if the phases of two rays differ in a multiple of 2p. Due to the incident-angle-dependant phase shift V the constraint for constructive interference becomes the following transcendent eigenvalue equation: 2 ncdcos\u00f0\u2019km\u00de l \u00bc m\u00feV p (8) where \u2018\u2018nc\u2019\u2019 is the refractive index of the core, \u2018\u2018d\u2019\u2019 is fibre core diameter, \u2018\u2018d\u2019\u2019 is wavelength and \u2018\u2018m\u2019\u2019 is the mode number. With regard to multi-mode fibres the second summand on the right side of the equation can be neglected since its maximum value is 1. Hence, the maximum number of modes mmax occur for the smallest possible angle \u2013 the critical angle for total reflection wg \u2013 which is calculated according to: \u2019g \u00bc arcsin nc ncl (9) where \u2018\u2018ncl\u2019\u2019 is the refractive index of the fibre cladding. The numerical aperture NA is calculated according to: NA \u00bc nc cos\u00f0\u2019g\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 c n2 cl q (10) The combination of Eqs. (8)\u2013(10) leads to the characteristic Vparameter for optical fibres: V \u00bc pd ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 c n2 cl q l (11) The number of modes for cylindrical fibres, N, is finally calculated according to: N \u00bc 4 p2 V2 (12) The probability to achieve a uniformly top hat shaped beam profile increases with the number of modes overlaying in an optical fibre. With regard to the optical setup used for the described prototype machine tool (NA = 0.11, l = 1030 nm) the mode number of the 50 mm fibre is calculated to 114, whereas the mode number of the 200 mm fibre is calculated to 1825. Although the absolute values do not indicate whether the resulting intensity profile is a top hat one or not, it becomes quite obvious that in the case of the smaller fibre core diameter (50 mm) the resulting intensity profile is more likely to be a Gaussian type than the intensity profile of the 200 mm fibre, whereas for the top hat intensity distribution it is vice versa. In summary it can be estimated that the intensity distribution for the manufacturing of the large volume core (where large build rates needs to be achieved) which is done with the 200 mm fibre, is likely to be a top hat one. In contrast, the outer skin is manufactured with the 50 mm fibre, whose intensity profile is more likely to be in between top hat and Gaussian shaped."
        ]
    },
    {
        "image_filename": "designv10_1_0002294_j.ymssp.2014.09.001-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002294_j.ymssp.2014.09.001-Figure1-1.png",
        "caption": "Fig. 1. Dynamic model of a reduction gear system with 6 DOF.",
        "texts": [
            " In the present work, four dynamic models were used to simulate the dynamic response. Inter-tooth friction was introduced in three of the studied models, and the effect of ignoring it was examined, as stated in Section 2.3. For simplicity the one-stage gear system can be modelled without considering the motor and load. This model consists of 6 DOF, is currently applied and was adopted in [5\u201310]. A schematic diagram of the 6 DOF model, which has 3 DOF (one rotational and two translational) for each gear disc, is shown in Fig. 1. The equations of motion for this model can be explained as follows. The equations of motion in the \u2018x\u2019 direction for the pinion and gear are mp \u20acxp \u00bc Kxpxp Cxp _xp\u00feFp \u00f01\u00de mg \u20acxg \u00bc Kxgxg Cxg _xg\u00feFg \u00f02\u00de The equations of motion in the \u2018y\u2019 direction for the pinion and gear are mp \u20acyp \u00bc N Kypyp Cyp _yp \u00f03\u00de mg \u20acyg \u00bcN Kygyg Cyg _yg \u00f04\u00de The equations of motion in the \u2018\u03b8\u2019 direction for the pinion and gear are Ip \u20ac\u03b8p \u00bc rpN\u00feTp\u00feMp \u00f05\u00de Ig \u20ac\u03b8g \u00bc rgN Tg\u00feMg \u00f06\u00de lease cite this article as: O.D. Mohammed, et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003021_j.optlaseng.2019.105950-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003021_j.optlaseng.2019.105950-Figure5-1.png",
        "caption": "Fig. 5. Comparison of experimental and calculated cross sections. Laser power 300 W, powder feed rate 4.479 g/min and scanning speed 3 mm/s.",
        "texts": [
            " Cladding track geometry and experimental validation Fig. 2 shows the simulation and corresponding experimental results f cladding track width and height. The detailed parameters used in he simulation are 300 W, 350 W, 400 W, 450 W for laser power, .135 g/min, 4.479 g/min, 5.823 g/min, 7.167 g/min for powder feed ate, and 3 mm/s, 5 mm/s, 7 mm/s, 9mm/s for scanning speed. It can be een that the simulation results vary periodically with the parameters. n example of direct comparison between experimental and simulated ross sections is shown in Fig. 5 . Except a little deviation, the simulated eometry agrees quite well with the corresponding experimental result. n order to quantify the accuracy of the powder-scale model, the relative rrors between experimental and simulation results are calculated using q. (15) . = \u2223 \ud835\udc3a \ud835\udc52 \u2212 \ud835\udc3a \ud835\udc60 \u2223 \ud835\udc3a \u00d7 100% (15) \ud835\udc52 Fig. 4. Simulation results under different manufacturing parameters: (a) track width, (b) track height. The X axis represents the sequence of each parameter group and the Y axis represents the simulation or experimental results of track width and height under different parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure2.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure2.12-1.png",
        "caption": "FIGURE 2.12. First Euler angle.",
        "texts": [
            "6 Euler Angles The rotation about the Z-axis of the global coordinate is called precession, the rotation about the x-axis of the local coordinate is called nutation, and the rotation about the z-axis of the local coordinate is called spin. The precession-nutation-spin rotation angles are also called Euler angles. Euler angles rotation matrix has many application in rigid body kinematics. To find the Euler angles rotation matrix to go from the global frameG(OXY Z) to the final body frame B(Oxyz), we employ a body frame B0(Ox0y0z0) as shown in Figure 2.12 that before the first rotation coincides with the global frame. Let there be at first a rotation \u03d5 about the z0-axis. Because Z-axis and z0-axis are coincident, we have: B0 r = B0 AG Gr (2.99) B0 AG = Az,\u03d5 = \u23a1\u23a3 cos\u03d5 sin\u03d5 0 \u2212 sin\u03d5 cos\u03d5 0 0 0 1 \u23a4\u23a6 (2.100) Next we consider the B0(Ox0y0z0) frame as a new fixed global frame and introduce a new body frame B00(Ox00y00z00). Before the second rotation, the two frames coincide. Then, we execute a \u03b8 rotation about x00-axis as shown in Figure 2.13. The transformation between B0(Ox0y0z0) and B00(Ox00y00z00) is: B00 r = B00 AB0 B 0 r (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000814_1.2335852-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000814_1.2335852-Figure1-1.png",
        "caption": "Fig. 1 Thin-walled geometry considered in this study",
        "texts": [
            " Although this research is pplied to the LENS\u00ae process, the approach taken is applicable to ny solid freeform fabrication process involving a moving heat ource, and the conclusions are relevant to a wide range of SFF rocesses involving thermal deposition of metals. The approach is lso applicable to other laser-based fusion processes for metals, uch as laser welding and laser cladding. Similarly, the approach aken can be applied to other alloy systems deposited by a moving eat source and this issue is the subject of ongoing research by the uthors. eometry Considered, Numerical Model and Nonimensional Variables Geometry Considered. In the current study, the thin-walled tructure shown in Fig. 1 is considered. Thin-walled geometries of his type are fabricated in a wide range of SFF processes. Also, umerical simulations of a wall of large height, h, with emperature-independent properties can be verified against an exsting analytical solution in the literature 15 . It is assumed that he thin wall is fabricated by depositing material along a single ow; thus, the thickness of the wall is comparable to the molten 02 / Vol. 129, FEBRUARY 2007 om: http://manufacturingscience.asmedigitalcollection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000337_1.1555660-Figure16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000337_1.1555660-Figure16-1.png",
        "caption": "Fig. 16 a! Finite element mesh of model, and b! contact zone indicating candidate contact points ~from Parker, Vijayakar, and Imajo @148#!",
        "texts": [
            " Recently, Parker, Vijayakar and Imajo @148# investigated oaded From: http://appliedmechanicsreviews.asmedigitalcollection.asme.org the dynamic response of a spur gear pair with time-varying mesh stiffness and backlash with a finite element/contact mechanics model @152#. One of the primary features of the model is that the dynamic mesh forces can be calculated with detailed contact analysis in each increment as the gears roll through the mesh. The finite element mesh used and contact zone indicating candidate contact points of model are as in Fig. 16. There is no need to specify externally the excitation in the form of time-varying mesh stiffness and static transmission error. A semi-analytical model near the tooth surface was presented, the solution of which matches the solution of the finite element approach. The response of a gear pair was analyzed in a wide range of operating speeds and torque. It was shown in their research that the source of non-linearity is the loss of meshing teeth contact, which, in contrast with the prevailing understanding, occurs even for large torque and high-precision gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000372_027836499801701205-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000372_027836499801701205-Figure1-1.png",
        "caption": "Fig. 1. Velocities along a rigid bar.",
        "texts": [
            " If vl and v2 can be calculated from 4 using Jacobians Ji and J2, respectively, then both of the velocities v, and We become Then, J&dquo;~ and Jw~ can be directly used in eq. (5) to compute the mass matrix of the robot. 3.3. Kinetic Energy of a Rigid Bar To save computational time, the problem can be further simplified if we consider the link as a bar, that is, that all the mass is concentrated along a unique line. In this case, the kinetic energy of the bar can be calculated considering the integral of the kinetic energy of elementary masses along the bar. As shown in Figure 1, the velocity along the bar can be calculated as The kinetic energy of an elementary mass is where S is the section of the bar, p is the density of the material, and dx is an elementary displacement along the bar. Based on this, the kinetic energy of the bar can be calculated as which leads to the result Introducing the Jacobian matrices Ji and J2 into this result, we find the contribution of the bar into the mass matrix of the robot: 3.4. A Lagrange-Based Dynamic Model It is well known that the dynamic model of any robot can be written in the following form: It is also known that the Coriolis and centrifugal terms are entirely determined by the mass matrix of the robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002798_tec.2020.2964942-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002798_tec.2020.2964942-Figure8-1.png",
        "caption": "Fig. 8. Examples magnetic cores fabricated using AM, a) rotor prototype for a surface mounted PM machine \u2013 University of Nottingham [24], b) rotor prototype for a switched reluctance motor \u2013 VVT Technical Research Centre of Finland Ltd. [25], c) family of rotor cores with non-magnetic bridges \u2013 University of Sheffield [26], d) stator and rotor hardware for an induction machine \u2013 Oak Ridge National Laboratory [27], e) CAD and hardware of rotor and stator core packs for a line start synchronous reluctance machine \u2013 National Cheng Tung University [28]",
        "texts": [
            " These include electromagnetic properties like magnetic saturation, magnetic permeability and specific power loss, and mechanical properties including yield strength, thermal expansion and resilience to thermal cycling. In this context, AM presents an interesting alternative to the well-established techniques for fabricating of magnetic parts and components. The research work related with this particular theme is rather broad, with a few interesting examples discussed in this section [24]-[32]. Fig. 8a) presents both optimised CAD and prototype of a rotor core pack for a surface mounted (SM) PM machine, as part of a design exercise. However, the main research effort has been placed on developing a suitable material and associated with AM processes to produce parts with \u2018good\u2019 magnetic properties [24]. It has been shown that the proposed process assures magnetic material with some of the properties to be comparable with the commercially available electrical steels like JNEX Super Core [24], [33]. Interestingly, the new material has relatively high 6.9% silicon content as compared with 6.5% for JNEX Super Core. However, the specific loss is four times higher for the developed material. With that being said, the specific power loss data is provided for a relatively low operating frequency of 50Hz. The mechanical properties of the material have not be explored in detail. A 50% reduction in mass of the rotor magnetic core shown in Fig. 8a) has been achieved by combining the developed material, manufacturing process, electromagnetic and mechanical design-optimisation [24]. Fig. 8b) shows rotor hardware designed for a lightweight, high-specific-output switched reluctance machine [34]. In contrast to the previous example, here the rotor core pack was manufactured using FeCo [25]. The material chemical composition, together with appropriate fabricating and postprocessing, e.g. Hiperco50, offers the highest magnetic saturation among commercially available electrical steels [35]. The experimental data from tests on materials samples fabricated using AM have shown that electromagnetic properties are comparable with the equivalent electrical steel, e",
            "4T a) d) Rotor core assembly CAD b) e) Rotor core assembly c) Family of rotor cores Non-magnetic bridges 0885-8969 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. (Hiperco 50) and similar mechanical properties subject to a specific annealing procedure [25]. Also, the authors mention that the electrical resistivity of the developed samples could be further improved to reduce the specific power loss. Fig. 8c) presents a family of rotors designed for a synchronous reluctance machine [26]. Such rotor construction requires careful considerations, as both the electromagnetic and mechanical design aspects need to be addressed jointly. The characteristic \u2018mechanical\u2019 bridges, indicated in Fig. 8c), have a detrimental effect on the overall motor performance. This is due to additional magnetic flux paths introduced by the structural design features (bridges). In [26], AM enabled for the rotor construction, with non-magnetic bridges eliminating the undesirable flux leakage effects. Altering magnetic properties of the selected rotor regions was achieved here by the use of rapid solidification and thermal strain associated with SLM. The next two examples presented in Figs. 8d) and 8e) illustrate parts of two different machine topologies: an induction machine with a cast aluminium squirrel cage [27] and a line start synchronous reluctance machine [28]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000084_physrevlett.96.058102-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000084_physrevlett.96.058102-Figure1-1.png",
        "caption": "FIG. 1. (a) Beating pattern of a cilium. The effective stroke and the recovery stroke are different (arrows) and a net flow is generated. (b) Simplified representation of the cilium by a small sphere, moving on a tilted elliptical trajectory.",
        "texts": [
            " They typically measure a few micrometers up to a few tens of micrometers in length and around 150\u2013300 nm in diameter. While the beat of sperm tails is typically a planar, sometimes helical wave, more complex, three-dimensional, asymmetric beating patterns occur typically in cells which propel fluids along surfaces. In this case, the working cycle of a cilium consists of a fast, upright, effective stroke and a recovery stroke which brings the cilium more slowly back to the original position on a path closer to the surface; see Fig. 1(a). Nodal cilia break the left-right symmetry of developing embryos by generating rotatory motion in a plane tilted with respect to the surface to which they are attached [5]. In this Letter, we discuss the hydrodynamic flow field generated by a single cilium which beats in an asymmetric pattern while attached to a surface. While the near field of the hydrodynamic flow depends on the detailed beating pattern and the whiplike geometry of the cilium, the far 06=96(5)=058102(4)$23.00 05810 field has general features which depend on only a few parameters characterizing the symmetry of the beat. Using the flow field generated by a beating cilium, we study the hydrodynamic interaction between two cilia. We discuss conditions that lead to synchronization of the two cilia by hydrodynamic interactions. Our minimal model of the ciliary beat [Fig. 1(b)] captures the essential features and symmetries\u2014the difference between the effective stroke and the recovery stroke of whiplike beating as well as the tilted rotatory motion of nodal cilia. We replace the cilium by a small sphere of radius a (essentially describing the center of mass position of the cilium), which moves on a fixed trajectory in the vicinity of a planar surface (defined as the plane z 0). The trajectory of the bead is elliptic; the phase of the oscillation (the position along the trajectory) is described by an angle "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002384_j.mechmachtheory.2010.11.005-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002384_j.mechmachtheory.2010.11.005-Figure1-1.png",
        "caption": "Fig. 1. Torsional model for a gear pair.",
        "texts": [
            " First of all, the parametric excitation due to the meshing stiffness fluctuation and the transmission error variations, caused by the tooth elastic deflections, must be included in themodel. Moreover, there is the possibility of loss of contact, due to the circumferential clearance between teeth. The present model has been widely used in the literature [15\u201317], and it allows to take into account the aforementioned phenomena; conversely, the compliance of bearings and shafts is neglected as well as the effect of manufacturing errors and misalignments. The meshing of a spur gear pair is represented by a two-DOF model (Fig. 1); the dynamics can be studied by means of a oneDOF model in terms of transmission error, without loss of generality (see Ref. [16] for details): where x :: \u03c4\u00f0 \u00de + 2\u03b6 x\u0307 \u03c4\u00f0 \u00de + \u03c8 \u03c4\u00f0 \u00deg x \u03c4\u00f0 \u00de\u2212e \u03c4\u00f0 \u00de\u00f0 \u00de = M \u00f01\u00de t is the time [s]; \u03c4 is the nondimensional time; x\u0303=r1\u03b81\u2212r2\u03b82 is the transmission error; x=x\u0303/b; 2b is the backlash where (Fig. 2); k(t) is the time varying meshing stiffness [N/m] (Fig. 1); \u03c8(\u03c4) is the nondimensional meshing stiffness; g(d ) is the backlash function; e\u0303(\u03c4) is the rigid body displacement due to intentional deviations from the pure involute (tip and root relief); e=e\u0303/b; (x\u0307)=d(x)/d\u03c4; and \u03b81 and \u03b82 are gear angular positions. Moreover: M = T1 r1bm\u03c92 n ; m = I1I2 r21 I2 + r22 I1 ; \u03c9n = ffiffiffiffiffiffiffi k 2m s ; \u03b6 = c 2m\u03c9n ; \u03c4 = \u03c9nt; \u03c8 \u03c4\u00f0 \u00de = k \u03c4 =\u03c9n\u00f0 \u00de m\u03c92 n ; 8>>>>>< >>>>>: \u00f02\u00de I1 and I2 are moments of inertia; r1 and r2 are base radii; k \u2013 is the average of k(t); T1 is the driving torque; \u03c9n is the l frequency of the linearized and averaged system; and \u03b6 is the damping ratio. natura The dynamical system of Fig. 1, governed by Eq. (1), is a piecewise linear time varying system, which can be represented by the one-dof model of Fig. 2. The mesh stiffness is periodic; therefore, it is expanded in Fourier series: \u03c8 \u03c4\u00f0 \u00de = A0 + \u2211 M\u0303 i=1 Ai cos ip\u03c4\u00f0 \u00de + Bi sin ip\u03c4\u00f0 \u00de \u00f03\u00de p = \u03c91z1 \u03c9n is the dimensionless excitation frequency,\u03c91z1 is the fundamental excitation frequency (meshing frequency),\u03c91 where is the rotational speed of the gear 1 and A0 is the mean value of the stiffness, \u03c8(\u03c4). The backlash function g(x(\u03c4)) is given by: g x \u03c4\u00f0 \u00de\u00f0 \u00de = x\u22121; x N 1; x + 1; xb\u22121; 0; otherwise: 8< : \u00f04\u00de Differential Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000113_70.105387-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000113_70.105387-Figure6-1.png",
        "caption": "Fig. 6. A typical path of a six-DOF manipulator.",
        "texts": [
            " Generally, there exists at every point some speed S , above which at least one of the actuators is saturated and the manipulator cannot stay on its specified path. Plotting s, in the phase plane, S - 3, forms the velocity limit curve, where the area above the curve represents a forbidden region for the trajectory. The time-optimal trajectory is obtained by maximizing the speed S at every point, using the maximum acceleration or deceleration at all times, so that the trajectory is below and at most tangent to the velocity limit curve [20]. Fig. 7 shows a typical time-optimal trajectory and the limit curve for the six-DOF manipulator and path shown in Fig. 6. The time obtained along such a trajectory is usually far shorter than the best feasible trapezoidal velocity profile. The limit curve is a reflection of the actuator constraints coupled with system dynamics and path geometry. We will use it for establishing lower bound estimates for the optimal motion time along a specified path. E. Lower Bound Tests We consider four tests for lower bound estimates on the motion time along a given path, each represented by a different velocity profile. To guarantee that the estimate is a lower bound, these velocity profiles are chosen to be above the true time-optimal profile for each path, as shown schematically in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000241_6.2009-1983-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000241_6.2009-1983-Figure3-1.png",
        "caption": "Figure 3. a) Coordinate system for vehicle dynamics definitions and b) free body diagram of quadrotor in the freestream.",
        "texts": [
            " The problem requires a detailed dynamic model of the vehicle which includes the effect of freestream velocity on forces and moments experienced by the vehicle. It also requires a compact model of expected wind disturbances, and an understanding of the effect of wind conditions on the vehicle. Instead of simply reacting to disturbances once they produce a measurable result in terms of position, velocity and acceleration error, the goal is to eliminate the effect of wind disturbances by predicting them as they occur. A. Vehicle Dynamics Modeling Coordinate systems and reference vectors for the problem of interest are defined in Figure 3-a), including the inertial frame (I) in North, East, Down (n\u0302, e\u0302, d\u0302) and the body fixed frame (B) with origin at the vehicle center of gravity (x\u0302, y\u0302, z\u0302). Euler angles of roll, pitch and yaw (\u03c6, \u03b8, \u03c8) define a rotation matrix RBI for rotation from inertial to body coordinates through three successive rotations in standard (3,2,1) form.10 The freestream velocity v\u221e and direction e\u0302\u221e are also depicted, which are the magnitude and direction of the combination of the wind velocity vw, and the vehicle velocity, vI, both in the inertial frame. The direction of the freestream velocity is broken into components e\u0302h, parallel to the rotor plane and e\u0302v perpendicular to it. Lastly, Figure 3-a) presents a clockwise rotor numbering scheme for the quadrotor vehicle, with rotor 1 along the positive x\u0302 axis, and rotor 2 along the positive y\u0302 axis, etc. A free body diagram of the quadrotor vehicle is depicted in Figure 3-b). The forces and moments considered for each rotor are visible for each rotor (vertical (Ti, Qi) and longitudinal (Di, Pi) relative to the direction of the freestream), and are labeled for rotor 1 only to avoid unnecessary clutter. In fact, both lateral forces and moments are also produced by each of the rotors during most flight regimes, but since quadrotors consist of two sets of counter-rotating pairs of rotors, these lateral effects tend to cancel and can be safely omitted from the analysis. Also visible in Figure 3-b) are the body drag force, DB and the 3 of 14 American Institute of Aeronautics and Astronautics gravitational force (mg) acting on the vehicle. The complete set of forces and moments acting on the vehicle can be summarized as follows, expressed in body coordinates: FB = 4\u2211 i=1 (\u2212Tiz\u0302 +Die\u0302\u221e) +DB e\u0302\u221e +RBI mgd\u0302, (1) MB = (Q1 +Q3 \u2212Q2 \u2212Q4)z\u0302\u2212 4\u2211 i=1 (Piet +Di(ri \u00d7 e\u0302\u221e) + Ti(ri \u00d7\u2212z\u0302)). (2) where ri defines the vector from the center of gravity to the center of rotation of each rotor i, and et defines the direction perpendicular to the freestream direction in the rotor plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002800_s00170-020-05201-4-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002800_s00170-020-05201-4-Figure2-1.png",
        "caption": "Fig. 2 Experimental rig representation for the NIAC concept",
        "texts": [
            " Another potential setback of the NIAC concept would be hydrogen contamination of the deposition pool from vaporized water. In view of the diversity of the foreseen related possibilities, some aspects of the NIAC concept are evaluated as following to validate it as a proof of concept as introduced for thermal management in WAAM. The experimental validation of the NIAC concept was based on a comparison among three cooling approaches applied to the preforms: the natural, the passive and, obviously, the NIAC. Figure 2 shows the experimental rig employed for the NIAC concept. The same arrangement was used for the passive and the natural approaches by fixing the cooling liquid level at the substrate-building platform and by draining it from the work tank, respectively, as illustrated in Fig. 3. Single-pass multi-layer linear preforms (single walls) were deposited under the three different cooling approaches. Considering that one potential setback of the NIAC concept would be hydrogen contamination of the deposition pool from vaporized water, an aluminum alloy was chosen as the preform material aiming at the proof of concept"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.29-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.29-1.png",
        "caption": "FIGURE 5.29. Spherical wrist of the Roll-Pitch-Roll or Eulerian type.",
        "texts": [
            " The PitchYaw-Roll and Pitch-Roll-Yaw are not distinguishable, and we may pick Pitch-Yaw-Roll as the only possible spherical wrist with the first rotation as a Pitch. Practically, we provide the Roll, Pitch, and Yaw rotations by introducing two links and three frames between the dead and living frames. The links will be connected by three revolute joints. The joint axes intersect at the wrist point, and are orthogonal when the wrist is at the rest position. It is simpler if we kinematically analyze a spherical wrist by defining three non-DH coordinate frames at the wrist point and determine their relative transformations. Figure 5.29 shows a Roll-Pitch-Roll wrist with three coordinate frames. The first orthogonal frame B0 (x0, y0, z0) is fixed to the forearm and acts as the wrist dead frame such that z0 is the joint axis of the forearm and a rotating link. The rotating link is the first wrist link and the joint is the first wrist joint. The direction of the axes x0 and y0 are arbitrary. The second frame B1 (x1, y1, z1) is defined such that z1 is 5. Forward Kinematics 275 along the gripper axis at the rest position and x1 is the axis of the second joint",
            " The placement of internal links\u2019 coordinate frames are predetermined by the DH method, however, for the end link the placement of the tool\u2019s frame Bn is somehow arbitrary and not clear. This arbitrariness may be resolved through simplifying choices or by placement at a distinguished location in 276 5. Forward Kinematics the gripper. It is easier to work with the coordinate system Bn if zn is made coincident with zn\u22121. This choice sets an = 0 and \u03b1n = 0. Example 161 Roll-Pitch-Roll or Eulerian wrist. Figure 5.29 illustrates a spherical wrist of type 1, Roll-Pitch-Yaw. B0 indicates its dead and B2 indicates its living coordinate frames. The transformation matrix 0R1, is a rotation \u03d5 about the dead axis z0 followed by a rotation \u03b8 about the x1-axis. 0R1 = 1RT 0 = \u00a3 Rx1,\u03b8 R T z0,\u03d5 \u00a4T = \u00a3 Rx,\u03b8 R T Z,\u03d5 \u00a4T (5.127) = \u23a1\u23a2\u23a3 \u23a1\u23a3 1 0 0 0 cos \u03b8 sin \u03b8 0 \u2212 sin \u03b8 cos \u03b8 \u23a4\u23a6\u23a1\u23a3 cos\u03d5 \u2212 sin\u03d5 0 sin\u03d5 cos\u03d5 0 0 0 1 \u23a4\u23a6T \u23a4\u23a5\u23a6 T = \u23a1\u23a3 cos\u03d5 \u2212 cos \u03b8 sin\u03d5 sin \u03b8 sin\u03d5 sin\u03d5 cos \u03b8 cos\u03d5 \u2212 cos\u03d5 sin \u03b8 0 sin \u03b8 cos \u03b8 \u23a4\u23a6 The transformation matrix 1R2, is a rotation \u03c8 about the local axis z2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure3.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure3.5-1.png",
        "caption": "Figure 3.5.2. Standard aerodynamic axes: (a) plan view, (b) rear view (only aerodynamic forces shown).",
        "texts": [
            " The selection of the vehicle center of mass as the axis center would be somewhat arbitrary in an aerodynamic sense, since the position of the center of mass is not aerodynamically significant. Also, the center of mass will be changed in the real vehicle by loading conditions. Hence, in vehicle aerodynamics, the standard axes are taken at the center of the wheelbase at ground level; Figures 3.5.1(a) and (b) show the partial vehicle free-body diagram in side view, with two alternative representations of the standard aerodynamic forces. In particular, in Figure 3.5.1(b) note that, for example, F A e L f is not a wheel reaction, it is an effective aerodynamic force exerted on the vehicle, and when it is positive it will reduce the force exerted by the ground on the wheel. Because of the use of the wheelbase as the reference length for non-dimensionalizing the moments, there are particularly simple relationships between the coefficients: Aerodynamics 161 The side force and yaw moment, which occur when the vehicle is yawed (Figure 3.5.2(a)), can be handled in a similar way. The standard axis origin is on the centerline, still at the mid-point of the wheelbase, and of course the drag is deemed to act at the origin. Alternatively the side force may be treated as forces at the front and rear axles. This gives similar relationships as for lift: 162 Tires, Suspension and Handling The side force plus yawing moment can be combined to give the side force a new line of action, no longer at the axis center. The distance of the line of action of the single total side force behind the axis center (the static margin from the wheelbase mid-point), hA, is given in terms of the wheelbase by We must distinguish here between the position of the line of action of this side lift and the position of the next increment of side lift, analogous to the center of pressure and aerodynamic center of a wing",
            ", the required tire slip angles, and hence the steering wheel position, but it is the position of the next force increment that determines the stability of that trim state. Thus it is not correct to say that a side lift in front of the center of mass necessarily tends to destabilize a steady state. It really depends on the position of the aerodynamic force increment in relation to the position of the tire force increment (see Chapter 6). The position of the force increments behind the axis center is given in terms of the wheelbase by Aerodynamics 163 In rear view (Figure 3.5.2(b)) the origin of coordinates is at ground level at the center of the track. The side lift acts at ground level. Because of the attitude angle in cornering, nose inward at higher lateral accelerations, the aerodynamic roll moment generally opposes normal body roll. Using coefficient values from the next section as estimates or, preferably of course, using vehicle-specific wind tunnel data and the following equations, the drag force, lift force, side lift force, pitch moment, yaw moment and roll moment may be found: In principle, the angular speed of the vehicle in yaw, pitch and roll may also influence the forces and moments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure28-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure28-1.png",
        "caption": "Fig. 28. Contour lines of tooth-contact stress.",
        "texts": [],
        "surrounding_texts": [
            "LTCA and TSCS calculations of the pair of spur gears as shown in Table 1 are performed at the outer limit separately when the quantity Q of lead crowning are 0, 10, 20, 30 and 40 lm. Figs. 27 and 28 are contour lines of TSCS when Q = 10 and 30 lm. It is found that lead crowning has great effect on TSCS distribution when Figs. 27 and 28 are compared with Fig. 15. Fig. 29 is a relationship between the maximum TSCS and Q. From Fig. 29, it is found that the maximum TSCS becomes greater when Q is increased. Influence factor of lead crowning is introduced here to evaluate the effect of lead crowning on TSCS quantitatively. So it can be calculated through dividing the maximum TSCS when there are lead crowning by the maximum TSCS when there are no ME, AE and TM. Relationship between the influence factor and Q is also shown in Fig. 29. From Fig. 29, it is found that influence factor of lead crowning is over 2.0 when Q = 40 lm. Fig. 29 can also be used as references when ISO 6336/2 is used to calculate TSCS of a pair of spur gears with lead crowning."
        ]
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.40-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.40-1.png",
        "caption": "FIGURE 5.40. A spherical arm with the arrangement of coordinate frames such that the overall transformation matrix reduces to an identity at rest position.",
        "texts": [
            "141) 1T2 = \u23a1\u23a2\u23a2\u23a3 cos \u03b82 0 sin \u03b82 0 sin \u03b82 0 \u2212 cos \u03b82 0 0 1 0 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.142) 2T3 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d3 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (5.143) The transformation matrix from B3 to the takht frame B4 is only a translation d4. 3T4 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d4 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.144) 286 5. Forward Kinematics x0 z0 z1 2\u03b8 x1 1\u03b8 z2 x2 x3 z3 x4 d4 B0 B1 z4 B2 B3 B4 d1 d3 5. Forward Kinematics 287 and the overall transformation matrix at the rest position becomes an identity matrix. To make link (1) to be R`R(\u221290), we may reverse the direction of z1 or x1-axis. Figure 5.40 illustrates the new arrangement of the coordinate frames. Therefore, the transformation matrix of the takht frame B4 to the base frame B0 at the rest position reduces to: 0T4 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d1 + d4 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.148) Example 168 F Assembling of a spherical wrist to a spherical manipulator. To transform the manipulator of Figure 5.40 to a robot, we need to attach a hand to it. Let us kinematically assemble the Eulerian spherical wrist of Example 161 to the spherical manipulator. The wrist, manipulator, and their associated DH coordinate frames are shown in Figures 5.28 and 5.40 respectively. Assembling of a hand to a manipulator is kinematic surgery in which during an operation we attach a multibody to the other. In this example we attach a spherical hand to a spherical manipulator to make a spherical arm-hand robot. The takht coordinate frame B4 of the manipulator and the neshin coordinate frame B4 of the wrist are exactly the same",
            " Attach the required DH coordinate frames to the Roll-Pitch-Yaw spherical wrist of Figure 5.30, similar to 5.28, and determine the forward kinematics of the wrist. 31. F Pitch-Yaw-Roll spherical wrist kinematics. Attach the required coordinate DH frames to the Pitch-Yaw-Roll spherical wrist of Figure 5.31, similar to 5.28, and determine the forward kinematics of the wrist. 32. F Assembling a R-P-Y wrist to a spherical arm. Assemble the Roll-Pitch-Yaw spherical wrist of Figure 5.30 to the spherical manipulator of Figure 5.40 and determine the forward kinematics of the robot. 322 5. Forward Kinematics z0 x5 z1 z2 z3 z4 z5 z6 z7 x0 y0 x1 x3 x4 x6 y7 x2 x7 1\u03b8 3\u03b8 2\u03b8 4\u03b8 5\u03b8 6\u03b8 7\u03b8 1 2 3 4 5 6 0 7 Camera Gripper x8 y8 z8 a b FIGURE 5.67. The space shuttle remote manipulator system (SSRMS) with a camere attached to the link (4). 33. F Assembling a P-Y-R wrist to a spherical arm. Assemble the Pitch-Yaw-Roll spherical wrist of Figure 5.31 to the spherical manipulator of Figure 5.40 and determine the forward kinematics of the robot. 34. F SCARA robot with a spherical wrist. Attach the spherical wrist of Exercise 22 to the SCARA manipulator of Exercise 29 and make a 7DOF robot. Change yourDH coordinate frames in the exercises accordingly and solve the forward kinematics problem of the robot. 35. F Modular articulated manipulators by screws. Solve Exercise 15 by screws. 36. F Modular spherical manipulators by screws. Solve Exercise 18 by screws. 37. F Modular cylindrical manipulators by screws"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001506_j.na.2009.02.132-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001506_j.na.2009.02.132-Figure2-1.png",
        "caption": "Fig. 2. Membership function of the fuzzy sets assigned to (a) output variable (uFSMC ) (b) input variables (s and s\u0307).",
        "texts": [
            " The equivalent control part is the same as that in (8) and the reaching law is selected as: ur = kfsufs (13) where kfs is the normalization factor of the output variable, and ufs is the output of the FSMC, which is determined by the normalized s and s\u0307. The fuzzy control rules can be represented as the mapping of the input linguistic variables s and s\u0307 to the output linguistic variable ufs as follows: ufs = FSMC(s, s\u0307) = [ufs(1), ufs(2), . . . , ufs(n)] = [FSMC(s1, s\u03071), FSMC(s2, s\u03072), . . . , FSMC(sn, s\u0307n)]T. (14) The membership function of input linguistic for each set of variables si and s\u0307i, and the membership functions of the output linguistic variable ufs(i), i = 1, . . . , n, are shown in Fig. 2, respectively. Here ufs(i) is denoted as: ufs(i) = FSMC(si, s\u0307i). (15) In Ref. [23], ur has been modeled using a fuzzy logic system as: ur = kfsufs while the sliding surface, s, is a scalar. In the above-mentioned reference, it has been shown that the product of multiplying s with ur is equal to:\u2212kfs |s| resulting from designed membership functions and a fuzzy rule table. In fact, a fuzzy rule table has been constructed by Her-Terng Yau and Chaieh-li chen in Ref. [23] and is explained in the following procedure: 1",
            " In the scheme proposed in [23] if multiplication of s and its change, s\u0307, is negative, the stability of the systemwill be achieved and it is seen that in this case ufs could be changed with negative or evenpositive sign but in our introducedmethod ifmultiplication of si and its change, s\u0307i is negative, generally, the stability of the system is not satisfied and we have to design our fuzzy rule table in such a way that for any variation of membership functions of s, the sign of ufs becomes opposite to s. Therefore some columns of our fuzzy rule table differ from those in [23] and the following relation would be satisfied: siufs(i) \u2264 \u2212 |si|. Our proposed FLC has two inputs and one output. These are s, s\u0307 and the control signal, respectively. Linguistic variables which imply inputs and outputs have been classified as: NB, NM, NS, ZE, PS, PM, PB. Inputs and outputs are all normalized in the interval of [\u22121, 1] with equal span as shown in Fig. 2. The linguistic labels used to describe the fuzzy sets were \u2018Negative Big\u2019 (NB), \u2018Negative Medium\u2019 (NM), \u2018Negative Small\u2019 (NS), \u2018Zero\u2019 (ZE), \u2018Positive Small\u2019 (PS), \u2019Positive Medium\u2019 (PM) and \u2018Positive Big\u2019 (PB). It is possible to assign a set of decision rules as shown in Table 1. The fuzzy rules are extracted in such a way that the stability of the system would be satisfied which was explained in more detail before. These rules contain the input/output relationships that define the control strategy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure8.21-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure8.21-1.png",
        "caption": "Fig. 8.21 Transversal interconnection by means of the anti-roll bar [6]",
        "texts": [
            "20, the floating device F just translates longitudinally, without affecting the suspension stiffnesses. This way we have introduced the third independent spring k3 in our vehicle. Obviously, hydraulic interconnections are much more effective, but the principle is the same. We have an additional parameter to tune the vehicle oscillatory behavior. 268 8 Ride Comfort and Road Holding Although only a few cars have longitudinal interconnection, almost all cars are equipped with torsion (anti-roll) bars, and hence they have transversal interconnection. An example is shown in Fig. 8.21. Using interconnected suspensions may lead to non-proportional damping, if proper counteractions are not taken, that is if the floating device F adds a stiffness k3 without also adding a damping coefficient c3. In this chapter, the ride behavior of vehicles has been investigated. To keep the analysis very simple, two two-degree-of-freedom models have been formulated. The first, called quarter car model, has been used for determining the right amount of damping to have good comfort and/or road holding when the vehicle travels on a bumpy road (forced oscillations)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001756_s11663-015-0477-9-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001756_s11663-015-0477-9-Figure1-1.png",
        "caption": "Fig. 1\u2014Schematic of the build design for the recyclability study.",
        "texts": [
            " Six builds were fabricated for the Inconel 718 alloy and five builds were fabricated for Ti-6Al-4V alloy. The build dimensions were designed such that at the end of each build the powder hoppers would completely run out of powder, thus exposing all the powder to the electron beam. This experiment was designed to understand the worst-case scenario since keeping the build heights constant would have required fresh powders to be added after every build andwould havemade it difficult to determine the changes in chemistry and physical properties of the bulk powders due to electron beam interaction. Figure 1 shows the build geometries that were fabricated for the present study. After each build, the powders were vacuumed out of the build chamber and the fabricated part was blasted in the powder recovery system (PRS) to recover the partially sintered powders. The powders recovered were then mixed with the vacuumed powders and then were sieved on a vibratory sieve with a 100-mesh (150 lm) screen. Powders greater than 150 lm were discarded. A sample was collected from these mixed powders for analysis before loading these powders in the hopper and the powder bed to prepare the Arcam for the next build"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000155_28.175288-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000155_28.175288-Figure6-1.png",
        "caption": "Fig. 6. Phasor diagram for an induction machine at the pull-out condition due to limited voltage.",
        "texts": [
            " As o, increases, point 0 moves towards A , resulting in more I , and less - - As wr (and w e ) is further increased, I,,,, (and hence A,) is reduced to a level such that the voltage drop across the leakage w, L, I , becomes dominant. In this case, the Thkvknin equivalent circuit in Fig. 5 , which is derived from Fig. 2 with the omission of r,, can be used to decide the situation for maximum torque in the machine. The torque capability in this case is limited by the pull-out condition corresponding to the voltage limit and we. The following equations must hold at the pull out condition: ~ 2 , rr UL: we - (6) - -- L; s L r i.e. 1 sw, = - U T , ' (7) A phasor diagram can be constructed for this mode of operation as shown in Fig. 6. In this case, the voltage triangle remains unchanged while the current triangle shrinks as w, is increased. The three subregions discussed above can be related to more commonly used terms in describing the torque capability of a variable-speed drive: The low-speed range corresponds to the constant torque range; the mid-speed range corresponds to the constant power range and the high-speed range to the torque breakdown range. It should be pointed out that the above results are derived under the assumption of unsaturable machines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001566_j.jallcom.2014.07.161-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001566_j.jallcom.2014.07.161-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of the laser melting deposition process.",
        "texts": [
            " The LMD system is equipped with a GS-TFL-8000 CO2 laser (maximum output power 8 kW), a BSF-2 power feeder together with a co-axial powder delivery nozzle, a HNC-21M computer numerical control multi-axis motion system, and an argon purged processing chamber with oxygen content less than 100 ppm. The LMD processing parameters were as follows: laser power 4\u20136 kW, laser beam diameter at melting pool 4\u20136 mm, laser scanning speed 800\u2013 1200 mm/min, powder feed rate 600\u20131000 g/h, and layer thickness 1\u20131.5 mm. The LMD process was schematically shown in Fig. 1. The raw powders were produced by plasma atomization, with the particle size mainly from 100 to 300 lm. Under these parameters, a TC11 plate was fabricated with a geometry size of 300 mm 200 mm 30 mm. 2.2. Microstructural characterization After LMD process, cubic specimens were cut from the as-deposited plate for microstructure observation. If not specially indicated, all the samples in this research were observed from the front view (YOZ section), as shown in Fig. 1. One heat-treated sample (HT sample) was prepared for the discussing by solution treatment at 1005 C for 1 h follow by quenched into water. Metallographic specimens were prepared by standard mechanical polishing and etched in a mixture solution of HF:HNO3:H2O with a ratio of 1:6:43. The microstructure was examined by Olympus BX51M optical microscope (OM) and Cambridge-S360 scanning electron microscope (SEM). A commercial metallographic image analysis software ImageJ was employed for quantitative metallography"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure8.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure8.1-1.png",
        "caption": "Figure 8.1. The resultant vector of gravity (W) and buoyancy (FB) will determine if an inanimate object floats. This golf ball will sink to the bottom of the water hazard.",
        "texts": [
            " When an object is placed in a fluid there is a resultant upward force or supporting fluid force called buoyancy. The fluid force related to how the fluid flows past the object is resolved into right-angle components called lift and drag. In most movement, people have considerable control over factors that affect these forces. Let's see how these fluid forces affect human movement. The vertical, supporting force of a fluid is called buoyancy. When an inanimate object is put in a fluid (like water), the vector sum of gravity and the buoyant force determines whether or not the object will float (Figure 8.1). The Archimedes Principle states that the size of the buoyant force is equal to the weight of the fluid displaced by the object. Folklore says that the famous CHAPTER 8 Fluid Mechanics 193 Greek physicist/mathematician realized this important principle when noticing water level changes while taking a bath. A sailboat floats at a level where the weight of the boat and contents are equal in size to the weight of the volume of water displaced. Flotation devices used for water exercise and safety increase the buoyancy of a person in two ways: having a lower density (mass/volume) than water and having a hollow construction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure13.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure13.4-1.png",
        "caption": "Fig. 13.4 Example of the three phases of DMU evolution",
        "texts": [
            " This first model fulfills the high level requirements to the part or assembly like space volume, position and interfaces (Fig. 13.3). In the second phase the form of the part is recognizable, although, certain details like rounding, tapers and threads are left out. In this phase, it is possible to take the decision to split the part into several parts and, thus, create an assembly. This model fulfills the next level of requirements regarding form and function. Models in this phase are suitable for further analysis using the DMU (Fig. 13.4). A third and last phase defines in every detail the form and function of the part including interfaces and relationships to interfacing parts or systems. This model has every necessary detail and fulfills the rest requirements for the part like weight, center of mass, etc. (Fig. 13.4). 362 R. Riascos et al. Product Structure for a DMU There are three strategies for 3D modeling and assembly building: bottom-up modeling, top-down modeling and a combination of both modeling strategies. CAD Systems offer the possibility to create an internal product structure inside the geometrical file or in a separate file that contains the product structure information. This functionality can be a disadvantage to create a DMU. Assemblies are built using the constraints among geometrical data, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001206_tmag.2012.2205014-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001206_tmag.2012.2205014-Figure5-1.png",
        "caption": "Fig. 5. Definition of washer-shaped magnet geometry.",
        "texts": [
            " The optimal dipole approximation for a rectangular-crosssection bar can be obtained by determining which values of and set the term in the multipole expansion defined in (21) to zero. Inspection of (21) shows that is the only solution that sets every component of the coefficient to zero. Conveniently, this cubic geometry also corresponds to the maximum dipole moment for a given minimum bounding sphere. As superposition holds for permanent magnet materials with low recoil susceptibilities (i.e., an externally applied or self-generated field does not appreciable affect the magnetization of the material), the optimal dipole shape for the washer shown in Fig. 5 can be defined by a linear combination of two cylinders of equal length. The larger diameter cylinder is taken to have a magnetization of and a diameter-to-length ratio of and the smaller is taken to have a magnetization of and a diameter-to-length ratio of . The volumes that these two cylinders overlap is equivalent to a hole in the larger cylinder. Following the procedure outlined previously, the equation that defines the optimal dipole approximation geometry for an axially magnetized washer is a linear combination of the coefficients from (15) of the two cylinders scaled by their volumes ( and ) (22) There is a real solution when (23) Outside this range, the optimal dipole approximation is defined by minimizing the square of the quadrupole coefficient and is equivalent to having no hole or no magnet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure4-4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure4-4-1.png",
        "caption": "Fig. 4-4 Current-excited transformer with secondary short-circuited.",
        "texts": [
            " In induction machines, in this emulation (called vector control), the PPU in Fig. 4-3b controls the stator current space vector i ts( ) as follows: a component of i ts( ) is controlled to keep B\u0302r constant, while the other orthogonal component of i ts( ) is controlled to produce the desired torque. 4-3 ANALOGY TO A CURRENT-EXCITED TRANSFORMER WITH A SHORTED SECONDARY To understand vector control in induction-motor drives, an analogy of a current-excited transformer with a short-circuited secondary, as shown in Fig. 4-4, is very useful. Initially at time t\u00a0=\u00a00\u2212, both currents and the core flux are zero. The primary winding is excited by a step-current at t\u00a0=\u00a00+. Changing this current as a step, in the presence of leakage fluxes, requires a voltage impulse, but as has been argued in Reference [2], the volt-seconds needed to bring about such a change are not all that large. In any case, we will initially assume that it is possible to produce a step change in the primary winding current. Our focus is on the shortcircuited secondary winding; therefore, we will neglect the leakage impedance of the primary winding. In the transformer of Fig. 4-4 at t\u00a0=\u00a00\u2212, the flux linkage \u03bb2(0\u2212) of the secondary winding is zero, as there is no flux in the core. From the theorem of constant flux linkage, we know that the flux linkage of a short-circuited coil cannot change instantaneously. Therefore, at t\u00a0=\u00a00+, ANALOGY TO A CURRENT-EXCITED TRANSFORMER 63 \u03bb \u03bb2 20 0 0( ) ( ) .+ \u2212= = (4-4) To maintain the above condition, i2 will jump instantaneously at t\u00a0=\u00a00+. As shown in Fig. 4-4 at t\u00a0=\u00a00+, there are three flux components linking the secondary winding: the magnetizing flux \u03c6m i, 1 produced by i1, the magnetizing flux \u03c6m i, 2 produced by i2, and the leakage flux \u03c6\u21132 produced by i2, which links only winding 2 but not winding 1. The condition that \u03bb2(0+)\u00a0=\u00a00 requires that the net flux linking winding 2 be zero; hence, including the flux directions shown in Fig. 4-4, \u03c6 \u03c6 \u03c6m i m i, ,( ) ( ) ( )1 20 0 0 02 + + +\u2212 \u2212 = or \u03c6 \u03c6 \u03c6m i m i, ,( ) ( ) ( ).2 10 0 02 + + ++ = (4-5) Choosing the positive flux direction to be in the downward direction through coil 2, the flux linkage of coil 2 can be written as \u03bb \u03c6 \u03c6 \u03c62 22 2 2 2 1 1 = \u2212 \u2212 +N N Nm i L i L i m i L im m , , (4-6a) or \u03bb2 2 2 1= \u2212 +L i L im , (4-6b) where Lm = the mutual inductance between the two coils (4-7) and L L Lm2 2 2= + = the self-inductance of coil . (4-8) Therefore at t\u00a0=\u00a00+, \u03bb2 2 2 10 0 0 0( ) ( ) ( )+ + += = \u2212 +L i L im (4-9) or i L L im 2 2 10 0( ) ( )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002782_j.optlastec.2016.11.002-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002782_j.optlastec.2016.11.002-Figure2-1.png",
        "caption": "Fig. 2. Selective laser melting system developed by Beijing Institute of Technology.",
        "texts": [
            " 1a shows the powder morphology under a scanning electron microscope (SEM). Fig. 1b shows the particle size distribution, with an average size of 37 \u03bcm (d10: 26 \u03bcm, d90: 56 \u03bcm). The chemical compositions of the Ti-47Al-2Cr-2Nb powder and Ti-6Al-4V substrate materials were measured by inductively coupled plasma optical emission spectrometry (ICP-OES) are listed in Table 1. Selective laser melting equipment was utilized in this study, which was developed by the Beijing Institute of Technology, as shown in Fig. 2. The system used a fiber laser (YLR-WC, IPG Photonics Corporation, Germany) with a maximum power of 500 W in continuous laser mode and a wavelength of 1070 nm. The laser beam was focused directly on the substrate surface with a spot size of 200 \u03bcm. Commercial Ti-6Al-4V alloy plate of 10 mm thickness was used as the forming substrate. The working chamber provided a closed environment that was filled with argon as a protective gas to maintain an oxygen concentration below 100 ppm. In this study, Ti-47Al-2Cr-2Nb powder was used to fabricate single laser tracks and samples on Ti-6Al-4V substrates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002306_tie.2017.2681975-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002306_tie.2017.2681975-Figure1-1.png",
        "caption": "Figure 1. Rotor structure of the 12/10 axial-flux machine. From left to the rotor centre: glass fibre rotor body, ten pole shoes made of laminated steel to avoid high permeance and current linkage harmonic losses in the magnets and to collect flux to the stator teeth, ten segmented magnets.",
        "texts": [
            " The machine slots are wider than normally (slot width 40 mm), resulting in not very efficient traditional cooling of the stator winding. However, direct liquid cooling is suitable for large slots, because it removes the heat all along the slot. The rotor is also developed to work together with the open-slot tooth-coil stator. With such a construction the rotor is burdened by high amount of high amplitude harmonics and therefore the rotor conductivity should be very low to prevent eddy currents to flow in the materials. The rotor structure of the test machine is illustrated in Fig. 1. The rotor body is made of electrically nonconductive impregnated glass fibre in order to have a light-weight rotor and to minimize the iron losses in the rotor. The details of the rotor structure are given in [4]. The permanent magnets used in the rotor have a remanence of 1.15 T, a coercive field strength of 870 kA/m, and a relative permeability of 1.05 (at 120 \u00b0C). The main dimensions and parameters of the machine are listed in Table I. TABLE I DIMENSIONS AND PARAMETERS OF THE 12-SLOT 10-POLE PROOF-OF- Parameter Value Design tangential stress value stan [kPa] indirect cooling/direct cooling 34/57 Stack total radial length ltot [mm] 70 Stator inner diameter Dsi [mm] 250 Stator external diameter Dse[mm] 390 Stator yoke thickness hsy [mm] 70 Number of stator slots in one stator Qs 12 Permanent magnet height hPM [mm] 2\u00d715 Average permanent magnet width hPM [mm] 70 Permanent magnet length lPM [mm] 70 Winding type: fractional-slot concentrated nonoverlapping, slots per phase and pole q = Qs/mp 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003017_j.jmapro.2019.05.001-Figure23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003017_j.jmapro.2019.05.001-Figure23-1.png",
        "caption": "Fig. 23. Schematic of a composite manufacturing processes of selective laser gelation [150].",
        "texts": [
            " In order to acquire higher accuracy and strength, the ceramic slurry as raw materials are supposed to offer good strength in ceramic parts as well as ceramic-matrix composite (CMC) parts. The slurry-based material can amplify the accuracy due to the fluidity of slurries used in this process. The gelation process itself is not a new one. Its roots are found in 1999 [148]. SLG combines traditional selective laser sintering (SLS) technique with solution\u2013gel technique. Schematic of SLG is shown in Fig. 23. SLG process adopts flexible slurries as raw materials to fabricate ceramic-matrix composite (CMC) parts while other SLS processes utilize powder-based materials. Fabrication of ceramic-matrix composite parts are difficult to be produced by conventional additive manufacturing techniques. That is why ceramics are seldom used in RP processes. Formability of ceramic parts in the context of rapid manufacturing (utilizing the concept of laser gelation and solvent-based slurry stereolithography and sintering) has been studied by different researchers [15,30,149]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.30-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.30-1.png",
        "caption": "Fig. 4.30 w1 and a slope w\u2032 1 at B. If we assume the axial rigidity to be infinite (EA \u2192 \u221e) the force F does not cause any deformation. This leads to a vertical displacement b w\u2032 1 at point C of part (small angles!). In a second step we consider part to be rigid and part to be elastic. This is equivalent to a clamping at B and yields the deflection w2 of a cantilever (Fig. 4.30c). Taking the individual terms from Table 4.3, the total deflection at C is given by",
        "texts": [
            "3 we take w (0) B = 14 q0 l4 384EI , w (1) B = \u2212 2X1 l 3 48EI , w (2) B = \u2212 5X2 l 3 48EI , w (0) C = 41q0 l4 384EI , w (1) C = \u2212 5X1 l 3 48EI , w (2) C = \u2212 16X2 l 3 48EI . Solving for the unknowns yields X1 = B = 19 56 q0 l, X2 = C = 12 56 q0 l. The method of superposition may also be applied to investigate the deformations of frames by combining the deformations of the individual beams making up the frame. Note, however, that the deformation of a beam has an effect on the displacement of the adjacent one. As an example we determine the vertical displacement wC of the angled member at point C (Fig. 4.30a). First, we consider only the deformation of part and its effect on the displacement of part (which is assumed to be rigid in the first step). Part is subjected to the internal moment M = b F and the axial load F at its end B (Fig. 4.30b). The moment M causes a deflection 4.5 Deflection Curve 149 wC = b w\u2032 1 + w2 = b (b F ) a EI + F b3 3EI = F b2 3EI (3 a+ b). If the axial rigidity EA is finite, part of the structure will be shortened by an amount Fa/EA. Then the total deflection of point C is wC = F b2 3EI (3 a+ b) + F a EA . Usually, the second term is small as compared with the term resulting from the bending. E4.11Example 4.11 Determine the support reactions and the deflection at point D for the beam in Fig. 4.31a. Solution The system is statically indeterminate to the first degree"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure4-1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure4-1-1.png",
        "caption": "Fig. 4-1 dc motor drive.",
        "texts": [
            " 4-2 EMULATION OF dc AND BRUSHLESS dc DRIVE PERFORMANCE Under vector control, induction-motor drives can emulate the performance of dc-motor and brushless-dc motor servo drives discussed 59 4 Vector Control of Induction-Motor Drives: A Qualitative Examination Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink\u00ae, First Edition. Ned Mohan. \u00a9 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. 60 VECTOR CONTROL OF INDUCTION-MOTOR DRIVES in the previous course. These are briefly reviewed in the following sections. In the dc-motor drive shown in Fig. 4-1a, the commutator and brushes ensure that the armature-current-produced magnetomotive force (mmf) is at a right angle to the field flux produced by the stator. Both of these fields remain stationary. The electromagnetic torque Tem developed by the motor depends linearly on the armature current ia: T k iem T a= , (4-1) where kT is the dc motor torque constant. To change Tem as a step, the armature current ia is changed (at least, attempted to be changed) as a step by the power-processing unit (PPU), as shown in Fig. 4-1b. In the brushless-dc drive shown in Fig. 4-2a, the PPU keeps the stator current space vector i ts ( ) 90\u00b0 ahead of the rotor field vector B tr ( ) EMULATION OF dc AND BRUSHLESS dc DRIVE PERFORMANCE 61 (produced by the permanent magnets on the rotor) in the direction of rotation. The position \u03b8m(t) of the rotor field is measured by means of a sensor, for example, a resolver. The torque Tem depends on \u00ces, the amplitude of the stator current space vector i ts( ): T k Iem T s= \u02c6 , (4-2) where kT is the brushless dc motor torque constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure11.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure11.2-1.png",
        "caption": "FIGURE 11.2. A body point mass moving with velocity GvP and acted on by force df .",
        "texts": [
            "30) The kinetic energy at the terminal time is K(tf ) =W +K(0) = 33 J (11.31) which shows that the terminal speed of the mass is: v2 = r 2K(tf ) m = \u221a 33m/ s (11.32) Example 299 Time varying force. When the applied force is time varying, F(t) = m r\u0308 (11.33) then there is a general solution for the equation of motion because the characteristic and category of the motion differs for different F(t). r\u0307(t) = r\u0307(t0) + 1 m Z t t0 F(t)dt (11.34) r(t) = r(t0) + r\u0307(t0)(t\u2212 t0) + 1 m Z t t0 Z t t0 F(t)dt dt (11.35) 11.2 Rigid Body Translational Kinetics Figure 11.2 depicts a moving body B in a global frame G. Assume that the body frame is attached at the center of mass C of the body. Point P indicates an infinitesimal sphere of the body which has a very small mass dm. The point mass dm is acted on by an infinitesimal force df and has a global velocity GvP . According to Newton law of motion we have df = GaP dm (11.36) 11. Motion Dynamics 587 however, the equation of motion for the whole body in global coordinate frame is GF = mGaB (11.37) which can be expressed in the body coordinate frame as BF = mB GaB +m B G\u03c9B \u00d7 BvB "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003443_bf02120338-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003443_bf02120338-Figure7-1.png",
        "caption": "Fig. 7. T h e c ross - sp r ing p i v o t n o t l oaded b y e x t e r n a l forces w h e n def lec ted t h r o u g h a la rge angle .",
        "texts": [
            " Since in its generality the problem of the cross-spring pivot for large angles of deflection is too complex to be treated analytically, in this section our investigations are confined to those cases where the flexible structure connecting the two members consists of two identical flat springs and is loaded by a (pure) bending moment only. We then have the advantage that there is symmetry with respect to the bisector of the angle enclosed by the lines joining the rigidly connected spring ends A and B or C and D (fig. 7). The lines joining the ends A and C or B and D are perpendicular to the bisector and make the angle 89 with the normal to AB or CD. The same holds for the line joining the points G and H, which points indicate the instantaneous position of the apexes of the equilateral triangles ABG and CDH originally bounded by the flat springs. Thus the mean perpendiculars GG' and HH' both make an angle 89 with GH, and we only have to know the distance d between G and H to be able to construct the mutual position of GG' and HH'",
            " I f this condi t ion is no t satisfied, t h u s if 7 < I (but 7 ~-: - - l), we in t roduce the no ta t ions k* and IV'* accord ing to k* = l /k , sin IV'* = k sin IV', (27) so t h a t aga in use can be m a d e of the exis t ing tables . I n s t ead of eq. (26) we now get /,(k, 10) -- F(k*, 10\"), I I 12(k, 10) = 2E (k*, lo*) - - F(k*, 10\"), [ (28) la(k, 10) = 2k* cos 10', J and have to in t eg ra t e be tween the l imits 10\" and 10, accord ing to . sin 100 9 sin 10, 10o = arc sin k ~ , 10z = arc sin k ~ - (29) The resul ts show t h a t the case where y < - - 1, k thus becoming imag ina ry , can be lef t out of cons ide ra t ion 2). In the beg inn ing of this sec t ion it was po in t ed out , and i i lus t ra ted in fig. 7, t h a t t he end D of the spr ing lies on the s t r a igh t line t h r o u g h B m a k i n g the angle 49 wi th the n o r m a l B J to A B . C o n s e q u e n t l y the c o o r d i n a t e s ~ = l /L and ~1 = / / L of this end D, the d i rec t ions of which are a t angles a and {-~z - - a wi th B J, are b o u n d to the condit ion t an }~0 = D J / B ] . Hence (L - - l) sin ~ + / cos a (1 - - ~) sin a + , / cos = = : , ( 3 0 ) t a n S - ~ ~ c o s a + / s i n a ~ c o s a + t / s i n a or, owing to (23) and (25), / # , 10) I v'' ~'o - - / l(k' 10) sin ,~ cos ",
            " (33) F r o m (24) and (29), g iving the l imits of ~' and 10'*, it will be ev iden t t h a t the l e f t -hand m e m b e r s of the equa t ions (32) and (33) for g iven va lues of a and q~ are d e p e n d e n t upon k or k* only. There fore , we are able to ca lcula te numer i ca l ly the p a r a m e t e r k or k * = l /k as a func t i cn of ct and ~o. At the same t ime the linfits of in t eg ra t ion 10o and ~/,~ or 10\" and ,/,* are known too. First we shall proceed to determine the distance d between the points G and H in fig. 7. Bearing in mind that the sides of the triangles BG and DH are both equal to }L, we can deduce from the equivalence of the projections of BGHD and BJD on BD that l cos a -r / sin a d + L cos (a - - } 9) = cos } ~0 Therefore, with $---= l/L and ~ / = / / L , d ~ cos a + ~ sin a - - cos (~ - - ,.1, 9). (34) L . cos 89 With the aid of (23), (25), (26) and (31), this equation can also be written as Z = - - - a - - V 2 ( y + cos 2~Oo) - - V 2 ( r + cos 2~o~) - - ~/ a 9} (35) - - ~ cos ~ cos ~- As to the state of stress in the springs, it is to be remarked that the bending moments have an extreme value at the two spring ends x = 0 (9' = Y'o) arid x ---- l (~v' = %)",
            " For large deflection,angles, on the contrary, the moment M appears again to undergo a cohsiderable change with respect to its elementary value 2M = 2EIg/L. If the forces to be transnfitted are negligible, in fig. 10 one can find the ratio M/2M as a function of 9 for various values of the intersection angle 2a, whereas the ratios Mo/M and MdM, needed to calculate the maximum bending moment M 0 or M~ present at the spring end, can be taken from fig. 9. At the same time a closer investigation shows that the deflection of the cross-spring pivot is accompanied by a small relative displacement d of the points G and H (see fig. 7), which points both coincided originally with the intersection of the springs. This displacement takes place in a direction making an angle ~0 with the two mean perpendiculars GG' and HH', both rigidly bound to the members that are connected by the cross-spring pivot. The value of d in relation to the spring length L is shown in fig. l l. The broken line G'GHH'can thus easily be constructed, as well as the paths described by points of the members during the relative movement. Usually the displacement d is so small that no trouble is experienced from the corresponding shift of the pivot point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000567_s00604-009-0165-z-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000567_s00604-009-0165-z-Figure3-1.png",
        "caption": "Fig. 3 Sensing layer structure for organophosphorous compounds",
        "texts": [
            " Paraoxon, the neurotoxic metabolite of OP insecticide parathion, exerts acute toxicity in target organisms by inhibition of acetylcholinesterase (AChE), leading to the accumulation of acetylcholine in cholinergic synapses and overstimulation of the cholinergic system. Recently, an interesting optical nanosensor for the detection of paraoxon has been presented by Constantine et al [52]. Layer-by-layer films of chitosan, organophosphorous hydrolase (OPH) and thioglycolic acid-capped CdSe quantum dots were arranged as a sensing assembly (Fig. 3) for the detection of paraoxon in solution. Luminescence of the quantum dots immediately decreased when exposed to \u03bcM solutions of the pesticide due to the hydrolysis of the organophosphorous compound by OPH, thus changing its conformation. Ji et al. [53] employed this same approach but using CdSe-ZnS quantum dots conjugat- ed with OPH to quantitatively determine paraoxon with a LOD as low as 10\u22128mol L\u22121. The results obtained verified that the quenching of fluorescence intensity of the OPH/QD bioconjugate was due to conformational changes in the enzyme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000272_s00170-011-3423-2-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000272_s00170-011-3423-2-Figure1-1.png",
        "caption": "Fig. 1 Hastelloy\u00ae X alloy aero-engine sample built by selective laser melting technology",
        "texts": [
            " There is, however, no literature available on the mechanical properties of Hastelloy\u00ae X alloy manufactured by rapid additive layer manufacture with selective laser melting technology. Selective laser melting (SLM) is a rapid additive layer manufacturing technology which uses a high energy intensity laser or electron beam to fuse fine metal particles into full density solid functional parts layer by layer directly from computer-aided design (CAD) data. This technology allows even highly complex geometries (Fig. 1) to be manufactured directly from 3D CAD files (without tooling) in a few hours. It has great potential in low volume, high added value aero-engine parts manufacture, and prototype development. Selective melting facilities generally use a laser as a heat source [6], although some facilities use an electron beam [7]. The advantage of electron beam based selective melting is that it can manufacture titanium and aluminium parts without oxidization because it is operated under a vacuum environment. Instead of working in a vacuum, laser-based selective melting facilities usually work under a controlled argon or nitrogen atmosphere",
            " An Amsler vibrophone machine with a 100-kN load cell was used to carry out all four-point bend fatigue tests. Specimens were tested at \u03c3max from 450 to 900 MPa and load ratio R \u00bc Pmin Pmax \u00bc 0:1= with a sinusoidal waveform at frequency 110 Hz. The four-point bend fatigue tests specimens, either in the as-deposited condition or after hot isostatic pressing, were grit blasted before testing to simulate the real case surface finish. Because some complex geometry engine parts cannot be post-machined after SLM manufacture (Fig. 1). S-N tension\u2013tension fatigue tests were carried out on the same Amsler vibrophone machine, with a 20-kN load cell. The \u03c3max is from 500 to 800 MPa and the load ratio is R=0.1 with a sinusoidal waveform at a frequency of 117 Hz. Specimen dimensions for four-point bend and tension\u2013tension fatigue tests are shown in Fig. 4. The fatigue endurance limit of four-point bend and tension\u2013tension test is defined when a sample reaches 107 cycles without failure. Fracture surfaces of all specimens were examined by a PHILIPS XL-30 scanning electron microscope"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000317_0278364909353351-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000317_0278364909353351-Figure6-1.png",
        "caption": "Fig. 6. Purely structural FEM eigenmode analysis of the relative hammer motion of the 07v6 prototype assuming a fixed base frame. (a) First and lowest eigenmode expected around 1,500 Hz is a rotation which can be used as principle motion leading to the eventual impact of the swinging mass into the fixed attractor mass. (b) Up/down motion around 1,700 Hz as second eigenmode. (c) Spring compression around 3,900 Hz as third eigenmode. Hammer movements are indicated with gray arrows. Regions of high displacement are highlighted in dark red, regions of no displacement in dark blue (i.e. base frame and attractor mass).",
        "texts": [
            " For good signal rectification and control of robot motion the surface area of the base frame must be large in order to ensure good electrostatically induced charge separation and thus sufficiently large clamping force. This force can then be used to increase friction when desired and only when desired. It is evident that many of the design parameters mentioned above are strongly coupled and conflict with one another. Most of them, however, can be summarized as conflicting space requirements. Iterative FEM modeling was used to ensure that the primary excitation coincided with the first mode and lowest excitation frequency on the mechanical model (Figure 6). In a second step magnetic simulations were used to ensure sufficient force and torque for a given excitation field. Magnetic forces scale inversely proportional to the distance between hammer and attractor (Figure 3(a)). Hence, it is sufficient to ensure induced displacement of the hammer in a ground state for computed forces at a given magnetic field strength. A good trade-off with large safety factors was achieved with the first design. at NEW MEXICO STATE UNIV LIBRARY on September 12, 2014ijr",
            " As a result, the symmetric devices seem to generally exhibit a faster, stronger, more robust, and straighter driving behavior than the initial asymmetrical design, which is beneficial both for controlled driving and the handling of objects. Both robots can be driven with very low fields. While stable driving can be observed for fields as low as 2 mT, the robots become increasingly susceptible to surface asperities and dust particles below this value. Along with a decrease in sensitivity to surface variations, driving at larger field amplitudes may lead to an increase in magnetic hysteresis effects and movement at eigenmodes other than the primary one (a representative illustration is given in Figure 6) which can result in the device driving sideways when excited at that frequency. All of these effects may be exploited in order to widen the range of available driving modalities. While 07v6b-MH is more prone to locking up for hours when exposed to magnetic field strengths above 3 mT due to remanence in the nickel bodies, 07g2-MH can be driven with at least up to 8 mT, thus exhibiting more power and robustness. This behavior can be expected based on the vibrometer results of Figure 13. Most of this difference can probably be attributed to a different device geometry, such as larger gaps and stiffer springs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure2.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure2.12-1.png",
        "caption": "Figure 2.12.1. Tire camber distortion.",
        "texts": [
            " The SAE defines positive rotation about the X-axis, as shown, as the inclination angle and defines camber as the modulus of the inclination, with a positive value if the top of the wheel is outward from the vehicle centerline. In practice, the term camber angle is frequently used to mean inclination angle, especially in the context of an isolated tire or wheel, when the SAE definition of camber is not applicable. Single-track two-wheeled vehicles operate at extreme camber angles in cornering; four-wheeled vehicles usually have angles less than 10\u00b0. Figure 2.12.1 represents a view down through a transparent cambered wheel showing the tread area distortion caused by the camber. The consequence is a lateral force. There is also a camber aligning moment about the Z-axis, often negative (associated with a negative camber trail), but this is small and usually neglected. The Tire 107 The lateral force produced is called the camber force, sometimes the camber thrust (an obsolescent term); because camber angles are fairly small, friction effects are generally secondary and the camber force is a function of the stiffness properties of the tire, of the camber angle and of the vertical force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000337_1.1555660-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000337_1.1555660-Figure12-1.png",
        "caption": "Fig. 12 Six-dof model of a gear system ~from Ozguven @190#!",
        "texts": [
            "org In 1991, based on the early research by Gregory, Harris, and Munro @85#; Retting @187#; Terauchi, Hidaka, and Nagashima @188#; and Sato, Kamada, and Takatsu @189#; who found the occurrence of jump phenomena, subharmonic oscillations and random-looking vibration, Sato, Yamamoto, and Kawakami @76# established a time-varying nonlinear model with the time dependence of tooth stiffness and backlash, and further investigated the bifurcation sets of periodic solution under some gear parameters and chaotically transitional phenomena by using a shooting method. Also in 1991, Ozguven @190# developed a 6-dof nonlinear model for the dynamic analysis of spur gears, as shown in Fig. 12. This model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics are also considered in model, the effect of coupled lateral torsion vibration on the dynamic behavior of gears can be studied. This nonlinear model takes into account time-varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications. The static transmission error method developed by Ozguven and Houser @174# was used to consider internal excitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.19-1.png",
        "caption": "Fig. 3.19 The offset-hinge model of rotorblade flapping",
        "texts": [
            "189) and the combined inertial acceleration function is given by the expression \ud835\udf0ex = (p\u2032 \u2212 2q) sin\ud835\udf13 + (q\u2032 + 2p) cos\ud835\udf13 (3.190) Finally, the flap frequency ratio is made up of a contribution from the spring stiffness and another from the offset hinge, given by \ud835\udf062 \ud835\udefd = 1 + K\ud835\udefd I\ud835\udefd\u03a92 + eRM\ud835\udefd I\ud835\udefd (3.191) The hub moment given by Eq. (3.184) is clearly in phase with the blade tip deflection. However, a more detailed analysis of the dynamics of the offset-hinge model developed by Bramwell (Ref. 3.34) reveals that this simple phase relationship is not strictly true for the offset-hinge model. Referring to Figure 3.19, the hub flap moment can be written as the sum of three components, i.e. M(r)(0, t) = K\ud835\udefd\ud835\udefd \u2212 eRSz + eR \u222b 0 F(r, t)rdr (3.192) The shear force at the flap hinge is given by the balance of integrated aerodynamic (F(r, t)) and inertial loads on the blade; thus Sz = \u2212 R \u222b eR [F(r, t) \u2212 m(r \u2212 eR)\ud835\udefd]dr (3.193) If we assume a first harmonic flap response so that \ud835\udefd = \u2212\u03a92\ud835\udefd (3.194) then the flap moment about the hub centre takes the form M(r)(0, t) = \u03a92I\ud835\udefd(\ud835\udf062 \ud835\udefd \u2212 1)\ud835\udefd(t) + eR R \u222b eR F(r, t)dr + eR \u222b 0 rF(r, t)dr (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001537_tnnls.2018.2876130-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001537_tnnls.2018.2876130-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the quadrotor system.",
        "texts": [
            " 3) By using the concept of the virtual parameter and incorporating NN through an indirect way, the number of parameters to be online updated is significantly reduced, and the resultant control is simple in structure and inexpensive in computation, providing a more affordable solution to position and attitude tracking control of quadrotor UAVs. 4) The robustness and fault-tolerant capability of the proposed control scheme are validated by simulations on several scenarios. Consider an UAV with four rotors (denoted by R1\u2013R4), as shown in Fig. 1, driven by the corresponding motors mounted at two orthogonal directions. That is, the front (R1) and the rear (R3) rotors turn counterclockwise, while rotor R2 (left) and R4 (right) turn clockwise. Let us consider the two main references as the inertia frame denoted by E = {xe, ye, ze} and the body-fixed frame denoted by B = {xb, yb, zb}. We assume that quadrotor is a rigid body so that the quadrotor dynamic equations can be derived by using Newton\u2013Euler formula. The Euclidean position and Euler angles of the UAV with respect to the frame E are represented by \u03c7 [x, y, z]T \u2208 R3 and p [\u03c6, \u03b8,\u03c8]T \u2208 R3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure1-1.png",
        "caption": "Fig. 1. Metal V-belt CVT drive: (a) basic configuration; (b) belt structure [15].",
        "texts": [
            " The basic configuration of a CVT comprises two variable diameter pulleys kept at a fixed distance apart and connected by a power-transmitting device like belt or chain. One of the sheaves on each pulley is movable. The belt/chain can undergo both radial and tangential motions depending on the torque loading conditions and the axial forces on the pulleys. This con- sequently causes continuous variations in the transmission ratio. The pulley on the engine side is called the driver pulley and the one on the final drive side is called the driven pulley. Fig. 1 [15] and Fig. 2 [16,72] depict the basic layout of a metal V-belt CVT and a chain CVT. In a metal V-belt CVT, torque is transmitted from the driver to the driven pulley by the pushing action of belt elements. Since there is friction between bands and belt elements, the bands, like flat rubber belts, also participate in torque transmission. Hence, there is a combined push\u2013pull action in the belt that enables torque transmission in a metal V-belt CVT system. On the other hand, in a chain CVT system, the plates and rocker pins, as depicted in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002882_j.commatsci.2018.06.019-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002882_j.commatsci.2018.06.019-Figure3-1.png",
        "caption": "Fig. 3. The Cartesian mesh used for thermal history simulations.",
        "texts": [
            " (3) represent the heat addition from the scanning laser, the heat loss due to convection, the heat loss due to radiation and the heat addition from powder deposition. We point out that a Gaussian distribution is assumed to represent the heat addition from the scanning laser; in the heat addition term from powder deposition, the function q r( )p is calculated from a powder flow model. Further explanations of Eqs. (2) and (3) can be found in [28,29]. The computation domain and the Cartesian mesh used for the thermal history simulation are shown in Fig. 3. The laser scans in X-Z plane and the+Y direction is referred as the building direction for a DLD process. The fine mesh (circled by the red1 dotted line) is a uniform Cartesian mesh with a size of 25 \u03bcm. The laser only scans in the fine mesh region to enhance the accuracy of the simulated thermal history. The fine mesh is surrounded by a non-uniform Cartesian coarse mesh which mesh size gradually increases from the fine mesh region outwards. The coarse mesh is used to provide a heat sink to avoid unphysical heat accumulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure2.15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure2.15-1.png",
        "caption": "Fig. 2.15 The modelling components of a helicopter",
        "texts": [
            " But control margin can be interpreted in a dynamic context, including concepts such as pilot-induced oscillations and agility. Just as with high-performance fixed-wing aircraft, the dynamic OFE can be limited, and hence defined, by flying qualities for rotorcraft. In practice, a balanced design will embrace these in harmony with the central flight dynamics issues, drawing on concurrent engineering techniques (Ref. 2.11) to quantify the trade-offs and to identify any critical conflicts. The behaviour of a helicopter in flight can be modelled as the combination of many interacting subsystems. Figure 2.15 highlights the main rotor element, the fuselage, powerplant, flight control system, empennage and tail rotor elements and the resulting forces and moments. Shown in simplified form in Figure 2.16 is the Helicopter and Tiltrotor Flight Dynamics \u2013 An Introductory Tour 23 Fig. 2.16 The orthogonal axes system for helicopter flight dynamics orthogonal body axes system, fixed at the centre of gravity/mass (cg/cm) of the whole aircraft, about which the aircraft dynamics are referred. Strictly speaking, the cg will move as the rotor blades flap, but we shall assume that the cg is located at the mean position, relative to a particular trim state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure7-1.png",
        "caption": "Fig. 7. 4\u20134\u20135 RPR-equivalent PMs in the first family. (a) 2-uvUvPR/uRPFS. (b) uvUvPR/uPRFS. (c) 2-uvUvPR/uRRFS. (d) 2-uvUvRR/uRRFS.",
        "texts": [
            " We neglect the architectures with limbs generating {X(u)}{X(v)} because it would be very lengthy to enumerate RPR-equivalent PMs with limbs generating {X(u)}{X(v)}. Then, the RPR-equivalent PMs in 4\u20134\u20135 subcategory can be obtained by two combinations, respectively. The first combination is {L1} = {G(u)}{S(F)} and {L2} = {L3} = {R(O,u)}{G(v)}. The second combination is {L1} = {S(D)}{G(v)} and {L2} = {L3} = {G(u)}{R(B,v)}, which results from the kinematic inversion of the previous family. For conciseness, Table V only enumerates 49 RPR-equivalent PMs belonging to the first family in 4\u20134\u20135 category. Fig. 7 shows four architectures belonging to the first family, and Fig. 8 shows four architectures belonging to the second family. RPR-equivalent PMs in subcategory 5\u20135\u20134 can be constructed with two 5-DOF limbs in Table II and one 4- DOF limb in Table III. The first combination is {L1} = {R(O,u)}{G(v)} and {L2} = {G(u)}{S(Fa)} {L3} = {G(u)}{S(Fb)}, with Fa \u2208 axis(B, u) and Fb \u2208 axis(B, v). The second combination is {L1} = {G(u)}{R(B,v)}, and {L2} = {S(Da)}{G(v)}, {L3} = {S(Db)}{G(v)} with Da \u2208 axis(O, u) and Db \u2208 axis(O, u), which is a kinematic inversion of the first family"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000260_s0013-4686(97)00125-4-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000260_s0013-4686(97)00125-4-Figure5-1.png",
        "caption": "Fig. 5. Calculated surface concentrations for H2O2, O2 and H+ as a function of [H2O2]bulk based on the optimized model parameters for a rotation rate of 630 r.p.m.",
        "texts": [
            " The methods used by these previous workers rely upon the assumption that the electrochemical reaction with H2O2 (either oxidation or reduction) is taking place under conditions where the reaction is entirely diffusion limited. We have shown in this work for oxidation of H2O2 at platinum that this assumption is inappropriate and consequently affords misleading values for DH2O2 from Koutecky\u2013Levich plots. This is demonstrated in Fig. 3 where, depending on H2O2 concentration, DH2O2 can be found in the range 0.6\u20131.4\u00d710\u22129 m2 s\u22121. These effects may be accounted for by inspection of the calculated surface concentration data for H2O2, H+ and O2 in Fig. 5 as a function of bulk [H2O2] based upon equations (25) to (28) and the optimised rate parameters (for the lowest rotation rate explored). It is clear that the surface concentration of H2O2 only approaches zero (and hence overall diffusion control) at low bulk concentrations; above 20 mM the surface concentration increases linearly and adopts a value some 18 mM below that of the bulk. Furthermore, we calculate that at the highest rotation rate explored a completely linear dependence between surface and bulk concentration develops at all concentrations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003089_978-3-319-04867-3-Figure7.14-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003089_978-3-319-04867-3-Figure7.14-1.png",
        "caption": "Fig. 7.14 Schematic illustration of alignment of triphenylene in microtrench. Reproduced with permission from [193]. Copyright 2012 Taylor & Francis Group, LLC",
        "texts": [
            " The hexagonal columnar to isotropic phase transition is modified as a result of geometrical constraints and interfacial interactions. The results demonstrate the importance of surface anchoring and topological constraints, which can occur in the nucleation process and the relative stability of confined phases in the case of DLCs. Recently, Chiang et al. produced microtrenches on substrates and studied the molecular stacking of triphenylene discotic molecules on the substrate [193]. They demonstrated that the discotic molecules in the trenches can assemble into uniaxially aligned columns (Fig. 7.14). The way in which the discotic molecules anchor on the walls of trenches and the over all orientation of the columns are determined by the energetic conditions of the walls. They show that the orientation direction of the columns can be controlled to align either parallel or perpendicular 244 H. K. Bisoyi and Q. Li to the wall of the primary trenches using properly designed controlling trenches. Such a technique would be particularly useful for organic semiconductor devices that require a local-planar-alignment of discotic columns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003370_j.addma.2018.04.024-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003370_j.addma.2018.04.024-Figure6-1.png",
        "caption": "Fig. 6. Gas flow over build plate in Concept Laser M2.",
        "texts": [
            " In contrast, there is a roughly linear increase in roughness of angled faces across the build plate. Surface roughness is controlled by a number of factors such as laser calibration, laser power, scanning parameters, and gas flow. Since all of the laser settings were held constant during the build, we believe the uneven variation in surface roughness across the build plate is due to an unstable flow of the protective gas across the build plate. A schematic representation of gas flow path in the build chamber can be seen in Fig. 6. Although positive laser focus shifts in the +3 to+5mm range resulted in a reduction in average surface roughness for vertical and angled faces, the roughness variation across the build plate (Fig. 5) indicates that adjusting the laser focus may lead to turbulent gas flow. It has been shown that inhomogeneous protective gas flow, such as is produced in turbulent flow conditions, can lead to increased surface roughness due to insufficient removal of process byproducts and interaction of the laser with these byproducts [8,9]",
            " This balling phenomenon is also commonly seen in lower laser power regimes [8,9,15], which explains why it is observed at regions of the build plate which have lower laser energy (below +2-mm focus shift) as well as in regions with uneven gas flow. For the Concept Laser M2 SLM system, gas flow is controlled as a blower speed percentage rather than an output volumetric flow rate. However, based on this system\u2019s specified maximum flow rate volumetric flow rate is on the order of 45 m3/h when blower speed is set to 70%. Gas flow path has a large influence over the flow rate and uniformity over the build plate. Fig. 6 shows an illustration of the gas path in the M2, but without detailed modeling of the build chamber and computational fluid dynamics (CFD) analysis, it is difficult to quantify the flow over the build plate. However, it has been found that increasing gas flow rate and improving the gas flow path through modification of inlet and/or chamber geometry improves material quality and decreases variation in surface roughness and porosity [8,9,11,14]. Finally, to better understand the effect of laser focus shift on mechanical properties, rods were printed at +3, 0, and \u22123mm laser focus shift"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001967_s11071-018-4314-y-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001967_s11071-018-4314-y-Figure3-1.png",
        "caption": "Fig. 3 Schematic of a surface ring crack [56]",
        "texts": [
            " [54] used vibration and AE signals to predict the rolling contact fatigue damage process in the alloy coating. Their results provided that the whole rolling contact fatigue process has four stages. This work denoted that the material deformation can be successfully detected by the AE method, as well as the fatigue crack initial and propagation; but the vibration can only predict the final failure. Zhao et al. [55,56] developed an experimental and a numericalmethods to predict the subsurface partial ring crack propagation under rolling contact loads. The profile of the ring crack is given in Fig. 3, where p(x, y) is the normal contact pressure in the contact area, q(x, y) is the tangential traction in the contact area, x , y, and z are the coordinates, a is the contact circle radius, d is the distance between the ring crack circle and contact circle, and \u03b8 is the angular position. In their work, a boundary element analysis was introduced to determine the crack propagation. The influences of the crack geometries on the crack propagation were discussed. The results described that the most important factor of crack geometrical parameters was crack length with crack radius, and crack arc length and angle having slight influence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002052_0954406213486734-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002052_0954406213486734-Figure2-1.png",
        "caption": "Figure 2. Approximation of the ring-planet contact.",
        "texts": [
            " More details of this work can be found in Ref.20 The same assumptions will be applied in this study. Hertzian stiffness, bending stiffness, axial compressive stiffness and shear stiffness will be considered. According to the Hertzian law, the elastic compression of two isotropic elastic bodies can be approximated by two paraboloidal bodies in the vicinity of the contact point.13 For the planet-ring contact, we approximate the planet gear as a cylinder with radius r1, and the ring gear as a circular groove with radius r2, as shown in Figure 2. The half-width of the contact region can be expressed as21 b \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8\u00f01 2\u00deF EL r1r2 r2 r1 s \u00f01\u00de where E,L and represent Young\u2019s modulus, tooth width and Poisson\u2019s ratio, respectively, and F is the acting force. The deformation of the contact teeth due to the force F can be calculated as \u00bc r1 r2 \u00feO1O2 \u00bc r1 r2 \u00fe r2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 b r2 2 s r1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 b r1 2 s \u00f02\u00de The square-root terms in equation (2) can be approximated by the first two terms of the binomial expansion (see equation (3))"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000324_ja00532a040-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000324_ja00532a040-Figure1-1.png",
        "caption": "Figure 1. Rotating cylinder electrode of glassy carbon: (A) glass tube; (B) mercury electrical connection; (C) main part of the electrode in stainless steel adjusted to fit the internal diameter of D; (D) glassy carbon tube 1.2 cm in diameter, 5 cm long; (E) 0 rings; (F) Altuglass devices providing mechanical support and carbon isolation.",
        "texts": [
            " This procedure must lead to a mono- or a quasi-monomolecular layer since carboxylic functions of protein cannot be reactivated by free carbodiimide. Under these conditions, the resulting enzyme activity was necessarily low, especially when dealing with a nonporous support, which provided a good model of mass transfer effects. Experimental Section Production of Glucose Oxidase Electrodes. A tube of glassy carbon'* was selected as a support. The external surface was used a s a rotating cylinder (17.5 cm2) (Figure 1). Owing to the difficulty in tooling glassy carbon, a maximum eccentricity of 0.5 mm was admitted. The surface was carefully polished with abrasive paper and with alumina powders exhibiting decreasing grain size. The resulting surface was observed by scanning electron microscopy. The maximal roughness found was around 0.05 p m (strips were especially observed). Each sample was submitted to the following steps: (a) Samples were treated with an alcohol-KOH solution and then ultrasonically cleaned"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002716_kem.554-557.1828-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002716_kem.554-557.1828-Figure1-1.png",
        "caption": "Fig. 1 Schematic illustration of the SLM process",
        "texts": [
            " Process parameters like the powder thickness or the cooling time between successive layers are studied in this paper. The SLM process is an additive process used to create metal parts with complexes shapes from CAD data. The basic concept of SLM is similar to that of selective laser sintering (SLS). A moving laser beam is used to melt selectively powdered metal into successive cross-sections of a three dimensional part. Parts are manufactured on a mobile table moving upward by steps equal to the thickness of the layer (see Fig. 1). Additional powder is laid down on the top of each solidified layer and with the cooling it solidifies to form finally a solid material. For example, this method is used in the polymer processing industry to manufacture tooling parts or moulds designed with internal channels for conformal cooling which could not be obtained by conventional milling and drilling [2]. Parts obtained by SLM are dense and can be directly functional. During the manufacturing, the interaction between the laser and the powder induces significant thermal gradients in the part thanks to high heating and cooling rates associated with cycling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001258_j.euromechsol.2010.03.002-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001258_j.euromechsol.2010.03.002-Figure10-1.png",
        "caption": "Fig. 10. Scheme of modelli",
        "texts": [
            " Such a result could be expected since after prolonged gearbox running in misalignment conditions, tooth pitting occurs, causing (due to overloading) distributed faults and an increase in \u201ce\u201d. The simultaneous influence of parameters \u201ca\u201d and \u201ce\u201d may result in a nonlinear loadediagnostic feature relation. A tendency towards nonlinearity was observed when investigating a planetary gearbox being in bad condition (Bartelmus and Zimroz, 2009b). A one-stage planetary gear train (Chaari et al., 2005) with N\u00bc 4 planets is modelled as shown in Fig. 10. The sun (s), the ring (r), the carrier (c) and the planets (p) are considered as rigid bodies. The bearings are modelled by linear springs. Gearmesh stiffness is modelled by linear springs acting on the lines of action. Each component has three degrees of freedom, two translations ui, vj and one rotation wj, where wj \u00bc rjqj (j\u00bc c, r, s, 1, ., 4), rj is the base radius of the gears (sun, ring, planet) and the distance between the centre of the sun and the planets\u2019 rotation centre. Damping is introduced as modal viscous damping"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure4-7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure4-7-1.png",
        "caption": "Fig. 4-7 Stator and rotor mmf representation by equivalent dq winding currents.",
        "texts": [
            " Noting that di1/dt\u00a0=\u00a00 for t\u00a0>\u00a00, solving for i2 in the circuit in Fig. 4-6 confirms the decay in i2 due to R2 i t i e t 2 2 0 2( ) ( ) .= + \u2212 \u03c4 (4-15) 4-4 d- AND q-AXIS WINDING REPRESENTATION A step change in torque requires a step change in the rotor current of a vector-controlled induction motor. We will make use of an orthogonal set of d- and q-axis windings, introduced in Chapter 3, producing the same mmf as three stator windings (each with Ns turns, sinusoidally distributed), with ia, ib, and ic flowing through them. In Fig. 4-7 at a time t, i ts( ) and F ts( ) are produced by ia(t), ib(t), and ic(t). The resulting mmf F t N p i ts s s( ) ( / ) ( )= can be produced by the set of orthogonal stator windings shown in Fig. 4-7, each sinusoidally distributed with 3 2/ Ns turns: one winding along the d-axis, and the other along the q-axis. Note that this d\u2013q axis set may be at any arbitrary angle with respect to the phase-a axis. In order to keep the mmf and the flux-density distributions the same as in the actual machine with three-phase windings, the currents in these two windings would have to be isd and isq, where, as shown VECTOR CONTROL WITH d-AXIS ALIGNED WITH ROTOR FLUX 67 in Fig. 4-7, these two current components are 2 3/ times the projections of the i ts( ) vector along the d-axis and q-axis. 4-5 VECTOR CONTROL WITH d-AXIS ALIGNED WITH THE ROTOR FLUX In the following analysis, we will assume that the d-axis is always aligned with the rotor flux-linkage space vector, that is, also aligned with B tr( ). 4-5-1 Initial Flux Buildup Prior to t\u00a0=\u00a00\u2212 We will apply the information of the last section to vector control of induction machines. As shown in Fig. 4-8, prior to t\u00a0=\u00a00\u2212, the magnetizing currents are built up in three phases such that i I i i Ia m b c m( ) and ( ) ( ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003272_tvt.2020.2993725-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003272_tvt.2020.2993725-Figure6-1.png",
        "caption": "Fig. 6. Mechanical and electrical angles in 3-phase 9/12 SRM and desired flux lines with non-coupled coil configuration [23].",
        "texts": [
            "org/publications_standards/publications/rights/index.html for more information. the fewer number of stator poles and less power converter legs due to the smaller number of phases [25]. Most of the conventional SRM configurations have an even number of stator poles per phase; for example, for a 3-phase 12/8 SRM, Ns/m = 4 and for a 4-phase 24/18 SRM, Ns/m = 6. As shown in Table 1, pole configurations calculated by (3) include SRMs with an odd number of stator poles per phase, such as 3-phase 9/12, 4-phase 12/9, and 3-phase 15/10 SRMs. Fig. 6 shows the mechanical and electrical angles in a 3- phase 9/12 SRM, which has 3 stator poles per phase. It can be seen that the 9/12 SRM has similar electrical angles as the 12/8 SRM in Fig. 4 and the 6/14 SRM in Fig. 5. As shown in Fig. 4, when the coils of a phase of the 12/8 SRM are energized, four magnetic poles are created, which is equivalent to the number of stator poles per phase. Only the stator poles belonging to the excited phase generate the magnetic flux lines; making the mutual coupling between phases negligible, which is an important feature of SRMs. In the 12/8 SRM, the coils of the consecutive stator poles of a phase have opposite directions. This enables the flux pattern shown in Fig. 4. If the same coil pattern is applied to a 9/12 SRM, it would not be possible to have the number of magnetic poles equal to the number of stator poles per phase (Ns/m = 3). As circled in Fig. 6, the opposing flux direction cannot be maintained, since one of the flux loops opposes the coil direction. As a result, the dotted flux line in Fig. 6 would not be generated and a 9/12 SRM would have an unbalanced operation. In SRMs with an odd number of stator poles per phase, balanced magnetic poles can be generated by using a mutually coupled coil configuration as shown in Fig. 7 [26]. In this case, all coils of each phase have the same polarity. As a result, the flux completes its path through the stator poles of the neighboring phases and the magnetic poles are symmetrically distributed around the stator circumference. In mutually-coupled SRMs, the mutual inductance cannot be neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002798_tec.2020.2964942-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002798_tec.2020.2964942-Figure5-1.png",
        "caption": "Fig. 5. Solid steel rotors with copper cladding for a high-speed induction machine \u2013 Rolls Royce Central Technology [17]",
        "texts": [
            " More importantly by introducing a rotor/shaft with a lattice structure, the overall mass of the rotor was reduced by 25% and the moment of inertia decreased by 23%, compared with a more conventional design. The next example here, Fig. 4b), shows the mechanical parts of an outer-rotor/shaft for an open-frame PM motor. Here, the intention was to provide a sufficient through air flow for removing heat from the motor active parts. The presented mechanical components have been designed and manufactured using titanium alloy (Ti6Al4V) to provide an ultra-lightweight motor assembly. Enabling high-performance and robust rotor designs for high-speed machines is another area, where AM has been showcased. Fig. 5 presents an interesting example of a solid steel rotor design with copper cladding for a high-speed induction machine [17]. 0885-8969 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Here, three stages from fabrication of the alternative rotors with smooth and wavy profiles are presented. The material jetting (cold spray) technique was used to manufacture the rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000378_a:1021153513925-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000378_a:1021153513925-Figure5-1.png",
        "caption": "Figure 5 Finite element mesh for the ANSYS analysis.",
        "texts": [
            " The parts built with this experimental set-up, and after process parameter optimization, are shown in Fig. 4. The comparison of experimental with simulated results allows the estimation of the relative importance and role of the complex physical interactions that govern direct laser metal powder deposition process. The comparison of experiment and simulation were done on the AISI 1006 steel plate with dimensions 50 \u00d7 20 \u00d7 10 mm. The MONEL 400-alloy powder with 100 mesh was used to build 40 mm deposits (please see Fig. 4). The finite element mesh is shown in Fig. 5. The numerical model was run for both the duration of the laser heating and for the subsequent cooling period using different powers (in the range of 300 to 1000 W) and scanning speeds (in the range of 5 to 15 mm/s). Figs 6 and 7 show the typical analysis resulting from the use of 10 mm/s scanning speed and 600 W laser power. The data generated during the solution procedure includes the depth of the 1325\u25e6C (1598 K) isotherms that approximately represent the fusion zone (FZ) boundary. These data were then used for comparison with experimental results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003791_j.jsv.2016.01.016-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003791_j.jsv.2016.01.016-Figure12-1.png",
        "caption": "Fig. 12. The faulty sun gear with a cracked tooth.",
        "texts": [
            " Since the rotation speed fluctuates during the experiment, there is a small error between the deduced orders in the model and the real orders in Fig. 11(b). Among the gear fault categories, fatigue crack frequently occurs due to heavy loads and high-frequency stresses. Therefore, we conduct an experiment on the sun gear with a fault of tooth crack in this section. According to the stress analysis, the tooth root often operates under the highest stress and the fatigue crack often occurs at the position of tooth root. Thus we create a crack along the normal line of the tooth root curve artificially. The faulty sun gear is displayed in Fig. 12. Fig. 13 shows a vibration signal collected from the epicyclic gearbox with a sun gear fault and its spectrum. It can be seen that additional frequency components appear at orders of 87, 114, etc. These orders reflect the fault characteristics of a sun gear local fault in the epicyclic gearbox and the results are consistent with the spectral structures described in Section 4.2. In addition, components also exist at orders of 97, 100 and 101 which are not integer multiples of the number of planet gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000847_j.msea.2010.12.010-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000847_j.msea.2010.12.010-Figure1-1.png",
        "caption": "Fig. 1. Schematic of (a) the deposition setup, based aro",
        "texts": [
            " The relatively high cost of nickel base uperalloys and titanium alloys, along with low fractions of mateial wastage, are making the LDMD process an increasingly viable ption [1]. Further, LDMD has significant potential as a repair techique for damaged, high precision aerospace components, such as urbine blades [2]. Because of the safety critical nature of many eroengine components, acceptance of LDMD into widespread use ill require a detailed knowledge of the residual stress fields. This s the focus of the current paper. Most modern LDMD systems use a coaxial powder feed nozle positioned around a defocused laser arranged perpendicular o the substrate (Fig. 1a). This arrangement eliminates anisotropic owder flow into the melt pool and allows for multi-directional eposition without the need for altering the nozzle alignment [3]. he defocused laser forms a melt pool on the surface of the subtrate and the coaxially fed powder stream adds material to this ool. This results in swelling of the melt-pool and the formation of raised track. By incorporating lateral movement of the substrate, \u2217 Corresponding author. Tel.: +44 161 306 3591; fax: +44 161 306 3586",
            " / Materials Science and Engineering A 528 (2011) 2288\u20132298 2289 und a high power diode laser and (b) the laser raster pattern. m ( \u2013 f s t m p p a d s a a c e p c s a i o v m o a c t s p m m 2 2 T s b I F Waspaloy powder having a particle size range 53\u2013105 m was fed coaxially into the laser beam using a SIMATIC OP3 disk powder feeder. Because different substrate traverse speeds were used, the powder flow rate was modified to obtain a constant line mass elt-pool, but significant stresses perpendicular to the substrate corresponding to the z-direction in results presented in this paper see Fig. 1). An exception to these trends was found within 5 mm rom the top of the structures where stress balance requires zero tress to be approached. Further, they found little sensitivity of he stresses to the track raster pattern used [20]. Finite element odelling work also predicts tensile stresses near surface and comressive stresses perpendicular to the substrate [21,22]. They also redicted little effect on laser speed when the laser power was djusted to maintain the same heat input. Wang et al. [21] preict compressive vertical stresses within the mid region of their tructures and tensile stresses towards the edges",
            " Powder was fed to he deposition nozzle using nylon tubing with argon as a carrier as. The carrier gas also acted as a shielding gas to reduce oxidation uring the deposition process. The Inconel 718 substrates were connected to a bespoke ater-cooling device, attached to a 3-axis motion control sysem, positioned directly beneath the stationary deposition head. ach sample comprised 20 layers, each put down using a 6-track, 0 mm long raster pattern (resulting wall thickness of 5 mm). he definitions for directions and the design of raster pattern are chematically represented in Fig. 1b. The offset of each track was .8 mm in the y-direction and the jog in the z-direction was preetermined from previous work where average track heights were easured for each set of parameters [23]. The values used for he z-direction jogs are found in Table 2. Between the deposiion of each track a dwell of approximately 2 s was required to ccommodate for deceleration and acceleration of the translations tages and a dwell of approximately 5 s was required between ach layer. A variation in sample height was found as a result f the different z-direction jogs used for each set of processing arameters, the height of each finished sample is summarised in able 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001031_pime_proc_1988_202_127_02-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001031_pime_proc_1988_202_127_02-Figure2-1.png",
        "caption": "Fig. 2 Dynamic model of thrust loaded ball bearing",
        "texts": [
            " In the following analysis the bearing excitation force F, is determined simply by summing ball loads for the case in which inner and outer rings are constrained to remain fixed in position. This enables the free amplitude of bearing vibration A, to be deduced from the first equation above and system amplitudes to be deduced by application of the second equation to an appropriate structural model. Proc Instn Mech Engrs Vol202 No CS The features of a thrust loaded ball bearing which determine its vibration forces are modelled as shown in Fig. 2. The bearing has N equispaced balls, all of which are in firm contact with inner and outer raceways and roll, without sliding, at a true epicyclic speed, given by (4) o = - 1-- , 2 \"'( \"fe,Sa) The reader is referred to the Notation for definitions of the variables used. Each ball is represented by a spring of stiffness k, (0 G j < N - 1) whose line of action passes through the centre of the inner and outer race contact areas. The analysis is restricted to applications in which bearing speeds are moderate, for which ball centrifugal force is negligible and hence inner and outer contacts are diametrically opposite",
            " For simplicity only the case of waviness on one ball is considered and this ball is assumed to remain rotating about an axis normal to the plane containing the centres of the inner and outer race contacts. For these conditions waviness is described by Fig. 5b: a=a,sinmy,, m = l , 2 , 3 ,... Proc Instn Mech Engrs Vol 202 No C5 at UQ Library on June 19, 2014pic.sagepub.comDownloaded from where yB is measured with respect to a point on the ball surface. Variation in ball load and hence spring force in the dynamic model of Fig. 2 is produced by changes in the ball diameter through inner and outer contacts, given by DB(t) = 2aB sin myB, m = 2, 4, 6, ... This results in a time-varying component internal clearance given by P D - { &)} = 2aB sin(mwB t + 4J, m = 2, 4, 6, . . . 2 where is the angular position of the ball with respect to the rotating frame Oxyz. Substituting for PD in equations (10) and removing the summations gives (20) F A - = -3~8\u2019/* tan a{sin(mw,t + 4J} F R - = -$~b\u2018~[sin{(mo, + wc)t + 241~} a, a, + sin{(moB - o,)t)] (21) - cos{(moB + o,)t} + 24i] m = 2, 4, 6, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.11-1.png",
        "caption": "Fig. 3.11 No-roll centers and no-roll axis for a swing arm suspension (left) and a double wishbone suspension (right)",
        "texts": [
            " 74 3 Vehicle Model for Handling and Performance So far the suspension geometry has played no role (except in Sect. 3.8.3), at least not explicitly. This was done purposely to highlight which vehicle features are not directly related to the suspension kinematics. The fundamental reason that makes the suspension geometry so relevant is that vehicle bodies are subject to horizontal forces (inertia and aerodynamic forces). Starting from a reference configuration, and according to the equilibrium equation (3.64), let us apply to the vehicle body a lateral force \u2212Y j, with Y = may . As shown in Fig. 3.11, be this force located at height h above the road and at distances ab 1 and ab 2 from the front and rear axles, respectively. As shown in (3.70), ab 1 and ab 2 differ from a1 and a2 whenever the yaw moment NY = 0. Exactly like in (3.70), in a two-axle vehicle the lateral forces exerted by the road on each axle to balance Y are given by Y1 = Yab 2 l and Y2 = Yab 1 l (3.96) It is very important to recall that these two forces can be obtained from the global equilibrium equations only. Therefore, they are not affected by the suspensions, by the type of tires, by the amount of grip, etc",
            "90), it immediately arises that \u0394Z1t1 = k p \u03c61 \u03c6 p 1 and \u0394Z2t2 = k p \u03c62 \u03c6 p 2 (3.99) and hence, from (3.97) Yh = k p \u03c61 \u03c6 p 1 + k p \u03c62 \u03c6 p 2 (3.100) However, to obtain \u0394Z1 and \u0394Z2, it is necessary to look at the suspension kinematics. More precisely, in a first-order analysis, it suffices to consider the roll centers and the roll axis, as discussed in the next section. Let us start having a closer look at the suspension linkages. In case of purely transversal independent suspensions, like those shown, e.g., in Fig. 3.11, it is easy to obtain the instantaneous center of rotation Bi of each wheel hub with respect to the vehicle body. Another useful point is the center Ai of each contact patch. The same procedure can be applied also to the MacPherson strut. The kinematic scheme is shown in Fig. 3.12, while a possible practical design is shown in Fig. 3.13. The MacPherson strut is the most widely used front suspension system, especially in cars of European origin. It is the only suspension to employ a slider, marked by number 2 in Fig",
            " To obtain the instantaneous center of rotation Bi of each wheel hub with respect to the vehicle body it suffices to draw two lines, one along joints 3 and 4, and the other through joint 1 and perpendicular to the slider (not to the steering axis, which goes from joint 1 and 3, as also shown in Fig. 3.12). In all suspension schemes, the intersection of lines connecting Ai and Bi on both side of the same axle provides, for each axle, the so-called roll center Qi (Figs. 3.11 and 3.12). The signed distance of Qi from the road is named qi in Fig. 3.11. A roll center below the road level would have qi < 0. Therefore, a two-axle vehicle has two roll centers Q1 and Q2. The unique straight line connecting Q1 and Q2 is usually called the roll axis (Fig. 3.11). Some comments are in order here: 76 3 Vehicle Model for Handling and Performance Fig. 3.12 No-roll center for a MacPherson strut \u2022 the procedure just described to obtain the roll centers Qi is not ambiguous, provided the motion of the wheel hub with respect to the vehicle body is planar and has one degree of freedom; \u2022 points Ai are well defined and are not affected by the tire vertical compliance; \u2022 a three-axle vehicle has three points Qi . Therefore, in general there is not a straight line connecting Q1, Q2 and Q3",
            " Summing up, application of a force to the vehicle body at any point of the roll axis does not produce suspension roll. More precisely, a force (of any direction) applied to the vehicle body and whose line of action goes through the roll axis may affect the vehicle roll angle, but only because of tire deflections, with no contribution from the suspensions. In addition, there may be variations of z1 and z2. Let us go back to a purely lateral force \u2212Y j applied at P (not necessarily the center of mass G), as shown in Fig. 3.11. Since the global equilibrium dictates in (3.96) the values of Y1 and Y2, we have to decompose the lateral force \u2212Y j into a force \u2212Y1j applied at the front no-roll center Q1 and a force \u2212Y2j applied at the other no-roll center Q2, plus a suitable couple. There is a simple two-step procedure to obtain this result. First, consider that \u2212Y j at P is equivalent to the same force \u2212Y j applied at point Q, on the no-roll axis 78 3 Vehicle Model for Handling and Performance right below P , plus a pure (horizontal) roll moment Lbi = Y ( h \u2212 qb ) i, where qb = ab 2q1 + ab 1q2 ab 1 + ab 2 (3",
            " This way we have decomposed the lateral force into two forces at the two noroll centers, each one of the magnitude imposed by the equilibrium equations, plus a horizontal moment. It is important to note that it would be wrong to take the shortest distance from P to the roll axis to compute the moment. It is precisely the vertical distance (h \u2212 qb) that has to be taken as the force moment arm. Summing up, a lateral force \u2212Y j at P is totally equivalent to a lateral force \u2212Y1j at Q1 and another lateral force \u2212Y2j at Q2, plus the horizontal moment Y(h \u2212 qb)i (Fig. 3.11) applied to the vehicle body. Figures 3.14 and 3.15 shows how each force Yi at Qi is transferred to the ground by the suspension linkage, without producing any suspension roll. This is the key feature of the roll center Qi . Quite remarkably, this is true whichever the direction of the force there applied, and hence it is correct to speak of a (no-)roll center point (at first, Fig. 3.15 might suggest the idea of a roll center height qi ). The moment Y(h\u2212qb) is the sole responsible of suspension roll",
            "109) and for the roll angles due to suspension (spring) deflections \u03c6s 1 = 1 ks \u03c61 k\u03c61k\u03c62 k\u03c6 [ Y(h \u2212 qb) k\u03c62 + Y1q1 k p \u03c61 \u2212 Y2q2 k p \u03c62 ] \u03c6s 2 = 1 ks \u03c62 k\u03c61k\u03c62 k\u03c6 [ Y(h \u2212 qb) k\u03c61 + Y2q2 k p \u03c61 \u2212 Y1q1 k p \u03c61 ] (3.110) where k\u03c6 = k\u03c61 + k\u03c62 = ks \u03c61 k p \u03c61 ks \u03c61 + k p \u03c61 + ks \u03c62 k p \u03c62 ks \u03c62 + k p \u03c62 (3.111) is the total roll stiffness, like in (3.86). Equations (3.109) and (3.110) show how the tire and suspension stiffnesses interact with each other and with the first-order suspension geometry (i.e., the no-roll axis position). According to them, the total roll angle \u03c6 produced by a lateral force Y j applied at P (Fig. 3.11) is given by k\u03c6\u03c6 = Y ( h \u2212 qb )+ Y1q1 k\u03c61 k p \u03c61 + Y2q2 k\u03c62 k p \u03c62 (3.112) If qb is almost constant (i.e., q1 \u2248 q2), then NY has little effect on the roll angle \u03c6 (see also (3.117)). However, NY affects quite strongly the lateral load transfers, because it redistributes the values of the lateral forces Y1 and Y2. 3.8 Suspension First-Order Analysis 81 Lateral load transfers \u0394Zi are among the most influential quantities in vehicle dynamics. They can be obtained, e.g., combining (3.99) and (3.109) \u0394Z1t1 = k\u03c61k\u03c62 k\u03c6 [ Y(h \u2212 qb) k\u03c62 + Y1q1 ks \u03c61 + Y1q1 ks \u03c62 + Y1q1 + Y2q2 k p \u03c62 ] \u0394Z2t2 = k\u03c61k\u03c62 k\u03c6 [ Y(h \u2212 qb) k\u03c61 + Y2q2 ks \u03c61 + Y2q2 ks \u03c62 + Y1q1 + Y2q2 k p \u03c61 ] (3",
            " A point that is like G, except that it does not roll. More precisely, we are looking for the origin O1 of the reference system S1 in Fig. 9.3, that is a reference system which yaws, but does not pitch and roll. For simplicity, we assume the tires are perfectly rigid in this chapter. Roll motion is part of vehicle dynamics. However, it is useful to start with a purely kinematic analysis to get an idea of the several effects of roll motion. This kinematic analysis should be seen as a primer for better investigating roll dynamics. Figure 3.11 shows how to determine the no-roll centers Qi for a swing arm suspension and a double wishbone suspension. The same method is applied in Fig. 3.12 to a MacPherson strut. In all these cases, the vehicle is in its reference configuration (no roll). When the vehicle rolls, the no-roll centers Qi migrate with respect to the vehicle body. They can be obtained, as shown in Fig. 9.1, using the same procedure of Fig. 3.11, i.e., as the intersection of the two lines passing through points Aij and Bij . However, determining the current position of Qi has little relevance in this context. Much more important are the following definitions. We define point M1 as the point of the vehicle body that coincides with Q1 in the vehicle reference configuration (Fig. 9.1). The same idea, applied to the rear axle, leads to the definition of M2. These points are called here track invariant points. Let us investigate their properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000599_tro.2004.842341-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000599_tro.2004.842341-Figure1-1.png",
        "caption": "Fig. 1. Different types of actuation for a 7-bar mechanism.",
        "texts": [
            " In control theory underactuation by definition refers to a control system which has less inputs then its DOF, while the number of inputs of a full-actuated system equals its DOF [29]. This is in accordance with Definition 1 because . A full-actuated system is completely actuated and an improvement is impossible. No other type of actuation beside these two can exist. Hence the term \u2018overactuation\u2019 is meaningless and shall not be used. As an example, if the joints 1 and 2 of the 7-bar mechanism in Fig. 1 are actuated the PM is nonredundantly full-actuated. If joint 1, 2, and 3 are actuated the PM is redundantly full-actuated. Controlling joint 1 and 3 yields a redundantly underactuated PM. The remaining part of the paper deals with simply RFA PMs, i.e., , and so . V. INVERSE DYNAMICS OF REDUNDANTLY FULL-ACTUATED PMS The inverse dynamics problem consists in finding the generalized control forces that produce a desired trajectory of the PM. That is, given find such that (9) holds. The DOA of a full-actuated PM equals its DOF "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003992_1350650117711595-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003992_1350650117711595-Figure10-1.png",
        "caption": "Figure 10. Average fiber orientation in glass fiber reinforced Nylon 6/6 gear (Source: Senthilvelan and Gnanamoorthy95).",
        "texts": [
            "91 Glass-filled polymer gears show better wear resistance in comparison to the unfilled polymer gears due to the improved elastic modulus and compressive strength.63,92 A study shows that when a trace amount of calcium salt of the octacosanoic acid (Ca-OCA) is added to POM/SiC composite, the wear rate of composite gear is reduced due to nucleating effect of SiC and Ca-OCA.93 Fibers are hard in nature and deteriorate the smoothness of the gear surface. The fibers aligned along the gear tooth involute profile restrict shrinkage that results in less total profile deviation.94 Fiber orientation significantly affects the linear shrinkage in polymers.95 Figure 10 shows an average fiber orientation in glass fiber reinforced Nylon 6/6 gear. Also, the fiber orientation in the molded reinforced gear near the tooth space region and tooth addendum region is shown in Figure 11. The fiber orientation in an injection molded component depends upon molding conditions (gating, pressure, temperature, and holding time), component geometry, matrix material, polymer melt viscosity, and fiber type (density, volume fraction, and aspect ratio).96 The orientation of fibers in a direction parallel to sliding direction results in a low wear resistance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001329_j.actamat.2014.09.028-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001329_j.actamat.2014.09.028-Figure17-1.png",
        "caption": "Fig. 17. (a) Schematic and (b) fracture morphology of the stress-relieved DMD AISI 4340 steel after three-point bend testing.",
        "texts": [
            " However, the fracture close to the de-bonding shows dimple rupture. This further indicates the bad effect of bonding defects in accelerating fracture. Fig. 16(g) shows the intergranular fracture. The dendrite nodules in the void (Fig. 16(h)) indicate that the cavity was caused by unfavorable directional solidification during laser deposition. The fracture was caused by overload. Pictures of the cross section and top view inset of stressrelieved DMD AISI 4340 steel after bend testing are given in Fig. 17. A schematic of the bend test is shown in Fig. 17(a). The bending angle varies for four samples (labeled B1\u2013B4), indicating their varied bend strength. Adjacent track boundaries can clearly be differentiated in the insets in Fig. 17(c)\u2013(e). Their load\u2013displacement curves are shown in Fig. 18. The average value of four measurements of the bend strength is 225 MPa (Table 3). The fracture morphology of the stress-relieved DMD AISI 4340 steel after bend testing is given in Fig. 19. Fig. 19(a) shows the top view of specimen B4. The magnified microstructures of the plan view and cross section are shown in Fig. 19(b) and (c), respectively. The elongated structure in the first layer close to the bending fracture plane is formed as a result of the stretching effect of the bending force, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure11-2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure11-2-1.png",
        "caption": "Fig. 11-2 (a) Aligned position for phase a; (b) unaligned position for phase a.",
        "texts": [
            " In order to achieve a continuous rotation, each phase winding is excited by an appropriate current at an appropriate rotor angle, as well as de-excited at a proper angle. For rotating it in the counterclockwise direction, the excitation sequence is a-b-c-d. 157 11 Switched-Reluctance Motor (SRM) Drives Advanced Electric Drives: Analysis, Control, and Modeling Using MATLAB/Simulink\u00ae, First Edition. Ned Mohan. \u00a9 2014 John Wiley & Sons, Inc. Published 2014 by John Wiley & Sons, Inc. 158 SWITCHED-RELUCTANCE MOTOR DRIVES An SRM must be designed to operate with magnetic saturation and the reason to do so will be discussed later on in this chapter. Fig. 11-2 shows the aligned and the unaligned rotor positions for phase a. For phase a, the flux linkage \u03bba as a function of phase current ia is plotted in Fig. 11-3 for various values of the rotor position. In the unaligned position where the rotor pole is midway between two stator poles (see Fig. 11-2b, where \u03b8mech equals \u03b8un), the flux path includes a large air gap, thus the reluctance is high. Low flux density keeps the magnetic structure in its linear region, and the phase inductance has a small value. SWITCHED-RELUCTANCE MOTOR 159 As the rotor moves toward the aligned position of Fig. 11-2a (where \u03b8mech equals zero), the characteristics become progressively more saturated at higher current values. 11-2-1 Electromagnetic Torque Tem With the current built up to a value I1, as shown in Fig. 11-4, holding the rotor at a position \u03b81 between the unaligned and the aligned 160 SWITCHED-RELUCTANCE MOTOR DRIVES positions, the instantaneous electromagnetic torque can be calculated as follows: Allowing the rotor to move incrementally under the influence of the electromagnetic torque from position \u03b81 to \u03b81\u00a0 +\u00a0 \u0394\u03b8mech, keeping the current constant at I1, the incremental mechanical work done is \u2206 = \u2206W Temmech mech\u03b8 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002760_j.jmatprotec.2014.12.029-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002760_j.jmatprotec.2014.12.029-Figure4-1.png",
        "caption": "Fig. 4. Illustrations showing that the LDS measures the deflection resulting from (a) longitudinal bowing mode of distortion in Cases 1\u20133 and (b) transverse angular mode of distortion in Cases 4\u20136.",
        "texts": [
            " A thermocouple is mounted to the LDS to monitor its temperature and to verify that it does not exceed its maximum allowable operating temperature (50 \u25e6C). A high-temperature bag is placed over all of the electronics, excluding the LDS, to protect them from metal powder during the deposition. Although both modes of distortion simultaneously occur, the measurement setup and two different deposition patterns allow the deflection from each mode to be measured independently. For example, deflection resulting from the longitudinal pattern in Cases 1 through 3 is dominated by the longitudinal bowing mode (Fig. 4(a)). Similarly, the deflection measured during the deposition of the transverse pattern in Cases 4 through 6 is dominated by the transverse angular mode (Fig. 4(b)). An additional benefit of this scheme is the ability to measure the deflection at varying distances from the deposition. Each pattern allows the relative position between the fixed LDS measurement location and the deposited track to vary. This will be discussed in greater detail in Section 3.1.1. Temperatures are measured at various locations on the top and bottom of the substrate plate using Omega GG-K-30 type K thermocouples, which have a measurement uncertainty of 2.2 \u25e6C or 0.75%, whichever is larger"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure61-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure61-1.png",
        "caption": "Fig. 61 a Schematic diagram of visual sensing system; b schematic diagram of detection positions in the image [86]",
        "texts": [
            " Although the method reduces the excessive accumulation of heat, the forming efficiency is greatly reduced, and the control process is relatively passive. Ouyang used a variable polarity GTAW process to form 4043 aluminum alloy parts, and CCD visual sensing monitors the arc length. He believes that the first few deposited layers should use a larger heat input (increasing the welding current) to better wet the substrate, and as the metal deposition progresses, the heat input should be reduced layer by layer [85]. Xiong designed passive vision devices (Fig. 61) and image processing algorithms to automatically detect the distance between the end of the welding wire and the surface of the workpiece being processed [86], and develop an innovative tracking algorithm to determine the position of the solid-liquid separation point at the tail of the molten pool through continuous images. Experiments show that the algorithm has excellent effectiveness and anti-jamming ability in additive manufacturing based on robot GTA. Xiong also designed a virtual binocular visual sensing system to monitor the geometry of the molten pool [87]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003696_j.apm.2018.11.014-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003696_j.apm.2018.11.014-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the dual-rotor system with inter-shaft bearing.",
        "texts": [
            " The results reveal that the system may resonate in some non-critical-speed region due to the local defect, wherein, a pair of abnormal RPs excited by the characteristic defect frequency and a pair of abnormal RPs excited by the combination frequency appear. These nonlinear resonant response characteristics are helpful for the fault diagnostics of the inter-shaft bearing in a dual-rotor system. CFM56 is one of most widely used dual-rotor aero-engines [27] . Based on the basic structure of CFM56, a two-disk dualrotor system supported by four points is obtained by using the simplified method of dynamic model [28] . The schematic diagram of the dual-rotor system with inter-shaft bearing is shown in Fig. 1 . The HP rotor and the LP rotor are connected by an inter-shaft bearing, which is a cylindrical roller bearing, including coupling nonlinear factors such as fractional exponential Hertzian contact restoring force, radial clearance, and parametric excitation caused by the periodic variation of the contact stiffness. Besides, the supports of LP rotor at both ends and the support of HP rotor at left end are simplified as linear elastic springs, where k i , c i (i = 1 \u223c3) are the stiffness and damping coefficients of the linear elastic springs; O 1 , O 2 are the geometric centers of LP rotor and HP rotor; \u03c9 1 , \u03c9 2 are rotation speeds of LP and HP rotors; l i (i = 1 \u223c5) are the lengths of the shafts; K b is the Hertz contact stiffness of the inter-shaft bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001657_tfuzz.2014.2310491-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001657_tfuzz.2014.2310491-Figure12-1.png",
        "caption": "Fig. 12: Trajectory of the system output for Example 2.",
        "texts": [
            " , \u03be 7 3(X3)) T . Choose the intermediate virtual control function (25) and (35), the parameter adaptive law (46), and the actual control (60). The initial conditions are chosen as x1(0) = 0.3, x2(0) = 0.2, x3(0) = 0, \u03b8\u0302(0) = 0, x\u03021(0) = x\u03022(0) = x\u03023(0) = 0. The design parameters in the whole control scheme are chosen as l1 = 56, l2 = 24, l3 = 24, r = 8, a1 = 0.9, a2 = 0.8, a3 = 1, k0 = 1, c1 = c2 = 30, c3 = 35, \u03c4 = 5, Q = [9, 0, 0; 0, 9, 0; 0, 0, 8]. The simulation results are given in Figs. 12\u201314. Fig. 12 shows the trajectory of the system output y = x1. It can be observed that, even though k\u0303 is a fuzzy value, the system output can still track the reference signal yr to a bounded compact set. Fig. 13 shows the trajectory of the parameter \u03b8\u0302, Fig. 14 shows the trajectory of the control u. It can be shown that the proposed control scheme can guarantee the boundedness of the closed-loop control system and the desired tracking performance. 0 5 10 15 20 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 x 10 \u22123 k\u0303 t \u03b8\u0302 Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001095_j.ijmecsci.2006.06.003-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001095_j.ijmecsci.2006.06.003-Figure1-1.png",
        "caption": "Fig. 1. A spur gear pair model.",
        "texts": [
            " Then by the IHBM some superharmonic solutions are found, and the accordance with the numerical results shows the validity of the method presented in this paper. Perhaps these phenomena have not been found in the latest literatures. At last the effect of some important parameters, including the damping ratio and the amplitude of excitation, on the frequencyresponse curves is investigated, and these results are useful to analyze and/or control the dynamics of gear system. Furthermore, the method presented here could be extended to the multi-degree gear system and other similar systems. 2. Physical model Here a spur gear pair shown as Fig. 1 is researched, where the shaft and bearing is assumed to be rigid. And all the symbols used are given in the Nomenclature. According to the Newtonian law of motion the equations of the torsional motion are Ia d2ya dt\u03042 \u00fe c Ra dya dt\u0304 Rb dyb dt\u0304 de\u0304 dt\u0304 Ra \u00fe RaK\u00f0t\u0304\u00def \u00f0Raya Rbyb e\u0304\u00f0t\u0304\u00de\u00de \u00bc Ta, \u00f01a\u00de Ib d2yb dt\u03042 c Ra dya dt\u0304 Rb dyb dt\u0304 de\u0304 dt\u0304 Rb RbK\u00f0t\u0304\u00def \u00f0Raya Rbyb e\u0304\u00f0t\u0304\u00de\u00de \u00bc Tb. \u00f01b\u00de Obviously this system is semi-definite, and it could be transformed into Eq. (2) by letting x\u0304 \u00bc Raya Rbyb e\u0304\u00f0t\u0304\u00de m d2x\u0304 dt\u03042 \u00fe c dx\u0304 dt\u0304 \u00fe k 1\u00fe 2 XL l\u00bc1 l cos\u00f0lot\u0304\u00de \" # f \u00f0x\u0304\u00de \u00bc F\u0304 m d2e\u0304\u00f0t\u0304\u00de dt\u03042 , \u00f02a\u00de m \u00bc IaIb IbR2 a \u00fe IaR2 b , (2b) f \u00f0x\u0304\u00de \u00bc x\u0304 b; x\u03044b; 0; bpx\u0304pb; x\u0304\u00fe b; x\u0304o b; 8>< >: (2c) F\u0304 \u00bc Ta Ra \u00bc Tb Rb , (2d) K\u00f0t\u0304\u00de \u00bc k 1\u00fe 2 XL l\u00bc1 l cos\u00f0lot\u0304\u00de \" # "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000024_s0022112072001612-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000024_s0022112072001612-Figure9-1.png",
        "caption": "FIGURE 9. Comparisons between experiment and theory for the mean velocity field in Pleurobrachia. -, t,heoretically predicted profiles; - - - - -, profiles observed experimentally (Sleigh & Aiello 1971) . 1 corresponds to the combplate beating with a frequency of 5 beatsls (although intermittently) while the profile in 2 is for a frequency of 12 beatsls.",
        "texts": [
            " We would expect the above theory to be reasonably valid in Opalina and Paramecium if they exhibited the two-dimensional beat used in the calculations. However, the only known observations are those of Sleigh & Aiello (1971) on Pleurobrachia. We do not expect OUT theory to be particularly appropriate on two counts: because the Reynolds number is probably greater than one and the slender-body theory is violated. Even with these difficulties we have included calculations of Pleurobrachia. For reasonable values of y, K and T the comparisons between experiment (Sleigh & Aiello 1971) and theory are shown in figure 9. As an estimation for y and T we can use the values of the drag for a disk moving broadside on and edgewise (Lamb 1932), which would give y = 1.5 and T = y L 2 / a b . The ratio L2/ab is of O( 1) . The diagram shows reasonable agreement between theory and experiment above x3 > 0.6 even with all the associated difficulties. Below this level observations are not particularly accurate anyway, so there is room for improvement in both the theoretical and experimental work. 6.3. Calculations of the force and bending moment The force and bending moment exerted by a cilium is of particular interest to the proto-zoologist as both experimental (Yoneda 1960, 1962) and theoretical work (Harris 1961) has been carried out on this subject"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000368_13552541211250391-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000368_13552541211250391-Figure1-1.png",
        "caption": "Figure 1 Schematic representation of sample build up",
        "texts": [
            " Once surface area is computed, roughness of the surface can be characterized. The objective of this study is to determine andunderstand the effect of part\u2019s thickness and variation in process parameter settings of EBM system on surface roughness/topography of EBM fabricated Ti-6Al-4V metallic parts. A mathematical model based upon response surface methodology (RSM) is developed to study the variation of surface roughness with changing process parameter settings. In this study four sets of rectangular test slabs each of contours and squares (Figure 1) were produced by melting Ti-6Al-4V powder of size 50-100mm, in Arcam\u2019s S12 EBM system under different process parameter settings. Each set consists of three slabs of approximately 55 \u00a3 50mm in two directions (x, y) (Figures 1 and 2). Each test slab in the set is of different thickness (w). Each set has different process parameter settings as described in Table I. To study the influence of different processing parameters, such samples are chosen that have similar build Effect of process parameters on EBM produced Ti-6Al-4V A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure3.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure3.5-1.png",
        "caption": "Fig. 3.5",
        "texts": [
            "2 Hooke\u2019s Law 87 where \u03b1T is the coefficient of thermal expansion (see Chapter 1). No shear strains are induced by \u0394T . Then, as a generalization of (3.12), Hooke\u2019s law can be written as \u03b5x = 1 E [\u03c3x \u2212 \u03bd(\u03c3y + \u03c3z)] + \u03b1T \u0394T , \u03b5y = 1 E [\u03c3y \u2212 \u03bd(\u03c3z + \u03c3x)] + \u03b1T \u0394T , \u03b5z = 1 E [\u03c3z \u2212 \u03bd(\u03c3x + \u03c3y)] + \u03b1T \u0394T , \u03b3xy = 1 G \u03c4xy , \u03b3xz = 1 G \u03c4xz , \u03b3yz = 1 G \u03c4yz . (3.14) E3.1Example 3.1 By using a strain gage rosette, the strains \u03b5a = 12 \u00b7 10\u22124, \u03b5b = 2 \u00b7 10\u22124 and \u03b5c = \u22122 \u00b7 10\u22124 have been measured in a steel sheet in the directions a, b and c (Fig. 3.5a). Calculate the principal strains, the principal stresses and the principal directions. Solution We introduce the two coordinate systems x, y and \u03be, \u03b7 according to Fig. 3.5b. Inserting the angle \u03d5 = \u221245\u25e6 into the first and second transformation equation (3.3), we obtain \u03b5\u03be = 1 2 (\u03b5x + \u03b5y)\u2212 1 2 \u03b3xy, \u03b5\u03b7 = 1 2 (\u03b5x + \u03b5y) + 1 2 \u03b3xy . Addition and subtraction, respectively, yields \u03b5\u03be + \u03b5\u03b7 = \u03b5x + \u03b5y, \u03b5\u03b7 \u2212 \u03b5\u03be = \u03b3xy. With \u03b5\u03be = \u03b5a, \u03b5\u03b7 = \u03b5c and \u03b5x = \u03b5b we get \u03b5y = \u03b5a + \u03b5c \u2212 \u03b5b = 8 \u00b7 10\u22124, \u03b3xy = \u03b5c \u2212 \u03b5a = \u221214 \u00b7 10\u22124 . The principal strains and principal directions are determined according to (3.5) and (3.4): \u03b51,2 = (5\u00b1\u221a9 + 49)\u00b710\u22124 \u2192 \u03b51 = 12.6 \u00b7 10\u22124, \u03b52 = \u22122.6 \u00b7 10\u22124 , tan 2\u03d5\u2217 = \u221214 2\u2212 8 = 2.33 \u2192 \u03d5\u2217 = 33.4\u25e6 . Introducing the angle \u03d5\u2217 into (3.3) shows that it is associated with the principal strain \u03b52. The principal directions 1 and 2 are plotted in Fig. 3.5b. Solving (3.13) for the stresses yields \u03c31 = E 1\u2212 \u03bd2 (\u03b51 + \u03bd \u03b52), \u03c32 = E 1\u2212 \u03bd2 (\u03b52 + \u03bd \u03b51) . With E = 2.1 \u00b7 102 GPa and \u03bd = 0.3 we obtain \u03c31 = 273 MPa, \u03c32 = 27 MPa . E3.2 Example 3.2 A steel cuboid with a quadratic base area (h = 60 mm, a = 40 mm) fits in the unloaded state exactly into an opening with rigid walls (Fig. 3.6a). Determine the change of height of the cuboid when it is a) loaded by the force F = 160 kN or b) heated uniformly by the temperature \u0394T = 100\u25e6 C. Assume that the force F is uniformly distributed across the top surface and that the cuboid can slide without friction along the contact faces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure6.7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure6.7-1.png",
        "caption": "Fig. 6.7",
        "texts": [
            "3 Principle of Virtual Forces and Unit Load Method 245 (6.23) and set Q = 1, we see that the first terms are equal. This leaves the result 1 \u00b7 u = \u2211 Si S\u0304i li EAi . (6.29) Thus, the virtual force \u201c1\u201c in the horizontal direction enables us to determine the real horizontal displacement u due to the vertical force F . Similar considerations lead to the displacement component in any given direction of an arbitrary pin of a general truss. Assume, for example, that the displacement component f of pin VI of the truss in Fig. 6.7a has to be determined (the direction of f is given by the angle \u03b1). In the first step, the forces Si in the members due to the applied load F have to be calculated. In the second step, the truss is subjected only to the virtual force \u201c1\u201c at pin VI in the direction of f (Fig. 6.7b) and the corresponding forces S\u0304i are calculated. Then, (6.29) yields f = \u2211 Si S\u0304i li EAi . (6.30) To obtain (6.30) we have divided (6.29) by the force 1. Thus, the forces S\u0304i in (6.30) are due to a dimensionless force 1; hence, they are from now on also dimensionless quantities. Note that they must have the dimension of a force in (6.28) so that Si and S\u0304i can be added. According to the principle of superposition, Equation (6.30) is valid for a truss subjected to arbitrarily many forces. In general, the quantities Si are the forces in the members due to the total loading"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001615_j.trac.2018.06.017-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001615_j.trac.2018.06.017-Figure13-1.png",
        "caption": "Figure 13. Schematic illustration of the detection process of the pesticide biosensor based on 1242 the N, S-CQDs. (Reproduced from [119], with permission from Elsevier). 1243",
        "texts": [
            " Photoluminescent biosensor 636 Although there are some CDs-based biosensors used in the monitoring of pesticide 637 residues, the optical properties of pure CDs still greatly limit the detection sensitivity and 638 accuracy. Doping can be adopted to solve this problem. The group of MacFarlane [119] 639 obtained N and S co-doped CQDs (N,S-CQDs) via adopting a single source of ILs, which 640 could dramatically improve their photoluminescence lifetime. Built upon the reaction system 641 with two-enzyme, the co-doped CQDs were used for carbaryl detection. According the 642 function mechanism (Figure 13), H2O2 generated by the enzyme can effectively cut down the 643 intensity of the N,S-CQDs to generate an extremely sensitive detector. They proved that the 644 high sensitivity derived from the N and S dopants, which could adsorb H2O2 tightly and 645 generate local states to trap hot electrons, accelerating the electron transfer to H2O2 and then 646 leading to the quenching of the CQD fluorescence. This N,S-CQDs-based biosensor could be 647 applied for ultrasensitive pesticide detection with the LOD of 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure1.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure1.4-1.png",
        "caption": "Fig. 1.4",
        "texts": [
            " Then the radius of an arbitrary cross section is given by r(x) = r0 + r0 l x = r0 ( 1 + x l ) . Using (1.4) with the cross section A(x) = \u03c0 r2(x) and the constant normal force N = \u2212F yields \u03c3 = N A(x) = \u2212F \u03c0r20 ( 1 + x l )2 . The minus sign indicates that \u03c3 is a compressive stress. Its value at the left end (x = 0) is four times the value at the right end (x = l). E1.2Example 1.2 A water tower (height H , density ) with a cross section in the form of a circular ring carries a tank (weight W0) as shown in Fig. 1.4a. The inner radius ri of the ring is constant. Determine the outer radius r in such a way that the normal stress \u03c30 in the tower is constant along its height. The weight of the tower cannot be neglected. Solution We consider the tower to be a slender bar. The relationship between stress, normal force and cross-sectional area is given by (1.4). In this example the constant compressive stress \u03c3 = \u03c30 is given; the normal force (here counted positive as compressive force) and the area A are unknown. The equilibrium condition furnishes a second equation. We introduce the coordinate x as shown in Fig. 1.4b and consider a slice element of length dx. The cross-sectional area of the circular ring as a function of x is A = \u03c0(r2 \u2212 r2i ) (a) where r = r(x) is the unknown outer radius. The normal force at the location x is given by N = \u03c30A (see 1.4). At the location x+ dx, the area and the normal force are A+ dA and N + dN = \u03c30(A+ dA). The weight of the element is dW = g dV where dV = Adx is the volume of the element. Note that terms of higher order are neglected (compare Volume 1, Section 7.2.2). Equilibrium in the vertical direction yields \u2191: \u03c30(A+ dA)\u2212 g dV \u2212 \u03c30A = 0 \u2192 \u03c30 dA\u2212 g Adx = 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001535_978-981-10-5355-9_1-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001535_978-981-10-5355-9_1-Figure2-1.png",
        "caption": "Fig. 2. Schematic of twin-wire welding torch for WAAM [25]",
        "texts": [
            " For a single-wire process, there is no limitation imposed on movement during deposition by the need to rotate the torch. Various transfer modes can be used in GMAW, such as spray and pulsed-spray. Cold metal transfer (CMT), as a modified GMAW variant based on the controlled dip transfer mode, has been widely used for WAAM due to its high deposition rate with low heat input [24]. Tandem GMAW, a twin-wire process, was recently reported for creating metallic objects with high deposition rates [25], as shown in Fig. 2. Although it has been stated that the tandem system has the potential to produce intermetallic alloy as well as the gradient materials, to date there are no reports of this in the literature. To increase the deposition rate and material efficiency, a double electrode GMAW using GTAW torch to provide the bypass current was developed as shown in Fig. 3. It was reported that the coefficient of materials utilization increased more than 10% using DE-GMAW for depositing thin-wall parts within a certain range of bypass current [26]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000987_j.engfailanal.2014.11.018-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000987_j.engfailanal.2014.11.018-Figure1-1.png",
        "caption": "Fig. 1. Schematic of tooth profile and crack propagation: (a) tooth profile of an involute spur gear, (b) schematic of crack propagation.",
        "texts": [
            " Before tooth profile curve equations are presented, some basic variable symbols are introduced first: m is the module, a the pressure angle of the gear pitch circle, aa the pressure angle of the gear addendum circle, aC the pressure angle of the involute starting point, r, rb, ra the radii of the pitch circle, base circle, addendum circle of the gear, h a the addendum coefficient, c\u2044 the tip clearance coefficient, N the number of teeth. The gear tooth profile which is defined by the involute curve BC and fillet curve CD is shown in Fig. 1. The x and y coordinates of the involute profile (curve BC) are given by the following equations. x \u00bc ri sin u y \u00bc ri cos u ; \u00f01\u00de u \u00bc p 2N \u00f0invai inva\u00de; \u00f02\u00de where ri = rb/ cos ai; ai (aC 6 ai 6 aa) is the pressure angle of the arbitrary point at the involute curve in which aC = arccos (rb/rC), aa = arccos (rb/ra); rC \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0rb tan a h am= sin a\u00de2 \u00fe r2 b q is the radius of the involute starting point circle; invai is the involute function and invai = tan ai ai, inva = tan a a. The equations of the fillet curve of the tooth profile CD are defined as follows [40]: x \u00bc r sin\u00f0U\u00de \u00f0a1= sin c\u00fe rq\u00de cos\u00f0c U\u00de y \u00bc r cos\u00f0U\u00de \u00f0a1= sin c\u00fe rq\u00de sin\u00f0c U\u00de \u00f0a 6 c 6 p=2\u00de; \u00f03\u00de U \u00bc \u00f0a1= tan c\u00fe b1\u00de=r; \u00f04\u00de where rq = c\u2044m/(1-sin a), a1 \u00bc \u00f0h a \u00fe c \u00de m rq and b1 \u00bc pm=4\u00fe h am tan a\u00fe rq cos a. The crack path is assumed to be a straight line. The crack starts at the root of the driven gear and then propagates, as is shown in Fig. 1b. The geometrical parameters of the crack (q, t, w) are presented in Fig. 1b, in which q denotes the crack depth, t the crack propagation direction, w the crack initial position (in this paper q = 1, 2, 3 and 4 mm, t = 45 , w = 35 ). To simplify the problem, the TVMS calculation is performed under the assumption of a plane strain problem. To improve the computational efficiency, the analysis is performed by a 2D model with only nine teeth established in ANSYS software, in which the crack tip is modeled using 2D singularity elements (see Fig. 2). In the figure, the inner ring of gear 2 is fixed; the inner ring of gear 1 is loaded with a constant torque T1, which is obtained through suitable tangential forces [2]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001258_j.euromechsol.2010.03.002-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001258_j.euromechsol.2010.03.002-Figure3-1.png",
        "caption": "Fig. 3. Model of two-stage gearing system.",
        "texts": [
            " In order to improve the reliability and accuracy of the results, in comparison with (Bartelmus, 1992), the technique proposed in (Bartelmus and Zimroz, 2009b), consisting in the statistical analysis of a set of data on spectral features calculated for signals captured at different load values, is employed. As suggested in (Bartelmus, Fig. 5. Simulation results: acceleration signal for 1992), regression analysis is used for the pair: spectral components arithmetic sum e load value and a linear relation is obtained. The conclusion is the same e the diagnostic relation becomes stronger when condition changes. In this paper this approach is used to investigate the involved phenomena by means of mathematical modelling and computer simulations. A system with a two-stage gearbox is shown in Fig. 3. The system\u2019s torsional vibration is considered assuming six degrees of freedom (DOF). 4i, _4i, \u20ac4i represent respectively the rotation angle, the angular velocity and the angular acceleration of the different system DOFs. The number of teeth in the gears is: Z1, Z2, Z3 and Z4. Ms _\u00f04\u00de is the electric motor driving moment characteristic. M1, M2, M3 stand for the internal moments transmitted by the shaft stiffness, depending on the operation factors. Is, Im are the moments of inertia for respectively the electric motor and the driven machine, depending on the design factors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000119_0304-4165(84)90131-4-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000119_0304-4165(84)90131-4-Figure2-1.png",
        "caption": "Fig. 2. The products of glyceraldehyde autoxidation. Glyceral~lehyde consumption, hydroxypyruvaldehyde, and hydroxypyruvate production were measured in an incubation",
        "texts": [
            " Control = 50 mM glyceraldehyde in 100 mM sodium phosphate, pH 7.4. Reaction mixture d A 550/d t Percentage (10-3 abs. units per min) of control Control Control (anaerobic) Control + 0.1 mg/ml superoxide dismutase Control + 1 mM DETAPAC Control + 1 mM DETAPAC and 0.1 mg/ml superoxide dismutase Control + 583 U/ml catalase 50 mM glyceraldehyde in 100 mM Na + Hepes, pH 7.4 50 mM glyceraldehyde in 100 mM Tris-HCl, pH 7.4 40+ 2 480 + 10 (12-fold increase) 25 _+ 2 62 40_+ 2 100 23 _+ 2 57 37 + 2 92 19 + 2 48 9+ 2 23 cay and fl-hydroxypyruvaldehyde production (Fig. 2). A high activity of catalase was used in these experiments as 50 mM glyceraldehyde was found to partly inhibit catalase (data not shown). Reduction of ferricytochrome c. Autoxidising glyceraldehyde reduces ferricytochrome c to ferrocytochrome c at 37\u00b0C - - for 50 mM glyceraldehyde with 10 # M ferricytochrome c, dA/55o/d t = 0.04 absorbance units per min (Table I). After ca. 10 min of reaction time the cuvette reaction mixture becomes anaerobic (the oxygen tension was monitored on the Clark-type oxygen electrode) and the rate of ferricytochrome c reduction rapidly increases to ca"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003761_s11663-019-01523-1-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003761_s11663-019-01523-1-Figure3-1.png",
        "caption": "Fig. 3\u2014Schematic detailing the dimensions of the samples used for mechanical property tensile testing.",
        "texts": [
            " A Keyence VHX-5000 was used for optical imaging and determination of the relative density of samples built. A FEI Scios Dual Beam scanning electron microscope (SEM) was used for microstructure investigations and EDS analysis. For the SEM micrographs shown in this work, an acceleration voltage of 20 kV and secondary electron contrast were used. The ceramic samples were sputtered with gold in order to form a thin layer guaranteeing electric conductivity. The samples manufactured for tensile testing of the bulk ceramic were processed according to the geometries given in Figure 3. All tests were conducted in as-built condition without any post treatment. The tensile tests were done with a DeFelsko PosiTest AT pull-off tester with a loading rate of 2 MPa/s. The dolly head was adhered to the top surface of the specimen using HTK Ultra Bond 100, the bottom surface was maintained on the build plate. For determination of the adhesive strength between ceramic and steel layers, the samples were manufactured in two parts. The lower half of the sample (Figure 3) was manufactured with steel, then the material was changed, and the ceramic was added starting from the middle of the overall height of the sample (the position highlighted by the horizontal arrow indicating the sample diameter). For determining the volumetric electrical resistance of the SLM-manufactured ceramic, an N&H Technology Hiresta UX equipped with a UR-SS measuring head was used. The sample geometry used in these tests was a cube featuring dimensions of 10 mm 9 10 mm 9 10 mm. Ceramic specimens featuring dimensions of 10 mm 9 10 mm 9 10 mm were built using a variety of manufacturing parameters",
            " However, the conclusions of the parameter study can be briefly summarized as follows: At high power, the ceramic evaporates, for low power unmolten areas are observed as already described by Wilkes.[17] The maximum relative density obtained for the ceramic samples based on the set of parameters provided above was approximately 94 pct. The experimentally determined volumetric electrical resistance of the SLM-processed ceramic including all structural features detailed in the following was 2.84 9 1010 Xcm, a value being sufficient for electric insulation according to Ivers-Tiffe\u0301e et al.[32] The tensile strength (sample geometries are shown in Figure 3 in the experimental section), which has been determined using five specimens, was 20.4 \u00b1 4.6 MPa. This is in good agreement with the measured flexural METALLURGICAL AND MATERIALS TRANSACTIONS B strength (9.5 \u00b1 1.2 MPa) in the 4-point bending tests (sample geometries: 46.6 mm 9 6 mm 9 5.5 mm) reported by Wilkes.[17] The scatter of data is in an acceptable range and, thus, indicates good reproducibility of bulk properties for the ceramic processed via SLM. Microstructural analysis by SEM revealed the formation of basically four microstructures, each one different in appearance, within a single melting line of the ceramic (Figure 5)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001868_s00158-010-0496-8-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001868_s00158-010-0496-8-Figure6-1.png",
        "caption": "Fig. 6 Compass passive dynamics walking",
        "texts": [
            " Therefore, the model is simple and energy-efficient, and it is suitable for analysis to gain insights into the basic principles of human walking such as the step length versus velocity relationship (Kuo 2001), energy expenditure (Kuo 2002; Kuo et al. 2005), and transition from walking to running (Srinivasan and Ruina 2006). Recently, the passive dynamics walking has evolved from 2D sagittal models to 3D spatial models. In addition, some form of actuation and control is added to the model to extend the passive dynamics walking on level ground. For a simplest compass gait model as shown in Fig. 6, the equation of motion is given as follows: M (\u03b8) \u03b8\u0308 (t) + H ( \u03b8, \u03b8\u0307 ) + G (\u03b8) = \u03c4 (t) (7) where \u03b8(t) are the joint angle profiles, M is the inertia matrix, H represents the Coriolis and centrifugal forces, G is gravity and external force vector, and \u03c4 is the joint torque vector. The most fundamental energy loss for passive dynamics walking is impact between the feet and ground. In passive dynamics walking, power comes from the potential energy gained by moving down the slope. The impact is assumed to be inelastic and without slippage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003607_j.proeng.2014.12.452-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003607_j.proeng.2014.12.452-Figure4-1.png",
        "caption": "Fig. 4. Face wear introduced on 1st gear.",
        "texts": [],
        "surrounding_texts": [
            "The experiment was conducted based on the Experimental conditions. 2 motor input speeds, 2 loads, 4 gear speeds and 2 gear fault conditions with total of 32 test conditions has been carried out as mentioned in Experimental conditions Table 1. Piezo electric accelerometer is used to acquire vibration data and it is temporarily fixed at the top of gearbox using additive glues. The output from accelerometer is connected to SO analyser DAQ. Initially the gearbox is fitted with all good gears and the test was started with motor input speed of 500rpm and gearbox engaged with 1st gear with load of 0-Nm. There should be some consistency in the speed and load operation, so the equipment is allowed to run for some time with that particular condition to make consistent operation. After consistency the data acquisition will start and acquisition will carry for a time period of 300seconds (5minutes) in the direction of Y-axis and the total of 8192 samples per second will be stored for further operations. The same procedure will be followed for remaining 31 experimental conditions."
        ]
    },
    {
        "image_filename": "designv10_1_0003524_tii.2018.2865522-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003524_tii.2018.2865522-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor UAV scheme with body fixed and the inertia frames.",
        "texts": [
            " The thrust on the rotors is generated by the aerodynamic lift forces, which is the primary source of control and propulsion for the UAV. At the same time, the Euler angle orientation to the flow generates the forces and moments to control the altitude and position of the system. The considered quadrotor is an under-actuated system, since it has four actual inputs applied to control six degrees of freedom, i.e., translational motions in three directions and rotational motions around three axes. The schematic diagram of the quadrotor adopt in this paper is shown in Fig.1. In this section, the mathematical mode of considered quadrotor UAVs is given including the navigation equations and the moment equations. Motivated by [27]- [29], the body-fixed frame which is represented by Obe b 1e b 2e b 3 with its origin at the center of the mass and the earth-fixed frame which is represented by Oae a 1e a 2e a 3 are as shown in Fig.1. The diagonal motors (Rotor 1 and Rotor 3) rotate counter clockwise, while the lateral ones (Rotor 2 and Rotor 4) rotate clockwise to generate the lift force and to balance the yaw torque. By changing the rotor speeds together with the same quantity, the lift forces are changed to affect the altitude z and perform vertical take-off/on landing. Yaw angle \u03c8 is obtained by speeding up/slowing down Rotor 1 and Rotor 3 depending on the desired direction. Roll angle \u03c6 axe enables the quadrotor to move towards y direction, similarly, pitch angle \u03b8 axe enables the quadrotor to move towards x direction. As shown in Fig. 1, the Euler orientation to the flow provides the forces and moments to control the altitude and position of the UAV. The absolute position is denoted by three coordinates (x0, y0, z0) and its attitude by Euler angles (\u03c8, \u03b8, \u03c6), under the conditions (\u2212\u03c0 \u2264 \u03c8 < \u03c0) for yaw, (\u22120.5\u03c0 \u2264 \u03b8 < 0.5\u03c0) for pitch, and (\u22120.5\u03c0 \u2264 \u03c6 < 0.5\u03c0) for roll. The measurable variables are [x0, y0, z0, \u03c8]T . By this choices, the state is in SE(3) and thus bounded. Define the linear velociy as u0, v0, w0. Define \u03c7 = [\u03c8, \u03c6, \u03b8]T and \u03c9 = [p, q, r]T with p, q and r are the angular velocity of roll, pitch and yaw with respect to the body-fixed frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001246_j.prostr.2017.11.055-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001246_j.prostr.2017.11.055-Figure12-1.png",
        "caption": "Fig. 12 Estimation method for the effective size (dotted line) of irregularly shaped defects and defects near surface. (Murakami, Y. 2002, and Murakami, Y., Nemat-Nasser, S., 1983) (a) Irregularly shaped internal defect. (b) Irregularly shaped surface defect.",
        "texts": [
            " It must be noted that defects opened to specimen surface cannot be eliminated by HIP. (c) Irregularly shaped internal defect in interaction with surface. (d) Interacting adjacent two defects. (e) Inclined defect in contact with surface. Since defects have various shapes, we need to define the relevant rule for estimating the effect of defects. In this regard, the representative dimension of a defect can be expressed with \u221aarea in terms of fracture mechanics concept (Murakami, Y. 2002, and Murakami, Y. and Endo, M., 1994). Figure 12 illustrates various possible configurations of defects for which we need to consider the effective defect size \u221aareaeff different from the real defect size. The initial fatigue crack growth for irregularly shaped cracks and defects as shown in Fig. 12 starts from the deepest concave corner point due to the extremely high stress intensity factor at that point (Murakami, Y. 2002 and Murakami, Y., Nemat-Nasser, S. 1983). However, as the crack grows and the shape of the crack front becomes round, the stress intensity factor once decreases and the crack continues growing to failure if the value of \u2206K exceeds the threshold stress intensity factor range \u2206Kth. If the value of \u2206K is lower than \u2206Kth, the crack stops growing and becomes nonpropagating crack. Therefore, if defects have configurations such as the examples of Fig. 12, we must consider the effective size of defect \u221aareaeff rather than the real size of defect. In this regard, when we apply the statistics of extremes analysis to fatigue design of AM materials, we need to consider the modification of defect size. Based on the values of the effective defect size \u221aareaeff at fracture origin and the Vickers hardness HV, the normalized S-N data were made as in Fig. 13 where the applied stress \u03c3a is normalized by the estimated fatigue limit \u03c3w. It can be seen that the value of \u03c3a /\u03c3w for failed specimens are mostly larger than ~0",
            " / Procedia Structural Integrity 7 (2017) 19\u201326 25 Hiroshige Masuo et Al./ Structural Integrity Procedia 00 (2017) 000\u2013000 7 materials, we need to consider the modification of defect size as Figs. 14 and 15. Figure 16 shows the statistics of extreme analysis of the largest defects which appeared on the sections cut from a specimen with the inspection area S0 = 28mm2. Figure 17 shows the statistics of extreme analysis of the defects which were observed at fatigue fracture origins. In this analysis, the modification of \u221aarea was applied based on the rule of Fig. 12. Figures 16 and 17 show that Material DMLS is graded higher than Material EBM within the current processing conditions and particle sizes and can be used as the measure for quality control of AM materials. Inserting the approximate values of fatigue limit for as-built specimens of Figs. 3 and 4 into Eq. (1), we can estimate the equivalent \u221aarea for surface roughness. The estimated values of \u221aarea exceed 1000\u00b5m for all the cases of EBM and DMLS. Since Eq. (2) is valid for \u221aarea <1000\u00b5m, it can be regarded that the surface roughness produced by AM is much larger and more detrimental than other defects"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.10-1.png",
        "caption": "FIGURE 5.10. A parallel RkR(0) link.",
        "texts": [
            " Therefore, 1T2 = \u23a1\u23a2\u23a2\u23a3 cos \u03b82 \u2212 sin \u03b82 0 l2 cos \u03b82 sin \u03b82 cos \u03b82 0 l2 sin \u03b82 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.29) 0T1 = \u23a1\u23a2\u23a2\u23a3 cos \u03b81 \u2212 sin \u03b81 0 l1 cos \u03b81 sin \u03b81 cos \u03b81 0 l1 sin \u03b81 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.30) and consequently 0T2 = 0T1 1T2 = \u23a1\u23a2\u23a2\u23a3 c (\u03b81 + \u03b82) \u2212s (\u03b81 + \u03b82) 0 l1c\u03b81 + l2c (\u03b81 + \u03b82) s (\u03b81 + \u03b82) c (\u03b81 + \u03b82) 0 l1s\u03b81 + l2s (\u03b81 + \u03b82) 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (5.31) Example 142 Link with RkR or RkP joints. When the proximal joint of link (i) is revolute and the distal joint is either revolute or prismatic, and the joint axes at two ends are parallel as shown in Figure 5.10, then \u03b1i = 0deg (or \u03b1i = 180 deg), ai is the distance between the joint axes, and \u03b8i is the only variable parameter. The joint distance di = const is the distance between the origin of Bi and Bi\u22121 along zi however we usually set xiyi and xi\u22121yi\u22121 coplanar to have di = 0. The xi and xi\u22121 are parallel for an RkR link at rest position. Therefore, the transformation matrix i\u22121Ti for a link with \u03b1i = 0 and RkR or RkP joints, known as RkR(0) or RkP(0), is i\u22121Ti = \u23a1\u23a2\u23a2\u23a3 cos \u03b8i \u2212 sin \u03b8i 0 ai cos \u03b8i sin \u03b8i cos \u03b8i 0 ai sin \u03b8i 0 0 1 di 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001663_j.commatsci.2016.01.044-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001663_j.commatsci.2016.01.044-Figure5-1.png",
        "caption": "Fig. 5. The residual stress distributions when the powder bed was cooled down at 100 s: (a) X-component of stress along the scan direction; (b) Y-component of stress transversal to the scan direction; (c) Z-component of stress through the thickness of the layer; (d) Von Mises stress.",
        "texts": [
            " On the other hand, the overlap area between two adjacent tracks is formed by partly scan of the previous track in order to guarantee the continuity of the formed parts. At the point of P2, the temperature ascends above its melting point again, leading to its re-melting when the laser beam scans over the second track. Therefore, more than one peak of residual stress is obtained owing to the multiple occurrence of temperature gradient. However, the residual temperature resulted from the first scanning process plays a pre-heating impact on P4, which in turn partially relieves stress and makes it lower than the first peak of P2. Fig. 5 depicts the residual stress distributions in different components after the part was cooled down totally. The quantitative description of stresses variations along the X-direction and Y-direction are shown in Figs. 6 and 7, respectively. As shown in Fig. 5, the larger stresses were obtained near the edge of the part, especially at the end of the scanning track. As can be seen in Fig. 5, the stresses distributions in the powder bed were various for different oriented components. It was worth noting that the values of the substrate stresses were generally negative. For the stresses distribution along X-direction depicted in Fig. 6, the largest stresses of all components were all in the third scan which could be reflected on P5. All the values were positive except for the stress in the Z-component. As shown in Fig. 7, the variation of stresses distribution along Y-direction was more complicated as the laser beam scanned over the points located at the same track in a short time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003992_1350650117711595-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003992_1350650117711595-Figure6-1.png",
        "caption": "Figure 6. Nylon gear with a steel stiffener in the core of the tooth (Source: Tsukamoto and Terashima27).",
        "texts": [
            " The obtained parameters included mold temperature, injection speed, back pressure, holding pressure, and cooling time. This approach generated over 91% qualified products. Some studies are focused on the change in the profile of plastic gears by tooth deflection.27\u201331 In the case of a polymer gear meshing with a metal gear, when the load was applied over the polymer gear tooth, it deflected, and a rotational lag occurred. To avoid this problem, a nylon gear was designed including a steel stiffener in the core of nylon tooth as shown in Figure 6.27 The deflection of the tooth in nylon gear with steel stiffener (SN-gear) was found to be smaller than that in the simple nylon gear tooth. Thus, the SN-gear tooth profile did not change largely during the operation. Melick28 investigated the effect of the stiffness of the gear material on the bending of the gear teeth. The results indicated a dramatic change in the load sharing of a steel\u2013plastic gear pair compared to the steel\u2013steel gear pair. It happened because of the significant tooth bending in polymer gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000793_pime_proc_1989_203_100_02-Figure16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000793_pime_proc_1989_203_100_02-Figure16-1.png",
        "caption": "Fig. 16 Stress intensity factors due to fluid trapped in inclined crack (p = 25\u201d, qo/po = -0.05, cja = 0.5, crack face friction coefl\u2018icient = 0.25)",
        "texts": [
            " This mechanism can only operate if the mouth passes under the load before the tip, which explains why the crack propagates in the direction of motion of the load. The volume of fluid trapped in the crack is sensitive to the direction of the tractive force at the surface: a driving traction opens the mouth before entry to the contact while a braking trac- Proc Instn Mech Engrs Vol 203 0 IMechE 1989 at UNIV OF WISCONSIN on September 8, 2014pic.sagepub.comDownloaded from 162 K L JOHNSON tion closes it. The calculated variation of K , and K , , through the cycle for such a crack is shown in Fig. 16a. By considering the stress intensities on a plane that makes an angle 0 to the line of a crack which carried mode I and mode I1 stress intensities K , and K, , the tensile and shear parameters can be defined as and 1 8 K , = ; cos { K , sin 8 + K,,(3 cos 0 - 1)) (1 1b) L L It may be shown that the maximum value of K , is found on the plane in which K , = 0, that is at an angle 0 = 4 given by where y = K, , /K, . The angle 4 defines the direction along which a mode I branch crack might be expected. From the values of K , and K,, given in Fig. 16a, a polar plot of the variation of (K,),,, and # throughout the cycle is shown in Fig. 16b. A downward branching crack at 4 N -53\" might be expected at the beginning of the cycle followed by an upward branch at 4 N 70\" at the end of the cycle. Continuously welded rails carry a thermally induced tensile stress in cold weather, in addition to some residual tension in the railhead from manufacture. Such tensile stresses could be responsible for propagating a branch crack across the rail section (as described in Section 2.2 and shown in Fig. 5) when the inclined contact fatigue crack runs out of the compressively stressed layer near the surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002086_j.engfailanal.2014.12.020-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002086_j.engfailanal.2014.12.020-Figure4-1.png",
        "caption": "Fig. 4. Load distribution in spur gear tooth (a) for aligned shaft, and (b) for misaligned shaft.",
        "texts": [
            " Load distribution on gear tooth for aligned shaft is assumed to be uniformly distributed, but for the misaligned shaft it is not the same. Ameen [20] in 2010 proposed that due to misalignment error load distribution will follow a parabolic distri- Table 1 Expression for various forces acting on gear tooth. Force For aligned shaft For misaligned shaft Tangential (Ft) F cosa1 F cosa1 cosh Radial (Fr) F sina1 F sina1 Axial (Fa) 0 F cosa1 sinh Fig. 3. Tooth model for (a) healthy tooth; (b) cracked tooth [4]. bution. Using this concept a load distribution curve for aligned and misaligned shaft can be drawn as shown in Fig. 4. In Fig. 4 load distribution of tangential force is shown. In Fig. 4(a) aligned shaft case is shown in which load distribution is uniform and the total load acts at its centre of gravity. For misaligned shaft case, load distribution is parabolic and the resultant load acts at its centre of gravity, which is located at 3/8th of length of contact from maximum load position as shown in Fig. 4(b). This resultant tangential force will try to twist the gear tooth with a torque \u2018T\u2019 as shown in Fig. 4(b). A new term is introduced to consider this phenomenon while calculating TVMS of the gear pair and is named as torsion stiffness (ks). In this study it is assumed that mating teeth are two isotropic elastic bodies and the torsion effect on gear tooth is only because of tangential component of the acting force as shown in Fig. 4(b). The torsion energy stored in a tooth can be expressed as Us \u00bc F2 2ks \u00f011\u00de where ks shows the effective torsion stiffness. The potential energy stored due to torque can be obtained by (refer to Eq. (5.26) in Ref. [22]): Us \u00bc Z d 0 T2 2GIpx dx \u00f012\u00de where Ipx represents polar moment of inertia of the section where the distance from the tooth root is x. It can be calculated as Ipx \u00bc 2hxL\u00f0L2 \u00fe 4h2 x \u00de 12 \u00f013\u00de And torque T represents the torsion effect of total tangential force \u2018Ft\u2019 on gear tooth. It can be expressed as T \u00bc Ft t \u00f014\u00de where t is the distance between point at which load is assumed to be acting (i.e. at C.G.) and mid-point of the line of contact as shown in Fig. 4(b). Its value can be expressed as t \u00bc L 2 3L 8 ; ) t \u00bc L 8 \u00f015\u00de Definition and values of G, L, hx can be obtained from Ref. [4]. To investigate the parameter properties at some angular displacement of the pinion/gear; relationship are expressed as angular variables instead of linear variables. Using the values given in Ref. [3] for L, d, hx, dx and substituting the values in Eqs. (11)\u2013(15) 1 ks \u00bc Z a2 a1 3L\u00f01\u00fe m\u00de\u00f0a2 a\u00de cos2 a1 cos2 h cos a 16Efsin a\u00fe \u00f0a2 a\u00de cos ag\u00bd4R2 b sin a\u00fe \u00f0a2 a\u00de cos af g2 \u00fe L2 da \u00f016\u00de In this study, a crack at tooth root with crack depth q along the width of the tooth has been considered as shown in Fig",
            " Nevertheless, it is chosen for demonstration purpose in order to enhance the effect of friction. The effect of friction force which acts perpendicular to the normal force cannot be completely ignored. During gear meshing, the gear and pinion undergo a rolling and sliding action, except at the pitch point, where pure rolling takes place. Considering friction, the gear tooth contact process can be divided into two phases; start of engagement to pitch point known as approach process and pitch point to disengagement known as recess process. Fig. 4 shows the direction of forces including friction force. In Fig. 4(a) F is a force acting on gear tooth surface along line of action (LOA), Fv and Fh are vertical and horizontal components of acting force F respectively. Similarly in Fig. 4(b) and (c) f is friction force which acts perpendicular to force F, fv and fh are vertical and horizontal components of friction force f respectively. Pressure angle is represented by a1 in Fig. 4. In Fig. 4(b) and (c) it has been shown that friction force f always acts perpendicular to the force F, and its value is equal to the product of coefficient of friction l and force F, i.e. f \u00bc lF \u00f021\u00de Using (21) and resolving force F and friction force f as shown in Fig. 5 modified value of tangential and radial forces acting on gear tooth can be calculated. Table 2 shows the expression for radial and tangential forces acting on gear tooth. Friction force changes the value of tangential force and radial force, due to which bending stiffness and axial compressive stiffness will change"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002131_j.sna.2014.03.011-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002131_j.sna.2014.03.011-Figure1-1.png",
        "caption": "Fig. 1. A depict for the quadrotor. XI \u2212 YI \u2212 ZI is the inertial coordinates and XB \u2212 YB \u2212 ZB is the body fixed coordinates.",
        "texts": [
            " The DOB-based conroller is designed in Section 3, and the stability analysis is provided n Section 4. Then the results from simulation and experiments are hown in Section 5, and Section 6 concludes this work. . Quadrotor model and problem statement To facilitate the controller design, the dynamic model of the uadrotor is developed in this section. In this model, external disurbances, input delays and model mismatches are considered as he lumped disturbance which will be handled by the following eveloped controller. .1. Quadrotor dynamics As shown in Fig. 1, the quadrotor is actuated by four rotors on the ndpoints of an X-shaped frame. The collective thrust of these four otors accelerates the quadrotor along its normal direction (ZB). n order to balance the yawing torque, rotors attached on the YB xis rotate in clockwise direction, and the rotors attached on the XB xis rotate in counterclockwise direction. As a result, the difference f collective torques between these two axes produces a yawing orque. Similarly, differences of thrusts between rotors on the XB xis and YB axis produce a pitching torque and a rolling torque espectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000878_j.jmapro.2014.04.001-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000878_j.jmapro.2014.04.001-Figure3-1.png",
        "caption": "Fig. 3. Particle size distribution for SS 316L powder.",
        "texts": [
            " Experimentation Stainless steel AISI 316L with chemical composition weight perentage 0.03 C, 18 Cr, 14 Ni, 3 Mo, 0.75 Si, 2 Mn, 0.03 S, 0.10 N and emaining Fe was used as a substrate. The material of the substrate pecimen of size \u223c50 mm \u00d7 40 mm \u00d7 3 mm was cut from stainless teel plate. These specimens were polished and grit blasted by sand last (Grit 60) before laser melting. Commercial powder of SS 316L ith average particle size of 15\u201320 m was used in this study. oreover, the particle size distribution was determined using Masersizer (USA) 2000 laser particle size analyser (Fig. 3). Initially, the stainless steel powder was spread over the subtrate and maintaining the thickness of 100 m using scraper blade. d:YAG pulsed laser JK 300P (UK) of pulse duration 0.6 ms was sed for single track formation by varying the laser power, scanning peed and beam size is shown in Table 1. For conducting the experments, Taguchi L9 orthogonal array has been followed as shown n Table 1. XRD (A BRUKER-D8 Advance) analysis and FTIR was also arried out to study the phase formation on the pre sintered power layer",
            " The numerical results suggested that at lower temperature and at higher scanning speeds, powder bed fails to form a continuous track but the distortion observed in this case is due to sudden drop of temperature with respect to time. Thus, it is clear that the energy input in to the powder bed is insignificant to melt the powder. The geometric characteristics measured from the numerical simulations are verified by conducting experiments as described in the previous section. The results of the experiments are described below. Particle size distribution analysis was performed on SS 316L with laser particle size analyser. Average particle size was found to be about 20 m as shown in Fig. 3. The SEM analysis of the powder (Fig. 7) depicts that the particles assume spherical morphology with dendritic structure. The phase evolution of 316L stainless steel powder was obtained by XRD analysis at the surface of the samples. The major peaks indicate the dominance of Fe, Cr, Ni (Fig. 8). Fourier transform infrared spectrum analysis shown in Fig. 9 is for un-sintered stainless steel 316L powder. From the results, it is observed that the band ranges from 3000 cm\u22121 to 3500 cm\u22121 and resembles the Fe content in the un-sintered powder which is the main composition in the SS316L"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001434_0094-114x(80)90021-x-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001434_0094-114x(80)90021-x-Figure8-1.png",
        "caption": "Figure 8.",
        "texts": [
            "3) 04 01 - 01 01 S'\u00a5$0/34 \"4- S-~C0/23S0112 + C02S'-~S0/23C0/12 q- S02\u00a2-2S0/23 = 0 (2.4) O1 / OI ~ Ol - ~ 04 -- OI - - R 3 S - ~ S O t 3 4 = 0 (2.5) a,2cy + a23 c-fc. - sTsO:0/,2 ) - a3.\u00a2-f + n:-fs0/ ,2 O. Equations (2.1-2.5) are a set of independent closure equations for the general plane-symmetric 6-R linkage. 3. The trihedral case This unique linkage, also described as \"rectangular\" and \"two-point\", was detailed and shown to be mobile in [9]. It is illustrated by the model of Fig. 7 and the schematic of Fig. 8 and has the geometrical properties, say, 7r 37r O~12 ~ O/34 = 0/56 = -2- 0/23 : O/45 = 0/61 - - Ri=0, all/ a~2 + a342 + a562 = a~3 + aZs + a26,. Screw system theory is eminently suitable for demonstrating the full-cycle mobility of this chain. Because each set of three alternate joint axes is concurrent, all six axes pass through a single line defined by the two points. The six axes therefore lie permanently on a special linear complex, and the loop is mobile. The line through which they pass contains the single screw (of zero pitch) which is reciprocal to their 5-system. Four independent closure equations are readily obtained from Fig. 8. Some elementary trigonometry applied to face A6A~A20' of the hexahedron depicted establishes that 1 A20' = _-7-(a61 + a12c00 SOl and A60' = ~01(a12 + a61c00. By obtaining analogous results for all six faces, we may write down two alternative expressions for the length of each of six edges, leading to six relations among joint angles, four of which are independent. We may then write, say, sO3(a61 + a12c01) = sOl(a34 + a23c03) (3.1) sOs(a23 + a~c03) = sO3(a56 + a4~c05) (3.2) sO4(a12 + a23c02) = sO2(a45 + a34c04) (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure7.50-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure7.50-1.png",
        "caption": "Fig. 7.50 Distribution of equipotential lines along the HV column of resistive LI voltage dividers. a Without field grading. b With field grading using a large shielding electrode",
        "texts": [
            " Among others, this is achieved by reducing the impact of the earth capacitance using a \u2018\u2018shielding\u2019\u2019 electrode as originally introduced by Davis in 1928 and Bellaschi in 1933. Under this condition, the partial currents Ie1, Ie2 \u2026 and Ie6 between divider column and earth are more or less compensated by the partial currents Ih1, Ih2 \u2026 and Ih6 between HV electrode and divider column, as illustrated in Fig. 7.49. Additionally, the field grading along the divider column was optimized, as qualitatively shown in Fig. 7.50. This is obtained by varying the pitch of the wire wounded around an insulating core such that the field distribution approaches the electrostatic field between the electrodes in absence of the divider column, 342 7 Tests with High Lightning and Switching Impulse Voltages originally proposed by Goosens and Provoost in (1946). Moreover, the inductance of the resistor providing the HV arm was minimized using bifilar windings where each is wounded in opposite direction around a cylindrical core and insulated by a thin dielectric layer (Spiegelberg 1966)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003115_j.mechmachtheory.2019.03.014-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003115_j.mechmachtheory.2019.03.014-Figure3-1.png",
        "caption": "Fig. 3. Beam model of an external gear tooth when the base circle is larger than the root circle.",
        "texts": [
            " Therefore, the single-tooth-pair mesh stiffness is described as: k = 1 1 k h + 1 k b1 + 1 k b2 + 1 k s 1 + 1 k s 2 + 1 k a 1 + 1 k a 2 + 1 k f 1 + 1 k f 2 (3) When the contact ratio of the spur gear between the driving and driven gear is 1 to 2, the double-tooth-pair mesh stiffness becomes: k = 2 \u2211 i =1 1 1 k h,i + 1 k b1 ,i + 1 k b2 ,i + 1 k s 1 ,i + 1 k s 2 ,i + 1 k a 1 ,i + 1 k a 2 ,i + 1 k f 1 ,i + 1 k f 2 ,i (4) where the subscript i = 1 is the first pair of meshing gear and i = 2 is the second pair of meshing gear. Case 1: The base circle is larger than the root circle When the tooth number of the spur gear is less than 42, the base circle is larger than the root circle [14] , as shown in Fig. 3 . The accurate potential energy should be the sum of two parts: the potential energy from the mating section to the base section, and the potential energy from the base section to the root section. In Fig. 3 , F is the force at the mating point and its direction is along the line of action; h is the distance between the mating point and the symmetric line of the single tooth; d represents the distance between the mating point and the tooth root section; h x is the distance between the point of the tooth surface and the symmetric line of the single tooth; x represents the distance between the point of the tooth surface and the tooth root section; d 1 is the distance between the base circle and the tooth circle; R r and R b represent the radius of the root circle and the base circle, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003736_j.matdes.2016.06.037-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003736_j.matdes.2016.06.037-Figure8-1.png",
        "caption": "Fig. 8. Sketch of longitudinal section along the clad centreline during LMD process.",
        "texts": [
            " (6), the energy obtained by GA powder and PREP powder are different. With the increase of energy input the cooling rate of the molten pool decreases, so the solidification time of the material is longer. Therefore, Nb segregation is stronger in the process using PREP powder, and in which the fraction of Laves phase in the inter-dendritic area is higher and the primary dendrite arm spacing is larger. The heat loss of the molten pool in the deposited track and the epitaxial growth of the columnar crystal are shown in Fig. 8. In the LMD process, grain growth orientations are affected by the horizontal and vertical heat fluxes [34,35]. As shown in Fig. 8, vector Q t represents the horizontal heat flux due to the moving laser energy input ET which is used to form the deposited track, and the laser scanning direction is in the opposite direction of Qt, and vector Q l represents the vertical heat flux due to the heat loss by the substrate as an efficient heat sink [36]. Therefore, the direction of vector Q , which represents the final heat flux as a combination of Qt andQ l, is down towards the rear of themolten pool, and thus the direction of -Q, is basically along the dendrite growth orientation in the LMD process according to the solidification theory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003990_tmag.2017.2679686-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003990_tmag.2017.2679686-Figure15-1.png",
        "caption": "Fig. 15. Magnetic flux density level of 6/4 conventional SRM due to phase-A (i = 50 A) in the 75\u00b0 rotor position.",
        "texts": [],
        "surrounding_texts": [
            "The proposed nonlinear AM predicts the magnetic field distribution and electromagnetic performance in SRM for any rotor positions and it has the ability in any number of stator slots, rotor poles and phases and for different type of stator winding. Currently, in this paper we chose to present only the 3-phases, and 6/4 conventional SRM. In this model, three regions are established. All the Laplace\u2019s and Poisson\u2019s equations are solved analytically with separation of variables method and by using the Cauchy product theorem. The equations are defined in terms of complex Fourier series. The boundary conditions are obtained from the continuity of the circumferential magnetic field intensity and vector potential in the interface. Iterative method effectively solves the nonlinearity of the soft magnetic material (i.e., B(H) curve) in teeth. Because the conventional winding distribution SRM always operates with certain saturation, the linear AM based on the subdomain method with assumption of infinite magnetic permeability is not accurate enough compared to the developed model. Therefore, the proposed model can be considered as a viable alternative to FEM for analysis of conventional SRM. Moreover, it should be noted that to minimize the torque ripple in SRM the proposed model can be extended by changing the geometric structure of the machine by using a non-uniform air-gaps [8] or by relocating of the rotor molding clinches [6] is by dividing teeth of the rotor into several subregions according to [26]-[27]. This technique also makes it possible to minimize the error observed in the mutual inductance and the electromagnetic torque caused by the increase in supply current in the proposed model (i.e., by creating other elements that are taking different value of permeability in teeth). 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON MAGNETICS xxx APPENDIX The matrix equation of field { \ud835\udc01\ud835\udc5f; \ud835\udc01\ud835\udf03} and { \ud835\udc07\ud835\udc5f; \ud835\udc07\ud835\udf03} in all regions are given by \ud835\udc01\ud835\udc5f \ud835\udc3c| \ud835\udc5f = \u2212 1 \ud835\udc5f \ud835\udc0d\ud835\udf03\ud835\udc16 \ud835\udc3c [( \ud835\udc5f \ud835\udc45\ud835\udc5a ) \ud835\udecc\ud835\udc3c \ud835\udc1a\ud835\udc3c + ( \ud835\udc451 \ud835\udc5f ) \ud835\udecc\ud835\udc3c \ud835\udc1b\ud835\udc3c] (63) \ud835\udc01\ud835\udf03 \ud835\udc3c| \ud835\udc5f = \u2212 1 \ud835\udc5f \ud835\udc16\ud835\udc3c\ud835\udecc\ud835\udc3c [( \ud835\udc5f \ud835\udc45\ud835\udc5a ) \ud835\udecc\ud835\udc3c \ud835\udc1a\ud835\udc3c \u2212 ( \ud835\udc451 \ud835\udc5f ) \ud835\udecc\ud835\udc3c \ud835\udc1b\ud835\udc3c] (64) \ud835\udc01\ud835\udc5f \ud835\udc3c\ud835\udc3c| \ud835\udc5f = \u2212 1 \ud835\udc5f \ud835\udc0d\ud835\udf03 [( \ud835\udc5f \ud835\udc45\ud835\udc60 ) \ud835\udecc\ud835\udc3c\ud835\udc3c \ud835\udc1a\ud835\udc3c\ud835\udc3c + ( \ud835\udc45\ud835\udc5a \ud835\udc5f ) \ud835\udecc\ud835\udc3c\ud835\udc3c \ud835\udc1b\ud835\udc3c\ud835\udc3c] (65) \ud835\udc01\ud835\udf03 \ud835\udc3c\ud835\udc3c| \ud835\udc5f = \u2212 1 \ud835\udc5f \ud835\udecc\ud835\udc3c\ud835\udc3c [( \ud835\udc5f \ud835\udc45\ud835\udc60 ) \ud835\udecc\ud835\udc3c\ud835\udc3c \ud835\udc1a\ud835\udc3c\ud835\udc3c \u2212 ( \ud835\udc45\ud835\udc5a \ud835\udc5f ) \ud835\udecc\ud835\udc3c\ud835\udc3c \ud835\udc1b\ud835\udc3c\ud835\udc3c] (66) \ud835\udc01\ud835\udc5f \ud835\udc3c\ud835\udc3c\ud835\udc3c| \ud835\udc5f = \u2212 1 \ud835\udc5f \ud835\udc0d\ud835\udf03 [\ud835\udc16 \ud835\udc3c\ud835\udc3c\ud835\udc3c ( \ud835\udc5f \ud835\udc454 ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c \ud835\udc1a\ud835\udc3c\ud835\udc3c\ud835\udc3c +\ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c ( \ud835\udc45\ud835\udc60 \ud835\udc5f ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c \ud835\udc1b\ud835\udc3c\ud835\udc3c\ud835\udc3c + \ud835\udc5f2\ud835\udc05] (67) \ud835\udc01\ud835\udf03 \ud835\udc3c\ud835\udc3c\ud835\udc3c| \ud835\udc5f = \u2212 1 \ud835\udc5f [\ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c\ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c ( \ud835\udc5f \ud835\udc454 ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c \ud835\udc1a\ud835\udc3c\ud835\udc3c\ud835\udc3c \u2212\ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c\ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c ( \ud835\udc45\ud835\udc60 \ud835\udc5f ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c \ud835\udc1b\ud835\udc3c\ud835\udc3c\ud835\udc3c + 2\ud835\udc5f2\ud835\udc05] (68) \ud835\udc07\ud835\udc5f \ud835\udc3c,\ud835\udc3c\ud835\udc3c,\ud835\udc3c\ud835\udc3c\ud835\udc3c = [\ud835\udecd\ud835\udc50,\ud835\udc5f \ud835\udc3c,\ud835\udc3c\ud835\udc3c,\ud835\udc3c\ud835\udc3c\ud835\udc3c] \u2212\ud835\udfcf \ud835\udc01\ud835\udc5f \ud835\udc3c,\ud835\udc3c\ud835\udc3c,\ud835\udc3c\ud835\udc3c\ud835\udc3c (69) \ud835\udc07\ud835\udf03 \ud835\udc3c,\ud835\udc3c\ud835\udc3c,\ud835\udc3c\ud835\udc3c\ud835\udc3c = [\ud835\udecd\ud835\udc50,\ud835\udf03 \ud835\udc3c,\ud835\udc3c\ud835\udc3c,\ud835\udc3c\ud835\udc3c\ud835\udc3c] \u2212\ud835\udfcf \ud835\udc01\ud835\udf03 \ud835\udc3c,\ud835\udc3c\ud835\udc3c,\ud835\udc3c\ud835\udc3c\ud835\udc3c (70) where \ud835\udecd\ud835\udc50,\ud835\udc5f \ud835\udc3c\ud835\udc3c = \ud835\udecd\ud835\udc50,\ud835\udf03 \ud835\udc3c\ud835\udc3c = \ud835\udf070 in the air-gap. Representing all the matrix equations obtained by interface condition in matrix-form yields [ \ud835\udc1a\ud835\udc3c \ud835\udc1b\ud835\udc3c \ud835\udc1a\ud835\udc3c\ud835\udc3c \ud835\udc1b\ud835\udc3c\ud835\udc3c \ud835\udc1a\ud835\udc3c\ud835\udc3c\ud835\udc3c \ud835\udc1b\ud835\udc3c\ud835\udc3c\ud835\udc3c] = [ \ud835\udc1711 \ud835\udc1712 0 \ud835\udc1721 \ud835\udc1722 \ud835\udc1723 \ud835\udc1731 \ud835\udc1732 \ud835\udc1733 0 0 0 \ud835\udc1724 0 0 \ud835\udc1734 0 0 0 0 \ud835\udc1743 0 0 \ud835\udc1753 0 0 0 \ud835\udc1744 \ud835\udc1745 \ud835\udc1746 \ud835\udc1754 \ud835\udc1755 \ud835\udc1756 0 \ud835\udc1765 \ud835\udc1766] \u22121 . [ 0 0 0 \ud835\udc183 \ud835\udc184 \ud835\udc185] (71) The entries of the matrix-form the sub-matrices are represented below \ud835\udc1711 = ( \ud835\udc451 \ud835\udc45\ud835\udc5a ) \ud835\udecc\ud835\udc3c (72) \ud835\udc1712 = \u2212\ud835\udc08 (73) \ud835\udc1721 = \ud835\udc16\ud835\udc3c (74) \ud835\udc1722 = \ud835\udc16\ud835\udc3c ( \ud835\udc451 \ud835\udc45\ud835\udc5a ) \ud835\udecc\ud835\udc3c (75) \ud835\udc1723 = \u2212( \ud835\udc45\ud835\udc5a \ud835\udc45\ud835\udc60 ) \ud835\udecc\ud835\udc3c\ud835\udc3c (76) \ud835\udc1724 = \u2212\ud835\udc08 (77) \ud835\udc1731 = \ud835\udc16\ud835\udc3c\ud835\udecc\ud835\udc3c (78) \ud835\udc1732 = \ud835\udc16\ud835\udc3c\ud835\udecc\ud835\udc3c ( \ud835\udc451 \ud835\udc45\ud835\udc5a ) \ud835\udecc\ud835\udc3c (79) \ud835\udc1733 = \u2212\ud835\udf070 \u22121\ud835\udecd\ud835\udc50,\ud835\udf03 \ud835\udc3c \ud835\udecc\ud835\udc3c\ud835\udc3c ( \ud835\udc45\ud835\udc5a \ud835\udc45\ud835\udc60 ) \ud835\udecc\ud835\udc3c\ud835\udc3c (80) \ud835\udc1734 = \ud835\udf070 \u22121\ud835\udecd\ud835\udc50,\ud835\udf03 \ud835\udc3c \ud835\udecc\ud835\udc3c\ud835\udc3c (81) \ud835\udc1743 = \ud835\udc08 (82) \ud835\udc1744 = ( \ud835\udc45\ud835\udc5a \ud835\udc45\ud835\udc60 ) \ud835\udecc\ud835\udc3c\ud835\udc3c (83) \ud835\udc1745 = \u2212\ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c ( \ud835\udc45\ud835\udc60 \ud835\udc454 ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c (84) \ud835\udc1746 = \u2212\ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c (85) \ud835\udc1753 = \ud835\udf070 \u22121\ud835\udecd\ud835\udc50,\ud835\udf03 \ud835\udc3c\ud835\udc3c\ud835\udc3c \ud835\udecc\ud835\udc3c\ud835\udc3c (86) \ud835\udc1754 = \u2212\ud835\udf070 \u22121\ud835\udecd\ud835\udc50,\ud835\udf03 \ud835\udc3c\ud835\udc3c\ud835\udc3c \ud835\udecc\ud835\udc3c\ud835\udc3c ( \ud835\udc45\ud835\udc5a \ud835\udc45\ud835\udc60 ) \ud835\udecc\ud835\udc3c\ud835\udc3c (87) \ud835\udc1755 = \u2212\ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c\ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c ( \ud835\udc45\ud835\udc60 \ud835\udc454 ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c (88) \ud835\udc1756 = \ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c\ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c (89) \ud835\udc1765 = \u2212\ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c\ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c (90) \ud835\udc1766 = \ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c\ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c ( \ud835\udc45\ud835\udc60 \ud835\udc454 ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c (91) \ud835\udc183 = \ud835\udc45\ud835\udc60 2\ud835\udc05 (92) \ud835\udc184 = 2\ud835\udc45\ud835\udc60 2\ud835\udc05 (93) \ud835\udc185 = 2\ud835\udc454 2\ud835\udc05 (94) The magnetic flux linkage over one coil side in the ith stator slot coil, is calculated by \ud835\udf111,\ud835\udc56 = \ud835\udc3f\ud835\udc62 \ud835\udc46 \u2211 \ud835\udc3c\ud835\udc5b\ud835\udf11\ud835\udc5b \ud835\udc5b (\ud835\udc52\u2212\ud835\udc57\ud835\udc5b(\ud835\udefc\ud835\udc56\u2212 \ud835\udf03\ud835\udc60\ud835\udc60 2 +\ud835\udc51) \u2212 \ud835\udc52\u2212\ud835\udc57\ud835\udc5b(\ud835\udefc\ud835\udc56\u2212 \ud835\udf03\ud835\udc60\ud835\udc60 2 )) \ud835\udc41 \ud835\udc5b=\u2212\ud835\udc41 (95) \ud835\udf112,\ud835\udc56 = \ud835\udc3f\ud835\udc62 \ud835\udc46 \u2211 \ud835\udc3c\ud835\udc5b\ud835\udf11\ud835\udc5b \ud835\udc5b (\ud835\udc52\u2212\ud835\udc57\ud835\udc5b(\ud835\udefc\ud835\udc56+ \ud835\udf03\ud835\udc60\ud835\udc60 2 ) \u2212 \ud835\udc52\u2212\ud835\udc57\ud835\udc5b(\ud835\udefc\ud835\udc56+ \ud835\udf03\ud835\udc60\ud835\udc60 2 \u2212\ud835\udc51)) \ud835\udc41 \ud835\udc5b=\u2212\ud835\udc41 (96) where \ud835\udc08\ud835\udc27\ud835\uded7 = [\ud835\udc3c\ud835\udc5b\ud835\udf11\u2212\ud835\udc41 \u2026 \ud835\udc3c\ud835\udc5b\ud835\udf11\ud835\udc41] (97) \ud835\udc08\ud835\udc27\ud835\uded7 = \ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c[\ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c + 2\ud835\udc08]\u2212\ud835\udfcf [\ud835\udc454 2\ud835\udc08 \u2212 \ud835\udc45\ud835\udc60 2 ( \ud835\udc45\ud835\udc60 \ud835\udc454 ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c ] \ud835\udc1a\ud835\udc3c\ud835\udc3c\ud835\udc3c \u2212\ud835\udc16\ud835\udc3c\ud835\udc3c\ud835\udc3c[\ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c \u2212 2\ud835\udc08]\u2212\ud835\udfcf [\ud835\udc454 2 ( \ud835\udc45\ud835\udc60 \ud835\udc454 ) \ud835\udecc\ud835\udc3c\ud835\udc3c\ud835\udc3c \u2212 \ud835\udc45\ud835\udc60 2\ud835\udc08] \ud835\udc1b\ud835\udc3c\ud835\udc3c\ud835\udc3c + \ud835\udc454 4 \u2212 \ud835\udc45\ud835\udc60 4 4 \ud835\udc05 (98)"
        ]
    },
    {
        "image_filename": "designv10_1_0003353_j.prostr.2016.06.380-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003353_j.prostr.2016.06.380-Figure3-1.png",
        "caption": "Fig. 3. (a) Crack plane of CT specimen and load direction of tensile specimen perpendicular to the building direction; (b) crack plane of CT specimen and load direction of tensile specimen parallel to the building direction.",
        "texts": [
            " / Structural Integrity Procedia 00 (2016) 000\u2013000 With this set of parameters, specimens like cubes (10 mm x 10 mm x 10 mm), tensile and CT specimens were produced to examine the mechanical and fracture mechanical properties. In order to investigate the influence of the building direction regarding possible anisotropic behaviour, specimens with different orientations were manufactured. The CT specimens with a crack growth perpendicular to the building direction and the tensile specimen with the load direction perpendicular to the building direction are figured in Fig. 3 a as well as parallel to the building direction, see Fig. 3 b. Fig. 3. (a) Crack plane of CT specimen and load direction of tensile specimen perpendicular to the building direction; (b) crack plane of CT specimen and load direction of tensile specimen parallel to the building direction. Two different conditions were taken into account. The condition \u201cas-built\u201d corresponds to the state immediately after the SLM\u00ae manufacturing process without any heat treatment. In order to achieve a better mechanical performance, the other specimens were heat treated, see Holt et al",
            " / Structural Integrity Procedia 00 (2016) 000\u2013000 With this set of parameters, specimens like cubes (10 mm x 10 mm x 10 mm), tensile and CT specimens were produced to examine the mechanical and fracture mechanical properties. In order to investigate the influence of the building direction regarding possible anisotropic behaviour, specimens with different orientations were manufactured. The CT specimens with a crack growth perpendicular to the building direction and the tensile specimen with the load direction perpendicular to the building direction are figured in Fig. 3 a as well as parallel to the building direction, see Fig. 3 b. Two different conditions were taken into account. The condition \u201cas-built\u201d corresponds to the state immediately after the SLM\u00ae manufacturing process without any heat treatment. In order to achieve a better mechanical performance, the other specimens were heat treated, see Holt et al. (2000). These specimens were solution annealed for 1.5 hours at 753.15 K following by rapid quenching in water (293.15 K) and then aged for 6 hours at 443.15 K. For the optical micrographs, each specimen was mechanically polished and as appropriate etched",
            " Reschetnik et al. / Procedia Structural Integrity 2 (2016) 3040\u20133048 W. Reschetnik et al. / Structural Integrity Procedia 00 (2016) 000\u2013000 5 The tensile mechanical properties from literature are compared to additively manufactured EN AW-7075 alloy in Table 3. The ultimate tensile strength (UTS) and elongation values are clearly lower than the values of the conventionally produced aluminium alloy. The UTS-values for the specimens manufactured with a load direction parallel to the building direction (Fig. 3 b) are in as-built condition by 203 MPa with a standard deviation of \u00b112 MPa and in heat treated condition by 206 MPa with a standard deviation of \u00b125.7 MPa. The elongation for parallel load to the building direction specimens are in as-built condition by 0.5 % with a standard deviation of \u00b10.2 % and in heat treated condition by 0.56 % with a standard deviation of \u00b10.11 %. The heat treatment has no significant influence on the mechanical properties. The quasi-static properties for the specimens with load direction perpendicular to the building direction (Fig 3 a) show a significant reduction in comparison to the other building direction. In the as-built condition, UTS decreases to 42 MPa with a standard deviation of \u00b17.5 MPa and in heat treated condition to 45 MPa \u00b10.5 MPa. These results indicate noticeable anisotropic behaviour related to the building direction. Findings of anisotropic behaviour for other additively manufactured materials can be found in Riemer (2015) and Gebhardt (2014). Furthermore, the mechanical properties of additively manufactured aluminium are significantly lower than the values from literature DIN EN 755-2 (2008) of conventionally produced aluminium alloy EN AW-7075 T651. The measured results of the analysis of fatigue crack growth employing direct current potential drop technique are illustrated in Fig. 4. These fatigue crack growth curves are determined on CT-specimens with crack plane parallel to the building direction (Fig. 3 b) for as-built and heat treated conditions. 6 W. Reschetnik et al. / Structural Integrity Procedia 00 (2016) 000\u2013000 The fatigue crack growth curves for both conditions have double S shape, which is typical of aluminium, see also Richard and Sander (2012). The threshold value \u0394Kth,I for the as-built condition (blue curves in Fig. 4) is by 1.77 MPa\u2219m1/2 with a standard deviation of \u00b1 0.08 MPa\u2219m1/2. The crack path of the as-built specimen with the building direction shown in Fig. 5 a is displayed in Fig",
            " Reschetnik et al. / Procedia Structural Integrity 2 (2016) 3040\u20133048 3045 W. Reschetnik et al. / Structural Integrity Procedia 00 (2016) 000\u2013000 5 The tensile mechanical properties from literature are compared to additively manufactured EN AW-7075 alloy in Table 3. The ultimate tensile strength (UTS) and elongation values are clearly lower than the values of the conventionally produced aluminium alloy. The UTS-values for the specimens manufactured with a load direction parallel to the building direction (Fig. 3 b) are in as-built condition by 203 MPa with a standard deviation of \u00b112 MPa and in heat treated condition by 206 MPa with a standard deviation of \u00b125.7 MPa. The elongation for parallel load to the building direction specimens are in as-built condition by 0.5 % with a standard deviation of \u00b10.2 % and in heat treated condition by 0.56 % with a standard deviation of \u00b10.11 %. The heat treatment has no significant influence on the mechanical properties. The quasi-static properties for the specimens with load direction perpendicular to the building direction (Fig 3 a) show a significant reduction in comparison to the other building direction. In the as-built condition, UTS decreases to 42 MPa with a standard deviation of \u00b17.5 MPa and in heat treated condition to 45 MPa \u00b10.5 MPa. These results indicate noticeable anisotropic behaviour related to the building direction. Findings of anisotropic behaviour for other additively manufactured materials can be found in Riemer (2015) and Gebhardt (2014). Furthermore, the mechanical properties of additively manufactured aluminium are significantly lower than the values from literature DIN EN 755-2 (2008) of conventionally produced aluminium alloy EN AW-7075 T651",
            "2 as-built perpendicular to building direction 42 \u00b17.5 0.51 \u00b10.25 heat treated parallel to building direction 206 \u00b125.7 0.56 \u00b10.11 heat treated perpendicular to building direction 45 \u00b10.5 0.2 \u00b10.05 literature (T651), DIN EN 755-2 (2008) - 540 7 The measured results of the analysis of fatigue crack growth employing direct current potential drop technique are illustrated in Fig. 4. These fatigue crack growth curves are determined on CT-specimens with crack plane parallel to the building direction (Fig. 3 b) for as-built and heat treated conditions. Fig. 4. Crack growth curves for SLM\u00ae-processed EN AW-7075 in different conditions. Crack plane and growth are parallel to the building direction. Data for conventionally processed reference material by Sander (2008) and Eberlein (2016) are displayed in black and gray color. 6 W. Reschetnik et al. / Structural Integrity Procedia 00 (2016) 000\u2013000 The fatigue crack growth curves for both conditions have double S shape, which is typical of aluminium, see also Richard and Sander (2012)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000668_j.msea.2009.02.019-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000668_j.msea.2009.02.019-Figure5-1.png",
        "caption": "Fig. 5. Representative 3D thermal finite element mesh.",
        "texts": [
            " Thermal finite element modeling As previously noted, the purpose of thermal finite element modling is to assess the utility of the Rosenthal solution for predicting rends in solidification microstructure. The finite element modeling mployed herein includes the nonlinear effects of temperatureependent properties and latent heat of transformation, which are eglected by the Rosenthal solution. In general, the modeling proedures discussed here follow those of Vasinonta et al. [24,27], and re in keeping with those employed for thin-wall geometries in [6]. A representative finite element mesh and boundary conditions or a half-symmetric model of the bulky 3D geometry of Fig. 1 is hown in Fig. 5. The dimensions of the bulky 3D geometry conidered herein are length (l) = 50.4 mm, breadth (b) = 17.36 mm nd height (h) = 8.68 mm respectively. The model uses 8-noded biinear thermal elements generated using the commercial software ackage ABAQUS. The finite element model approximates the laser r electron beam as a moving point heat source \u02dbQ , which is sucessively applied to adjacent nodes (beginning at the left end) at ime intervals corresponding to a beam velocity V. As in the previus sections, the parameter \u02db represents the fraction of absorbed ower, and has been estimated as \u02db = 0.35. The boundary condiions imposed are insulation (q = 0) on the top and the vertical ree edges, while the initial reference temperature of T0 = 25 \u25e6 C is pecified along the bottom. Finally, the finite element model uses emperature-dependent specific heat, density and thermal conducivity, and includes latent heat effects for Ti\u20136Al\u20134V. NS TM) deposition of Ti\u20136Al\u20134V from (a) 3D FEM and (b) 3D Rosenthal. The mesh dimensions shown in Fig. 5 have been used to investigate small-scale (LENS TM) fabrication of bulky 3D geometries. For the case of temperature-independent properties, these dimensions were found to be sufficient for the existence of steady-state Rosenthal conditions within the melt pool. In order to investigate large-scale (higher power) processes, the mesh of Fig. 5 was scaled in all three dimensions until the solution in the vicinity of the melt pool was independent of the boundaries. In general, the mesh resolution of Fig. 5 has provided more than 10 elements through the depth of the melt pool, from which solidification cooling rates and thermal gradients have been extracted. In order to ensure the validity of the numerical results, a rigorous convergence study was conducted in both space and time. Spatial convergence was studied by increasing the mesh resolution by a factor of two in the x, y and z directions, while convergence in time was investigated by successively doubling the time increments. For the case of temperature-independent properties, the finite element results for solidification cooling rates and thermal gradients converged to within two percent of the Rosenthal solution, which ensured the validity of the numerical modeling procedures",
            " / Materials Science and Engineering A 513\u2013514 (2009) 311\u2013318 317 highe t s c m 6 s F e a b d t m l g o F s w n s s fi a r t t R l t f c c r i l R m he solidification cooling rate and thermal gradient determine the olidification velocity R through evaluation of Eq. (11). Following the alculation of G and R, results can be plotted on the solidification ap for direct comparison with the Rosenthal predictions. .2. Comparison of FEM and Rosenthal results A comparison of the 3D FEM and Rosenthal results for smallcale (LENS TM) deposition of bulky Ti\u20136Al\u20134V deposits is shown in ig. 6. The results of Fig. 6(a) have been extracted from the 3D finite lement model of Fig. 5, with temperature-dependent properties nd latent heat effects for Ti\u20136Al\u20134V. The results of Fig. 6(b) have een extracted directly from the 3D Rosenthal solution at the same epths within the melt pool as the nonlinear FEM solution, and with hermophysical properties for Ti\u20136Al\u20134V assumed constant at the elting temperature Tm = 1654 \u25e6C. As shown in Fig. 6, trends in G vs. R predictions from the 3D noninear FEM solution and the 3D Rosenthal solution are in reasonably ood agreement. In particular, both the FEM and Rosenthal results f Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure2.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure2.1-1.png",
        "caption": "Fig. 2.1 How a tire carries a vertical load if properly inflated",
        "texts": [
            " These features arise from the highly composite structure of tires: a carcass of flexible, yet almost inextensible cords encased in a matrix of soft rubber, all inflated with air.1 Provided the (flexible) tire is properly inflated, it can exchange along the bead relevant actions with the (rigid) rim. Traction, braking, steering and load support are the net result. It should be appreciated that the effect of air pressure is to increase the structural stiffness of the tire, not to support directly the rim. How a tire carries a vertical load Fz if properly inflated is better explained in Fig. 2.1. In the lower part, the sidewalls bend and, thanks to the air pressure pa , they apply more vertical forces Fa in the bead area than in the upper part. The overall effect on the rim is a vertical load Fz. The higher the air pressure pa , the lower the sidewall bending. The contact patch, or footprint, of the tire is the area of the tread in contact with the road. This is the area that transmits forces between the tire and the road via pressure and friction. To truly understand some of the peculiarities of tire mechanics it is necessary to get some insights on what happens in the contact patch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure1.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure1.6-1.png",
        "caption": "FIGURE 1.6. Illustation of a 3R manipulator.",
        "texts": [
            " Typically the manipulator should possess at least six DOF : three for positioning and three for orientation. A manipulator having more than six DOF is referred to as a kinematically redundant manipulator. 1.2.3 Manipulator The main body of a robot consisting of the links, joints, and other structural elements, is called the manipulator. A manipulator becomes a robot when the wrist and gripper are attached, and the control system is implemented. However, in literature robots and manipulators are utilized equivalently and both refer to robots. Figure 1.6 schematically illustrates a 3R manipulator. 1.2.4 Wrist The joints in the kinematic chain of a robot between the forearm and endeffector are referred to as the wrist. It is common to design manipulators 6 1. Introduction with spherical wrists, by which it means three revolute joint axes intersect at a common point called the wrist point. Figure 1.7 shows a schematic illustration of a spherical wrist, which is a R`R`R mechanism. The spherical wrist greatly simplifies the kinematic analysis effectively, allowing us to decouple the positioning and orienting of the end effector",
            " Two perpendicular joint axes become orthogonal if the length of their common normal tends to zero. 1. Introduction 9 Out of the 72 possible manipulators, the important ones are: RkRkP (SCARA), R`R\u22a5R (articulated), R`R\u22a5P (spherical), RkP`P (cylindrical), and P`P`P (Cartesian). 1. RkRkP The SCARA arm (Selective Compliant Articulated Robot for Assembly) shown in Figure 1.8 is a popular manipulator, which, as its name suggests, is made for assembly operations. 2. R`R\u22a5R The R`R\u22a5R configuration, illustrated in Figure 1.6, is called elbow, revolute, articulated, or anthropomorphic. It is a suitable configuration for industrial robots. Almost 25% of industrial robots, PUMA for instance, are made of this kind. Because of its importance, a better illustration of an articulated robot is shown in Figure 1.9 to indicate the name of different components. 3. R`R\u22a5P The spherical configuration is a suitable configuration for small robots. Almost 15% of industrial robots, Stanford arm for instance, are made of this configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure3.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure3.6-1.png",
        "caption": "Fig. 3.6 Metal tank transformer 800, 1,000 kVA, for connection to a metal-enclosed test circuit",
        "texts": [
            " The core is on the same ground potential as the tank is, the lower end of the HV winding is usually also grounded via a bushing. At this bushing, the current in the HV test circuit can be measured. For an HVAC testing in ambient air, the transformer must be equipped with an oil-to-air bushing (Fig. 3.4), but metal tank transformers can also be connected by oil-to-SF6 bushings to metal-enclosed test circuits that are mainly applied for testing of gasinsulated systems (GIS) and their components (Fig. 3.6; see also Sects. 3.2.3 and 10.4.1). 3.1 Generation of HVAC Test Voltages 87 Because of the grounded tank, the tank-type test transformer does not require any clearance to neighbouring walls from the electrical point of view. In case of horizontal or diagonal bushings, other components (voltage divider and coupling capacitor) can be placed below or very near to the end electrode of the bushing. This enables a very compact and space-saving arrangement in a test laboratory, often the ground space is lower than that for a cylinder-type transformer (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003487_tcyb.2020.2987811-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003487_tcyb.2020.2987811-Figure1-1.png",
        "caption": "Fig. 1. Structure of the quadrotor.",
        "texts": [
            " Third, the experiments on the platform of the Quanser Qball-X4 quadrotor are successfully implemented and the effectiveness of the proposed control scheme is verified via the experimental data. The remainder of this article is arranged as follows. Section II introduces the mathematical model of the quadrotor and some preliminaries. The control algorithms are formed in Section III. Section IV gives the analysis of the stability and tracking performance. The implementation of experiments and corresponding results is shown in Section V, and the conclusion is drawn in Section VI. The structure of the quadrotor is shown as Fig. 1, from which it can be seen that the entire control system consists of four actual control inputs actuated by motors and six spatial freedom outputs, including three displacement motions and three attitude motions. Here, the displacement motions are denoted by the motions along the x, y, and z axes of the bodyfixed coordinate system, and the attitude motions are denoted by the motions of roll, pitch, and yaw. Hence, the quadrotor is physically an underactuated system which implies that only four control signals can be utilized to control six degrees"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002297_j.cirp.2013.03.032-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002297_j.cirp.2013.03.032-Figure3-1.png",
        "caption": "Fig. 3. Experimental setup for temperature measurement.",
        "texts": [],
        "surrounding_texts": [
            "Layered manufacturing technology was presented initially by Kodama as a new rapid prototyping technology to fabricate threedimensional plastic models [1]. This technique became the common technology for additive manufacturing (AM) to produce prototypes, tools and functional end products with a variety of components, such as polymer, ceramic and metal powder [2]. The development of three-dimensional CAD system also contributed to the commercial uses of the layered manufacturing techniques. Indeed, the use of metal powder in layered manufacturing is especially remarkable because the structures obtained are sufficiently strong for practical application [3]. Laser consolidation of metal powder is classified into several types of mechanism according to the energy density on area irradiated by laser beam [4]. Selective laser sintering (SLS) and selective laser melting (SLM) enable the fabrication of three-dimensional models from the powdered materials by selectively heating and fusing powder particles using a laser beam irradiation. Problems encountered in SLS and SLM are the accuracy of the structures obtained by the layered manufacturing processes. The dimensional accuracy and the surface quality of the structures are inferior to conventional technologies such as a milling and grinding, and these are important limitations to layered manufacturing technology. The improvement of these problems was proposed symptomatically such as an employment of secondary laser irradiation without depositing a new metal powder layer [5] The principal factor which causes the deformation of consolidated structure in SLS and SLM is the residual stress, wh is induced by the thermal gradient brought on by rapid heating cooling during layer consolidation. Shiomi et al. measured distribution of residual stress within the consolidated structur the SLM process [8]. They reported that the tensile residual st remaining in the surface layer of the consolidated structure improved by re-scanning of the laser beam without depositio new powder. The influence of the thickness of substrate and height of consolidated structure on the residual stress in the sur layer was also investigated in our previous study [9]. It was sho that the deformation of the consolidated structure was related to value of residual stress and that residual stress increased with increase in the number of layers. It is quite difficult to eliminate residual stress induced inside the consolidated structure altho pre-heating of the powder bed is effective in reducing it. In order to improve the dimensional accuracy causally layered manufacturing technology, it is essential to monitor visualize the laser irradiation area during powder consolidat This research focuses on the measurement of surface temperat of ferrous based metal powder by irradiation with Yb:fiber la beam. Surface temperature was measured with two-color pyro eter employing an optical fiber with a different accepta wavelength of InAs and InSb detectors, which were develo by the authors [10]. Additionally, the powder surface during la irradiation was monitored with high speed video camera in or to clarify the consolidation mechanism. A R T I C L E I N F O Keywords: Additive manufacturing Temperature Monitoring A B S T R A C T This paper deals with the measurement of surface temperature on metal powder during the l consolidation process with two-color pyrometer. Additionally, the aspect of selective laser sintering ( and selective laser melting (SLM) of metal powder is visualized with high speed video camera. As a result surface temperature during the laser irradiation was ranged 1520\u20131810 8C and the consolida phenomena was classified according to the melting point of metal powder. The metal powder at the hea process cohered intermittently to the melt pool although the laser beam was continuously irradiated to powder surface. 2013 C Contents lists available at SciVerse ScienceDirect CIRP Annals - Manufacturing Technology journal homepage: http: / /ees.elsevier.com/cirp/default .asp and an application of the atmospheric plasma spraying system (APS) on the consolidated structure [6]. Additionally, Abe et al. developed a multitasking machine in which a laser consolidation of metal powder and an end milling of the edge of consolidated structure were performed alternately [7]. n in r, a ors;* Corresponding author. 0007-8506/$ \u2013 see front matter 2013 CIRP. http://dx.doi.org/10.1016/j.cirp.2013.03.032"
        ]
    },
    {
        "image_filename": "designv10_1_0001137_bfb0039268-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001137_bfb0039268-Figure1-1.png",
        "caption": "Figure 1: Mobile robot configuration",
        "texts": [
            " S amson,\"Vclocity and torque feedback control of a nonholonomic cart\" Int. Workshop in Adaptive and Nonlinear Control: Issucs in Robotics, Grenoble, 1990. APPENDIX: Simplified model of a mobile wheeled robot. We consider a mobile robot moving on an horizontal plane, constituted by a rigid troliey equipped with non deformable wheels. During the motion, the plane of cach wheel rcmaias vcrtical and the whccl rotates around its (horizontal) axis. The orientation of 2 wheels with respect to the trolley is fLxed, while the orientation of the third wheel is varying (see Figure 1). The contact between the wheels and the ground satisfied the pure roiling and non slipping conditions. The motion of the robot is achieved by 2 motors which provide torques acting on the rotation of the 2 wheels whose orientation is f'Lxcd. In order to characterize the position of the trolley, we dcfine an inertial reference frame in the plane of motion {0, I1 ,I 2}, a reference point Q on the trolley and a basis {xt, x2 } auachcd to the trolley. The position of the trolley in the plane is therefore characterized by - x, y : the coordinates of the reference point Q in the inertial frame, -0: the orientation of the basis {xl, x2 } with respect to the inertial frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure5.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure5.9-1.png",
        "caption": "Fig. 5.9",
        "texts": [
            " If the warping is restrained by supports (or if MT varies along x), additional normal stresses occur. The evaluation of these is the subject of the theory of warping torsion, which cannot be covered within this introductory book. The displacements of an arbitrary point P on the centerline of the profile in x- or s-direction are denoted by u and v, respectively. If the cross section rotates about the infinitesimal angle d\u03d1 (the shape of the profile remains unchanged due to the first kinematic assumption), point P is shifted by r d\u03d1 to the position P \u2032 (Fig. 5.9). The component of this displacement in the direction of the tangent at the centerline of the profile is dv = r d\u03d1 cos\u03b1. Here \u03b1 denotes the angle between the line orthogonal to r and the tangent of the centerline of the profile. The same angle occurs between r and the perpendicular distance r\u22a5 of the tangent in P (the 5.3 Thin-Walled Tubes with Closed Cross Sections 207 sides of the angle are pairwise perpendicular). Using r\u22a5 = r cos\u03b1 we obtain dv = r\u22a5d\u03d1 . (5.22) The shear strain \u03b3 of an element of the tube wall is given by \u03b3 = \u2202v/\u2202x+ \u2202u/\u2202s by analogy to (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003360_j.mechmachtheory.2017.03.012-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003360_j.mechmachtheory.2017.03.012-Figure4-1.png",
        "caption": "Fig. 4. Analysis of forces applied to the ball.",
        "texts": [
            " \u03c9 m \u03c9 i = ( 1 \u2212 \u03b3i ) cos ( \u03b1o \u2212 \u03b2) ( 1 + \u03b3o ) cos ( \u03b1i \u2212 \u03b2) + ( 1 \u2212 \u03b3i ) cos ( \u03b1o \u2212 \u03b2) (27) \u03c9 b \u03c9 i = d m D ( 1 \u2212 \u03b3i ) ( 1 + \u03b3o ) ( 1 + \u03b3o ) cos ( \u03b1i \u2212 \u03b2) + ( 1 \u2212 \u03b3i ) cos ( \u03b1o \u2212 \u03b2) (28) Based on the above analysis, the ball pitch angle \u03b2 is an important parameter for the angular speed ratios calculation. Jones made a simplified assumption that the ball spins on one of the contact raceways and rolls on the opposing raceway (\u201cRaceway Control Hypothesis\u201d) to solve the ball pitch angle \u03b2 . As shown in Fig. 4 , Wang [7] and Ding [8] calculated the ball pitch angle \u03b2 by applying the d\u2019Alember\u2019s principle, it can be written as: P f + M si \u03c9 \u2032 si \u2212 M so \u03c9 \u2032 so = 0 (29) where M s i and M so respectively denotes the spinning friction moment of the inner and outer raceway, and P f is the work of external forces except for M s i and M so . In addition, \u03c9 \u2032 si and \u03c9 \u2032 so are the inner and outer spinning angular speeds relative to ball, and \u03c9 \u2032 si , \u03c9 \u2032 so are the inverse vectors of \u03c9 s i and \u03c9 so . As shown in Fig",
            " Assuming that bearing under the combined loads F = ( F x , F y , F z , M y , M z ), the displacements of inner ring relative to outer ring are d = ( \u03b4x , \u03b4y , \u03b4z , \u03b8 y , \u03b8 z ), where \u03b4x , \u03b4y , \u03b4z are translational displacements and \u03b8 y , \u03b8 z are angular displacements, As shown in Fig. 5 , the distances between the inner and outer raceway groove curvature centers at any ball position can be written as: { A 1 k = BD sin \u03b1o + \u03b4x \u2212 \u03b8z i cos \u03c8 k + \u03b8y i sin \u03c8 k A 2 k = BD cos \u03b1o + \u03b4y cos \u03c8 k + \u03b4z sin \u03c8 k (34) According to the Pythagorean Theorem, one can obtain: { ( A 1 k \u2212 X 1 k ) 2 + ( A 2 k \u2212 X 2 k ) 2 \u2212 [ ( f i \u2212 0 . 5 ) D + \u03b4ik ] 2 = 0 X 2 1 k + X 2 2 k \u2212 [ ( f o \u2212 0 . 5 ) D + \u03b4ok ] 2 = 0 (35) As shown Fig. 4 , the equilibrium equations of forces in the horizontal and vertical directions can be written as: { Q ik sin \u03b1ik \u2212 T ik cos \u03b1ik \u2212 Q ok sin \u03b1ok + T ok cos \u03b1ok = 0 Q ik cos \u03b1ik + T ik sin \u03b1ik \u2212 Q ok cos \u03b1ok \u2212 T ok sin \u03b1ok + F ck = 0 (36) where the friction forces T i , T o and the contact forces Q i , Q o can be determined by the following expressions: \u23a7 \u23aa \u23a8 \u23aa \u23a9 ( T ik + T ok ) D 2 = M gk T ik Q ik = T ok Q ok (37) { Q ik = K ik \u03b4 3 / 2 ik Q ok = K ok \u03b4 3 / 2 ok (38) In addition, the centrifugal force and gyroscopic moment of bearing ball can be calculated by Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000814_1.2335852-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000814_1.2335852-Figure2-1.png",
        "caption": "Fig. 2 Two-dimensional thermomech",
        "texts": [
            " Although use of a point heat source will generally yield smaller melt pool lengths and larger melt pool depths, simulations by the authors using a distributed heat source have shown that the effect is only significant for small powers outside of the operating range of LENS\u00ae and similar processes. Results presented by Vasinonta et al. 8,9 and results presented later in this paper also demonstrate reasonable agreement between measured and predicted melt pool sizes and thermal gradients away from the melt pool. The mesh and boundary conditions used for a typical 2D thermomechanical model in this study are shown in Fig. 2. In each set of simulations, the meshes used in both thermal and mechanical models are identical. Four-noded bilinear elements are used as part of the ABAQUS finite element software package. The laser beam focused on the top surface of the wall is simulated by a point source of power subsequently applied at model nodes at a rate equivalent to the laser velocity. Because of high temperature and displacement gradients in the region near heat source, the grid is biased toward the region that will surround the heat source at the time when results are to be extracted from the model",
            " This biasing resulted in the melt pool containing roughly 8\u201315 elements at this time. In addition to comparisons of the thermal model results with those of an analytical solution valid for a large wall 15 , the convergence of this mesh was checked against thermal and mechanical models with roughly half the resolution in the x0 and z0 directions, with no noticeable change in the results. Transactions of the ASME /2014 Terms of Use: http://asme.org/terms b o fi t f a n c m f v t b s s b w c t t c t c m a a s o a t i t t o o i t p l w F \u00af \u00af an J Downloaded Fr As illustrated in Fig. 2, in the thermal simulations an insulated oundary condition is imposed on the top and both vertical sides f the thin wall. The temperature along the wall bottom is specied as fixed at a value equal to the temperature of the comparaively large base plate. Sensitivity studies have shown that speciying boundary conditions along the wall vertical and top surfaces s being insulated or convective has little effect on thermal results ear the heat source. Most of the heat transferred from the laser is onducted out through the bottom of the wall"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000008_tec.2005.853765-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000008_tec.2005.853765-Figure1-1.png",
        "caption": "Fig. 1. Open-circuit field and air-gap flux-density distributions. (i) 12-slot/10pole. (a) Field distribution and (b) flux-density distribution. (ii) 15-slot/10-pole. (a) Field distribution and (b) flux-density distribution.",
        "texts": [
            " KB (n)fBr(r) cos(np\u03b8) (1) where KB (n) and fBr(r) are given in the Appendix and depend on the pole number, the stator bore radius, the rotor outer radius, and the magnet inner radius, as well as the harmonic order. The air-gap flux-density distribution for a slotted motor is obtained by introducing a relative permeance function \u03bbrel(\u03b8) [13], such that Bairgap(r, \u03b8) = Bslotless(r, \u03b8)\u03bbrel(\u03b8). (2) Typical open-circuit field and air-gap flux-density distributions for the 12-slot and 15-slot, 10-pole motors are shown in 0885-8969/$20.00 \u00a9 2005 IEEE Fig. 1. As will be seen, analytically predicted results, from (2), are in good agreement with finite-element predictions. When each stator tooth carries a coil, the Magnetomotive force (MMF) vectors are as shown in Fig. 2 for a 12-slot/10-pole motor, the winding arrangement being AA\u2019B\u2019BCC\u2019A\u2019ABB\u2019C\u2019C (coils A and A\u2019 being of opposite priority). If only alternate teeth carry a coil, the winding arrangement is AB\u2019CA\u2019BC\u2019, the number of coils being halved while the number of turns per coil is doubled so as to maintain the same number of total series turns per phase",
            " For motors having 2p = Ns \u2212 2, the coil-pitch will be slightly smaller than the slot-pitch, 2\u03c0/Ns , while for motors having 2p = Ns + 2, the coil-pitch will be slightly larger than the slot-pitch, which, in turn, is almost equal to the pole-pitch. The flux-linkage per coil is given by \u03c8coil = NclaRs \u222b \u03b1/2 \u2212\u03b1/2 Bairgap(Rs, \u03b8)d\u03b8 (5) while the flux-linkage per phase is given by \u03c8phase = 2NplaRs \u00d7 \u221e\u2211 n=1,3,5... 1 np KBnfBrnKdpn cos(np\u03b8) (6) where Nc,Np, la , \u03b1 are the number of turns per coil, the number of turns per phase, the active stator axial length, and the slot pitch angle, respectively. For the two motors shown in Fig. 1, Kdpn is given by (3) and (4). The variation of the flux-linkage per coil as calculated analytically is shown in Fig. 3. As expected, the maximum flux-linkage per coil of the 12-slot/10-pole motor is significantly higher than that for the 15-slot/10-pole motor, and this trend is also reflected in the flux-linkage per phase, as shown in Fig. 4. The phase back-EMF, derived from the rate of change of flux-linkage, is EMF = \u2212d\u03c8 dt (7) EMF = 2NplaRs\u03c9r \u00d7 \u221e\u2211 n=1,3,5... KBnfBrnKdpn sin(np\u03c9r t). (8) As expected, the winding factor Kdpn has a significant effect on the phase back-EMF waveform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000337_1.1555660-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000337_1.1555660-Figure4-1.png",
        "caption": "Fig. 4 Physical model: helical gear pair model showing plane-ofaction, tooth normal vector and vibratory motions ~Blankenship and Singh @24#!",
        "texts": [
            " are not properly included in the corresponding gear mesh interface model, which must consider a multi-dimensional vector of forces and moments generated within and transmitted via the gear mesh. Therefore, a new generalized six-dof gear mesh interface model was presented, which can be employed for the dynamic analysis of internal and external spur. Later, Blan- oaded From: http://appliedmechanicsreviews.asmedigitalcollection.asme.org kenship and Singh @24# extended this gear mesh model to describe the mesh force transmissibility in a helical gear pair, as shown in Fig. 4. The tooth profile modification is an important approach to reduce the tooth mesh excitation and further to improve the dynamic behavior of a geared system @94,95#. In 1989, Lin, Townsend, and Oswald @96,97# reported that tooth profile modification could effectively reduce the maximum dynamic load in the gear dynamic modeling analysis by Lin and Houston @98#. They also suggested that a profile modification with linear or parabolic curve be optimized for the best performance of the gear drive in terms of the variation, due to dynamic load at the contact point along the line of action"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003173_acs.chemrev.9b00401-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003173_acs.chemrev.9b00401-Figure4-1.png",
        "caption": "Figure 4. Optically induced torques for driving nanomotors. Light carrying either spin angular momentum (SAM) or orbital angular momentum (OAM) can be used to drive the motion of a nanoparticle. Left: A beam of circularly polarized light can transfer SAM to a particle via light absorption or polarized scattering, causing the particle to rotate around its own axis. Right: A beam of structured light that carries OAM can cause a particle to orbit around the optical axis.",
        "texts": [
            " However, because this simply involves translating a macroscopic movement of the excitation laser beam to movement of the nanoparticle, it does not qualify as a nanomotor. Hence, these types of studies are excluded from this review. Below, we describe rotary nanomotors driven by transfer of optical angular momentum (a summary is given in Table 1). 4.1.1. Principle of Operation. Apart from the linear momentum that is the basis for optical tweezing, a light beam can carry angular momentum via its intrinsic polarization state and/or via its spatial phase and intensity distribution (Figure 4). The two types of light angular momentum are referred to as spin angular momentum (SAM)28 and orbital angular momentum (OAM).62 Both can be transferred to an optically trapped nanoparticle, causing it to rotate around its own axis or around the optical axis of the beam of light, respectively. The particle thus actively rotates without any changes to the external potential. Hence, a nanoparticle subject to lightinduced optical torque constitutes a light-driven rotary nanomotor. The first studies combining optical tweezers and optical rotation involved microparticles driven by SAM63,64 and/or OAM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003427_j.jmapro.2019.11.020-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003427_j.jmapro.2019.11.020-Figure11-1.png",
        "caption": "Fig. 11. As-built residual stress formation (MPa) in the bridge structure. To clearly illustrate the stress formation within the structure, results were also displayed for one-half of the geometry.",
        "texts": [
            " After residual stress magnitude in a single layer was determined based on chosen process conditions, the steady-state solver performed mechanical calculation for force and momentum equilibrium layer-bylayer until the entire product was completed. A user-defined subroutine UEXPAN provided by Abaqus was used to prescribe inelastic strains so that the residual stress in a deposited layer could be generated. Moreover, a model change interaction in Abaqus allowed the activation of a new layer in each iteration. Fig. 11 showed as-built residual stress distribution of the bridge structure when the scanning length of 20 mm was chosen. Of note, to clearly illustrate the stress formation within the structure, residual stress results for one-half of the geometry were also displayed. According to Fig. 11, high tensile stress was observed at the top surface for stresses normal to a built direction (\u03c3xx and \u03c3zz). However, \u03c3xx and \u03c3zz became mostly insignificant when considering location far away from top surface. On the other hand, negligible stress was seen at the top surface for stress parallel to the built direction (\u03c3yy). However, high compression was noticed around the middle part of the structure. These observations were much agreeable with previously reported experimental data, which employed the contour method to reconstruct residual stress map in L-PBF samples [11,21]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003215_j.ijfatigue.2018.08.023-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003215_j.ijfatigue.2018.08.023-Figure1-1.png",
        "caption": "Fig. 1. Specimen manufacturing conditions, specifically the (a) orientation of manufactured specimens, (b) principle of scanning strategy for a vertically built specimen regarding inner hatch/filling and contour and (c) geometry of fatigue test specimens according to standard ASTM E 466 [24].",
        "texts": [
            " The defect population, microstructure, hardness, dimensions, roughness and residual stresses were therefore compared for both specimen categories to look for an explanation for the fatigue behaviour. The authors expect with this work to encourage further studies on the effect of the process parameters and the contour scanning feature on the fatigue behaviour, envisioning the adjustment and improvement of the Processing-Structure-Properties-Performance relationships of AlSi10Mg produced via AM. AlSi10Mg fatigue specimens were produced in the horizontal and vertical orientation, see Fig. 1a, on an EOS M400 machine. Table 1 gives an overview of the 12 different groups manufactured and of the respective conditions used. 7 specimens were manufactured for each group using a scan strategy combining an inner hatch/filling parameter and a contour parameter which is illustrated in Fig. 1b. The contour scanning is executed after the inner hatch for each layer individually and can almost be considered as instantaneously when compared to the inner hatch parameter. An exception is condition ID 7 where the contour parameter was not performed. Two different parameter sets were applied for the inner hatch/filling: a set with 30 \u00b5m layer thickness with an energy input (E) of approximately 50 Jmm\u22123, used to produce high quality parts, and a set with 90 \u00b5m layer thickness at about 22 Jmm\u22123 for a drastically increased build up rate",
            " (1) where P is the laser power (in J s\u22121), v is the scan velocity (in mm s\u22121), dh is the hatch distance (in mm) and hth is the layer thickness (in mm) [21]. Both inner hatch parameter sets used a scan regime which rotates the hatch orientation for about 67\u00b0 from layer to layer to reduce the texture [22]. Furthermore, the majority of the samples were produced on a preheated build plate at 165 \u00b0C except condition ID 1 where the base plate heating was set to 35 \u00b0C. = \u00d7 \u00d7E P v d h/( )h th (1) The milled specimens (ID 1 to 6) were printed as cylindrical bars and then machined to the geometry shown in Fig. 1c. For the net shaped specimens, the surface was either jet blasted (ID 9 to 11) with the zirconium - aluminium oxide jet blasting agent \u201cIEPCONORM_C\u201d (iepco ag), or treated through vibratory polishing (ID 7 and 8), also called tumbling, with a R300/600 TE 15 machine using compound \u201cZF 113\u201d and media \u201cRM 07/15 ZS\u201d (R\u00f6sler Oberfl\u00e4chentechnik GmbH), or left in its \u201cas built\u201d condition without surface treatment (ID 12). The 12 parameter sets were chosen considering which combination of variables could improve the fatigue behaviour of additively manufactured AlSi10Mg space hardware applications",
            " This can be explained by the influence of a 90 \u03bcm layer thickness on the porosity (ID 4 and ID 6), the decrease of the yield strength caused by the heat treatment (ID 3 and ID 5) and the dominating influence of the surface roughness (ID 10 and ID 11). Further, this work shows that different post processing treatments, such as jet blasting (ID 9 to 11) or vibratory polishing (ID 8), result in very similar fatigue performances for the same process parameters. However, when the contour parameter (illustrated in Fig. 1b) was excluded (ID 7), the fatigue behaviour significantly improved to levels similar to the ones exhibited by the milled specimens. To the best of our knowledge, the influence of this parameter on mechanical properties has never been studied, hence this is further discussed in Section 3.2. As a final remark regarding the fatigue results, when comparing the best results obtained in this work (machined samples manufactured with 30 \u00b5m layer thickness, ID 2) with the fatigue performance of common wrought and machined Al 6061 samples, it is seen that the specimens of this work offer an improved fatigue behaviour",
            " The small standard deviations confirm as well that no large variations occur in the gauge for varying building height. The defect distribution analysis can only correlate the occurrence of larger pores close to the outer surface in samples produced with contour directly to the fatigue behaviour. Table 3 shows the measured diameters of samples without contour (ID 7) and with contour (ID 8) which were not tested in fatigue. All values are slightly smaller than the design gauge diameter of 5.5mm (Fig. 1). For all measurement methods (calliper, XCT and optical microscope images), the vibratory polished samples produced without contour had consistently a larger diameter than similar ones produced with contour. Net shaped samples of the same sample batch, but without post processing were not available to measure the diameter before any treatment was applied. For other analyses (Section 3.2.1), the average value of the gauge diameters measured with a calliper and the XCT data was used: 5.45mm for without and 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure7.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure7.9-1.png",
        "caption": "Figure 7.9. The distribution of mass most strongly affects moment of inertia, so wheel A with mass close to the axle would have much less resistance to rotation than wheel B. Wheel A would make it easier for a cyclist to make quick adjustments of the wheel back and forth to balance a unicycle.",
        "texts": [
            " Diving and skilled gymnastic tumbling both rely on decreasing the moment of inertia of the human body to allow for more rotations, or increasing the length of the body to slow rotation down. Figure 7.8 shows the dramatic differences in the moment of inertia for a human body in the sagittal plane for different body segment configurations relative to the axis of rotation. 176 FUNDAMENTALS OF BIOMECHANICS Variations in the moment of inertia of external objects or tools are also very important to performance. Imagine you are designing a new unicycle wheel. You design two prototypes with the same mass, but with different distributions of mass. Which wheel design (see Figure 7.9) do you think would help a cyclist maintain balance: wheel A or wheel B? Think about the movement of the wheel when a person balances on a unicycle. Does agility (low inertia) or consistency of rotation (high inertia) benefit the cyclist? If, on the other hand, you are developing an exercise bike that would provide slow and smooth changes in resistance, which wheel would you use? A heavy ski boot and ski dramatically affect the moments of inertia of your legs about the hip joint. Which joint axis do you think is most affected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001100_j.optlastec.2017.05.006-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001100_j.optlastec.2017.05.006-Figure3-1.png",
        "caption": "Fig. 3. (a) 3D plot and (b) limit diagram showing relationship between laser energy",
        "texts": [
            "01 0.03 <0.2 Balance 0 20 40 60 80 100 120 140 160 180 200 0 2 4 6 8 0 \u00b5m Particle size (\u00b5m) Raw ( ) Spherical ( ) D[10] 27 33.9 D[50] 52.6 59.5 D[90] 96.8 92.8 Raw powder \u00b5m 0 20 40 60 80 100 \u00b5m C um ul at iv e di st ri bu tio n (% ) Spherical powder i10Mg powder: (a) SEM image of AlSi10Mg powder and (b) particle size distribution In this study, P = 400W, h = 0.14 mm, d = 0.025 mm. Consequently, LED \u00bc 8 105Te=\u00f07Pd\u00de \u00f04\u00de According to Eq. (4), LEDs in the SLM process are calculated and displayed in Fig. 3. Typical LEDs of 89, 109, 131, 174 and 200 J/mm3 are selected to analyze in experiments. A solid densitometer (Beyong, DE-120M) was selected for density measurement. At least three test results were collected for every type of specimen and the average values were adopted as results. Porosities of the SLM manufactured AlSi10Mg samples at different LEDs were tested by an industrial X-ray and CT detection system (Nikon Metrology, XT H225). The surface morphologies of the SLM manufactured AlSi10Mg samples perpendicular to building directions at different LEDs were characterized by a field emission scanning electron microscope (JEOL, JSM-7800F, FESEM)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001965_j.snb.2017.10.079-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001965_j.snb.2017.10.079-Figure8-1.png",
        "caption": "Fig. 8. Normalized amperometric I\u2212t response of the 5 mM glucose recorded initially (for fresh electrode) and after a period of one, two and three weeks. Potential constant +0.6 V, pH=7.0 (PBS).",
        "texts": [
            " However, 1 mM l-ascorbic acid significantly affects the signal response to glucose due to the fact that both species can be oxidized at applied potential of +0.6 V. Such a problem can be avoided by using a permselective layer against anions. Nafion thin films are often used as an interferent rejection coating [8,46,47]. Thus, casting a thin film of Nafion polymer onto the top of the CPE/GOxSiO2/Lig/Fc electrode greatly diminishes the interfering AA species and enhances selectivity of the electrode (Fig. S9, see Supplementary Material). <here Fig. 8.> The operational stability of the CPE/GOx-SiO2/Lig/Fc electrode was tested by continuous CV cycles between -0.4 and 0.6 V (50 mV s-1). It was found that peak currents retained 96% of their initial value after 150 scans, indicating good cycling stability. The storage stability revealed that the peak current of the biosensor decreased by approx. 25% within 3 weeks (Fig. S10, see Supplementary Material). The stability of the resulting biosensor toward glucose oxidation was also investigated for 3 weeks. When not in use, it was stored at 4 \u00baC in a refrigerator. The amperometric response signal of 5 mM glucose decreased after one week by 8%. The response current of the proposed electrode was reduced to 82% and 73% of its initial value after two and three weeks, respectively (Fig. 8). To identify the feasibility of the proposed biosensor, the content of glucose in Liquid Glucose 1WW - strawberry taste (sample 1) and 5% Glucose infusion solution (sample 2) has been determined. Samples were purchased from local pharmacy. The amperometric assays were carried out by standard addition method (three additions of 2 mM glucose). Before determination, the original samples were diluted with PBS to 100 mL (100-fold) in order to fit in the concentration range of the biosensor. The measurement results were shown in Table 3",
            " (B) and (C) correspond to the relationship between I vs v and I vs v1/2, respectively. Fig. 6. CV spectra of CPE/GOx-SiO2/Lig/Fc in PBS (pH=7.0) with increasing glucose concentration. Scan rate 10 mV s-1. Fig. 7. (A) Amperometric response of (a) CPE/GOx/Fc, (b) CPE/GOx-SiO2/Fc and (c) CPE/GOx-SiO2/Lig/Fc towards successive addition of 0.5, 1 and 2 mM glucose in pH=7.0 (PBS) at 0.6 V under stirring conditions. (B) Calibration curve between response current of CPE/GOx-SiO2/Lig/Fc and glucose concentration. Scheme 1 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Silica Graphite SiO2/Lig) hybrid material 12.88 7.58 25.28 7.34 3.26 11.75 * This means that the units in such cases are (\u00b5A mM-1 cm-2) instead of (\u00b5A mM-1) a Chitosan containing nanocomposites of graphene and gold nanoparticles with glucose oxidase at gold electrode b Redox polymer nanobeads of branched polyethylenimine binding with ferrocene with PEDOT:PSS and glucose oxidase dropped on a screen-printed carbon electrode c Film of chitosan\u2013polypyrrole\u2013gold nanoparticles with immobilized glucose oxidase d Cobalt phthalocyanine nanorods on graphene with nafion and glucose oxidase e Immobilized glucose oxidase in electropolymerized poly(o-phenylenediamine) film on a platinum nanoparticles-polyvinylferrocenium modified electrode f Glassy carbon electrode (GCE) with covalently modified ordered mesoporous carbon (OMC) with glucose oxidase (GOD) g Highly ordered mesoporous carbons with nafion and glucose oxidase h Glucose oxidase (GOx) at the gold and platinum nanoparticles-modified carbon nanotube (CNT) electrode with nafion i Indium thin oxide (ITO) electrode with glucose oxidase (GOx) entrapped at single-walled carbon nanotubestitanium dioxide composit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure3.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure3.5-1.png",
        "caption": "Fig. 3.5 Principle design of the active part of a metal tank test transformer (winding and magnetic core)",
        "texts": [
            " 86 3 Tests with High Alternating Voltages Tank-type test transformers guarantee best cooling conditions because its active part is arranged in a metal (steel) tank that can additionally be equipped with \u2018\u2018radiators\u2019\u2019 to increase the cooling surface of the tank (Fig. 3.4). Therefore, these transformers can be designed for the highest test currents, respectively, test powers, and enable continuous operation (Table 3.1). The magnetic core of the transformer has often three legs, and the inner LV and the outer HV winding are arranged around the central leg (Fig. 3.5). The core is on the same ground potential as the tank is, the lower end of the HV winding is usually also grounded via a bushing. At this bushing, the current in the HV test circuit can be measured. For an HVAC testing in ambient air, the transformer must be equipped with an oil-to-air bushing (Fig. 3.4), but metal tank transformers can also be connected by oil-to-SF6 bushings to metal-enclosed test circuits that are mainly applied for testing of gasinsulated systems (GIS) and their components (Fig",
            " There is a phase shift of 90 between the rectangular voltage, which replaces the active power losses of the circuit and the test voltage at the capacitive test object. 3.1 Generation of HVAC Test Voltages 107 With respect to the high quality factors of ACRF test systems, the adjustment of the frequency must be guaranteed with high precision (better than \u00b10.1 Hz). The height of the voltage is determined by pulse-width modulation. The frequency converter\u2014together with the control-and-measuring system\u2014can be arranged in one cubicle (Fig. 3.26b) or\u2014for lower power\u2014in a movable desk (Fig. 3.28b). Tank-type fixed reactors: As tank-type test transformers (Fig. 3.5), tank-type fixed reactors (Fig. 3.29) are related to high test power (50 Hz equivalent power up to the order of 50 MVA). Their design with oil\u2013paper insulation is derived from that of test transformers. In the central leg, the magnetic core has several small gaps of very low stray flux. Therefore, the fixed reactors have a higher quality factor than tuneable reactors. The tank of a single reactor is grounded, but they can be arranged in cascades when the higher stages are arranged on insulating support (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002645_1.4032168-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002645_1.4032168-Figure2-1.png",
        "caption": "Fig. 2 Support structures used for the (a) horizontal, (b) 45 deg, and (c) vertical build directions",
        "texts": [
            " Therefore, any feature of the test coupons that was less than 40 deg to horizontal required supports. Using this criteria, the upper surface of the horizontal cylindrical channels required supports; however, it would be difficult to remove these supports after the build was completed. As such, the horizontal surfaces of the channels were intentionally left unsupported to replicate situations where internal channels require supports, but cannot be accessed for support removal. Resulting support structures are shown in Fig. 2. In addition to surfaces below 40 deg, supports were placed on other features, such as the coupon flanges required for the testing facility, to anchor them to the build plate to prevent distortion. For the study presented in this paper, the support structures were generated using a commercial stereolithography file editing and build preparation software. A state-of-the-art DMLS machine was used to manufacture the coupons. Three duplicates of each test case were manufactured from the Inconel 718 powder for a total of 15 coupons"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001994_tpas.1969.292379-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001994_tpas.1969.292379-Figure7-1.png",
        "caption": "Fig. 7. Regions of instability for changes in magnetizing reactance.",
        "texts": [
            " An increase from this value of leakage reactance also tends to decrease the region of instability; however, in this case the region of instability moves to the left (lower frequencies) and does not entirely disappear. Also, it may be noted that at a given frequency of operation, the machine can be stabilized for either an increase or decrease in leakage reactances. Hence at fR = 0.28 and Xi, XIr' = 0.15 the machine is unstable, but for Xi, = Xir' 0.10 or 0.20 the machine is stable for all loading conditions. The effects of an increase or decrease in magnetizing reactance is given in Fig. 7. The curves demonstrate that a small magnetizing reactance is desirable from the point of view of system stability. Variation in the region of instability due to different system inertias is given in Fig. 8. Regions of instability are shown for H = 0.05, 0.075, and 0.1 second. The machine is stable over all regions of operation when H = 0.15. It is clear that an increase in inertia tends to promote system stability. It is interesting to note that at a fixed frequency an increase or decrease in system inertia may tend to stabilize the machine",
            " What seems to be desirable are analytic conditions, which show the bifurcations in the parametric space, for various regions of stability, instability, etc. It should be noted that Lyapunov's second or direct method offers a possibility of obtaining such conditions. It would be interesting to know if the authors have actually observed sustained oscillations similar to those predicted in Fig. 3 in an actual motor. Under saturated conditions it can be shown that the magnetising inductance decreases. In this case from Fig. 7 the stability would be improved. However, Fig. 9 shows an adverse effect on the performance when the supply voltage is increased. As the increase in supply voltage increases saturation it would seem by combining the results of Figs. 7 and 9 that in practice the two effects would tend to nullify each other. The authors' comments on this would be much appreciated. Finally, the neglect of mechanical damping in the mechanical equation would give pessimistic results. Would the authors remark on the significance of this term"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002131_j.sna.2014.03.011-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002131_j.sna.2014.03.011-Figure4-1.png",
        "caption": "Fig. 4. A test bench designed to identify the parameters of the rotor.",
        "texts": [
            " System identification and parameter selecting To verify previous formulations and obtain further understandng for the quadrotor, experiments are carried out to identify the arameters of the quadrotor model firstly. Based on the results of he identification, control gains are then selected for the developed ontrollers. .1.1. Attitude control According to (1), (2), (4) and (25), it is necessary to identify the arameters of the rotor and the quadrotor airframe prior to the ttitude controller design. The identification for the rotor is carried out on a specially esigned test bench. As shown in Fig. 4, one rotor from the quadroor is set up on a stress sensor (model YP-L1, Yeepo Automation) nd a torque sensor (model YP-NJ, Yeepo Automation). The stress ensor is capable of measuring the stress from 0 N to 50 N with a tolrance of 0.02%, and the torque sensor is capable of measuring the orque from 0 N m to 5 N m with a tolerance of 0.3%. As the electrical ignals from these sensors are very small, a transducer (model YPD, Yeepo Automation) is implemented to convert them into 0\u20135 V oltage signals. The converted voltage signals are then sampled by data acquisition (model USB-6363, National Instrument) at a freuency of 1000 Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003503_j.measurement.2016.03.001-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003503_j.measurement.2016.03.001-Figure2-1.png",
        "caption": "Fig. 2. Gear tooth with applied loading.",
        "texts": [
            " The elastic strain energy U stored in the volume element of a structure can be expressed as [33], U \u00bc Z vol r2 2E dV \u00f04\u00de where integration is over the entire volume of the beam. E is the modulus of elasticity and r is the stress distribution in the beam. As the bending stress varies along the length of tooth and depth of tooth the bending stress r is replaced by average bending stress rav . So it is constant for a given position of load on the tooth profile. The elastic strain energy stored in the gear tooth due to force F can be written as; U \u00bc Z vol r2 av E dV \u00f05\u00de In the present case, gear tooth is considered as a cantilever beam as shown in Fig. 2. Bending stress variation at different cross sections along the tooth length is calculated as [33]; r \u00bc Mc I \u00f06\u00de where M is the bending moment, c is the half tooth thickness at a particular cross section in the present case and I is the area moment of inertia. The bending stress distribution by using Eq. (6) is plotted in Fig. 3. Which is calculated along the tooth length on the top edge (half of the tooth thickness) of different cross sections of the tooth for loading position at tooth tip. The geometry data of the gears are taken as given in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000672_tpel.2009.2027905-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000672_tpel.2009.2027905-Figure2-1.png",
        "caption": "Fig. 2. (a) Permanent-magnet synchronous motor. (b) Heat flow diagram.",
        "texts": [
            " Heat transfer between two different structures can be modeled by determining the nodes and the thermal impedances of each material. Different characteristics of a specific machine part, such as temperature distribution, mechanical complexity, and material properties, were considered when the nodes and their assignments were considered. Ten nodes have been considered, i.e., the ambient, chassis, stator yoke, rotor, end winding, stator winding, shaft, ball bearings, internal air, and the mechanical structure where the motor is attached to. In Fig. 2(a), the PMSM and the geometrical dimensions of the motor used to calculate the thermal resistance and capacitances are shown. Similarly, in Fig. 2(b), heat flow between the different parts is illustrated. Additionally, the dimensions of the motor are summarized in Table VII in the Appendix. The red arrows (Cond) represent the heat transport due to conduction, the green arrows (Conv) the heat flow due to convection, and the purple (Rad) due to radiation. Radiation is also present internally, but it has not been considered in this paper. The (Cond) (Conv) and (Rad) are indicated in Fig. 2(b) in the proximity of the arrows. The nodes of interest and the thermal resistances between the nodes are clearly shown. Additionally, in Fig. 3, the power losses in the different parts of the PMSM, such as iron losses, stator winding, and end winding losses, are represented as current sources. The thermal impedances due to conduction and convection have been considered. It must be noted that no finiteelement (FEM) calculations have been required to obtain the thermal model described in the following paragraphs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure27-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure27-1.png",
        "caption": "Fig. 27. Contour lines of tooth-contact stress.",
        "texts": [],
        "surrounding_texts": [
            "LTCA and TSCS calculations of the pair of spur gears as shown in Table 1 are performed at the outer limit separately when the quantity Q of lead crowning are 0, 10, 20, 30 and 40 lm. Figs. 27 and 28 are contour lines of TSCS when Q = 10 and 30 lm. It is found that lead crowning has great effect on TSCS distribution when Figs. 27 and 28 are compared with Fig. 15. Fig. 29 is a relationship between the maximum TSCS and Q. From Fig. 29, it is found that the maximum TSCS becomes greater when Q is increased. Influence factor of lead crowning is introduced here to evaluate the effect of lead crowning on TSCS quantitatively. So it can be calculated through dividing the maximum TSCS when there are lead crowning by the maximum TSCS when there are no ME, AE and TM. Relationship between the influence factor and Q is also shown in Fig. 29. From Fig. 29, it is found that influence factor of lead crowning is over 2.0 when Q = 40 lm. Fig. 29 can also be used as references when ISO 6336/2 is used to calculate TSCS of a pair of spur gears with lead crowning."
        ]
    },
    {
        "image_filename": "designv10_1_0003905_j.ijfatigue.2020.105659-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003905_j.ijfatigue.2020.105659-Figure3-1.png",
        "caption": "Fig. 3. Geometry of Gaussian specimens used for the VHCF tests.",
        "texts": [
            " Vickers hardness was also measured on the Gaussian specimens used for ultrasonic tests, according to [25]. Ultrasonic VHCF tests were carried out on large Gaussian specimens [14,26] with a 90% risk-volume [27], V90, equal to 2300 mm3. The geometry of the specimens was defined according to [14]; the specimen dynamic elastic properties were experimentally assessed through the Impulse Excitation Technique (IET) on bars with rectangular crosssection. Since the dynamic elastic properties were found to be almost the same, the specimen geometry, shown in Fig. 3, was the same for horizontally and vertically built specimens. Before the experimental tests, all the specimens were mechanically polished with sandpapers to smooth the surface and avoid premature crack propagation from large superficial scratches [15]. Fully reversed tension-compression tests at constant stress amplitude were carried out up to failure or up to 109 cycles (runout specimens) by using the UFTMs (Ultrasonic Fatigue Testing Machines) developed at the Politecnico di Torino. The stress amplitude was kept constant with a proportional closed loop control, with the strain measured by a strain gage attached to the horn used as feedback signal",
            " It should be noted that, even though AB-V and HT samples were characterized by an almost constant hardness all over the cross section [15,16], the variation of Vickers hardness in AB-H was larger, with a significant reduction in the area lying above the region where supporting structures were removed, as discussed in [29]. The effect on the VHCF response of the HV reduction in HT-320 specimens due to the microstructural changes will be investigated in Section 3.4. The experimental dataset is reported in the S-N plot of Fig. 3. Since all the fatigue failures originated from defects (Section 3.3), the local stress amplitude in the proximity of the defect is reported on the ordinate axis of Fig. 4 and was considered for the analysis of the experimental data in the following [15]. In total, 52 valid experimental tests were carried out in the stress range [50: 102] MPa, with a number of cycles to failure in the range [6.8\u00b710 : 9.7\u00b7104 8]. According to Fig. 4, the experimental data show a large scatter, mainly due to the random size of the critical defects, as will be discussed in the following",
            " It can be concluded that residual stresses are more detrimental for large defects and that there is a significant interaction between residual stresses and defect size. The effect of the building orientation was finally investigated. It is well-known in the literature that the building orientation significantly affects the defect population and the fatigue response [46]. However, no results are present in the literature about the effect of the building orientation on the VHCF response of AlSi10Mg specimens. Fig. 12 compares the marginal P-S-N curves for AB-H and AB-V specimens. Since the experimental failures show a large scatter (Fig. 3), the 0.001-th P-S-N curves, which were below all the experimental failures for both AB-H and AB-V, were compared. According to Fig. 12, the P-S-N curve for AB-V lies below the curve for AB-H. This is related to the large experimental scatter of AB-V, which is correlated to the large range of ac (Fig. 6). For example, the premature failure at 55 MPa and =N 5.7\u00b710f 6 originated from the largest ac in AB-V, which is about 50% larger than the largest ac in ABH. The effect of the building orientation on the VHCF response is therefore mainly associated to the larger ac range and scatter for the vertically built specimens"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure8-1.png",
        "caption": "Fig. 8. 4\u20134\u20135 RPR-equivalent PMs in the second family. (a) 2- uRPuvU/DSvPR. (b) 2-uRRuvU/DSvPR. (c) 2-uRPuvU/DSvRR. (d) 2- uRRuvU/DSvRR.",
        "texts": [
            " Then, the RPR-equivalent PMs in 4\u20134\u20135 subcategory can be obtained by two combinations, respectively. The first combination is {L1} = {G(u)}{S(F)} and {L2} = {L3} = {R(O,u)}{G(v)}. The second combination is {L1} = {S(D)}{G(v)} and {L2} = {L3} = {G(u)}{R(B,v)}, which results from the kinematic inversion of the previous family. For conciseness, Table V only enumerates 49 RPR-equivalent PMs belonging to the first family in 4\u20134\u20135 category. Fig. 7 shows four architectures belonging to the first family, and Fig. 8 shows four architectures belonging to the second family. RPR-equivalent PMs in subcategory 5\u20135\u20134 can be constructed with two 5-DOF limbs in Table II and one 4- DOF limb in Table III. The first combination is {L1} = {R(O,u)}{G(v)} and {L2} = {G(u)}{S(Fa)} {L3} = {G(u)}{S(Fb)}, with Fa \u2208 axis(B, u) and Fb \u2208 axis(B, v). The second combination is {L1} = {G(u)}{R(B,v)}, and {L2} = {S(Da)}{G(v)}, {L3} = {S(Db)}{G(v)} with Da \u2208 axis(O, u) and Db \u2208 axis(O, u), which is a kinematic inversion of the first family"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002696_978-1-4471-4474-8-Figure8.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002696_978-1-4471-4474-8-Figure8.1-1.png",
        "caption": "Fig. 8.1 A graph showing interactions that were extracted from an article. A vertex represents a gene or protein, and an edge represents the interaction. The arrow represents the direction of the interaction so that the agent is represented by the outgoing end of the arrow and the target by the incoming end",
        "texts": [
            " In biosurveillance, for instance, one can extract symptoms from a chief complaint field in a note written for a patient admitted to the emergency department of a hospital (Chapman et al. 2004) or from ambulatory electronic health records (Hripcsak et al. 2009). The extracted data, when collected across many patients, can help understand the prevalence as well as the progression of a particular epidemic. In biology, biomolecular interactions extracted from one article or from different articles can be merged to construct biomolecular pathways. Figure 8.1 shows a pathway in the form of a graph that was created by extracting interactions from one article published in the journal Cell (Maroto et al. 1997). In the clinical domain, pharmacovigilance systems can use structured data obtained by means of NLP on huge numbers of patient records to discover adverse drug events (Wang et al. 2009a). \u2022 The techniques for information extraction may be limited to the identification of names of people or places, dates, and numerical expressions, or to certain types of terms in text (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure7.31-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure7.31-1.png",
        "caption": "Fig. 7.31 Low-speed display symbology format used in the AH-64A Apache (Ref. 7.26)",
        "texts": [
            " HQR data for two DVE tasks from ADS-33, the recovery to hover and sidestep, are superimposed on the results in Figure 7.29 for comparison. In the AFS trials, the UCE 3 was obtained with a combination of a sparse outside world scene and superimposed symbology; strictly speaking, the data cannot be directly compared with the VMS data, where the pilots flew with the outside world scene alone. Nevertheless, the data correlate very well and confirm the marked change in performance and workload with level of stability augmentation. One of the symbology sets evaluated in Ref. 7.32 is illustrated in Figure 7.31 and is based on the horizontal situation display featured in the AH-64A helicopter. We shall discuss this type of format in more detail later in this section. Results from the AFS trial have highlighted the importance of the height hold facility to ensure Level 1 ratings with the ACAH and TRC response types. Another result of the AFS trial questioned the value of attitude bars on displays during very-low-speed MTEs, particularly when attitude stabilization is provided artificially, as in the ACAH and TRC response types",
            " There are times when the crew need to gaze down a narrow field-of-view \u2018soda straw\u2019 and see fine detail with precision symbology, and others when they need to scan continuously a 220\u2218 field-of-view scene overlaid with guidance symbology cues. Each makes different demands on the Flying Qualities: Subjective Assessment and Other Topics 453 Fig. 7.33 Central symbology variables in AH-64A display format (Ref. 7.26) display technology but, ultimately, field of view and symbology content, like many display attributes, need provide only the functionality required for a given task. A good example of how symbology can be designed to aid specific tasks is provided by the AH-64A format shown previously in Figure 7.31, in the so-called hover \u2018pad capture\u2019 or \u2018bob-up\u2019 mode. We supplement Figure 7.31 with Figures 7.32 and 7.33, taken from Ref. 7.26, showing how the pilot uses this particular display to position the aircraft in the very-low-speed regime. The display is intended to aid the pilot maintain an accurate hover in a DVE. By \u2018flying\u2019 the acceleration cue into the hover pad and \u2018flying\u2019 both the cue and pad to the fixed aircraft reticle, the pilot can achieve a hover at a prescribed location, defined by the hover pad. Other flight data on the display include the heading, height and rate of climb and airspeed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003586_s00170-019-03716-z-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003586_s00170-019-03716-z-Figure1-1.png",
        "caption": "Fig. 1 Illustrations of the sample geometry with a small cylinder section diameter of 5.08 mm. a Sample geometry, b radial measurement locations, c spot measurement locations, and d sectioned and mounted cross sections for profile measurement",
        "texts": [
            " However, as discussed in this paper, areal measurements of AM surface typically used are obscured by powder particles attached to the surface providing a superficial measurement with little bearing on the true surface roughness that would relate to mechanical properties such as fatigue performance. Therefore, it is critical to fully understand surface roughness measurement procedures and metrics that are tailored to AM surfaces when relating to the PPPs. The component geometry used for this study was designed to mimic the fillet transition and the gage section of a cylindrical fatigue test bar as seen in Fig. 1a. The gage section has a diameter of 0.2 in. (5.08 mm), a height of 0.25 in. (6.35 mm), and the total height of the component is 0.5 in. (12.7 mm). This test geometry is selected such that the developed measurement techniques and PPP relations could be used to measure the gage section of an actual fatigue bar before testing to complete the PSPP relationship. This sample is measured using both nondestructive areal measurement and destructive profile measurement methods. Figure 1b and c show the measurement locations for the areal method and Fig. 1d shows example cross sections used in the profile measurement which are described in further details in the following sections. The goal of this experiment was to define the relationship between contour laser parameters and as-built vertical surface roughness for LPBF nickel superalloy 718. The test components were fabricated in an EOS M290 machine with a 20 \u03bcm layer thickness. The contour laser power and laser speed parameters are varied. The contour processing parameters control the laser settings that trace around the outside of the component geometry on each layer",
            " This system uses angled overhead light sources and sensors to measure the reflected light and calculate the height of the sample on its measurement plate. A fixture of a cutaway mold was 3D printed using Fused Deposition Modeling to hold the components in place for measurement. A total of 8 measurements were taken per sample. Two different spot measurements were taken at four radial locations of the sample, which resulted in 8 total measurements per sample. The radial locations were based off of the orientation of the embossed number on the top of the sample, which was also related to the recoater direction in the machine as shown in Fig. 1b. Each radial location was approximately 90 degrees from the previous radial location. The first spot measurement was taken near the top of the cylindrical section, while the second spot measurement was taken at the bottom of the cylindrical section right before the fillet, which ensured both measurements are in the gage section as shown in Fig. 1c. The measurements were taken using \u00d7 160 magnification and the Keyence camera was autofocused. Each spot measurement was taken over a region measuring 1.4 \u00d7 1.89 mm (0.055 \u00d7 0.074 in) with an accuracy of \u00b1 3 \u03bcm in the height direction and \u00b1 2 \u03bcm within the plane. To account for the curvature of the bar, a secant curved surface correction was applied in the Keyence software. The curvature corrected raw height data was exported to a .csv file for further calculations and analysis. A Matlab script utilizing the ",
            " Destructive profile measurements were used to view the melted surface and deepest notches, unobscured by any powder particles on the superficial surface. To begin the profile analysis, the samples were cut into four sections utilizing a metallographic saw. The cuts were taken along approximately the same radial locations where the surface roughness measurements were taken resulting in four pieces from a single sample. After the samples were cut, they were mounted in such a way that each of the exposed surfaces corresponded to a cut from a different radial location. An example of the mounted sample pieces can be seen in Fig. 1d and sample destructive cross section images for several parameters are shown in Fig. 3. The specimens were mechanically polished to a 0.5 \u03bcm finish, and the surface profile was extracted from optical microscope images for use in the measurements. The images were cropped to include only the gage section portion and rotated using ImageJ [19] to ensure that the cross section was horizontal for the surface roughness metric calculation. The images were then imported into Matlab, where they were converted to binary, and a tracing function (bwtraceboundary) was used to identify the surface profile [20]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000050_tpel.2004.839785-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000050_tpel.2004.839785-Figure3-1.png",
        "caption": "Fig. 3. Block diagram of the current control system. The dashed box is the model for the doubly-fed induction machine.",
        "texts": [
            " If the estimate of the slip frequency, , is put to zero in (9), the and the components of the rotor current will not be decoupled. In [4], it is stated that the influence of the decoupling term is of minor importance, since it is an order of magnitude smaller than the term . Nevertheless, in this paper, the and components of the rotor current will be decoupled, since for a digital signal processor (DSP)-based controller it is easy to implement. Substituting (9) in (7), the rotor current dynamics formed by the inner loop in Fig. 3 are now given by (11) where the estimated parameters in the control law are assumed to have correct values. If the back EMF is not compensated for, i.e., in (9), it is treated as a disturbance to the rotor current dynamics. The transfer function from to is (12) Due to the convenience of internal model control (IMC) for designing controllers, this method is here used [16]. IMC can be used for current or speed control of any ac machine [17]\u2013[19]. The controller for a first-order system typically becomes an ordinary PI controller when using IMC [17] (13) where the parameter is a design parameter, which is set to the desired bandwidth of the closed-loop system, and is an estimate of the transfer function. The relationship between the bandwidth and the rise time (10%\u201390%) is . Then, from (13), the following controller parameters are found: (14) giving the following closed-loop system: (15) If the \u201cactive resistance\u201d is set to , the transfer function from the back EMF, , to the current, , cf. Fig. 3, is given as (16) if all model parameters are assumed to be accurate. A parameter is introduced in a fashion similar to (10) for control without active resistance for control with active resistance. (17) This yields . (18) This implies that the previous choice of will force a change in the back EMF to be damped out with the same bandwidth as the closed-loop current dynamics. Since should be greater than zero, the minimum bandwidth of the current control loop when using \u201cactive resistance\u201d becomes , which is usually an unrealistically small value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure8.28-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure8.28-1.png",
        "caption": "Fig. 8.28 Flight path angle",
        "texts": [
            " The results suggest a relationship between the UCE and the margin between the postulated, 12 xe, look-ahead point and any obscuration; this point will be revisited towards the end of this section, but prior to this, the variation of flight path angle during the climb will be analysed to investigate the degree of \ud835\udf0f guide following during the manoeuvre. 498 Helicopter and Tiltrotor Flight Dynamics \ud835\udf49 on the Rising Curve For the \ud835\udf0f analysis, the aircraft flight path angle \ud835\udefe is converted to \ud835\udefea, the negative perturbation in \ud835\udefe from the final state, as illustrated in Figure 8.28. If the aircraft\u2019s normal velocity w is small relative to the forward velocity V, the flight path angle can be approximated as \ud835\udefe \u2248 \u2212w V (8.35) \ud835\udefea = \ud835\udefe \u2212 \ud835\udefef (8.36) The \ud835\udefe\u2019s-to-go and associated time rates of change are plotted in Figure 8.29 for the UCE= 1 and UCE= 2 fog-line cases, although it should be noted that the 240-m case is actually borderline UCE= 2/UCE= 3. In Figure 8.29, time has been normalised by the duration of the climb transient (fog= 240 m, T= 2.5 s; fog= 480 m, T= 4.3 s; fog= 720 m, T= 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001524_s0022112075003126-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001524_s0022112075003126-Figure2-1.png",
        "caption": "FIGURE 2. Slender body near i d k i t e plane wall(s).",
        "texts": [
            " In such a case it is instructive to view the slender body as a segmented contiguous assemblage of short, rigid, straight slender bodies; see figure 1 . If end effects on the overall body are neglected, then a single value of Ci can be used for all sub-bodies. It is this situation, then, which motivates our study. We consider a cylindrical body of radius r, and length 21 such that r, < 1. The body axis translates while remaining in a plane situated at a distance h from either a single infinite plane wall, or two such walls; see figure 2. In all cases ro h Q 1. For a single wall, we represent the flow field by a distribution of appropriate singularities located along the body axis and its image line. Aspects of this problem have been studied numerically by Blake (1974), and his results will be of comparative interest here. In the case of two walls, we represent the flow field using an application of the Faxen (1923) technique introduced by de Mestre (1973). In this section we consider a slender body situated a distance h from a single stationary plane wall; cf. figure 2 . The slender body may translate in the xl, xz or x3 direction, i.e. longitudinally, transversely in a plane parallel to the wall or Movement of slender bodies near plane boundaries 53 1 transversely in a plane normal to the wall, respectively. For such motions, it is convenient to represent the velocity field in the fluid using a distribution of appropriate singulwities along the centre-line of the body. Thus we can pose the following integral equation for the velocity u(x): where F(s) is the force per unit length acting on the body and G,,(x,s) is the Green's function appropriate to the geometry of the problem (and the no-slip boundary condition)",
            "6) and table 1 indicates that to this order of approximation the local force per unit length is constant along the body, and is therefore equal to the average force. The results here are then conveniently expressed in terms of resistance coefficients C, = Sn,u,/(4. +&) [cf. ( l . l ) ] as 2v c - 4np c - 47v c1 = In (2h/r0)\u2019 - In (2h/r0)\u2019 - In (2h/r0) - 1\u2019 In this section we consider a slender body whose centre-line remains in a plane a distance h from stationary plane walls above and below it; cf. figure 2. The body may translate in the x1 or x2 direction, i.e. either longitudinally or transversely parallel to the walls. Here it is convenient to study the flow field by employing the technique introduced by Faxen (1923; see also Happel & Brenner 1965, pp. 323-324) in connexion with a sphere falling between two parallel walls. The technique develops a sum of integral expressions for the velocity field which are appropriate to the solid boundaries present. However a straightforward physical interpretation, such as that in Q 2, is not possible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002854_j.engfailanal.2013.07.005-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002854_j.engfailanal.2013.07.005-Figure3-1.png",
        "caption": "Fig. 3. (a) Finite element mesh of pinion tooth, (b) cracked tooth.",
        "texts": [
            " A single tooth two-dimensional model is used in the present study for the ease of computation. The mesh is then imported to FRacture Analysis Code (FRANC). FRANC is a finite element code which uses principles of linear elastic fracture mechanics (LEFM) for static analysis of cracked structure. It has unique automatic crack propagation capabilities after an initial crack is inserted in a mesh [35,36]. The tooth is rigidly held at the edges of the rim and the load is applied at the highest point of single tooth contact (HPSTC), normal to the surface as shown in Fig. 3a. The point of largest stress has been identified using finite element analysis and the crack has been introduced at the fillet region of tooth root. The crack propagation path has been obtained for different crack lengths viz. 1 mm 2 mm and 4 mm. The complete crack trajectory is shown in Fig. 3b. The crack trajectory obtained can be used to introduce the crack in the specimen for experimental study of the cracked tooth for calculation of SIF. The specimen material used in the experimental study in the following section, has birefringent photoelastic property. The cracks will be induced in the specimens on one of the pinion tooth at the location identified by finite element analysis. The standard involute pinion and gear specimens, main specification of which is given in Table 1, were produced using polycarbonate birefringent material on advanced CNC milling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure2.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure2.9-1.png",
        "caption": "Fig. 2.9 Features limiting rotor performance in high-speed flight",
        "texts": [
            " Entering the vortex-ring state, the helicopter will increase its rate of descent very rapidly as the lift is lost; any further application of collective by the pilot will tend to reduce the rotor efficiency even further \u2013 rates of descent of more than 3000 ft/min can build up very rapidly. The consequences of entering a vortex ring when close to the ground are extremely hazardous. Chapter 10 discusses the peculiar characteristics of tiltrotors in vortex ring state, including so-called asymmetric vortex ring, where only one rotor enters the condition. Rotor Stall Boundaries While aeroplane stall boundaries in level flight can occur at low speed, helicopter stall boundaries typically occur at the high-speed end of the OFE. Figure 2.9 shows the aerodynamic mechanisms at work at the boundary. As the helicopter flies faster, forward cyclic is increased to counteract the lateral lift asymmetry due to cyclical dynamic pressure variations. Forward cyclic increases retreating blade pitch/incidence and reduces advancing blade pitch/incidence (\ud835\udefc); at the same time, forward flight brings cyclical Mach number (M) variations and the \ud835\udefc versus M locus takes the shape sketched in Figure 2.10. The stall boundary is also Helicopter and Tiltrotor Flight Dynamics \u2013 An Introductory Tour 17 Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002798_tec.2020.2964942-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002798_tec.2020.2964942-Figure12-1.png",
        "caption": "Fig. 12. Examples of electrical machine assemblies fabricated using AM, a) complete stator-winding assembly - Chemnitz University of Technology [51], b) a new machine concept with conical air-gap \u2013 Persimmon Technologies Corporation [52]",
        "texts": [
            " Although, AM provides a virtually unrestricted way of designing and manufacturing new components, there is a need to understand how this translates to successful implementation when it comes to in-volume manufacturing of electrical machines. Several aspects including: materials, manufacturing techniques and new design concepts fully utilising AM need to be considered. A more comprehensive design approach seems a natural step forward in developing AM of the next generation of electrical machines. Some of the early examples of MM AM of integrated machine subassemblies or new machine concepts look very promising indeed, Fig. 12. However, AM of electrical machines is not limited to the machines themselves. Integrating power electronics, magnetic components and motor-drives using AM technology is another exciting prospect [54] \u2013 [60]. The electrical, thermal and mechanical aspect are the key consideration points here, which have had some attention in the literature. The research activities have been focused predominantly on enhancing selected performance measures, e.g. increased power-density, improved heat removal and reduced mechanical stresses, while maintaining compact, robust and cost effective design solutions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000757_978-0-387-49312-1-Figure6.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000757_978-0-387-49312-1-Figure6.18-1.png",
        "caption": "Figure 6.18. The mechanical work done on a weight in this rowing exercise is the product of the force and the displacement.",
        "texts": [
            " Now we must define work and understand that this mechanical variable is not exactly the same as most people's common perception of work as some kind of effort. The mechanical work done on an object is defined as the product of the force and displacement in the direction of the force (W = F \u2022 d). Joules are the units of work: one joule of work is equal to one Nm. In the English system, the units of work are usually written as foot-pounds (ft\u2022lb) to avoid confusion with the angular kinetic variable torque, whose unit is the lb\u2022ft. A patient performing rowing exercises (Figure 6.18) performs positive work (W = 70 \u2022 0.5 = +35 Nm or Joules) on the weight. In essence, energy flows from the patient to the weights (increasing their potential energy) in the concentric phase of the exercise. In the eccentric phase of the exercise the work is negative, meaning that potential energy is being transferred from the load to the patient's body. Note that the algebraic formula assumes the force applied to the CHAPTER 6: LINEAR KINETICS 155 load is constant over the duration of the movement",
            " Typical units of power are Watts (one J/s) and horsepower. One horsepower is equal to 746 W. Maximal mechanical power is achieved by the right combination of force and velocity that maximizes the mechanical work done on an object. This is clear from the other formula for calculating power: P = F \u2022 v. Prove to yourself that the two equations for power are the same by substituting the formula for work W and do some rearranging that will allow you to substitute v for its mechanical definition. If the concentric lift illustrated in Figure 6.18 was performed within 1.5 seconds, we could calculate the average power flow to the weights. The positive work done on the weights was equal to 35 J, so P = W/t = 35/1.5 = 23.3 W. Recall that these algebraic definitions of work and power calculate a mean value over a time interval for constant forces. The peak instantaneous power flow to the weight in Figure 6.18 would be higher than the average power calculated over the whole concentric phase of the lift. The Force\u2013Motion Principle would say that the patient increased the vertical force on the resistance to more than the weight of the stack to positively accelerate it and would reduce this force to below the weight of the stack to gradually stop the weight at the end of the concentric phase. Instantaneous power flow to the weights also follows a complex pattern based on a combination of the force applied and the motion of the object"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003020_j.ijfatigue.2019.105260-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003020_j.ijfatigue.2019.105260-Figure3-1.png",
        "caption": "Fig. 3. Geometry and build directions of FCGR specimens: (a) 0\u00b0 sample, (b) 45\u00b0 sample, (c) 90\u00b0 sample.",
        "texts": [
            " The definition of build direction and diameters for all samples are shown in Figs. 1\u20133. The red arrows are the build direction, and the black arrows are the load direction. The sample with the deposition layer parallel to the load direction is defined as the 0\u00b0 samples shown in Fig. 1(a) and 2(a), while the sample with the deposition layer perpendicular to the load direction are defined as the 90\u00b0 samples shown in Figs. 1(c) and 2(b). The 45\u00b0 sample has a 45\u00b0 angle between the deposition layer and the load direction, as shown in Fig. 1(b). In Fig. 3(a), the CT specimen with the crack growth direction parallel to deposition layers is defined as the 0\u00b0 sample, that with the crack growth direction perpendicular to the deposition layers, as the 90\u00b0 sample, shown in Fig. 3(a) and (c) respectively. As mentioned previously, the 45\u00b0 sample mean that there is a 45\u00b0 angle between the deposition layer and the crack growth direction, shown in Fig. 3(b). The width (W) and thickness (B) of all CT specimens was 50mm and 10mm respectively. Tensile tests were performed at room temperature conditions using a DDL100 electronic universal testing machine at the tensile rate of 0.5 mm/min. Samples with different build directions were tested. Extensometer and strain gauges were used to measure the strain and calculate Young\u2019s Modulus. Fatigue tests were performed at room temperature conditions using a MTS 810 fatigue testing machine. The test frequency was 20 Hz at a stress ratio R=\u22121"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002089_tia.2010.2103915-Figure19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002089_tia.2010.2103915-Figure19-1.png",
        "caption": "Fig. 19. Basic experimental apparatus.",
        "texts": [
            " Although we already verified the loss calculation by the experiment of the motor, as shown in Fig. 5, the measured loss includes not only the magnet eddy-current loss but also the core loss. They cannot be separated by this experiment. As a consequence, the effect of the magnet segmentation cannot be directly confirmed only by this experiment. Therefore, the basic experiments using only magnet specimens [9] are carried out in order to support the calculated variation in the magnet eddy-current loss with the number of segmentations and the frequency. Fig. 19 shows the experimental apparatus. The magnets with a thermal sensor are placed at the center of an exciting coil. After surrounding the magnet by heat-insulation material, the coil is excited by an alternating current of which frequency is 1\u201330 kHz. Then, the eddy-current loss is estimated by the following expression [8], with the increase in the temperature for 5 min: Wmag = mc dT dt (11) where m is the mass, c is the specific heat, and T is the temperature. The heat conduction from the magnets to outside of the heat-insulation material is neglected",
            " (18) Finally, the eddy-current loss Wn can be calculated by integrating the eddy currents as follows: Wn = 2d \u03c3 b\u222b 0 a\u222b 0 ( |Jx(x, y)|2 + |Jy(x, y)|2 ) dxdy. (19) Substituting (17) and (18) into (19), we have (8). To understand the difference between the magnetsegmentation effect in Fig. 14 and that in Fig. 20, the magnet eddy-current loss in Fig. 22 is calculated by the 3-D FEM. The calculated result is compared with the theoretical solution. In this model, an iron core is added to the experimental apparatus shown in Fig. 19. The relative permeability of the iron core is assumed as 1000. In addition, the loss of the core is assumed as zero. Fig. 23 shows the results of the magnet eddy-current loss. The result of the 3-D FEM without the iron core is also shown; this is the same result in Fig. 20. When the frequency is low, all the results are almost identical. It can be stated that the theoretical solution in (8) can be applied to both models with/without the core when the frequency is low, and the skin effect is negligible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000718_j.optlaseng.2007.06.010-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000718_j.optlaseng.2007.06.010-Figure2-1.png",
        "caption": "Fig. 2. Angles of incidence and reflection.",
        "texts": [
            " Assuming an s-polarized beam, the reflectivity factor can be obtained by [29] R \u00bc \u00f0n cos ji\u00de 2 \u00fe k2 \u00f0n\u00fe cos ji\u00de 2 \u00fe k2 , (11) where R is the reflectivity, ji is the incident angle, n is the refraction coefficient, and k is the material extinction coefficient. Assuming an opaque material (e.g., metal), the relation between the reflectivity and absorptivity is as follows: b \u00bc 1 R. (12) For the sake of simplicity, an average angle of incidence can be calculated for each deposited layer based on the boundary of a non-planar surface within its intersection with the laser beam. Fig. 2 shows a typical laser ray direction and the angle of incidence during the multilayer LSFF process. 2.2.2.4. Power attenuation. A portion of the laser energy is directly absorbed by the workpiece. The powder particles also absorb and carry some of the laser energy into the melt pool. To consider this effect in the modeling, a method ARTICLE IN PRESS M. Alimardani et al. / Optics and Lasers in Engineering 45 (2007) 1115\u20131130 1119 developed by Picasso et al. [30] is used. Based on this method, the total absorbed power by the workpiece Pw can be defined as Pw \u00bc bePl, (13) where be is the effective absorption factor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001214_j.rcim.2017.02.002-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001214_j.rcim.2017.02.002-Figure6-1.png",
        "caption": "Fig. 6. The displacement between the J5 center and the spindle axis.",
        "texts": [
            " It can be found that no matter what values \u03b84 and \u03b85 take, kstif has the same distribution characteristics of \u03b82 and \u03b8 real3 . It means that the orientation of the robot EE don\u2019t influence the distribution characteristics of the index kstif in the whole robot position. Thus, the distribution characteristics of the index kstif in the whole robot position can be estimated in any orientation. Simultaneously, let \u03b82 and \u03b8 real3 be determined values, and then the influence of \u03b84 and \u03b85 on kstif can be plotted when d6 shown in Fig. 6 takes different values. In Fig. 7, \u03b82 and \u03b8 real3 are set to be 1.5 rad and \u22121.2 rad, respectively. From Fig. 7, it can be seen that the stiffness has the same distribution characteristics for any specified d6. But the stiffness has a confirmed value when d6 equals to zero, which means \u03b84 and \u03b85 have no influence on the stiffness under such condition. Thus, it is proved that \u03b84 and \u03b85 affect kstif only when d6 is unequal to zero. Combined with the conclusion from Fig. 5, it can be seen that if d6 is a nonzero, which is usually a truth, \u03b84 and \u03b85 only affect the value of kstif rather than the distribution characteristics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000865_s0065-2423(08)60401-1-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000865_s0065-2423(08)60401-1-Figure7-1.png",
        "caption": "FIG. 7. Results of three field trials concerning the determination O f & in Dutch hospitals. All data have been recalculated to a mean value of 15 g/dl. The horizontal arrows indicate 2 x SD. A = 1960; B = 1964; C = 1968.",
        "texts": [
            " Secondary HiCN reference solutions are HiCN solutions made by private or governmental manufacturers, following as closely as possible the procedure used in preparing the international HiCN reference solution. The international HiCN reference solution should always be used in checking the spectral properties of the secondary reference solution. 2.6. QUALITY CONTROL After the introduction of the HiCN method in its standardized form (57, 71, 72), the routine use of this method for the determination of c;Ib steadily increased (Fig. 1). Concomitantly, the precision of the determination of ckb as found in three field trials held in The Netherlands improved considerably (Fig. 7). The spread, expressed as 2 X SD, decreased from 4 g/dl in 1960 to 2 g/dl in 1964 and to 1 g/dl in 1968. The coefficient of variation thus fell from 13 to 3.3% in a period of 8 years. These data seemed to confirm the original concept of the standardized HiCN method: that the availability of an HiCN reference solution for providing a single calibration point would suffice to yield optimum measuring results. In actual fact, however, this did not prove to be the case. In 1973,57 laboratories in Europe and Africa participated in an interlaboratory trial organized on behalf of the ICSH Expert Panel on Hemoglobinometry (47)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure7.29-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure7.29-1.png",
        "caption": "Fig. 7.29 Vehicle model for a Formula car",
        "texts": [
            "6 Handling of Formula Cars 221 of power-on for a rear-wheel-drive car is evident in both cases. However, the locked differential makes this phenomenon stronger. The maps \u03b2\u2013\u03c1 for power-off and power-on for a vehicle equipped with a locked differential are shown in Fig. 7.27. Again, the lines at constant steer angle clearly show, and do it in a quantitative way, the oversteer effect of power-on. For comparison, the same maps for a vehicle with open differential are given in Fig. 7.28. It is in the handling of Formula Cars that aerodynamics comes really into play (Fig. 7.29). Thanks to well designed wings, very high downforces are generated at high speeds, although at the price of high drag as well. A mathematical model that takes aerodynamics into account has been developed in Sect. 7.2. Here we discuss some of the main phenomena that make the handling of this kind of cars so 222 7 Handling of Race Cars 7.6 Handling of Formula Cars 223 Fig. 7.30 Formula car with open differential: different handling curves obtained in constant speed, variable steer tests peculiar"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000144_j.mechmachtheory.2004.10.005-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000144_j.mechmachtheory.2004.10.005-Figure1-1.png",
        "caption": "Fig. 1. Layout of the 3-RRR manipulator.",
        "texts": [
            " The method of using scaling factors to determine the maximum allowable wrench magnitude, as used for the non-redundantly-actuated case, can be used for the optimization-based solution. Eq. (14), where t is found by solving the optimization problem defined in Eq. (17), is used in lieu of Eq. (2). The smallest scaling factor is again found which determines the maximum amount that $F can be scaled. The manipulator being considered is a three-branch, three-revolute joints per branch (3-RRR) planar parallel manipulator. Fig. 1 shows the layout of the 3-RRR manipulator. For the examples, the manipulator s dimensions and actuation capabilities are modelled after the Reconfigurable Planar Parallel Manipulator (RPPM) [27]. For the RPPM, the link lengths and platform edge lengths are all equal to 0.200 m, i.e., q1 to q6 = l2 = l3 = 0.200 m and a = 60 . The bases of the branches are all 0.500 m apart from each other. The maximum torque capability for each actuated joint of the RPPM is \u00b14.2 N m. Choosing a reference frame to be coincident with frame 3 of branch 1 (see Fig. 1), allows the joint screws 3 for the 3-RRR manipulator to be written as: 3 F $ji (L, ref$11 \u00bc f1;q4s\u00f0h21 \u00fe h31\u00de \u00fe q1sh31 ;q4c\u00f0h21 \u00fe h31\u00de \u00fe q1ch31g T ref$21 \u00bc 1;q1sh31 ;q1ch31 T ref$31 \u00bc f1; 0; 0gT ref$12 \u00bc 1; q5s h22 \u00fe h32\u00f0 \u00de q2sh32 ; q5c h22 \u00fe h32\u00f0 \u00de q2ch32 l3 T ref$22 \u00bc f1; q2sh32 ; q2ch32 l3gT ref$32 \u00bc 1; 0; l3f gT ref$13 \u00bc 1 q6s\u00f0h23 \u00fe h33 a\u00de q3s\u00f0h33 a\u00de \u00fe l2sa q6c\u00f0h23 \u00fe h33 a\u00de q3c\u00f0h33 a\u00de l2ca 8><>: 9>=>; ref$23 \u00bc 1; q3s h33 a \u00fe l2sa; q3c h33 a l2ca T ref$33 \u00bc f1; l2sa; l2cagT \u00f018\u00de where shji \u00bc sin\u00f0hji\u00de, chji \u00bc cos\u00f0hji\u00de, sa \u00bc sin\u00f0a\u00de and ca \u00bc cos\u00f0a\u00de"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure8.6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure8.6-1.png",
        "caption": "FIGURE 8.6. A spherical manipulator.",
        "texts": [
            " Each column is a Jacobian generating vector, ci(q), and is associated to joint i. If joint i is revolute, then ci(q) = \u2219 0k\u0302i\u22121 \u00d7 0 i\u22121dn 0k\u0302i\u22121 \u00b8 (8.133) and if joint i is prismatic then, ci(q) simplifies to ci(q) = \u2219 0k\u0302i\u22121 0 \u00b8 . (8.134) Equation (8.117) provides a set of six equations. The first three equations relate the translational velocity of the end-effector joint speeds. The rest of the equations relate the angular velocity of the end-effector frame to the joint speeds. Example 246 Jacobian matrix for a spherical manipulator. Figure 8.6 depicts a spherical manipulator. To find its Jacobian, we start with determining the 0k\u0302i\u22121 axes for i = 1, 2, 3. It would be easier if we use the homogeneous definitions and write, 0k\u03020 = \u23a1\u23a2\u23a2\u23a3 0 0 1 0 \u23a4\u23a5\u23a5\u23a6 (8.135) 456 8. Velocity Kinematics 0k\u03021 = 0T1 1k\u03021 (8.136) = \u23a1\u23a2\u23a2\u23a3 cos \u03b81 0 \u2212 sin \u03b81 0 sin \u03b81 0 cos \u03b81 0 0 \u22121 0 l0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u23a1\u23a2\u23a2\u23a3 0 0 1 0 \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a3 \u2212 sin \u03b81 cos \u03b81 0 0 \u23a4\u23a5\u23a5\u23a6 0k\u03022 = 0T2 2k\u03022 (8.137) = \u23a1\u23a2\u23a2\u23a3 c\u03b81c\u03b82 \u2212s\u03b81 c\u03b81s\u03b82 0 c\u03b82s\u03b81 c\u03b81 s\u03b81s\u03b82 0 \u2212s\u03b82 0 c\u03b82 l0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u23a1\u23a2\u23a2\u23a3 0 0 1 0 \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a3 cos \u03b81 sin \u03b82 sin \u03b81 sin \u03b82 cos \u03b82 0 \u23a4\u23a5\u23a5\u23a6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000617_s00170-011-3776-6-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000617_s00170-011-3776-6-Figure2-1.png",
        "caption": "Fig. 2 Three-dimensional model of powders and platform of SLM process",
        "texts": [
            " Namely, Y axis is scanning direction where the laser will pass 21 steps. Once point 21 has been scanned, the laser beam scanned along the opposite direction until point 2, the laser beam scanned like this until the last point 41. In order to save time and reduce the amount of simulation, the simulation has been carried out from point 1 to point 21 along the Y direction, and the time step of simulation was defined as 0.01 s to realize small steps instead of the actual time of continuous movement. The parameter of simulation was shown in Table 3. Figure 2 shows the three-dimensional model of powders and platform. It is clearly seen that the region of powder bed is very small compared with that of platform. This model suggests that the temperature of platform cannot be affected by the temperature of powder bed, which is based on the previous hypothesis. Figure 3 presents the three-dimensional temperature contour of Ti6Al4V powder bed with laser power of 110 W and scan rate of 0.2 m/s. It was found with great interest that there exists a great temperature gradient from the surface of powder bed to the experimental platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001409_1.1698540-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001409_1.1698540-Figure2-1.png",
        "caption": "FIG. 2. The device for rotating and dropping a ball in the wind tunnel.",
        "texts": [],
        "surrounding_texts": [
            "T HE force acting on a sphere or cylinder rotating in a wind stream about an axis perpendicular to the stream is generally not in the direction of the wind. It may be resolved into two components, one in the direction of the wind and one perpendicular to the wind and to the axis of rotation. Magnus! and Newton! discussed the transverse force and gave the accepted explanation for its existence many years ago but ap parently only a limited number of experimental studies have been made. Several measurements~-8 have been 1 (a) Magnus, Poggendorf's Ann. d. Physik Chemie 88, 1 (1853); (b) Newton, Phil. Trans. 6, 3078 (1672); (c) Rayleigh, Messenger of Math. 7, 14 (1877); (d) Thomson, Nature 85, 251 (1910), reviewed in Sci. Am. p. 136 (February 11, 1911); (e) Goldstein, Modern Developments in Fluid Dynamics (Oxford University Press, New York, 1938), Vol. 1, p. 83; (f) Prandtl, Tietjens, and den Hartog, Applied Hydro and Aeromechanics (McGraw-Hili Book Company, Inc., New York, 1934), first edition, pp. 82-85. 2 (a) Lafay, Rev. Mecanique 30, 417 (1912); (b) Int. Crit. Tab. 1,408 (1926). 3 (a) Reid, N.A.C.A. Tech. Note 209 (1924); (b) see reference 2(b); (c) see reference l(e), Vol. 2, p. 545. 4 (al Betz, Zeits. des Vereines deutscher Ingenieure 69, 11 (1925); (b) see reference l(e), Vol. 2, p. 545. \u2022 Thorn, Brit. Aero. Res. Comm. Rep. and Memo. No. 1018, Annual Reports 1925-26, p. 82 (1927). 6 Acheret, Zeits. f. Flugtech. Motorluftschiffahrt 16, 45 (1925). 7 Flettner, Zeits. f. Flugtech. Motorluftschiffahrt 16, 52 (1928). 8 Thorn, Brit. Aero. Res. Comm. Rep. and Memo. No. 1082, Annual Reports 1926-27, p. 66 (1928). For a smooth ball the lift was negative at all rotational speeds below 5000 r.p.m. Above this speed, the lift was positive but was less than for the standard ball. The drag for these balls was nearly constant at about 0.08 lb. Balls with shallower dimples than standard gave intermediate results. Driving tests were consistent with the wind tunnel results. These results explain why a golfer cannot obtain long drives with a ball having a smooth surface and why the standard dimple or mesh surface gives him greater distance and better control of the ball. made of the forces acting on rotating cylinders in air and photographs have been taken of the flow around cylinders in air3 and in water. 9,!0 The Flettner rotor ship7 was an attempt to make a practical application of these forces. Robinsll observed the effect of such forces on bullets fired from gun barrels curved in such a way as to produce rotation of the bullet. MaccolF2 measured the forces on a 6-inch diameter sphere rotating at speeds up to about 1800 r.p.m. in a wind stream having velocities up to 34 feet per second. These forces are important in many ball games, for example, baseball, tennis, and golf, but little definite information seems to be available. Measurements on non-rotating golf balls have been made at the Bureau of Standards13 and by Derieux,14 but in both cases relatively low velocities were used. Thomson! measured the difference in pressure between opposite sides of a golf ball rotating in a wind stream and showed qualita tively how the forces would affect the flight of the ball. 9 See reference 1(f) pp. 281-287. 10 Relf and Lavender, Brit. Aero. Res. Comm. Rep. and Memo. No. 1009, Annual Reports 1925-26, p. 74 (1927). 11 Robins, \"New principles of gunnery,\" p. 206 (1805) ; presented before the Royal Society in 1747, discussed in reference 15(d). 12 (a) Maccoll, J. Roy. Aeronautical Soc. 32, 777 (1928); (b) see reference l(e), Vol. 2, p. 504. 13 Unpublished results by Dr. H. L. Dryden, now at N.A.C.A. 14 Derieux, J. Elisha Mitchell Soc. 51, 207 (1935). 821 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 128.114.34.22 On: Sat, 22 Nov 2014 12:57:39 Tait15 calculated the forces on a golf ball in flight by observing the trajectory and the time of flight and then attempted to explain the trajectory in terms of these forces. However, he had no convenient way of determin ing the ball velocities and, in general, the values he assumed were too high and the air forces correspond- ingly high but he was able to show that the transverse force had a significant effect on the trajectory. A typical golf ball trajectory is shown in Fig. 1, with a convenient way of defining the aerodynamic forces. The total force, R, is resolved into two com ponents, a drag, D, in the line of and opposite to the motion, and a lift, L, perpendicular to the motion. The lift is upward for the usual case of under spin and down ward for over spin. Frequently the axis of rotation is not exactly horizontal and then these forces have hori zontal components which cause \"hooking\" and \"slicing.\" In play velocities vary over a wide range; translational velocities of more than 225 feet per second and rota tional velocities up to 8000 r.p.m. have been observed at the A. G. Spalding and Brothers laboratoryi6 with Edgerton's high speed photographic technique. 17 To learn more about the lift and drag under flight condi- tions, the motions of different types of golf balls spinning in a wind stream were studied in the B. F. Goodrich wind tunnel. METHOD OF MEASURING LIFT AND DRAG The spinning device is shown in Figs. 2 and 3. The ball was held between shallow cups and rotated about a horizontal axis perpendicular to the wind stream with a variable speed motor whose speed was measured with a tachometer. When the trigger was released, the springs pulled the cups apart, allowing the ball to fall freely through the wind stream. The wind tunneP8 is of the horizontal, open type, with the throat about 18 inches high and 36 inches wide. It was modified somewhat for these tests by adding the top and bottom sections, A and B, and a screen, as indicated in Fig. 4. The ball was rotated at C and the landing spot was marked on waxed paper at B. In some cases the ball struck the screen before falling to Band for those tests a raised platform, j inch thick, was used at E. The various heights of fall were from 0.67 to 1.3 feet. The wind speed was 105 feet per second. The motion of the ball under the action of gravity and the aerodynamic forces is indicated in Fig. 5. With no spin, the ball is pulled down by its weight and horizontally by the drag, so that it travels a horizontal distance Xo while dropping a vertical distance y. With the ball spinning, the value of the drag is different and there is an additional vertical force, ordinarily up for clockwise rotation and down for counterclockwise rota tion. This increases or decreases the rate of fall, allow ing the ball to travel a horizontal distance Xl or X2 while falling the vertical distance y in a time 11 or t2\u2022 Neglect ing any variation in lift and drag arising from the in crease in ball velocity during fall and the variation in wind velocity throughout the testing space, the equa- 1. Tait, (a) Nature 42, 420 (1890); (b) ibid. 44, 497 (1891); (c) ibid. 48, 202 (1893); and (d) Trans. Roy. Soc. Edinburgh 37, 427 (1893). 16 (a) Ind. Eng. Chern., News Edition, 16, 673 (1893); (b) other results by Mr. George H. Temple, not published. 17 Edgerton and Germeshausen, American Golfer, 17 (November 1933). 18 Geer, Aero. Eng. 4, 33 (1932). 822 JOURNAL OF ApPLIED PHYSICS [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 128.114.34.22 On: Sat, 22 Nov 2014 12:57:39 dons of motion are: Clockwise spin (W / g) (cf2x/ dt2) = D, (W /g)(d2y/df2) = - W+L, xl=DgtN2W, y= - (W - L)gtN2W, (1) (2) (3) (4) Counterclockwise spin (W / g) (d2:i/ dt2) = D, (W / g) (cf2y/ dt2) = - W - L, x2=DgtN2W, y= - (W+L)gtN2W, D= -2WXIXZ!y(Xl+X2), L= W(XI-X2)/(Xl+X2). (5) (6) (7) (8) (9) (10) By spinning the ball first in one direction and then the other, values of the drag and lift can be obtained."
        ]
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure1.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure1.16-1.png",
        "caption": "FIGURE 1.16. A planar 3R manipulator and position vector of the tip point P in second link local coordinate B(x, y).",
        "texts": [
            " A vector r may be a function of a variable in one reference frame, but be independent of this variable in another reference frame. Example 2 Reference frame and parameter dependency. In Figure 1.15, P represents a point that is free to move on and in a circle, made by three revolute jointed links. \u03b8, \u03d5, and \u03c8 are the angles shown, then r is a vector function of \u03b8, \u03d5, and \u03c8 in the reference frame G(X,Y ). The length and direction of r depend on \u03b8, \u03d5, and \u03c8. If G(X,Y ), and B(x, y) designate reference frames attached to the ground and link (2), and P is the tip point of link (3) as shown in Figure 1.16, then the position vector r of point P in reference frame B is a function of \u03d5 and \u03c8, but is independent of \u03b8. 1.5 Problems of Robot Dynamics There are three basic and systematic methods to represent the relative position and orientation of a manipulator link. The first and most popular method used in robot kinematics is based on the Denavit-Hartenberg notation for definition of spatial mechanisms and on the homogeneous transformation of points. The 4\u00d7 4 matrix or the homogeneous transformation 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002042_adem.201900617-Figure40-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002042_adem.201900617-Figure40-1.png",
        "caption": "Figure 40. Using Bionics for design AM-enabled lightweight structures. Reproduced with permission.[193] Copyright 2014, Airbus Group Innovations.",
        "texts": [
            "[192] Airbus has rated SLM as a level-six technological readiness, meaning that the technology is approaching operational conditions and may soon be implemented. EOS and Airbus have teamed up in their effort to reduce weight on aircraft. Some of the parts under consideration were the aircraft brackets and hinges used on the nacelle. As a first step, the generic bracket fabricated by a conventional casting process was used as the baseline to benchmark the DMLS process. When comparing the lifecycle of a steel bracket (casting process) with the lifecycle of a design-optimized titanium bracket (DMLS) shown in Figure 40, the energy consumption and CO2 emissions over the whole lifecycle of the bracket are reduced. CO2 emissions over the whole lifecycle of the nacelle hinges were reduced by nearly 40% via weight savings that resulted from an optimized geometry, which is enabled by the design freedom offered by the DMLS process and the use of titanium. Most significantly, using DMLS to build the hinge may reduce the weight per aircraft by 10 kg, a noteworthy savings when looking at industry buy-to-fly ratios. A similar bracket was designed by Laser Zentrum Nord GmbH (Germany) and manufactured using LAM (laser AM with a powder bed)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001290_j.gaitpost.2009.02.009-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001290_j.gaitpost.2009.02.009-Figure1-1.png",
        "caption": "Fig. 1. The double inverted pendulum model (a) describes the external mechanical work (W) generated by the leading and trailing leg to redirect the centre of mass velocity (vcom) from v com at heel strike to v\u00fecom at toe-off during the step-to-step transition in walking. Negative work from impact impulse (S) at heel strike (W S2) is lower when the trailing leg generates a push off impulse (P) at the same time or just prior to heel strike (b), compared to a situation in which propulsion has to be generated substantially prior to heel strike by generating a hip extensor torque (c). Adapted from Donelan et al. [11].",
        "texts": [
            " Likewise, analyses of the mechanical work performed on the swing leg did not reveal differences between amputees and able-bodied subjects [13]. Recently, an extension of the inverted pendulum model was proposed that could potentially account for the increased energy cost of amputee walking [14\u201316]. This model explicitly models the step-to-step transition of walking, which is proposed to be an important determinant of the energy cost of walking. The double inverted pendulum model consists of two rigid legs and a point mass, representing the BCM, on top (Fig. 1). During the transition from one leg to the next the velocity of the BCM needs to be redirected from one circular trajectory to the next. This redirecting of BCM velocity is performed by a force generated under the leading limb directed towards the BCM, which goes at the expense of negative mechanical work performed on the BCM. It has been shown analytically [14\u201316] that the most efficient way to regenerate this work is to generate a push off force through ankle plantar flexion in the trailing leg at or just before heel strike of the leading leg (Fig. 1b). Alternatively, this positive work can be generated around the hip, substantially prior to heel strike. However, as shown in Fig. 1c this strategy is more costly, since it increases impact velocity and hence the negative work at heel strike [14\u201316]. The double inverted pendulum model predicts a potential source for the increase in the energy cost of amputee walking. Since lower limb prostheses lack the ability to actively plantar flex the ankle and generate sufficient power during the push off of walking, amputees are forced to use a more costly hip strategy to generate positive work. In this study we will test the hypothesis that walking with a lower limb prosthesis increases the mechanical work required for the step-to-step transition and that this increase is correlated with the increase in metabolic energy consumption during walking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002365_j.ast.2020.105745-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002365_j.ast.2020.105745-Figure1-1.png",
        "caption": "Fig. 1. Configuration of the studied quadrotor helicopter.",
        "texts": [
            " A brief description of the quadrotor helicopter model is presented in Section 2. Section 3 addresses the detailed design procedures of the proposed active FTC scheme. The experimental results are followed in Sec- tion 4 to demonstrate the effectiveness of the proposed control strategy. Finally, general conclusions and future works of this paper are summarized in Section 5. The quadrotor helicopter studied in this paper is produced by Quanser Inc., which is very well modeled with four motors in a plus configuration as shown in Fig. 1. In this configuration, each two opposite motors contribute to the motion along xe- and ye-axis, respectively. In order to obtain an accurate nonlinear model of the quadrotor helicopter, the gyroscopic effects produced by propeller rotations, the translational motion induced drag forces, and the rotational motion induced torques are all taken into account. The detailed nonlinear dynamics of the quadrotor helicopter can be formulated as follows: \u03c6\u0308 = (I yy \u2212 Izz)\u03b8\u0307 \u03c8\u0307 Ixx + Ku Ld(u3 \u2212 u4) Ixx \u2212 K1Ld\u03c6\u0307 Ixx \u03b8\u0308 = (Izz \u2212 Ixx)\u03c6\u0307\u03c8\u0307 I yy + Ku Ld(u1 \u2212 u2) I yy \u2212 K2Ld \u03b8\u0307 I yy \u03c8\u0308 = (Ixx \u2212 I yy)\u03c6\u0307\u03b8\u0307 Izz + K y(u1 + u2 \u2212 u3 \u2212 u4) Izz \u2212 K3\u03c8\u0307 Izz "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000403_j.actamat.2011.03.033-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000403_j.actamat.2011.03.033-Figure13-1.png",
        "caption": "Fig. 13. EBM scan geometry ideally forming precipitate\u2013dislocation architectures in fabricated Cu components (Fig. 5). Preheat scans are marked q(x) and q(y), while the corresponding melt scans are denoted m(x) and m(y).",
        "texts": [
            " 7\u201312, appears to be the result of either reprecipitation in the preheat and melt scans or the rearrangement of the precipitates during the melt scan, or both. The spatial precipitate\u2013dislocation arrays observed in the horizontal plane and illustrated in Figs. 7\u201312 appear to be related to, and controlled by, the preheat and melt scan parameters, especially the change in direction (x, y). This scan geometry creates thermokinetic zones whose spatial features are particularly dependent on the EBM-scan dimensions or spacing. Fig. 13 illustrates these features schematically in creating the microstructural architectures. As these electron beam parameters are altered, the regularity of the architectures can vary as well. Similar features have been discussed for the SLM fabrication of Ti\u20136Al\u20134V components by Thijs et al. [3], who describe the parameter variations, etc. in the context of beam-scanning strategies, while similar precipitate architectures have also been described for an Ni-base alloy fabricated by EMB [2]. On examining the rectangular EBM-fabricated test blocks, irregular architectures can be seen to occur (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure2-1.png",
        "caption": "Fig. 2. Chain CVT drive: (a) basic configuration; (b) chain structure [16,72].",
        "texts": [
            " The basic configuration of a CVT comprises two variable diameter pulleys kept at a fixed distance apart and connected by a power-transmitting device like belt or chain. One of the sheaves on each pulley is movable. The belt/chain can undergo both radial and tangential motions depending on the torque loading conditions and the axial forces on the pulleys. This con- sequently causes continuous variations in the transmission ratio. The pulley on the engine side is called the driver pulley and the one on the final drive side is called the driven pulley. Fig. 1 [15] and Fig. 2 [16,72] depict the basic layout of a metal V-belt CVT and a chain CVT. In a metal V-belt CVT, torque is transmitted from the driver to the driven pulley by the pushing action of belt elements. Since there is friction between bands and belt elements, the bands, like flat rubber belts, also participate in torque transmission. Hence, there is a combined push\u2013pull action in the belt that enables torque transmission in a metal V-belt CVT system. On the other hand, in a chain CVT system, the plates and rocker pins, as depicted in Fig. 2b, transmit tractive power from the driver pulley to the driven pulley. Unlike a belt CVT, the contact forces between the chain and the pulleys are discretely distributed in a chain CVT drive. This leads to impacts as the chain links enter and leave the pulley groove. Hence, excitation mechanisms exist, which are strongly connected to the polygonal action of chain links. This causes vibrations in the entire chain CVT system, which further affects its dynamic performance. Both belt and chain CVT systems fall into the category of friction-limited drives as their dynamic performance and torque capacity rely significantly on the friction characteristic of the contact patch between the belt/chain and the pulley"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000126_05698197408981435-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000126_05698197408981435-Figure12-1.png",
        "caption": "Fig. 12-Half films in EHD circular contact",
        "texts": [
            " 11 shows no rebounding at Tt/2qal < 28, which implies for the high viscosity oil (B) in the present tests the rebounding is zero a t 21 > 12 in/sec and for the low viscosity oil, (A) thel'e is no rebound a t -56 in/sec. For a value of al = 0.005 in and al/lzm = 2.5, one calculates using the viscosity and surface tension values given in Table 1, a delay time corresponding to Tt/2qal = 28 of 0.08 sec for the high viscosity oil (B) and 0.003 sec for the low viscosity oil (A). DETERMINATION OF EHD FILM THICKNESS AS A FUNCTION OF HALF-FILM HEIGHT The finite upstream oil layers clinging to the rolling bodies cause a finite flow rate upstream of the inlet as shown in Fig. 12. The film thickness a t the meniscus line can be greater than the combined height of the upstream half-films, since a volume of the fluid a t the junction of the two half-films can be stagnant in spite of the fact that the fluid adjacent to the surfaces is moving rapidly toward the Hertzian region (15, 16). A hydrodynamic analysis of elliptical point contact having two principal radii of curvature R, and R, (parallel and transverse to the rolling direction, respectively) has been conducted by considering finite thicknesses of half films (hal and ha)) far upstream from the inlet and setting the flow rate in the center plane a t the meniscus line equal to the incoming flow rate q, a t the contact centerline. Referring to Fig. 12 showing the central plane of an elliptical contact, the following assumptions are made, 1. p = 0 a t x = r*, i.e., pressure starts to rise a t the meniscus line. 2. The flow rate a t y = 0 and x = r' is q, = ulhml + u2hm2. 3. The pressure distribution in a starved point contact is a truncated Kapitza distribution (11) of the \"reduced\" pressure @). The actual pressure taking into account an exponential pressure-viscosity law is equal to a- ' loge(l - a$). 4. Surface deformation is negligible. a-I",
            " Chiu on his work. I t is extremely elegant and it is most pleasing to see good experimental work allied to excellent theory. I naturally am pleased to see the optical method used to such effect and also to see the original work on starvation we described in 1971 applied so effectively. One question I would like to pose, does the air pressure in the inlet zone contribute to increased starvation? Air has a small but definite viscosity and will be dragged into the inlet gap. When the meniscus forms a t r* of his Fig. 12 the air gap will be very smallwithout surface tension it would be vanishingly smallhence the hydrodynamic and \"ram\" pressures of the air could be large and would tend to displace the oil adhering to the surfaces. I have not done any calculations, and do not know if it would correct any second order deviations between his theory and experiment. Perhaps the author could comment. D ow nl oa de d by [ U ni ve rs ity o f Il lin oi s at U rb an a- C ha m pa ig n] a t 1 3: 14 1 3 M ar ch 2 01 5 An Analysis and Prediction of Lubricant Film Starvation in Rolling Contact Systems 33 DISCUSSION D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000680_mbio.00551-13-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000680_mbio.00551-13-Figure1-1.png",
        "caption": "FIG 1 (A) A schematic of the E. coli flagellar motor. Torque is generated by ion flow through the membrane bound stator units, causing rotation of the rotor, hook and flagellar filament. (B) A schematic of the apparatus used for simultaneous speed/fluorescence measurements. Cells were immobilised on glass surfaces, and beads attached to exposed flagellar filament stubs. Bead movement was measured through the quadrant photodiode signal from a 1064 nm laser (red), while epifluorescence measurements were taken of the motor spot (excitation in blue, emission in green). In experiments with magnetic beads, motors could be stalled by addition of a linear magnetic field with field lines parallel to the coverslip (see text for details).",
        "texts": [
            "0 Unported license, which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original author and source are credited. Address correspondence to Judith P. Armitage, judith.armitage@bioch.ox.ac.uk. Many bacterial species swim, driven by transmembrane molecular motors rotating extracellular flagellar filaments. In some species, for example, Salmonella, motor rotation is required both for swimming through liquid media (1) and for swarming across solid surfaces (2). Flagellar motors contain a series of rotating protein rings (3). A schematic of the Escherichia coli flagellar motor can be seen in Fig. 1a. The C-ring, also called the switch complex, is made of 26 or more copies of FliG, 34 to 35 of FliM, and ~140 of FliN. The C-ring connects via the transmembrane rod to the extracellular flagellar filament and interacts with cell wallanchored transmembrane stator complexes formed by the proteins MotA and MotB. E. coli motors are bidirectional: motors can switch between counterclockwise (CCW) and clockwise (CW) rotation in response to chemosensory signals, with switching transmitted through C-ring proteins FliM and FliN on the cytoplasmic side of FliG",
            " We investigated the relationship between motor speed and the number of stators bound to a functioning flagellar motor. Previous \u201cresurrection\u201d studies have shown that stator binding results in an increase in speed, but those experiments do not rule out the possibility of a semistable \u201cbound but inactive\u201d state for stators (10). We measured the fluorescence intensity of motor spots in functioning motors while simultaneously measuring motor speed by monitoring the rotation of attached polystyrene beads. A sche- matic of the experiment can be seen in Fig. 1b. Figure 2a shows the mean intensity of GFP-MotB spots localized to functioning motors, each driving a 1- m-diameter bead attached to the filament stub (high load), versus the simultaneously measured motor speed. Spot intensity was measured by epifluorescence microscopy using constant illumination intensity and exposure time, allowing direct comparison of relative motor spot intensities, and was normalized by dividing by the intensity of the fastest motor measured. The intensity of each motor spot is proportional to the number of GFP-tagged MotB molecules in the motor (4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000238_iros.2005.1545143-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000238_iros.2005.1545143-Figure8-1.png",
        "caption": "Fig. 8 Optimized parameters",
        "texts": [
            " Knowing these points, halfperimeter of ellipse can be approximated [23] by: d zc-T1/2(A2+B2) (18) where A is the length of big half-axis of ellipse and B is length of little half-axis. As proposed in [22], equation of ellipse can by easily approximated using projection of curvilinear abscissa of a circle on the ellipse. Applying a time law s(t), absolute positions can be expressed: X(t) =A.cos(;T.s(t)/d).e \u00b1+B.cos(;T.s(t)/d).e, + C (19) where C is the center of ellipse. This simple solution has been kept in the optimization algorithm described at \u00a7 III.A. C. Optimization results The described method has been applied to Par4 robot. Optimized parameters (see Fig. 8) were length of arms L, length of sub-arms 1, position of actuators R (corresponding to a radius) and the altitude of workspace center Zo. In order to be in accordance with industrial requirements, diameter of workspace D has been fixed to 1 meter. Characteristics of Adept Motion are: length of 305 altitude of 25 mm, and round trip time of 0.28 s. For each L, a set of \"optimum parameters\" has obtained (see Fig. 9). 51I mm, been Optimal parameters chosen are a compromise among the sets of parameters described on Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003263_asjc.1946-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003263_asjc.1946-Figure2-1.png",
        "caption": "Fig. 2. Three different transformation matrix.",
        "texts": [
            " And the \ud835\udf4d is controlled directly by U4. Remark 3. The model analysis of the quadrotor UAV is based on Newton-Euler\u2019s theorem. It is known from the structure of the quadrotor UAV that the XY plane is coupled with\ud835\udf53 and \ud835\udf3d . Therefore, the design of the controller U2,U3 needs to calculate the \ud835\udf53,\ud835\udf3d. Remark 4. The transformation matrix describes the transformation between the earth coordinate system and the body coordinate system. The basic transformation and its matrix, which are around the X ,Y and Z axis respectively, are shown in Fig. 2. Rx = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 cos\ud835\udf53 sin\ud835\udf53 0 \u2212sin\ud835\udf53 cos\ud835\udf53 \u23a4\u23a5\u23a5\u23a6 ,Ry = \u23a1\u23a2\u23a2\u23a3 cos\ud835\udf3d 0 \u2212sin\ud835\udf3d 0 1 0 sin\ud835\udf3d 0 cos\ud835\udf3d \u23a4\u23a5\u23a5\u23a6 , Rz = \u23a1\u23a2\u23a2\u23a3 cos\ud835\udf4d sin\ud835\udf4d 0 \u2212sin\ud835\udf4d cos\ud835\udf4d 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (16) This study assumes that the body coordinate system rotates around the X, Y, Z axes on the basis of the earth coordinate system. The corresponding rotation equation is Fb = RB EFe = RxRyRzFe, so Equation (3) can be obtained. Then, the following Lemma 1 is applied to design the FO SMC. Lemma 1 [23,24]. Considering 0Dq t f (t) = 1 \u0393(1\u2212q) d dt \u222b t 0 f (\u0393) (t\u2212\ud835\udf0f)q d\ud835\udf0f with the fractional order q satisfying 0 \u2264 q < 1 and the sign function, we get the following equation 0Dq t sgn(s(t)) { > 0, if s(t) > 0, t > 0, < 0, if s(t) > 0, t > 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002008_s40192-019-00130-x-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002008_s40192-019-00130-x-Figure11-1.png",
        "caption": "Fig. 11 Spatial distribution of a thermal gradient, b solidification rate, c predicted PDAS, and d experimentally measured PDAS at the crosssection for case B (195 W, 800 mm/s). Experimental data is released by the AM-Bench Committee [54]",
        "texts": [
            " The combination of the magnitude of thermal gradient G and solidification rate R around the liquidsolid interface plays an important role in determining the solidification modes and grain morphology [59] as illustrated in Fig. 10. Rather than resolving the detailed grain structure, the PDAS as defined in Fig. 10 is predicted using G and R from the thermal\u2013fluid\u2013vaporization model and compared with experimental data. In order to perform the comparison, G and R are first projected onto a cross section of the track (as seen in Fig. 11a and b, respectively, for case B). Then, according to Eq. 10, a contour of the PDAS distribution over the cross section is plotted in Fig. 11c showing a nonuniform PDAS field corresponding to the distribution of G and R. It is found that the predicted PDAS has a maximum of 0.79 \u03bcm in this case located at the center of the cross-section and a minimum of 0.23 \u03bcm near the periphery of the cross-section. This trend is validated by a sample of eight experimental measurements as shown in Fig. 11d. The experimental PDAS decreases from the center to the periphery of the cross section of the sample. The maximum and minimum values of PDAS are presented in Fig. 12 for all three cases, demonstrating a good agreement with experimental results. Another conclusion we can draw from the comparison in Fig. 12 is that the PDAS decreases with the increase of scan speed due to higher solidification rates leading to finer dendrites. To estimate the microsegregation between dendrite arms, the non-equilibrium model [26] described in \u201cSolidification Models\u201d is used to predict the concentration profiles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure38-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000904_j.mechmachtheory.2006.06.002-Figure38-1.png",
        "caption": "Fig. 38. Teeth engagement at Position 3.",
        "texts": [
            " So it can be calculated through dividing the maximum CRS of the pair of gears with lead crowning by the maximum CRS of the gears without ME, AE and TM. Relationship between the influence factor and Q is also shown in Fig. 37. It is found that the influence factor of lead crowning is over 1.4 when Q = 40 lm. Fig. 37 can also be used as references when ISO 6336/3 is used to calculate the maximum CRS of a pair of spur gears with lead crowning. LTCA and tooth load calculations are performed separately at all the 12 engagement positions as shown in Table 2 when MEmax = 0, 10, 20, 30 and 40 lm. Then LSR are calculated separately. Fig. 38 is a section view of 3D, FEM model of the pair of gears at the engagement position 3. Since the Position 3 is a double pair tooth-contact position as shown in Table 2, two pairs of teeth share the total load P of the gears as shown in Fig. 38. Figs. 39 and 40 are contour lines of contact stress distributions on tooth 1 and tooth 2 separately when MEmax = 0. Figs. 41 and 42 are contour lines of contact stress distributions on tooth 1 and tooth 2 separately when MEmax = 10 lm and Figs. 43 and 44 are contour lines of contact stress distributions on tooth 1 and tooth 2 separately when MEmax = 30 lm. By comparing Figs. 41 and 42 with Figs. 39 and 40, also Figs. 43 and 44 with Figs. 39 and 40, it is found that ME has great effect on tooth-contact pattern"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000156_r-168-Figure6.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000156_r-168-Figure6.18-1.png",
        "caption": "Figure 6.18.1. Free-body diagram for a car driving uphill at constant speed, no aerodynamic forces.",
        "texts": [
            " On ice, taking the maximum lateral force coefficient \u00b5Y as 0.1, with 5\u00b0 camber the speed is increased 38% for favorable camber, and reduced 65% for adverse camber. At \u00b5Y = 1, the changes are +9% and 9%. Front-to-rear differences of maximum lateral force friction sensitivity p would imply some final handling variation on banking, but this is normally unimportant because the required side force coefficients are generally small. However, there may still be significant changes of primary handling. 6.18 Hills On longitudinal slopes, uphill at an angle of \u03b8 (Figure 6.18.1), at steady speed, there is a front-to-rear load transfer. The axle reactions are When driving uphill, the load transfer to the rear leads to increased primary understeer and reduced attitude coefficient, but these are not large effects; for example, at 1 in 5 (12\u00b0) uphill \u0394k\u03b2 is 0.25 deg/g and \u0394k is 0.5 deg/g, and the opposite (negative values) downhill. The effect on final handling is more important: Steady-State Handling 411 412 Tires, Suspension and Handling For a vehicle which is initially neutral on level ground, for small \u03b8, For a b L/2 This is about 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure5.19-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure5.19-1.png",
        "caption": "Fig. 5.19 Examples of undesirable kinematics in a turn",
        "texts": [
            "27) \u03b2\u03071 u \u03c11 \u2212 r u (5.28) \u03b2\u03072 u \u03c12 \u2212 r u (5.29) where \u03c1i are the curvatures, that is the inverse of the radii of curvature. The kinematics of a vehicle exiting properly a turn is shown in Fig. 5.18. We see that many things go the other way around with respect to entering. In both cases, the knowledge of the inflection circle immediately makes clear the relationship between the position of the velocity center C and the centers of curvature E1 and E2. But things may go wrong. Bad kinematic behaviors are shown in Fig. 5.19. We see that the time derivatives of \u03b21 and \u03b22 are not as they should be. Indeed, point C is travelling also longitudinally. Again, the positions and orientations of the inflection circle immediately conveys the information about the unwanted kinematics. But, let us go back to good turning. The evolute of a curve is the locus of all its centers of curvature. The evolutes of the trajectories of points A1 and A2, that is the midpoints of each axle, are shown in the lower part of Figs. 5.20 and 5.21"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000065_j.bios.2004.09.005-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000065_j.bios.2004.09.005-Figure1-1.png",
        "caption": "Fig. 1. The structure of the cholesterol biosensor.",
        "texts": [
            " The similarity in length scales between nanotubes and redox enzymes suggests interactions that may be favorable for biosensor electrode applications. However, the detection mechanism of carbon nanotubes is not fully understood. A systematic study has not been reported so far. In this paper, we used carbon nanotubes to modify carbon paste electrode, which can promote electron transfer and enhance the response current. All reagents, except multi-walled carbon nanotubes, were commercially available and of analytical-reagent grade c c d w m t 2 n ( c a sensor is shown in Fig. 1. The sensor consists of two carbon paste electrodes. One electrode was used as working electrode while the other was used as reference electrode. The function of the silver leads was to improve electric conductivity of the electrodes. The reaction area, where the carbon paste film was modified by carbon nanotubes and immobilized enzymes, was defined by the insulating film coated on the carbon paste film. There were 20 sensor bases on each plate. Once the sensor array was ready, sensor strips were cut out of the array to be measured"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003409_978-3-319-13776-6-Figure27.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003409_978-3-319-13776-6-Figure27.4-1.png",
        "caption": "Fig. 27.4 EDAG light car",
        "texts": [
            " The defined functions are used as input for the logical structure that represents a technological implementation of the functional structure. The next view on the product to be developed consists of the geometry representation, that is, the physical product form. The latter can be used, for instance, for performing a FEA to predict the impact of the battery (e.g., thermal influence) on surrounding parts. Input for the analysis of the process chain of the battery module has been the EDAG Light Car (Fig. 27.4), which is a vehicle concept for mobility of the near future. Some of the particularities of the EDAG Light Car are the light weight for energy efficiency, the light which is used as a central element to display functions and communication as well as the architecture in compliance with electric vehicle requirements. Furthermore, scalability has been an important requirement; therefore, the platform of the EDAG Light Car can be varied to build a car family. The integrated electric drive enables a drive-line variation for urban traffic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure49-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure49-1.png",
        "caption": "Fig. 49 a Decomposed volumes; b offset surfaces; c trimmed surfaces; d five-axis toolpaths; e robotic FDM system; f parts printed by the proposed method; g part printed by the proposed cylinder surface slicing approach [69]",
        "texts": [
            " In the decomposition-based method, the threedimensional model is decomposed into different parts, based on the sub-components. In the transformation-based cylindrical face cutting method, the latter surface is extracted from a cylindrical surface-based model, which is then converted into a plane-based model, and then a planar slice strategy is implemented on the transformation model. The planar tool path is then reversed to 3D space to generate a five-axis tool path; the research results are shown in Fig. 49. Because the WAAM forming metal parts react violently, and it is not suitable to use the support system, the surface slicing algorithm for WAAM has rarely been tried. Compared with the surface slicing algorithm, the algorithm processing of multi-directional planar slicing is simpler, and it is more suitable for the processing of complex parts than the fixeddirection slicing algorithm. Therefore, the application of multi-directional slice algorithm in WAAM has been studied a lot. Ding studied multi-directional slicing algorithms: for complex model structures, contour boundaries were searched for and then the model was decomposed into simple 3D models [70]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002203_j.ymssp.2013.06.040-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002203_j.ymssp.2013.06.040-Figure7-1.png",
        "caption": "Fig. 7. Illustration of different load distribution cases. (a) Uniform load distribution, (b) uniform load distribution represented analytically, (c) non-uniform or one-sided load distribution and (d) non-uniform load distribution represented analytically.",
        "texts": [
            " Crack extended through the whole tooth width with a parabolic crack depth distribution. This scenario is presented in [4]. The propagation case data of this scenario are shown in Table 5. Fig. 6a explains the propagation cases of this scenario, and the time-varying mesh stiffnesses for all the studied cases are shown in Fig. 6b. 3. Crack propagating in both the depth and the length directions together. This scenario is presented in [30]. Practical experience shows that the load distribution along the tooth width is usually non-uniform [36,37], see Fig. 7, with a number of factors causing the deviation from the ideal uniform load distribution, e.g. manufacturing errors, gear shaft misalignment, and deformations in the bearing and/or housing. Experimental tests using a one-sided load distribution have shown that the fatigue crack propagates in two directions: the crack length and the crack le 3 gle tooth mesh stiffness comparison. rack case FEM result from [3] Result from the programme used in this research study Difference (%) ealthy case 1.58 108 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001467_s10514-012-9294-z-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001467_s10514-012-9294-z-Figure5-1.png",
        "caption": "Fig. 5 By expressing GRF applied to each foot with respect to the local frame of the foot located at the ankle, we can factor out the moments \u03c4 r , \u03c4 l applied to the ankle by the foot GRFs f r and f l . rr and r l are the positions of the ankles",
        "texts": [
            " If f d and pd computed above are valid, then we directly use these values. Otherwise, as mentioned previously, we give higher priority to linear momentum. If f d is outside the friction cone, we project it onto the friction cone to prevent foot slipping. Determining foot GRFs and foot CoPs for double support is more involved. Let us first rewrite (1) and (2) for the double support case. Following Sano and Furusho (1990), we will express the GRF at each foot in terms of the forces and torques applied to the corresponding ankle (Fig. 5). The benefit of this representation is that we can explicitly express the torques applied to the ankles. k\u0307 = k\u0307f + k\u0307\u03c4 (15) k\u0307f = (rr \u2212 rG) \u00d7 f r + (r l \u2212 rG) \u00d7 f l (16) k\u0307\u03c4 = \u03c4 r + \u03c4 l (17) l\u0307 = mg + f r + f l (18) In (15), we have divided k\u0307 into two parts, k\u0307f , due to the ankle force, and k\u0307\u03c4 , due to ankle torque. This division enables us to take ankle torques into account in determining foot GRFs. f r and f l are the GRFs at the right and left foot, respectively, and rr , r l are the positions of the body frames of the foot, located at the respective ankle joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.97-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.97-1.png",
        "caption": "Fig. 17.97a\u2013c Examples of protection techniques: (a) grounding without a special grounding conductor; (b) protective grounding; (c) current-operated earth-leakage circuit breaker, N \u2013 neutral conductor, PE \u2013 protective grounding conductor (grounded), PEN \u2013 zero conductor",
        "texts": [
            "\u2022 In a protective conductor system all respective devices of the electric system are connected to each other as well as to conducting parts of the building, the piping, and grounding electrode.\u2022 Voltage-operated earth-leakage protection is able to disconnect all phase conductors within 0.2 s in the case of high contact voltages.\u2022 The current-operated earth-leakage circuit breaker is able to disconnect within 0.2 s in the case of a fault current (e.g., 60 mA), thus there will not be any contact voltage at the devices. The operating currents, which usually sum up to zero, pass through a summation current transformer whose secondary winding is guided to an overcurrent relay. Figure 17.97 shows examples of protection techniques. Storage Power Stations Electric energy cannot be stored in its original form. Nevertheless, in electric energy systems the possibility of storing exists by using reservoir power stations. During periods of weak load water is pumped upstream into a reservoir and during peak load periods the potential Part C 1 7 .6 energy of this water is used to produce electrical energy again. For this type of storage system, synchronous machines are used. The synchronous machine is mechanically connected to a water turbine and a pump"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.12-1.png",
        "caption": "FIGURE 5.12. An orthogonal R`R(90) link.",
        "texts": [
            " Therefore, the transformation matrix i\u22121Ti for a link with \u03b1i = 90deg and R\u22a5R or R\u22a5P joints, known as R\u22a5R(90) or R\u22a5P(90), is i\u22121Ti = \u23a1\u23a2\u23a2\u23a3 cos \u03b8i 0 sin \u03b8i ai cos \u03b8i sin \u03b8i 0 \u2212 cos \u03b8i ai sin \u03b8i 0 1 0 di 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.34) while for a link with \u03b1i = \u221290 deg and R\u22a5R or R\u22a5P joints, known as R\u22a5R(\u221290) or R\u22a5P(\u221290), is i\u22121Ti = \u23a1\u23a2\u23a2\u23a3 cos \u03b8i 0 \u2212 sin \u03b8i ai cos \u03b8i sin \u03b8i 0 cos \u03b8i ai sin \u03b8i 0 \u22121 0 di 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (5.35) Example 144 Link with R`R or R`P joints. When the proximal joint of link (i) is revolute and the distal joint is either revolute or prismatic, and the joint axes at two ends are intersecting orthogonal, as shown in Figure 5.12, then \u03b1i = 90deg (or \u03b1i = \u221290 deg), ai = 0, di = const is the distance between the coordinates origin on zi, and \u03b8i is the only variable parameter. Note that it is possible to have or assume di = 0. The xi and xi\u22121 of an R`R link at rest position are coincident (when di = 0) or parallel (when di 6= 0). Therefore, the transformation matrix i\u22121Ti for a link with \u03b1i = 90deg and R`R or R`P joints, known as R`R(90) or R`P(90), is i\u22121Ti = \u23a1\u23a2\u23a2\u23a3 cos \u03b8i 0 sin \u03b8i 0 sin \u03b8i 0 \u2212 cos \u03b8i 0 0 1 0 di 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure3.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure3.18-1.png",
        "caption": "Fig. 3.18 Force distribution and no-roll center Qi for a dependent suspension with Panhard rod",
        "texts": [
            " Most of the analysis developed for independent suspensions is applicable to dependent suspensions as well. For instance, the suspension internal coordinates listed at p. 69 are still meaningful (except track variation, which is obviously zero in the present case). Vertical stiffness and roll stiffness are also well defined. The only thing that needs to be addressed is the determination of the no-roll center Qi . Following the method explained in Sect. 3.8.8, we apply a lateral force Yi , like in Fig. 3.18 (top). This force can be decomposed into a force Hi , which is counteracted by the Panhard rod, and a vertical force Vi , which must be counteracted 3.9 Dependent Suspensions 83 Fig. 3.16 Planar scheme of a dependent suspension with Panhard rod Fig. 3.17 Dependent suspension with Panhard rod [3] by the springs, and whose line of action is located at a distance si from the vehicle centerline (Fig. 3.18 (bottom)). It is easy to obtain Hi = Yi cos\u03c7i Vi = Yi tan\u03c7i si = h \u2212 qi tan\u03c7i and hence Lb i = Visi = Yi(h \u2212 qi) (3.119) where \u03c7i is the inclination of the Panhard rod. The lower \u03c7i , the better. The moment Lb i = Visi = Yi(h \u2212 qi) is the sole responsible of the vehicle body roll, as shown in Fig. 3.19 (top), and the force Vi is the only responsible for the body vertical displacement, as shown in Fig. 3.19 (bottom). To have zero suspension roll we need zero moment, and this is possible if and only if h = qi . Therefore, the no-roll center is point Qi in Fig. 3.18. In any case, we have a small body vertical displacement, either upward or downward, depending if we are turning left or right. The vertical displacement would be zero if and only if \u03c7i = 0, which is clearly impossible in practice. Therefore, 84 3 Vehicle Model for Handling and Performance the Panhard rod is a simple linkage, with the disadvantage of a certain degree of asymmetry. Of course, dependent suspensions do not exhibit suspension jacking, nor camber variations. In a vehicle like an automobile or a motorcycle, it is useful to distinguish between sprung mass and unsprung mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure3.44-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure3.44-1.png",
        "caption": "Fig. 3.44 The tail rotor in quartering flight",
        "texts": [
            "73, 3.74), aimed at providing data for interactional modelling developments. In Ref. 3.73, from an analysis of Lynx flight test data with an instrumented tail rotor, Ellin identified several regions of the flight envelope where the interactional aerodynamics could be categorised. Particular attention was paid to the so-called quartering-flight problem, where the tail rotor control requirements for trim can be considerably different from calculations based on an essentially isolated tail rotor. Figure 3.44 shows a plan view of the helicopter in quartering flight \u2013 hovering with a wind from about 45\u2218 to starboard. There exists a fairly narrow range of wind directions when the tail rotor is exposed to the powerful effect of the advancing blade tip vortices as they are swept downstream. A similar situation will arise in quartering flight from the left, although the tail rotor control margins are considerably greater for this lower (tail rotor) power condition. From a detailed study of tail rotor pressure data, Ellin identified the passage of individual main rotor tip vortices through the tail rotor disc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000599_tro.2004.842341-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000599_tro.2004.842341-Figure10-1.png",
        "caption": "Fig. 10. Heptapod in its initial posture.",
        "texts": [
            " The problem (21) is solved for the 23 independent coefficient with a standard method for constrained optimization [4], [28]. The applied algorithm converges rapidly but the necessary computation time makes a real time solution impossible. The admissible sign vector yields smaller control torques as shown in Figs. 6 and 7. The second task consists in following the surface of a cylindrical object with the EE orthogonally aligned to the surface (Fig. 8). For this task the required preload of nm can only be achieved with . Results are shown in Fig. 9. The heptapod (a hexapod with one additional strut) in Fig. 10 serves as second example. It is closely related to the Falcon [9], a PM equipped with seven cable drives. The seven prismatic joints are actuated. For this spatial RFA PM the task was to draw a circle on a spherical surface with orthogonally aligned EE and without rotation about the longitudinal axis. The ask must be accomplishes in 10 s. There are possibilities, but the required preload of 100 N can only be achieved with , or . Fig. 11 shows the pointwise solution for the controls according to "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001530_978-3-642-81857-8-Figure3.82-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001530_978-3-642-81857-8-Figure3.82-1.png",
        "caption": "Fig. 3.82. Manipulator motion during the transfer of the working object",
        "texts": [
            "79 presents the compensating moments of degrees of freedom of the gripper Pi(t), (i = 4,5,6) which develop from the force feedback and which realize the motion of the gripper, annulling the rotational moment of the object and thus ensuring the perpendicularity of the object. These moments are realized by D.C. electro-motors of degrees of freedo~of the gripper. Fig. 3.80 presents the components of the force measured by transducers on the gripper, and Fig. 3.81 shows the components of rotational mo- 296 ment of the working object about the axes of the rectangular system, the measurement of which is a basis for on-line calculation of compen sating moments of the gripper. Finally, Fig. 3.82 shows the spatial motion of the manipulator in three-quarter projection. the axes of the Carterian coordinate system during the transfer 'of the wor king object 6101 [NmJ Fig. 3.81. Components of the ro tational moment of the working object The manipulator tip moves along a straight line from the point A to the point B, while the gripper maintains an approximately vertical po sition (with the allowable limits deviation). The results of this si mulation show that the simple control structure introduced may provide a satisfactory system performance and may ensure the performance of the control task imposed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000878_j.jmapro.2014.04.001-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000878_j.jmapro.2014.04.001-Figure4-1.png",
        "caption": "Fig. 4. Temperature distribution at power 150 (W), laser speed 2.4 (m/min), and spot diameter (400 m).",
        "texts": [
            " In addition, Scanning Electron Microscope (SEM) was used to nalyze the cross sectional morphology, zone of powder consoli- Please cite this article in press as: Antony K, et al. Numerical and exp metal powders. J Manuf Process (2014), http://dx.doi.org/10.1016/j.jm ation, solidified melt droplet, balling effect, smoothness, wetting ngle, track width and re-melted depth zone. The appearance of can tracks was categorized into 5 models which were un-melted, alling, smooth, irregular, and over-melt. 6L powder on AISI 316L substrate. 4. Results and discussions In this section, three dimensional results of temperature profiles are discussed elaborately. Fig. 4 indicates the range of heat transfer after laser irradiation. All the external areas have a natural boundary condition which will help the cooling process after melting, it is noticed clearly that the temperature distribution occurring in the powder bed after a single pass of Nd-YAG laser beam. In addition, the figure indicates the range of heat transfer happens after laser irradiation at the time spot of 1 s. Fig. 4 represents the temperature distribution of laser heat flux when keeping the laser power P = 150 W, laser speed V = 2.4 m/min, and spot diameter d = 400 m. The maximum average temperature attained by the powder bed is 3500 K in the x direction. From the numerical results, it is observed that the temperature involved in the powder bed is optimum to melt the powder to form a smooth continuous track which is also noted in Figs. 10(d) and 12(a). The numerical model accounts the phase change by considering different heat capacities in the solid and liquid regions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure10.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure10.4-1.png",
        "caption": "Fig. 10.4 Mobile ACRF test system for HV and EHV cable systems",
        "texts": [
            " There should be few assembling work on site until the test system is ready for tests. Smaller test systems\u2014ready for the connection of the test object via a shielded cable\u2014can be arranged inside a van, trailer or container 10.1 General Requirements to HV Test Systems Used on Site 421 completely (Fig. 10.3a; see Sect. 10.2.1.1). The HV components (exciter transformer, reactor, voltage divider) of the shown ACRF test system are metalenclosed to fulfil the safety requirements. Heavy and large systems\u2014as, e.g. for testing HV and UHV cable systems\u2014are arranged on a trailer (Fig. 10.4). The total weight of HV test system, trailer and truck must not exceed the permitted value for roads (e.g. in Europe 42 t) to avoid special transportation. A second possibility is the use of components which can easily assembled on site. Figure 10.3b shows an ACRF test system with three modular reactors and a separate voltage divider. Figure 10.3c shows a test circuit for OLI voltages (see Sect. 10.2.1.3), consisting of a DC charging unit, three generator modules for 300 kV each, the HV inductance connecting the generator to the last component and the voltage divider/basic load capacitor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003038_tro.2014.2344450-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003038_tro.2014.2344450-Figure11-1.png",
        "caption": "Fig. 11. 5\u20135\u20135 RPR-equivalent PMs with idle pairs. (a) 2-uRPRijU / ijUvRRR. (b) 2-uRPRijU / ijUvPRR",
        "texts": [
            " In the uRPRijU limb, the unit vectors i, j,u are linearly independent, and generally, i and j can belong to the vector plane orthogonal to u without being v and w. For the same reason, in the ijUvRRR limb, the unit vectors i, j,v are linearly independent, and generally i and j can belong to the vector plane orthogonal to v without being u and w. However, for example, one can set i = v and j = w for a uRPRijU limb and i = w and j = u or a ijUvRRR or a ijUvRPR limb. A 2- uRPRvwU/wuUvRRR and a 2-uRPRvwU/wuUvRPR PM is, thus, obtained as shown in Fig. 11. We can readily verify that the wR pairs in vwU and wuU are idle, and the 2-uRPRvwU/wuUvRRR works like an overconstrained 2-uRPRvR/uRvRRR PM. Table VII enumerates 49 RPR-equivalent PMs in this category Fig. 12 shows four RPR-equivalent PMs belonging to the first family in 5\u20135\u20135 category. For the readers\u2019 sake, Fig. 13 shows four RPR-equivalent PMs belonging to the second family in the 5\u20135\u20135 category. B. {L1} = {X(u)}{X(v)} and {L2} = {G(u)}{S(F )} With F (B,v) and {L3} = {S(D)}{G(v)} With D \u2208 axis(O, u) When {L1} = {X(u)}{X(v)} and {L2} = {G(u)}{S (F)}, the intersection of {L1} and {L2} is given by {L1} \u2229 {L2} = {X(u)}{X(v)} \u2229 {G(u)}{S (F) } = {G(u)}{R(B, v)}{T(u)} \u2229 {G(u)}{R(B,v)} \u00d7{R(F, i)}{R(F, j)} = {G(u)}{R(B,v)}({T(u)} \u2229 {R(F, i)}{R(F, j)}) = {G(u)}{R(B,v)}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000238_iros.2005.1545143-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000238_iros.2005.1545143-Figure2-1.png",
        "caption": "Fig. 2 Par4 prototype",
        "texts": [
            " Indeed, the second part of the paper presents the improvements of Par4 compared to 14 and H4. The third part exposes an optimization method dedicated to pick-and-place robots, applied to Par4. The last part presents experimental results showing that the prototype is able to reach accelerations up to 13 G. The particularity of Par4 compared to H4 and 14 is its articulated traveling plate. It is composed of four parts: two main parts (1,2) linked by two rods (3,4) thanks to revolute joints (see Fig. 2). The shape of this assembly is a planar parallelogram and the internal mobility of the traveling plate is a PI joint [12] (circular translation) which produces the rotational motion about the vertical axis of the global robot. The range of this rotation is \u00b1 T/4 . That's why, an amplification system has to be added in order to obtain a complete turn: \u00b1T . The amplification system can be made of gears or belt/pulleys. The chosen mechanism for the prototype is belt/pulleys with an amplification ratio p = 4 (see Fig. 2b). The overall architecture is similar to H4 or 14R as described in [9] and [11]. Arms and forearms, made of carbon fiber, are taken from ABB Flexpicker robot. Par4 is a Deltalike mechanism. The key difference with the Delta robot is the use of four kinematic chains instead of three. In addition, it uses the concept of articulated traveling plate in order to avoid the central telescopic leg. The key difference with H4 and 14 robots will be explained in the following. Remark about modelsfor kinematics solutions",
            " 51I mm, been Optimal parameters chosen are a compromise among the sets of parameters described on Fig. 9 : L = 0.825 m, l= 0.375 m, R = 0.275 m, Z0= -0.58 m It leads to the maximum articulated velocity: Qmax = 21.9 rad.s-1 This compromise has been chosen in order to obtain a correct maximum actuated joint velocity while geometrical constraints L, / and R have reasonable values. Using optimal parameters presented in \u00a7 III, and architecture developed with the aim of reaching very high speed in \u00a7 II, a prototype (see Fig. 2) has been built. All tests have been performed using Adept Motion (as described at III.B.3) with a length of 305 mm and an altitude of 25 mm. The control loop is P/PI applied on actuated variables. The first experimentations have been done with the following characteristics: maximal velocity (v) = 2.5 m.s'1, maximal acceleration (a) = 100 m.s-2. Obtained cycle time (round trip) is: 0.45 s. Records of this experimentation are presented at Fig. 10. The second experimentations have been made applying high speed and accelerations: v = 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003265_tpel.2019.2900559-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003265_tpel.2019.2900559-Figure1-1.png",
        "caption": "Fig. 1. Simulation results of magnetic saturation in different operating conditions. (a) id=0, iq=0. (b) id=-in, iq=0. (c) id=in, iq=0. (d) id=0, iq=in.",
        "texts": [
            " According to the definition equation of inductance, the inductance of manganic path can be represented as 2 2=    A L N N l (1) where N is the number of stator winding turns, \u03bb is the magnetic conductance, A and l represent the average sectional area and the length of manganic path respectively. The operating conditions of PMSMs include rated condition, overload condition with high level q-axis current iq and flux-weakening condition with minus d-axis current id. Different operating conditions result in different degree of magnetic saturation and cross-coupling, then affect the inductance. Fig. 1 shows the magnetic saturation effect of the test PMSM under different operating conditions by FEA, where in is the per unit value of current, Bl is the magnetic flux density whose degree can be indicated by the density of magnetic lines, l=1, 2\u00b7\u00b7\u00b75. As shown in Fig. 1(a)-(c), the increase of the d-axis current will aggravate the magnetic saturation. The d-axis magnetic flux density distribution satisfies B3>B1>B2, and then the d-axis inductance satisfies L2>L1>L3. In Fig. 1(a) and (d), the existence of iq causes the q-axis armature reaction, which aggravates and weakens the magnetic flux density in region 1 and in region 2, respectively. Considering the magnetic saturation, the overall magnetic flux density decrease, B4>B1>B5. In addition, the q-axis armature reaction influences inductances by redistributing the magnetic field of yokes, resulting in the cross-coupling and the mutual inductance between dq-axes. The simulation results of the test PMSM are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003202_0278364913495932-Figure10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003202_0278364913495932-Figure10-1.png",
        "caption": "Fig. 10. Kinematic chain made of two links connected with a rotational joint.",
        "texts": [
            " Two links connected with a rotational joint The method using only the motion data under the law of conservation of momentum shown in Section 6.2 was tested on two examples: a simple chain made of two links and the human body dynamics. In this section we show that the proposed identification method is still valid when the legged system is jumping or there are no force sensors. For practical use, the ground force measurement should be needed if accurate sensors are available. First, this section shows the identification results of a simple two-link system as shown in Figure 10. Two links are connected with a single rotational joint, which has no at UNIVERSITY OF WINDSOR on July 10, 2014ijr.sagepub.comDownloaded from at UNIVERSITY OF WINDSOR on July 10, 2014ijr.sagepub.comDownloaded from actuator and whose axis is simply supported by bearings. For identification, the links were thrown into the air several times. The motion in the air was recorded with the motion capture system mentioned in the previous section. The links were equipped with optical markers as shown in Figure 10, and the motion were totally recorded for about 20 seconds. From the measured position of markers, the generalized coordinates q0 of the base-link and the joint angle qc were computed. The derivatives q\u03070, q\u0307c, q\u03080, q\u0308c were also obtained numerically. Here Y all was also computed using those variables and the geometric parameters of the system at every sampling time. This system has two links and one rotational joint. Thus, the total number of base parameters \u03c6B of the system is 17; 10 of the parameters \u03c6B0 of L0, and 7 of the parameters \u03c6B1 of L1, where the notation L0 is defined as the base-link of the system, and L1 as the other side"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002224_j.ymssp.2018.02.028-Figure9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002224_j.ymssp.2018.02.028-Figure9-1.png",
        "caption": "Fig. 9. Test rig of single stage spur gears (Input gear with 70 teeth; output gear with 35 teeth).",
        "texts": [
            " As was found in the original signals, the difference is also identified in the two sets of IMFs, in which the first four IMFs C1\u2013C4 tend to show more distinct characteristics at the fault location that differentiates the spall and crack. Comparing the two side by side, greater signals are observed at the IMFs C2\u2013C4 for the spall due to the larger fault size. The IMF C1 however has similar magnitude for the spall and crack. From the observations, it may be noted that the IMF\u2019s can be used to distinguish the behaviors of the spalled and cracked RTE. Test rig is prepared to measure the TE for the fault diagnosis as shown in Fig. 9. The system consists of a 2.9 kW motor to drive the gear, a pair of SCM440 steel spur gears, and powder brake to apply counter torque. Rotary encoders with resolution 8192 ppr are attached to the input and output shafts to measure the angular displacement. The gears are made of module 4, pitch diameters 280 and 140 mm and number of teeth 70 and 35, in which the larger one is the input gear. The TE are mea- sured with the input speed of 30 rpm and the output torque of 450 Nm. Two gears denoted as A and B are prepared for the output gear, in which the spall of width depth being 1",
            " The performance of the EEMD is compared with the result without EEMD, in which the 5 features are extracted from the original filtered signal directly, and 2 best features are chosen by J3 criterion for the classification. The result is given in Fig. 13(b), in which the J3 value is 29.13 and the two features are crest factor and EOP. Even without EEMD, the performance of fault detection is still favorable but that of the fault identification is marginal since some points overlap the distinction boundary. The performance is also compared with those obtained by the same procedure for the vibration signal measured by the accelerometer as given in Fig. 9. The result is given in Fig. 13(c) where the J3 value is 5.68 and the best two features are crest factor of C2 and shape factor of C1. As shown in the figure, the method fails to classify the fault. The reason may be due to the remote location of the sensor from the faulty gear, which may hinder the accurate detection of the signal. In this study, a new method for gear fault diagnosis is presented, which employs the transmission error as the sensor signal, ensemble EMD as the method for feature extraction, and kNN as the classification tool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001165_tie.2010.2046579-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001165_tie.2010.2046579-Figure1-1.png",
        "caption": "Fig. 1. 3-DOF helicopter manufactured by Quanser Consulting Inc. [24].",
        "texts": [
            " mf , mb Masses of the front- and back-propeller assembly (in kilograms). mh Mass of the helicopter (in kilograms). mw Mass of the counterweight (in kilograms). La Distance between the travel axis and the helicopter body (in meters). Lh Distance between the pitch axis and each motor (in meters). Lw Distance between the travel axis and the counterweight (in meters). g Gravity constant (9.8 m \u00b7 s2). The helicopter manufactured by Quanser Consulting Inc. is a mechanical device with 3 DOF: the elevation, pitch, and travel. Fig. 1 shows the photograph of the Quanser 3-DOF helicopter used in the Control Theory and Technology Laboratory, Tsinghua University. The 3-DOF helicopter consists of a base that carries a long arm capable of rotating about the elevation axis. One end of the arm is attached to a counterweight, while two dc motors with propellers are installed at the other end to create forces that drive the propellers. Two motors\u2019 axes are parallel, and the thrust vector is normal to the frame. Three encoders are connected to the helicopter in order to measure the elevation, pitch, and travel angles of the body, and two voltage amplifiers are used to realize the control action in the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002913_j.scriptamat.2017.07.020-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002913_j.scriptamat.2017.07.020-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of (a) the vertical, (b) the inclined struts and (c) the scan strategy. The red arrows indicate the thermal fluxdensity and direction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " It is thusworth noting that none of these studies have evidenced the combined influence of the strut orientation and spatial location (upwards or downwards orientated part) on the microstructure and porosity. The present study thus aims at demonstrating the very specific micro- and meso-structures resulting from SLM processing of fine AlSi10Mg struts. In the present study, lattice structures with a built strut diameter of 820 \u03bcm presenting two different building orientations have been compared (Fig. 1): one referred to as the \u201cvertical\u201d strut (a) and one referred to as the \u201cinclined\u201d strut, orientated at 35.5\u00b0 from horizontal plane (b). This orientation of the strut corresponds to the one of struts in a body centred cubic (BCC) unit cell of a lattice structure. The analyzed struts were thus part of a larger lattice structure to avoid border effects. The aluminum alloy contains 9.53wt% of Si and 0.36wt% ofMg. The powder particles size before laser melting ranged from 10 to 80 \u03bcm with a median value of 44 \u03bcm",
            " The processing parameters of the SLM 250 equipmentwere a laser power of 250W, a scanning speed of 571mm/s, a layer thickness of 60 \u03bcm and an argon gas atmosphere. These process parameters were shown to bring low porosity in vertical struts and were voluntarily kept identical for all struts, whatever their building direction in order to assess the consequences on the microstructure and porosity. Because of the thin diameter of the struts, only two concentric round melting paths with a central strip were applied to build a strut section, with a following distance between each path of 0.15 mm (Fig. 1(c)). The microstructure was investigated by light microscopy to highlight the melt pools while Scanning Electron Microscopy (SEM) was used to characterize the microstructure at higher magnification. Chemical etching with a Flick's reagent [14] revealed the Si-rich eutectic structure. SEM image analysis and 3D X-ray microtomography [15] were used to characterize the internal porosity of the struts. In this last case, the voxel size was set to 0.8 \u03bcm3 with operating voltage of Fig. 2. Light and SEM(zoom)micrographsof themicrostructure in an inclined strut",
            " In the present case, the radiation and convection processes are assumed to be constant since each sample section is constant and built similarly. Consequently, themajor part of heat injected in the successive melt pools is transferred and evacuated by conduction in two directions: (i) towards the previous lower layers which have already cooled down, (ii) towards the unmelted surrounding powder bed. Obviously, the heat losses by conduction are influenced by the sample geometry. As depicted by the red arrows in Fig. 1, the thermal behavior (density and direction) differs during SLMprocess according to the building orientation and leads to solidification rate specific to each geometry [16]. Compared to the vertical strut, the inclined strut presents two zones with different thermal conductivities: the bottom zone, also called downwards orientated zone (DOZ) (zone B \u2013 Fig. 2), laying on support layers made of previous unmelted powder and the top zone (upwards orientated zone (UOZ)(zone A \u2013 Fig. 2), laying on dense material",
            " Indeed, a larger cooling rate avoids microstructure coarsening. Consequently, the mean size of the cells is roughly 2.5 to 3 times smaller in zone A and comparable to the 0.55 \u03bcm cell size measured in bulk AlSi10Mg samples presenting the same process parameters. Moreover, it appears that the cell size in the core of the melt pool of the vertical struts is similar to zoneA of the inclined strut due to the vertical building direction of these struts. The thermal flux density and orientation are indicated by the red arrows in Fig. 1. The successive layers always lay on dense material (except for the first one) and cool down faster by conduction just like in zone A of the inclined strut. As a consequence of these cell sizes, hardness measurements performed in the center of the melt pool in parts A and B of the inclined strut and in the vertical strut are compared in Table 1. The hardness is about 14 HV larger in the fine cell size zone A (UOZ) than in the DOZ of the inclined strut. The vertical strut presents only a slightly higher hardness than zone A of the inclined strut consistent with the similar cell size in these two samples",
            " Nevertheless, understanding the pore formation can not alone explain the heterogeneous distribution of porosity, i.e. almost all the porosities are observed in zone B of inclined struts. Since the porosities are preferentially located in the coarser microstructure zone B (DOZ), their nucleation could be justified by the difference in time spent at high temperature by both zones A and B. Based on the strut orientation of the lattice, two reasons can explain why zone B stays longer at high temperature than zone A. Firstly, zone B cools down more slowly since it lays on powder (Fig. 1(b)). This lower cooling rate induces a higher local pre-heating in zone B for the next layer.Weingarten et al. [17] discussed the influence of the local pre-heating on the hydrogen pore formation by studying the evolution of bulk density with the scan break, i.e. the time between the end of one scan vector and the starting point of the following scan vector in bulk samples. This timedictates the temperature of the previously solidified part before building the upper layer. These previous researches showed that if the scan break decreases, the hydrogen pore density increases due to more local pre-heating of the following scan track"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001386_ijma.2012.046583-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001386_ijma.2012.046583-Figure3-1.png",
        "caption": "Figure 3 Mechanism of master system (see online version for colours)",
        "texts": [
            " If the catheter contacts a blood vessel wall, the force is detected and transmitted to the surgeon\u2019s hand, realising force feedback. Figure 2 is a flow chart of the control instructions for our robotic catheter system. The robotic system avoids danger during the operation via force and visual feedback. Both master manipulator and slave manipulator employ DSP (TI, TMS320F28335) as their control units, communication between master manipulator and slave manipulator is realised by the TCP/IP protocol communication. On the master side, the slide platform is fixed on the supporting frame (Figure 3). The master system devices, including a left handle with one switch, a right handle, step motor, load cell, and maxon motor, are on the slide platform. A switch placed on the left handle is used to control these two graspers in slave side, only one switch is enough because the catheter is clamped by one grasper at the same time. Operator\u2019s action is measured by using the right handle. The handle takes the same movement motion with the slave manipulator, it has two DOFs, one is axial motion and the other one is radial motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003820_j.jmapro.2020.01.051-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003820_j.jmapro.2020.01.051-Figure3-1.png",
        "caption": "Fig. 3. FE model of the test case.",
        "texts": [
            " The deposition process was simulated using a FE heat transfer analysis in order to obtain the full temperature field of the part, as similarly carried out by Casalino et al. [29], where FE simulation has used to predict the temperature profile in a laser surface transformation hardening with a cylindrical heat source of AISI 4130. The simulations were carried out using the commercial FE solver, LS-DYNA. The WAAM modelling techniques, such as the moving heat source, the elements activation algorithm, and the material behavior models, are based on previous research [30,31]. Fig. 3 shows the FE model used to simulate the deposition of the test cases. The geometry was discretized using 60,274 1st order solid hexahedral elements, resulting in 75,017 nodes. The modelling domain was extended to the mild steel workpiece holding table since the conductive heat flux from the substrate is a relevant contribution to the overall heat extraction. The conduction between the substrate and the workpiece holding table was included using a contact algorithm. The interface conductance was set to 2000 W/m2\u00b0C based on literature data [32]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure5.23-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure5.23-1.png",
        "caption": "Fig. 5.23 Sketches of helicopter motion following cyclic inputs in hover: (a) lateral cyclic step; (b) longitudinal cyclic step",
        "texts": [
            " the steady-state rate response per degree of cyclic) are similar, the control sensitivities and dampings are scaled by the respective inertias (pitch moment of inertia is more than three times the roll moment of inertia). Thus, the maximum roll rate response is achieved in about one-third the time it takes for the maximum pitch rate to be reached. The short-term cross-coupled responses (q and p) exhibit similar features, with about 40% of the corresponding direct rates (p and q) reached less than 1 s into the manoeuvre. The accompanying sketches in Figure 5.23 illustrate the various influences on the helicopter in the first few seconds of response from the hover condition. The initial snatch acceleration is followed by a rapid growth to maximum rate when the control moment and damping moment effectively balance. The cross-coupled control moments are reinforced by the coupled damping moments in the same time frame. As the aircraft accelerates translationally, the restoring moments due to surge and sway velocities come into play. However, these effects are counteracted by cross-coupled moments due to the development of nonuniform induced velocities normal to the rotor disc (\ud835\udf061s and \ud835\udf061c)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000048_j.jmps.2011.01.010-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000048_j.jmps.2011.01.010-Figure5-1.png",
        "caption": "Fig. 5. The surface topography after mucosal buckling.",
        "texts": [
            " Finite element calculations are performed to simulate the wrinkling process of a growing mucosa using the commercial finite element software, ABAQUS (Version 6.8.1). Eight-noded plane-strain hybrid elements (CPE8RH) are used for both mucosa and submucosa. In the first stage of mucosal growth, the thickness of the mucosa uniformly increases and the compressive stresses are built up due to the constraint of the outer submucosa and muscular wall. When the circumferential stress reaches a critical value, the deformation becomes unstable and the mucosa buckles into a wavy pattern to partially release the circumferential compression. Fig. 5 schematically depicts the morphological characteristic of buckling in the system. In what follows, we will examine the prominent features of mucosal wrinkling and the effects of such factors as mucosal thickness, submucosal thickness, and elastic moduli on the surface patterns. The results of finite element simulations will be compared to those from the theoretical analysis whenever possible. We first analyze the effects of the initial mucosal thickness Hm/C on the surface wrinkling pattern in response to growth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003657_j.measurement.2020.108855-Figure17-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003657_j.measurement.2020.108855-Figure17-1.png",
        "caption": "Fig. 17. General methodological approach [62].",
        "texts": [
            " Analyzed results revealed that types and parameters had the largest influence on plastic deformations in the contact zone. Liu [61] used traction-only nonlinear springs to model rolling elements for a single-row four-point contact ball slewing bearing. Daidie\u0301 [62] used nonlinear traction springs X. Jin et al. Measurement 172 (2021) 108855 to represent rolling elements under compression. This method can not only reduce calculation time but also obtain the variation in the contact angle, shown in Fig. 17. Aguirrebeitia [63] used rigid beam elements to replace rolling elements to obtain static load-carrying capacity. He [64] provided maximum loads in the contact zone by using non-linear springs in FEM model. Layers under the raceway (hardened layer, transition layer and core layer) were modeled based on each layer\u2019 distinct elastic\u2013plastic parameters respectively. Detailed modeling has more accuracy while more computational resource consumed. Based on 3D numerical model, Kania [65] investigated effects of raceway profiles on pressure in the contact zone, shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure11.8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure11.8-1.png",
        "caption": "FIGURE 11.8. A rigid rectangular link in the principal and non principal frames.",
        "texts": [
            "178) Since the coordinate frame is central, the products of inertia must be zero. To show this, we examine Ixy. Ixy = Iyx = \u2212 Z B xy dm = Z v xy\u03c1dv = m lwh Z h/2 \u2212h/2 Z w/2 \u2212w/2 Z l/2 \u2212l/2 xy dx dy dz = 0 (11.179) Therefore, the moment of inertia matrix for the rigid rectangular link in its central frame is I = \u23a1\u23a3 m 12 \u00a1 w2 + h2 \u00a2 0 0 0 m 12 \u00a1 h2 + l2 \u00a2 0 0 0 m 12 \u00a1 l2 + w2 \u00a2 \u23a4\u23a6 . (11.180) 606 11. Motion Dynamics Example 307 Translation of the inertia matrix. The moment of inertia matrix of the rigid link shown in Figure 11.8, in the principal frame B(oxyz) is given in Equation (11.180). The moment of inertia matrix in the non principal frame B0(ox0y0z0) can be found by applying the parallel-axes transformation formula (11.154). B0 I = BI +m B0 r\u0303C B0 r\u0303TC (11.181) The center of mass position vector is B0 rC = 1 2 \u23a1\u23a3 l w h \u23a4\u23a6 (11.182) and therefore, B0 r\u0303C = 1 2 \u23a1\u23a3 0 \u2212h w h 0 \u2212l \u2212w l 0 \u23a4\u23a6 (11.183) that provides B0 I = \u23a1\u23a3 1 3h 2m+ 1 3mw2 \u221214 lmw \u221214hlm \u221214 lmw 1 3h 2m+ 1 3 l 2m \u221214hmw \u221214hlm \u221214hmw 1 3 l 2m+ 1 3mw2 \u23a4\u23a6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002492_j.rcim.2016.05.011-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002492_j.rcim.2016.05.011-Figure4-1.png",
        "caption": "Fig. 4. Robot axes and their possible motions.",
        "texts": [
            " The error compensation is performed by sending \u2032 ( )Ppx 0 , \u2032 ( )Ppy 0 and \u2032 ( )Ppz 0 as the controlling commends to the robot. Fig. 3 shows the experimental setup of this study. A FARO SI laser tracker was used to measure the position errors of a KUKA KR 210\u20132 industrial robot. According to the specifications, the absolute distance measuring accuracy of the laser tracker is \u03bc + \u03bc10 m 0.8 m/m. The robot is a 6-DOF (degree-of-freedom) open-chain manipulator with 6 revolute joints (A1, A2, \u2026, A6), as is shown in Fig. 4. The repeatability of the robot is 70.06 mm according to ISO 9283. Unfortunately there is no information that shows the positional accuracy of this robot in its technical documents.The position measurements were performed with a SMR (spherically mounted reflector, diameter 38.1 mm) attached on the flange of the robot. The centre of the SMR was the robot TCP. The indoor temperature was between 22 \u00b0C and 24 \u00b0C when all the measurements were performed. In real robot applications, the positions of the robot TCP and the installation positions of all the devices and products should be defined in a certain measuring frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000437_027836499801700201-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000437_027836499801700201-Figure1-1.png",
        "caption": "Fig. 1. Rover-mounted manipulator.",
        "texts": [
            " The kinematics of the rover and the manipulator subsystems are studied in Sections 2.1 and 2.2, followed by the motion control scheme in Section 2.3. 2.1. Nonholonomic Rover Subsystem Consider a front-wheel-drive, four-wheeled, carlike rover, where the rear wheels are aligned with the rover body and the front wheels can be steered relative to the rover body (Barraquand and Latombe 1989).1 The rover is represented by a two-dimensional rectangular object translating and rotating in the plane of motion, as illustrated in Figure 1. Let F(x f\u2019 y f) denote the midpoint between the two front wheels and R(x,, yr) represent the midpoint between the two rear wheels of the rover, where the coordinates are expressed with respect to the fixed world frame { W } with axes (Ox, Oy) shown in Figure 1. Let the angle 0 denote the orientation of the main axis of the rover RF relative to the ~-axis of the world frame. Then, the rover configuration can be represented by three variables: the two position coordinates (xf, y f) together with the orientation angle 0. Therefore, the 3 x 1 configuration vector p = [~ f, y f, 0] T succinctly characterizes the position and orientation of the rover in the plane of motion; that is, p embodies the two translational and one rotational Cartesian degrees of freedom ~ f, y f, and 0 of the rover. Assuming a pure rolling contact between the rover wheels and the ground (i.e., no slipping), the velocity of the rear point R is always along the main axis of the rover; that is, the !-axis of the rover-attached frame { V } in Figure 1. Hence, we have where A is a scalar. Eliminating A, we obtain Note that the expression [xrsin4> - ~,coso] represents the velocity of the rear point R in the orthogonal direction to the rover axis; that is, along the y-axis in Figure 1. Hence, satisfaction of eq. (2) ensures that the rear wheels of the rover do 1. The kinematic analysis presented here can easily be modified to treat other types of rovers. at BROWN UNIVERSITY on November 24, 2012ijr.sagepub.comDownloaded from 109 not slip sideways along the y-axis. Equation (2) can be expressed in terms of the coordinates (x f , y f) of the front point F on the rover. The coordinates of the rear point R(a~ yr) and the front point F(x f\u2019 y f) are related by where denote the distance between R and F; that is, the rover length",
            " The Cartesian velocities (~ f, y f, ~) are related to the control variables (v, 7) by where the third equation is derived from the first two equations and the nonholonomic constraint (5). Observe that the first two equations of (8) yield which implies that the front wheels do not slip sideways in the orthogonal direction to the velocity vector of the point F. Given (tf, ~-, ~), the rover velocity v and the steering angle 7 are found from eq. (8) as provided that v # 0. Notice that when v = 0, -y is undetermined from eq. (9). 2.2. Holonomic Manipulator Subsystem For simplicity of presentation, we consider a planar twolink manipulator arm mounted on the rover, as illustrated in Figure 1. However, the methodology presented in this paper is general and is equally applicable to any type of n-jointed rover-mounted manipulator. Suppose that a tool of length lo is grasped by the end effector. Let 01 and 92 represent the joint angles and 11 and l2 denote the link lengths of the manipulator arm. Consider a moving vehicle frame {V} with axes (F:~, Fy) attached to the rover at the front midpoint F. Let the position of the tool tip T in the world frame {W } be the primary task variable of interest",
            " Given task-space trajectories with constant final values, Xd(t) = 0 for t > T where T is the mo- tion duration, by using (23) we obtain 4(t) = 0 for t > T; that is, the manipulator and rover degrees of freedom will cease motion for t > T, and any task tracking-error at t = T will continue to exist for t > T. However, by using (24), the manipulator and rover degrees of freedom continue to move for t > T until the desired configuration vector is reached; that is, X ~ Xd as t - oo. A comment about the nonslipping assumption of rover motion is now in order. The preceding analysis assumes that the rover wheels do not slip sideways; that is, the rear point R on the rover moves only along the :r-axis in Figure 1. When slipping occurs, the rover nonholonomic constraint (5) becomes x fsin4> - y fcos~ + 4>l = c, where c is some known (measured or estimated) nonzero slip rate; that is, the velocity of the rear point R along the y-axis (see Figure 1). In this case, the kinematic equation of motion becomes which can be solved for q using eq. (24). Since the acquired solution satisfies the equations J~g = kdt and J~q = 2d, the tool tip will continue to move on the desired trajectory, and the kinematic constraint will continue to be satisfied. In other words, the arm motion &dquo;compensates&dquo; for the rover slippage. Let us now revisit the two-jointed manipulator arm mounted on the rover as illustrated in Figure 1. On combining the rover nonholonomic constraint (5) and the tool tip motion (13), we obtain the integrated model of the roverplus-manipulator system as where the symbols are defined in Section 2.2. There are five independent configuration variables q = [z j , y f, 0, 91, B2] T to be manipulated while there are only two tool tip position coordinates Xt = [Xt, yt] T to be controlled and one nonholonomic rover constraint (5) to be satisfied. Therefore, two additional configuration dependent kinematic functions z, (q) and z2(q) can be specified and controlled independently of the tool tip motion and the nonholonomic rover constraint. In this example, we consider two different sets of kinematic functions to illustrate the versatility of the proposed motion control scheme. 2.3.1. Case Study 1 In this case study, we choose the tool orientation a relative to the world frame and the manipulator elbow angle Q between the upper arm and forearm as the additional task variables (see Figure 1). These task variables are related to the configuration variables by or, in velocity form, where 4 = [Xf,Yf,\u00d8,\u00d6I,\u00d62] T . On combining the roverplus-manipulator model (25) with the additional task specifications (27), we obtain where the subscript d denotes the desired value. Note that (28) embodies the nonholonomic rover constraint (5). Equation (28) represents a set of five linear equations in the five unknown elements of q. By direct calculation, the determinant of the 5 x 5 augmented Jacobian matrix appearing on the left-hand side of (28) is found to be3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003950_j.ymssp.2018.09.027-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003950_j.ymssp.2018.09.027-Figure8-1.png",
        "caption": "Fig. 8. Geometric model of the spur gear profile.",
        "texts": [
            " The gear tooth structure stiffness Kstr can be either obtained by the Potential Energy (PE) method or finite element techniques, where the PE method is the most widely used analytical method in modeling the structural TVMS of a gear-tooth pair [41\u201344]. The loss of tooth surface material due to gear tooth spalling reduces the strength (or stiffness) of the gear tooth. The modelling of the spalling defect is generally represented by a specific geometric shape, such as rectangular, round, V-shaped or ellipsoid spalls [23,41\u201344]. The severity of the fault is generally controlled by shape parameters such as length, width, radius and depth. The geometric model of a typical gear tooth profile with spalling defect, as reported in [42], is shown in Fig. 8, where the tooth spalls are assumed as identical in-line round shapes. Here, r and d are the radius and depth of the tooth spalling, DL is the magnitude of the reduced contact length at the mesh point. AB and BC are the tooth transition curve and involute curve, Pm is an arbitrary contact point, aPm is the corresponding pressure angle. xA,xB, and xPm are distances of points A, B, and Pm from the gear geometrical center O. F is the tooth contact force and is resolved into Fx and Fy. Here, hx represents the halftooth thickness at an arbitrary point and s is the corresponding pressure angle",
            " Uai, Ubi, Usi, Ufi and Uh are, respectively, axial compressive energy, bending energy, shear energy, fillet foundation energy, and Hertzian energy. kai, ksi, kbi, kfi, and kh are tooth axial compressive stiffness, shear stiffness, bending stiffness, fillet foundation stiffness, and Hertzian contact stiffness, respectively. Due to the loss of surface materials, the occurrence of tooth spalling results in a direct influence on the bending strength, axial compressive strength, shear strength, and Hertzian contact strength of the gear pair. Based on the geometric model (see Fig. 8), these stiffnesses can be calculated as [25,45] 1 kai \u00bc R xB xA sin2aPm EAxt dx\u00fe R xPm xB sin2aPm EAx dx; 1 kbi \u00bc R xB xA f xt EIzt dx\u00fe R xPm xB f x EIz dx; 1 ksi \u00bc R xB xA 1:2cos2aPm GAxt dx\u00fe R xPm xB 1:2cos2aPm GAx dx; 1 kf \u00bc cos2aPm EW L uf Sf 2 \u00feM uf Sf \u00fe P 1\u00fe Q tan2aPm ; kh \u00bc pELe 4 1 v2\u00f0 \u00de ; 8>>>>>>< >>>>>>: \u00f017\u00de where f xt \u00bc cosaPm\u00f0xPm xt\u00de hPmsinaPm\u00f0 \u00de2, f x \u00bc cosaPm\u00f0xPm x\u00de hPmsinaPm\u00f0 \u00de2, in which aPm is the pressure angle of the contact point Pm, hPm is the corresponding half tooth thickness, see [25] for further details"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001300_j.surfcoat.2011.09.051-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001300_j.surfcoat.2011.09.051-Figure2-1.png",
        "caption": "Fig. 2. A 3D microstructure of the as-deposited Al 4047 sample. This structure was constructed by combining three microstructures of the longitudinal, transverse, and plan sections.",
        "texts": [
            " The microstructure of the longitudinal section revealed the pattern of layer-by-layer deposition. In addition, it is important to note that a periodic circular light and dark band structure was observed in each layer of both deposits. However, the orientation of the band altered with the laser scan direction as shown in Fig. 1(c). For a better understanding of the foundation of the band structure, a three dimensional (3D) microstructure was constructed by combining three microstructures of the longitudinal, transverse, and plan sections. Fig. 2 shows the 3D overview of the microstructural morphology of deposit 2. Note that the periodic band structure was found in all three faces. The interesting feature of this band is that the band basically consists of alternate coarse (dendrites) and fine (featureless region) microstructures. The morphology of the fine microstructure was not resolvable under the optical microscope. It should be pointed out that this band is circular in nature in the longitudinal section, whereas, it is parallel straight boundaries in the transverse and plan sections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003126_j.jsv.2015.08.002-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003126_j.jsv.2015.08.002-Figure1-1.png",
        "caption": "Fig. 1. Interactions between a ball and raceways. The symbols in this figure are for the interaction between a ball and the inner raceway. The interaction between a ball and the outer raceway is similar to that between a ball and the inner raceway as shown in this figure. This figure is a simplified version of the figure which was originally shown in Ref. [39] for investigating the interaction between a ball and a raceway.",
        "texts": [
            " Both the normal force and traction force can now be added to determine the net force vector. The net moment vector is the cross product of the vector that locates the point of interaction relative to the mass center and the net force vector. Finally, based on the obtained force and moment vectors, the dynamic equations of these bearing components can be determined. Integrating the dynamic equations numerically will give positions and velocities at the next time step. Take ball/inner raceway interactions for instance, as shown in Fig. 1. Similar method can be used to calculate ball/outer raceway interactions. It should be noted that Fig. 1 is a simplified version of the figure which was originally shown in Ref. [39] for investigating the interaction between a ball and a raceway. Three coordinate frames are established in Fig. 1. Raceway fixed frame Orxryrzr is established to describe the position of the raceway center in inertial frame Oixiyizi, and azimuth frame Oaxayaza is used to determine the radial and orbital positions of the ball in the inertial frame. In order to calculate the interaction between a ball and a raceway, two position vectors, i.e., the position vector locates the center of the raceway and the position vector locates the center of the ball are determined firstly. As shown in Fig. 1, these two vectors are expressed as rr and rb, respectively. Now, the geometrical interaction between a ball and a raceway can be determined by locating the ball center relative to the raceway center. This vector is denoted by rb r in Fig. 1 and is given as rb r \u00bc rb rr (3) The relative position between the raceway groove curvature center and the ball center is given by rbc \u00bc rbr rcr (4) where vector rcr locates the raceway groove curvature center relative to the raceway center. Contact angle is an important parameter for a ball bearing. Under unloaded conditions, the raceways have the same contact angle. In this paper, the contact angle of the bearing under unloaded conditions is called \u2018initial contact angle\u2019 [43]. However, under dynamic conditions, contact angles of raceways are time-varying",
            " Moreover, the contact angle largely depends on operating conditions, such as external loads, shaft speeds, and lubrication characteristics. When the bearing is operated at high speeds, the contact angle of inner raceway is larger than that of outer raceway due to large centrifugal force [19,26]. The contact angle of a raceway under dynamic conditions can be determined based on the intersection angle between vector rbc and plane yaza which is perpendicular to the bearing axis of rotation, as shown in Fig. 1. \u03b1\u00bc arctan rbc1 rbc3 (5) where subscripts 1 and 3 denote the first and the third components of vector rbc. In Eq. (5), vector rbc should be described in azimuth frame Oaxayaza, as shown in Fig. 1. Next, the elastic deformation between the ball and the raceway can be obtained. \u03b4\u00bc rbc3 f 0:5\u00f0 \u00deD (6) where f is the raceway groove curvature factor which is defined as the ratio of the radius of raceway groove to the ball diameter. In Eq. (6), vector rbc should be described in contact frame Okxkykzk, as shown in Fig. 1. Contact frame can be established based on azimuth frame and contact angle. More details can be found in Refs. [26,39]. The contact force between the ball and the raceway is given by Hertzian point contact theory [43]: Q \u00bc K\u03b41:5 \u03b440 0 \u03b4r0 ( (7) where K is the Hertzian contact stiffness coefficient which largely depends on the curvature radii of two contacting bodies. Moreover, it can be found from Eqs. (6) and (7) that raceway groove curvature factors have certain effect on the contact force. The friction forces between balls and raceways mainly rely on relative slip velocities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001812_jmes_jour_1962_004_018_02-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001812_jmes_jour_1962_004_018_02-Figure6-1.png",
        "caption": "Fig. 6. Pressure distributions for a compressible lubricant W = 3 x 10-5, G = 5000.",
        "texts": [],
        "surrounding_texts": [
            "The influence of lubricant compressibility has not so far been included in elasto-hydrodynamic theory; but in view Vol4 No 2 1962 at MCGILL UNIVERSITY LIBRARY on April 3, 2016jms.sagepub.comDownloaded from 124 D. DOWSON, G. R. HIGGINSON AND A. V. WHITAKER of the high pressures involved in applications where this theory is appropriate, it seems worth while to find out whether the influence is significant. The effects of compressibility on the five results described in detail in the last section will be examined. Reynolds equation with variable fluid density is If ph and p+ are used in place of h and 7 in the hydrodynamic analysis, the overall calculation is not substantially altered. The variation of density with pressure is roughly linear at low pressures, but the rate of increase of density falls away at high pressure. The limit of the compression of mineral oils is about 25 per cent (I), giving a maximum density increase of about 33 per cent. Figures supplied by Thornton Research Centre for a mineral oil are plotted in Fig. 5. It will be seen that these fit closely to the expression Po - '+l+O.O26p where p is in ton/$; this gives a maximum density increase of about 33 per cent. This expression for density was used in all the calculations described below. The value of E' is that for steel. The most important effect of compressibility is on the peak in the pressure distribution. Comparison of Figs 2 and 6 shows that in all cases the pressure peak has moved downstream and has been reduced in height; the reduction is particularly spectacular in the high-speed cases. An interesting change is in the envelope of the pressure peaks. The general form of the film shape is not altered, but there are changes in detail. Fig. 7 shows the shapes for U = 10-11 for compressible and incompressible lubricants. P 0.009p -- This result is typical of the whole set: (a) the minimum film thickness is not significantly changed, (b) the parallel film of the incompressible case becomes a curved channel in which the product of density and film thickness is much the same as in the incompressible case, (c) the fairly sharp corner associated with the pressure peak is removed; this is shown in the detail in Fig. 8. A result of (a) and (b) is that the minimum film thickness is no longer a fixed 25 per cent less than that under the Hertzian maximum pressure; the difference depends on the compressibility and the value of the pressure. Under the load applied in the present examples, the minimum film thickness is 14 per cent less than that under the Hertzian maximum pressure (in those cases where the pressure curve goes through the Hertzian maximum). The theoretical film shape agrees very favourably with that measured by Crook recently (10). Although compressibility does not alter the overall picture, it does make some of the details of the solutions more credible. J O U R N A L M E C H A N I C A L E N G I N E E R I N G S C I E N C E Vol4 No 2 1962 at MCGILL UNIVERSITY LIBRARY on April 3, 2016jms.sagepub.comDownloaded from ELASTO-HYDRODYNAMIC LUBRICATION: A SURVEY OF ISOTHERMAL SOLUTIONS 125 JOURNAL MECHANICAL ENGINEERING SCIENCE COEFFICIENT OF FRICTION The resistance to rolling arising from the viscous stresses on the roller surface can be evaluated from the curve of pressure against film thickness. The variation of p, the coefficient of friction, with U is shown in Fig. 9 for W = 3 x 10 -5. At this load, p varies with speed at about the same rate as does the film thickness. The values, as expected in pure rolling, are small; but at very high speed they are not negligible. For comparison Fig. 9 also shows the variation of p with U according to elementary theory, namely assuming rigid cylinders and constant viscosity lubricant. Introducing pressure-dependent viscosity into the simple theory would probably reduce p by about a half, bringing the two lines close together at high speed; this means, as would be expected, that the importance of the elasticity of the rollers declines as the speed becomes very high. This result is characteristic of elasto-hydrodynamic theory. At U = 10-11, a tenfold increase in the load does not change the friction force, so the coefficient of friction is correspondingly reduced. CALCULATION OF MINIMUM FILM THICKNESS The method used by the authors to obtain a full solution to a rolling-contact lubrication problem is too cumbersome to be used by a designer. However, the feature of the solution which is the designer\u2019s chief concern is the minimum lilm thickness. With this in mind, the authors some time ago (14) fitted a formula to the minimum film thickness over the wide range of their theoretical solutions. The formula is Vo14 No 2 1962 at MCGILL UNIVERSITY LIBRARY on April 3, 2016jms.sagepub.comDownloaded from D. DOWSON, G. R. HIGGINSON AND A. V. WHITAKER I I ,6 lo-\u2019 \u201d+ 10-4 10-3 Fig. 11 expression can be used with some confidence to calculate the minimum 6lm thickness, in pure r o w at any rate, is shown in Fig. 11, where its predictions are compared with values determined experimentally by Crook (9) and Sibley and Orcutt (11). A f d discussion of the derivation of this formula and comparison with experiments can be found in reference (14)."
        ]
    },
    {
        "image_filename": "designv10_1_0002714_j.triboint.2011.08.019-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002714_j.triboint.2011.08.019-Figure1-1.png",
        "caption": "Fig. 1. Schematic of ball bearing. (a) Bearing parameters. (b) Angular position of rolling element.",
        "texts": [
            " In Section 2, the distribution of internal loading in a ball bearing is analyzed. Section 3 discusses calculation of the friction torque and sliding torque in ball bearing. And more, some experiments and testbed used for these test are analyzed in Section 4 and the difference between theoretic analytic method and experiment are discussed. Finally in Section 5, we conclude the results of this study and give the prospect research in the future. The ball baring can be illustrated in its simple form as shown in Fig. 1. The ability of a ball bearing to carry load depends in large measure on the osculation of the rolling elements and raceway, which is the rate of radius of rolling element (rb) to that of the raceway in a direction transverse to the direction of rolling (ri 0 , ro 0 ). Also from Fig. 1, it can be seen that the free contact angle is made by the line passing through the points of contact of the ball and both raceways and a plane perpendicular to the bearing axis of rotation. The free contact angle a0 can be described as follows: a0 \u00bc cos 1 1 ro ri rb BD \u00f01\u00de In a ball bearing, depending on the contact angles, ball gyroscopic moments and ball centrifugal forces can be of significant magnitude such that inner raceway contact angles tend to increase and out raceway contact angles tend to decrease. Under zero load the centers of the raceway groove curvature radius are separated by a distance BD defined by (as shown in Fig. 1 a) BD\u00bc \u00f0r0i\u00fer0o 2rb\u00de \u00bc \u00f0f i\u00fe f o 1\u00deD \u00f02\u00de where rb is the radius of ball, while D is the diameter of the ball. f is defined by f\u00bcr 0 /D. Under an applied load, a centrifugal force acts on the ball, and then because the inner and outer raceway contact angles are dissimilar, the line of action between raceway groove curvature radius centers is not collinear with BD, but is discontinuous as indicated by Fig. 2. It is assumed in Fig. 2 that the outer raceway groove curvature center is fixed in space and the inner raceway groove curvature center moves relative to that fixed center",
            " In the case of balls contacting the inner or outer raceway in the ball bearings, it is assumed that the angle between the two planes containing the principal radius of curvature of the contacting bodies is perpendicular, and the following expressions can be derived. a\u00bc an 3 4 P A\u00feB 1 n2 1 E1 \u00fe 1 n2 2 E2 1=3 b\u00bc bn 3 4 P A\u00feB 1 n2 1 E1 \u00fe 1 n2 2 E2 1=3 \u00f026\u00de A\u00bc 1 2 1 r1 \u00fe 1 r2 , B\u00bc 1 2 1 r01 \u00fe 1 r02 \u00f027\u00de in which r1, r1 0 are the radius of curvature for inner or outer race and groove, respectively. And r2, r2 0 are the radii of rolling ball. Considering the bearing model shown in Fig. 1, for the contact at inner ring side, the radius of curvature r1 0 of the inner groove must be treated as negative in (27); while at the outer ring side contact, r1, r1 0 must be treated as negative. The values of an and bn are calculated as follows: I\u00bc 2 e2 F e, p2 E e, p2 J\u00bc 2 e2 E\u00f0e,\u00f0p=2\u00de\u00de 1 e2 F e, p2 h i I J \u00bc A B an \u00bc I\u00fe J p 1=3 bn \u00bc an\u00f01 e2\u00de 1=2 8>>>>< >>>>: \u00f028\u00de in which e is the eccentricity of contact ellipse, and F (e, p/2) and E (e, p/2) are the complete elliptic integrals of the first and second, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001868_s00158-010-0496-8-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001868_s00158-010-0496-8-Figure1-1.png",
        "caption": "Fig. 1 Planar inverted pendulum",
        "texts": [
            " Inverted pendulum walking simulation uses a simple pendulum model with concentrated body mass at the COG. The COG trajectory along the walking direction is analytically derived by assuming the COG height to be fixed during the motion. The IPM and its several modified versions are reviewed in this section. Kajita and Tani (1991) and Kajita et al. (1992) were the first to use the IPM to develop a practical biped robot in real time. The mechanical gait model was a planar inverted pendulum with a concentrated point mass and a massless leg with variable length as depicted in Fig. 1. The walking motion was modeled as successive swing motion in the single support phase. The COG was assumed to move at a constant height in the sagittal plane. In addition, the ankle torque around the contact point with the ground was assumed to be zero. Therefore, the equation of motion was a simple linear equation, and the closed-form solution was easy to obtain with the given boundary conditions: x\u0308 \u2212 g yh x = 0 (1) where x is the horizontal trajectory of the COG, and yh is its constant height"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000267_pnas.74.1.221-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000267_pnas.74.1.221-Figure3-1.png",
        "caption": "FIG. 3. (a) Bacterium with two flagella pointing rearwards and intersecting the plane P. (b) Plane P; c is the connection vector between intercepts I1 and 12 of the helices with P, and is at an angle t' to d, the interaxial separation vector. I1 and I2 have mean phase 0 = (01 + 02)/2 and phase difference AO = 01 - 02.",
        "texts": [
            " Translational velocity v = 20 Mm sec-1 (5, 6), angular velocity of flagellar bundle about helical axis Wb = 50 Hz (15), angular velocity of cell body Wcb = 10 Hz (ref. 15 and Macnab, unpublished observations). Flexural rlgidity\u00a7 offlagellum: E= 5 X 10-16 dyne cm2 (10), somewhat lower than the value of Fujime et al. (16). RESULTS Geometry of Static Helices. Consider two similar LH helices of radiusr( with parallel axes separatedbyofrh (0<if < 2). The geometry corresponds to a bacterium with two flagella pointing rearwards, as shown in Fig. 3a. In a plane P intersected normally by the helical axes (Fig. 3b), the two helices have a mean phase 0 and a phase difference AOk. A vector c connects the intercepts of the two helices with P and is inclined at i/i to the interaxial separation vector d. On moving P along the axial direction, the intercepts rotate about the helical axes,, i.e., 4 increases, and the connection vector c changes in both magnitude and direction. Direction is given byi0 = arctans[sina sin (Alo2)]/[cos sin (A/2) +f/256), and magnitude by c I = 2rh sin O sin (AO/2)/sin iP. 4i proves to have quite different properties (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure6.8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure6.8-1.png",
        "caption": "FIGURE 6.8. A spherical robot, made of a spherical manipulator attached to a spherical wrist.",
        "texts": [
            "28993061 deg (6.159) \u03b82 = \u2212.4880908073 rad \u2248 \u221227.96554327 deg (6.160) Having \u03b82, we can calculate \u03b83 from the last column of (6.156) and (6.155). \u03b83 = atan2 \u00b5 1.486 6 cos \u03b82 + 0.2 sin \u03b82 \u2212 1.05 0.2 cos \u03b82 \u2212 1.486 6 sin \u03b82 \u00b6 (6.161) If \u03b82 = .755 rad then we have: \u03b83 = atan2 (\u22120.194 37) = \u22120.19198 rad \u2248 \u221211 deg (6.162) If \u03b82 = \u2212.488 rad then we have: \u03b83 = atan2 (0.194 37) = 0.19198 rad \u2248 11 deg (6.163) Example 192 Inverse kinematics for a spherical robot. Transformation matrices of the spherical robot shown in Figure 6.8 are 0T1 = \u23a1\u23a2\u23a2\u23a3 c\u03b81 0 \u2212s\u03b81 0 s\u03b81 0 c\u03b81 0 0 \u22121 0 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 1T2 = \u23a1\u23a2\u23a2\u23a3 c\u03b82 0 s\u03b82 0 s\u03b82 0 \u2212c\u03b82 0 0 1 0 l2 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 2T3 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d3 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 3T4 = \u23a1\u23a2\u23a2\u23a3 c\u03b84 0 \u2212s\u03b84 0 s\u03b84 0 c\u03b84 0 0 \u22121 0 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 4T5 = \u23a1\u23a2\u23a2\u23a3 c\u03b85 0 s\u03b85 0 s\u03b85 0 \u2212c\u03b85 0 0 1 0 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 5T6 = \u23a1\u23a2\u23a2\u23a3 c\u03b86 \u2212s\u03b86 0 0 s\u03b86 c\u03b86 0 0 0 0 1 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (6.164) 6. Inverse Kinematics 347 Therefore, the position and orientation of the end-effector for a set of joint variables, which solves the forward kinematics problem, can be found by matrix multiplication 0T6 = 0T1 1T2 2T3 3T4 4T5 5T6 = \u23a1\u23a2\u23a2\u23a3 r11 r12 r13 r14 r21 r22 r23 r24 r31 r32 r33 r34 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000238_iros.2005.1545143-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000238_iros.2005.1545143-Figure4-1.png",
        "caption": "Fig. 4 Presentation of internal singularities",
        "texts": [
            " In order to explain these categories of singularities, a simple two-dofparallel mechanism is proposed: - On one hand, under-mobilities occur when Jq is singular. In that case, a velocity q can be applied without producing any motion on the traveling plate (Fig. 3a), - On the other hand, over-mobilities occur when JX is singular. In that case, it is possible to have x X 0 without moving the actuators (Fig. 3b). At last, \"internal\" singularities can occur for some mechanisms. They cannot be enlightened thanks to JX or Jq, and a more complete study has to be done. On Fig. 4, an internal singularity occurs when the parallelogram becomes flat. In that case, orientation of traveling plate cannot be guaranteed (this orientation does not belong to operaltional velocities). Placing actuators of H4 with a homogeneous repartition, i.e. placed at 90\u00b0 one relatively to each other, leads to internal singularities. Thus, a particular arrangement has to be adopted. This particularity involves a non-homogeneous behavior of H4 in the workspace and a bad stiffness, as demonstrated in [17]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000625_revmodphys.82.1607-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000625_revmodphys.82.1607-Figure12-1.png",
        "caption": "FIG. 12. Dimensionless growth rate a2 / vs dimensionless wave number qa for the buckling instability of a tubular polymersome, in which membrane surface viscosity dominates the dissipation. The solid lines have SD/a=1000 and the dashed line has SD/a= .",
        "texts": [
            ", 1996 . Figure 11 shows the growth rate for the pearling instability for various pressures and SD/a=1000. Also shown for comparison is the growth rate for p=3 /a3 and SD/a= . Note how , which arises from the dynamics of the incompressible solvent, forces the growth rate to vanish at q=0, even when SD/a!1. When p\"\u22122 1+ 2 /a3 \u22124.828 /a3, the cylinder is also unstable. Since negative pressure corresponds to compressive stress, this instability is analogous to the Euler buckling instability of a rod. Figure 12 shows the growth rate for the buckling instability. Note the contrast with the pearling instability. In the buckling instability, when the pressure is just sufficient to induce the instability, only a narrow band of wave number centered about a nonzero wave number q a 2= 1+ 2 has positive growth rate. In the pearling instability, the band extends from q=0 to a finite value, and therefore there is no limit to the wavelength of the unstable modes. The aim of this review has been to give a practical overview of the geometrical tools necessary to formulate the equations of motion of polymers and membranes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.3-1.png",
        "caption": "Fig. 4.3",
        "texts": [
            " The second moments of area have the dimension length4; they are given, for example, in the unit cm4. The magnitude of a moment of inertia depends on the location of the origin and on the orientation of the axes. Whereas Iy, Iz and Ip are always positive (the integrals involve the squares of the distances), the product of inertia Iyz may be positive, negative or zero (the integrals contain the product of y and z which need not be positive). In particular, Iyz = 0 if one of the axes is an axis of symmetry of the area A. Let, for example, the z-axis be an axis of symmetry (Fig. 4.3a). Then for every infinitesimal area dA located at a positive distance y, there exists a corresponding element located at a negative distance. Therefore, the integral (4.6b) is zero. In some cases it is practical to use the radii of gyration instead of the second moments of area. They have the dimension \u201c length\u201d 4.2 Second Moments of Area 103 and are defined by rgy = \u221a Iy A , rgz = \u221a Iz A , rgp = \u221a Ip A . (4.7) These equations yield, for example, the relation Iy = r2gyA. Therefore, one may interpret the radius rgy as the distance from the y-axis at which the area A can be imagined to be \u201cconcentrated\u201d in order to have the moment of inertia Iy . Frequently, an area A is composed of several parts Ai, the moments of inertia of which are known (Fig. 4.3b). In this case, the moment of inertia about the y-axis, for example, is obtained as the sum of the moments of inertia Iyi of the individual parts about the same axis: Iy = \u222b A z2 dA = \u222b A1 z2 dA+ \u222b A2 z2 dA+ . . . = \u2211 Iyi . The other moments of inertia can also be found by summation from similar expressions: Iz = \u2211 Izi , Iyz = \u2211 Iyzi . The methods to calculate the second moments of area either by integration (in particular, the considerations of how to choose an infinitesimal area dA) or by summation (in the case of a composite area) are quite analogous to those discussed in Volume 1, Chapter 4, for the determination of centroids, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003392_rob.21597-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003392_rob.21597-Figure11-1.png",
        "caption": "Figure 11. (a) HRI interface and (b) gamepad for multirobot control.",
        "texts": [
            " The primitive actions determined by the MAXQ multicooperative learning approach were provided to the corresponding robots to implement using their onboard low-level controllers. Communication between the wheeled robot and the workstation was achieved through a wireless network, whereas communication between the tracked robot and the workstation was achieved through a tether. An HRI interface was used on the workstation to allow the human operator to take over control of robot tasks, as shown in Figure 11(a). The interface provides 2D views of a scene, the 3D map of the environment, which is obtained by the SLAM module, and the robot status, where the latter provides feedback as to whether the robot being controlled has received control commands and when they have been implemented. An Xbox 360 Microsoft gamepad was utilized as the operator control input, whose functions are shown in Figure 11(b). Namely, using the gamepad, the operator was able to provide control for the mid-level (NUR, VI) and lowlevel (NG) robot tasks. The operator was also able to use the gamepad to switch control between the two robots. The experiments were carried out with four different scene layouts to test the performance of the multirobot Journal of Field Robotics DOI 10.1002/rob cooperative exploration and victim identification approach, Figure 12. The Scene 1 layout contained a combination of both open spaces and nonclimbable rubble piles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001228_0005-1098(79)90042-6-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001228_0005-1098(79)90042-6-Figure4-1.png",
        "caption": "FIG. 4. Steady state relation between rudder angle 6 and turning rate r for a 350,000 tdw tanker in an unstable loading condition.",
        "texts": [
            " (8) The steering performance of a stable ship can be improved by using a non-zero value of q, but simulations and experiments have shown that q=0 is the only acceptable value for unstable ships. Both stable and unstable tankers were investigated in the simulations and the practical experimenls. The same ship could in fact be stable or unstable depending on trim and loading. Turning regulator The major concern when turning is to keep a tight control of the motion of the ship, possibly at the expense of rudder motions. This is true at least for tankers. The steady state relation between turning rate and rudder angle for a typical tanker is shown in Fig. 4. It is seen from this figure that the relation is linear for small variations in turning rate. This is true for normal course keeping when the turning rate is typically below 0.05degs-1. It is also clear from Fig. 4 that the nonlinear characteristics must be taken into account in manoeuvres which involve high turning rates. The normal course keeping regulator can handle small changes in heading. It can, however, not handle large manoeuvres because of the nonlinearities discussed above. A special turning regulator was therefore designed. Several different approaches were considered for this design. Both adaptive and non-adaptive schemes were explored. It was finally decided to use a high gain regulator. This decision was partly motivated by the results in A.str6m (1977) where it was shown that tankers could indeed be controlled by a regulator having fixed high gain. Such a regulator will control the motion of the ship well at the expense of increased steering drag. This property is in good harmony with the requirements on turning. To explain the turning regulator let us first discuss how a typical turn is made. Let the ship initially be on a straight line path, i.e. at point -I in Fig. 4. A turn is initiated by a rudder deflection, the yaw rate then increases until the desired yaw rate is obtained, e.g. at B in Fig. 4. The desired yaw rate is maintained until the ship has almost completed the turn. The yaw rate is then brought to zero in such a way that the ship points in the desired direction. It follows from Fig. 4 that the characteristics of the ship may change substantially when the turning is initiated and interrupted. Based on this discussion it seems natural to have a turning regulator with three different phases. These are described in detail below. A fourth phase is also included after the turn has been interrupted to make sure that the course keeping regulator starts with a good heading and a good estimate of the rudder bias. Phase 1 Initialization. The turn is initialized using a proportional rate feedback"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003826_j.jmapro.2020.07.035-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003826_j.jmapro.2020.07.035-Figure4-1.png",
        "caption": "Fig. 4. Test specimen, dimensions in mm.",
        "texts": [
            " A Concept Laser M2 Cusing SLM machine (Lichtenfels, Germany) equipped with a fibre laser system that delivers power levels of up to a maximum of 400 W was used to build the parts. The SLM parameters used in this study are presented in Table 2. A chessboard scanning strategy was used to fabricate the test parts and shown in Fig. 3. The test parts were built within the SLM machine chamber in an argon atmosphere with less than 0.1 % oxygen, to reduce oxidation during the melting process. The part dimensions are shown in Fig. 4. The manufactured parts were carefully cut from the substrate using a wire-EDM machine. The relative density of the samples manufactured by SLM was measured on both the top surface and the core using the image analysis method. In this method, the porosity was measured using an optical microscope (Zeiss Axio Imager M2m) and image software (Axio Vision SE64 V4.9), which counts the number of black dots (pores) as a function of the color of the base image (white, for example). The relative density values of the surface and core were averaged from at least 23 and 26 measurements, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001530_978-3-642-81857-8-Figure3.55-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001530_978-3-642-81857-8-Figure3.55-1.png",
        "caption": "Fig. 3.55. Nominal trajectories: Accelerated motions \u00a3rom Fig. 3.45 (UMS-l)",
        "texts": [
            "45, but with the time interval for the mo tion shorter than in Fig. 3.45. In order to do this, we increase the permissable manipulator tip acceleration. Th~ee cases were considered. Case I: amax2 1.48 m/s2, case II: amax = 2.25 m/s2 and case III: amax = 3 mls \u2022 All other conditions are the same as before (same ini tial and terminal states and the same straight-line trajectory of the manipulator tip and the gripper). Thus, the nominal trajectories for all three cases are calculated and presented in Fig. 3.55. In Fig. 3.55a the change of tip velocity is presented. Fig. 3.55b shows the nominal trajectories of the angles qO(t).Figs. 3.55c and 3.55d show the nominal dri~ing torques and nominal control. The time intervals for the motion are TI = 0.9 sec for case I (Fig. 3.45), TII = 0.76 seQ and TIII = 0.66 sec. Obviously, if the manipulator velocity is in creased, the nominal torques also increase. Now, the tracking of the nominal trajectories for all three cases is considered. The tracking is realized in two ways. (a) By decentralized control, which does not take into account the coupling among subsystems (K~ 0, Vie I and without programmed l",
            "78Ipilsgn(~ui) i=4,5,6 0.2 0.1 0.5 o. 0.2 0.8 0.6 0.4 .-',\\ I \"-.,, i / 1\\ 'I \\' I I ,\\ / I ,\\ , I \\ /1 ' / 1 \\\\ \" 1./ ,\\ 1/ '\\ ~/ I. i\u00b7\u00b7'-. \\\\ I ! ,_\\~, 0.2 0.4 0.6 0.8 ,r, I /1\\ \u2022 I ,\\ I I '\\ \u2022 I \\ \\ ! / \\ \\ I I .'~ ',\\ I : \\ /': :.\\\\ 1/ f \\ \\\\ / / f ~ \\\\ / ' /: : /: . /:'< ...... . 0.2 0.4 0.6 0.8 I'\"' . \\ I ' i A, . / \u2022 I I I \\ \\ I I \\ \\ \u2022 I \u2022 I I I \\ \\ i I \\ \\ I / \\\\ . , '\\ I I \\\\ I I '~ \u2022 I ...... ~~ / I \\, ',,/ '.\\ \\\\ '. '. 0.2 0.4 0.6 0.8 amax amax 2.25 [;7] 3 [;7] Fig, 3.56. Tracking of trajectories from Fig. 3.55 (UMS-l) t[sec] t[sec] .... t [sec] 253 (a) and (b) is greater if the nominal motion is faster. This means that we have to take care of the dynamics of the system if the level of dynamic influence is so high that the actuators cannot reduce it by linear decentralized output feedback of the subsystems. In order to further demonstrate this fact, the tracking of these two nominal trajectories are simulated when very weak local control is applied. That is, we consider the case when the subsystems are locally exponentially stable of degree ITi = ITi3 = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure9.26-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure9.26-1.png",
        "caption": "Fig. 9.26 Frame of a test generator with air cushions",
        "texts": [
            " Number and size of the single-air-cushion modules depend on the load and the load distribution. But they require a well-levelled, smooth and stable floor. The surface can be a fine concrete, in most cases covered with a special epoxy resin. Air cushions can damage the floor if it shows gaps and cracks or is not smooth enough. Usually, the air pressure is 0.2 MPa, in special cases up to 0.4 MPa. It is recommended to order HV test equipment with frames and with the necessary stability suitable for air cushion transportation (Fig. 9.26). When the movement of air cushions suddenly stops due to an obstacle, the mechanic stress to the insulating supports, for example of an impulse voltage generator, is considerable. single rail for the crane portal crane rail rail (a) (b) 406 9 High-Voltage Test Laboratories The electric power supply is described in Sect. 9.2.3. In the single test and control rooms, a sufficient number of LV sockets should be arranged. This includes the sockets in the control desk or rack for instruments. Everywhere, sockets are necessary for electric tools, spot lights or additional instruments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure10.37-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure10.37-1.png",
        "caption": "Fig. 10.37 In-plane velocity distribution due to yaw rate leading to positive Lr",
        "texts": [
            " The instability is attributed to the rolling moment due to yaw rate, Lr. But what is the physical source of this effect, that is so much weaker on a conventional helicopter, where the principal contributor is the tail rotor? At first thought, one might imagine that the rolling moment from the increasing thrust on the port rotor due 646 Helicopter and Tiltrotor Flight Dynamics to the yaw rate is balanced by the same on the starboard rotor. But that misses the asymmetry arising from the very scale of the rotors. Figure 10.37 reveals how this rolling moment develops during yaw motion. The (outboard) advancing blade of the port rotor meets the higher velocities due to yaw rate than the (inboard) advancing blade of the starboard rotor. A rolling moment to starboard is the result, hence the positive value of Lr, and with a magnitude of 0.183/s, this leads to an effective Nr given by Eq. (10.41), overpowering the natural yaw damping Nr (\u22120.046/s); with no tail rotor, the yaw damping is very small in the hover. According to this theory, the spiral mode does not stabilise until about 80 kts, and the approximation also captures this recovery (Figure 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000308_j.electacta.2006.03.050-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000308_j.electacta.2006.03.050-Figure3-1.png",
        "caption": "Fig. 3. Proposed structure of polymers IIIa and IIIb designed for the glucose oxidizing anode, where m is 8.75, n is 1, o is 0.25, x is 9 and y is 1, assuming complete reaction of starting material.",
        "texts": [
            " Two other redox polymers were synthesized for the anode. The redox active center in these polymers was an osmium bis(4,4\u2032-diamino-2,2\u2032-bipyridine)chloride coordination complex linked to the polymer backbone via one imidaz p ig. 2. Cyclic voltammetry of films of polymer IIa and IIb deposited onto 3 mm iameter glassy carbon electrodes. Scan rate 50 mV/s in 0.05 M phosphate buffer H 7.4, 25 \u25e6C. ole moiety of respectively, poly(vinylimidazole) (IIIb) and oly(vinylimidazole)/polyacrylamide copolymer (IIIa), Fig. 3. Both polymers IIIa and IIIb have indistinguishable redox potentials of E0\u2032 = \u22120.11 (\u00b10.01) V versus Ag/AgCl, within the precision of cyclic voltammetry, Fig. 4. Once again, films of both of these metallopolymers on the carbon electrodes exhibit surface behaviour up to 50 mV/s scan rates and semi-infinite diffusion behaviour at higher scan rates. Polymer IIb (0.49 V) and IIIb (\u22120.11 V) were selected for further investigations because of their superior solubility in water. Slow scan cyclic voltammograms of films of polymer IIb co-immobilized with laccase and polymer IIIb co-immobilized with glucose oxidase on graphite electrodes (6 mm diameter) are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure7.9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure7.9-1.png",
        "caption": "Fig. 7.9 Parallel compensation unit in combination with voltage divider and chopping gap",
        "texts": [
            " The necessary adjustment covers a certain range of load cases, but if fine tuning is required, the compensation unit must be adapted. For larger impulse generators, the series compensation unit can be distributed to the different stages of the generator (with elements of the stage voltage, e.g. 200 kV) and without components of high-rated voltage (e.g. 3,000 kV). The parallel compensation unit (Fig. 7.8a; Hinow and Steiner 2009; Hinow 2011) is always a separate unit which might be combined with a chopping gap and a voltage divider to one compact unit (Fig. 7.9). Its adjustment has to consider the natural frequency range caused by internal and external inductances. The efficiency of the two principles is about the same. It seems that especially for LI testing of UHV equipment the handling of compensation units becomes too time-consuming and does not fit to the operation of an industrial test field. The problem can be easily solved by increased damping due to larger front resistors, but this requires larger tolerances for the front time of LI impulses (for details see Sect",
            " The other one\u2014on suitable insulating support\u2014is 298 7 Tests with High Lightning and Switching Impulse Voltages moveable by a motor drive and can be adjusted for the relevant voltage value. The parallel capacitor column controls the voltage distribution linearly. This column might also be used as a damped capacitive voltage divider, which is usually a separate component (see Sect. 7.5). The instant of the chopping can be triggered as described above for the generator (Fig. 7.6). Also the combination with an overshoot compensation unit is applied (Fig. 7.9). Electrodes for the HV components: An impulse voltage generator and the other HV components require a sufficient clearance D from grounded or energized 7.1 Generation of Impulse Test Voltages 299 300 7 Tests with High Lightning and Switching Impulse Voltages objects in an HV test laboratory (Fig. 7.15a) to avoid breakdowns of the air gap between the HV circuit and the surroundings. The necessary clearance depends on the kind of pre-discharges which determine the breakdown process. The optimum design of the electrodes of the HV components enables not only the correct operation of an LI/SI test system but ensures also their minimum space in the test laboratory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure6-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000035_j.mechmachtheory.2008.06.007-Figure6-1.png",
        "caption": "Fig. 6. Slip mechanism due to elemental gap redistribution in a metal belt CVT [34].",
        "texts": [
            " A simulation procedure was outlined to predict the slip ratio and slip-limit torque of a metal V-belt CVT system under steady-state quasi-static equilibrium conditions. Their research focused on the microslip characteristic of a V-belt CVT, which is due to the redistribution of elemental gaps in the belt. The slip hypothesis was based on the assumption that slip only occurred on the pulley where the gaps were present and those gaps were distributed evenly in an idle sector at the entrance of the loading pulley. The authors observed the existence of active and idle arcs during different phases of transmission, as depicted in Fig. 6 [34]. The active arcs are those regions of belt\u2013pulley wrap that contribute effectively to torque transmission, whereas the idle arcs do not participate in torque transmission. The band tension remains nearly constant in these idle arcs. Since the compressive force in belt elements decreases in the idle arc region, there is redistribution of elemental gaps, which consequently causes microslip phenomenon in a metal belt CVT system. Sun [35] did performance-based analysis of a metal V-belt drive, using quasi-static equilibrium concepts, to obtain a set of equations to describe belt behavior at steady state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure7.67-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure7.67-1.png",
        "caption": "Fig. 7.67 Principle of inductive current sensors. a Single-turn current probe. b Rogowski coil",
        "texts": [
            " 200 % of the peak voltage measurable across an \u2018\u2018ideal\u2019\u2019 shunt after the instant t 3sc \u00bc 6 ls given by (1 kA) (10 mX) = 10 V. 358 7 Tests with High Lightning and Switching Impulse Voltages To minimize the measuring error due to the induced voltage, the area of the measuring loop must be as small as possible. This is usually realized using either coaxial shunts or even disc-shaped shunts as illustrated in Fig. 7.66. The simplest way to eliminate the voltage induced in the measuring loop is to apply a pure inductive converting device. As illustrated in Fig. 7.67, this may consist either of only a single turn or even numerous turns known as Rogowski coil (Rogowski 1913). Based on the inductance law, the voltage detectable at the output of the coil without load (i.e. open loop) can be approximated by: 7.5 Measurement of High Currents in LI Voltage Tests 359 vl t\u00f0 \u00de \u00bc M di dt \u00bc l0 n b 8 ln 2a\u00fe b 2a b di dt ; \u00f07:43\u00de with M mutual inductance l0 permeability of air n number of turns a distance between conductor and Rogowski coil b diameter of turns As the voltage v(t) induced in the Rogowski coil is proportional to the derivate of the current, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002121_s00170-020-05966-8-Figure38-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002121_s00170-020-05966-8-Figure38-1.png",
        "caption": "Fig. 38 The forged sample with added AM structure [57]",
        "texts": [
            " 37, and the formed samples are mechanically characterized. The samples have obtained improvements in yield strength and ultimate tensile strength. In order to combine WAAM and forging processes, Bambach [57] proposed two process chains. The first is to first use WAAM to form semi-finished products, and then use forging to form a complete workpiece; the second is to forge into semi-finished products first, and then use WAAM to add more complex features on the final workpiece to the semi- finished products to obtain the final parts, shown in Fig. 38. The results confirmed that the mechanical properties of WAAM materials can be greatly improved by hot forging and subsequent heat treatment. For example, the yield stress (YS) and ultimate tensile strength (UTS) of WAAM samples in the transverse direction are increased to 922 MPa and 980 MPa, respectively, and 842 MPa and 945 MPa in the forging direction. The tensile ductility is also significantly improved, for example, 14.5% after forging and heat treatment, and 7% in the manufactured state. The combination of WAAM and forging can be used to develop new manufacturing chains, resulting in higher material yield and flexibility than traditional forging"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure20-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure20-1.png",
        "caption": "Fig. 20. Dynamical model of helical gears.",
        "texts": [
            " On the other hand, the effects of tooth crack on mesh stiffness change with the length of contact line. In Fig. 19, thefirst four curves are the casewhen q=5mm, q0=0mm, crack length Lc changes from0mmto30mm, the last curve (crack length of 30(2mm)) is the casewhen Lc=30mm, q0=2mm, a reduction phenomenon in single and total mesh stiffness can also be observed. Similar effects of tooth crack length on mesh stiffness can be found. A dynamic model of a single stage helical gears system proposed by Li [33] is illustrated in Fig. 20. A pair of meshing gears is modeled by rigid disks representing their mass/moment of inertia. Each disk has three degrees of freedom (two translations and one rotation). Pinion and gear are supported by bearingswhich aremodeled as linear spring\u2013damping system. The central coordinate vector can be expressed as qf g \u00bc yp zp \u03b8p yg zg \u03b8g h iT : \u00f030\u00de According to the equilibrium of the force, and the torque for each gear, the equations of motion of a gear pair can be obtained by applying Lagrange formulation: mp yp \u00fe cpy yp \u00fe kpyyp \u00bc \u2212Fy \u00f031\u00de mp zp \u00fe cpy zp \u00fe kpyzp \u00bc Fz \u00f032\u00de Ip \u03b8p \u00bc \u2212Tp\u2212FyRp \u00f033\u00de mg yg \u00fe cgy yg \u00fe kgyyg \u00bc Fy \u00f034\u00de mg zg \u00fe cgy zg \u00fe kgyzg \u00bc \u2212Fz \u00f035\u00de Ig \u03b8g \u00bc \u2212Tg\u2212FyRg \u00f036\u00de Fy \u00bc kmy yp \u223c \u2212 yg \u223c \u00fe cmy yp \u223c \u2212 yg \u223c ; yp \u223c \u00bc yp \u00fe Rp\u03b8p; yg \u223c \u00bc yg\u2212Rg\u03b8g ; kmy \u00bc km cos \u03b2 \u00f037\u00de Fz \u00bc kmz zp \u223c \u2212 zg \u223c \u00fe cmz zp \u223c \u2212 zg \u223c ; zp \u223c \u00bc zp \u00fe yp \u223c tan \u03b2; zg \u223c \u00bc zg\u2212 yp \u223c tan\u03b2; kmz \u00bc km sin \u03b2 \u00f038\u00de wheremp andmg represent themasses, Ip and Ig are the polarmoments of inertia, km and cm are the total mesh stiffness and damping of gears, kpy/kgy and cpy/cgy are stiffness anddamping of supporting bearings,Rp and Rg are the gear base circles, and\u03b2 is the helix angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure4.29-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure4.29-1.png",
        "caption": "FIGURE 4.29. A pyramid.",
        "texts": [
            " F Zero translation screw motion. If the translation h is zero, then the screw motion is a rotation about a non-central axis. Show that a zero translation screw is equivalent to Equation (4.118) for rotation about a non-central axis. 33. F Pl\u00fccker line coordinate. Find the missing numbers l = \u00a3 1/3 1/5 ? ? 2 \u22121 \u00a4T . 4. Motion Kinematics 231 34. F Pl\u00fccker lines. Find the Pl\u00fccker lines for AE, BE, CE, DE in the local coordinate B, and calculate the angle betweenAE, and the Z-axis in the pyramid shown in Figure 4.29. The local coordinate of the edges are A(1, 1, 0) B(\u22121, 1, 0) C(\u22121,\u22121, 0) D(1,\u22121, 0) E(0, 0, 3). Transform the Pl\u00fccker lines AE, BE, CE, DE to the global coordinate G. The global position of o is at o(1, 10, 2). 35. F Angle between two lines. Find the angle between OE, OD, of the pyramid shown in Figure 4.29. The coordinates of the points are D(1,\u22121, 0) E(0, 0, 3). 36. F Distance from the origin. The equation of a plane is given as 4X \u2212 5Y \u2212 12Z \u2212 1 = 0. Determine the perpendicular distance of the plane from the origin. 5 Forward Kinematics Having the joint variables of a robot, we are able to determine the position and orientation of every link of the robot, for a given set of geometrical characteristics of the robot. We attach a coordinate frame to every link and determine its configuration in the neighbor frames using rigid motion method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001064_j.mechmachtheory.2015.06.011-Figure7-1.png",
        "caption": "Fig. 7. Cracked tooth model of helical gears.",
        "texts": [
            " 6, the double-tooth-pair meshing duration and three-tooth-pair meshing duration are [0, (\u03b5 \u2212 2)2\u03c0/z1], [(\u03b5 \u2212 2)2\u03c0/z1, 2\u03c0/z1], respectively. A tooth crack typically starts at the point of the largest stress in thematerial. Lewicki [23,32] indicated that crack propagation paths are smooth, continuous, and inmost cases, rather straight with only a slight curvature. In this paper, assume that the cracked tooth is still considered as a cantilevered beam and crack depth is linear change along facewidth, as shown in Fig. 7. Then, the tooth crack can be described as a function of crack length and crack depth: q u\u00f0 \u00de \u00bc q\u2212 q Lc u Lcb L q\u2212 q\u2212q0 L u Lc \u00bc L 8>< >: \u00f025\u00de where q is the crack depth on the front face, Lc is crack length, L is facewidth, and q0 is the crack depth on the back facewhen the crack propagates through the whole face width. The dash line in Fig. 7(b) indicates the case when the crack doesn't propagate through the whole face width, the solid line indicates the case when the crack propagates through the whole face width. As shown in Fig. 8, the gear tooth with crack is divided into many thin pieces. One of the pieces is used to explain the method to calculate themesh stiffness of helical with tooth crack. Since the curve of the tooth profile remains perfect, the Hertzian contact stiffness kh and axial compressive stiffness kawill not change"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002378_055605-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002378_055605-Figure2-1.png",
        "caption": "Figure 2. Two-stage planetary gearbox test rig: (a) experimental system and (b) its schematic model.",
        "texts": [
            " The two proposed diagnostic parameters simplify considerably the visual inspection and comparison of the frequency spectra between the faulty and the healthy planetary gearboxes, therefore providing diagnosis results independent of the expertise of the investigators and their ability to eyeball the spectra. Since the parameters FRMS and NSDS are specially designed for planetary gearboxes and overcome the shortcomings of the existing diagnostic parameters, they are expected to work better in detecting and diagnosing planetary gearbox faults. This section introduces an experimental system of a planetary gearbox test rig. Experiments are conducted on the test rig and data collected to test the presented diagnostic parameters. The experimental system is shown in figure 2(a) and the threedimensional simulated model of the test rig in figure 2(b). The test rig includes two gearboxes, a 3-hp motor for driving the gearboxes and a magnetic brake for loading. The motor rotating speed is controlled by a speed controller, which allows the tested gear to operate under various speeds. The load is provided by the magnetic brake connected to the output shaft and the torque can be adjusted by a brake controller. As shown in figure 2(b), there are two gearboxes in the test rig: a twostage planetary gearbox and a two-stage fixed-axis gearbox. The two-stage planetary gearbox is our concern in the current study. In each stage of the planetary gearbox, an inner sun gear is surrounded by three or four rotating planet gears, and a stationary outer ring gear. Torque is transmitted through the sun gear to the planets, which ride on a planetary carrier. The planetary carrier, in turn, transmits torque to the output shaft. In a planetary gearbox, sun gear teeth are easily subject to faults as their multiple meshes with the planet gears increase the potential for damage [2]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure5.16-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure5.16-1.png",
        "caption": "Fig. 5.16 Inflection circle and definition of some relevant quantities",
        "texts": [
            "8) xf (t) = xG 0 (t) + S(t) cos\u03c8(t) \u2212 R(t) sin\u03c8(t) yf (t) = yG 0 (t) + S(t) sin\u03c8(t) + R(t) cos\u03c8(t) (5.11) The inflection circle, that is all those points whose trajectory have an inflection point, can be easily obtained at any instant of time from the telemetry data. Here we list, 124 5 The Kinematics of Cornering Fig. 5.14 Comparison of the fixed centrodes and of the trajectories of a Formula car making Turn 5 of the Barcelona circuit Fig. 5.15 Comparison of the moving centrodes of a Formula car making Turn 5 of the Barcelona circuit with reference to Fig. 5.16, some relevant formul\u00e6 d = 1 r2 \u221a( v\u0307r \u2212 vr\u0307 r )2 + ( u\u0307r \u2212 ur\u0307 r )2 = \u221a R\u03072 + S\u03072 r2 (5.12) d sin\u03c7 = ( v\u0307r \u2212 vr\u0307 r ) 1 r2 = \u2212 S\u0307 r (5.13) d cos\u03c7 = ( u\u0307r \u2212 ur\u0307 r ) 1 r2 = R\u0307 r (5.14) 5.2 The Kinematics of a Turning Vehicle 125 d = d cos\u03c7 i + d sin\u03c7j = R\u0307i \u2212 S\u0307j r (5.15) aC = r2d(cos\u03c7 i + sin\u03c7j) = r2d = r(R\u0307i \u2212 S\u0307j) (5.16) V C\u0302 = rd(\u2212 sin\u03c7 i + cos\u03c7j) = S\u0307i + R\u0307j (5.17) D\u0307 = S\u0307i + R\u0307j \u2212 S\u03c7\u0307 j + R\u03c7\u0307 i = (S\u0307 + R\u03c7\u0307)i + (R\u0307 \u2212 S\u03c7\u0307)j (5.18) d\u0307 = 1 r3d [ r(R\u0307R\u0308 + S\u0307S\u0308) \u2212 r\u0307 ( R\u03072 + S\u03072)] (5.19) d dt ( D d ) = D\u0307d \u2212 Dd\u0307 d2 = 1 d2 {[ (S\u0307 + R\u03c7\u0307)d \u2212 Sd\u0307 ] i + [(R\u0307 \u2212 S\u03c7\u0307)d \u2212 Rd\u0307 ] j } (5.20) r(d \u00b7 D) = R\u0307S \u2212 RS\u0307 (5.21) They cover many aspects, like: \u2022 the diameter d of the inflection circle; \u2022 its orientation \u03c7 with respect to the vehicle; \u2022 the speed V C\u0302 of the geometric point C\u0302; \u2022 the acceleration aC of the velocity center C; \u2022 the rate of change of d ; \u2022 the rate of change of GC = D. It is worth noting that almost all quantities depend on r , R\u0307 and S\u0307. 126 5 The Kinematics of Cornering Along the axis of the vehicle there are, at any instant of time, some special points (Fig. 5.16). Point Z has zero slip angle, that is, \u03b2Z = 0, or equivalently VZ = ui. Point N has \u03b2\u0307N = 0. To truly understand the kinematics of a turning vehicle, we must also consider the curvature of the trajectories and how they change in time under the driver action on the steering wheel. In particular, we monitor the trajectories of the midpoints A1 and A2 of both axles, and their centers of curvature E1 and E2, respectively. There is a nice interplay between radii of curvature, the velocity center and the inflection circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003154_j.jmrt.2016.11.002-Figure13-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003154_j.jmrt.2016.11.002-Figure13-1.png",
        "caption": "Fig. 13 \u2013 Exaggerated cartoon view showing large-scale AM of aircraft structure and components using wire fed, metal droplet generator clusters in vacuum enclosure. The metal or alloy wires are fed from spools (upper left). Modular analytical components which can be strategically placed during the build process are denoted, S, for diagnostic source (electron, X-ray beam, etc.) and, D, detector (secondary electron, energy-dispersive X-ray spectra, etc.). S can also represent electron or laser beam sources for thermal manipulation during layer building. The multiaxial, clustered droplet-emitter heads can be mounted on movable gantry arrays or movable robots or robot arms.",
        "texts": [
            " 12(a) will be limited to a narrow ngle of deflection using deflection plates below the charging lectrodes (in Fig. 12(a)), as in Fig. 10, multiple emitters n clusters as shown in Fig. 12(b) can increase growth or eposition rates or deliver different materials (metals and lloys) or droplet sizes necessary for component or subomponent fabrication in large, integrated AM systems. As oted previously, clustered droplet generator (emitter) heads an be mounted on flexible gantry arrays, robot arms, etc. roviding multi-material, multi-axial deposition as shown in he exaggerated cartoon in Fig. 13. It should be emphasized hat large-scale AM, 3D printing systems envisioned in Fig. 13 re in high vacuum in order to eliminate or drastically reduce roplet oxidation or other contamination issues. In addition, he nozzle spacing to the printing surface would be considrably reduced from the exaggerated view provided in Fig. 13. ecause the deposition occurs in relatively thin layers (assumng droplet sizes \u223c20 m), the prospect for creating initial, morphous structures (since cooling rates will be \u2265107 \u25e6C/s) r nanostructures, as implicit on comparing Fig. 9(a) and (f), Please cite this article in press as: Murr LE, Johnson WL. 3D metal droplet pr J Mater Res Technol. 2017. http://dx.doi.org/10.1016/j.jmrt.2016.11.002 s very good. In addition, large, integrated deposition systems mplicit in Fig. 13 can also incorporate electron or laser beams o pre-heat or post-heat (and anneal) deposited layers or ayer portions to control the residual microstructures and associated properties; or act as sources (S) along with selective detectors (D) for in situ, real-time process observation, analysis and diagnostics. It can be recognized that necessary CAD and related, integrated computer control for emitter head operation and metal droplet stream direction, as well as their orientation for optimal deposition will require a very large and sophisticated computer control platform as a major process component. 4. Discussion and summary Fig. 13 can be visualized as epitomizing the smart factory where software (CAD) driven integrated advanced manufacturing concepts are combined with various levels of AM to fabricate large, complex structures. This includes 3D metal droplet printing of complex structures, such as those illustrated in models in Fig. 7, as well as closed cell structures, into a variety of structural members (including automotive, aerospace, etc.) to dramatically reduce weight and cost and inting development and advanced materials additive manufacturing",
            " It is apparent that in addition to prospects for large-scale AM using wire feed technologies implicit in Figs. 12 and 13, 3D droplet printer design can also be utilized in smaller-scale machines which could allow efficient customized product or component fabrication as well as scale up to larger production arenas. Such smaller-scale application would also benefit from lower precursor material costs and improved net shaping, as well as the elimination of material removal and recovery processes which currently limit powder bed fusion processes. Droplet printing implicit in Fig. 13 can also be combined with or integrated into other modular processes such as conventional EBM or SLM processes to fabricate components which can be integrated into larger modular manufacturing systems, including joining and finishing processes in an automated, CAD-driven manufacturing arena. Conflicts of interest The authors declare no conflicts of interest. e f e r e n c e s [1] Zhai Y, Lados DA, Lagoy JL. Additive manufacturing: making imagination the major limitation. JOM 2014;66(5):808\u201316. [2] Deyer GF, Deyer D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure5.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure5.2-1.png",
        "caption": "Fig. 5.2",
        "texts": [
            " In the following we will derive the formulas which are needed to calculate the stresses and deformations due to torsion. The theory of torsion for arbitrarily shaped cross sections is rather complicated, therefore we restrict ourselves to specical cases. As an introductory problem we examine the torsion of a circular shaft in the next section. 5.2 5.2 Circular Shaft We consider a straight circular shaft with a constant radiusR. The shaft is clamped at one end and subjected to an external torque Mx (acting about the longitudinal axis) at its free end (Fig. 5.2a). 5.2 Circular Shaft 193 To derive the basic equations, we need to combine relations from kinematics, statics and Hooke\u2019s law. We start by making the following kinematical assumptions: a) The cross sections remain unchanged during torsion, i.e. all the points of a cross section undergo the same twist. Points on a straight line within the cross section before twisting remain on a straight line after the deformation: radial lines of a cross section remain straight. b) Plane cross sections remain plane, i",
            " they do not warp. Therefore, we do not observe any deformation perpendicular to the cross sections. With the aid of the theory of elasticity it can be shown that these assumptions are exactly fulfilled for a circular shaft (see Volume 4, Chapter 2.6.3). Therefore, an infinitesimal cylinder with arbitrary radius r isolated from the circular shaft remains a cylinder after twisting. We solely observe a relative rotation of two adjacent cross sections (distance dx) by an infinitesimal angle of twist d\u03d1 (Fig. 5.2b). Thereby, the angle of twist is positive if it rotates according to the right-hand rule (corkscrew rule), i.e. if we look in the direction of the positive x-axis, a positive angle of twist rotates the cross section clockwise. For small deformations the relation between the infinitesimal angle of twist d\u03d1 and the shear strain \u03b3 is (see Fig. 5.2b) r d\u03d1 = \u03b3 dx \u2192 \u03b3 = r d\u03d1 dx . (5.1) A linear distribution of the shear strain \u03b3 corresponds to a linear distribution of the shear stress \u03c4 along any radial line of the cross section. At the boundary of the cross section the radial components of the shear stresses vanish since there are no applied forces at the boundary (symmetry of the stress tensor: complementary stresses, cf. (2.3)). Therefore, the shear stresses are tangential to the outer surface and also perpendicular to any radial line on the cross section. The shear stresses acting on an element isolated from the shaft are depicted in Fig. 5.2d. Using Hooke\u2019s law \u03c4 = G\u03b3 (cf. (3.10)) and inserting (5.1) yields \u03c4 = Gr d\u03d1 dx = Gr \u03d1\u2032 , (5.2) where we have used the abbreviation \u03d1\u2032 = d\u03d1 dx . Hence, the shear stress \u03c4 varies linearly from zero at r = 0 to a maximum value at the outer surface r = R of a circular shaft (Fig. 5.2e). The torque MT must be statically equivalent to the moment resulting from the shear stresses shown in Figs. 5.2c, that is: MT = \u222b r \u03c4 dA . (5.3) The torque is positive if it points in the positive direction of the coordinate at a positive face (cf. Volume 1, Section 7.4). Inserting (5.2) into (5.3) yields MT = G\u03d1\u2032 \u222b r2 dA = G\u03d1\u2032 Ip . (5.4) The integral Ip in (5.4) is a purely geometrical quantity and is known as the polar moment of inertia, see (4.6c). In order to ensure that we use a consistent notation when dealing with arbitrary 5",
            "2 Circular Shaft 195 cross sections, we now identify this geometrical quantity as torsion constant IT (cf. Table 5.1). In the case of a circular shaft we have IT = Ip and (5.4) can be rewritten as GIT \u03d1 \u2032 = MT . (5.5) The quantity GIT is known as torsional rigidity. Given the torque MT and the torsional rigidity GIT , we can calculate the angle of twist \u03d1 from (5.5). Note that IT = Ip in the case of a non-circular cross section (see Section 5.4). Let us consider again a circular shaft which is clamped at one end and subjected to a torque Mx at the free end, see Fig. 5.2a. In each arbitrary section perpendicular to the x-axis the stress resultant is a torque MT , which is constant over the length l of the member and equal to the external moment: MT = Mx . (5.6) The total angle of twist \u03d1l at the free end in the case of constant GIT is found through integration: \u03d1l = l\u222b 0 \u03d1\u2032dx \u2192 \u03d1l = MT l GIT . (5.7) A comparison with (1.18) shows an analogy between the the tensile and the torsional member. If we eliminate \u03d1\u2032 from (5.2) with the aid of (5.5) we obtain the torsion formula which gives the distribution of the shear stress: \u03c4 = MT IT r . (5.8) The maximum value appears at the outer boundary, i.e. at r = R: \u03c4max = MT IT R , see Fig. 5.2e. In order to obtain an analogy to bending (cf. (4.28)), we introduce the so-called section modulus of torsion WT : \u03c4max = MT WT . (5.9) For the circular shaft WT = IT /R holds. Using (4.10a) we obtain IT = Ip = \u03c0 2 R4 , WT = \u03c0 2 R3 . (5.10) The formulas (5.1) to (5.9) do not only hold for solid but also for hollow circular cross sections. In this case the torsion constant IT and the section modulus of torsion WT are IT = \u03c0 2 (R4 a \u2212R4 i ) , WT = \u03c0 2 R4 a \u2212R4 i Ra , (5.11) where Ra andRi denote the outer and the inner radius, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003505_j.mechmachtheory.2016.10.006-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003505_j.mechmachtheory.2016.10.006-Figure2-1.png",
        "caption": "Fig. 2. Geometrical parameters for the fillet-foundation deflection [26].",
        "texts": [
            " The stiffness with consideration of gear fillet-foundation deflection can be calculated as per Eq. (8). \u23aa \u23aa \u23aa \u23aa \u23a7 \u23a8 \u23a9 \u239b \u239d\u239c \u239e \u23a0\u239f \u239b \u239d\u239c \u239e \u23a0\u239f \u23ab \u23ac \u23adk \u03b1 EL L u S M u S P Q \u03b11 = cos * + * + *(1 + * tan ) f m f f f f m 2 2 2 (8) where, L is the tooth width and \u03b1m is acting pressure angle of gear tooth. The coefficients L*, M*, P*, Q* can be calculated by following polynomial functions as given in Eq. (9). X h \u03b8 A \u03b8 B h C h \u03b8 D \u03b8 E h F*( , ) = / + + / + / + +i fi f i f i fi i fi f i f i fi i 2 2 (9) where Xi *denotes the coefficients L*, M*, P*, Q*; hfi=rf/rint; rf, rint and hf are described in Fig. 2, the values of Ai, Bi, Ci, Di, Ei and Fi are listed in Table 1. The description of remaining parameters of Eq. (8) is shown in Fig. 2. Thus for the single \u2013 tooth pair meshing, the total effective TVMS can be expressed as k k k k k k k k k k = 1 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/t h b s a f b s a f1 1 1 1 2 2 2 2 (10) where kh , kb , ks, ka and kf represent the Hertzian, bending, shear, axial compressive and fillet foundation deflection mesh stiffness, respectively and the subscript 1, 2 denote the pinion and gear, respectively. For the double-tooth-pair meshing duration, the total effective TVMS is the sum of the two pairs\u2019 stiffness, which can be expressed as \u2211k k k k k k k k k k = 1 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ + 1/ 1/t i h i b i s i a i f i b i s i a i f i=1 2 , 1, 1, 1, 1, 2, 2, 2, 2, (11) where i (=1, 2) represents the first pair and second pair of meshing teeth respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002706_tmag.2014.2364988-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002706_tmag.2014.2364988-Figure12-1.png",
        "caption": "Fig. 12. Flux density distribution due to armature reaction for the 12-slot/10pole three-phase machine. (a) Conventional winding. (b) Proposed winding.",
        "texts": [],
        "surrounding_texts": [
            "The performance of both machines with different winding connections is quantitatively analysed using 2D FE simulation based on JMAG-Studio10.0. Both machines are simulated as motors running at the same rated speed of 600rpm. A. Simulation Results for The Three-Phase Machine Initially, to show the effect of the proposed winding on the stator MMF distribution, the flux distribution as well as the air gap flux density distribution variation with the peripheral angle are shown in Figs. 12 and 13 respectively, with the magnets removed from the model. It is clear that the 1 st component of the air gap flux density is completely cancelled in the air gap flux density. Moreover, the magnitude of the 5 th harmonic, torque producing flux component increased by approximately 3.5%. The machine is simulated with both winding configurations under rated phase current, rated speed, and maximum load angle assumed. The simulation results are given in Fig. 14 while the main conclusions are tabulated in Table V. Based on these results, the following conclusions can be drawn:  The induced eddy losses are generally decreased, with a significant reduction in both magnet and rotor core eddy losses.  The torque density is improved by approximately 3.5%; nearly the same as the enhancement obtained in the 5 th harmonic magnitude torque producing flux component. Moreover, the torque ripple magnitude is slightly reduced.  The THDs in both phase and line voltages are reduced with a slight increase in the fundamental voltage components.  A small zero sequence component, 0.07 pu, is induced in the delta connected winding. This component will depend on the magnitude of the third order harmonic voltage component of the three-phase voltages induced in the delta winding. This will be highly dependent on the PM design and magnetization direction. A parallel magnetization is used in the design to obtain a more sinusoidal voltage waveform and hence smaller zero sequence component. It is worth noting that this component will give rise to an increase in the total stator copper loss. However, it is evident from the simulation results that this effect is neglected. Moreover, stator cooling is generally simpler than rotor cooling. 0018-9464 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. TABLE V. SIMULATION RESULTS FOR THE THREE PHASE 12-SLOT/10-POLE MACHINE Conventional winding Proposed winding Average Torque (Nm) 13.8 14.3 (3.5% increase) Torque ripples (Nm) 1.87 (13.8%) 1.54 (10.8%) Copper loss (W) 40.5 40.6 Stator core loss (W) 21.6 16.5 (24% reduction) Magnet loss (W) 5.2 2.93 (44% reduction) Rotor loss (W) 14.14 5.63 (60% reduction) Fundamental phase voltage (V) 26.9 27.33 Phase voltage THD (%) 11.59 5.11 Fundamental line voltage (V) 46.59 47.35 Line Voltage THD (%) 5.14 3.36 Phase current harmonic component in delta winding (A) No delta winding I1 = 17.3A, I3 = 1.19A (a) B. Simulation Results for The Five-phase Machine Similar to the three-phase case, the flux distribution as well as the air gap flux density distribution with the peripheral angle for the designed five-phase machines are shown in Figs. 15 and 16 respectively, with the magnets removed from the model. It is clear that the fundamental air gap flux component is completely cancelled. Moreover, the magnitude of the 9 th harmonic, torque producing flux component, increased by approximately 1%, which yields an increased torque density by the same factor. This is clearly shown from the simulation results at rated conditions given in Table VI. The simulation results for rated conditions are also plotted in Fig. 17. Based on these results the following conclusions can be drawn:  The torque gain in the five-phase machine is smaller than the three-phase case. 0 0.005 0.01 0.015 0.02 12 13 14 15 16 Time, s T o rq u e , N m Conventional winding Proposed winding 0018-9464 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.  Although the operating frequency at rated speed is 1.8 times that in the three-phase machine, the corresponding eddy losses are smaller. This is because the space harmonics are inherently reduced using a multiphase winding when compared with the three-phase case.  The reduction in eddy loss is higher in the three-phase machine than in the five-phase machine.  The magnitude of the induced zero sequence component in the pentagon connected winding is neglected, 0.004pu, and its effect on the stator copper loss is also small.  Both phase and line voltage waveforms are highly improved and the corresponding THDs are significantly reduced. 0018-9464 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information."
        ]
    },
    {
        "image_filename": "designv10_1_0000238_iros.2005.1545143-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000238_iros.2005.1545143-Figure5-1.png",
        "caption": "Fig. 5 Par4 parameters for complete singularity analysis",
        "texts": [
            " That's why, a complete kinematic analysis has been done on Par4 in order to show that this architecture overcomes drawbacks of H4 and 14 while keeping all the advantages for high speed. The method of the analysis has been introduced in [11] and [18] for 14 case. The analysis assumes that the mechanism is constituted of 2 sub-unit (actuators and traveling plate) linked by 8 rods having spherical joints. Each rod adds between those two sub-sets a pure geometrical length constraint. This complete study can be done writing equiprojectivity of speeds for the 8 rods joining the actuators to the traveling plate. It leads to the following equation: Jtp Xl Jact q (2) As shown in Fig. 5, the following parameters are introduced: - i: number of kinematic chain. i = 1,4 - j: number of rod in each kinematic chain. j = 1,2 - k: number of half traveling plate. k = 1,2 - Aij: center of spherical joints on actuated side of forearms - Bij: center of spherical joints on traveling plate side of forearms - Ai: geometrical point situated at the middle of Ai, and Ai2 - Bi: geometrical point situated at the middle of Bil and Bi2 - Cki: center of revolute joints of traveling plate - D: controlled point (located on one of the parts of traveling plate) - li: vector between Bi and Ai - f: vector between Bil and Bi2 - vki: unitary vector of collinear revolute joint axis ki - di: vector linking Cki and Bi - Ck: vector linking Cki and D - ei=Ck+ di - ki :velocity of part k respectively to parallelogram rod (in revolute joint # ki oriented by vki) - w, -Y, w: internal angular velocities -(ex"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000079_978-3-642-12886-8-Figure4.38-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000079_978-3-642-12886-8-Figure4.38-1.png",
        "caption": "Fig. 4.38",
        "texts": [
            " As can be seen by inspection of Fig. 4.37d, the shear stresses cause a resultant moment about the x-axis. This is due to the fact that the cross section is not symmetrical with respect to the zaxis. In order that the shear force V is statically equivalent to the shear stresses, i.e., that it has the same moment, its line of action has to be located to the left of the z-axis. In the present example, the resultant of the shear stresses in the upper flange is given by Pu = 1 2 ( 6 16V/t a)a t = 3 16V ; it points to the left (Fig. 4.38a). The resultant Pl = 3 16V in the lower flange has the same magnitude; it points to the right. Finally, the resultant force in the web is Pw = V . The condition of the equivalence of the moments (the lever arms can be taken from Fig. 4.38a) yields yO V = a 3 16 V + a 4 V + a 3 16 V \u2192 yO = 5 8 a. The point O on the y-axis is called the shear center. In order to prevent a torsion of the beam (see Chapter 5) the applied forces F have to act in a plane that has the distance yO from the x, zplane (Fig. 4.38b). Only then the bending moment and the shear force are in equilibrium with the applied loads and a torque is not caused by the loads. E4.12 Example 4.12 Determine the distribution of the shear stresses due to a shear force in a solid circular cross section with radius r (Fig. 4.39). z\u2217c y r z z C\u2217 \u03b1\u03b1 A\u2217 b Fig. 4.39 Solution The first moment S of the circular segment A\u2217 (shown in green) is obtained as the product of the area A\u2217 and the distance z\u2217c of its centroid C\u2217 from the y-axis (Fig. 4.39). Introducing the auxiliary angle \u03b1 we have A\u2217 = r2 2 (2\u03b1\u2212 sin 2\u03b1), z\u2217c = 4 r 3 sin3 \u03b1 2\u03b1\u2212 sin 2\u03b1 , (see Volume 1, Table 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000683_978-3-540-30738-9-Figure17.11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000683_978-3-540-30738-9-Figure17.11-1.png",
        "caption": "Fig. 17.11a,b Transfer locus diagram of an RL load: (a) serial circuit; (b) parallel circuit",
        "texts": [
            " Unsymmetrical system conditions are mainly caused by unsymmetrical shortcircuits or heavily unsymmetrical loads. The symmetrical components method is effective in short-circuit calculations of electrical machines and networks. Transfer Locus Diagram. A transfer locus for one complex surface is a geometrical area for the end points of all phasors and depends on one real parameter. which is usually the angular frequency \u03c9, but may also be the frequency of oscillation. Taking into account the circuit in Fig. 17.11a, the impedance transfer locus will be represented as Z = R + j\u03c9L . The result for the admittance Y = 1/Z is a semicircle, because Z(\u03c9) is only valid for positive imaginary values. By suitable scale fitting and fixed applied voltage V , the Y (\u03c9) locus also represent the current locus I (\u03c9). In this case the voltage drops on resistance and inductance add to the supplied voltage. The complex admittance of the circuit, which consists of the parallel connected resistance and inductance, can be seen in Fig. 17.11b. Y = 1 R + j\u03c9C (17.87) More complicated circuits naturally create more highly organized transfer locus diagrams. Oscillating Circuits and Filters Passive equivalent circuits, which consist of capacitors and inductors, are oscillatory structures. Excitation between different energy storages (capacitors and inductors) could create interchange in the form of oscillations. A circuit is resonant at a certain frequency if the reactive components of the impedance (admittance) are equal to zero. Parallel and serial resonant circuits are two of the simplest resonant circuits"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure4-2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure4-2-1.png",
        "caption": "Fig. 4-2 Current-controlled brushless dc (BLDC) motor drive.",
        "texts": [
            " 4-1a, the commutator and brushes ensure that the armature-current-produced magnetomotive force (mmf) is at a right angle to the field flux produced by the stator. Both of these fields remain stationary. The electromagnetic torque Tem developed by the motor depends linearly on the armature current ia: T k iem T a= , (4-1) where kT is the dc motor torque constant. To change Tem as a step, the armature current ia is changed (at least, attempted to be changed) as a step by the power-processing unit (PPU), as shown in Fig. 4-1b. In the brushless-dc drive shown in Fig. 4-2a, the PPU keeps the stator current space vector i ts ( ) 90\u00b0 ahead of the rotor field vector B tr ( ) EMULATION OF dc AND BRUSHLESS dc DRIVE PERFORMANCE 61 (produced by the permanent magnets on the rotor) in the direction of rotation. The position \u03b8m(t) of the rotor field is measured by means of a sensor, for example, a resolver. The torque Tem depends on \u00ces, the amplitude of the stator current space vector i ts( ): T k Iem T s= \u02c6 , (4-2) where kT is the brushless dc motor torque constant. To produce a step change in torque, the PPU changes the amplitude \u00ces in Fig. 4-2b by appropriately changing ia(t), ib(t), and ic(t), keeping i ts ( ) always ahead of B tr ( ) by 90\u00b0 in the direction of rotation. 4-2-1 Vector Control of Induction-Motor Drives We will look at one of many ways in which an induction motor drive can emulate the performance of dc and brushless dc motor drives. Based on the steady state analysis in Reference [1], we observed that in an induction machine, F tr( ) and \u2032F tr( ) space vectors are naturally at 90\u00b0 to the rotor flux-density space vector B tr( ), as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.39-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.39-1.png",
        "caption": "FIGURE 5.39. A spherical arm.",
        "texts": [
            "137) to find Twrist = 3T6 (5.138) = \u23a1\u23a2\u23a2\u23a3 \u2212s\u03b84s\u03b86 + c\u03b84c\u03b85c\u03b86 \u2212c\u03b86s\u03b84 \u2212 c\u03b84c\u03b85s\u03b86 c\u03b84s\u03b85 0 c\u03b84s\u03b86 + c\u03b85c\u03b86s\u03b84 c\u03b84c\u03b86 \u2212 c\u03b85s\u03b84s\u03b86 s\u03b84s\u03b85 0 \u2212c\u03b86s\u03b85 s\u03b85s\u03b86 c\u03b85 l3 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . The rest position of the robot can be checked to be at 0T7 = \u23a1\u23a2\u23a2\u23a3 1 0 0 l2 0 1 0 d2 + l3 0 0 1 d1 + d7 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.139) because 6T7 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d7 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (5.140) Example 167 A spherical manipulator. The spherical manipulator simulates the spherical coordinate for positioning a point in a 3D space. Figure 5.39 illustrates a spherical manipulator. The coordinate frame B0 is the global or base frame of the manipulator. The link (1) can turn about z0 and the link (2) can turn about z1 that is perpendicular to z0. These two rotations simulate the two angular motions of spherical coordinates. The radial coordinate is simulated by link (3) that has a prismatic joint with link (2). There is also a takht coordinate frame at the tip point of link (3) at which a wrist can be attached. 5. Forward Kinematics 285 The link (1) in Figure 5.39 is an R`R(90), link (2) is also an R`P(90), and link (3) is an PkR(0), therefore, 0T1 = \u23a1\u23a2\u23a2\u23a3 cos \u03b81 0 sin \u03b81 0 sin \u03b81 0 \u2212 cos \u03b81 0 0 1 0 d1 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.141) 1T2 = \u23a1\u23a2\u23a2\u23a3 cos \u03b82 0 sin \u03b82 0 sin \u03b82 0 \u2212 cos \u03b82 0 0 1 0 0 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.142) 2T3 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d3 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 . (5.143) The transformation matrix from B3 to the takht frame B4 is only a translation d4. 3T4 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d4 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 (5.144) 286 5. Forward Kinematics x0 z0 z1 2\u03b8 x1 1\u03b8 z2 x2 x3 z3 x4 d4 B0 B1 z4 B2 B3 B4 d1 d3 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure3-9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure3-9-1.png",
        "caption": "Fig. 3-9 Torque on the rotor q-axis.",
        "texts": [
            " Substituting for B\u0302rq from Eq. (3-40) into Eq. (3-41), T p r N p i L L id g s sq r m r, / rotor =             + 2 3 20 2 \u03c0 \u00b5 q rdi       . (3-42) Rewriting Eq. (3-42) below, we can recognize Lm from Eq. (2-13) T p r N p d g s Lm ,rotor =            2 3 2 0 2 \u03c0 \u00b5 i L L i isq r m rq rd+       . Hence, T p L i L i i p id m sq r rq rd rq rd rq , ( ) .rotor = + = 2 2 \u03bb \u03bb (3-43) 3-5-2 Torque on the Rotor q-Axis Winding On the rotor q-axis winding, the torque produced is due to the flux density produced by the d-axis windings in Fig. 3-9. This torque on the rotor is clockwise (CW), hence we will consider it as negative. The derivation similar to that of the torque expression on the rotor d-axis winding results in the following torque expression on the q-axis rotor winding: T p L i L i i p iq m sd r rd rq rd rq rd , ( ) .rotor = \u2212 + = \u2212 2 2 \u03bb \u03bb (3-44) 44 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS 3-5-3 Net Electromagnetic Torque Tem on the Rotor By superposition, adding the torques acting on the d-axis and the q-axis of the rotor windings, the instantaneous torque is T T Tem d q= +, , ,rotor rotor (3-45) which, using Eq",
            " PROBLEMS 57 PROBLEMS 3-1 Derive that each of the two windings with 3 2/ Ns turns in an equivalent two-phase machine has the magnetizing inductance of Lm, leakage inductance of L\u2113s, and the resistance Rs, where these quantities correspond to those of an equivalent threephase machine. 3-2 Show that the instantaneous power loss in the stator resistances is the same in the three-phase machine as in an equivalent twophase machine. 3-3 Show that the instantaneous total input power is the same in a-b-c and in the dq circuits. 3-4 Rederive all the equations used in obtaining the torque expressions of Eq. (3-46) and Eq. (3-47) for a p-pole machine from energy considerations. 3-5 Draw dynamic equivalent circuits of Fig. 3-9 for the following values of the dq winding speed \u03c9d: 0 and \u03c9m. What is the frequency of dq winding variables in a balanced sinusoidal steady state, including the condition that \u03c9d\u00a0=\u00a0\u03c9syn? 3-6 The \u201ctest\u201d motor described in Chapter 1 is operating at its rated conditions. Calculate \u03bdsd(t) and \u03bdsq(t) as functions of time, (a) if \u03c9d\u00a0=\u00a0\u03c9syn, and (b) if \u03c9d\u00a0=\u00a00. 3-7 Under a balanced sinusoidal steady state, calculate the input power factor of operation based on the d- and the q-axis equivalent circuits of Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001209_tmag.2010.2040144-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001209_tmag.2010.2040144-Figure1-1.png",
        "caption": "Fig. 1. Proposed novel magnetic navigation system.",
        "texts": [
            " experimentally demonstrated that a MNS with one pair of Helmholtz and Maxwell coils can generate the plane motion of a micro-robot by mechanically rotating the MNS [5]. Choi et al. showed that a MNS with two stationary pairs of Maxwell and Helmholtz coils can manipulate a micro-robot in a plane [6]. However, this system suffers from the geometrical weakness such that the radius of one pair should be at least twice as large as that of the other pair. This increases the amount of space required by the MNS, and requires a great amount of electrical power to generate an effective magnetic field. This research proposes a novel MNS shown in Fig. 1, composed of one conventional pair of Maxwell and Helmholtz coils Manuscript received October 31, 2009; accepted January 02, 2010. Current version published May 19, 2010. Corresponding author: G. H. Jang (e-mail: ghjang@hanyang.ac.kr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2010.2040144 and one newly developed pair of gradient and uniform saddle coils. It determines the relationships of the currents in each coil to generate the magnetic force and torque",
            " Magnetic forces and torques applied to a micro-robot composed of permanent magnetic material in a magnetic field can be expressed by the following equations: (1) (2) where , , , and are the magnetic permeability of free space, the volume, the magnetization of a micro-robot, and the magnetic field intensity, respectively. The magnetic force is proportional to the magnetic field gradient and the magnetic torque is proportional to the magnetic field intensity. A Maxwell coil is composed of two identical coils separated by the distance of times the coil radius. The currents in the 0018-9464/$26.00 \u00a9 2010 IEEE coils flow in opposite directions. The magnetic field induced from a current source can be determined by the Biot-Savart\u2019s law, and the magnetic field near the center of the Maxwell coil shown in Fig. 1 can be expressed as follows [6]: (3) (4) where and are the current and radius of the Maxwell coil, respectively. Equation (3) shows that the Maxwell coil generates the largest uniform magnetic field gradient along the -axis. From (1), the Maxwell coil can generate uniform magnetic force to propel a micro-robot if a micro-robot is located near the center of the coil and if the magnetization direction of the micro-robot is aligned along the -axis. The magnetic field near the center of the Helmholtz coil in Fig. 1 can be expressed as follows [6]: (5) (6) where and are the current and radius of the Helmholtz coil, respectively. Since the Helmholtz coil generates a uniform magnetic field intensity along the -axis, the Helmholtz coil can generate uniform magnetic torque to align a micro-robot located near the center of the coil along the -axis. This research develops saddle-shaped coils referred to as gradient and uniform saddle coils as shown in Fig. 1. Since each coil is intended to replace the -directional Maxwell and Helmholtz coils of the conventional MNS in [6], they should generate a uniform magnetic field gradient and intensity along the -direction, respectively. They are composed of the straight and arc coils as shown in Fig. 2(a) and (b), and the magnetic fields can be determined by the summation of each straight and arc coils. The magnetic fields of general straight and arc coils along the -axis in Fig. 2 can be expressed as follows: (7) (8) where , , , , , , , , and are , the length of the straight coil, the distance between the straight coils located along the -axis, the distance between the straight coils located along the -axis, the radius of the arc coil, and the starting and ending angles of the upper and lower arc coils, respectively",
            " The uniform saddle coil, in which the currents in the upper and lower coils flow in the same direction should satisfy the following conditions: (12) The second condition of (12) provides the relationship between and . Fig. 4 shows the geometrical relationship of the uniform saddle coil and the magnetic field distribution in the -plane. The linearized magnetic field of the gradient saddle coil near the center can be expressed as follows: (13) (14) where and are the current and radius of the uniform saddle coil, respectively. This research utilizes one pair of Maxwell and Helmholtz coils and one pair of gradient and uniform saddle coils to develop the proposed MNS as shown in Fig. 1. The magnetic field near the center of the MNS can be expressed as follows: (15) Since the uniform magnetic field exists only in the -plane, the micro-robot can be aligned within the -plane. Assuming that the micro-robot is initially positioned along the line with an angle of from the -axis, the micro-robot is to be aligned to an angle of . With (6) and (14), the condition of a uniform magnetic field along the direction produces the following relationships of the currents between the uniform saddle coil and Helmholtz coil, and the magnetic torque: (16) (17) Once the torque aligns the micro-robot along the direction, the micro-robot can be propelled by the magnetic force which is generated along that direction",
            " In the conventional MNS, the radius of the Helmholtz coil in the -axis should theoretically be at least two times larger than the radius of the Helmholtz coil in the -axis because of the geometrical constraint of the Helmholtz coil. This geometrical restriction in the conventional MNS makes the construction ineffectively large. On the other hand, the proposed MNS theoretically uses the same radius for the Maxwell coil, Helmholtz coil, gradient saddle coil, and uniform saddle coil so that the overall structure is compact and suitable for a patient to lie down along the MNS as shown in Fig. 1. The magnetic torque to align the micro-robot from 0 to 30 and the magnetic force to propel it along 30 were theoretically examined, considering the same effective region in the conventional and the proposed MNS. Table II shows that the proposed MNS generates a 12.8% larger magnetic force than the conventional one even though the applied current to the gradient saddle coil is 78.7% smaller than that applied to the Maxwell coil of the conventional MNS. And Table III shows that the applied current to the uniform saddle coil is 30"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002353_j.jmatprotec.2017.07.023-Figure12-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002353_j.jmatprotec.2017.07.023-Figure12-1.png",
        "caption": "Fig. 12. The schematic diagram showing the extraction of tensile and impact toughness specimens.",
        "texts": [
            " Hence, the HDMR process provides a novel way for the full transformation of columnar dendrites to equiaxed grains in the production of multi-pass multi-layer samples, as seen in Fig. 11(b). The hot deformation can also weaken the degree of the crater collapse without the arc stopping control. To assess the mechanical properties such as strength, plasticity and toughness of WAAM and HDMR samples, the tensile and impact toughness measurements have been conducted. Six tensile specimens and three impact toughness specimens were measured in each direction, and they were extracted from the block using the arrangement shown in Fig. 12. The tensile specimens have a rectangle shape with a gauge length of 10 mm and a 2.2 mm\u00d7 1.2 mm cross section as shown in Fig. 13, which were measured on the AG\u2013100 kN electronic universal testing machine with a 0.5 mm/min stretching rate at room temperature. The tensile and impact toughness measurement results are presented in Fig. 14, with the error bars to show the standard deviation. It can be seen that the average tensile strength/elongation of the WAAM samples are 1258 MPa/11.0 pct, 1019 MPa/4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure2.10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure2.10-1.png",
        "caption": "Fig. 2.10 Free rolling: T = 0 and Fxh = Fzex",
        "texts": [
            " However, it is more common to assume that five parameters suffice, like in (2.22) (as already discussed, it is less general, but simpler) F\u0303x ( h,\u03b3, Vox \u03c9c , Voy \u03c9c , \u03a9z \u03c9c ) = 0 (2.26) F\u0303y ( h,\u03b3, Vox \u03c9c , Voy \u03c9c , \u03a9z \u03c9c ) = 0 (2.27) M\u0303z ( h,\u03b3, Vox \u03c9c , Voy \u03c9c , \u03a9z \u03c9c ) = 0 (2.28) It is worth noting that pure rolling and free rolling are not the same concept [14, p. 65]. They provide different ways to balance the rolling resistance moment My = \u2212Fzex . According to (2.12), we have pure rolling if Fx = 0 (Fig. 2.9), while free rolling means T = 0 (Fig. 2.10). However, the ratio f = ex/h, called the rolling resistance coefficient, is typically less than 0.015 for car tires and hence there is not much quantitative difference between pure and free rolling. First, let us consider Eq. (2.26) alone F\u0303x ( h,\u03b3, Vox \u03c9c , Voy \u03c9c , \u03a9z \u03c9c ) = 0 (2.29) 7We have basically a steady-state behavior even if the operating conditions do not change \u201ctoo fast\u201d. 2.6 Tire Global Mechanical Behavior 23 which means that Fx = 0 if Vox \u03c9c = fx ( h,\u03b3, Voy \u03c9c , \u03a9z \u03c9c ) (2.30) Under many circumstances there is experimental evidence that the relation above almost does not depend on Voy and can be recast in the following more explicit form8 Vox \u03c9c = rr (h, \u03b3 ) + \u03c9z \u03c9c cr(h, \u03b3 ) (2",
            " Of course there are high peaks near the tread edges. A very simple pressure distribution p(x\u0302, y\u0302) on the contact patch P , which roughly mimics the experimental results, may be parabolic along x\u0302 p = p(x\u0302, y\u0302) = p0(y\u0302) (x\u03020(y\u0302) \u2212 x\u0302)(x\u03020(y\u0302) + x\u0302) x\u03020(y\u0302)2 (10.12) where p0(y\u0302) = p(0, y\u0302) is the pressure peak value. The corresponding vertical load is given by Fz = \u222b b \u2212b dy\u0302 \u222b x\u03020(y\u0302) \u2212x\u03020(y\u0302) p(x\u0302, y\u0302)dx\u0302 (10.13) Other pressure distributions may be used as well in the brush model, including nonsymmetric ones like in Fig. 2.10 to include the rolling resistance. On a rectangular contact patch x\u03020(y\u0302) = a. Equation (10.12), with uniform p0, becomes simply p = p(x\u0302, y\u0302) = p0 [ 1 \u2212 ( x\u0302 a )2] (10.14) and hence Fz = \u222b b \u2212b dy\u0302 \u222b a \u2212a p(x\u0302, y\u0302)dx\u0302 = 2 3 p02a2b (10.15) which yields p0 = 3 2 Fz (2a)(2b) (10.16) On an elliptical contact patch (10.12) and (10.2) provide p = p(x\u0302, y\u0302) = p0 [ 1 \u2212 x\u03022 a2(1 \u2212 y2 b2 ) ] (10.17) again with the same peak value p0 for any y. 10.1 Brush Model Definition 297 Let V\u03bc = |V\u03bc| be the magnitude of the sliding velocity V\u03bc, that is the velocity of the bristle tip with respect to the road, and \u03bc the local friction coefficient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000726_j.mechmachtheory.2008.05.008-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000726_j.mechmachtheory.2008.05.008-Figure1-1.png",
        "caption": "Fig. 1. Physical and dynamic models of the two-stage spur gear system studied.",
        "texts": [
            " The main objective of this paper is to (1) develop an analytical model for the two-stage spurs gears system that incorporates the deformability of the essential bodies such as the teeth, the shafts and the bearings, (2) modelize backlash nonlinearity between teeth, thanks to the elastic gear load discontinuous function, (3) and study the nonlinear dynamic behaviour of the system. Gearing systems used in the industrial sectors (automobile, machines and helicopters) are composed of two or several stages to ensure a minimal reduction ratio and a maximal receiving torque [9]. In this paper, the nonlinear dynamic model of the two-stage gears reducer takes account of the teeth deformability and the nonlinear character coming from the phenomenon of loss of teeth contact which appears during working. The dynamic model and the associated physical model are represented on Fig. 1. Gears are modelled by concentrated masses, because each gear is supposed rigid except punctually on the level of the teeth [6,7]. Bearings are modelled by linear springs in the gears plans. Shafts are supposed flexible with neglected masses. The generalized co-ordinates vector of the nonlinear dynamic model includes 12 degrees of freedom and can be defined by fqg \u00bc \u00bdx1; y1; x2; y2; x3; y3; hm; h1; h2; h3; h4; hr T \u00f01\u00de where xj and yj are the bearings displacements, hi (i = 1, . . .,4) are the dynamic angular displacements the of the gears, hm and hr are dynamic angular displacements of motor and brake"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000916_70.97871-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000916_70.97871-Figure4-1.png",
        "caption": "Fig. 4. A 3-DOF planar manipulator with a fixed point contact to ground.",
        "texts": [
            " We now discuss two additional singularities in the closedloop calibration procedure to the three singularities in the open-loop procedure that also apply here. Singularity 4: Inherent Singu larities in the Mechanism: Certain mechanisms have particular symmetries that allow the kinematics to be described in less than four parameters per joint. It is difficult to provide a general rule for when this will happen, but it is usually restricted to mechanisms of mobility one. A simple example is a 3-DOF planar manipulator that makes a point contact with the ground (Fig. 4). If the resulting closed-loop, four-bar linkage happens to be a parallelogram, then the opposite x axes are always parallel: x2 + x4 = 0. (24) This satisfies the condition (23), and thus the lengths of the opposite sides, a2 and a4, are not identifiable (except as a sum). Clearly, this problem may be eliminated by having the manipulator change its endpoint location so that a parallelogram is not formed. Singularity 5: Structural Immobility: If a particular joint j is immobile, then two consecutive joint coordinates are fixed relative to one another"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001867_j.measurement.2012.08.012-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001867_j.measurement.2012.08.012-Figure1-1.png",
        "caption": "Fig. 1. Test rig for bearing defect identification. Inset shows the enlarged view at different angle for mounting of accelerometer at the bearing housing.",
        "texts": [
            " The size of defect present on bearing race can be calculated with the knowledge of vibration burst duration Dt which is estimated using Symlet based decomposition, fundamental train frequency (FTF) and average outer race inner diameter (tapered one) DOI of the bearing. The outer race defect width Lod is [13] Lod \u00bc p Dt DOI FTF \u00f04\u00de For the bearing NBC 30205 at inner race rpm 2050, the FTF is 14.316. Putting the given geometric parameter and value of FTF for the bearing, Eq. (4) is simplified as Lod \u00bc 1993:61 Dt mm \u00f0where Dt is in seconds\u00de \u00f05\u00de Experiments were performed on a customized test rig shown in Fig. 1. The shaft in the test rig is supported by two self aligned taper roller bearings (Make: NBC, Bearing number: 30205). The shaft is driven by an alternating current motor of 0.75 kW capacity (Make: Crompton, frequency 50 Hz, current 4.2 amp and speed 1440 rpm) with the help of V-belt and step pulley arrangement. This arrangement provides option of three different speeds of 1050 rpm, 2050 rpm and 3080 rpm approximately to the test rig shaft. During each experiment speed of the shaft is measured using an optical tachometer with digital display. The condition of the bearing mounted towards loading arrangement side as shown in Fig. 1 is monitored using a PCB make uni-axial accelerometer having sensitivity 1000 mV/g. Bearing under test is placed at this position only. The accelerometer is placed right above the bearing casing perpendicular to the axis of the rotation of the shaft in such a way so that it can acquire vertical acceleration. A personal computer based data acquisition system (Make: National Instrument, Model: SCXI-1000 having 4 channel input) is used to acquire the vibration data obtained from accelerometer. A program has been developed in Labview environment to acquire and display the signal along with its Fourier Transform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001978_9781119401087-Figure2.18-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001978_9781119401087-Figure2.18-1.png",
        "caption": "Fig. 2.18 Sketches of rotor flapping and pitch: (a) rotor flapping in vacuum; (b) gyroscopic moments in vacuum; (c) rotor coning in air; (d) before shaft tilt; (e) after shaft tilt showing effective cyclic path",
        "texts": [
            " The reader of this Tour may feel too quickly plunged into abstraction with the above equations and their descriptions; the intention is to give some exposure to mathematical concepts that are part of the toolkit of the flight dynamicist. Fluency in the parlance of this mathematics is essential for the serious practitioner. Perhaps even more essential is a thorough understanding of the fundamentals of rotor flapping behaviour, which is the next stop on this Tour; here we shall need to rely extensively on theoretical analysis. A full derivation of the results will be given later in Chapters 3\u20135. The equations of motion of a flapping articulated rotor will be developed in a series of steps (Figure 2.18a\u2013e), designed to highlight several key features of rotor behaviour. Figure 2.18a shows a rotating blade (\u03a9, rad/s) free to flap (\ud835\udefd, rad) about a hinge at the centre of rotation; to add some generality we shall add a flapping spring at the hinge (K\ud835\udefd , Nm/rad). The flapping angle \ud835\udefd is referred to the rotor shaft; other reference systems, e.g. relative to the control axis, are discussed in Appendix 3A. It will be shown later in Chapter 3 that 26 Helicopter and Tiltrotor Flight Dynamics this simple centre-spring representation is quite adequate for describing the flapping behaviour of teetering, articulated, and hingeless or bearingless rotors, under a wide range of conditions",
            " Typically, the stiffness of a hingeless rotor blade can be represented by a spring giving an equivalent \ud835\udf062 \ud835\udefd of between 1.1 and 1.3. The higher values are typical of the first generation of hingeless rotor helicopters, e.g. Lynx and Bo105, the lower more typical of modern bearingless designs. The overall stiffness is therefore dominated by the centrifugal force field. Before including the effects of blade aerodynamics, we consider the case where the shaft is rotated in pitch and roll, p and q (see Figure 2.18b). The blade now experiences additional gyroscopic accelerations caused by mutually perpendicular angular velocities, p, q, and \u03a9. If we neglect the small effects of shaft angular accelerations, the equation of motion can be written as \ud835\udefd\u2032\u2032 + \ud835\udf062 \ud835\udefd \ud835\udefd = 2 \u03a9 (p cos\ud835\udf13 \u2212 q sin\ud835\udf13) (2.9) The conventional zero reference for blade azimuth is at the rear of the disc and \ud835\udf13 is positive in the direction of rotor rotation; in Eq. (2.9) the rotor is rotating anticlockwise when viewed from above. For clockwise rotors, the roll rate term would be negative",
            " Unless the initial conditions of the blade motion were very carefully set up, the response would actually be the sum of two undamped motions, one with the one-per-rev forcing frequency and the other with the natural frequency \ud835\udf06\ud835\udefd . A complex response would develop, with the combination of two close frequencies leading to a beating response or, in special cases, nonperiodic chaotic behaviour. Such situations are somewhat academic for the helicopter, as the aerodynamic forces distort the response described above in a dramatic way. Figure 2.18c shows the blade in air, with the distributed aerodynamic lift \ud835\udcc1(r,\ud835\udf13) acting normal to the resultant velocity; we are neglecting the drag forces in this case. If the shaft is now tilted to a new reference position, the blades will realign with the shaft, even with zero spring stiffness. Figure 2.18d,e illustrates what happens. When the shaft is tilted, say, in pitch by angle \ud835\udf03s, the blades experience an effective cyclic pitch change with maximum and minimum at the lateral positions (\ud835\udf13 = 90\u2218 and 180\u2218). The blades will then flap to restore the zero hub moment condition. For small flap angles, the equation of flap motion can now be written in the approximate form \ud835\udefd\u2032\u2032 + \ud835\udf062 \ud835\udefd \ud835\udefd = 2 \u03a9 (p cos\ud835\udf13 \u2212 q sin\ud835\udf13) + 1 I\ud835\udefd\u03a92 R \u222b 0 \ud835\udcc1(r, \ud835\udf13)rdr (2.16) \ud835\udcc1(r, \ud835\udf13) = 1 2 \ud835\udf0cV2ca0\ud835\udefc (2.17) where V is the resultant velocity of the airflow, \ud835\udf0c the air density, and c the blade chord"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001404_j.engfailanal.2013.08.008-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001404_j.engfailanal.2013.08.008-Figure3-1.png",
        "caption": "Fig. 3. Geometrical parameters for fillet foundation deflection [1].",
        "texts": [
            " Therefore, to apply method 1 on our model, qo will be equal to q2, which means that qz is constant and equal to qo. Sainsot et al. [29] studied the effect of fillet foundation deflection on the gear mesh stiffness, derived this deflection, and applied it for a gear body. The fillet foundation deflection can be calculated as follows [29]: df \u00bc F: cos2\u00f0am\u00de W:E L uf Sf 2 \u00feM uf Sf \u00fe P \u00f01\u00fe Q tan2\u00f0am\u00de\u00de ( ) \u00f014\u00de where the following notation is used: am is the pressure angle, uf and Sf are illustrated in Fig. 3, L\u2044, M\u2044, P\u2044, and Q\u2044 can be approximated using polynomial functions as follows [29]: X i \u00f0hfi; hf \u00de \u00bc Ai=h 2 f \u00fe Bih 2 fi \u00fe Cihfi=hf \u00fe Di=hf \u00fe Eihf \u00fe Fi \u00f015\u00de X i represents the coefficients L\u2044, M\u2044, P\u2044, and Q\u2044. hfi \u00bc rf =rint: rf, rint, and hf are illustrated in Fig. 3. The coefficients Ai, Bi, Ci, Di, Ei and Fi are given in Table 1. Then the stiffness due to fillet foundation deflection can be obtained as: 1 Kf \u00bc df F For a pinion it can be denoted byKfp: \u00f016\u00de Yang and Sun [28] ascertained that the stiffness of the Hertzian contact of two gears in mesh is constant during the whole contact period, and therefore has the same value at all the contact positions along the path of contact. The Hertzian contact stiffness Kh can be calculated as stated in Eq. (3). After calculating the stiffness of a cracked pinion tooth, Ktp, due to bending, shear, and axial compression, and then calculating the stiffness due to the fillet foundation deflection, Kfp, the same calculations can be performed for an uncracked mating gear tooth to find Ktg and Kfg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002785_s11012-017-0746-6-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002785_s11012-017-0746-6-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the tooth slice",
        "texts": [
            " Taking the exact involute and transition curves into consideration, the TVMS calculation accuracy for each slice gear pairs is improved. In order to extend the scope of application of the model and improve the calculation accuracy, the effects of the fillet-foundation correction coefficient, the nonlinear Hertzian contact, the effective elastic modulus, the friction between teeth faces and addendum modification on TVMS are also involved in the proposed method. 2.1 TVMS of spur gear slices The schematic of the tooth slice is shown in Fig. 1 where the tooth is divided into N independent slices along the tooth width. As for each thin gear slice (see Fig. 1), it can be regarded as a spur gear and TVMS of the nth thin gear slice can be calculated by: \u00f0kn\u00dej \u00bc 1 , 1 \u00f0k1k n f1\u00dej \u00fe 1 \u00f0kntooth\u00dej \u00fe 1 \u00f0k2k n f2\u00dej ! ; \u00f01\u00de where kf1 and kf2 are the fillet-foundation stiffness of the driving and driven gears; n denotes the nth thin gear slice; j denotes the meshing position; k1 and k2 are the coefficients of the fillet-foundation stiffness of the driving gear and the driven gear, and they can be determined by the method in Ref. [32]. The mesh stiffness of m tooth pairs ktooth can be given as: kntooth j \u00bc Xm i\u00bc1 kitooth; kitooth \u00bc 1 , 1 \u00f0knhi\u00dej \u00fe 1 \u00f0knt1\u00dej \u00fe 1 \u00f0knt2\u00dej ",
            " (an)j is the pressure angle of the nth gear slice at meshing position j and it can be written as: \u00f0an\u00dej \u00bc arctan\u00f0\u00f0sn1;i\u00dej \u00fe hb1\u00de; \u00f07\u00de where n is the nth slice, \u00f0sn1;i\u00dej is the operating pressure angle of the ith meshing tooth pair of the nth thin slice at meshing position j and subscript 1 denotes the driving gear, hb1 is the half tooth angle corresponding to base circle of the driving gear, where Z1 denotes tooth number of the driving gear, and at is transverse pressure angle. Different from the meshing characteristics of spur gear pairs, the contact line of the helical gear changes at different moments and the number of contact slices changes at the same time. The operating pressure angle of the nth gear slice at meshing position j located at the driving gear can be written as: \u00f0sn1;i\u00dej \u00bc umin \u00fe \u00f0n 1\u00de 2p Z1 \u00fe \u00f0zni \u00dej tan bb rb1 ; \u00f08\u00de where (zi n)j is z coordinate value of the nth slice center (see Fig. 1), umin is the minimum rolling angle, which can be obtained by: umin \u00bc tan\u00f0amin\u00de L 2 tan\u00f0bb\u00de rb1 ; \u00f09\u00de where bb is the helix angle of the base circle, and rb1 is the radius corresponding to base circle of the driving gear. TVMS calculation schematic of helical gear pairs is displayed in Fig. 2. 2.3 Mean mesh stiffness calculation using ISO standard Based on the ISO standard (ISO 6336-1), the mean mesh stiffness of the gear pair cc is given as follow: cc \u00bc \u00f00:75ea \u00fe 0:25\u00dec0; \u00f010\u00de where ea is the transverse contact ratio, and c\u2019 is the mesh stiffness of single tooth pair: c0 \u00bc c0thCMCRCB cos b; \u00f011\u00de where CM = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure7.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure7.4-1.png",
        "caption": "FIGURE 7.4. A body coordinate frame moving with a fixed point in the global coordinate frame.",
        "texts": [
            " Angular Velocity Using this definition, the acceleration of a fixed body point in the global frame is GaP = Gd dt \u00a1 G\u03c9B \u00d7 GrP \u00a2 = G\u03b1B \u00d7 GrP + G\u03c9B \u00d7 (G\u03c9B \u00d7 GrP ). (7.157) Example 216 F Alternative definition of angular velocity vector. The angular velocity vector of a rigid body B(\u0302\u0131, j\u0302, k\u0302) in global frame G(I\u0302 , J\u0302 , K\u0302) can also be defined by B G\u03c9B = \u0131\u0302( Gdj\u0302 dt \u00b7 k\u0302) + j\u0302( Gdk\u0302 dt \u00b7 \u0131\u0302) + k\u0302( Gd\u0131\u0302 dt \u00b7 j\u0302). (7.158) Proof. Consider a body coordinate frame B moving with a fixed point in the global coordinate frame G. The fixed point of the body is taken as the origin of both coordinate frames, as shown in Figure 7.4. In order to describe the motion of the body, it is sufficient to describe the motion of the local unit vectors \u0131\u0302, j\u0302, k\u0302 . Let rP be the position vector of a body point P . Then, BrP is a vector with constant components. BrP = x\u0131\u0302+ yj\u0302+ zk\u0302 (7.159) When the body moves, it is only the unit vectors \u0131\u0302, j\u0302, and k\u0302 that vary relative to the global coordinate frame. Therefore, the vector of differential displacement is drP = x d\u0131\u0302+ y dj\u0302+ z dk\u0302 (7.160) which can also be expressed by drP = (drP \u00b7 \u0131\u0302) \u0131\u0302+ (drP \u00b7 j\u0302) j\u0302+ \u00b3 drP \u00b7 k\u0302 \u00b4 k\u0302"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002137_j.mechmachtheory.2015.03.013-Figure4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002137_j.mechmachtheory.2015.03.013-Figure4-1.png",
        "caption": "Fig. 4. The scheme of data acquisition (a) the fault simulator and sensor installation; (b) the structure of the two-stage gear in the gearbox; (c) the miss tooth gear; (d) the chip tooth gear; and (e) the normal gear.",
        "texts": [
            " Calculating the average fitness of bee populations, if the following condition ismet, then stop iterating and return the best bee which has the maximum fitness, otherwise, go to step 4. Error \u00bc avefitnessi\u2212avefitnessi\u22121j jb\u03b5 \u00f019\u00de where, avefitness is the average fitness of bee populations, the index i is the ith iteration. The gear vibration experiments were performed onmachinery fault simulator whichwasmade by SpectraQuest, Inc. of USA. Eight acceleration sensors were installed, and were labeled s1\u2013s8, as shown in Fig. 4(a), the position of s1 is located on the back side of the gear box and correspondingwith the position of the arrow, the positions of s6 and s8were correspondingwith s5 and s7 on the back of the gearbox. In the experiment, a variable speed motor drives a shaft directly, and the shaft drives the gear by two pulleys, the transmission ratio is 0.24. The gearbox used for the experiments is a two-stage parallel shaft gearbox, which consists of two pairs of spur gears, input shaft, intermediate shaft, output shaft and amagnetic brake, the four standard spur gears were labeled g1, g2, g3, g4, and g1 was the fault gear, which can be replaced by different fault gear. The numbers of teeth of four gears are 32, 96, 80, 42 respectively, as shown in Fig. 4(b). In the gearbox, some parts of the gears are soaked in lubricants. The test rig is equipped with a variety of typical gear fault components, such as the miss tooth gear, the chip tooth gear and the normal gear, as shown in Fig. 4(c) to (e). Setting the sampling frequency Fs= 20000Hz, the rotation speed of themotor is 1500 rpm, so the rotation speed of the input shaft is 360 rpm, the mesh frequency of g1 and g2 is 192 Hz, meanwhile, the mesh frequency of g3 and g4 is 160 Hz. The experiment collected three kinds of fault gear vibration data, the waveform and the FFT spectrum of s3 are shown in Fig. 5 to Fig. 7. It can be seen from Fig. 5 to Fig. 7 that the signals of the fault gears are greatly nonlinear and non-stationary, it is difficult to identify the fault type fromwaveform or FFT spectrum directly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003065_j.surfcoat.2018.10.099-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003065_j.surfcoat.2018.10.099-Figure7-1.png",
        "caption": "Fig. 7. Finite element mesh division of the laser cladding.",
        "texts": [
            " Establishment and property setting of the finite element model The substrate is ASTM 1045, and the cladding powder is Fe60 powder. Using the COMSOL Multiphysics software platform, the coupled thermo-elastic-plastic-flow multi-physics field finite element model for the laser cladding process is established. Considering the right to left symmetry of the cladding workpiece, a 1/2 model is constructed sized 20\u00d7 10\u00d76mm. The model uses free tetrahedra to divide a grid to open the grid automatic encryption function, including 315,988 domain units, 11,324 boundary elements and 360 edge units, as shown in Fig. 7. In the calculation, thermal stress, laminar flow, a two phase flow level set and a thin material transfer module are used to calculate the multi-physics field coupling changes in the temperature field and the flow field during the laser cladding process, and the dynamic shape change of the melt pool surface is described by a dynamic grid based on an arbitrary Lagrangian\u2013Eulerian method (ALE). The model properties are selected as shown in Table 3. The initial temperature of the system is ambient temperature, and the initial velocity of the melt pool is 0 m/s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002058_0022-2569(68)90016-5-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002058_0022-2569(68)90016-5-Figure2-1.png",
        "caption": "Figure 2. Six-bar linkage formed from two Bennett linkages, a sin/7= b sin 0~ and d sin s= e sin &",
        "texts": [
            " Now, as is shown in reference (5), four parallel screw pairs will, in general, define a screw system which contains all screws, whatever their pitches, parallel to the given screws. Thus the ESS of the six-bar cannot have order greater than four. Since the ESS's of the four-bars were both of order 3, the order of their intersection is at least two, as is the mobility of the six-bar. Many of the overconstrained six-bars given in the table do not appear to have been noticed before. One of these is a combination of two Bennett linkages which is shown in Fig. 2. Several of the other linkages are in common use. In some of those cases in which screw pairs are present, they may be replaced by revolutes without increasing the mobility of the linkage. Most of these are among the linkages discussed in references [9] and [5], as are many of the other linkages. It should also be noted that in none of these cases does the elimination of a screw pair with pitch other than zero or infinity result in a linkage with mobility one. Thus six-bars with fixed relative axes of pitch other than zero or infinity can only be formed by combination of a three-bar with a five-bar",
            " The Sarrus linkage, a special case [5, 6, 9] of the linkage obtained by elimination of the prismatic joints of two screw slider cranks, is used in this manner. The double Hooke's joint [6], which is obtained from two spherical four-bars having different centers, is very widely used as a transmission coupling. This is because of its constant velocity characteristics in certain configurations. However, none of the other linkages would seem to be suited to this function unless a non-steady output is required. The linkage of Fig. 2 does have constant velocity configurations. Acknowledgment Theauthor wishesto acknowledgethe financial assistanceoftheNational Science Foundation (grant NSF GK 660) and the advice and criticism of Professor Bernard Roth of Stanford University during the course of this work. i ~. ~I ~ \u00b0- ~ Q s _ .Q 0 I L ! ! e +.~ ~ ~I \u00b0 ~i~ ~o r- \u00ae ~ o J ~ - ~ ' [1] WALDRON K. J. The constraint analysis of mechanisms. J. Mechanisms 1, 101-114 (1966). [2] DEL~SUS E. Sur les syst~mes articul~s gauches. Ann. l~cole Normale Paris 17, 446--448 (1900)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001995_tvt.2010.2041260-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001995_tvt.2010.2041260-Figure15-1.png",
        "caption": "Fig. 15. Experimental setup of the prototype.",
        "texts": [
            " Operation I maximizes the average torque, operation II maximizes the average torque per rms current, operation III maximizes the torque smoothness factor, and operation IV maximizes the multiple objectives. It can be seen that the optimal turn-off and turn-on angles under the best motoring operation result in the large Tave/Tb, TC/TCb, and TSF/TSFb, which indicate high average torque, low copper loss, and low torque ripple, respectively. Clearly, the proposed optimal control method meets the requirements of the best motoring operation of SRM drives for EVs. The experimental setup of the prototype is depicted in Fig. 15. Fig. 16 shows the simulated and experimental current waveforms when the in-wheel SRM drive runs at a speed of 752 r/min. The measured output torque is 7 N \u00b7 m, and the predicted average output torque is 7.368 N \u00b7 m. The predicted torque smoothness factor is equal to 1.831. The agreements between the simulated and measured current waveforms indicate that the simulation model and simulation results are accurate. Figs. 17 and 18 illustrate the experimental comparisons between the proposed optimal motoring control and the traditional motoring control with the constant turn-on and turnoff angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002042_adem.201900617-Figure22-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002042_adem.201900617-Figure22-1.png",
        "caption": "Figure 22. Orientation designation for AMmaterials for a) tensile specimens and b) crack growth direction.[142] Part (b) reproduced with permission.[143] Copyright 2015, Springer US.",
        "texts": [
            " KGaA, Weinheim Metallic parts fabricated with DED usually exhibit higher cooling rates and a layered structure; this layered structure is more pronounced when a wire feed is used due to the higher deposition rate of each pass. In addition, defects exist in AM materials, these include lack of melting, distortion, cracking, porosity, and oxidation. The lack of melting (occurs between passes), together with columnar structure and texture, are the three main contributing factors to anisotropy seen in mechanical properties.[12] Based on ISO and ASTM standards,[142] reporting mechanical properties should follow the designations given in Figure 22 so that anisotropy can be compared. In a DED Ti-6Al-4V alloy, no significant anisotropy in tensile strength was observed[92]; however, for a SLM Ti-6Al-4V specimen, the anisotropy in tensile strength and ductility is much greater, reaching 15.4% and 77.6%, respectively.[93] Similarly, the SLM Ti-6Al-4V exhibits anisotropic behavior in fracture toughness. In horizontal specimens, cracks propagate through the columnar grains, whereas in the vertical orientation, cracks propagate along the columnar grain boundaries",
            "[235] Depending on the function of the part, there are a variety of tests that can be conducted including tensile and compressive strength, elastic modulus, hardness, fracture toughness, creep, fatigue, oxidation, and chemical exposure. MSFC-SPEC-3717 presents a testing matrix with the testing conditions and the minimum number of samples to qualify a metallurgical process[231] (this topic is further described in Section 5.3.2). The test matrix considers if an AM process is restarted; however, it does not consider the effects of oxidation or chemical exposure. One key consideration for testing is the coupon orientation (Figure 22) so that anisotropy can be accounted for. Data should also be collected on modified processes where process parameters are intentionally varied to produce unideal material properties. The result of such a database would create a conservative estimate for worst-case material properties. Some parts produced with these flawed parameters may even meet certification requirements, which can potentially reduce the strict stance that certification authorities may have on parts produced using AM processes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001428_j.ymssp.2018.05.038-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001428_j.ymssp.2018.05.038-Figure2-1.png",
        "caption": "Fig. 2. Mesh stiffness calculation for non-uniformly distributed tooth crack: (a) whole tooth, (b) one slice, and (c) effective cross section of tooth.",
        "texts": [
            " The power is transmitted from the pinion to the gear through the flexible deformation of their teeth in engagement represented by spring\u2013 damper elements (Km, Cm) along the line of action (LOA). In most of the analytical methods for mesh stiffness calculation, gear tooth is usually regarded as a cantilever beam with variable cross section. Once a crack happens to the gear tooth root, its stiffness to resist the tooth deformation under load will be reduced due to reduction of the effective load carrying zone of the tooth cross section (see Fig. 2) [20,24]. At the same time, the presence of a tooth root crack will also decrease the stiffness of tooth fillet-foundation [22]. Thus, in order to consider the effects of the non-uniformly distributed tooth root crack on both of the tooth stiffness and the fillet-foundation stiffness, the gear should be divided into a series of independent slices along tooth width (see Fig. 2a). In this case, the gear could be regarded as being composed of many thin gears. So, it is reasonable to regard the depth of the crack in each gear slice as constant when the thickness is small (see Fig. 2b), which enables that the tooth stiffness calculation method in [20,24] and the fillet-foundation stiffness calculation method in [22] could be applied for the mesh stiffness calculation in presence of non-uniformly distributed tooth root crack. It should be noted that the elastic couplings between slices are neglected due to that they are generally of secondary importance when the shape deviations and/or mounting errors are not considered [40]. According to [20], the single-tooth mesh stiffness, K, can be calculated as 1 K \u00bc 1 Kp \u00fe 1 Kg \u00fe 1 Kh \u00f01\u00de where Kp and Kg indicate respectively the stiffness of the pinion and gear in mesh, while Kh represents the Hertzian contact",
            " They are calculated as, K j \u00bc XNs k\u00bc1 1 Ktk \u00fe 1 K fk 1 ; j \u00bc p; g \u00f02\u00de where Kt and Kf denote the tooth stiffness and the fillet-foundation stiffness, respectively. The subscript k denotes the slice number, and Ns is the number of the divided tooth slices. The stiffness of one tooth slice (Kt) can be calculated as [20] Kt \u00bc 1 Kb \u00fe 1 Ks \u00fe 1 Ka 1 \u00f03\u00de where the bending (Kb), shear (Ks), and axial compressive stiffness (Ka) are calculated respectively by [20,26,41] 1 Kb \u00bc Z d 0 \u00f0y cosa1 h sina1\u00de2 EIy dy \u00f04\u00de 1 Ks \u00bc Z d 0 1:2 cos2 a1 GAy dy \u00f05\u00de 1 Ka \u00bc Z d 0 sin2 a1 EAy dy \u00f06\u00de where some of the symbols can be found in Fig. 2. E and G denote the Young\u2019s modulus and the shear modulus, respectively. Iy and Ay are the area moment of inertia and area of the section, respectively. According to Fig. 2c, they can be calculated as, Iy \u00bc 1 12 \u00f0hy \u00fe hcy\u00de3dx \u00f07\u00de Ay \u00bc \u00f0hy \u00fe hcy\u00dedx \u00f08\u00de It should be noted that the presence of tooth crack will not change the area of the cross section in the calculation of axial compressive stiffness, namely hcy = hy in Eq. (8) when it is plugged into Eq. (6). While for the fillet-foundation stiffness of a gear foundation slice, an improved calculation method developed by Chen et al. [22] is employed here. It can be calculated as, 1 K f \u00bc cosa Edx L u0 f S0f !2 \u00feM u0 f S0f \u00fe P\u00bd1\u00fe Q tana 2 4 3 5 \u00f09\u00de The detailed explanations on the symbols in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002454_j.jallcom.2019.02.121-Figure11-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002454_j.jallcom.2019.02.121-Figure11-1.png",
        "caption": "Fig. 11. DED-LAM Ti-15Mo sample deposited on Ti grade 2 substrate.",
        "texts": [
            " P (W) V (mm/min) f (g/min) 1 1900 300 4 2 1900 400 3 3 1900 400 5 Fig. 10. Cross section morphology of deposits for constant powder feed rate (3 g c. At each parameter settings, due to rapid solidification the columnar grain followed by epitaxial growth of the equiaxed grain is observed in the building direction. For multi-layer deposits, the presence of columnar grains generate anisotropy in the fabricated parts. The adoption of cross-directional and island scan strategy can be used to reduce the anisotropy effect [25,26]. The DED-LAM sample (shown in Fig. 11) fabricated using unidirectional scan strategy at the optimum parameter settings is used to observe the microstructure and characterize the mechanical properties. Convex surfaces are formed at the start and end of track deposition with larger convexity observed at the track end. This is owing to the fact that accumulation of heat takes place at the ends during acceleration and deceleration of the laser beam. For multilayer deposition the convexity goes on increasing, impairing part geometry and necessitating time consuming finishing operations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003505_j.mechmachtheory.2016.10.006-Figure5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003505_j.mechmachtheory.2016.10.006-Figure5-1.png",
        "caption": "Fig. 5. First four bending mode shapes of the coupled geared rotor (a) 1st mode, (b) 2nd mode, (c) 3rd mode and (d) 4th mode;.",
        "texts": [
            " Table 4 shows the comparison of the damped natural frequencies (obtained from the imaginary part of the eigenvalues) for the coupled geared rotor system with that of uncoupled geared rotor system (km=0; cm=0). The two consecutive natural frequencies for the uncoupled system are found to be the same. This is due to the fact that both the driving and driven rotors are supported on isotropic bearings. It is seen that coupling due to the gear pair caused reduction in the natural frequencies in first, third, ninth and eleventh mode. In the next step, the corresponding twelve mode shapes are studied in detail. The first four mode shapes of the coupled geared rotor system are shown in Fig. 5. The mode shapes are plotted in the X\u2013Y and X\u2013Z plane for clarity of visualization of motion. Initial four modes, i.e. shown from Fig. 5(a)\u2013(d), are first four bending modes of the driving and driven rotors in the X\u2013Y and X\u2013Z plane as is evident from the bending deflection pattern. Fig. 5(a) clearly shows the effect of coupling, as the displacement is reflected in both the shafts due to the gear pair contact. The effect of coupling is not visible in the 3rd mode shape, as the corresponding reduction in the natural frequency is very small. However, the 2nd and 4th mode shapes remain uncoupled, i.e. the displacement is either in the driving shaft or the driven shaft. The second four bending modes for the driving and driven rotors in the X\u2013Y and X\u2013Z plane are shown in Fig. 6(a)\u2013(d)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003377_j.corsci.2019.04.028-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003377_j.corsci.2019.04.028-Figure1-1.png",
        "caption": "Fig. 1. a) Schematic view of the jet impingement apparatus was used in this research that includes: (1) pump (2) nozzle (3) specimen holder (4) plastic tubes (5) stainless steel tank. (b) SEM image of the original/uncrushed sand particles used for erosion-corrosion tests, indicating a particle size range of 200\u2013800 \u03bcm.",
        "texts": [
            " Preparation for the electrochemical measurements was done by contacting the specimens from the backside with a copper wire, followed by embedding in a suitable epoxy resin, grinding using SiC papers from 240 down to 4000 grit, washing with ethanol and distilled water and finally drying in hot air. For CPP measurements, the potential was swept from -0.2 V to +1.4 V relative to the open circuit potential (OCP) at a fixed scan rate of 10mV/min. The reverse current density for the CPP tests was set at 100 \u03bcA, and tests were stopped when the potential reached to -0.3 V relative to OCP. All the electrochemical experiments were done at room temperature (\u02dc 25\u00b0C). Erosion-corrosion measurements were conducted using a jet impingement system schematically shown in Fig. 1a, which is able to provide high flow speeds and various impact angles. The system consisted of a high-pressure pump, a 20-liter stainless steel tank, a specimen holder, a nozzle, a flow rate gauge and valves. A 0.6 M NaCl solution containing 2.5 wt% sand particles was delivered through a nozzle impinging on the specimen surface at velocities up to 17m/s. The mean size of the sand particles in the uncrushed state was measured to be in the range of the 200\u2013800 \u03bcm, according to the SEM image shown in Fig. 1b. The distance between the nozzle and the specimen was set to be about 5 cm and the working temperature was measured to be below 30 \u00b0C during the test. In order to investigate the depassivation/repassivation behaviour, potentiostatic measurements were done when the erosion-corrosion test was being conducted. According to the CPP curves, an appropriate potential in the passive region was applied during potentiostatic measurements, while the flow velocity was changed from 3.5 to 17m/s with a step of 1",
            " 2 and 3 confirm that the highly dense SLM-produced 316L SS possesses a combination of superior pitting corrosion resistance and high hardness. The former is believed to be due to the elimination/refinement of MnS inclusions [6,7], while the latter is mostly related to the grain refinement and presence of nanoscale inclusions [13\u201315] within SLM-produced 316L SS. Owing to its higher pitting potential and higher hardness, such a material is expected to possess better erosion-corrosion resistance. However, erosion-corrosion testing in a flow-loop shown in Fig. 1 has generated unexpected results. Fig. 4 shows potentiostatic polarisation curves recorded under erosion-corrosion test conditions for both commercial and SLM-produced 316L SS specimens. The potentiostatic polarisation method has been commonly used as an effective technique to monitor the current fluctuations during the erosion-corrosion test to evaluate the critical flow speed for passive metals and alloys [30,31]. Fig. 4 depicts the current density as a function of time/flow speed, while the specimens were polarised to an anodic potential of +100 mV (Ag/AgCl) to keep both specimens in the stable passive range (based on the potentiodynamic polarisation curves presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003288_j.engfailanal.2014.01.008-Figure7-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003288_j.engfailanal.2014.01.008-Figure7-1.png",
        "caption": "Fig. 7. An example of spalling defect on one of the tooth of a helical gear.",
        "texts": [
            " 1 and 2 Pt base pitch of gear S1, S2 defined variables L, Lt length of contact line for single gear pair and total mesh gear pairs Li length of ith contact line Lir, Lil length of contact line of right and left parts for ith mesh tooth pair Fir, Fil frictional force of the right and left side of ith contact line Ffp, Ffg total frictional force on pinion and gear Ffpi, Ffgi frictional force of ith mesh tooth pair for pinion and gear, respectively Fm mesh force of gear pair l friction coefficient of gear pair Xpri, Xpli moment arm on the right and left side of ith contact line Xpr, Xpl moment arm on the right and left side contact line Tfpi, Tfgi frictional torque of each contact line on pinion and gear Tfp, Tfg frictional torque on pinion and gear ls, ls1, ls2 length of the spalling ws width of the spalling dov, doh, dv, dh, R1, R2, R3, R4 various distances show in Fig. 7 DL(t), DLr(t) loss of contact line Rbp, Rbg base radius of pinion and gear km mesh stiffness of gear pair ko mesh stiffness density per unit length kb, combined bending, shear and axial compressive stiffness kh, ksh Hertzian contact stiffness u Poisson\u2019s ratio e contact ratio hi, _hi, \u20achi angular position, angular velocity and angular acceleration Ip, Ig inertia of pinion and gear Tp, Tg input torque and brake torque Fmi dynamic mesh forces of ith meshing tooth e static transmission error fmi damping ratio of ith meshing tooth Ie equivalent moment of inertia mp, mg mass of pinion and gear xp, xg, yp, yg displacement of pinion and gear along LOA direction and OLOA direction _xp; _xg ; _yp; _yg velocity of pinion and gear along LOA direction and OLOA direction \u20acxp; \u20acxg ; \u20acyp; \u20acyg acceleration of pinion and gear along LOA direction and OLOA direction CiBj, KiBj damping and stiffness of bearing along LOA direction and OLOA direction d composite dynamic transmission error FiBJ dynamic bearing forces Ls(t) contact line of single tooth pair for spalling defect gear Lsr(t), Lsl(t) contact line at the right side and left side of the pitch plane for spalling defect gear D(t), O(t), P(t) shape, size and location function of spalling defect tc time of one mesh circle stiffness into an analytical spur and helical gear model",
            " 4 for the calculation of all the length of contact line, all the results of the next series of frictional excitation in Figs. 5 and 6 will be changed.According to the actual datum, the spalling defect usually arises near the pitch line, and peels off in sheets. In this study, the spalling defect is modeled as a rectangular indentation near the pitch line, and parallel to the contact line on one of the tooth. The example of scoring on the defective tooth profile and the variation of the length of contact line for the spalling defect are shown in Fig. 7. By defining the centroid of the spalling defect to be point So, Sa and Sb are the lowest and highest point of spalling defect. The horizontal distance and vertical distance from point So to point D are doh and dov, respectively. dh and dov are the hori- zontal distance and vertical distance from point Sa to point D which are expressed by the relative location of the point Sa and So. When the point Sa at the left side of the centroid So, (i.e. ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l2 s \u00few2 s q ls sec bb P 0) the horizontal distance dh and vertical distance dov are given by dh \u00bc doh 1 2 ws 1 2 ls tan bb cos bb \u00f03\u00de dv \u00bc dov 1 2 ws 1 2 ls tan bb sin bb 1 2 ls sec bb \u00f04\u00de When the point Sa on the right side of the centroid, (i.e. ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l2 s \u00few2 s q ls sec bb < 0) the horizontal distance dh and vertical distance dov are given by dh \u00bc doh \u00fe 1 2 ws cot bb \u00fe 1 2 ls sin bb 1 2 ws sec bb \u00f05\u00de dv \u00bc dov 1 2 ws cot bb \u00fe 1 2 ls cos bb \u00f06\u00de The other terminologies described in Fig. 7 are given below R1 \u00bc dh \u00fe dv tan bb \u00f07\u00de R2 \u00bc R1 \u00fews sec bb \u00f08\u00de R3 \u00bc R1 \u00fe \u00f0LPD dh\u00de sec2 bb \u00f09\u00de R4 \u00bc R3 \u00fe ls tan bb sec bb \u00f010\u00de The modified equations of the length of contact line for the modeled spalling defect of helical gears are derived as follows. The loss part of the length of contact line of single tooth meshing which is expressed as DL\u00f0t\u00de \u00bc 0 0 6 vt < R1 ls R1 6 vt < R2 0 R2 6 vt 6 npt 8>< >: \u00f011\u00de Then, the length of contact line of one period for single tooth meshing can be obtained as Ls\u00f0t\u00de \u00bc L\u00f0t\u00de DL\u00f0t\u00de \u00f012\u00de The loss part of the length of contact line of single tooth meshing on the right side of pitch plane can be defined as DLr\u00f0t\u00de \u00bc 0 0 6 vt < R3 ls1 \u00fe \u00f0vt R3\u00de cos bb cot bb R3 6 vt < R4 ls2 R4 6 vt < R2 0 R2 6 vt 6 npt 8>>< >>: \u00f013\u00de where the variables ls1 and ls2 are determined by the conditions whether the point Sa and point Sb on the left side or right side of the pitch plane, and can be given by ls1 \u00bc 0 ws cot bb ls P 0 \u00f0dh LPD\u00decscbb ws cot bb ls < 0 \u00f014\u00de ls2 \u00bc ls R4\u2013R2 0 R4 \u00bc R2 \u00f015\u00de Then, the length of contact line for single tooth meshing on both the right side and left side of pitch plane can be obtained as, Lsr\u00f0t\u00de \u00bc Lr\u00f0t\u00de DLr\u00f0t\u00de \u00f016\u00de Lsl\u00f0t\u00de \u00bc Ls\u00f0t\u00de Lsr\u00f0t\u00de \u00f017\u00de It should be noted that the other equations are the same as described in Section 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001107_j.jsv.2007.12.013-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001107_j.jsv.2007.12.013-Figure2-1.png",
        "caption": "Fig. 2. Representation of profile modification parameters. Tooth shape: (a) linear modifications; (b) parabolic modifications. K-chart: (c) linear modifications; (d) parabolic modifications.",
        "texts": [
            " Since no manufacturing errors are included, the mesh stiffness is periodic within a mesh cycle; therefore, it is expanded in terms of Fourier series: k\u00f0t\u00de \u00bc k0 \u00fe XN j\u00bc1 kj cos\u00f0jomt jj\u00de, (8) where om is the mesh circular frequency, amplitudes kj and phases jj are obtained using the discrete Fourier transform (DFT); the number of samples n is related to the number of harmonics N \u00bc \u00f0n 1\u00de=2; in the following, n \u00bc 15 is considered to ensure enough accuracy in the expansion. Similarly we have kbs\u00f0t\u00de \u00bc k0 \u00fe XN j\u00bc1 kj cos jomt jj \u00fe sts;1 dg1 , (9) where sts;1 is the thickness of the pinion tooth space at the pitch operating diameter, see Eq. (3.2.32) of Ref. [21] for details. A dimensionless form of Eq. (1) is obtained by letting: on \u00bc ffiffiffiffiffiffi k0 me s ; z \u00bc c 2meon ; t \u00bc ont; T\u0304g \u00bc Tg bmeo2 n ; x\u0304 \u00bc x b (10) and k\u0304j \u00bc kj meo2 n ; k\u0304\u00f0t\u00de \u00bc 1\u00fe XN j\u00bc1 k\u0304j cos j om on t jj , k\u0304bs\u00f0t\u00de \u00bc 1\u00fe XN j\u00bc1 k\u0304j cos j om on t\u00fe jj sts;1 dg1 . (11) Fig. 2(a) shows standard profile modifications on a spur gear tooth, which consist in a removal of material from the tip (tip relief) or the root (root relief), according to different manufacturing parameters. The \u2018\u2018start roll angle at tip\u2019\u2019 ats and the \u2018\u2018magnitude at tip\u2019\u2019 magt specify the point on the profile at which the relief starts and the amount of material removed at the tip radius; ars, magr and are have similar meaning, where the current roll angle a is given by a \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0d=dg1\u00de 2 1 q , see Fig. 2. Typical manufacturing gear processes, such as grinding, allow to control whether the variation of the removed material is linear or parabolic with respect to the roll angle. Since the removal of material is measured along the direction normal to the profile, usual representations of the reliefs are given as deviation from the theoretical involute profile: Figs. 2(c,d) show examples of linear and parabolic modifications. ARTICLE IN PRESS G. Bonori et al. / Journal of Sound and Vibration 313 (2008) 603\u2013616 607 In the present work the following assumptions are made: (1) the type of profile modification (linear or parabolic) is chosen before the optimization process and remains unchanged; (2) the \u2018\u2018end roll angle at root\u2019\u2019 are is the roll angle corresponding to the diameter of the initial point of contact along the tooth profile; (3) 2D plain strain FEM analyses are carried out; therefore, no crowning effects are taken into account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure4.5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure4.5-1.png",
        "caption": "FIGURE 4.5. A cubic rigid body with a unit length of edges.",
        "texts": [
            " A body coordinate frame B(oxyz), that is originally coincident with global coordinate frame G(OXY Z), rotates 45 deg about the X-axis and translates to \u00a3 3 5 7 1 \u00a4T . Then, the matrix representation of the global posi- tion of a point at Br = \u00a3 x y z 1 \u00a4T is: Gr = GTB Br = \u23a1\u23a2\u23a2\u23a3 X Y Z 1 \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a3 1 0 0 3 0 cos 45 \u2212 sin 45 5 0 sin 45 cos 45 7 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u23a1\u23a2\u23a2\u23a3 x y z 1 \u23a4\u23a5\u23a5\u23a6 (4.28) Example 77 An axis-angle rotation and a translation. Consider a cubic rigid body with a unit length of edges at the corner of the first quadrant as is shown in Figure 4.5. If we turn the cube 45 deg about u u = \u00a3 1 1 1 \u00a4T (4.29) then \u03c6 = \u03c0 4 u\u0302 = u\u221a 3 = \u23a1\u23a3 0.577 35 0.577 35 0.577 35 \u23a4\u23a6 (4.30) 4. Motion Kinematics 157 and its Rodriguez transformation matrix is: Ru\u0302,\u03c6 = I cos\u03c6+ u\u0302u\u0302T vers\u03c6+ u\u0303 sin\u03c6 = \u23a1\u23a3 0.804 74 \u22120.310 62 0.505 88 0.505 88 0.804 74 \u22120.310 62 \u22120.310 62 0.505 88 0.804 74 \u23a4\u23a6 (4.31) Translating the cube by Gd Gd = \u00a3 1 1 1 \u00a4T (4.32) generates the following homogeneous transformation matrix GTB. GTB = \u23a1\u23a2\u23a2\u23a3 0.804 74 \u22120.310 62 0.505 88 1 0.505 88 0.804 74 \u22120"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002480_j.surfcoat.2012.10.044-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002480_j.surfcoat.2012.10.044-Figure1-1.png",
        "caption": "Fig. 1. Schema of temperature measurements.",
        "texts": [
            " TiAl6V4, +50\u2013100 \u03bcm (measured by optical granulo-morphometer ALPAGA 500 NANO) powder fabricated by TLS Technik GmbH & Co (Bitterfeld, Germany) was used in LC. Spatial distribution of emitted thermal radiation from laser cladded bead was acquired by infrared camera FLIR Phoenix RDAS\u2122. The camera is equipped by an InSb sensor with 3 to 5 \u03bcm band pass arranged on 320\u00d7256 pixel array. The brightness temperature measurements were realized under the following conditions: exposition time of 10 \u03bcs, observation zone of 15\u00d710 mm2, and angle of observation of 40\u00b0 relative to the surface normal. The infrared camera was fixed with laser cladding head (Fig. 1). 3. Method of brightness temperature definition and true temperature restoration Infrared camera calibration using black body model MICRON M390 was carried out to transform raw signal to brightness temperature: Raw signals from camera were written with 50 \u00b0C step from 600 \u00b0C to 1300 \u00b0C. At the black body temperature 1300 \u00b0C raw signal has reached 7100 a.u., which exceeds the maximum value of experimental signals. To verify the infrared photo detector response on the variation of incoming radiation, the energy density flux in the 3\u20135 \u03bcm spectral range (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003309_jas.2017.7510679-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003309_jas.2017.7510679-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor model.",
        "texts": [
            " The construction of this paper is organized as follows: In Section II, a nonlinear dynamic model with actuator faults and wind gusts is derived. The fault tolerant method based on ADRC is developed in Section III. To analyze the performance of the developed fault tolerant controller, several simulations are carried out and presented in Section IV. Conclusions and future work are finally discussed in Section V. A quadrotor aircraft is actuated by four rotors. The coordinate systems and free body diagram for the quadrotor are shown in Fig. 1. There are two reference frames subjected to the quadrotor: The earth-fixed frame E = (OE , xE , yE , zE) and the body-fixed frame B = (OB , xB , yB , zB). It is assumed that the body-fixed frame and the center of gravity of the quadrotor must coincide. A cross formed by two arms holds the four rotors, two rotors at the two ends of one arm rotate in the clockwise direction, while the other pair of rotors rotates in the opposite direction to cancel the yawing moment. To describe the behavior of the quadrotor, its absolute position vector is denoted as \u03be = [x, y, z]T \u2208 E and attitudinal vector is denoted as Euler angles \u03b7 = [\u03c6, \u03b8, \u03c8]T \u2208 E"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0003937_j.engfailanal.2017.08.028-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0003937_j.engfailanal.2017.08.028-Figure3-1.png",
        "caption": "Fig. 3. Geometric model of gear with tooth root crack.",
        "texts": [
            " Therefore, the gear tooth fillet-foundation stiffness can be obtained by, \u2032 \u2032= K \u03b4 F 1 f f (20) It should be noted that the two improved models aforementioned have not considered the effect of the tooth root crack propagation path variations on the stiffness of the gear fillet-foundation. And the propagation path of the tooth root crack is limited to being in the tooth zone, but not in the gear body. To verify the proposed methods in Section 2, finite element models of the spur gear with tooth root crack are established in this section. Firstly, the three-dimensional geometrical model of the gear with tooth root crack is established and shown in Fig. 3, and the geometric parameters of the gear are shown in Table 1. There have been many research work on the tooth root crack propagation path, such as, Lewicki [28\u201330] concluded that the tooth root crack propagation path is an approximate circular curve. Therefore, the three-dimensional geometry model of the gear is developed with the tooth root cracks having different curves. Three forms are assumed in this study (see Fig. 3) for the crack propagation path in order to reveal their effects on gear tooth fillet-foundation stiffness, which are also introduced as follows: Case 1: A straight line which is symmetrical about the symmetrical line of the tooth; Case 2: An arc curve with the radius of 16 mm, and the center of the corresponding circle lies at the symmetrical central line of the tooth; Case 3: An arc curve with the radius of 8 mm, and the center of the corresponding circle lies at the symmetrical central line of the tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002301_978-3-642-45352-6-Figure3.62-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002301_978-3-642-45352-6-Figure3.62-1.png",
        "caption": "Fig. 3.62 SF6-filled standard capacitor (rated voltage 800 kV, nominal capacitance 100 pF)",
        "texts": [
            " Here, the standard capacitor providing the reference divider is located at the left (red), and the divider under calibration in the middle (blue). The 1,000 kV test transformer cascade is located at the right-hand side. Standard capacitors are generally composed of coaxial cylinder electrodes with guard rings at the LV side, as originally suggested by Schering and Vieweg in 1928. To achieve a high breakdown voltage at low gap distance, standard capacitors are filled with compressed gas, such as SF6, which ensures an excellent stability against temperature changing. The construction principle is obvious from Fig. 3.62 which reveals that the capacitance between the coaxial electrodes may not be affected by earth capacitances, so that a proximity effect typical for stacked capacitors must not be taken into account. As the capacitance of \u2018\u2018long\u2019\u2019 coaxial cylinder electrodes is proportional to the cylinder length l and inversely proportional to the logarithm of the ratio between outer and inner conductor radius ra/ri, the following simple equation can be used to estimate the geometrical parameters: C1 \u00bc 2 p e l In ra rt 55:7 pF m l In ra rt ; \u00f03:36\u00de Example For compressed gas capacitors rated C500 kV, the ratio of radii is chosen such that the breakdown voltage becomes a maximum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001441_0040-9383(67)90034-1-Figure1.2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001441_0040-9383(67)90034-1-Figure1.2-1.png",
        "caption": "Fig. 1.2.",
        "texts": [
            " There is no problem about making this list, since f only has a finite number of critical points on M'+ 1 - M~. Let a o < ax < \"'\" be a sequence of real numbers with ao = eo and lira a I = 0% i\"* go and such that any two of the ej are separated by an a i. Then let Wk = f - l [ a o , ak]. The Uj are constructed as follows. Let Uo be the n-disc W1, and suppose Uj = Wk. Case (a). I f there are no critical values in [ak, ak+X], let Uj+x = W~+l. Clearly U~+~ is a collarlike neighborhood of Uj. (See Fig. 1.2.) Case (b). I f there is a critical point p Ef-l[ak, ak+l] , truncate Wk+ * by cutting out the product of D x and D~ -~, the \"right-hand disc\" (cf. [13] p. 28) associated to p. This is shown in Fig. 1.2. Note that by construction of f , 2 __< n - 1. Let Uj+ 1 be the union of W k and the complement of the deleted portion of Wk+l. (Then, s ince fhas no critical points in Uj+, - Uj, the flow lines o f f can be used to show that Uj+I is a collarlike neighborhood of Uj.) Let %+ 2 = Wk+ 1. Thus %+ 2 is Uj+I with a handle of index 2 _< n - 1 attached. Note that in case p was a minimum (Fig. 1.3) this should be understood to mean Uj+I = Wk+a less the introduced disc, Uj+2 = Wk+a. Then Uj+ 1 is in fact 0-truncated, and Uj+2 is Uj+I with a handle of index 0 attached"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002975_j.addma.2019.100941-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002975_j.addma.2019.100941-Figure1-1.png",
        "caption": "Fig. 1 The HDR-LDEDed Inconel 718 alloy: (a) block sample; (b) specimen size for tensile test 2.2 Thermal cycle simulation",
        "texts": [
            " This system consists of a 6 kW semiconductor laser, a threedimensional numerical controlled working table, an inert atmosphere processing chamber (oxygen content \u226450 ppm), a powder feeder with a coaxial nozzle and an adjustable automatic feeding device with high precision (type DPSF-2). A set of HDR-LDED parameters (diode laser power, 4000 W; scanning speed, 1600 mm/min; beam diameter, 5 mm; overlap, 50%; layer thickness: 1.3 mm) was utilized to fabricate an Inconel 718 cube with the dimension of 45 mm\u00d745 mm\u00d775 mm (length \u00d7 width \u00d7 height) on a C45E4 stainless steel substrate with the dimension of 140 mm\u00d750 mm\u00d75 mm (length \u00d7 width \u00d7 height). The deposition rate was about 2.2 kg/h. The HDR-LDEDed Inconel 718 cube is shown in Fig. 1 (a). The substrate surface was polished to remove the oxide film by abrasive paper and cleaned with acetone beforehand. Spherical powder Inconel 718, which has been manufactured by the Plasma-Rotating Electrode Process (PREP), was used as the deposition material. The chemical composition of the Inconel 718 powder is as follows (wt. %): 18.48Cr, 0.54Al, 5.30Nb, 3.04Mo, 0.95Ti, 0.03C, 52.76Ni and balance Fe. The diameters of the used PREP powder particles range from 45 \u03bcm to 90 \u03bcm. Jo ur al Pre -p r f The microstructures were revealed by using the etchant of 1 g CrO3+2 ml H2O+6 ml HCl and the microstructure of the sample was examined by optical microscopy (OM), transmission electron microscopy (TEM) and scanning electron microscope (SEM) equipped with energy disperse spectrometer (EDS)",
            " %) of Inconel 718 is as follows: Fe: 4.91%, Cr: 21.82%, Ni: 59.437%, Nb: 3.52%, Mo: 9.28%, Ti: 0.34%, C: 0.033%, Al: 0.29%, Si: 0.27%, Mn: 0.10%. ANSYS software was used to calculate the thermal cycles of the bottom region (Z=~6 mm), the middle region (Z=~37 mm) and the top region (Z=~69 mm) during HDR-LDED process. Room temperature tensile tests were performed at a constant crosshead displacement rate of 1 mm/min on sheets with gage dimensions of 24 mm \u00d7 6 mm \u00d7 2 mm by an INSTRON3382 machine. As shown in Fig. 1(a), three plate-shaped tensile specimens were cut from the bottom, middle and top region of the bulk sample Jo ur na l P re -p ro of along the x-axis direction and were sequentially labeled as 1#, 2# and 3#, respectively. The tensile specimen size is shown in Fig. 1(b). Three tensile specimens at different regions were prepared and the results were averaged out. The thermal history is calculated by performing a three-dimensional transient thermal analysis using the finite element model (FEM). The establishment of the thermal model is mainly based on the following equations and follow the law of conservation of energy. That is, the heat stored inside the entire material volume is equal to the external input sum minus the heat flow loss caused by radiation and convection",
            ", Microstructural control of alloy 718 Jo ur na l P r -p ro of fabricated by electron beam melting with expanded processing window by adaptive offset method, Mater. Sci. Eng. - A 764 (2019) 138058. https://doi.org/10.1016/j.msea.2019.138058. [57] S.H. Sun, Y. Koizumi, T. Saito, et al., Electron beam additive manufacturing of Inconel 718 alloy rods: Impact of build direction on microstructure and hightemperature tensile properties, Addit. Manuf. 23 (2018) 457-470. https://doi.org/10.1016/j.addma.2018.08.017. Jo ur na l P re -p ro of Fig. 1 The HDR-LDEDed Inconel 718 alloy: (a) block sample; (b) specimen size for tensile test. Three plate-shaped tensile specimens were cut from the bottom, middle and top region of the bulk sample along the x-axis direction and were sequentially labeled as 1#, 2# and 3#, respectively. Three tensile specimens at different regions were prepared and the results were averaged out. Fig. 2 The microstructures of the HDR-LDEDed Inconel 718 sample from the bottom region to the top region: a), d) and g) the bottom region; b), e) and h) the middle region; c), f) and i) the top region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002255_978-3-319-09287-4-Figure9.4-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002255_978-3-319-09287-4-Figure9.4-1.png",
        "caption": "Fig. 9.4 Methods for determining advancing and receding contact angles: a tilted plane and b dynamic contact angle",
        "texts": [
            " The smaller this parameter, the easier the movement of a drop on the surface; this concept is particularly important in the case of superhydrophobicity-driven self-cleaning, where the cleaning effect is assured by water rolling on the surface, collecting dust deposited on it and carrying it away (see Sect. 9.2.2). DCA (dynamic contact angle) is generally used to quantify it and different methods can be applied. Although the correct observation method of hysteresis would be the one schematized in Fig. 9.4a\u2014i.e., a drop deposited on a tilted surface, generally, first a drop is dispensed to read the advancing angle, while the receding one is measured by drop retraction (Fig. 9.4b). Additionally, the material can be immersed directly 9 Bioinspired Self-cleaning Materials 215 in water (or other liquid), which produces the advancing contact angle, and subsequently extracted, generating the receding contact angle. While the characterization of a superhydrophilic surface (h * 0 ) is rather simple\u2014being related to the spreading of water on the surface to cover the largest area possible, superhydrophobic surfaces (h[ 150 ) are more complex to describe. In fact, based on surface tension equilibria and Young\u2019s equation, no known chemistry allows water to configure with a contact angle larger than 120 on a smooth surface (Hunter 2010): therefore, surface morphology must necessarily be involved to reach a superhydrophobic state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002366_j.jmatprotec.2020.116689-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002366_j.jmatprotec.2020.116689-Figure1-1.png",
        "caption": "Fig. 1. Geometry of the forged sample with added AM structure.",
        "texts": [
            " Also, the procedures used for microstructural analysis and for determining the mechanical properties are presented. Section 3 details the results of metallographic examinations of WAAM material compared to hot forged WAAM material. In addition, the mechanical properties are investigated and the results are discussed. Finally, conclusions and outlook are presented. The most widely used titanium-alloy Ti\u20136Al\u20134 V was selected for the investigations in the present work. The geometry used in the current study for the representation of the hybrid processing chain \u2018hot forming + AM\u2019 is shown in Fig. 1 (left) and represents a forged T-section with a length of 99 mm. The width of the rib is 10 mm. Higher ribs cause much higher tool wear and increase the appearance of forging defects. Using WAAM, the height of the rib was extended to a total of 108 mm. A sixaxis FANUC\u00ae robot with the welding power source TPS/i 500 by Fronius\u00ae equipped with an argon gas chamber was used to deposit the layers on the forged substrate material (Fig. 2). As a base material, a Ti6Al-4 V forged T-section with a cross-section of 99 mm x 42 mm x 10 mm was used. On the rib of this section, material was added using WAAM. The hot forging process was performed on a mechanical crank press with 2.500 t press force in the \u03b1 + \u03b2-temperature field. After the forging process, the top face was milled to obtain a flat top to obtain reproducible results in the WAAM process. The machined and deposited parts are presented in Fig. 1 (right). To deposit the layers on the forged material, wire with a diameter of 1 mm was fed into the melt pool produced by an electric arc. In order to prevent oxidation during deposition, the hybrid parts were produced in an inert gas chamber filled with argon. The applied WAAM process parameters were as following: the current was 120 A, the voltage was 14 V, the wire feed rate was 10 m/min, the layer thickness was approximately 3.3 mm and argon flow rate was approximately 15 l/min. The analysis of the chemical composition of the WAAM material was performed with three replications using a GDA 650 HR analyzer (Spectruma analytic GmbH) and is presented in Table 1",
            " Selected samples were analyzed using scanning electron microscopy (SEM). Tensile specimens were extracted parallel, perpendicular and at an angle of 45\u00b0 to the build direction, both from the welded section and from the transition zone between forged and deposited material. Besides, tensile samples were extracted from the forged T-section. The round tensile specimens M10 had a dog-bone shape with a gauge length of 25 mm and a diameter of 5 mm. Tensile tests were carried out at room temperature in accordance with the DIN EN 2002-001:2005 standard. Fig. 1 (right) shows the hybrid part with a 66 mm WAAM-produced wall which exhibits a shiny surface without signs of oxidation. The horizontally deposited layers can be seen clearly due to the surface undulation of each deposited layer. Fig. 3 shows a typical microstructure of Ti-6Al-4 V produced by WAAM. The macrostructure of the arc-deposited Ti-6Al-4 V is characterized by epitaxial growth of large columnar prior \u03b2-grains which stretch through the deposited layers. The \u03b2-grain size of WAAM samples is extremely large"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001025_j.euromechsol.2010.05.001-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001025_j.euromechsol.2010.05.001-Figure2-1.png",
        "caption": "Fig. 2. Planetary gear lumped-parameter model.",
        "texts": [
            " introduce tooth wedging, tooth contact loss, and bearing clearance into a lumped-parameter model, 2. investigate the interplay between tooth wedging and bearing clearance, 3. physically explain the mechanism of tooth wedging and its impact on dynamic response. The present model extends the two-dimensional lumpedparameter one in Lin and Parker (1999). The carrier, ring, sun, and planets are rigid bodies each having two translational and one rotational degree of freedom. The model has 3(N\u00fe 3) degrees of freedom, where N is the number of planets. This model, depicted in Fig. 2, is extended to include back-side contact, bearing clearance, mesh stiffness variation, gravity, and other excitation sources. Bearings are modeled as springs with clearance nonlinearity. Gear meshes are modeled as nonlinear lumped springs that act only when the teeth are in contact on the drive-side, back-side, or both sides simultaneously for the case of tooth wedging. This model captures the tooth separation nonlinearity. Excitations consist of gravity, externally applied loads, and the parametric excitations from fluctuating gear mesh stiffnesses. The gear and carrier eccentricities as well as tooth spacing, indexing, and pitch-line run-out are not believed to be the primary concern for tooth wedging. These errors are not included in the model. Because friction is usually small for well-lubricated gears, it is modeled through modal damping. Particularly for the low-speed cases examined in the current paper, the specific dissipation model will not significantly affect the results. The coordinates are shown in Fig. 2. Translational displacements xl, yl, (l\u00bc c, r, s) are assigned to the carrier, ring, and sun, respectively, with respect to the basis {Ei} (i\u00bc 1, 2, 3) that is fixed to the carrier as shown in Fig. 3. The originO is at the center of the planetarygear. The radial and tangential displacements of the planets are denoted by xj, hj, j \u00bc 1, ., N with respect to the basis {ei} rotating with the carrier and oriented for each planet as shown in Fig. 3. The rotational displacements are uv\u00bc rvqv, v\u00bc c, r, s, 1,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000139_978-1-4419-1750-8-Figure5.60-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000139_978-1-4419-1750-8-Figure5.60-1.png",
        "caption": "FIGURE 5.60. A design of an articulated manipulator.",
        "texts": [],
        "surrounding_texts": [
            "316 5. Forward Kinematics\nx0\ny0\nx1\na\nl\nz0\nP\nSpherical manipulators are made by attaching a polar manipulator shown in Figure 5.56, to a one-link R`R(\u221290) manipulator shown in Figure 5.51 (b). Attach the polar manipulator to the one-link R`R(\u221290) arm and make a spherical manipulator. Make the required changes to the coordinate frames Exercises 3 and 9 to find the link\u2019s transformation matrices of the spherical manipulator. Examine the rest position of the manipulator.\n19. F Non-industrial links and DH parameters.\nFigure 5.61 illustrates a set of non-industrial connected links. Complete the DH coordinate frames and assign the DH parameters.",
            "5. Forward Kinematics 317\nz0\nzi",
            "318 5. Forward Kinematics\n20. Modular cylindrical manipulators.\nCylindrical manipulators are made by attaching a 2 DOF Cartesian manipulator shown in Figure 5.57, to a one-link R`R(\u221290) manipulator shown in Figure 5.51 (a). Attach the 2 DOF Cartesian manipulator to the one-link R`R(\u221290) arm and make a cylindrical manipulator. Make the required changes into the coordinate frames of Exercises 3 and 11 to find the link\u2019s transformation matrices of the cylindrical manipulator. Examine the rest position of the manipulator.\n21. Disassembled spherical wrist.\nA spherical wrist has three revolute joints in such a way that their joint axes intersect at a common point, called the wrist point. Each revolute joint of the wrist attaches two links. Disassembled links of a spherical wrist are shown in Figure 5.62. Define the required DH coordinate frames to the links in (a), (b), and (c) consistently. Find the transformation matrices 3T4 for (a), 4T5 for (b), and 5T6 for (c).\n22. F Assembled spherical wrist."
        ]
    },
    {
        "image_filename": "designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure8-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000697_j.mechmachtheory.2006.01.009-Figure8-1.png",
        "caption": "Fig. 8. FEM models used for LTCA of multi-pairs of teeth engagement: (a) engagement of two pairs of teeth, (b) engagement of three pairs of teeth and (c) engagement of four pairs of teeth.",
        "texts": [
            " Then tooth contact pattern can be obtained by drawing contour lines of {F}. Since gear transmission has a very high efficiency (about 95\u201398%), friction between the contact tooth surfaces is ignored in LTCA. P \u00bc Transmitted Torque=rb \u00f020\u00de A tooth usually has one tooth engagement position (single pair tooth-contact area as shown in Fig. 13) and two teeth engagement position (double pair tooth-contact area as shown in Fig. 13) when it rotates in one meshing period. This engagement position is given by a parameter in the program developed for LTCA. Fig. 8(a) is an image of two pairs of teeth engagement. When to perform LTCA of two pairs of teeth with AE, ME and TM, akj, ak0j0 and {e} are built at the two places of the two pairs of teeth as shown in Fig. 8(a) with s at the same time. Then they are submitted into Eqs. (17)\u2013(19) to calculate {F} and d. In this time, {F} includes loads shared by tooth 1 and tooth 2. Tooth load-sharing rate can be calculated when loads at all the contact points on the reference face of tooth 1 are summed and loads at all the contact points on the reference face of tooth 2 are summed according to the results of {F}. FEM software is built to be able to solve contact problems of 1\u20134 pairs of teeth engagement. When gearing parameters are given, the software shall calculate contact ratio of the pair of gears firstly, then automatically determine how many teeth there are in contact based on tooth engagement position parameter given, then divide FEM model and make pairs of contact points on tooth surfaces automatically, finally calculate akj, ak0j0 , {e} and build mathematical model of Eqs. (17)\u2013(19) automatically. Fig. 8(b) and (c) are three teeth engagement and four teeth engagement FEM models built by the software automatically when a pair of high contact ratio gears is analyzed (see Fig. 9). Hertz formula is often used to calculate SCS of gears when tooth load is given. But it is difficult to be used here for a pair of gears with AE, ME and TM. So this paper calculates the SCS of gears with a \u2018\u2018Unit Force\u2019\u2019 method. It means to calculate tooth load distributed on unit contact area of a tooth surface. That is to say, dividing the tooth load with a contact area on the reference face as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002084_j.cirpj.2010.03.005-Figure3-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002084_j.cirpj.2010.03.005-Figure3-1.png",
        "caption": "Fig. 3. Schematic representation of the skin\u2013core concept.",
        "texts": [
            "8 mm [15]. Yet, the accuracy and detail resolution of additive manufactured parts are negatively influenced by larger melt pools, which as a general rule, grow with larger beam diameters and layer thicknesses [2]. In order to avoid this negative influence of larger melt pool geometries the so-called skin\u2013core strategy has to be taken into consideration. According to this strategy the part to be built needs to be divided into an inner core and a skin which forms the outer contour of the part (see Fig. 3). Thus, different parameters for the outer skin and the inner core of a component can be chosen. Both, skin and core must have a density of approximately 100% to assure the same mechanical properties as conventionally manufactured components. However, the core does not have strict limitations and/ or requirements concerning accuracy and detail resolution. Hence, the core can be fast manufactured with a large beam diameter while the skin is manufactured with a small beam diameter in order to assure the part\u2019s accuracy and detail resolution. Fig. 3 depicts the skin\u2013core concept with different focus diameters. As discussed above an increase of the build rate by means of increasing the beam diameter and scanning velocity needs to be supported by higher laser power. Besides that, the new prototype plant must be equipped with a variable focus diameter in order to assure the accuracy of additively manufactured components. To realize this new concept a Trumaform LF250 was completely rebuilt, both in terms of hardware and software. In order to increase the process related build rate beyond [15] the maximum laser power should be extended to more than 500 W"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001329_j.actamat.2014.09.028-Figure2-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001329_j.actamat.2014.09.028-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram showing the DMD process.",
        "texts": [
            " The particles are mainly spherical, with an average particle size of 75 lm and 85% of the particles within the 60\u2013109 lm range. Powder was also mounted in epoxy, ground and polished to examine the powder particle cross sections, using SEM, for particle morphology, size and porosity measurements. A cross section of the as-received powder particles is shown in Fig. 1(b). Approximately 100 particles per micrograph were selected for measurement, and always the largest diameter and the diameter in the direction perpendicular to the long axis were measured. The average powder particle porosity was found to be 0.45%. Fig. 2 shows a schematic of the DMD process. The DMD system consisted primarily of a laser generation system, a powder delivery system, a feedback control system and the CNC motion stage [30]. The DMD process could be performed either in air or under a controlled atmosphere. DMD samples for this investigation were prepared at Focus, HOPE, using a 1 kW fiber coupled diode laser (Laserline GmbH, Germany) POM DMD 105D system. The authors have investigated the laser processing ers: (a) morphology; (b) cross section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002730_j.jmatprotec.2018.06.019-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002730_j.jmatprotec.2018.06.019-Figure1-1.png",
        "caption": "Fig. 1. Different types of samples with complex surface geometry. (a) Convex surface, (b) concave surface and (c) slant surface.",
        "texts": [
            " Based on the geometric model, the working distance could remain constant when conducting the experiments by using a 2D fiber laser, which is important in achieving a final smooth surface morphology. Characteristic observations of the complex surface geometry were conducted using optical profiling, scanning electron microscopy (SEM), Energy Dispersive XRay Spectroscopy (EDX), metallographic microscopy, and a Vickers hardness tester to analyze and quantify the surface properties of the samples before and after laser polishing. CoCr alloy samples with planar surface and complex surface geometry (convex surface, concave surface, slant surface as shown in Fig. 1) fabricated independently by means of selective laser melting were used in the experiments. Each sample was clearly labelled to distinguish the particular type of surface geometry to be studied. The CoCr powders used were supplied by SLM SOLUTIONS company with a density of 4.36 g/cm3 (composition: Cr= 28.23%, Co=64.76%, Mo=5.84%, Si= 0.46%, N=0.06%, Mn=0.50%, Fe=0.04%, Ni=0.04%, others\u22480.07%). The as-received surface morphology of the CoCr alloy samples was relatively rough, and could not meet the requirements for practical applications, so post processing is necessary to improve the surface quality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure2-10-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure2-10-1.png",
        "caption": "Fig. 2-10 all rotor space vectors are collinear (stator open-circuited).",
        "texts": [
            " assuming that the rotor \u201csomehow\u201d has currents while the stator is open-circuited, by analogy, we can write the expression for the rotor flux linkage space vector as \u03bbr i A r r A m r A r t L i t L i t, ( ) ( ) (= + due to leakage flux ) ( ) , due to magnetizing flux stator open = ( )L i tr r A (2-27) 20 INduCTIoN MaCHINE EQuaTIoNS IN PHaSE QuaNTITIES where the superscript \u201cA\u201d indicates that the rotor phase-A axis is chosen as the reference axis with an angle of 0\u00b0, and Lr\u00a0=\u00a0L\u2113r\u00a0+\u00a0Lm. Similar to the stator case, all the field quantities with the stator open circuited are collinear, as shown in Fig. 2-10. 2-7-3 Stator and Rotor Flux Linkages (Simultaneous Stator and Rotor Currents) When the stator and the rotor currents are present simultaneously, the flux linking any of the stator phases is due to the stator currents as well as the mutual magnetizing flux due to the rotor currents. The magnetizing flux density space vectors in the air gap due to the stator and the rotor currents add up as vectors when these currents are simultaneously present. Therefore, the stator flux linkage, including the leakage flux due to the stator currents can be obtained using Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0001724_j.ymssp.2011.04.018-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001724_j.ymssp.2011.04.018-Figure1-1.png",
        "caption": "Fig. 1. Single stage spur gear system model [5].",
        "texts": [
            " Actually, it studies the influence of both rotational speed variation and the fluctuations of an electric motor torque on the dynamic behavior of a single stage geared system. Section 3 uses the numerical simulation based on the Newmark integration method, to study the dynamic behavior of spur gear system powered, at a first stage, by an electric motor, then at a second stage, by four strokes four cylinders inline diesel engine. Conclusions are given in Section 4. A single stage spur gear transmission model with eight degrees of freedom is proposed [5] (Fig. 1). It is divided into two main blocks. Block 1 includes the driving motor and the pinion connected by a shaft. This block is supported by a bearing. Block 2 includes the wheel and the load connected by a shaft; it is supported by a second bearing. The Pinion has Z1 teeth and moment of inertia J11. The wheel has Z2 teeth and moment of inertia J22. A driving torque Cm is applied on the transmission loaded by a torque Cr. The gearmesh stiffness ke(t) is modeled by linear spring acting on the line of action of the meshing teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0002882_j.commatsci.2018.06.019-Figure1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0002882_j.commatsci.2018.06.019-Figure1-1.png",
        "caption": "Fig. 1. Summary of possible nucleation and growth mechanisms and their effects on the grain structure in MAM processes.",
        "texts": [
            " The characterization of these structural features is critical to understand MAM processes and helps to construct a map that links process parameters, structural features, and build properties [10]. In this paper, we focus on the meso-scale grain structure. Despite the variety of MAM processes and metal alloys, certain characteristics of grain structure can be identified from the literature. Both columnar and equiaxed grains are observed in MAM builds. Columnar grains are commonly observed growing epitaxially from the substrate or the previously deposited layer (collectively referred as the underlying layer) and toward the scanning direction of the heat source [4,8], as shown in Fig. 1. Equiaxed grains can be found distributed among columnar grains. Ref. [9] reported an interesting \u201csandwich\u201d grain structure where layers of equiaxed grains are observed between every two layers of columnar grains. In general, columnar grains are larger and have a stronger texture than equiaxed grains. Different grain morphology, size, and texture can be achieved by varying the input power, scanning velocity as well as the scanning pattern of the heat source, as widely reported in the literature [1\u20139]. Theories in welding metallurgy [11] can be conveniently utilized to qualitatively explain the occurrence of the above-mentioned characteristics of grain structure, as both in welding and MAM the metal material is subjected to a moving heat source with high energy input. Upon solidification, nucleation will preferably occur at the fusion line (Fig. 1) due to the lower activation energy. If the layer being built is of the same material as the underlying layer, which is often the case in MAM, the nuclei will preferably adopt the same crystallographic orientations as those of the partially melted grains in the underlying layer. This nucleation mechanism is referred as epitaxial nucleation [11]. After the epitaxial nucleation, grains will grow across the fusion line and along the local temperature gradient direction, which is approximately the local moving direction of the solidification front. This directional solidification leads to columnar grain shapes (the purple grains in Fig. 1). The grains with their certain crystal directions, e.g., the \u23291 0 0\u232a directions for the face-centered-cubic (FCC) and body-centered-cubic (BCC) materials, better aligned with the local temperature https://doi.org/10.1016/j.commatsci.2018.06.019 Received 17 February 2018; Received in revised form 8 June 2018; Accepted 9 June 2018 \u204e Corresponding author. E-mail address: wenda.tan@mech.utah.edu (W. Tan). Computational Materials Science 153 (2018) 159\u2013169 0927-0256/ \u00a9 2018 Elsevier B.V. All rights reserved. T gradient will outgrow the less aligned ones (such as the shaded purple grains in Fig. 1). This competitive growth mechanism [11] leads to \u201cfavored\u201d grains dominating the grain structure, and therefore, larger grains and stronger texture can be observed, as reported in [5,12,13]. Nucleation may also occur in the molten metal ahead of the solidification front, which is referred as the bulk nucleation as opposed to the \u201csurface\u201d epitaxial nucleation at the fusion line (Fig. 1). The nuclei from the bulk nucleation can grow to become equiaxed grains. The equiaxed grains can coexist with columnar grains, or even stop the growth of columnar grains, referred as the Columnar-to-Equiaxed Transition or CET (Fig. 1). In literature, analytical CET models [14\u201316] have been used to predict the volume percentage of equiaxed grains according to the local thermodynamic conditions of the solidification front. There have been multiple studies that utilize the CET models to explain the grain structure in MAM [7,17,18]. From the above discussion, it can be seen that the grain structure in MAM is complicated by a combination of different mechanisms. The qualitative welding theories and the analytical CET models, although having a solid physical background, cannot capture the complex scanning patterns in MAM as well as the randomness from a large quantity of grains, and thus fail to quantitatively predict the grain structure in MAM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_1_0000109_s0007-8506(07)63450-7-Figure15-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000109_s0007-8506(07)63450-7-Figure15-1.png",
        "caption": "Figure 15: Optical pressure on a microparticle caused by refraction (a) levitation and trapping, (b) rotation [ 561.",
        "texts": [
            " The part is retained by suction nozzles in the gripper on the one hand and - similar to an air bearing - separated from the gripper surface by an air cushion. The equilibrium of the forces holds the part in a suspended state without any mechanical contact. Laterally mounted stops on the gripper head prevent lateral slipping of the part from the gripper. 6.2 Optical trap or laser tweezers The optical pressure that occurs when light is refracted, absorbed or reflected by an object, can be used to manipulate objects with sizes ranging from a few micrometre to a few hundred micrometres. Figure 15a shows the forces that occur due to refraction in a microparticle. To trap the object, a focussed laser beam with a spot diameter of a few micron is aimed at the object. When the object moves away from the beam, the optical forces result in a restoring force. It works as well in liquid as in gas or vacuum. A liquid has the advantages that viscous damping increases the trap\u2019s stability and that the buoyancy force helps to levitate the object. For metallic objects, which have a high density, an additional levitating electrostatic force is best used, otherwise the required laser power will cause heating effects [55]",
            " Besides Brownian motions, fluid motions can also be generated by thermal gradients caused by absorbed laser light. Manipulation of the objects can also be disturbed by van der Waals forces which are orders of magnitude larger than the optical forces. This causes the objects to stick to other objects or to the recipient wall. Morishima et al. [57] successfully used laser tweezers to trap single Escherichia coli bacteria, while the rest of the bacteria are carried off by dielectrophoretic forces. Rotation of the object can be obtained by asymmetry of that object geometry. In the example given in figure 15b, the laser beam enters the object in the centre and perpendicular to the paper. The optical pressure on surface 1 generates a torque as indicated, while the resultant force on surface 2 goes through the object\u2019s centre and generates no resultant torque. No rays reach surface 3. Torques of lo-\u2019\u2019 Nm at rotational speeds of 500 rpm are reported for 3 pm diameter glass rods, 10 pm long [56]. Rotation can also be obtained by circularly polarised [58] or rotating higher-order mode laser beams [59], but reported rotational speeds are low: 0"
        ],
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    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure2-9-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure2-9-1.png",
        "caption": "Fig. 2-9 all stator space vectors are collinear (rotor open-circuited).",
        "texts": [
            " (2-23) (where the stator flux linkage due to the rotor currents is not included), the stator flux linkage space vector is \u03bbs i a s s a m s a s t L i t L i t, ( ) ( ) (= + due to leakage flux ) ( ) . due to magnetizing flux rotor open = ( )L i ts s a (2-26) as in the case of stator current and voltage space vectors, the projection of the stator flux-linkage space vector along a phase axis, multiplied by a factor of 2/3, equals the flux linkage of that phase. Flux lINKagES 19 We have seen earlier that i ts a( ) and F ts a( ) space vectors are collinear, as shown in Fig. 2-9; they are related by a constant. Collinear with F ts a( ), related by a constant \u03bc0/\u2113g, is the B ts i a s, ( ) space vector, which represents the flux density distribution due the stator currents only, \u201ccutting\u201d the stator conductors. Similarly, the stator flux linkage \u03bbs i a s t, ( ) in Fig. 2-9 (not including the flux linkage due to the rotor currents) is related to i ts a( ) by a constant Ls as shown by Eq. (2-26). Therefore, all the field quantities, with the rotor open-circuited are collinear, as shown in Fig. 2-9. Note that the superscript \u201ca\u201d is not used while drawing the various space vectors; it needs to be used only while expressing them mathematically, as defined with respect a reference axis, which here is phase-a magnetic axis. 2-7-2 Rotor Flux Linkage (Stator Open-Circuited) The currents in the rotor equivalent windings sum to zero, as expressed by Eq. (2-16). assuming that the rotor \u201csomehow\u201d has currents while the stator is open-circuited, by analogy, we can write the expression for the rotor flux linkage space vector as \u03bbr i A r r A m r A r t L i t L i t, ( ) ( ) (= + due to leakage flux ) ( ) , due to magnetizing flux stator open = ( )L i tr r A (2-27) 20 INduCTIoN MaCHINE EQuaTIoNS IN PHaSE QuaNTITIES where the superscript \u201cA\u201d indicates that the rotor phase-A axis is chosen as the reference axis with an angle of 0\u00b0, and Lr\u00a0=\u00a0L\u2113r\u00a0+\u00a0Lm"
        ],
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    },
    {
        "image_filename": "designv10_1_0000663_9781118910962-Figure3-5-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0000663_9781118910962-Figure3-5-1.png",
        "caption": "Fig. 3-5 Stator \u03b1\u03b2 and dq equivalent windings.",
        "texts": [
            " Using this logic, we can write the following flux expressions for all four windings: Stator Windings \u03bbsd s sd m rdL i L i= + (3-19) and \u03bbsq s sq m rqL i L i= + , (3-20) where in Eq. (3-19) and Eq. (3-20), Ls\u00a0=\u00a0L\u2113s\u00a0+\u00a0Lm. Rotor Windings \u03bbrd r rd m sdL i L i= + (3-21) and \u03bbrq r rq m sqL i L i= + , (3-22) where in Eq. (3-21) and Eq. (3-22), Lr\u00a0=\u00a0L\u2113r\u00a0+\u00a0Lm. 3-3-3 dq Winding Voltage Equations Stator Windings To derive the dq winding voltages, we will first consider a set of orthogonal \u03b1\u03b2 windings affixed to the stator, as shown in Fig. 3-5, where the \u03b1-axis is aligned with the stator a-axis. In all windings, the voltage polarity is defined to be positive at the dotted terminal. In \u03b1\u03b2 windings, in terms of their variables, v R i d dt s s s s\u03b1 \u03b1 \u03b1\u03bb= + (3-23) and v R i d dt s s s s\u03b2 \u03b2 \u03b2\u03bb= + . (3-24) The above two equations can be combined by multiplying both sides of Eq. (3-24) by the operator (j) and then adding to Eq. (3-23). In terms of resulting space vectors v R i d dt s s s s_ _ _\u03b1\u03b2 \u03b1 \u03b1\u03b2 \u03b1 \u03b1\u03b2 \u03b1\u03bb= + , (3-25) where v v jvs s s_\u03b1\u03b2 \u03b1 \u03b1 \u03b2= + and so on. As can be seen from Fig. 3-5, the current, voltage, and flux linkage space vectors with respect to the \u03b1axis are related to those with respect to the d-axis as follows: v v es s dq j da _ _\u03b1\u03b2 \u03b1 \u03b8= \u22c5 (3-26a) i i es s dq j da _ _\u03b1\u03b2 \u03b1 \u03b8= \u22c5 (3-26b) MATHEMATICAL RELATIONSHIPS OF THE dq WINDINGS 37 38 ANALYSIS OF INDUCTION MACHINES IN TERMS OF dq WINDINGS and \u03bb \u03bb\u03b1\u03b2 \u03b1 \u03b8 s s dq je da _ _= \u22c5 , (3-26c) where v v jvs dq sd sq_ = + and so on. Substituting expressions from Eq. (3-26a through c) into Eq. (3-25), v e R i e d dt es dq j s s dq j s dq jda da da _ _ _\u22c5 = \u22c5 + \u22c5\u03b8 \u03b8 \u03b8\u03bb( ) or v e R i e d dt e j d dt s dq j s s dq j s dq j da s da da da d _ _ _\u22c5 = \u22c5 + \u22c5 + \u22c5\u03b8 \u03b8 \u03b8 \u03c9 \u03bb \u03b8 \u03bb _dq je da\u22c5 \u03b8 . Hence, v R i d dt js dq s s dq s dq d s dq_ _ _ _= + +\u03bb \u03c9 \u03bb , (3-27) where ( / )d dt da d\u03b8 \u03c9= is the instantaneous speed (in electrical radians per second) of the dq winding set in the air gap, as shown in Fig. 3-3 and Fig. 3-5. Separating the real and imaginary components in Eq. (3- 27), we obtain v R i d dt sd s sd sd d sq= + \u2212\u03bb \u03c9 \u03bb (3-28) and v R i d dt sq s sq sq d sd= + +\u03bb \u03c9 \u03bb . (3-29) In Eq. (3-28) and Eq. (3-29), the speed terms are the components that are proportional to \u03c9d (the speed of the dq reference frame relative to the actual physical stator winding speed) and to the flux linkage of the orthogonal winding. Equation (3-28) and Equation (3-29) can be written as follows in a vector form, where each vector contains a pair of variables\u2014the first entry corresponds to the d-winding and the second to the q-winding: v v R i i d dt sd sq s sd sq sd sq d         =         +         + \u2212\u03bb \u03bb \u03c9 0 1 1 0               [ ] "
        ],
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    },
    {
        "image_filename": "designv10_1_0001224_978-94-017-8533-4-Figure6.1-1.png",
        "original_path": "designv10-1/openalex_figure/designv10_1_0001224_978-94-017-8533-4-Figure6.1-1.png",
        "caption": "Fig. 6.1 Single track model",
        "texts": [
            " The axle characteristics are so important that they need an in-depth discussion. This is done in Sect. 6.4.2. Summing up, the single track model is governed by the following set of six fairly simple equations: \u2022 two equilibrium equations m(v\u0307 + ur) = Y = Y1 + Y2 = may Jzr\u0307 = N = Y1a1 \u2212 Y2a2 (6.31) 6.4 Single Track Model 139 \u2022 two congruence equations \u03b11 = \u03b4v\u03c41 \u2212 v + ra1 u \u03b12 = \u03b4v\u03c42 \u2212 v \u2212 ra2 u (6.32) \u2022 two constitutive equations (axle characteristics) Y1 = Y1(\u03b11) Y2 = Y2(\u03b12) (6.33) A pictorial version of the single track model is shown in Fig. 6.1, where \u03b41 = \u03b4v\u03c41 and \u03b42 = \u03b4v\u03c42. Indeed, the equations governing such dynamical system are precisely (6.31), (6.32) and (6.33). Therefore, the system of Fig. 6.1 can be used as a shortcut to obtain the simplified equations of a vehicle. However, the vehicle model still has four wheels, lateral load transfers, camber and camber variations, roll steer. These aspects deserve further attention and will be addressed shortly. The main feature of this model is that the two wheels of the same axle undergo the same apparent slip angle \u03b1i , and hence can be replaced by a sort of equivalent wheel, like in Fig. 6.1. However, that does not imply that the real slip angles of the two wheels of the same axle are the same. Neither are the camber angles, the roll steer angles, the vertical loads. Therefore, the single track model is not really single track! 140 6 Handling of Road Cars Among the governing equations, only the two equilibrium equations are differential equations, and both are first order. Therefore, the single track model is a dynamical system with two state variables (namely, but not necessarily, v(t) and r(t), as discussed in Sect",
            " Here we suggest other possible couples of state variables, which may result in a more intuitive description of the vehicle motion. None of them is commonly employed, but nonetheless it is our opinion that they may provide some better insights into vehicle handling, if properly handled. It is worth remarking that these choices of state variables are by no means limited to the single track model. 6.5 Alternative State Variables 145 The first set, \u03b2(t) and \u03c1(t), has been already introduced in (3.16) and (3.17). They are repeated here for ease of reading (Fig. 6.1) \u03b2 = v u = \u2212 S R (3.16\u2032) and \u03c1 = r u = 1 R (3.17\u2032) The corresponding governing equations of the single track model becomes: 146 6 Handling of Road Cars \u2022 equilibrium equations m ( \u03b2\u0307u + \u03b2u\u0307 + u2\u03c1 )= Y Jz(\u03c1\u0307u + \u03c1u\u0307) = N (6.37) \u2022 congruence equations \u03b11 = \u03b4v\u03c41 \u2212 \u03b2 \u2212 \u03c1a1 \u03b12 = \u03b4v\u03c42 \u2212 \u03b2 + \u03c1a2 (6.38) \u2022 constitutive equations (from the axle characteristics) Y = Y(\u03b11, \u03b12) = Y1(\u03b11) + Y2(\u03b12) N = N(\u03b11, \u03b12) = Y1(\u03b11)a1 \u2212 Y2(\u03b12)a2 (6.39) 6.5 Alternative State Variables 147 Fig. 6.8 Comparison of axle characteristics obtained with very different set-ups The two first order differential equations (6.34), governing the single track model, become m ( \u03b2\u0307u + \u03b2u\u0307 + u2\u03c1 )= Y(\u03b2,\u03c1; \u03b4v) Jz(\u03c1\u0307u + \u03c1u\u0307) = N(\u03b2,\u03c1; \u03b4v) (6.40) where the terms on the r.h.s. do not depend on u (vehicle without wings). Another useful set of state variables may be the vehicle slip angles at each axle midpoint (Fig. 6.1) \u03b21 = \u03b2 + \u03c1a1 \u03b22 = \u03b2 \u2212 \u03c1a2 (6.41) The inverse equations are \u03b2 = \u03b21a2 + \u03b22a1 l \u03c1 = \u03b21 \u2212 \u03b22 l (6.42) The corresponding governing equations of the single track model become: 148 6 Handling of Road Cars \u2022 equilibrium equations \u03b2\u03071u + \u03b21u\u0307 + (\u03b21 \u2212 \u03b22) u2 l = Y m + N Jz a1 = Y1 mJz ( Jz + ma2 1 )+ Y2 mJz (Jz \u2212 ma1a2) \u03b2\u03072u + \u03b22u\u0307 + (\u03b21 \u2212 \u03b22) u2 l = Y m \u2212 N Jz a2 = Y2 mJz ( Jz + ma2 2 )+ Y1 mJz (Jz \u2212 ma1a2) (6.43) \u2022 congruence equations \u03b11 = \u03b4v\u03c41 \u2212 \u03b21 \u03b12 = \u03b4v\u03c42 \u2212 \u03b22 (6.44) \u2022 constitutive equations (from the axle characteristics) Y1 = Y1(\u03b11) Y2 = Y2(\u03b12) (6",
            "40), governing the dynamical system, become \u03b2\u03071u + \u03b21u\u0307 + (\u03b21 \u2212 \u03b22) u2 l = Y1(\u03b4v\u03c41 \u2212 \u03b21) mJz ( Jz + ma2 1 )+ Y2(\u03b4v\u03c42 \u2212 \u03b22) mJz (Jz \u2212 ma1a2) \u03b2\u03072u + \u03b22u\u0307 + (\u03b21 \u2212 \u03b22) u2 l = Y2(\u03b4v\u03c41 \u2212 \u03b22) mJz ( Jz + ma2 2 )+ Y1(\u03b4v\u03c41 \u2212 \u03b21) mJz (Jz \u2212 ma1a2) (6.46) where, again, the terms on the r.h.s. do not depend on u. These equations highlight an interesting feature. The last terms in both equations are often very small, and could even be purposely set equal to zero. Indeed, in road cars Jz ma1a2. Therefore, the coupling between the two equations is fairly weak. 6.6 Inverse Congruence Equations 149 Another possible set of state variables may be (Fig. 6.1) S = \u2212v r = \u2212\u03b2 \u03c1 = \u2212\u03b21a2 + \u03b22a1 \u03b21 \u2212 \u03b22 R = u r = 1 \u03c1 = l \u03b21 \u2212 \u03b22 (6.47) already introduced in (3.12) and (3.13). The corresponding governing equations of the single track model become: \u2022 equilibrium equations \u2212uS\u0307 R + u2 R = Y m + N Jz S uR\u0307 \u2212 u\u0307R R2 = \u2212N Jz (6.48) \u2022 congruence equations \u03b11 = \u03b4v\u03c41 + S R \u2212 a1 R \u03b12 = \u03b4v\u03c42 + S R + a2 R (6.49) \u2022 constitutive equations (from the axle characteristics) Y1 = Y1(\u03b11) Y2 = Y2(\u03b12) (6.50) The state variables v and r appear in both congruence equations (6.32)",
            "1, is the real measure of understeer/oversteer. The handling of road cars equipped with either a locked or a limited slip differential is addressed in Sect. 7.5, that is in the chapter devoted to race car handling behavior. This has been done because the limited slip differential is a peculiarity of almost all race cars, whereas very few road cars have it. The simplest dynamical systems are those governed by linear ordinary differential equations with constant coefficients. The single track model of Fig. 6.1 is governed by the nonlinear ordinary differential equations (6.111), unless the axle characteristics are replaced by linear functions Y1 = C1\u03b11 and Y2 = C2\u03b12 (6.145) where C1 = dY1 d\u03b11 \u2223\u2223\u2223\u2223 \u03b11=0 and C2 = dY2 d\u03b12 \u2223\u2223\u2223\u2223 \u03b12=0 (6.146) The axle lateral slip stiffness Ci is usually equal to twice the tire lateral slip stiffness, firstly introduced in (2.77). It is affected by the static vertical load (Fig. 2.18), but not by the load transfer, neither by the amount of grip. The influence of roll steer is quite peculiar (Fig",
            " Many modern cars use rack and pinion steering mechanisms. The steering wheel turns the pinion gear, which moves the rack, thus converting circular motion into linear motion. This motion applies steering torque to the front wheels via tie rods and a short lever arm called the steering arm. So far we have assumed the steering system to be perfectly rigid, as stated at p. 47. More precisely, Eq. (3.123) have been used to relate the steer angles \u03b4ij of each wheel to the angle \u03b4v of the steering wheel. In the single track model (Fig. 6.1) we have taken a further step, assuming that the left and right gear ratio of the steering system are almost equal, that is (\u03c411 = \u03c412) = \u03c41 and (\u03c421 = \u03c422) = \u03c42 (6.22\u2032) 6.18 Compliant Steering System 199 Fig. 6.45 Single track model with compliant steering system thus getting (6.74) (1 + \u03c7\u0302 )\u03b4 = \u03b41 = \u03c41\u03b4v \u03c7\u0302\u03b4 = \u03b42 = \u03c42\u03b4v (6.74\u2032) Now, in the framework of the linear single track model, we relax the assumption of rigid steering system. This means making a few changes in the congruence Eq. (6.148), since \u03b41 and \u03c41\u03b4v are no longer equal to each other"
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