diff --git "a/designv10-3.json" "b/designv10-3.json" new file mode 100644--- /dev/null +++ "b/designv10-3.json" @@ -0,0 +1,12811 @@ +[ + { + "image_filename": "designv10_3_0000547_1.3013844-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000547_1.3013844-Figure2-1.png", + "caption": "Fig. 2 Schematic arrangement of the cradle-style machine", + "texts": [ + " The position vector pe , represents the position of the points belonging to the generating tool surface. The parameter is the arc length measured on the blade profile and is the revolution angle about the tool axis z and are the surface Gaussian parameters . The parametric equations of the tool surface are assumed as known see, e.g., Ref. 5 . Modern six-axis CNC \u201cfree-form\u201d machines such as the Gleason Phoenix\u00ae II series reproduce the basic motions of the well known Gleason\u2019s cradle-style machine Fig. 2 . In addition, their modern controllers are provided with the so-called universal motion concept UMC , i.e., the basic machine settings can vary during generation as polynomial functions of the cradle rotation angle which acts as the motion parameter 19,20 . For instance, the basic blank offset EM0 and sliding base XB0 are just the constant terms of their corresponding UMC polynomials Xp p x=0 cutter axis R Zp fR1 x=L f P Q X f Zf x z Rp (II) (I) (III) f O pe Fig. 1 Outside blade of the grinding wheel \u201econjugate to the tooth concave side\u2026 Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use R r T n d t p e I t i v p n c T l g b e T fi B g f l m w t l R g t t d J Downloaded Fr XB = XB0 + H1 + 1 2H2 2 + 1 3H3 3 helical motion 2 atio of roll m0 is the coefficient of the linear term of the modified oll = m0 \u2212 2C 2 2 \u2212 6D 6 3 \u2212 24E 24 4 \u2212 120F 120 5 3 he UMC framework also includes other machine settings, amely see Fig. 2 , radial setting Sr known as modified raial motion , tilt angle , swivel angle , machine centero-back XD , and machine root angle m . 3.2 Tooth Surface Generation and Discretization. The aplication of the invariant approach 17,18 allows to obtain the nvelope surface, i.e., the tooth surface, as p , , with f , , = me , \u00b7 he , , = 0 4 n system 4 , p , , is the enveloping family of surfaces i.e., he sequence of tool surfaces as seen from an observer rotating by with the pinion/gear blank and f =0 is the equation of mesh- ng" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003887_s00170-019-04517-0-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003887_s00170-019-04517-0-Figure1-1.png", + "caption": "Fig. 1 Zemax simulation snapshot of laser irradiation of powder bed deposited on", + "texts": [ + " Notably, with this distribution, approximately 50% of the sample\u2019s mass comprised of particles with diameters less than d50 value (d50 = 38.52 \u03bcm); 10% of the tested sample\u2019s mass contain particles that have diameter smaller than d10 value (d10 = 22.94 \u03bcm); and 90% of sample\u2019s mass having particles with a diameter below the d90 (d90 = 56.88 \u03bcm). Based on the simulated powder size distribution, the sequential addition simulation model developed in a previous study by the present group [10] was used to construct 316L powder beds with thickness ranging from 10 to 70 \u03bcm. Figure 1 shows the typical simulation results of powder particles deposited on the solid substrate. Table 2 shows the calculated values of the packing density of the various powder layers. It is seen that the powder layers with thickness ranging from 10~30 \u03bcm have a packing density of less than 0.5, and are hence unsuitable for SLM processing [14]. Accordingly, the minimum powder layer thickness was set as 40 \u03bcm in the remaining analyses. The absorptivities of the powder beds with thickness of 40~70 \u03bcm were investigated using the Monte Carlo raytracing simulation model proposed in [10, 11]. In performing the simulations, it was assumed that the powder layer and the substrate were irradiated by a laser beam with a central wavelength of \u03bb = 1064 nm, and the powder and substrate material (SS 316L) had a refractive index of n = 3.27\u20134.48i [13]. Figure 1 presents a snapshot of the ray-tracing simulation process for the case of a powder bed with a thickness of 40 \u03bcm. Table 3 shows the simulation results obtained for the absorptivities of the powder layer, substrate below the powder layer and total system, respectively, for each considered value of the powder layer thickness. Observing the results presented in Table 3, it is seen that the absorptivity at the substrate for the powder layer with thickness of 40\u03bcm accounts for 40% of the total absorptivity, while that for the powder layer thickness of 50\u03bcm accounts for 26" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001623_tro.2012.2226382-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001623_tro.2012.2226382-Figure5-1.png", + "caption": "Fig. 5. (a) Configuration q\u0303 conforming to a part of the pathway along the colon below the splenic flexure. (b) Bending configuration \u0394 q (\u03b1, \u03b2) is a combination of odd and even joint angle values; therefore, it spans a different motion plane from the ones shown in Fig. 4(c). It is also one of the optimized configurations within the spatial constraint. (c) By superposing the two configurations in (a) and (b), the resultant configuration q = q\u0303 l+1 . . . l+ L + \u0394q 1 . . . L is obtained, which determines the bending of the last L links due to external manipulation. The remaining joints are fixed as q\u03031 . . . l to ensure conformance to the constraint pathway.", + "texts": [ + " ,\u03a9k+\u0394k} is selected, the distance from the constraint is calculated, as in (8). The positions of the surface vertices evenly covering robot link l can be automatically selected from the CAD model. They are only affected by the joint values q1...l = [q1 , q2 , . . . , q2l ]T ; therefore, the maximum deviation dl deduced from (9) will also be determined by joint values q1...l . When considering the deviation caused by the distal L links when the bending configuration \u0394qi is applied to the corresponding joint values q\u0303 L\u2212 L +1...L , as shown in Fig. 5(a), the robot vertices l+ixl+i i=1...Vl on link l + i relative to link frame {l + i} will be transformed to the world frame {w} as follows: [ xl+i i=1...Vl , 1 ]T =w l T [ l l+iT (q\u0303l+1...l+i +\u0394q1...i) ][ l+ixl+i i=1...Vl , 1 ]T . (15) Therefore, the distance constraint for the distal links i = 1, . . . , L can be expressed as follows: Dk,\u0394k i = dk,\u0394k l+i ( xl+i j=1...Vl (q\u0303l+1...l+i + \u0394q1...i) ) (16) where l = L \u2212 L. Note that every element of (q\u0303l+1...l+i + \u0394q1...i) will be limited by the physical bounds \u00b1qmax ", + " 4(d) shows four intermediate bending configurations at polar angles \u03c6j of 45\u25e6, 135\u25e6, 225\u25e6, and 315\u25e6. The optimal parameters \u03b1 and \u03b2 can be found by minimizing the same cost function as in (14) and considering the deviation constraint (17) but performing the search in a different domain ( \u03b1, \u03b2 ) = arg min \u03b1,\u03b2>0 { lzeff ( \u0394q(r,\u03c6j )(\u03b1, \u03b2) )} s.t. Dk,\u0394k i ( q\u0303l+1...l+i + \u0394q(r,\u03c6j ) 1...i (\u03b1, \u03b2) ) \u2264 bi, i = 1, . . . , L (20) where the same optimization solver used to find (m, qc) is adopted. With a new bending configuration \u0394 q(r,\u03c6j )( \u03b1, \u03b2 ) optimized as in Fig. 5(b), a list of control bending configurations { q(r,\u03d1j )} will then be updated by adding q(r,\u03c6j ) = q\u0303l+1...L + \u0394 q(r,\u03c6j ) so that n will be increased by 4. Fig. 5(c) shows a resultant bending configuration. Once the number of control configurations is fixed, we can describe the motion transition among them for panoramic visualization using cubic Hermite spline interpolation. For example, within the domain of \u03d1, the vector of Hermite basis functions in the interval [\u03d1i, \u03d1i+1] can be denoted by H \u03d1i + 1 \u03d1i (\u03d1) := [h1(u), . . . , h4(u)]T \u2208 4\u00d71 s.t. u = \u03d1 \u2212 \u03d1i \u03d1i+1 \u2212 \u03d1i \u2223 \u2223 \u2223 \u2223 \u03d1i \u2264\u03d1\u2264\u03d1i + 1 \u2208 [0, 1] i = 1, . . . , n, \u03d1 n +1 := \u03d11 . (21) Given the parameter r, the parametric configuration in the domain of \u03d1 can be expressed as \u0398r (\u03d1) = [ q(r,\u03d1i ) , ( q(r,\u03d1i + 1 ) \u2212 q(r,\u03d1i\u22121 )), q(r,\u03d1i + 1 ) , ( q(r,\u03d1i ) \u2212 q(r,\u03d1i + 2 ))] \u00b7 H\u03d1i + 1 \u03d1i (\u03d1), i = 1, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure5.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure5.8-1.png", + "caption": "Fig. 5.8 6-PSU parallel manipulator. A Hexaglide-type robot", + "texts": [ + " (2010), who concluded that the transmission wrench in each leg is a pure force, the main advantage of parallel manipulators equipped with 5.3 Equations of Acceleration in Screw Form 127 linear actuators. Jong et al. (2012) considered some relevant characteristics of the Hexaglide such as motor acceleration and torque as well as workspace accuracy for application in safe human interaction. The workspace and stiffness analyses of a Hexaglide-type robot were approached by Wang et al. (2013) by resorting to screw theory. Example 5.6. With reference to Fig. 5.8, we need to determine the input\u2013output equations of velocity and acceleration of the Hexaglide-type robot illustrated there. Let ! be the angular velocity vector of the moving platform .6/ as measured from the fixed platform .0/. Furthermore, let vC be the velocity vector of point C embedded in the moving platform where point C is chosen as the reference pole of the manipulator. Then the velocity state of the moving platform as observed from the fixed platform, the six-dimensional vector VC D ." + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure9.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure9.3-1.png", + "caption": "Fig. 9.3 Infinitesimal screws of the RR + RRR parallel wrist", + "texts": [ + "3 Example 8.1. Time history of the angular and linear velocities of the center of the moving platform . . . . . . . . . . . . . . . . . . . . 201 List of Figures xxi Fig. 8.4 Example 8.1. Time history of the angular and linear accelerations of the center of the moving platform . . . . . . . . . . . . . . . . 201 Fig. 9.1 The RR + RRR spherical parallel manipulator . . . . . . . . . . . . . . . . . . . . 206 Fig. 9.2 Geometric scheme of the RR + RRR parallel wrist. . . . . . . . . . . . . . . . 207 Fig. 9.3 Infinitesimal screws of the RR + RRR parallel wrist . . . . . . . . . . . . . . 211 Fig. 9.4 Example 9.3. Time history of the angular quantities of the knob as measured from the base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Fig. 10.1 The 3-RRPS parallel manipulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Fig. 10.2 3-RRPS parallel manipulator. Active revolute joint . . . . . . . . . . . . . . . 222 Fig. 10.3 Example 10.2. Time history of the infinitesimal kinematics of the center of the moving platform ", + " On the other hand, the forward velocity analysis consists of computing the velocity state VO given the generalized speeds Pq1 and Pq2. Example 9.2. The input\u2013output equation of velocity of parallel manipulators may be obtained using different sets of reciprocal screws. This example shows how the input\u2013output equation of velocity of the parallel wrist at hand may be obtained by using a different strategy than that used at the beginning of this subsection. For clarity, most of the notations used in Fig. 9.2 are repeated here (see Fig. 9.3). Solution. The procedure avoids the inclusion of virtual screws. The velocity state of the knob as measured from the base may be written in screw form through the 2-DOF kinematic chain as follows: Pq1 0$1 1 C 1!1 2 1$2 1 D VO: (9.15) Let L1 be a line of Pl\u00fccker coordinates passing through point P1 parallel to the OC line. Applying the Klein form of this line to both sides of Eq. (9.15) and canceling terms leads to Pq1 \u02da 0$1 1IL1 D fVOIL1g : (9.16) 212 9 Two-Degree-of-Freedom Parallel Wrist On the other hand, based on the 3-DOF kinematic chain, the velocity state VO may be written in screw form as follows: Pq2 0$1 2 C 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002817_tro.2016.2597314-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002817_tro.2016.2597314-Figure3-1.png", + "caption": "Fig. 3. Internal forces for various robots. Internal forces in point-foot robots correspond to tensions or compressions between pairs of supporting contacts.", + "texts": [ + " After various trials, we concluded that a proportional feedback control with motor velocity feedback in the torque controller and a PID control in WBOSC gives the best performance for the stance leg. Internal forces are associated with joint torques that produce no net motion. As such, internal forces correspond to mutually canceling forces and moments between pairs or groups of contact points, i.e., tensions, compressions, and reaction moments. For instance, a triped point-foot robot has three internal force dimensions, while a biped point-foot robot has a single internal force dimension, as shown in Fig. 3. Internal forces are fully controllable, since they are orthogonal to the robot\u2019s motion. As such, both the robot\u2019s movements and its internal forces can be simultaneously controlled. Moreover, in many types of contact poses, internal forces are easily identifiable using some physical intuition. For instance, in the triped pose of Fig. 3, the three feet can generate three virtual tensions between the points of contact. The physics of tension forces were analyzed in greater detail using a virtual linkage model in [13]. Internal forces are part of the core WBOSC. In Appendix A, we describe the model-based control structures enabling direct control of internal forces. In particular, the basic torque structure derived in (43) is \u03c4int = J \u2217T i|l ( Fint,ref \u2212 Fint,{t} + \u03bc\u2217 i + p\u2217i ) (3) where Fint,ref is the vector of desired internal forces, and Fint,{t} corresponds to the mapping of task torques into the internal force manifold" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000320_ip-b.1988.0042-Figure58-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000320_ip-b.1988.0042-Figure58-1.png", + "caption": "Fig. 58A Homopolar linear synchronous machine", + "texts": [ + " For a short secondary machine this additional cost is offset by the reduced weight of power conditioning equipment on the moving member and sliding contacts for main power transmission. To minimise the cost of the inverter required to supply long lengths of active track, the 3-phase winding is often divided into sections which are switched onto the inverter supply rails only when the short rotor is coupled to them. A synchronous machine which uses an unwound sec- Heteropolar linear synchronous machine DC winding AC coil plan Fig. 58B HLSM configuration, with staggered pole track and diamond shaped armature windings IEE PROCEEDINGS, Vol. 135, Pt. B, No. 6, NOVEMBER 1988 401 are on the moving member, and the track or reaction-rail consists of unwound steel. Fig. 57 shows a heteropolar, inductor type of synchronous motor, which has been investigated by several groups [60, 61]. The track bars are staggered alternately left and right of the longitudinal centre line and therefore receive flux from either the north or south pole outer limbs of the primary core", + " The return flux path through the centre limb therefore provides the centre limb with alternate north and south poles. This centre limb also contains a polyphase winding that reacts with the induced track poles to produce a propulsion thrust. The polyphase winding currents must obviously be synchronised to the track pole frequency using an inverter that is phase locked to the track poles. A simpler motor results if a homopolar principle is used. Figs. 58 show two versions of this type of motor, The one shown in Fig. 58A is really a transverse-flux [60, 61] variant of that in Fig. 58B [62, 63]. The two limbs of the primary are excited by the two DC coils to produce north poles on the left limb and south poles on the right. The polyphase winding on the right limb therefore experiences alternate strong and weak (owing to fringing) south poles moving along its length with the track bars. The left hand limb experiences a similar flux pattern of north poles. If the polyphase coils have a pitch approximately equal to the track bar longitudinal width, then AC voltages are induced in each winding proportional in magnitude to the DC excitation with a frequency synchronised to the track relative velocity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002621_s00170-015-8216-6-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002621_s00170-015-8216-6-Figure3-1.png", + "caption": "Fig. 3 Design of overhanging curved surface model and its orientation in Magics", + "texts": [ + "15 % O2. The material used in this paper was gas-atomized 316-L stainless steel, with an average particle size of about 17 \u03bcm, and the apparent density of the powder was about 4.04 g/cm3. Figure 2 shows the SEM image of the 316-L stainless steel powder with a mesh size of 500. Initially, the almost 100 % dense cube was fabricated in the experiment. The upper and side surface characteristics of the cube were analyzed. Then, 1/4 arc with a radius of 20 mm along the Z axis was designed, as shown in Fig. 3a. The part had a width of 10 mm and a thickness of 3 mm, and the scanned area was 10\u00d73 mm2 for each layer. The proposed model had the ability to ensure that the oblique angle between the current layer and the previous layer changed from 90\u00b0 at the bottom to an angle of approximately 0\u00b0 at the top. Hence, the proposed model could simulate the overhanging structure with an oblique angle of 0\u00b0~90\u00b0. The amount of overlap between the upper and lower layers decreased from the initial 100 to the final 0 %. To observe the distortion of the curved overhanging structure in a better way, a stainless-steel comb and a flexible scraper were used for recoating in the experiment to ensure that the manufacturing process progressed smoothly. To facilitate the analysis, the overhanging structure in Fig. 3 was divided into two surfaces, upper surface and downward surface. The points on the curved surface, whose oblique angles (represented by \u03b8) were equal to 80\u00b0, 60\u00b0, 45\u00b0, 30\u00b0, and 10\u00b0, were selected for analysis of surface morphology and measurement of roughness. The SLM technical parameters for the curved-surface model are shown in Table 1. In the model, the slice thickness was 25 \u03bcm, the scanning space was 80 \u03bcm, the diameter of the focusing spot was 70~80 \u03bcm, and X-Y orthogonal scanning was chosen as the scanning strategy", + " Nitrogen was used as protection gas, and the oxygen content was maintained below 0.02 % during the manufacturing process. The laser power of 120 W was maintained during the manufacturing process. Different laser energy inputs (i.e., \u0424=P/v (0.6, 0.3, 0.2, 0.15) J/mm) were obtained by setting different scanning speeds of (200, 400, 600, and 800 mm/s), respectively. The impact of laser energy input on the manufacturing quality was analyzed. The orientation, in which the curved overhanging structures were placed under four energy input conditions, is shown in Fig. 3b. The fabrication error could be measured by comparing the fabricated overhanging structure and the designed pattern, and the position where the morphology of the surface varied were labeled leveled. The fabrication technique of the overhanging structures could be optimized from the summary of the above parameters. Finally, this technique was verified by directly fabricating nonassembly parts with complicated curved overhanging structures. In this study, the JB-8c type contact stylus roughness meter was used for measuring Ra and Rz, where Ra was the deviation from the contour\u2019s arithmetic average and Rz was the contour\u2019s maximum height" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.17-1.png", + "caption": "FIGURE 5.17. A planar slider-crank linkage, making a closed loop or parallel mechanism .", + "texts": [ + " Because in DH method of setting coordinate fram es, a translation D and a rotat ion R are about and along one axis, it is immaterial if we apply the trans lation D first and then the rotation R or vice versa. Therefore, we can change the order of D and R about and along the sam e axis and obtain the same DH transformation matrix 5.11. Therefore, (5.52) Example 142 * 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 satis fied by this connection. Figure 5.17 depicts a planar slider-crank linkage R.l.A-RIIRIIR and DH coordinat e fram es installed on each link . 5. Forward Kinematics 223 where the transformation matrix [T ] contains elements that are functions of a2, d, a3, 03, a4, 04, and 01 . Th e parameters a2, a3, and a4 are constant while d, 03, 04, and 01 are variable. Assuming 01 is input and specified, we may solve for other unknown varia bles 03, 04, and d by equating corre sponding elements of [T] and I. Example 143 * Non-standard Denavit-Hartenberg notation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000339_s0022112005004829-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000339_s0022112005004829-Figure6-1.png", + "caption": "Figure 6. (a) The boxed figure depicts the fibre-flow plane and the dihedral angle \u03c8 it makes with the plane of shear. The disturbance velocity field of the fibre in the fibre-flow plane is shown on (b) for an orientation with \u03c6 >\u03c6c . (c) The resulting streamlines, again in this plane, and the resulting array of inertial point forces. The sense of the net inertial torque is shown by the two curved arrows.", + "texts": [ + " More fundamentally, the symmetry of the leading-order quasi-steady disturbance velocity field about the fibre-flow plane implies that Eulerian unsteadiness by itself, while affecting the orbit phase (and thus, the precise value of \u03c6c), will not induce a motion orthogonal to the fibre-flow plane, leaving the orbit constant unchanged in the slender-body limit. We therefore base our physical arguments on the quasi-steady disturbance velocity field. The instantaneous streamlines in the fibre-flow plane (\u03c8 = constant) for fluid motion around the slender fibre are shown in Figs 6 and 7. In figure 6 where \u03c6 <\u03c6c < \u03c0/2, the perturbed streamlines meet the fibre at right angles to its length, satisfying the boundary condition of solid-body rotation; the directions of the inertial forces (\u221d u \u00b7 \u2207u) resulting from the streamline curvature are indicated by the little arrows. The tighter spacing of streamlines on the side where the fibre makes an acute angle with the flow axis implies an acceleration of the fluid here relative to the obtuseangled region, so the corresponding point forces are greater in magnitude, indicated by longer arrows in the figure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003603_tie.2020.2977578-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003603_tie.2020.2977578-Figure6-1.png", + "caption": "Fig. 6. Entail structural FE model.", + "texts": [ + " It can be calculated based on the modal superposition method and expressed as [ ] [ ] [ ] { ( , )} N N N i i i i i i r i i i M x C x K x F t (12) The synthetic vibration deformation can be written as 1 N i i i x (13) However, the contribution of high-order modes and high-order radial force harmonics to the vibration response is weak. It is sufficient to consider low-order radial force harmonics and low-order modes for the vibration response calculation. The entail structural FE model of the 48-slot/22-pole DTP-PMSM is shown in Fig. 6. The structural FE model contains housing, end caps, bolts and stator cores. The windings are equivalent to the stator tooth as an additional mass. The front and rear end caps of the FE model have same restrictions condition with that of the actual installation. At present, there are two prevailing radial force transfer methods for motor vibration prediction, i.e. concentrated nodal force mapping method and distributed nodal force mapping method. In fact, the radial force act on stator teeth is distributed rather than concentrated at one point. The force distribution of distributed radial force mapping method is closer to that of the actual situation [28]. In order to improve the accuracy of vibration calculation, the distributed radial force mapping method is adopted as shown in Fig. 6. Furthermore, the multiphysics vibration predicted model is established to compare the vibration behaviors of the 7.5\u00b0, 30\u00b0 and 60\u00b0 configurations. As shown in Fig 7, the multiphysics vibration prediction model contains three parts, namely electromagnetic force calculation module, modal analysis module and vibration response module. The electromagnetic force and structural modes are calculated by FE method, and the modal superposition method is adopted to calculate the motor vibration response. It should be emphasized that the actual modal damping and orthotropic material parameters should be obtained by modal test" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000855_tie.2011.2159357-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000855_tie.2011.2159357-Figure1-1.png", + "caption": "Fig. 1. Magnetic spur gear.", + "texts": [ + "1109/TIE.2011.2159357 I. INTRODUCTION MAGNETIC gears have some advantages such as low mechanical loss and maintenance-free operation that are not observed in conventional mechanical gears. In addition, magnetic gears have inherent overload protection. Therefore, magnetic gears are expected to be used in special applications. e.g., in humanoid robot joints. However, most of the previous magnetic gears, such as a magnetic spur gear, have problems with transmission torques. The magnetic spur gear in Fig. 1 has a simple structure, but the area of interaction between the two gears is extremely small, and a lot of loss from magnetic short circuiting occurs. Therefore, the transmission torque is insufficient for practical use. Recently, various types of new magnetic gears have been proposed [1]\u2013[11]. Reference [1] proposes a surface-permanentmagnet-type (SPM-type) magnetic gear employing magnetic flux harmonics, [2], [5], and [11] propose a cycloid-type magnetic gear, [3] proposes an axial-gap-type magnetic gear, [4] proposes a variable-speed magnetic gear, [7] and [8] propose a magnetic harmonic gear, [6] proposes a magnetic gear with coils in the high-speed rotor, [9] proposes a linear-type magnetic gear, and [10] proposes a magnetic planetary gear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003053_978-0-8176-4962-3-Figure3.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003053_978-0-8176-4962-3-Figure3.1-1.png", + "caption": "Fig. 3.1. Inverted cart\u2013pendulum.", + "texts": [ + ", the initial conditions x (k) a (0) should satisfy the equations CAk\u22121x (k\u22121) a (0)\u2212 Cx (k) a (0) = 0 for k > 1 Cy (0)\u2212 Cx (1) a (0) = 0 for k = 1 So, the realization of the observer in (3.31) takes the form x\u0302 (t) := x\u0303 (t) +O+vav (t) vav = [( Cx (1) a \u2212 Cx\u0303 (t) )T ( v (1) av )T \u00b7 \u00b7 \u00b7 ( v (l\u22121) av )T ]T (3.34) An example of the proposed observer design is given in Chap. 4. To illustrate the procedure given above, let us take again the linearized model of an inverted pendulum over an inverted cart\u2013pendulum (Fig. 3.1). The motion equations are as follows: x\u0307 (t) = Ax (t) +B (u0 + u1) +B\u03b3 (x, t) y (t) = Cx (t) (3.35) 3.6 Example 29 A = \u23a1 \u23a2 \u23a2 \u23a3 0 0 1 0 0 0 0 1 0 1.2586 0 0 0 7.5514 0 0 \u23a4 \u23a5 \u23a5 \u23a6 , B = \u23a1 \u23a2 \u23a2 \u23a3 0 0 0.1905 0.1429 \u23a4 \u23a5 \u23a5 \u23a6 , C = [ 1 0 0 0 0 0 0 1 ] \u03b3 (t) = {\u22120.4 n\u2212 5 \u2264 t < n\u2212 2.5 0.4 n\u2212 2.5 \u2264 t < n , n = 5, 10, . . . The state vector x consists of four state variables: x1 is the distance between a reference point and the center of inertia of the cart; x2 represents the angle between the vertical and the pendulum; x3 represents the linear velocity of the cart; finally, we have that x4 is equal to the angular velocity of the pendulum" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure14.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure14.12-1.png", + "caption": "Figure 14.12.1 Example axle with link location, using a Watt\u2019s linkage at each end.", + "texts": [ + "With the pushrod system this allows the front dampers to lie above the driver\u2019s legs, permitting the best aerodynamic shape for the front part of the vehicle. In these more complex systems, when analysed as a series of two-dimensional sub-mechanisms, it may be necessary to incorporate some cosine factors to correct for out-of-plane motions, but these are usually quite small. Solid car axles, driven or undriven, may be located either by leaf springs, the Hotchkiss axle if driven (\u2018live\u2019), or, more often nowadays, by links. The springs and dampers may act on the axle itself, or on the links, as in Figure 14.12.1. For bumpanalysis, if the spring or damper acts directly on the axle, as in Figure 14.12.2, above thewheel centreline, and the springs or dampers are vertical, then the motion ratio is very close to 1.0. However, the springs or dampers are sometimes angled, inwards at the top, inwhich case the bumpmotion ratio is cos uK or cos uD. If the springs act on the locating links, then the velocity diagram needs to be drawn, as in Figure 14.12.1. With this configuration, some rising rate can be achieved by angling the springs or dampers in side view. The vertical wheel velocity is found from thewheel centre, and its relationship to points B and C. The axle angular speed vA is Installation Ratios 289 and the pitch/heave velocity ratio or coefficient \u00abAPH is \u00abAPH \u00bc vA VS rad=m\u00bd Toanalyse the roll stiffness or dampingof thevehicle, for a simple axle, consider thevehicle to roll about the rollcentre for theaxle,which is thepointof lateral location in thecentreplane.Forexample, in thecaseof the use of a Panhard rod for lateral location, it is the point at which the rod pierces the longitudinal central vertical plane. The velocity diagram in Figure 14.12.2 shows that the damper velocity VD is VD \u00bc vl1cos\u00f0f1 \u00fe uK\u00de so the damper velocity ratio in roll is RKf \u00bc l1cos \u00f0f1 \u00fe uK\u00de \u00bdm s--1=rad s--1 \u00bc m=rad This will generally be substantially less than would be achieved with the springs acting directly at the wheels. This is because l1 is typically only about 0.7 of half the track, to allow the springs to clear the wheels. This substantially reduces the roll stiffness, which may therefore be supplemented by an anti-roll bar. On the other hand, on a driven axle, the lower roll stiffness may be held to be an advantage, giving better traction during cornering" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002587_9783527684984-Figure13.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002587_9783527684984-Figure13.5-1.png", + "caption": "Figure 13.5 Step response curve for the determination of PID parameters.", + "texts": [ + " The ultimate gain method is performed by the following steps. 2) increase Kp until continuous oscillations occur; 3) record the ultimate gain of Kp when oscillations occur as K c and the oscilla- tion cycle time, Tc; and 4) Determine parameters according to Table 13.2. The step response method uses the process response to the step change of input as illustrated below. The step response method is performed using the following steps. 2) Determine the slope,R, of the slope line and a lag time, L, as graphically shown in Figure 13.5. 3) Determine the parameters according to Table 13.3. Figure 13.6 compares the typical response of P, PI, and PID controllers against the step change of a set-point. As can be seen, a well-tuned PID controller realizes Kp T I Td P control 1/LR \u221e 0 PI control 0.9/LR 3.5L 0 PID control 1.2/LR 2.0L 0.5L a quick response with minimum off-set. For more information, please refer to the Further Reading section at the end of the chapter. 13.3.3.1 pH and Temperature Control As previously mentioned, the control of pH and temperature is of great importance in any bioprocess, since all biocatalysts have their optimal pH and temperature for cell growth and product formation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002696_s11071-014-1745-y-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002696_s11071-014-1745-y-Figure8-1.png", + "caption": "Fig. 8 Schematics of the defect size used in vibration response comparisons applying different defect models: a front view of the ball bearing and b top view of the ball bearing", + "texts": [ + " The elevation angle \u03b3 and the length l of the small surfaces at defect edge are assumed to be 0.4 rad and 0.02 mm. The different defect models include Rafsanjani et al.\u2019s model [2], Patel et al.\u2019s model [18], time-varying deflection excitation model [23], and the proposed model considering both the time-varying deflection excitation and the time-varying contact stiffness excitation. For these four different defect models, the surface areas are assumed to be same, which means the length L and width B of the defect are same, as shown in Fig. 8. Figure 9a\u2013d shows the time- and frequency-domain acceleration response in the X -direction from Rafsanjani et al.\u2019s model, Patel et al.\u2019s model, time-varying deflection excitation model, and the proposed model. Note that the time delay between the impulses caused by the defect is same for the four different models, which is equal to 0.0098 s as shown in Fig. 9a. However, there are significant differences between the waveforms of the acceleration response from the four different models. As shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000759_s1560354708050079-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000759_s1560354708050079-Figure1-1.png", + "caption": "Fig. 1. Body on a plane.", + "texts": [ + " In addition, we will consider the rolling of bodies, when only slipping is absent (i.e., the spinning is allowed by constraints); this system will be called the smooth, or marble body (the term is suggested in [14]). Configuration space and kinematic relations. The configuration space of the system considered is the product M = R 3 \u2297 SO(3), here the first factor describes the position of the center of mass of the body and the second \u2014 the orientation of the body. We introduce the following two coordinate systems (see Fig. 1): \u2022 immovable system OXY Z, whose origin O is located at some point of the plane and the OZ-axis is perpendicular to the plane; \u2022 movable system Cxyz, whose origin C is located at the center of mass of the body and the axes are directed along the principal axes of inertia of the body. Let \u03b1,\u03b2,\u03b3 be the projections of the orths of the immovable space (i.e., the unit vectors of OXY Z) on the movable axes Cxyz and R = (R1, R2, R3) be the coordinates of the center of mass of the body in the system OXY Z", + " Note that this simple form of the equations of constraints is due to the special choice of the basis of vector fields (1.11); for example, in the Euler angles the constraints have a cumbersome form. The Lagrange function of a free rigid body has the form L = T \u2212 U. The kinetic energy in the coordinate system Cxyz has the form T = 1 2 mv2 + 1 2 (\u03c9, I\u03c9), where m is the mass of the body and I = diag(I1, I2, I3) is the tensor of inertia. The potential energy in the gravity field can be represented in the form (see Fig. 1) U = mgh = \u2212mg(r,\u03b3), (1.16) where g is the free fall acceleration. Since r = r(\u03b3), the potential U depends only on \u03b3 (i.e., U = U(\u03b3)). REGULAR AND CHAOTIC DYNAMICS Vol. 13 No. 5 2008 Equations of motion with undetermined multipliers. Writing Eqs. (1.9) taking (1.12) and (1.13) into account, we obtain the system, which describes motions of a heavy rigid body on the plane with constraints (1.14) and (1.15): mv\u0307 = mv \u00d7 \u03c9 + \u03bb, I\u03c9\u0307 = I\u03c9 \u00d7 \u03c9 \u2212 \u2202U \u2202\u03b3 \u00d7 \u03b3 + r \u00d7 \u03bb + \u03bb0\u03b3, \u03b1\u0307 = \u03b1 \u00d7 \u03c9, \u03b2\u0307 = \u03b2 \u00d7 \u03c9, \u03b3\u0307 = \u03b3 \u00d7 \u03c9, R\u03071 = (\u03b1,v), R\u03072 = (\u03b2,v), R\u03073 = (\u03b3,v), (1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001098_tmech.2008.2008802-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001098_tmech.2008.2008802-Figure2-1.png", + "caption": "Fig. 2. NH-WMM nomenclature.", + "texts": [ + " Section II briefly reviews the mathematical model of the NH-WMM. Section III develops the decoupled yet dynamically consistent redundancy resolution method. Section IV develops the two variants of the null-space controllers. The virtual prototyping (VP) and hardware-in-the-loop (HIL) experimentation framework is presented in Section V. In Section VI, the framework is used for evaluation of the proposed controller. Section VII concludes the paper with a brief discussion. We first present the dynamic modeling of the NH-WMM, as shown in Fig. 2, focusing primarily on the notation to be used in this paper. We broadly follow the development of the The WMR subsystem is actuated by two independently driven wheels of radii r located at an equal distance b on either side of the midline. The wheel axes are collinear and are located at a perpendicular distance d from the center of mass (CM). The other related physical properties and parameters are listed in Table I. The instantaneous WMR configuration can be fully described by the extended set of generalized coordinates qT B = [xc yc \u03c6 \u03b8R \u03b8L ], where (xc, yc) is the Cartesian coordinates of the CM, \u03c6 is the orientation of the WMR, and \u03b8R and \u03b8L are the angular positions of the right and left wheels, respectively", + " The NH-WMM is constructed using two geared motor powered wheels and one passive Mecanum-type casters. A passive Mecanum-type front caster is preferred (over a conventional wheel caster) to eliminate any constraints on the maneuverability. The mounted manipulator arm has two active revolute joints with axes of rotation parallel to each other and perpendicular to the mobile platform (and the ground). The first joint can be placed anywhere along the midline on top frame of the platform at a distance Ld = d + La from the center of the wheel axle (see Fig. 2). The end-effector is a flat plate supported by a passive revolute joint that ensures that no moment can be transferred to the manipulator. Each of the two joints is instrumented with an optical encoder that can measure the joint rotations and has a dc motor attached. Independent lead\u2013acid batteries provide power supplies for the actuator systems and the electronic controllers. The complete assembled two-link mobile manipulator is shown in Fig. 1(b). A PC/104 system equipped with an xPC Target real-time operating system (RTOS) serves as the embedded controller" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000214_j.ymssp.2007.07.007-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000214_j.ymssp.2007.07.007-Figure1-1.png", + "caption": "Fig. 1. Spherical roller bearing [1].", + "texts": [ + " Xiao / Mechanical Systems and Signal Processing 22 (2008) 467\u2013489468 ARTICLE IN PRESS M. Cao, J. Xiao / Mechanical Systems and Signal Processing 22 (2008) 467\u2013489 469 The most widely applied bearings are ball bearings and roller bearings. While ball bearings are usually used for moderate loading scenarios, roller bearings have much higher load-supporting capacity due to the larger structure stiffness compared with ball bearings. A sketch of a double-row spherical roller bearings (SRBs), as shown in Fig. 1, have seen a lot of applications, largely due to its self-aligning capability inherently comes from the fact that the outer race of this type of bearings is a portion of a sphere. Although SRB has been extensively applied [1], comprehensive investigation of its dynamic behaviors has yet to be addressed, largely due to the lack of dynamic modeling effort. While the roller dynamics of single row deep-grooved-ball bearings under certain imperfect configurations have been addressed by Harsha et al. [2,3], the works reported so far are not applicable to double-row SRB because of the different geometry configuration", + " Providing an alternative way to formulate the inner race/outer race stiffness coefficients, Bercea\u2019s model is mainly a static model, and thus cannot deliver detailed analysis of the complex dynamic behaviors of SRB systems involving nonlinear interactions between rollers and inner/outer races. Compared with the single-row deep-grooved ball (DGB) bearing, the degree of freedom (DOF) of doublerow SRBs significantly increases, and the axial displacements of the shaft and moving race (inner race for fixed-outer-race configuration, and outer race for fixed-inner-race configuration) have to be accounted. As demonstrated in Fig. 1, now the contact forces between each one of a pair of rollers and the inner race/outer race could be different. To further improve the state of the art in dynamic system modeling of SRBs, in this paper, an analytical spherical-roller-bearing excitation source model is developed and studied. In addition to the vertical and horizontal displacements considered in previous investigations, the impacts of axial displacement/load are addressed by introducing a DOF in the axial shaft direction. Hence, instead of being treated as pre-assumed constants, the roller-inner/outer race contact angles are formulated as functions of the axial displacement of the moving race to reflect their dependence on the axial movement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002127_j.addma.2016.10.009-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002127_j.addma.2016.10.009-Figure6-1.png", + "caption": "Fig. 6. A diagrammatic sketch of laser inclination and reflection angle.", + "texts": [ + " Mazumder and Steen [48] nvestigated the effect of the plasma working gas. Zhang et al. [49] eveloped a sandwich method which considered both Fresnel and nverse Bremsstrahlung absorption during keyhole formation. An ssumption of multiple reflections of laser energy along the keyhole alls was proposed and then analyzed using a ray-tracing method 43,50,45]. It was assumed that a laser ray hit the keyhole on the th segment of the keyhole wall for the jth time with an angle of j and then reflected with an angle of \u02c7j with respect to the verical direction as shown in Fig. 6. The segment of keyhole wall has n angle of i with respect to the horizontal direction. The relation etween these angles can be represented as: j = 2 i \u2212 \u02dbj (1) lso, the reflected ray from Eq. (1) will become the j + 1th ray with n incident angle of: j+1 = \u2212 \u02c7j (2) he jth incident angle of the laser ray also has an angle of j with espect to the ith segment of keyhole wall normal Ni: j = i \u2212 \u02dbj (3) he reflectivity Rj of the jth laser ray can be calculated from the ngle j for different types of lasers, such as the CO2 laser from 35]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure5.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure5.2-1.png", + "caption": "Fig. 5.2 a Example of an inequality constraint further reducing the feasible solution space. b Example of an instance where the value of the cost places its linear equation within the feasible solution space", + "texts": [ + " This valid region of R2 can be called a feasible solution space. Then, the goal is to find an optimal point in that space that minimizes, or maximizes, the cost function. Figure5.1 shows how the first 4 inequality constraints reduce the feasible solution space to a polygon (in this case a parallelogram) in the first quadrant of R2. By the same logic, the last inequality constraint equation is the non-trivial line x1+ x2 \u2264 c that excludes an open half-plane, and can further limit the solution space depending on the relative values of a, b, and c. Figure5.2a, shows an example where this last inequality constraint further reduces the feasible solution space. Note also that the cost function itself is a linear equation, but whose value is yet to be determined. To see this more clearly, assume the cost is equal to the value of b. Then, the cost function cost = b = x1 + 2 x2 can be rewritten as x2 = \u2212 1 2 x1 + b 2 (5.32) the latter version being in the more commonly known slope-intercept form, with a slope of \u2212 1 2 and intercept of the ordinate axis at the value of b 2 . In Fig. 5.2b we see an example where some portion of the cost function line lie within the feasible solution space. Note that in that case all points on the cost function line that also lie within the feasible solution space are valid, and produce the same cost. This is another interpretation of an underdetermined system (i.e., redundancy): There can be infinitely many valid solutions (i.e., x points in the feasible solution space) that produce a same result (i.e., a same cost). Last, Fig. 5.3 shows the purpose of linear programming: Find a value of the cost (i", + "19) \u2022 Linear inequality constraints representation: This is the converse process where you use linear inequality constraints to define the lines, planes, or hyperplanes that form the facets of the convex (and bounded) set. The intersections among them define the vertices. This is precisely what is shown in Fig. 5.1. You see that the unit square is well defined by the set of 4 linear inequality constraints as in Eq. 5.31 5In the case of unbounded polygons, polyhedra, and polytopes you also need to specify the direction of the rays that emanate from some of the vertices. 7.6 Anatomy of a Convex Polygon, Polyhedron, and Polytope 109 x1 \u2264 1 x2 \u2264 1 x1 \u2265 0 x2 \u2265 0 (7.20) Moreover, Fig. 5.2 shows a critical departure from a Minkowski sum. This is done by adding another inequality constraint that truncates the unit square (or cube or N-cube) to create an irregular polygon, polyhedron or polytope. Generally, the square is a zonotope that can be generated by the Minkowski sum of its generators, the unit vectors (1, 0)T and (0, 1)T . And the feasible sets in Figs. 7.3 and 7.5 are created in a similar way. But the truncated square in Fig. 5.2 is not necessarily a zonotope, but rather a convex polygon that can be represented by its vertices or a set of linear inequality constraints. The distinction that all zonotopes are bounded polygons, but not all bounded polygons are zonotopes will become important in the next chapter. Regardless of whether you use the vertex or linear inequality constraint representation, what makes a set convex (as opposed to concave) is the fact that any point belonging to the set can be calculated as some linear combination of its vertices [13]", + "3 shows you need to define a cost function and constraints to define the desired direction, and then use a numerical algorithm to maximize force magnitude in that given direction. However, if the feasible wrench set is known (the feasible force set in Fig. 7.7 for this example), all we need to do is to send a ray from the origin in any desired direction. The point where that ray meets the boundary of the feasible force set is, by definition, the maximal possible force in that direction [20]. More general cases, however, do not have the generic unit positive N-cube as their feasible activation set. Take, for example, the linear programming problem in Fig. 5.2, where we have the system of inequality constraints that define the unit square, plus the constraint x1 + x2 \u2264 c as shown in Eq.5.31. The feasible activation set is thus a convex polygon that is a subset of the unit square, Fig. 5.2. This same principle applies in higher dimensions. Consider the questions I approached for my doctoral dissertation: what are the feasible activation and feasible force sets for a human index finger [20, 21]? In this case we have an extended version of Eq.5.22 where we have a 3D finger with 4 DOFs and 7 muscles, shown in Fig. 8.1 and Eq.8.1 w = \u239b \u239c\u239c\u239d fx fy fz \u03c4z \u239e \u239f\u239f\u23a0 = J\u2212T RF0 \u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d a1 a2 a3 a4 a5 a6 a7 \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 = J\u2212T R F0 a w \u2208 R 4 (8.1) J\u2212T \u2208 R 4\u00d74 R \u2208 R 4\u00d77 F0 \u2208 R 7\u00d77 a \u2208 R 7 8.2 Calculating Feasible Sets for Tasks with Functional Constraints 117 You could of course map the 7D N-cube as the feasible activation set, but what you would get is a 4D convex polytope in wrench space (the feasible wrench set) with 3 dimensions of force and 1 dimension of torque" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.4-1.png", + "caption": "Fig. 1.4 Determining the center of gravity in a motor vehicle; a) Horizontal position; b) Tilted position", + "texts": [ + " For larger bodies, such as cranes and motor vehicles, the mass distribution is frequently determined by measuring the support forces. Figure 1.3 shows the measurement on a connecting rod. If the support force m1g has been determined, the centroidal distance is 16 1 Model Generation and Parameter Identification \u03beS = m1l m . (1.5) For a symmetrical connecting rod, an axis through the center of gravity is provided by the symmetry line. Otherwise, the missing second axis through the center of gravity can be found by tilting the body axis. This will be demonstrated using the example of a motor vehicle. According to Fig. 1.4, the following are given: l = 2450 mm; h = 500 mm; d = 554 mm. Measurements were taken a) in horizontal position F1 = 4840 N b) in tilted position F2 = 5090 N The overall weight is FG = 9918 N. The following results for the horizontal position (a): l1 = lS = F1l FG . (1.6) The following applies to the tilted position (b): l2 = F2l cos \u03b1 FG ; sin\u03b1 = h l . (1.7) The height of the center of gravity hS is calculated as follows: hS = ( l2 cos \u03b1 + l\u2217 \u2212 l1 ) 1 tan \u03b1 ; l\u2217 = d 2 tan \u03b1 hS = d 2 + F2 \u2212 F1 FG \u00b7 l2 h \u221a 1\u2212 ( h l )2 (1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure10.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure10.9-1.png", + "caption": "Fig. 10.9 Direct-axis flux path of a turbo-generator.", + "texts": [ + " One suggestion is to use an empirical value of p, based on earlier test results, to allow for both the temperature and the end-effects. A simple assumption led to a useful method of studying the asynchronous operation of a turbo-generator at low slip. Consider the condition when the rotor is at rest in a position where the d-axis coincides with the flux axis of two armature phases in series. The direct-axis flux, when the two stator phases are excited at low frequency by a single-phase voltage, is assumed to flow as indicated by the dotted lines in Fig. 10.9. Because of the skin effect caused by the eddy currents in the rotor iron, the flux is forced outwards and is concentrated in a band of iron material at each side of the rotor body. Since the area of the surface at which the skin effect occurs is known, the flux due to a given m.m.f. and hence the effective impedance can be calculated. Details of the calculation are given in [28]. Fig. 10.10 gives the frequency locus of the direct-axis operational impedance, with the field circuit open, by measurement and calculation for a 75 MV A turbo generator", + " (d) A further error occurs because the direct and quadrature axis fluxes flow together in some of the iron material during any practical operating condition, and cannot strictly be superimposed if there is any saturation. A synchronous motor with a rotor built entirely of solid iron, can develop an\u00b7 adequate starting torque for many purposes. During the starting operation, the rotor frequency varies over the full range from zero to the supply frequency. The configuration of a salient-pole motor is more complicated than that shown in Fig. 10.9 and it was necessary to divide the iron surface into small sections, as in Fig. 10.11. Moreover an appreciable leakage flux passes between the pole tips. Both quadrature and direct-axis fluxes, due to given excitation ampere-turns, can be calculated by allowing for these additional factors. Equivalent circuits of the type shown in Fig. 10.12 were used to develop the computer programme which calculated the 100 values of impedance rep resenting 100 divisions of the iron surface. It was necessary to use the non-linear theory and the computation therefore required an iteration procedure to obtain the correct impedances corre sponding to the voltages across them" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001578_tmag.2010.2093509-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001578_tmag.2010.2093509-Figure4-1.png", + "caption": "Fig. 4. Dimensions of an FSPMLG.", + "texts": [ + " In order to obtain three-phase sinusoidal emf, the physical distance between the central axis of the phase coils is 0018-9464/$26.00 \u00a9 2011 IEEE TABLE I DATA OF THE SINGLE-SIDE FSPMLG , and the electrical angle is , where and are the integers, and , which is the distance between two teeth, is the pole pitch of the translator. The distance between the central axis of the tips of two teeth in one U-shaped stack is approximately , and the electrical angle is , where and are integers. As shown in Fig. 4, FSPMLG parameters, including PM thickness , angle of , angle of , teeth width , and slot depth are important to obtain perfect sinusoidal waveforms of emf and less cogging force. An adaptive GA method is used to optimize the parameters [11]. The magnitude and waveform of emf are selected as constraint parameters to limit emf harmonic components, and the cogging force is selected as an optimization objective. Parameters , , , , , and are chosen as variables. FEM is employed to calculate emf and cogging force after a population of parameters is obtained by the GA method" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001368_978-3-642-41196-0-Figure2.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001368_978-3-642-41196-0-Figure2.1-1.png", + "caption": "Fig. 2.1 Schematic diagram of ACO shows that ant colony has succeeded in finding the shortest route", + "texts": [ + " In this chapter, we focus on four popular bio-inspired optimization algorithms, which are, respectively, ant colony optimization (ACO), particle swarm optimization (PSO), artificial bee colony (ABC), and differential evolution (DE). 38 2 Bio-inspired Computation Algorithms ACO is a metaheuristic for solving hard combinatorial optimization problems (Duan 2005, 2010; Duan et al. 2011). The inspiring source of ACO is the pheromone trail laying and following behavior of real ants, which use pheromones as a communication medium (Fig. 2.1). In analogy to the biological example, ACO is based on indirect communication within a colony of simple agents, called (artificial) ants, mediated by (artificial) pheromone trails. The pheromone trails in ACO serve as a distributed, numerical information, which the ants use to probabilistically construct solutions to the problem being solved and which the ants adapt during the algorithm\u2019s execution to reflect their search experience. The first example of such an algorithm is ant system (AS), which was proposed using as example application the well-known traveling salesman problem (TSP)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001110_iet-epa.2010.0159-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001110_iet-epa.2010.0159-Figure7-1.png", + "caption": "Fig. 7 Amplitude variation of the side-band component against SE degree and DE degree at a frequency of (1 2 1/P)fs", + "texts": [ + " 6, amplitude of the side-band components at frequencies (A\u2032 + B\u2032/P)fs rises because of eccentricity fault noticeably which can be utilised for fault detection. Furthermore, increases in eccentricity degree causes to raise the amplitude of side-band components at frequencies (A\u2032 + B\u2032/P)fs which can be employed for determination of eccentricity degree. In addition, perceptible differences between amplitude of side-band components at frequencies (A\u2032 + B\u2032/P)fs because of static and dynamic eccentricities can be used for eccentricity-type recognition in PMSMs. Fig. 7 demonstrates the variation of amplitude of side-band components at frequencies (1 + B\u2032/P)fs for different static and DE degrees. Referring to Fig. 7 reveals that the incremental rate of amplitude of side-band components at IET Electr. Power Appl., 2012, Vol. 6, Iss. 1, pp. 35\u201345 doi: 10.1049/iet-epa.2010.0159 frequencies (1 + B\u2032/P)fs because of occurrence of SE is much larger than that of DE. Furthermore, impacts of increase in SE degree on the radial magnetic stress in the PMSM are more sensible than that of the DE fault. The UMP in the direction of SE is computed by UMP(t) = \u222b2p 0 s(w, t) Cos(w) \u2113effective dw (23) Substituting (20) into (22) gives UMP(t) = \u222b2p 0 \u22111 A\u2032=0 \u22111 B\u2032=0 \u22111 C\u2032=0 sA\u2032,B\u2032,C\u2032 \u00d7 Cos A\u2032 + B\u2032 P ( ) vst + C\u2032w ( ) Cos(w) \u2113effective dw (24) Equation (23) is simplified as follows UMP(t) = \u22111 A\u2032=0 \u22111 B\u2032=0 s\u2032 A\u2032,B\u2032,C\u2032Sin A\u2032 + B\u2032 P ( ) vst (25) According to (25), eccentricity generates side-band components at frequencies (A\u2032 + B\u2032/P)fs in the UMP profiles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000759_s1560354708050079-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000759_s1560354708050079-Figure4-1.png", + "caption": "Fig. 4. Ball on an arbitrary surface.", + "texts": [ + " Taking into account the fact that the tensor of inertia is spherical, we see that the equations of motion of the ball in the immovable axes OXY Z have the form mv\u0307 = N + F , \u03bc\u03c9\u0307 = r \u00d7 N , R\u0307 = v, (2.6) where N is the reaction of constraint (2.5). Differentiating constraint (2.5) and taking into account the relation r\u0307 = 0 and the first two equations (2.6), we obtain \u03bcv\u0307 = \u03bcr \u00d7 \u03c9\u0307 = r \u00d7 (r \u00d7 N) = r \u00d7 (r \u00d7 (mv\u0307 \u2212 F )). Regrouping the terms, we finally find ( m + \u03bc b2 ) v\u0307 = F \u2212 (F ,ez)ez. 2.3. Homogeneous Rubber Ball on (Convex) Surface As above, we introduce the immovable coordinate system OXY Z and consider the equation of the surface passing through the center of the ball (see Fig. 4): f(R) = 0, (2.7) where R is the position vector of the center of the ball. It is clear that surface (2.7) is equidistant to the support surface and their normals coincide and have the same direction as the vector r joining the center of the ball with the contact point: r = \u2212bn, n = \u2207f(R) |\u2207f(R)| , where b is the radius of the ball. REGULAR AND CHAOTIC DYNAMICS Vol. 13 No. 5 2008 The constraints that express the conditions of the absence of slipping and spinning can be represented in the form v + \u03c9 \u00d7 r = 0, (\u03c9, r) = 0, (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002545_j.ymssp.2017.07.044-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002545_j.ymssp.2017.07.044-Figure9-1.png", + "caption": "Fig. 9. Normal, starved and spalled bearing at 1000 rpm.", + "texts": [ + " Compared to contact sensors that provide single point measurements, thermography allows estimating and visualizing the temperature distribution over the surface of a mechanical system. Experimental investigation [30] used the maximum temperature estimation. Grease lubricated bearing were running at speed from 1000 to 3000 rpm without load. A 20 K difference could be observed between spalled and normal bearing. Kim [31] with similar setup and operating condition analyzed the temperature distribution between spalled and normal bearing. Fig. 9 shows the difference in temperature distribution according to fault type. This study also investigated the influence of excessive wear. It was quantified by measuring the raceway roughness. For the same operating condition a 7 K increase was observable between lower and higher roughness. Mazioud [32] also performed experimental investigation on a bearing running at 1500 rpm. The impact of ring deformation on the temperature distribution and vibratory signal was measured. It has been shown that there is a link between temperature rise and vibration level according to the fault magnitude", + " Reference Fault type Test condition Diagnostic method Temperature variation Tonks 2016 [47] Type 2 50 rpm No load Experimental approach Trend: 1\u20133 C Mohanty 2015 [48] Type 2 1740 and 2220 rpm 5 kg mass Experimental approach Trend: 1 C Jedrezejrwski 1985 [49] Type 2 1500 rpm Computed temperature limit Trend: 5\u201315 C Younus 2010 [33] Type 1 and 2 3750 rpm No load Thermograph form factor analysis + data treatment NA Tran 2013 [34] Type 1 and 2 3750 rpm No load Thermograph form factor analysis + fuzzy logic NA Janssens 2015 [35] Type 1,2 and 3 1500 rpm No load Thermograph form factor analysis NA Ramirez 2016 [50] Type 2 3600 rpm 2.5 kW Thermograph region analysis 1.5 C Fig. 10. Low and adequate lubrication from Janssens [35] study. cation loss severity. Kim [31] and Dongyeon [30] used their bearing test bench under starved conditions. Temperature distribution was different according to the failure type in Kim\u2019s experiments (Fig. 9). The outer ring is hotter under starved conditions compared with nominal ones whereas the cage temperature is the hotter part for the spalled bearing. Dongyeon made the same global observation and also measured and compared the maximum temperatures. Under starved conditions, a 10\u201315 K increase was observed on the outer ring. Janssens [35] investigated the effect of grease quantities on lubrication and the temperature distribution in bearings (Fig. 10). As in the previous studies form factor estimated from the thermograph histogram revealed differences between a healthy bearing and an incorrectly lubricated one" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002174_s00170-012-4560-y-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002174_s00170-012-4560-y-Figure3-1.png", + "caption": "Fig. 3 Structure diagram of the two-stage planetary gearbox (LS1, LS2, HS1, and HS2 are four vibration sensors) [1]", + "texts": [ + "1 Planetary gearbox test rig Figure 2 shows a planetary gearbox test rig designed to perform fully controlled experiments for developing a reliable diagnostic system. The planetary gearbox test rig has an over-hung floating configuration that can mimic the operation of field mining. It mainly includes a 20-HP drive motor, a one-stage bevel gearbox, a two-stage planetary gearbox, a two-stage speed-up gearbox, and a 40-HP load motor. Table 1 lists the number of teeth and transmission ratio achieved by each stage. The study object in this paper is the two-stage planetary gearbox diagramed in Fig. 3. The sun gear of the first-stage planetary gearbox is mounted on the right end of shaft 1 with a driven bevel gear mounted on the left end. The firststage planet gears are mounted on the first-stage carrier that is connected to shaft 2 with the second-stage sun gear mounted on the other end. The second-stage planet gears are mounted on the second-stage carrier located on output shaft 3. Ring gears of the first and the second stages are mounted on the housing of their stage, respectively. Four vibration sensors, including two identical lowsensitivity sensors (denoted by LS1 and LS2) and two identical high-sensitivity sensors (denoted by HS1 and HS2), are mounted on the housing of the planetary gearbox" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000875_j.ins.2011.01.040-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000875_j.ins.2011.01.040-Figure15-1.png", + "caption": "Fig. 15. Schematic of electromechanical system.", + "texts": [ + "5, c2 = 0.05 and qm = 1. The simulation results are also expressed Figs. 11\u201314 (dash-dotted). Figs. 11\u201314 show our control scheme can achieve the better control performances than the one in [31]. Moreover, comparing with these two control schemes, one can find that our control scheme has removed the restrictions that the controlled systems satisfy the strictly positive real condition (SPR) and the strict matching conditions imposed on [31]. Example 3 [5]. Consider the electromechanical system shown by Fig. 15. The dynamics of the electromechanical system is described by the following equation. M\u20acq\u00fe B _q\u00fe N sin\u00f0q\u00de \u00bc I; L_I \u00bc Ve RI KB _q; ( \u00f074\u00de where M \u00bc J Ks \u00femL2 0 3Ks \u00feM0L2 0 Ks \u00fe 2M0R2 0 5Ks ; N \u00bc mL0G 2Ks \u00feM0L0G Ks ; B \u00bc B0 Ks : 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), I(t) is the motor armature current, and Ks is the coefficient which characterizes the electromechanical conversion of armature current to torque" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000976_rspa.2010.0135-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000976_rspa.2010.0135-Figure2-1.png", + "caption": "Figure 2. A cantilever of thickness 2h (a) before and (b) after imposed or spontaneous distortion into a saddle shape, that is, with curvatures in two directions of opposite sign. (c) A nematic solid \u2018swimmer\u2019 supported on a pin and forming a saddle in response to illumination from above. Adapted from Prof. P. Palffy-Muhoray.", + "texts": [ + " Having achieved a gradient in natural length by either a gradient of stimulus or a gradient of the director field, a sheet of material will bend, perhaps in more than one dimension, in order to minimize the elastic energy penalties associated with deviations from these induced changes in natural length. We analyse here the changes when spontaneous distortion is small. The spontaneous or natural strain (denoted by s), es(z), is that which would be attendant on a body deforming as if uniformly exposed to the conditions currently pertaining at depth z , see figure 2a,b. It is locally the change in the natural shape away from which there is then an elastic energy cost if there is further distortion. The effective strain is the geometric strain e geom (z) minus the spontaneous strain: e(z) = e geom (z) \u2212 es(z), (2.1) Proc. R. Soc. A (2010) a simple subtraction since strains are small. We shall need the geometric strain in the material mid-plane (initially at z = 0) and denote it by e. The geometric strain e geom (z) has a curvature-induced part, z/R, where z is the distance from the mid-plane and 1/R is a curvature", + " Analogous to the elastic Poisson ratio, in our locally uniaxial solids, it relates e\u22a5 in the perpendicular directions to e\u2016 along the director: e\u22a5 = \u2212nthe\u2016, where nth \u223c+0.3 to 2 would be typical for nematic glasses (Mol et al. 2005). For bending, the relevant in-plane elements of e are as follows: exx(z) = z Rxx + exx \u2212 es xx(z) and eyy(z) = z Ryy + eyy \u2212 es yy(z). (2.3) Rxx and Ryy are the radii of curvature in the xx- and yy-directions and exx and eyy are the mid-plane xx- and yy-strains in the appropriate sections of the cantilever (see equation (2.1) and figure 2). For n not along a principal axis of cantilever bend, then es in equation (2.2) has off-diagonal response, for instance es xy in the case of a cantilever with a twist director field treated specifically below, and which has similarities to the spontaneous distortions of a cholesteric elastomer (Warner 2003). We show in twist cantilevers that it is the response along the principal curvature directions that is important. We analyse bend in the approximation of isotropic elasticity, rather than that of a uniaxial solid defined by the local nematic director field", + " Conversely, when penetration is very deep, d/h 1, then there are weak gradients in response and thus little bend, only some uniform contraction. Optimal bend in this model arises when d/h \u223c 1/3. There are two neutral planes in this limit of weak spontaneous bend. Note that rotating the director field and the polarization of the light in the plane of the cantilever simply rotates the directions of the principal curvatures relative to the material. A vivid example of curvature and saddle formation can be found in elastomers (Camacho-Lopez et al. 2004), see figure 2c, systems that bend in tens of milliseconds to light and which swim by virtue of their flexing into saddles while resting on the surface of water. (ii) Strong absorption If, on the other hand, the incident light intensity I0 is high, then the cis (excited) population becomes high and the material becomes bleached, that is the absorbing trans population is depleted. The material\u2019s ability to absorb light is reduced and the intensity profile through the thickness changes from exponential to linear, at least until at depths where the beam is sufficiently attenuated that Beer\u2019s law decay is restored" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure4.47-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure4.47-1.png", + "caption": "Fig. 4.47 Pendulum absorber a) Physical pendulum, b) Rotating rings, c) Internal roller, d) Calculation model", + "texts": [ + " Several types of pendulum absorbers were proposed by B. SALOMON in the 1930s (Patent DRP 597 091), which either consist of swinging rings or of rollers and run on circular paths. The various design implementations that have been created since then all strive for the same goal of achieving a large mass and a short pendulum length, as these are required for high frequencies and large torques. Pendulum absorbers are attached to the crank web, if possible, to absorb the interfering variable torque at the location where it is initiated. Figure 4.47 shows various shapes of pendulum absorbers by Salomon [16]. A periodic moment M1(t) = M\u03021 sin k\u03a9t acts on a rotating disk (rotating mass J1) on the input shaft. Without the pendulum absorber, the rotation would be at a variable 4.4 Absorbers and Dampers in Drive Systems 293 angular velocity (\u03d51 = \u03a9t + \u03d5\u03021 sin k\u03a9t). A physical pendulum (mass m, distance to the center of gravity \u03beS, moment of inertia JS) is pivoted at the disk at point A (distance R), see Fig. 4.47a. In rolling pendulums (Figs. 4.47b and 4.47c), half the diameter difference \u03beS = (D \u2212 d)/2 corresponds to the distance to the center of gravity of the physical pendulum since both move as if they were supported at point A. The system shown in Fig. 4.47d has two degrees of freedom (angle of rotation \u03d51 and relative swing angle \u03d52). The potential energy is not considered (horizontal position of the plane of rotation). The kinetic energy is the sum of the rotational energy of the rotating masses and the translational energy of the mass m: 2Wkin = J1\u03d5\u0307 2 1 + m(x\u03072 S + y\u03072 S) + JS(\u03d5\u03071 + \u03d5\u03072) 2. (4.205) The center of gravity of the pendulum absorber has the coordinates xS = R cos \u03d51 + \u03beS cos(\u03d51 +\u03d52); yS = R sin \u03d51 + \u03beS sin(\u03d51 +\u03d52). (4.206) The resulting velocities are x\u0307S = \u2212\u03d5\u03071R sin \u03d51 \u2212 (\u03d5\u03071 + \u03d5\u03072)\u03beS sin(\u03d51 + \u03d52); y\u0307S = \u03d5\u03071R cos \u03d51 + (\u03d5\u03071 + \u03d5\u03072)\u03beS cos(\u03d51 + \u03d52)", + " The linearly varying angular velocity \u03d5\u03071 = \u2212\u03b1t = \u2212(M/Jred)t enters a resonance area when the meshing frequency fz is reached, which occurs earlier for model a than for model b. The meshing frequency according to (4.237) is fz = 23\u03a91/(2\u03c0) = 23\u03b1t/(2\u03c0) = (17.4t/s)Hz for 23 teeth of the first gear step. This second frequency is strongly excited because the teeth of the gear step are severely deformed at the second natural frequency. The wider resonance range in case b is due to the fact that the third subharmonic is excited as well. The dimensions of a Salomon pendulum absorber according to Fig. 4.47c that absorbs the second excitation harmonic of an input torque are to be determined. 4.5 Parameter-Excited Vibrations 307 Distance of the center of rotation R = 100 mm Distance to the center of gravity \u03beS = 1 mm Mass of the roller m = 0.05 kg Moment amplitude of the second harmonic M\u03021 = 15 N \u00b7m at k = 2 1.Diameter of the roller d 2.Diameter of the hole D 3.Amplitude \u03d5\u03022 of the roller at angular velocity \u03a9 = 300/s 4.Discussion of the influence of the order of the harmonic on the magnitude of the absorber mass The drive system to be examined consists of a straight plunger (constant cross-section A, length l), to which a rigid body of mass m is coupled using a spring assumed to be massless with stiffness c" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001874_tmech.2018.2818442-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001874_tmech.2018.2818442-Figure3-1.png", + "caption": "Fig. 3. Continuum module of the sinus robot (a) motion schematic diagram, (b) structure of the manipulator.", + "texts": [ + " Each joint can be tilted up to 30 degrees, so that the manipulator needs at least ten joints, in order to make the continuum module bend up to 270 degrees. These joints are connected by NiTiNol tubes and stainlesssteel cables pierced through four holes of joints. Two cables which are inserted into two holes will lead to deflection in opposite directions. The remaining two holes are the channels of NiTiNol tubes, and another two cables are inserted into the tubes to enable scissoring as shown in Fig. 2 (b). The cable-driven continuum module is illustrated in Fig. 3. The manipulator is actuated by stainless-steel cables, and the cable diameter is important to endure enough strength during surgical operation. As a result, the size of the diameter is chosen after analytic calculation. By pulling and releasing the four cables, different length of two cables will lead to deflect in different direction as shown in Fig. 3 (a). Holding the cables keep the joints in place, while moving cables can realize the deflection of the joints. This mechanism enables flexible and two directional motion. Two superelastic NiTiNol tubes are the continuum module\u2019s backbones, along which the joints are mounted. The length of NiTiNol tubes is slightly longer than the sum of each joints, so that the continuum module can be deflected smoothly. Each joint is modeled as a rigid body. The continuum module is regarded as discretization into subsegments" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000850_pnas.0705442105-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000850_pnas.0705442105-Figure1-1.png", + "caption": "Fig. 1. The model. (a) A schematic view of lateral undulation (after ref. 1). The snake is moving at x direction with a velocity vx. Solid dots indicate the location of inflection points. The shaded areas qualitatively describe the pattern and amplitude of muscle activity (4, 5). The dotted lines show the track left behind. For undulations without lateral slip, the flexural waves are stationary relative to the ground, and thus the pattern of muscle activity is stationary relative to the lab frame. For undulations with lateral slip, the dashed arrows show the slip velocity in the lab frame U and its components along the tangent and normal. (b) A small segment of the organism shows the internal forces and moments at a cross-section. (c) A visco-elastic model of the same segment contains three parallel elements, a passive elastic element (spring), a passive viscous element (dashpot), and an active muscular element.", + "texts": [ + " At first glance, motion by lateral undulation seems paradoxical; the animal glides forward continuously at a constant velocity, tangential to itself everywhere, despite the fact that the only forces in that direction are due to friction, which constantly retards this motion. The resolution of this apparent paradox is clear: propulsion arises due to the in-plane lateral forces generated when the organism braces the sides of its body against the medium or substrate in the presence of an anisotropy of resistance to lateral and longitudinal motion of the slender, curved body (1, 8). A wave of flexure that is fixed in the laboratory frame leads to alternating sideways thrust, which then lead to forward (or backward) movement as shown schematically in Fig. 1a. Locomotion, which is achieved through the appropriate coupling of endogenous dynamics to exogenous dynamics, involves four components: (i) the endogenous dynamics of force production by muscle, (ii) the exogenous dynamics due to the interaction of the organism with its environment, (iii) the consideration of linear and angular momentum balance in the body\u2013environment system, and finally (iv) the proprioceptive feedback that involves sensorimotor coupling as the organism responds to the forces on and in it", + " Here we will focus on the first three components by considering the steady lateral undulatory movements of a snake or similar organism on a solid substrate to determine its shape and speed. Equations of Motion. Because snakes are long slender limbless vertebrates, we model one as an inextensible, unshearable filament of length L and circular cross-section (radius R), lying on a plane whose normal is along z, with arc-length s [0, L] parameterizing each cross-section along the snake. We denote the position vector of any cross-section of the filament as r(s, t), so that the tangent to its center line t(s, t) rs (s, t) makes an angle (s, t) with the x direction (Fig. 1 a and b). Conservation of linear and angular momentum leads to the equations of motion (10) Fs f rtt, Msz t F 0I ttz. [1] Here (.)a (.)/ a, F(s, t) is the internal force resultant, M(s, t)z is the internal moment resultant, f(s, t) is the external force per unit length at each cross-section, 0 is the mass density, 0 R2 is the mass per unit length, and I R4/4 is the second moment of the cross section. The kinematic conditions that determine the location of the snake are given by xs cos , ys sin , s , [2] where is the curvature of the centerline", + " This article contains supporting information online at www.pnas.org/cgi/content/full/ 0705442105/DCI. \u00a9 2008 by The National Academy of Sciences of the USA www.pnas.org cgi doi 10.1073 pnas.0705442105 PNAS March 4, 2008 vol. 105 no. 9 3179\u20133184 A PP LI ED M A TH EM A TI CS BI O PH YS IC S For such a filament moving along its own tangent, rt (t)t, where (t) is the speed of any (all) point along the filament. Using the identity (.)t (.)/ s, rtt tt 2 n, where n(s, t) is the normal to the centerline of the filament (Fig. 1b). Decomposing the internal and external forces along the tangent and normal, we write F Tt Nn and f pn ( p p w g)t, where T(s, t) is the tension, N(s, t) is the transverse shear force, p(s, t) is the normal force per unit length of the filament due to its lateral interaction with the substrate, p is the lateral friction coefficient associated with sliding tangentially against the lateral protuberances, and w is the longitudinal friction coefficient associated with sliding on the substrate. Using tt 2 s t , Eq", + " The internal moment M(s, t) at any crosssection consists of a passive component with its origins in the response of tissue that resists deformation, and an active component with its origins in muscular contraction. A simple model for the passive response of tissue is afforded by the linear Voigt model for viscoelasticity (11), which states that the uniaxial stress in bulk tissue E \u0307, with and \u0307 being the strain and strain rate in the tissue, E being the Young\u2019s modulus, and being the viscosity of the tissue (12, 13) (Fig. 1c). For the inextensible bending of slender body, this implies that the passive moment Mp Me M , where Me and M are the elastic and viscous moments, and Me EI , M I t I s. During lateral undulatory locomotion, muscles on either side of the body are activated alternatively (4), become active at the point of maximal convex flexion, and cease activity at the point of maximal concave flexion. This leads to an alternating active flexural moment generated by the muscles which connect the vertebrae and skin of the snake; the pattern and amplitude of muscle activity are qualitatively described by the shaded area shown in Fig. 1a. In general, there is a time delay between muscle activation and the development of contractile force ( 0.1 s, ref. 14); however, since this time is much smaller than the period of muscle contraction ( 1 s, ref. 5), we will neglect the effects of this delay here. The simplest form of the active moment that is consistent with this periodic pattern of muscle activity is Ma ma sin (2 s/l), s [0, l], where l is the arc-length within one period and ma is the amplitude of the active moment. Then, the total internal moment, which is the sum of the passive and active moments, is given by M masin 2 s / l EI I s", + ", it is proportional to the active moment, because a larger active moment results in a large normal force. (III) p C sin , i.e., it is determined by the local shape of the snake. To understand this last limit, we first consider the creeping motion of a worm or snake in a viscous liquid. Then the viscous force on the body is proportional to its relative speed to the medium (15), so that the lateral force per unit length p(s) C U sin , where C is the drag coefficient along the normal n(s, t), U is the slip velocity relative to the medium, and U sin is the lateral slip velocity (Fig. 1a). For undulations without lateral slip [see supporting information (SI) Appendix for the case of undulations with lateral slip], we consider the limiting process where C 3 , U3 0, but C U C constant, which leads to the above formula for p. For all three forms of p, C 0 has the dimensions of force per unit length, and is a phenomenological characterization of the organism\u2019s interaction with its environment. These closure relations for M, p do not account for sensorimotor feedback or proprioception, but do allow us to formulate a series of problems for gait selection as a function of the endogenous and exogenous dynamics", + ", it is in a tetanized state, the contractile stress and velocity of the muscle are related by the Hill relation (20) P/P0 1 V/V0 / 1 cV/V0 , [24] where P is the contractile stress in muscle, P0 is the maximal contractile stress, V is the velocity of muscle contraction, V0 is the maximum velocity of muscle contraction and c is the Hill parameter characterizing muscle type (see SI Appendix). In lateral undulatory locomotion, assuming that the contractile stress P acts over an areal fraction of muscle at each cross-section and an effective moment arm R (see Fig. 1a), for a simple sinusoidal form of the contractile moment, we may write masin 2 s / l P R2 /2 R , [25] where a factor of 1/2 accounts for the fact that muscles are activated only on one side of the snake at a given instant of time. From Eq. 25, we see that the contractile stress required to produce the active bending moment reaches its maximum at s l/4. The velocity of contraction V for a steadily moving organism is the strain rate of the muscle times its length l0, so that V R tl0 R s l0. [26] From Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003860_s10846-018-0927-0-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003860_s10846-018-0927-0-Figure1-1.png", + "caption": "Fig. 1 a A surgical system including a Robot (7DoFs iiwa KUKA) arm with a two DoFs surgical instrument, and the assigned frames. b The incision point with more details", + "texts": [ + " In Section 5 and Section 6 the proposed formulation is verified numerically and empirically in a 7DoF and 9DoF MIRS scenarios. Finally the paper is concluded in Section 7. In order to obtain a generic formulation for a constrained surgical system, the kinematic of the whole system is studied here. The system mainly consists of a serial robot manipulator with n joints and a surgical instrument with two additional DoFs at the tool-tip (similar to the Endowrist) which is held by the EEF of the robot (Fig. 1). Note that, in active RCM control of surgical robots, any mechanical structure for the robot arm such as lightweight robot arm can be employed. Since the RCM constraint restricts two DoFs of the system in 3D space, to achieve a desired task with m dimension, the system must have additional DoFs. To deal with the RCM constraint, the penetration of the surgical tool is considered as a virtual prismatic joint which its location is denoted by \u2019\u03b7\u2019. Considering a virtual prismatic joint in RCM point and two additional DoFs for tool to compensate RCM constraint, the joint velocity vector q\u0307, contains n + 3 elements", + " Thus, the sequence of joint velocities includes two parts as q\u0307 = [ q\u0307r q\u0307e ] (1) where q\u0307r = [q\u03071, q\u03072, \u00b7 \u00b7 \u00b7 , q\u0307n]T is the contribution of robot joint velocities, and q\u0307e = [\u03b7\u0307, q\u0307n+1, q\u0307n+2]T is for virtual prismatic joint and 2DoFs surgical tool. To relate the velocity of the endpoint to the joint velocities of the robot and the surgical tool, the relative velocity equations are written as follows,{ 0ve =0 vr + 0vr e + 0\u03c9r \u00d7 0rr e 0\u03c9e = 0\u03c9r + 0\u03c9r e, (2) where 0ve and 0\u03c9e indicates the translational and rotational velocity of the endpoint, respectively. Moreover, 0rr e is the position vector of the endpoint (Fe) in EEF frame (Fr ) as illustrated in Fig. 1, and 0vr e and 0\u03c9r e are the relative velocities of the endpoint relative to the EEF. Note that all of the above vectors are expressed in the base frame F0. Rewriting (2) in matrix form yields,[ 0ve 0\u03c9e ] = [ 0vr 0\u03c9r ] + [ 0vr e 0\u03c9r e ] + [ \u2212S ( 0rr e ) 03\u00d73 ] 0\u03c9r, (3) where S(.) is skew-symmetric cross product matrix. By using kinematic principles, the velocity of the endpoint is obtained as,[ 0ve 0\u03c9e ] = 0Jr q\u0307r + 0J r e q\u0307e + [ \u2212S ( 0rr e ) 03\u00d73 ] 0J rAq\u0307r , (4) where, 0Jr is the Jacobian matrix of the EEF and 0J rA is its angular sub-matrix", + " Figure 6 shows the robot configurations captured at different times during the simulation of linear path scenario in the VR environment. The yellow plane shows the tangent plane of the body holding the trocar and the tracked trajectory by tool-tip has been shown by blue path. The approaches in Section 3 are evaluated on a (7+2)DoFs surgical system to follow a desired 6D position/orientation trajectory in the task space. A surgical instrument with shank length l = 0.3m and two perpendicular links with length 0.02m is considered at the end of the tool (see Fig. 1a). Thus, the system has one degree of redundancy. In this case, the transformation matrix T is chosen such that q\u0302 = [ q6 q7 q8 q9 q1 q2 q3 q4 q5 \u03b7 ] . The trocar follows a trajectory as in the first case. The scenarios related to the moving trocar are not reported for brevity. The proposed control laws are applied to this case and the results of position/orientation errors in task space as well as RCM errors for two different trajectories are illustrated in Fig. 7 and Fig. 8, respectively. The figures indicate that the task space and RCM errors are almost equal to zero" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000156_1.2958070-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000156_1.2958070-Figure3-1.png", + "caption": "Fig. 3 The reference axes of the bearing", + "texts": [ + " Having calculated the deflection for the ith ball in its contact irection, therefore, since the balls undergo i\u2212 bi contact deection, the force in the same direction Wi can easily be found s follows: Wi = K i \u2212 bi 3/2 12 n which bi is the displacement of the ith ball center in the conact direction and it may be expressed as follows: bi = zb 2 + r 2 1/2 13 his force can be split into two components in the radial Wri and xial Wai directions for angular contact ball bearings. Hence the orces in the X, Y, and Z directions are WX = Wri cos i , WY = Wri sin i , WZ = Wai 14 here i is the angle between the X axis and the axis of the ith all and this angle is a combination of different angles, as shown ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 07/05/2013 Terms in Fig. 3. In this work, two sets of reference axes are described, as depicted in Fig. 3. The first one X, Y, and Z axes are fixed in space and the X axis is vertically downward in the gravitational force direction. The second set of the axes x, y, and z has its origin at the shaft center but is rotating cage speed c 25 . If the angle between two adjacent balls is defined as , it will be = 2 m 15 where m is the number of balls in the bearing. Thus, the ith ball position is now found easily since it is fixed with respect to the xyz set, = ct + i 16 where the cage speed c is given by 25 c = 1 2 i 1 \u2212 db dm cos + 1 2 o 1 + db dm cos 17 where i = 2 ni 60 and o = 2 no 60 18 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure12.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure12.4-1.png", + "caption": "FIGURE 12.4. A four-bar linkage, and free body diagram of each link.", + "texts": [ + ";] depict s a link atta ched to the ground via a jo int at O . Th e free body diagram of the link is m ade of an extern al force and moment at 512 12. Robot Dynamics the endpoint, gravity , and the driving force and moment at the joint. The Newton-Eul er equations for the link are Fo +Fe +mgK Mo + Me + n X F\u00b0 + m X Fe ma /0. . (12 .34) (12.35) Example 281 A four-bar linkag e dynamics. Figu re 12.4(a) illustrates a closed loop four-b ar linkag e along with the free body diagrams of the links , shown in Figure 12.4(b). Th e position of the mass centers are given, and therefore the vectors ani and ami for each link are also kno wn. Th e Newton-Euler equations for the link (i) are \u00b0 \u00b0 'F i - I - F , +mig J \u00b0Mi_I - \u00b0Mi + ani X \u00b0Fi_ I - ami x F, m , \"a, (12.36) t, Oo. i (12 .37) and therefore, we have three sets of equations. \u00b0 \u00b0 'F o - F I +mIgJ \u00b0Mo - \u00b0MI + \u00b0nI x \u00b0Fo - \"m, x F I \u00b0 \u00b0 'F I - Fz + mzgJ \u00b0MI - \u00b0Mz + \u00b0nz x \u00b0FI - \u00b0mz x Fz \u00b0 \u00b0 'Fz - F3 + m 3g J \u00b0Mz - \u00b0M3 + \u00b0n3 x \u00b0Fz - \u00b0m3 x F3 (12.38) (12.39) (12.40) (12" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002270_1464419314546539-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002270_1464419314546539-Figure5-1.png", + "caption": "Figure 5. Two surface defected models: (a) Hd>He and (b) Hd\u00bcHe.", + "texts": [ + " For the interaction between the roller and the defect surface, it is complicated and time varying. A single sine function is not enough to describe this interaction. Shao31 proposed valid models for the time-varying deflection. The models are split into two cases based on the relationship between defect length and the maximal additional deflection. First, according to the geometrical property, the maximal additional deflection He can be expressed as He \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2b 0:5Wd\u00f0 \u00de 2 q \u00f030\u00de As shown in Figure 5(a), defect length is larger than the maximal additional deflection (Hd>He) in the first case. When the roller rolls through the defect zone, it contacts with the defect edge A and B, not the defect bottom surface. By this time, the defect deflection excitation d is d\u00bc He sin d mod i,2 \u00f0 \u00de 0 04mod i,2 \u00f0 \u00de4 d 0 other ( \u00f031\u00de xk\u00bc Le 2 \u00fe\u00f0k1 0:5\u00de Ldr rrc s1 for distance zone Le 2 \u00feLdr rrc\u00fe\u00f0k2 0:5\u00de Ld s2 for defect zone Le 2 \u00feLdr rrc\u00feLd\u00fe\u00f0k3 0:5\u00de Le Ldr rrc\u00feLd\u00f0 \u00de s3 other 8>>>>>< >>>>>: \u00f027\u00de xk \u00bc Le 2 \u00fe \u00f0k1 0:5\u00de Ldr rrc s1 for distance zone Le 2 \u00fe Ldr rrc \u00fe \u00f0k2 0:5\u00de Ld Ld \u00fe Ldr Lb\u00f0 \u00de rrc s2 for defect zone 8>>< >>: \u00f028\u00de xk \u00bc Le 2 \u00fe \u00f0k1 0:5\u00de Ld Ldr rrc s1 for distance zone Le 2 \u00fe Ld Ldr rrc \u00fe \u00f0k2 0:5\u00de Lb Ld Ldr\u00f0 \u00de rrc s2 for defect zone 8>< >: \u00f029\u00de at University of Sydney on September 6, 2014pik.sagepub.comDownloaded from But in Figure 5(b), the defect length is equal to the maximal additional deflection (Hd\u00bcHe) in the second case. When the roller contacts with the defect edge A, it initially enters the defect zone. If the roller reaches the edge B, it will contact the defect bottom surface. The roller begins to leave the bottom surface while it comes to the edge C. The edge D is the end of the defect. The deflection excitation d can be described by the following equations where d1 is the arc length between the edge A and B, and the same as that between the edge C and D" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001002_j.bios.2009.03.007-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001002_j.bios.2009.03.007-Figure3-1.png", + "caption": "Fig. 3. CVs of Cyt c/GA/GCE (a), Cyt c/GA/Chit/GCE (b), Cyt c/GA/PAMAM\u2013Chit/GCE (c) and Cyt c/GA/MWNT\u2013PAMAM\u2013Chit/GCE (d) in 0.1 M pH 7.0 PBS at 0.05 V s\u22121.", + "texts": [ + " Nyquist plots of EIS in 0.1 M KCl solution containing 5.0 mM 3(Fe(CN)6)/K4(Fe(CN)6) (1:1) for bare GCE (a), PAMAM\u2013Chit/GCE (b), WNT\u2013PAMAM\u2013Chit/GCE (c), GA/MWNT\u2013PAMAM\u2013Chit/GCE (d), Cyt /GA/MWNT\u2013PAMAM\u2013Chit/GCE (e). The amplitude: 0.005; the potential: 0.169 V. attached Cyt c. It is in close accord with the previous reports (Zhao et al., 2005; Wang et al., 2002a). The cyclic voltammetry was performed to investigate the influences of Chit, PAMAM dendrimers and MWNT on the direct electrochemistry of Cyt c, respectively. Fig. 3 shows the cyclic voltammetric behaviors of different modified electrodes in 0.1 M pH 7.0 PBS at 0.05 V s\u22121. Neither Cyt c/GA/GCE (Fig. 3a) nor Cyt c/GA/Chit/GCE (Fig. 3b) appeared any peaks, but a slight oxidation\u2013reduction was observed on Cyt c/GA/PAMAM\u2013Chit/GCE (Fig. 3c). This result clearly demonstrated that PAMAM dendrimers successfully acted as a substrate for the immobilization of Cyt c on the surface of glass carbon electrode and facilitated the electron exchange between the Cyt c and the electrode. In addition, it must be pointed out that GA, served as the coupling agent in the process of immobilization of Cyt c, could react with the amino groups of PAMAM dendrimers on the electrode surface and the lysine residue of Cyt c (pI 10), respectively. The amount of amino groups on the surface of PAMAM\u2013Chit/GCE was much more than that of the bare GCE and Chit/GCE. In other words, PAMAM\u2013Chit/GCE would provide more binding sites for reacting with GA and finally leading to the increase of the fixation chamber of Cyt c on the electrode surface. The subtle electronic properties suggested that carbon nanotubes had the ability to promote electron transfer reactions when used as an electrode material in electrochemical reactions (Wang et al., 2002b). In our work, this notable promotion was also confirmed. Upon comparison of Fig. 3c and d, the modified electrode involving MWNT, Cyt c/GA/MWNT\u2013PAMAM\u2013Chit/GCE, exhibited a couple of stable redox peaks at 0.203 V (anodic peak) and 0.104 V (cathodic peak), which was 2.5 times larger than that of Cyt c/GA/PAMAM\u2013Chit/GCE. The influence of the amount of doped MWNT on the electrochemical property of the immobilized Cyt c was further investigated, and the data are listed in Table 1. As we can see from Table 1, both the anodic and cathodic peak currents firstly increased with the increasing doped amount of MWNT, and then decreased remarkably after doping 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003377_j.addma.2020.101093-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003377_j.addma.2020.101093-Figure6-1.png", + "caption": "Figure 6: Schematic for AM printed wall using mild steel wire ER70S-6 and MBAAM system showing tensile samples size and configuration", + "texts": [ + "3 mm, as the Zbuild direction (perpendicular to the deposition direction) was under closed loop control by varying the deposition rate per unit of length. In order to evaluate the mechanical characteristics of the printed structure, a wall of 600 mm x 325 mm x 12 mm (length, width, and thickness, respectively) was printed using the MBAAM system at 2.35 Kg/hr. A variety of tensile test coupons were cut out of the printed wall in the bead direction (Tensile longitudinal (TL)), perpendicular to the bead direction (Tensile vertical (TV)) and with an angle of 45\u00ba (Tensile angled (TA)) from the bead direction, as shown schematically in Figure 6. The tensile testing was performed using the ASTM E8/E8M \u2212 13a standards. A total of 5 samples from each direction were tested. The sample size was 200 mm long x 20 mm wide and 5 mm (4.74 mm) J ur na l P re -p oo f thick. Samples were pulled at a rate of 1.5 mm/min (0.001 in/s) using a MTS-900 kN hydraulic testing frame. Element (%) Element (%) C 0.06 \u20130.15 Ni 0.15 max Mn 1.40 \u20131.85 Cr 0.15 max Si 0.80 \u20131.15 Mo 0.15 max P 0.025 max V 0.03 max S 0.035 max Cu(4) 0.50 max There is a growing need for molds and dies, especially in the automotive and mass-transit industries" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002300_s11666-016-0480-y-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002300_s11666-016-0480-y-Figure4-1.png", + "caption": "Fig. 4 Tensile specimen orientation and designation for samples machined from 3-D LENS hexagon", + "texts": [ + " Complementary optical microscope (OM) and scanning electron microscope SEM imaging were used to characterize the 3-D induced metallurgical features on the metallographically prepared cross sections. Solidification cell morphology and size were characterized using SEM with backscattered electron image (SEM/BEI) at 15 kV, and SEM with electron backscattered diffraction (EBSD) on the as-polished cross section. The measurement was conducted with a standard Vickers diamond indentation method using a 50-g load. Round tension test specimens were machined from the multi-tier hexagon along the axial and transverse directions, as shown in Fig. 4. The length and diameter of the gage section were *18 and *2.5 mm, respectively. The test was quasi-static with a strain rate of 0.001 s-1. Surface contours and morphology among all the current 3-D LENS 316L stainless steel deposits are consistent, regardless of prototype geometry and dimensions. Complementary SEI/BEI images show that the deposit surfaces contain alternating layered ridges, originating from the multi-pass deposition (Fig. 4). Within each ridge, there are curved molten metal trails (Fig. 4\u2014lower right arrows) perpendicular to the interpass boundaries, similar to the morphology seen in the metal welds. In addition, the surface also contains un-melted or partially melted particles, which are fused to the deposit surface and tend to gather along the molten metal flow trails and/or interpass boundaries. In many cases, several particles were fused together without direct contact with the surface. The size and shape of these fused-on particles are comparable to that of the 316L feedstock powders used for the current 3-D LENS deposition (Fig", + " 16 OM/BF micrographs: (a) area of interest; (b) interpass boundary with coarse recrystallized grains (light arrow); (c) interpass with an unmelted powder inclusion (light arrow) Vickers microhardness [(222 HV) for wrought 316L stainless steel] (Ref 5). The calculated standard deviation is \u00b114 HV, compared to \u00b19 HV measured in the wrought 316L substrate. In addition, the average Vickers microhardness from the 5-point measurements for all tiers shows the hardness decreases with increasing distance from the substrate interface, from the base to narrow Tier 1 (Fig. 23). Tensile testing was performed for the four specimens, two for axial and two for transverse direction, taken from the 3-D LENS hexagon (Fig. 4). The stress-strain curves (Fig. 24) show yield strength for the two axial specimens is 448 and 455 MPa, which is 15-20% lower than those measured for two transverse specimens, which is consistent, 538 and 552 MPa. The average ultimate yield strength (UTS) for the axial and transverse specimens is 586 and 690 MPa, respectively. Both the yield strength and the UTS for the 3-D LENS deposits are relatively higher than those listed nominal strength for the wrought 316L stainless steel (Ref 5). Most notably, the strain-to-failure measured among the four specimens varied greatly, ranging from 4 to 38%" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure5.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure5.6-1.png", + "caption": "Fig. 5.6 Dependence of the four natural circular frequencies on the angular velocity \u03a9", + "texts": [ + "29) at the place where only the moment of inertia Ja occurs for the non-rotating beam (\u03a9 = 0). Therefore, if the ratio \u03a9/\u03c9 is given, one can calculate using JR as for a non-rotating rigid body. Due to \u03b4 = \u03b3, the characteristic equation \u03c94mJa(\u03b1\u03b2\u2212\u03b32)\u2212 \u03c93mJp\u03a9(\u03b1\u03b2\u2212\u03b32)\u2212 \u03c92(\u03b1m+\u03b2Ja) + \u03c9\u03b2Jp\u03a9 + 1 = \u03c94mJR(\u03b1\u03b2 \u2212 \u03b32)\u2212 \u03c92(\u03b1m + \u03b2JR) + 1 = 0 (5.31) is obtained from the determinant (5.28) after solving and performing brief conversions. Thus, there is a total of four (signed) natural circular frequencies \u03c9i, which can be determined by solving (5.31). They depend on the angular velocity \u03a9 of the shaft. Figure 5.6 shows the general curve. The natural circular frequencies are independent of Jp for \u03a9 = 0 because there is no gyroscopic effect for a non-rotating shaft. (5.31) becomes simpler and turns into a quadratic equation that yields the natural circular frequencies: \u03c910,20 = \u221a\u221a\u221a\u221a \u03b1m + \u03b2Ja 2mJa(\u03b1\u03b2 \u2212 \u03b32) [ 1\u2213 \u221a 1\u2212 4mJa(\u03b1\u03b2 \u2212 \u03b32) (\u03b1m + \u03b2Ja)2 ] . (5.32) The influence of the gyroscopic effect is mainly determined by Jp/Ja and by \u03a9. (5.31) is solved for \u03a9 to represent the dependence transparently for any speed", + " The inverse function \u03a9 = Ja Jp \u03c9 + \u22121 + \u03c92\u03b1m [\u03b2 \u2212 (\u03b1\u03b2 \u2212 \u03b32)m\u03c92] Jp\u03c9 (\u2212\u221e < \u03c9 < \u221e) (5.33) is obtained after a few conversions. One can determine the following asymptotes for the 4 natural circular frequencies from the frequency equation in the form of (5.31) or (5.33) by means of the limiting process \u03a9 \u2192\u221e: \u03c91 = \u2212 1 \u03b2Jp\u03a9 \u03c93 = \u2212 \u221a \u03b2 m(\u03b1\u03b2 \u2212 \u03b32) = \u2212\u03c9\u221e \u03c92 = \u221a \u03b2 m(\u03b1\u03b2 \u2212 \u03b32) = \u03c9\u221e \u03c94 = Jp Ja \u03a9 (5.34) 5.2 Fundamentals 323 It is not common to have negative natural circular frequencies, which is why only the magnitudes |\u03a9| have been plotted in Fig. 5.6 (natural circular frequencies are independent of the direction of rotation of the rotor). The negative sign in the case presented here indicates that the shaft center rotates in the opposite direction of the shaft rotating at \u03a9 during the vibration at \u03c91 or \u03c93, see (5.26). This is called rotation in opposite direction. The direction of rotation of the shaft vibration and the direction of rotation of the rotating shaft are the same for the positive values of the natural circular frequencies \u03c92 and \u03c94. This is called rotation in the same direction, see Fig. 5.7. The four natural circular frequencies that the shaft has at an angular velocity \u03a91 are depicted in Fig. 5.6 as small full circles. The associated mode shapes, which indicate the ratio of radial to angular amplitude at the respective natural frequency, are obtained by inserting the calculated \u03c9i in (5.29). One can see from Fig. 5.6 that both for opposite and same directions of rotation there are two natural frequencies of the rotating shaft, the magnitude of which depends on the angular velocity \u03a9. Furthermore, it follows from this figure that for the same direction of rotation the natural frequencies are increased as compared to the non-rotating shaft due to the gyroscopic effect. The upper branch of the curve asymptotically approaches the straight line that results from (5.34). Critical speeds occur when the rotating shaft is excited by one of its natural frequencies", + " As in this case, a natural frequency \u03c9i coincides with the angular velocity \u03a9 of the shaft, the resonance points are found as intersections of the straight line \u03c9 = \u03a9 and the curves according to (5.33). The critical speeds of rotation in the 324 5 Bending Oscillators same direction result from (5.31) where JR = Ja \u2212 Jp: 1 \u03c92 2,4 = 1 2 { \u03b1m+\u03b2(Ja\u2212Jp)\u00b1 \u221a [\u03b1m+\u03b2(Ja\u2212Jp)] 2\u22124(\u03b1\u03b2\u2212\u03b32)m(Ja\u2212Jp) } . (5.35) For all rotors where Jp/Ja > 1, see Fig. 5.5 and Table 5.2 where h d : Jp/Ja = 2, the root expression becomes larger than the preceding terms, and a negative \u03c92 emerges. In other words: There is only one resonance of rotation in the same direction for disk-shaped rotors (Fig. 5.6, point P1). Ja > Jp can apply to drum-shaped rotors. Then there are two resonance points also during rotation in the same direction because the curve of \u03c94(\u03a9) is flatter, see Fig. 5.6. The special case Ja \u2248 Jp is worth noting because for high speeds the frequency of unbalance excitation approaches asymptotically the second natural frequency for rotation in the same direction. This means that for such rotors (e. g. milk centrifuges and spin driers), for which Ja/Jp depends on the load status and may come close to one, resonance occurs at all higher speeds, and passing through the second critical speed becomes impossible. The designer should avoid such phenomena by selecting favorable system parameters", + "67) and correspond to the mode shapes shown in Fig. 5.15b. S5.3 The natural circular frequencies of the non-rotating shafts (\u03a9 = 0) are obtained with JR = Ja, and the circular frequencies of synchronous rotation in the same direction (\u03a9 = \u03c9) are derived from (5.31). The numerical values are contained in Table 5.4. One can see that \u03c91 decreases with increasing distance of the mass from the bearings and that the gyroscopic effect increases the natural frequencies for synchronous rotation in the same direction, see also Fig. 5.6. The gyroscopic effect changes the second natural frequency considerably because the rotor has a larger tilt in the second mode shape. Since Jp > Ja for cases a) and c), there is no second resonance point for synchronous rotation in the same direction. \u221a \u221a 338 5 Bending Oscillators The calculation model of the continuum is an alternative to the calculation model with multiple degrees of freedom. This model features continuous distributions of the mass and elasticity. The vibration behavior of the beam is mainly determined by the bending stiffness and mass distribution as well as the bearing conditions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001280_j.mechatronics.2013.04.002-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001280_j.mechatronics.2013.04.002-Figure4-1.png", + "caption": "Fig. 4. Hysteresis model of Seyfferth [7].", + "texts": [ + " The nonlinear spring, Tb(Dh), can be approximated by a third order polynomial function of the torsion angle: Tb\u00f0Dh\u00de \u00bc a3\u00f0Dh\u00de3 \u00fe a1 Dh \u00f02\u00de or a piecewise linear function of the torsion angle: Tb\u00f0Dh\u00de \u00bc k1 Dh\u00fe 0 ; jDhj 6 h0 k0 Dh k0h0 sign\u00f0Dh\u00de ; jDhj > h0 \u00f03\u00de where Dh is the relative angular motion between circular-spline, hCS, and wave generator, hWG, or flexspline, hFS, depending on which part is fixed, while h0 is the piecewise linear threshold. In particular, Seyfferth et al. estimated the hysteresis losses in the torsional stiffness as a combination of Coulomb friction and a weighted friction function (see Fig. 4), represented by a hyperbolic function as: Th\u00f0Dh\u00de \u00bc T h \u00fe \u00bdTC T hsgn\u00f0D _h\u00de tanh\u00f0c\u00f0Dh Dh \u00de\u00de \u00f04\u00de where TC is the Coulomb torque, c determines the shape of the hyperbolic curve, while T h and Dh represent the last reversal point of the hysteresis feature. In order to evaluate the torsional stiffness, we developed a test setup utilizing a low torque type of harmonic drive of Wave-Drive from Oechsler AG, which has a transmission ratio of 50:1. The schematic of the setup is shown in Fig. 5. The circular spline is fixed to the ground with a locked-load mechanism, while a shaker applies a low torque to the output shaft, which is connected to the flexspline, through a small lever arm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure4.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure4.9-1.png", + "caption": "Fig. 4.9 Diagram of an induction motor with the reference axes attached to the", + "texts": [ + " Because of the uniform air gap, two alternative theoretical treatments are possible, according to whether the axes of the reference frame are assumed to be attached to the secondary or the primary member: If the reference frame of the idealized machine is attached to the secondary member, the induction motor can be considered as a special case of the synchronous machine, and the equations are those of Eqns. (4.27) in a simplified form. If, on the other hand, the reference frame is attached to the primary member, different equations are obtained and different trans formations are needed. The equations in the latter form are referred to as Kron's equations [8]. The primitive diagram for an induction motor with the primary winding rotating is shown in Fig. 4.9, in which the suffixes I and 2 are used to denote primary and secondary. Because of the uniform air gap, corresponding inductances are the same on both axes. There are no self-evident direct and quadrature axes but the analysis is simplified by choosing the d-axis to coincide with the axis of phase A2 on the secondary winding. The current transformation from frame (a2,b2,c2) to (d2,q2,Z2) is Eqn. (4.10). The three-phase primary coils Al , BI and C1 are replaced by fictitious tw~axis coils DI and QI and the transformation equations are those given in Eqns", + " Machines 95 R d2 +L22P LmP LmP R d1 +LllP LllW Lm w = Uql -Lm w -LIIW Rq1+LllP LmP iq 1 Uq 2 LmP Rq2 + L22P iq2 M Wo (L .. L\u00b7\u00b7) e = - m ld 2lq I - m ld Ilq 2 2 (4.44) (4.45) where Lm is the magnetizing inductance and LII and L22 are the self-inductances. secondary member. The alternative arrangement in which the reference frame is attached to the primary member with the direct axis chosen to coincide with the primary phase AI, is shown in Fig. 4.10. The only essential difference compared with Fig. 4.9 is that the primary and secondary applied voltages are changed over. The form of the equations is therefore exactly as before with the suffixes interchanged. The voltage and torque equations are: Rdl +LIIP LmP Ud2 LmP Rd2 + L22P L22W Lm w = Uq 2 -Lm w -L22W Rq2 + L22P LmP Uql LmP Rql +LllP M WO (L .. L\u00b7\u00b7) e = 2 m ld 1 lq 2 - m ld 21q 1 (4.46) (4.47) The primary current transformations are obtained from Eqns. (4.10) with suffix I, and the secondary current transformations from Eqns. (4.4) with suffix 2", + " The practical cage winding consists of many coupled circuits interconnected through the end-rings, each circuit being strictly a mesh in a network and each current being the current in a bar. Since the impressed voltage in every circuit is zero, all the symmetrical component voltages are also zero. Consequently all the current components except id and iq are also zero. Hence the cage is equivalent to the two-phase winding formed by coils D2 and Q2 in Fig. 4.10 and for most purposes it is not necessary to introduce the actual currents at all. The equations of a double-cage induction motor can be written down by including an additional pair of two-phase coils in Fig. 4.9 or 4.10 and adding two more voltage equations (see Section II. 2). Chapter Five Types of Problem and Methods of Solution and Computation For a machine represented in the primitive diagram by n coils there are n voltage equations and a torque Eqn. (1.6). If the n applied voltages and the applied torque are known, as well as initial conditions, the (n + 1) equations are sufficient to determine the n currents and the speed. Hence theoretically the performance of the machine is completely determined" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001874_tmech.2018.2818442-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001874_tmech.2018.2818442-Figure2-1.png", + "caption": "Fig. 2. Design of the continuum joint. (a) continuum joint with four holes, (b) layout of actuation cables and tubes.", + "texts": [ + " In this section, the design of the manipulator components is presented. The developed bending robotic system is composed of a control system, a driving module and a continuum module. The flexible feature of the mechanical structure is obtained using superelastic NiTiNol tubes (Memry\u00ae) as backbone. The main reasons to choose NiTiNol were its kink, its large elastic deformation, its long life span and its excellent hyperelastic performance. As a result, the proposed manipulator is safe when getting in touch with human tissue. Figure 2 (a) shows the design of the continuum joint with four holes. Joints\u2019 diameter is about 4 mm, and the central hole has a diameter of 1.4 mm. A rotary mechanism is proposed consisting of a ball and socket joint. It can withstand loads to 1083-4435 (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. TMECH-07-2017-6836.R1 3 improve structural stability", + " Each joint can be tilted up to 30 degrees, so that the manipulator needs at least ten joints, in order to make the continuum module bend up to 270 degrees. These joints are connected by NiTiNol tubes and stainlesssteel cables pierced through four holes of joints. Two cables which are inserted into two holes will lead to deflection in opposite directions. The remaining two holes are the channels of NiTiNol tubes, and another two cables are inserted into the tubes to enable scissoring as shown in Fig. 2 (b). The cable-driven continuum module is illustrated in Fig. 3. The manipulator is actuated by stainless-steel cables, and the cable diameter is important to endure enough strength during surgical operation. As a result, the size of the diameter is chosen after analytic calculation. By pulling and releasing the four cables, different length of two cables will lead to deflect in different direction as shown in Fig. 3 (a). Holding the cables keep the joints in place, while moving cables can realize the deflection of the joints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002912_1.4039092-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002912_1.4039092-Figure6-1.png", + "caption": "Fig. 6 FE mesh of large part at last discretization step", + "texts": [], + "surrounding_texts": [ + "4.1 Performance Evaluation of the New Framework Using the Simulation of Small-Sized Parts. The computational efficiency of the new FE framework was determined by comparing the total computational time of the simulation based on the new FE framework with that of the conventional framework. Then, the residual stress and plastic strain predicted by the simulation based on the new framework was compared with those predicted by the simulation based on the conventional framework. Results are first discussed for the rectangular part, followed by cylindrical part. The parts being thin-walled, only the dominant components of Table 5 Application of selective mesh coarsening at each discretization step for small parts Additive step no. Newly added layers Mesh coarsening regions 1 1\u20134 F1 2 5\u20138 F1,F2 3\u20138 9\u201332 F1,F2,C1 041009-6 / Vol. 140, APRIL 2018 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 05/15/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use stress and the corresponding plastic strain components were used for the comparison. The dominant components of stress are inplane normal stress components in the scanning and build directions. The predicted results after removing the build plate were also studied. 4.1.1 Computational Efficiency. The computational efficiency of the new framework is demonstrated first by comparing the increase in the total DoF of the system between the two frameworks and then by comparing the total simulation time between them. The increase in the total DoF in the system as the simulation progresses is shown as a function of the number of layers in the system in Figs. 6 and 7. In the conventional framework, the total DoF of the system increased linearly since the mesh density was uniform and the part had a uniform cross section in the build direction. On the contrary, with selective mesh coarsening, the total DoF in the new framework remained relatively low as indicated by the very small slope of the DoF curve. Note that the top four layers were discretized with the same fineness in all the discretized geometries used in the new framework. Therefore, as seen in the results, the total DoFs in the system up to fourth layer in the new framework and the conventional framework were equal. For the next few layers, a slight deviation can be seen due to moderate selective mesh coarsening implemented in the bottom layers in the new framework. Subsequently, the deviation between the new framework and the conventional framework progressively enlarged as the selective mesh coarsening increased in the new framework. The area under the curve, which is cumulative of the total DoF in the system, is a first cut approximation of the size of the problem. Accordingly, the decrease in the size of the problem in terms of the cumulative of the total DoF was estimated for the Table 6 Application of selective mesh coarsening at each discretization step for the large part Additive step no. Newly added layers Mesh coarsening regions 1 1\u20134 F1 2 5\u20138 F1, F2 3 9\u201312 F1, F2, F3 4\u201310 13\u201340 F1, F2, C1, F3 11\u201375 41\u2013300 F1, F2, C1, C2, C3, F3 Journal of Manufacturing Science and Engineering APRIL 2018, Vol. 140 / 041009-7 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 05/15/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use thin-walled rectangular part and the cylindrical part as 1.5 106 and 4.2 106, respectively. A considerable saving in simulation time was achieved for the new framework (Table 7). The total simulation time shown is the sum of the simulation times of the thermal analysis step, the structural analysis step, and the analysis performed to simulate removal of build plate, although it is very small. For the thin-walled rectangular part, the savings in total simulation time was well over 50% (Table 7), with the total simulation time for the new framework and conventional framework being 6.5 and 14.0 h, respectively, In the simulation of the thin-walled cylindrical part using the conventional method, the analysis failed at the 20th layer due to a convergence issue caused by excessive element distortion. However, in the simulation using the new framework, all 32 layers were simulated without any numerical error, which indicates the robustness of the new framework. The total simulation time to complete 32 layers for the new framework was 26.7 h compared to 45 h to complete only 20 layers using the conventional framework (Table 7). In both the frameworks, since the structural analysis step consumed significantly more simulation time compared to thermal analysis, a large portion of the savings in the total simulation time was contributed from the structural analysis. The consequence of the progressively increasing total DoF of the system due to continued addition of layers in any AM simulation is that the computational time for the simulation of the newly added layer increases. In Fig. 8, the increase in simulation time with the increase in number of layers is shown for the thermal and structural analysis steps in the new framework. The simulation time per layer remained almost constant due to selective mesh coarsening. Typically, the simulation time is expected to increase with the increase in the total DoF. However, a small decrease in computational time immediately after the introduction of a new discretized model with a relatively larger total DoF can be seen at a few locations. For example, the computational time for the simulation of the printing of fifth layer in the second discretization step was lower than the fourth layer in the first discretization step. This can be attributed to the dependence of computational time on other factors, such as the number of iterations it takes to achieve convergence. The convergence may vary with local mesh density, especially in the case of simulations with temperature-dependent material properties and plastic behavior. 4.1.2 Stress and Plastic Strain Distribution Comparison for Rectangular Part. The distribution of residual stress after the part cooled down to room temperature is shown in Fig. 9. The normal component in the scan direction rxx and in the build direction rzz Table 7 Comparison of the total simulation time for thin-walled rectangular plate and cylinder Framework Thin-walled rectangular plate (h) Thin-walled cylinder (h) Conventional Thermal 5.4 15.2a Structural 8.6 29.8a Total 14.0 45.0a SMC Thermal 2.8 11.8 Structural 3.7 15.8 Total 6.5 26.7 aConventional model stopped at 20th layer due to a convergence issue. 041009-8 / Vol. 140, APRIL 2018 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 05/15/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use is shown in Figs. 9(a) and 9(b), respectively. The distribution of the normal stress components shows a region near at the top with large tensile stress in the scan direction and nearly zero stress in the build direction. The tensile stress in the scan direction decreased gradually as it got closer to the build plate. The decrease was very large toward the bottom region of the part, though it remained tensile. The stress component in the build direction was compressive in the lower region of the part near the interface with the build plate. The gradients of both stress components were high near the interface due to the higher constraint to deformation at the interface. The comparison of the predicted stress fields by the simulations based on the new framework and the conventional framework showed excellent agreement. The transition of the stress component in the scan direction from a higher value in the top region to a lower value near the interface was captured fairly well by the new framework. High compressive stress in the build direction near the interface was also well captured by the new framework, although a slight increase in the compressive stress can be seen near the interface between the part and the build plate. Once the part has been built, it will be removed from the build plate which redistributes some of the stress. Redistribution of stress as a result of the removal of the build plate is shown in Fig. 10. The low tensile stress in the scan direction observed at the very top region of the part became compressive. The region immediately below the very top regions where a high tensile stress in the scan direction was observed decreased substantially. Instead of a single high tensile region, two regions with high tensile stress had formed on both sides of this top region as shown in the figure. Right below these two tensile regions, regions of high compressive stress had also formed. In addition, two high tensile stress regions near the interface moved from the sides toward the middle as shown in the figure. Similar to the stress in the scan direction, the stress in the build direction also changed substantially upon the removal of the build plate. The high compressive region at the middle redistributed to two regions more toward the sides of the part as shown in Fig. 10(b). The comparison of stress distributions both in the scan and build directions shows that the predicted results by the simulation based on the new framework are in very good overall agreement with those predicted by the simulations based on the conventional framework. The distribution of the in-plane normal components of plastic strain is shown for the part after the removal of the build plate in Fig. 11. Since the removal of the build plate does not affect the plastic strain distribution, the plastic strain distribution shown is the same for the part before the removal of the build plate as well. Overall, a uniform tensile in-plane plastic strain is developed in the scanning direction in the middle region of the part. However, a large gradient in the plastic strain distribution was seen toward the sides: changing from tensile in the interior to compressive toward the vertical edges. The component of plastic strain in the build direction also showed a uniform distribution in the middle region of the part, but with a compressive strain. A gradient in plastic strain can also be observed for the strain component in the build direction near the vertical edges. However, it varies from the uniform compressive strain in the middle to a large tensile strain toward the vertical edges. In addition to the gradient near the vertical edges, the component of plastic strain in the build direction has compressive strain accumulated near the top and Journal of Manufacturing Science and Engineering APRIL 2018, Vol. 140 / 041009-9 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 05/15/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use bottom edges. The comparison of plastic strain distribution shows that the simulation based on the new framework agrees quite well with that predicted by the simulation based on the conventional framework, especially in the middle region where the plastic strain distribution is uniform. The predicted results also agree fairly well near the edges where the gradient is very high. Minor differences in the results between the conventional framework and the new framework are mainly due to the difference in the mesh as a result of the mesh coarsening. Better accuracy can be achieved by increasing the mesh density and by increasing the number of layers per discretization step, but at the cost of increased overall computational time. 4.1.3 Stress and Plastic Strain Distribution Comparison for Cylindrical Part. In the cylindrical part, stress and plastic strain have an axisymmetric distribution. The choice of arbitrary starting locations for the heat source in individual layers does not have any significant effect. Therefore, the results are shown on a cross section of the thin wall. The residual stress distribution in the hoop direction and the build direction after the part cooled down to room temperature is shown in Fig. 12. Residual stress in the hoop direction was tensile in a region close to the top of the part, with a positive stress gradient toward the inner wall. Closer to the build plate, the outer region of the part showed a tensile stress and the inner region showed a compressive stress. Hoop residual stress is mostly a low tensile stress in the middle of the part. The predicted residual stress distribution in the hoop direction by the simulation based on the new framework agreed quite well with the overall behavior predicted by the simulation based on the conventional framework. The residual stress in the build direction was mostly a low uniform tensile stress in the top region of the part. Near the interface, with the build plate, a large gradient in the stress distribution was found in the thickness direction of the wall. The stress was mostly compressive near the inner wall and mostly tensile near the outer wall. The simulation based on the new framework predicted the distribution of stress in the build direction quite accurately in the whole part, even near the interface where the gradient of stress distribution was very high. The removal of the build plate introduced redistribution of the residual stress field in order to maintain static equilibrium. The residual stress distribution after the removal of the build plate is shown in Fig. 13. The hoop stress near the top edge changed from a relatively small tensile stress to a compressive stress. In the middle region of the part, the hoop-stress, in general, showed a transition from a low tensile stress to a low compressive stress. Closer to the build plate, the hoop stress remained tensile in the outer region, but with a relatively lower magnitude. The low compressive stress in the inner wall region transitioned into a low tensile stress. The change in the stress distribution due to the removal of the build plate was relatively more dominant in the build direction. A large stress release was observed near the part to the build-plate interface, with the two large regions of compressive and tensile stress near the part vanishing almost completely, leaving only two very small regions of concentrated tensile and compressive stress. The comparison of stress distribution after the removal of the build plate, for both stress components, showed very good agreement between the simulations based on the new framework and the conventional framework. The plastic strain distribution showed that the plastic strain component in the hoop direction is overall in a tensile state, with higher values in the regions close to the top and bottom of the part 041009-10 / Vol. 140, APRIL 2018 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 05/15/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use (Fig. 14). The tensile stress is highest in the bottom region toward the inner wall of the part. In the middle region, the plastic strain in the hoop direction is close to zero. The plastic strain in the build direction is very low and tensile in general, except in the region near the bottom edge, close to the inner wall where the significant compressive strain was formed. There is also a region with large tensile stress near the outer edge. The predicted plastic strain distribution agrees quite well between the simulations based on the new framework and the conventional framework. 4.2 Experimental Validation. The elastic strain distribution predicted in the thin-walled rectangular part after its removal from the build plate was compared with the experimental results obtained from neutron diffraction measurements (Fig. 15). The elastic strain component in the build direction was measured along two vertical paths (B1 and B3) and one horizontal path (B2) as shown. The experimental results showed a large tensile strain near the interface along the vertical path B1. The large tensile strain decreased to a small value as the distance from the build plate increased, and then became a large compressive strain. The compressive strain appeared to be decreasing toward the top region. The experimental result agreed well with predictions from both the simulations, especially in the middle region, However, the high tensile strain close to the interface and the high compressive strain close to the top region were not accurately predicted. The experimental results along the longitudinal direction (line B2) showed a high tensile elastic strain close to the edges of the part while going toward the center of the part it showed rapid fluctuations between compressive and tensile states. The simulations based on both the conventional and the new frameworks predicted similar behavior along line B2. In comparison with the experimental results, the predicted results followed similar trend, although the predictions showed a relatively lower level of fluctuations in the interior region. The elastic strain measurements along the path B3 showed large tensile strain in the middle region, then decreasing to very low values in the regions close to interface and the top free surface. As in the case of paths B1 and B2, the predictions of both simulations for path B3 also showed very good agreement with the trend exhibited by the measurements. Overall, the predicted results showed fairly good agreement with the trends shown by the experimental measurements for all three different paths. Although the results also agreed quantitatively in some regions, there were other regions where the difference between the predicted and experimental results was significant. This disagreement could be attributed to the selection of gage volume based on standard test data obtained from conventionally manufactured material samples. The microstructure of the same material manufactured with AM could be quite different, requiring a very different size for the gage volume. It is important to note that the predictions by both the simulations agreed extremely well between them. The comparison of part distortions is illustrated for the rectangular and the cylindrical parts in Fig. 16. Experimental Journal of Manufacturing Science and Engineering APRIL 2018, Vol. 140 / 041009-11 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 05/15/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use measurements were taken at several locations on each part using a digital caliper. Overall, the predicted distortions agreed very well with the measured values for both the new and the conventional frameworks. The distortion predicted at the middle of the vertical edges of the part was slightly lower than that measured. The maximum error observed at the center of the rectangular sample is 4.0%. In the thin-wall cylindrical part, the prediction by the simulation based on the new framework was slightly higher than the experimental results, especially at the center of the horizontal edge of the part (Fig. 16(b)). The maximum error observed at the center of the cylindrical sample is 18.0%. Apart from those minor disagreements, the predictions were fairly close to the experimental results. Note that the predictions based on the conventional framework were not available for the thin-walled cylindrical part since the simulation failed after building 20 layers. Although the repeated failures of the simulation based on conventional framework for relatively large parts due to numerical issues were not investigated further, the fact that the simulation based on the new framework for the same parts under exactly same conditions except for the difference in discretization never encountered such an issue indicates the robustness of the new framework owing to the smaller size of the system. 4.3 Simulation of the Large-Scale Model. The change in total DoF of the system with the addition of more layers is shown for the large-scale part in Fig. 17. While the DoF for the simulation based on the conventional framework increased rapidly with the increase in the number of layers, the total DoF remained almost constant throughout for the simulation based on the new framework. The simulation time for the completion of each discretization step is shown in Fig. 18. The plot shows that the simulation time, consistent with the total DoF, also remained constant throughout the analysis. The variation of simulation time for the new framework is consistent with the variation of DoFs (the variation of DoF is not clearly visible in Fig. 17 due to rapid growth in DoFs for the conventional framework, but can be validated by changing the scale of the graph). The distribution of residual stress component along the build direction, rzz, is shown in Fig. 19 as an example result for the large part. According to the distribution, the variation of rzz along the length is not very significant, but a large variation from a compressive stress on the inside surface of a tensile stress on the outside surface can be seen." + ] + }, + { + "image_filename": "designv10_3_0002702_1.4029988-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002702_1.4029988-Figure4-1.png", + "caption": "Fig. 4 (a) The toppling event and (b) force deformation behavior at the contact between ball and defect edge", + "texts": [ + " (5) as: XZ i\u00bc1 kid 3=2 i ci cos wi \u00bc W with ci \u00bc 1 if di > 0 0 if di < 0 ; i \u00bc 1; 2; :::; Z (5) where Z is the total number of balls, ki is the stiffness at the contact formed between two races at the ith ball location and is evaluated using the following relation [33] ki \u00bc \u00bd1=f\u00f01=Ki\u00de2=3 \u00fe\u00f01=Ko\u00de2=3g 3=2 ; Ki/o are the load deflection constants between the inner and outer ball race respectively given by Ki=o \u00bc 2:15 105 P q 1=2 i=o \u00f0d i=o\u00de 1:5\u00f0N=mm 1:5\u00de, and di is the deflec- tion at the ith ball location given by di \u00bc \u00bd\u00f0xIR xOR\u00de cos wi cl biDh (6) where bi\u00bc 1 for the ith ball when it passes through the defect and bi\u00bc 0 for all other cases, xIR and xOR are the quasi-static displacement of the inner and outer raceways, respectively, cl is the clearance and Dh is the amount by which the center of the ball sinks when it enters into the defect and is a function of width of the defect as Dh \u00bc rb 2 1 cos\u00f0hb=2\u00de\u00f0 \u00de; hb \u00bc width of the defect radius of the ball (7) Therefore, using the force\u2013displacement relationship for the contact springs, the revised contact forces may be given by below equation as Fci \u00bc kid 3=2 i ci (8) Hence, in the destressing phase, the forces acting onto the structure through the outer race reduces from Fs to Fc. The commencement of reduction of the force marks the point of entry which is used as a marker to estimate the defect size. 2.1.2 Impact Event (II) Magnitude of the Impact (Fi). The strength of impact felt by the bearing components when the ball topples about point PTO as the instantaneous center and hits point PTR on the trailing edge of the defect as shown in Fig. 4 depends on the speed of the ball with which it hits the defect, inertia of the ball, external load applied, material properties, defect size, and position of the defect in the load zone. Figure 4(a) shows the toppling event with the forces on the ball where a defect has been considered in the load zone on the outer race and Fig. 4(b) depicts the approximation of contact between the ball and the trailing edge with a restoring element for the evaluation of impact force and its duration. When the ball reaches a point PTO on the leading edge of the defect, it topples about this point as the instantaneous center and hits point PTR on the trailing edge of the defect. Hertzian contact theory is used to evaluate the magnitude of impact force Fi with the understanding of maximum compression at the hitting edge/trailing edge as Fi \u00bc kcx 3=2 imax (9) With reference to Fig. 4(a), let the defect located at an angle a from the line of maximum load (vertical X axis here) subtend an 051002-4 / Vol. 137, OCTOBER 2015 Transactions of the ASME Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/22/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use angle ho at the bearing center O and the radius of the ball PTOB topple about the point PTO with an initial angular velocity xb (rad/ s) by rotating through an angle b until the center B is at O0, i", + " (12) as xf \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 b\u00fe 10g 7rb cos\u00f0a\u00feho\u00de cos a\u00fe\u00f0hb\u00feho\u00de 2 \u00fe10Fc 7mrb bsin hb 2 s (13) From the knowledge of xf, the component of linear velocity along the impact line O0PTR and the maximum deformation of the defect edge may be obtained. The issue of maximum compression ximax has been addressed next. For this purpose, the contact between the defect edge and ball, i.e., between two convex surfaces has been assumed to have only restoring forces approximated by a spring of stiffness \u201ckc\u201d (as shown in Fig. 4(b)) based on the Hertzian contact theory and negligible dissipation forces. Lagrange\u2019s principle has been used to draw up the equation of motion after the ball strikes the trailing edge. Considering that \u201cx\u201d and \u201cx\u201d denotes the compression of the spring of stiffness \u201ckc\u201d and the instantaneous angular velocity of the ball with respect to an inertial frame of reference at an instant after the ball touches the trailing edge, the kinetic energy \u201cT\u201d may be written as a summation of translational and rotational kinetic energies of the ball (mass m and mass moment of inertia about center, I) as T \u00bc 1 2 m _x2 \u00fe 1 2 I _x2 \u00bc 1 2 m _x2 \u00fe 1 2 2 5 mr2 _x2 \u00bc 7 10 m _x2 (14) The strain energy \u201cV\u201d at this instant may be expressed in the equation below: V \u00bc \u00f0x 0 kcx3=2dx \u00bc 2 5 kcx5=2 (15) where kc is the stiffness parameter for nonconforming spherical contact and is given by kc \u00bc 4E ffiffiffiffiffi R p =3; E is the equivalent Young\u2019s modulus\u00bcEbEr=f\u00f01 t2 b\u00deEb \u00fe \u00f01 t2 r \u00deErg; Eb;Er (\u201cb\u201d for ball and \u201cr\u201d for race) being the elastic moduli of the ball and race respectively, tb; tr are the corresponding Poisson\u2019s ratios, and R is the reduced radius of curvature", + " The expression for final angular velocity with which ball comes on the raceway is written as xTEf \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 TEi \u00fe 10g 7rb cos\u00f0a b\u00de cos af g 10Fc 7mrb b sin hb 2 s (23) Therefore, the time tD taken by the ball to restress and return to its original state is given as under tD \u00bc xTEi xTEf dx0=dt (24) 2.1.4 Time to Impact. It is defined as the time taken by the ball to impact the trailing edge of the defect when it is at the leading edge. This will represent the period of separation between the point of entry and point of impact as illustrated in Fig. 2 and the average time to impact (TTI) may be expressed as TTI \u00bc b xavg ddef 2xavg 1 rb 1 ro (25) where b is defined in Fig. 4(a), xavg \u00bc \u00f0xb \u00fe xf \u00de=2 is the average angular speed of the ball, ddef is the circumferential width of the defect on the outer raceway, and rb and ro are radius of the ball and outer raceway. 2.2 Forcing Function Generated by the Defect. The periodic excitations (with periodic time T) caused by defect during different events are shown schematically in Fig. 6, where the top pulse shape correspond to the case when impact force (Fi) is greater than the static load (Fs) the ball was bearing before entry into the defect and the pulse shape at the bottom depict the case when impact force magnitude is less than the static force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000357_j.triboint.2010.03.019-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000357_j.triboint.2010.03.019-Figure2-1.png", + "caption": "Fig. 2. (a) Cylindrical roller bearing and (b) equivalent model of two cylinders.", + "texts": [ + " In previous studies [3,4] the subsurface stress history was captured by moving a Hertzian pressure distribution in discrete steps over the computational domain. Using the explicit formulation of this study, the pressure distribution can be moved continuously across the domain. The continuous motion of the Hertzian pressure provides a more complete history of the subsurface stresses. This is especially significant as damage initiates and stress concentrations develop within the domain. The rolling contact fatigue model for this investigation was developed to simulate spall formation in a cylindrical roller bearing shown in Fig. 2(a). For computational purposes it is advantageous to use an equivalent model of the two contacting cylinders as shown in Fig. 2(b). In this figure the radius of the roller is denoted as R1 and the radius of the inner race is denoted as R2. The elements are in contact over a length l and support a load of magnitude w. The half-width of contact obtained from Hertz theory is given by b\u00bc 8w plE0 \u00f01=R1\u00de\u00fe\u00f01=R2\u00de 0 @ 1 A 0:5 \u00f01\u00de where 1 E0 \u00bc 1 2 1 n2 1 E1 \u00fe 1 n2 2 E2 : \u00f02\u00de The pressure distribution within the contact is elliptical and is given by P\u00bc Pmax 1 x2 b2 0:5 \u00f03\u00de where Pmax \u00bc 2w pbl To compute the subsurface stress history for a rolling pass a two-dimensional elastic half-space under plane strain conditions is constructed as depicted in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001831_j.mechmachtheory.2011.08.009-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001831_j.mechmachtheory.2011.08.009-Figure4-1.png", + "caption": "Fig. 4. Coordinate systems for the five-axis CNC gear profile grinding machine.", + "texts": [ + " 3): zp u;\u03b2;\u03d51\u00f0 \u00de \u00bc zt u;\u03b2;\u03d51\u00f0 \u00de yp u;\u03b2;\u03d51\u00f0 \u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2t u;\u03b2;\u03d51\u00f0 \u00de \u00fe y2t u;\u03b2;\u03d51\u00f0 \u00de q : ( \u00f04\u00de 3. Mathematical model of the five-axis gear profile grinding machine The DOF of the proposed Cartesian-type gear profile grinding machine is arranged based on the universal CNC gear form grinder, which has five numerically closed-loop controlled axes: three rectilinear motions (Cx,Cy,Cz) and two rotational motions (\u03c8a,\u03c8b) (see Fig. 4). Such a vertical machine configuration is recognized to have high stiffness for grinding large-size gears. Its coordinate systems St(xt,yt,zt) and S1(x1,y1,z1), whose relative positions are described by the auxiliary coordinate systems from Sd to Sf, are rigidly connected to the grinding wheel and work gear, respectively. Here, \u03c8a is the rotation angle of the work gear, and \u03c8b denotes the swivel angle of the wheel. The vertical stroke motion Cx and the wheel axial motion Cz are used for wheel positioning, while Cy is the radial motion for infeeding the wheel down to tooth depth. Parameters K1 and K2 are machine constants that depend on the individual machine and are calibrated immediately after machine installation. Assuming that, as shown in Fig. 4, the surface position of the wheel is represented in coordinate system St in two-parametric form rt(u,\u03b2) which is determined by the solved wheel axial profile in Section 2, and the transformation matrices St to S1 yield the following surface locus for the wheel represented in coordinate system S1: r C\u00f0 \u00de 1 \u00f0u;\u03b2;Cx;Cy;Cz;\u03c8a;\u03c8b\u00de \u00bcM C\u00f0 \u00de 1f \u03c8a\u00f0 \u00deM C\u00f0 \u00de fe Cx;Cy M C\u00f0 \u00de ed \u03c8b\u00f0 \u00deM C\u00f0 \u00de dt Cz\u00f0 \u00dert\u00f0u;\u03b2\u00de \u00bcM C\u00f0 \u00de 1t Cx;Cy;Cz;\u03c8a;\u03c8b rt\u00f0u;\u03b2\u00de \u00f05\u00de where M C\u00f0 \u00de 1f \u03c8b\u00f0 \u00de \u00bc 1 0 0 0 0 cos \u03c8a sin \u03c8a 0 0 \u2212 sin \u03c8a cos \u03c8a 0 0 0 0 1 2 664 3 775 M C\u00f0 \u00de fe Cx;Cy \u00bc 1 0 0 Cx 0 1 0 Cy 0 0 1 \u2212K1 0 0 0 1 2 664 3 775 M C\u00f0 \u00de ed \u03c8b\u00f0 \u00de \u00bc cos \u03c8b 0 sin \u03c8b K2 cos \u03c8b 0 1 0 0 \u2212 sin \u03c8b 0 cos \u03c8b \u2212K2 sin \u03c8b 0 0 0 1 2 664 3 775 M C\u00f0 \u00de dt Cz\u00f0 \u00de \u00bc 1 0 0 0 0 1 0 0 0 0 1 Cz 0 0 0 1 2 664 3 775: The relative spatial position of the wheel axis with respect to the work gear axis should be the same whether the work gear is ground on a universal or a CNC machine" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure9-1.png", + "caption": "Fig. 9. and (c", + "texts": [ + " Therefore, a new type of geometry has been developed wherein the tooth surface of the pinion (respectively, of the shaper) is determined as an envelope to a rack-cutter of a parabolic profile. The following is the description of the two types of geometry of helical pinion (shaper). Fig. 3 shows involute cross-profiles of a shaper (pinion) represented in an auxiliary coordinate system S\u00f0i\u00de q (i = 1, s) by vector function r\u00f0i\u00deq \u00f0hi\u00de (i = 1, s) where hi is the profile parameter [7]. The screw involute tooth surface Ri (i = 1, s) is generated in Si (Fig. 9(c)) while coordinate system S\u00f0i\u00de q (together with the cross-profiles) performs a screw motion about the axis zi (i = 1, s) of the pinion (the shaper). Surface Ri is represented as ri\u00f0 i; hi\u00de \u00bc M \u00f0i\u00de iq \u00f0 i\u00der\u00f0i\u00deq \u00f0hi\u00de; \u00f08\u00de where i is the angle of rotation in the screw motion. The surface normal is represented as Ni\u00f0hi; i\u00de \u00bc ori ohi ori o i : \u00f09\u00de The derivation of the screw involute surface by a rack-cutter is based on the following considerations: (1) The generating surface of the rack-cutter is a plane and the rack-cutter is provided with skew teeth (Fig. 9(a)). (2) The transverse and normal sections of the rack-cutter are indicated as b b and a a (Fig. 9(a)). Angle b shows the orientation of the rack-cutter in plane P. For derivation of pinion and shaper surfaces Ri (i = 1, s): (a) skew teeth of the rack-cutter surface Rc, (b) normal section of Rc, ) coordinate systems used in the meshing between Rc and Ri (i = 1, s). The profiles of the rack-cutter in normal section a a (Fig. 9(b)) and in transversal section b b are straight lines. The tooth thickness so and the space width wo (Fig. 9(b)) are related as so \u00fe wo \u00bc pmn; \u00f010\u00de so wo \u00bc kc: \u00f011\u00de In the case of conventional design kc = 1. Parameter kc 5 1 may be used for optimization by variation of tooth thickness so. (3) Fig. 9(c) shows that in the process of generation the rack-cutter and the pinion (shaper) being generated perform related motions represented as sc \u00bc rpiwi; \u00f012\u00de where rpi is the radius of the pitch cylinder. (4) Parameters ui (Fig. 9(b)) and li (Fig. 9(a)) represent surface parameters of the skew rack-cutter. Surface Ri (i = 1, s) of the pinion (shaper) is derived as an envelope to the family of surfaces Rc in Si (i = 1, s) [7] and is represented as ri\u00f0ui; li;wi\u00de \u00bc Mic\u00f0wi\u00derc\u00f0ui; li\u00de \u00f0i \u00bc 1; s\u00de; \u00f013\u00de fci\u00f0ui; li;wi\u00de \u00bc nc v\u00f0ci\u00dec \u00bc 0 \u00f0i \u00bc 1; s\u00de: \u00f014\u00de Here, rc(ui, li) and nc represent the rack-cutter surface and its unit normal; vector function ri(ui, li,wi) represents the family of rack-cutter surfaces; fci = 0 is the equation of meshing; matrix Mic(wi) (i = 1, s) is applied for coordinate transformation; vector v\u00f0ci\u00dec of relative velocity and unit normal nc are represented in Sc", + " (ii) Rack-cutters Rc1 and Rcs are provided by mismatched parabolic profiles that deviate from the straight line profiles of reference rack-cutter Rc. Fig. 4(a) shows schematically an exaggerated deviation of Rc1 and Rcs from Rc. The parabolic profiles of one tooth side of rack-cutters Rc1 and Rcs are shown schematically in Fig. 4(b) and (c). The parabola coefficients for the pinion and the shaper rack cutters are designated by a1 and as, respectively. Rack cutter surfaces Ri (i = c1,cs) are represented in coordinate system Sc (Fig. 9(c)) by vector function rc(ui, li) that yields xc\u00f0ui; li\u00de \u00bc s0 2 cos an sin an \u00fe \u00f0ui uo\u00de cos an \u00fe aiu2i sin an; yc\u00f0ui; li\u00de \u00bc s0 2 cos2an \u00f0ui uo\u00de sin an \u00fe aiu2i cos an cos b li sin b; zc\u00f0ui; li\u00de \u00bc s0 2 cos2an \u00f0ui uo\u00de sin an \u00fe aiu2i cos an sin b\u00fe li cos b: \u00f015\u00de Here, uo indicates the location of the parabola apex wherein parabolic and straight profiles are in tangency (Fig. 4(a)). (iii) The tooth surfaces R1 and Rs of the pinion and the shaper are determined as envelopes to the tooth surfaces of rack-cutters Rc1 and Rcs, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002621_s00170-015-8216-6-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002621_s00170-015-8216-6-Figure13-1.png", + "caption": "Fig. 13 Copper abacus and data processing (in Magics 15.0)", + "texts": [ + " The above studies show that the curved overhanging structure can be fabricated effectively by optimizing the orientation of the parts, adding proper support, and controlling the energy input. The technical parameters of the curved overhanging structure were optimized to fabricate complicated assemblyfree parts. An innovative assembly-free copper abacus was designed in our experiments, which includes many parts with relative motions. It cannot be fabricated using traditional methods. To ensure that the rods are able to move up and down, an interval of 0.2 mm was maintained. The location of the parts was determined properly (Fig. 13a). Supports were added to the overhanging surface of the parts (Fig. 13b) to avoid warpage during the fabricating process. While fabricating parts of the two assembly-free metallic abacuses, the following technical parameters of the curved overhanging structure were optimized: laser power of 120 W, scanning speed of 600 mm/s, scanning interval of 80 \u03bcm, and a recoating thickness of 25 \u03bcm. The fabricated abacus was post-processed to remove the supports and was subjected to sand blasting. The part obtained finally is shown in Fig. 14. All components with relative motions can operate smoothly" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001858_s00170-017-0066-y-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001858_s00170-017-0066-y-Figure2-1.png", + "caption": "Fig. 2 The scraper conveyor and its sprocket", + "texts": [ + "hat of the heat-affected zone and base metal. Furthermore, the results reveal that the Taguchi method can effectively acquire the optimal combination of process parameters, and the laser cladding process exhibits good feasibility and effectiveness for repairing the machinery components with complex shapes. Keywords Parameter optimization . Sprocket repair . Laser cladding . Taguchimethod . Cladding geometry The sprocket (Fig. 1) is a critical part of the scraper conveyor (Fig. 2), which is a kind of equipment for coal conveying in the coal mine industry. Due to the harsh working conditions, the sprocket is easily damaged (as shown in Fig. 1b), such as corrosion and wear, leading the scraper conveyor to work improperly. However, the cost of the direct replacement sprocket is expensive. A large number of surface repair techniques have been applied in the remanufacturing of mechanical components, such as thermal spraying [1], gas metal arc welding (GMAW) [2], and brushing electroplating [3]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002932_j.matdes.2019.107583-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002932_j.matdes.2019.107583-Figure3-1.png", + "caption": "Fig. 3. Design model for bonding strength test and microstructure test: (a) without remelting, (b) remelting twice, (c) remelting three times, (d) CuSn/18Ni300 bimetallic cube (10 mm \u2217 10 mm \u2217 10 mm) for SEM and XRD tests.", + "texts": [ + " For the purpose of manufacturing the CuSn/18Ni300 bimetallic materials, the former half of layers was manufactured using 18Ni300 powder, and then 18Ni300 powder was replaced by CuSn powder for the remaining half of layers. The rendering effect is shown in Fig. 2, and half of the lattice structure is 18Ni300 alloy and other half of the lattice structure is CuSn alloy. For the purpose of investigating the interface bonding strength of CuSn/18Ni300, the bimetallic tensile specimens were prepared, as show in Fig. 3. In order to study whether the remelting process can improve the performance of interface, the interfaces remelting twice and three times. CuSn/18Ni300 bimetallic cube (10 mm \u2217 10 mm \u2217 10 mm) is shown in Fig. 3(d), and this cube was used in the SEM and XRD tests for the observation of interface. The parameters for manufacturing 18Ni300 alloy and CuSn alloy are given in Table 3. Specimens were polished and etched with a mixed solution (H2O: HNO3:HCl = 6:1:3) for 1 min. XRD (Rigaku SmartLab SE, Japan) tests were carried in a step-by-step manner: step scan 2\u03b8 = 30\u00b0\u201395\u00b0, step width = 0.02\u00b0, step time = 1 s. The surface morphology of the porous structure was detected by super depth of filed microscope (VHX-5000, Japan)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000657_tmag.2009.2024159-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000657_tmag.2009.2024159-Figure13-1.png", + "caption": "Fig. 13. The 3-D finite-element mesh for basic experimental apparatus.", + "texts": [ + " Then, the eddy current loss is estimated by the following expression [4] with the increase in temperature during 5 min: (4) where is the mass, is the specific heat, and is the temperature. The loss of the ferrite core is neglected. Except for this point, we employ the same method as described in [4]. To estimate the loss-reduction effect by the segmentation, four-segmented magnets shown in Fig. 12 and a single magnet without the segmentation are examined. In addition, the experiments without the cores are carried out in order to simulate the difference between the IPM and SPM motors. The 3-D FEM is also applied to this apparatus. Fig. 13 shows the finite-element mesh for 1/8 of the apparatus. Fig. 14 shows the ratio of the eddy current loss in the case of four-segmentation to that before segmentation. The experimental and calculated results are found to be in good agreement. In addition, both results indicate the similar tendency to the result of the motors in Section II. The loss-reduction effect decreases in the case with the cores, particularly, at high frequency. It can be stated that this phenomenon is caused by the increase in the reaction field by the magnet eddy currents and that it is the same in the IPM motor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000218_j.mechmachtheory.2003.06.001-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000218_j.mechmachtheory.2003.06.001-Figure10-1.png", + "caption": "Fig. 10. Model of a gear set (for clarity, damping is not shown and only one tooth pair model is represented).", + "texts": [ + " Tooth form errors, modifications and misalignments are introduced via distributions of equivalent normal deviations de(Mij) dependent on the axial co-ordinate along the face width and which vary with time to account for evolutions in the involute direction. de(Mij) behave as initial gaps for the contact stiffnesses (Fig. 9) and influence mesh deflections D(Mij) and contact force distributions P(Mij) expressed as D\u00f0Mij\u00de \u00bc d2j d1j \u00fe de\u00f0Mij\u00de \u00f010\u00de P \u00f0Mij\u00de \u00bc Kc ijH\u00f0D\u00f0Mij\u00de\u00deD\u00f0Mij\u00de \u00f011\u00de where H( ) is the unit Heaviside function; Kc ij the discrete contact stiffness at the jth cell of the ith foundation. The complete model of a geared train is shown in Fig. 10, it comprises: (i) a gear element as described in Section 2 including gear body, tooth and contact stiffnesses as well as tooth form deviations and mounting errors, (ii) shaft elements, (iii) lumped parameter elements to account for bearings, couplings and load machines. As in the majority of the gear dynamic models, the high-frequency modes related to tooth eigenfrequencies are neglected and the kinetic energy associated with the teeth is not individualised but considered as part of gear body contributions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003459_s00170-017-1364-0-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003459_s00170-017-1364-0-Figure6-1.png", + "caption": "Fig. 6 Setup of the electronic speckle pattern interferometry (ESPI)", + "texts": [ + " Electronic speckle pattern interferometry (ESPI) was used for investigating the distribution of residual stress of the AMed and wrought samples subjected to milling. ESPI is a method of measuring relative displacement and strain in surface by laser interferometry. Combined with the hole drilling method, it can be used to measure the displacement after each hole drilling to calculate residual stress. In this paper, Prism (StressTech) was used to measure residual stresses. The experimental setup is shown in Fig. 6. A cutter with 0.8 mm in diameter was used to drill the hole. The largest drilling depth was set at 0.3 mm. In each measurement, ten points were measured evenly in the depth direction. The residual stress distribution along the depth direction can be obtained. To ensure reproducibility, three points located on the centerline of the slot were measured for the machined surface. The chemical compositions (wt.%) of the ASHMed and wrought samples are given in Table 2 and compared to that of the nominal maraging steel of grade 300" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure6.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure6.1-1.png", + "caption": "Fig. 6.1 A 3-link, 5 DOF simplified human arm model. Its fixed base is the shoulder and its endpoint is the hand as a whole. a Top view. b 3D view", + "texts": [ + " There are many standard textbooks on kinematics to which the reader should refer, such as [1\u20133]. For the purpose of introducing the overdetermined nature of tendon lengths and velocities, it suffices to use the prescribed or measured joint angles and angular velocities for a given task. Knowing these joint angles and their sequences, we can find the tendon excursions and velocities on the basis of the moment arm matrix introduced in Eq. 4.26. Let us use the forward kinematic approach to find the tendon excursions and velocities for a human arm model assumed to have 5 DOFs, Fig. 6.1. In principle we only need to know the moment arm matrix of the limb, but for completeness I will present the full forward kinematic model to place the results in a functional context. This kinematic model of the arm is inspired by the anatomical DOFs in [4] and published in [5]. Using Eqs. 2.7 and 2.10 we can define the sequential rotational DOFs, which follow the general case of configuration coordinate transformation matrices presented in Eq. 2.4: T 1 0 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 1 0 0 0 0 c1 \u2212s1 0 0 s1 c1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (6", + " are used routinely to measure limb movements by locating fiducial markers on the body\u2014and then either human operators or algorithms are used to extract the joint angles. These classical methods commonly use regression models, model-based estimation, Kalman filters, etc., and are described in, say, [6, 7]. More recently consumer products have been developed for \u2018markerless\u2019 motion capture [8]. As an example, Fig. 6.3 takes the joint angles extracted from motion capture recordings on an arm during a disc throw from [4], and plots them using the 5 DOF arm model in Fig. 6.1 and Eq. 6.7. Now that we have the basic kinematic concepts in place, we can define the problem of overdetermined tendon excursions. First, we need some definitions that go beyond those presented in Chap. 4. Tendon excursion is a clinical term that relates the distance a tendon traverses as the limbs move and muscles contract. Mechanically speaking, we need to be more precise to understand the overall changes in the length of the musculotendon. As discussed in Chap. 4, musculotendons are the combined entity of the tendon of origin, the muscle fibers, and the tendon of insertion [9]", + " As in [5], these muscles can be those listed in Table 6.1. From such a table of anatomical data one can assemble a moment arm matrix that, as per the convention in Eq. 4.21, has as many rows as there are degrees of freedom (i.e., 5), and as many columns as there are muscles (i.e., 17). Such a moment arm matrix can be transposed to calculate tendon excursions as per Eq. 4.26. Consider the disc throw motion shown in Fig. 6.3 using the moment arm matrix for the arm as per the data in Table. 6.1, the kinematic model in Fig. 6.1, and the timehistories of joint angles from [4]. From this we can calculate the muscle velocities for all 17 muscles in the model. We assumed, conservatively, that the initiation of forward motion, release, and follow-through portions of the throw lasted 450 ms; and approximated it as 45 unique postures at 10 ms time steps, as illustrated in Fig. 6.3. Figure 6.6 shows that the muscle fiber velocities in many muscles are either very fast concentrically (<\u22125 muscle fiber lengths per second), or eccentrically (<5 muscle fiber lengths per second) throughout the motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001095_rm2010v065n02abeh004672-Figure19-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001095_rm2010v065n02abeh004672-Figure19-1.png", + "caption": "Figure 19. A typical form of the set Wc(R, S) = 0 (a\u0303 = 1, c = 0.7).", + "texts": [ + " Because the system is invariant under mirror reflections with respect to the meridian \u03d5 = \u03c0/2, it is sufficient in this case to consider the domain \u03b8 \u2208 (0, \u03c0/2), \u03d5 \u2208 (0, \u03c0/2). 306 A. V. Bolsinov, A.V. Borisov, and I. S. Mamaev We perform the change of variables R = cos2 \u03b8, S = (sin\u03c8 cos \u03b8 sin2 \u03b8)1/3, (30) which reduces the subsequent equations to an algebraic form, and then the region of possible motion of the system is bounded by the line segment S = 0, R \u2208 (0, 1) and the curve R(1\u2212R)2\u2212S3 = 0 intersecting the straight line S = 0 in the points R = 0 and R = 1 (see Fig. 19). The set S0 (fixed points) is found from the condition of a minimum of the potential U = 3 2 a\u0303 S + 2c2 R(1\u2212R) R(1\u2212R)2 \u2212 S3 (31) of the system (24), which in the variables (30) can be reduced to a system of two algebraic equations of the form S3 \u2212 R2(1\u2212R)2 1\u2212 2R = 0, 4Sc2 \u2212 (1\u2212 3R)2(1\u2212R) 1\u2212 2R a\u0303 = 0. It is easy to show that for all values c2 > 0 and a\u0303 > 0 there is only one solution of this system in the region of possible motion: P0 = (R0, S0). Consequently, inside the domain \u03b8 \u2208 (0, \u03c0/2), \u03c8 \u2208 (0, \u03c0/4) there is a unique extremum point (in this case, a minimum) of the potential (31)", + " Substituting these conditions into equation (32), we obtain an equation determining the initial values of R and S for critical trajectories, in the form Wc = \u22129(\u22128R5 + 8R6 + 2S2R\u2212 10S3R2 + 20S3R3 \u2212 S6) \u00d7 (R\u2212 2R2 +R3 \u2212 S3)3S2a\u03033 + 12S3R(16R5 \u2212 32R6 + 16R7 + 10S3R2 \u2212 60S3R3 + 46S3R4 + 2S6 + S6R) \u00d7 (R\u2212 2R2 +R3 \u2212 S3)2c2a\u03032 \u2212 16S4R3(R\u2212 2R2 +R3 \u2212 S3) \u00d7 (8R7 \u2212 24R6 + 24R5 \u2212 8R4 + 32S3R4 \u2212 62S3R3 + 30S3R2 + 5S6R\u2212 4S6)a\u0303c4 + 64S8R5(\u22124R3 + 2R2 + S3R\u2212 2S3 + 2R4)c6 = 0. Inside the region of possible motion the function Wc has a unique saddle point, at which it also vanishes (see Fig. 19), and this point coincides with the minimum point of the potential (31). From it four curves go out, which correspond to two pairs of stopping points of two families of critical periodic trajectories (see Fig. 19). Topology and stability of integrable systems 307 Calculating the values of the first integrals for points of the set Wc = 0, we get the bifurcation diagram of the system, shown in Fig. 20. As in the preceding case, the bifurcation complex consists of a single leaf in this case; consequently, all the critical periodic solutions are stable in this case, and there are no other stable periodic trajectories. In conclusion we point out some prospects for further development of this approach, both in the general theoretical direction and in the applied direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002270_1464419314546539-Figure17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002270_1464419314546539-Figure17-1.png", + "caption": "Figure 17. The experimental research: (a) the setup of test rig and (b) a tested cylindrical roller bearing with defect width 1 mm and depth 1 mm.", + "texts": [ + " If the defect appears on inner raceway, impact forces become lighter while the contact length is smaller than the key value (see Figure 16(c)). Otherwise, impact forces increase with defect length. The trend of the changes in accelerations is also the same as that of impact forces (see Figure 16(b) and (d)). In order to validate the proposed model, an experiment about the vibration measurement of a cylindrical roller bearing with localized defects on outer raceway was carried out. This system is shown in Figure 17(a): the shaft is supported by two ball bearings and one cylindrical roller bearing, the drive is a variable speed motor and the coupling is utilized to connect the shaft and the motor. The tested bearing can be seen in Figure 17(b) and its parameters are listed in Table 5. The shaft performs at the speed of 1500 rpm with a 500N radial load (through the at University of Sydney on September 6, 2014pik.sagepub.comDownloaded from hydraulic loading system) on outer raceway of the left supporting ball bearing. The acceleration vibrations are measured by an accelerometer (the type is DYTRAN 3255A6) mounted on the housing, and CoCo8062 is used for collecting the data. The signals are sampled at 2560Hz with a sampling time of 5 s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003628_j.mprp.2016.04.004-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003628_j.mprp.2016.04.004-Figure5-1.png", + "caption": "FIGURE 5 SLM of molybdenum at standard parameters for volume buildup (standard power P0, Mo [W], standard energy input rE0,Mo [J/m]): simulation results at different process stages.", + "texts": [], + "surrounding_texts": [ + "S P E C IA L F E A T U R E\nenthalpy Hv \u00bdJ=kg are considered by an adopted heat capacity ~Cp \u00bc Cp \u00fe d\u00f0T Tm\u00deHm \u00fe d\u00f0T Tv\u00deHv\u00bdJ=\u00f0kg K\u00de . The function d [1/K] is a Dirac pulse accounting for the latent heats at the melting temperature Tm [K] and the evaporation temperature Tv \u00bdK . The fluid mechanical description of the model is based on the Navier\u2013Stokes equation\nr @u\n@t \u00fe r\u00f0u r\u00deu \u00bc rp \u00fe mr2u \u00fe rg \u00fe Fs (2) with the velocity u [m/s], the pressure p [N/m2], the viscosity m [Pa s], the gravity constant g [m/s2] and the surface tension force Fs [N/m3]. Based on the temperature in the metal phase it is distinguished between solid, liquid and vapor phase. In the solid phase the viscosity m[Pa s] is strongly increased and the surface tension force Fs [N/m3] is restricted to the surface of the liquid metal.\nThe continuity equation\nr u \u00bc Qv (3)\nassures the conservation of mass and includes a source term\nQv \u00bc _m G 1\nrvap\n1\nrmet\n! \u00bd1=s (4)\nwith the evaporation rate _m \u00bdkg=\u00f0m2 s\u00de , the vapour density rvap \u00bdKg=m3 and the metal density rmet [kg/m3] accounting for the density change during evaporation. The vapor density rvap \u00bdKg=m3 is calculated on the base of the ideal gas law.\nThe multi-phase description of the model follows the phase field approach and is based on the Cahn\u2013Hillard equation for the phase function F[ ]\n@F @t \u00fe u rF \u00bc r gl e2 c \u00fe Q 0v (5)\nc \u00bc r e2rF \u00fe \u00f0F2 1\u00deF (6)\nwith the mobility g [(m s)/kg], the mixing energy density l N\u00bd , the surface tension coefficient s[N/m] and the capillary width\ne \u00bc 2 ffiffiffi 2 p l=\u00f03 s\u00de \u00bdm . The source term\nQ 0v \u00bc _m G 1 f\nrvap\n\u00fe F\nrmet\n! \u00bd1=s (7)\naccounts for the evaporation process.\nPlease cite this article in press as: K.H. Leitz, et al., Met. Powder Rep. (2016), http://dx.doi.o\nTABLE 1\nTemperature dependent material data (blue: low temperature regim\nThe described implementation of evaporation by source terms in continuity and Cahn\u2013Hillard equation follows an approach described by Sun and Beckermann in [9]. The evaporation rate _m \u00bdkg=\u00f0m2 s\u00de is calculated on the base of the Hertz\u2013Knudsen formula [10]: _m \u00bc \u2019vap \u00f0pvap p0\u00de ffiffiffiffiffiffiffiffiffiffiffiffi M\n2pRT\nr (8)\npvap \u00bc p0 exp HvM R 1 Tv 1 T\n(9)\nwith the vapor phase fraction \u2019vap \u00bd , the vapour pressure pvap \u00bdN=m 2 , the molar mass M [kg/mol] and the ideal gas constant R [J/(mol K)].\nThe multi-physical simulation model described in the previous paragraph was used to analyze the influence of laser power P [W] and energy input rE [J/m] on process dynamics and melt track width in SLM of stainless steel (1.4404) and pure molybdenum. In the present study a simple cubic monomodal layer of spheroidal powder (powder size d = 40 mm) irradiated with a Gaussian laser beam (focus size dfocus = 130 mm) was regarded. The scan length was s = 360 mm. Temperature dependent material properties were applied and have been taken from Refs. [11\u201318], see Table 1.\nFigs. 4 and 5 show the simulation results at different process stages for the two investigated materials at standard parameters for volume buildup (standard power P0 [W], standard energy input rE0 [J/m]). A comparison of the results makes obvious that SLM of steel and molybdenum operate in different process regimes. Whereas for steel a long melt pool is observed and evaporation plays a significant role, for molybdenum the melt pool size is restricted to the focal spot area and temperatures are far below evaporation temperature. This has its origin in the different phase transition temperatures and thermal conductivities of the two materials (compare Table 1). In SLM of molybdenum due to the high thermal conductivity heat losses are significantly higher, restricting the size of the melt pool. Besides that, the high heat losses in combination with the high evaporation temperature prevent the occurrence of evaporation.\nrg/10.1016/j.mprp.2016.04.004\ne, red: high temperature regime) [11\u201318].\n3", + "FIGURE 4 SLM of steel at standard parameters for volume buildup (standard power P0, steel [W], standard energy input rE0, steel [J/m]): simulation results at different process stages.\nS P E C IA L F E A T U R E\nIn order to analyze the influence of process parameters for both materials power P [W] and energy input rE [J/m] were varied with respect to standard parameters for volume buildup. The simulation results for steel and molybdenum are shown in Figs. 6 and 7. A look at the mere process appearance at different parameter sets makes obvious that for steel there is a dependence on both power P [W] and energy input rE [J/m], with the energy input dependency being more pronounced. For molybdenum a completely different picture can be observed. There is only a minor dependency on the energy input rE [J/m], however a strong power dependency.\nThis behavior becomes even more obvious when comparing the calculated widths of the molten tracks for the both materials. These are plotted vs. power P [W] respectively energy input rE [J/m] in Figs. 8 and 9. Whereas for steel the calculated widths of the molten tracks show a strong dependence on the energy input and only a weak power dependency, for molybdenum the opposite situation is found and the power P [W] is the dominant process parameter. This behavior can be qualitatively understood when considering the Taylor evolution of the temperature distribution of a moving point heat source of power P [W] and\nPlease cite this article in press as: K.H. Leitz, et al., Met. Powder Rep. (2016), http://dx.doi.o\n4\nvelocity vx \u00bdm=s on a semi-infinite substrate [19]:\nT\u00f0y\u00de \u00bc 2P\n4pyrCpk exp\nvx\n2k\n2P 4pyrCpk 2Pvx 8pyrCpk2\n\u00bc 2P 4pyrCpk 2P2\n8pyrCpk2rE\n(10)\nWhereas for steel with a thermal conductivity k [W/(m K)] approximately one order of magnitude smaller than that of molybdenum, the second term of Eq. (10) is dominant and the width of the temperature field respectively the molten track depends both on power P [W] and energy input rE [J/m], for molybdenum with a high thermal conductivity, the pure power dependency of the first term is more dominant.\nExperimental verification In order to demonstrate that the presented multi-physical simulation is able to describe material specific process characteristics of SLM, the calculated widths of the molten tracks were compared to experimental data. In Figs. 6 and 7 for each parameter set a scanning electron microscope (SEM) image of a molten track\nrg/10.1016/j.mprp.2016.04.004", + "S P E C IA L F E A T U R E" + ] + }, + { + "image_filename": "designv10_3_0003053_978-0-8176-4962-3-Figure8.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003053_978-0-8176-4962-3-Figure8.1-1.png", + "caption": "Fig. 8.1. Inverted cart\u2013pendulum.", + "texts": [ + " Here the matched uncertainties are assumed to represent a signal indicating the level of the control performance, that is, in the absence of actuator failures, the matched disturbances do not exist, and when the actuator has a fail, the disturbances appeared in the system. Thus, after the observer is designed and the control law is given, a third step is followed to estimate the fault signal by using the equivalent control method and a low-pass filter. Let us take again the linearized model of an inverted pendulum over an inverted cart\u2013pendulum given in Fig. 8.1. The aim here is to do a fault estimation allowing to indicate the level of the actuator failure, if it exists. The equations governing the dynamics of the system are as follows: x\u0307 (t) = Ax (t) +Bu+B\u03b3 (t) y (t) = Cx (t) (8.1) The state vector x consists of four state variables: x1 is the distance between a reference point and the center of inertia of the trolley; x2 represents the angle between the vertical and the pendulum; x3 represents the linear velocity of the trolley; finally, we have that x4 is equal to the angular velocity of the pendulum" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002744_s00170-017-1392-9-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002744_s00170-017-1392-9-Figure12-1.png", + "caption": "Fig. 12 The meshing condition of the welding substrate and trajectory", + "texts": [ + " As discussed above, the abnormal bead geometry at the start and end is related to the weld pool dynamics and the dimension. To analyze the correlation quantitatively, another simplified welding thermal simulation was conducte d w i t h t h e c omm e r c i a l s o f t w a r e p a c k a g e SIMUFACT.WELDING, in which the filler material and arc forces were ignored for observing the weld pool profile and reducing the processing time. The welding parameters were set as the group 8 in Table 1, with the arc efficiency of 0.85. Figure 12 shows the plate (150 \u00d7 100 \u00d7 10 mm3) and meshing quality, and the central line (100 mm) was set as the welding trajectory with the arrow denoting the torch angle. The double-ellipsoidal heat source applied on the welding trajectory was moving along the specified direction, and the temperature of the welding area increased rapidly as is shown in Fig. 13. The red area showed shape of the weld pool where the temperature exceeded the melting point (1517 \u00b0C). As the time incrementally growing, the length of the weld pool increased significantly" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001133_systol.2010.5675968-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001133_systol.2010.5675968-Figure1-1.png", + "caption": "Fig. 1. Qball-X4 axes and sign convention", + "texts": [ + " In addition, the total torque created by these two rotors will remain constant. Similarly, the pitch rate is controlled by varying the relative speed of the front and rear rotors. The yaw rate is controlled by varying the relative speed of the clockwise (right and left) and counter-clockwise (front and rear) rotors. The collective thrust is controlled by varying the speed of all the rotors simultaneously. 978-1-4244-8154-5/10/$26.00 \u00a92010 IEEE 371 The paper is undertaken in a nonlinear quadrotor model Qball-X4, developed by Quanser Inc. [5]. See Fig. 1. The following nonlinear models are described for using in baseline controller development and reconfigurable control allocation design. For the following discussion, let { }e e e eE O x y z= denote an earth-fixed inertial frame and { }B Oxyz= a body-fixed frame whose origin O is at the center of mass of the Qball-X4, as shown in Fig. 2. The absolute position of the Qball-X4 is defined by ( ), , Tx y z and roll, pitch, and yaw ( ), , T\u03c6 \u03b8 \u03c8 are defined as the angles of rotation about the x, y, and z axis, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000320_ip-b.1988.0042-Figure57-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000320_ip-b.1988.0042-Figure57-1.png", + "caption": "Fig. 57 slots for AC winding", + "texts": [ + " To minimise the cost of the inverter required to supply long lengths of active track, the 3-phase winding is often divided into sections which are switched onto the inverter supply rails only when the short rotor is coupled to them. A synchronous machine which uses an unwound sec- Heteropolar linear synchronous machine DC winding AC coil plan Fig. 58B HLSM configuration, with staggered pole track and diamond shaped armature windings IEE PROCEEDINGS, Vol. 135, Pt. B, No. 6, NOVEMBER 1988 401 are on the moving member, and the track or reaction-rail consists of unwound steel. Fig. 57 shows a heteropolar, inductor type of synchronous motor, which has been investigated by several groups [60, 61]. The track bars are staggered alternately left and right of the longitudinal centre line and therefore receive flux from either the north or south pole outer limbs of the primary core. The return flux path through the centre limb therefore provides the centre limb with alternate north and south poles. This centre limb also contains a polyphase winding that reacts with the induced track poles to produce a propulsion thrust" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000578_tac.2008.919853-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000578_tac.2008.919853-Figure1-1.png", + "caption": "Fig. 1. Vertical coin.", + "texts": [ + " The conditions BC1 are relevant for, say, rest to rest state transfer problems and BC2 are relevant in the case when one just needs to transfer the system to a rest terminal configuration, regardless of the initial condition. In this case, as seen in Theorem 3.1, the necessary conditions could be made significantly simpler than those for BC1. A. Constrained Equations of Motion We now give an example to illustrate the earlier approach and compare the result to traditional methods. In this section, we study the optimal control of the vertical sliding coin (i.e., it cannot fall sideways and the rolling motion is ignored). The system is shown in Fig. 1. Other than the downward gravitational field, which does not contribute to the zero-slope planar motion of the vertical coin, we assume that there are no other sources of a potential field. The mass of the coin is M and its mass moment of inertia about the vertical axis is J . The position of the point of contact between the coin and the plane is denoted by (q1 , q2) while its heading direction is denoted by q3 , as shown in the figure. The configuration q is then given by q = (q1 , q2 , q3) and the configuration space is simply (2)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000491_978-3-540-79029-7-Figure5.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000491_978-3-540-79029-7-Figure5.4-1.png", + "caption": "Fig. 5.4 Definition of the switching hysteresis in two-point current controllers in field synchronous coordinates", + "texts": [ + " Upon the actual current vector leaving the tolerance hexagon the comparators will become active. 146 Dynamic current feedback control in drive systems The figure 5.3 shows the realization of the control with two-point behaviour in field synchronous coordinates (cf. [Pfaff 1983], [Nabae 1985], [Rodriguez 1987] and [Kazmierkowski 1988]). The current error is calculated in field synchronous coordinates. The field angle provides the necessary address to find, depending on the control errors, the fitting predefined pulse patterns. The figure 5.4 explains this. Survey about existing current control methods 147 The actual error vector si and the position of the coordinate system are shown in figure 5.4a. Following the definition in figure 5.4b the controller behaviour can be summarized as follows: , , , , , , , , if , then 1 and if , then 0 d q d q xd xq d q d q d q xd xq d q u U u U > = = = = The values 1 and 0 are the logical values which are assigned to the voltages ,d qU\u00b1 . Index \u201cx\u201d can assume one of the values 0...7 and represents the standard voltage vector to be selected. The projection of s s s= *i i i to the axes dq like in the figure 5.4a yields: , thus 1 , thus 1 d d xd q q xq u u > = > = Accordingly, a pulse pattern or a voltage vector has to be chosen whose d and q components minimize these control errors. In the example of figure 5.4 the choice u2 follows immediately. The assignment logical values and position of field synchronous coordinate system \u2192 firing pulse was determined off-line beforehand and then stored in table form in EPROM. [Rodriguez 1987] shows concrete examples. To control the stator currents, also controllers with three-point behaviour may be used. In [Kazmierkowski 1988] details about this approach can be found which is illustrated in the figure 5.5. In this method the control errors \u03b5\u03b1 and \u03b5\u03b2 of the stator current are obtained by projection of the error vector to the \u03b1\u03b2 axes of the stator-fixed coordinate system", + " 148 Dynamic current feedback control in drive systems [Kazmierkowski 1988] further introduced a structure with three-point controllers in the field synchronous coordinate system as shown in the figure 5.6. In principle this variant works exactly like the one in figure 5.3. The only difference between both versions consists in aiming at a higher precision by a finer division of the overall vector space (figure 5.7) into 24 sectors, combined with three-point behaviour. The EPROM table containing the pulse patterns accordingly gets more extensive. In contrast, Rodriguez keeps the six original sectors (figure 5.4). Survey about existing current control methods 149 The most intelligent version in the family of the nonlinear current controllers is the predictive control (more in [Holtz 1983, 1985]). This control reacts (figure 5.8) on the actual current vector leaving the tolerance-circle by a predictive calculation of the following, optimized voltage vector. Therefore, it also shows two-point behaviour. The method can be used in field synchronous as well as in stator-fixed coordinates. The principle block structure is shown in the figure 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure11.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure11.10-1.png", + "caption": "Figure 11.10.1 Semi-transverse arm in planview, axis sweep anglecAx from theY axis, axis yawangle uAx from theX axis.", + "texts": [ + " Single-Arm Suspensions 213 Analogous to the semi-trailing arm, the semi-transverse arm has a pivot axis in the horizontal plane, but angled in planview, the pivot axis being fairly closely but not exactly parallel to theX axis. For consistency with semi-trailing arms, the angle of the axis can be measured alternatively from the negative Y-axis direction (left wheel), giving the sweep angle cAx. However, as in Figures 11.0.1 and 11.10.1, the actual deviation from a simple transverse arm is the complementary angle, the axis yaw angle, which will be denoted by uAx: uAx \u00bc p 2 cAx This angling of the axis has several effects. In Figure 11.10.1, dropping a perpendicular from the wheel centre to the pivot axis, it may be seen that thewheel centre Amoves in an arc about point C, the foot of the perpendicular. The radius of the arc of point A is the arm length LA. As the wheel bumps or droops, the wheel centre A moves, in plan view, towards C, by a distance p given by p \u00bc LA\u00f01 cos uA\u00de \u00bc LA 1 2 zS RA 2 1 2RA z2S The movement of the wheel centre in the longitudinal X direction is XA \u00bc p sin uAx uAx 2RA z2S There is therefore a bump steer angle, approximately d \u00bc XA LAB \u00bc XA RA \u00bc uAx 2R2 A z2S consequently giving a second bump steer coefficient \u00abBS2 \u00bc uAx 2R2 A The pitch and roll force characteristics are solved in the usual way, projecting the axis into the relevant planes to obtain the swing centre ES and pitch centre EP points" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure4.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure4.2-1.png", + "caption": "Fig. 4.2 Example of a image shaft; a) Original model of the gear mechanism, b) Image shaft", + "texts": [ + "3 Spring Characteristics 29 Thus, the following applies: cT = GI\u2217 lred . (1.39) It follows from (1.38) lred = l1 I\u2217 Ip1 + l2 I\u2217 Ip2 = lred1 + lred2. (1.40) The reduced length of a shaft consisting of multiple sections is derived from the total of the reduced lengths of all sections. It replaces the overall spring constant and has the advantage that it allows better identification of the effect of each section on the overall system. The resulting shaft can be drawn using these reduced lengths, see Fig. 4.2. Table 1.5 shows a compilation of various reduced lengths. Machines consist of many sub-assemblies mounted together, which undergo microscopically small relative motions when subjected to a load. All (seemingly immobile) contact points have a lower stiffness than the solid material, and furthermore larger damping occurs there due to microscopic slippage. These lower stiffnesses reduce the natural frequencies, and these influences should be taken into account when generating a calculation model. In past decades, stiffness and damping values were determined experimentally for many sub-assemblies", + " The moments of inertia are then proportional to the radius and the compliance of the torsional springs (that is, the inverse of the torsional stiffness) is proportional to the lengths lred of the sections between the disks, see Sect. 1.3 and Table 1.5. The reduction is performed such that the kinetic and potential energy of the original system and the image shaft match. The representation of an oscillator chain as an image shaft is popularly used to illustrate the stiffness and mass distributions. This illustrative method (formerly used quite often) has lost significance, so it will not be described in detail here. One example, however, shall suffice. Figure 4.2a shows the calculation model of a two-step gear mechanism and Fig. 4.2b the associated image shaft. Given are the 228 4 Torsional Oscillators and Longitudinal Oscillators parameter values i12 = r1 r2 = 1 2 ; i34 = r3 r4 = 1 3 ; i13 = ( r1 r2 )( r3 r4 ) = 1 6 (4.15) J1 = 2J ; J21 = J ; J22 = 3J ; J23 = 2J ; J24 = 3J ; J3 = 12J (4.16) c\u2032T1 = 3cT; c\u2032\u2032T1 = cT; cT2 = cT. (4.17) One can show that these two systems are dynamically equivalent by performing the following transformations (using linear conversion of the angles and conversion of the torsional spring constants and moments of inertia with the squared gear ratios): \u03d51r = \u03d51; \u03d52r = \u03d52; \u03d53r = \u03d53/i13 (4", + "3 The equations of motion of this vibration system are known from (4.8) to (4.10). Using the equations given in Table 4.2 (Case d), the parameter values of the problem are converted into those of the image shaft (Table 4.2, Case a): J1=\u0302J4 = 0.8 kg \u00b7m2; J2=\u0302J5 + J6 ( r5 r6 )2 = 1.4309 kg \u00b7m2; J3=\u0302J7 ( r5 r6 )2 = 0.3286 kg \u00b7m2. (4.100) The torsional spring constants of the shafts result from cTj = GIpj lj = G\u03c0d4 j 32lj ; j = 4, 6 (4.101) and are converted for the coordinates of the image shaft of the system according to Fig. 4.2, Case a: 258 4 Torsional Oscillators and Longitudinal Oscillators cT1=\u0302cT4 = 29 833 N \u00b7m; cT2=\u0302cT6 ( r5 r6 )2 = 22 831 N \u00b7m. (4.102) The natural frequencies fi = \u03c9i/(2\u03c0) of the unconstrained gear mechanism are derived with the data given in (4.100) and (4.102) from (4.12) or from (1) in Table 4.4: f1 = 0 Hz; f2 = 35.2 Hz; f3 = 48.9 Hz. (4.103) The natural frequencies of the blocked (constrained) system are derived from the same equations by setting J1 = J4 \u2192\u221e: f1 = 20.2 Hz; f2 = 47.8 Hz. (4.104) All natural frequencies increase due to the braking, and f3 \u2192\u221e applies for the third natural frequency" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002270_1464419314546539-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002270_1464419314546539-Figure2-1.png", + "caption": "Figure 2. The roller\u2013raceway interaction.", + "texts": [ + " The radius reduction cb of each slice is expressed as48,50 cb\u00bc 0 Lp 2 4xk4 Lp 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 c L2 p 4 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 c x 2 k q Le 2 4xk4 Lp 2 , Lp 2 4xk4Le 2 8< : \u00f01\u00de where xk is the axial coordinate value of the slice element k relative to the roller centre, which is described as xk \u00bc 0:5\u00fe k 0:5 n Le \u00f02\u00de where n is the slice number, and Le\u00bcLb 2Rrc. Contact geometry between roller and raceway The geometrical interactions between the roller and a raceway in the inertial frame of reference (Xi,Yi,Zi) is described in Figure 2. The position vectors rib\u00bc [0 rjsin yj rjcos yj] T and rir\u00bc [0 yr zr] T denote the positions of the roller centre B and the raceway centre R; at University of Sydney on September 6, 2014pik.sagepub.comDownloaded from rj is the distance from roller j to the bearing centre; j is the azimuthal angle of roller j; and xr and yr are the coordinates of the raceway centre in the inertial frame, respectively. For describing the interactions between the roller and raceways preferably, the roller-fixed coordinate frame (Xb,Yb,Zb) and the race-fixed coordinate frame (Xr,Yr,Zr) should also be established", + " The transformation matrix from the race-fixed frame to the race azimuth frame is Trra\u00bc [T(\u2019k, 0, 0)]. The vector from the contact point P on the circumference of the slice k to the raceway centre is written as rrapr \u00bc Trra rrbr \u00fe TirT 1 ib rbpb \u00f06\u00de where T 1ib \u00bc [T(\u2019bj, 0, 0)] 1 is the transformation matrix from the roller-fixed frame to the inertial frame, \u2019bj is the rotation angle of the roller j along its axis Xb; the vector rbpb\u00bc [xk (db/2 cb)sin (db/ 2 cb)sin ] T is from the contact point P to the roller centre in the roller-fixed frame as shown in Figure 2. The value of the second component of vector rrapr should be zero to confirm in the vector rbpb. There will be two values of \u00bc arctan T23 T22 \u00fe arcsin rrabr2 \u00fe T21xkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T2 22 \u00fe T2 23 q 0 B@ 1 CA \u00f07\u00de or \u00bc \u00fe arctan T23 T22 \u00fe arcsin rrabr2 \u00fe T21xkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T2 22 \u00fe T2 23 q 0 B@ 1 CA \u00f08\u00de where T\u00bcTrraTirT 1 ib , the subscripts 21, 22 and 23 are three parameters in the second row of matrix T. rrabr2 is the second component of vector rrabr\u00bcTrrar r br in the race-fixed azimuth frame and is the value that makes rrapr3 smaller for inner raceway and larger for outer raceway" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000029_elan.200302849-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000029_elan.200302849-Figure3-1.png", + "caption": "Fig. 3. Cyclic voltammograms of catalase at a SWNT-modified gold electrode in 0.05 M phosphate buffer solutions at pH values of a) 3.1, b) 4.8, c) 5.9 and d) 7.9. The arrow indicates the scan direction. The inset shows the relationship between the reduction peak current Epc and the solution pH value.", + "texts": [ + " Having a high aspect ratio (length over diameter), carbon nanotubes have been suggested to be more suitable substrates than amorphous glassy carbon for the immobilization of biomolecules [16, 38 \u00b1 40]. All these factors improve the reversibility and the signal-to-noise ratios associated with the faradaic process of Ct and explain why the overall redox behavior of curve b (Fig. 1) is superior to those observed at other electrodes [29, 31, 32]. We also found that the peak potential of Ct is dependent on the solution pH. Figure 3 depicts a series of CVs of Ct collected from 0.05 M phosphate buffer solutions of different pH values. As can be seen, within the pH range of 3.1 \u00b1 8.9, the peak potential shifts to the cathodic direction with a slope of 36 mV per decade of [H ] (assuming the proton activity to be approximately the same as the concentration). Therefore, it appears that there is one proton involved per transfer of two electrons. This is consistent with the voltammetric studies of other heme-containing enzymes[41 \u00b1 43]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003816_j.ymssp.2020.106903-Figure27-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003816_j.ymssp.2020.106903-Figure27-1.png", + "caption": "Fig. 27. Diagram of the unbalanced mass.", + "texts": [ + " This is because that the amplitudes are related to the relative position of the resultant force and defect, the resultant force is determined by gravity and unbalanced force. So the closer the phase of the defect and unbalanced force is, the greater the resultant force which applies at the defect is, and the higher the amplitudes are. Besides, after the introduction of unbalanced force, the superharmonic (2fi, 50 Hz) of rotation frequency becomes the most prominent and the amplitude of rotation frequency decreases in envelope spectrum. All the parameters used in experiments are the same as those in simulations. The diagram of unbalanced mass is shown in Fig. 27. The vibration responses and envelope spectra of bearing with/without unbalanced force are shown in Fig. 28, Fig. 29 and Fig. 30. According to the result, it can be found that the experimental results are consistent with simulation results. The introduction of unbalanced force will make the superharmonic (2fi, 50 Hz) of rotation frequency prominent in the envelope spectrum. The amplitude of acceleration responses is related to the relative position between unbalanced force and defect. When the phase difference between inner raceway defect and unbalanced force is 0 , the amplitudes are lower; and when the phase is 180 , the vibration is more intense" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000969_1.4005234-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000969_1.4005234-Figure5-1.png", + "caption": "Fig. 5 Example of (a) a standard ease-off representation and (b) the corresponding contour plot of it (drawn on the gearbased PCA)", + "texts": [ + " On this plane (gear projection plane), the face, front and back cones delimiting the pinion and gear teeth define the boundaries of the potential contact area (PCA), in which a tooth pair can potentially have contact. The PCA depends on the relative position between the pinion and the gear in mesh, hence, it is influenced by the assembly errors. As a consequence, its general shape is (with approximation) an irregular convex quadrilateral. A typical grid-based representation of an example ease-off topography is given in Fig. 5(a), while a contour plot of it is shown in Fig. 5(b). Hereafter, the latter type of representation will be adopted. For graphical convenience, the PCA quadrilateral is mapped here to a rectangular domain, where u and v mark the lengthwise and profile directions, respectively. To accomplish the initial task of defining appropriate design variables to manipulate the ease-off surface, one could start by selecting a suitable mathematical basis for representing such surface. For instance, if polynomial basis functions are chosen, their polynomial coefficients can be used to control the shape of the ease-off surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure11.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure11.12-1.png", + "caption": "Figure 11.12.1 Pivot axis throughA andwheel axis throughW, each axis defined by a point and direction cosines. P is a methodological second point on the wheel axis.", + "texts": [ + " At the horizontal arm position, these angles are different, introducing additional effects, and compensating for the above term. The bump scrub coefficients continue as in Table 11.10.1 with appropriate evaluation of the swing centre height HS. The computer numerical solution of the rigid arm is quite easily performed, given certain standard threedimensional coordinate geometry routines discussed in a subsequent chapter. The basic problem is specified by the static position in vehicle coordinates, Figure 11.12.1, by (1) the coordinates of a point A on the pivot axis (xA, yA, zA), (2) the direction cosines of the pivot axis (lA, mA, nA), (3) the coordinates of a point W on the wheel axis (xW, yW, zW), (4) the direction cosines of the wheel axis (lW, mW, nW). Other information required includes the track, and thewheel centre position, if this is not already known to be point W. Two distinct analyses are required, static (the initial position) and displacement (arm rotated, leading to bump coefficients)", + " Then the initial position of point P is xP \u00bc xW \u00fe LlW yP \u00bc yW \u00fe LmW zP \u00bc zW \u00fe LnW At the scale of vehicle suspensions, it is convenient to use a separation of 1 metre. The direction cosines of the new axis then follow easily, and thence the wheel steer and camber angles for that bump position. The residual problem, then, is the rotation of one point about a line by a specified angle. This is easy in two dimensions, so one approach is to specify a local coordinate system with the circular motion of the point in a local coordinate plane with perpendicular unit vectors (v\u0302; w\u0302) in the plane perpendicular to the axis u\u0302, Figure 11.12.2. The axis unit vector is already known. Drop a perpendicular from the point P onto the axis, with foot F. The length PF is the arc radius R for that point. One in-plane unit vector can be determined as being along FPand of unit length. The third unit vector, also in the plane of rotation, can then be determined by a vector cross product of the two known unit vectors, w\u0302 \u00bc \u00f0lw;mw; nw\u00de \u00bc u\u0302 v\u0302 \u00bc i\u0302 j\u0302 k\u0302 lu mu nu lv mv nv where the determinant is to be expanded with the usual sign alternations. For a right-hand rotation by angle u about the axis direction, the coordinates of the new position of P are then given by xP \u00bc xF \u00fe lv cos u\u00fe lw sin u yP \u00bc yF \u00fe mv cos u\u00fe mw sin u zP \u00bc zF \u00fe nv cos u\u00fe nw sin u with P rotating in the \u00f0v\u0302; w\u0302\u00de plane as desired" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002261_1.4007348-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002261_1.4007348-Figure10-1.png", + "caption": "Fig. 10 Cage model verification with ABAQUS: (a) cage loading, (b) EFEM, and (c) ABAQUS results", + "texts": [ + " SISO procedure was repeated for four sensor locations, and the results are shown in Table 1. In the above explicit FE model, the damping is assumed mass proportional. The mass proportional damping coefficient a is given by a \u00bc 2xnf (28) Excitation frequency observed in the bearings is below the first natural frequency. Thus, the mass proportional coefficient was evaluated for the first natural frequency. EFEM Verification. The finite element model of the cage was verified with the results from Explicit ABAQUS. Figure 10 shows a loading scenario where a cage is compressed against a rigid wall. The same mesh, loads, and material properties were used as input for explicit ABAQUS and the EFEM. Figures 10(b) and 10(c) depict the qualitative similarities in the von Mises stress patterns from both simulations, and Table 2 quantifies these results in terms of the maximum values for six load magnitudes. The relative error is less than 5%, demonstrating the adequacy of the EFEM of the cage. Flexible Cage Validation and Discussion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000339_s0022112005004829-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000339_s0022112005004829-Figure2-1.png", + "caption": "Figure 2. The meridional trajectories of a line element (slender fibre) in simple shear flow. The flow\u2013vorticity plane comprises a degenerate set of stationary fibre orientations.", + "texts": [ + " It was shown earlier in this section, using general continuum mechanics arguments, that this similarity arises because terms representing the first effects of inertia and elasticity in simple shear flow are both quadratic functions of E and \u2126 , and reduce to the same tensorial form in the slender-body limit. The resulting alteration of the fibre motion due to fluid inertia for small Re is thus qualitatively similar to that induced by weak elasticity but opposite in sense. For Re = 0, the system (3.20) can be integrated to obtain cot\u03c6 = t, tan \u03b8 = C/ sin\u03c6, (3.21) showing that the slender-fibre trajectories, at leading order, are identical to those of a fluid line element in simple shear flow when projected onto the unit sphere. As shown in figure 2, they coincide with the meridians of the unit sphere with the flow direction as its polar axis. Here, C is the orbit constant; C = \u221e represents motion in the flow\u2013 gradient plane, while C =0 corresponds to the degenerate set of fibre orientations in the flow\u2013vorticity plane. Note that neglect of the finite thickness of the fibre, and thence the O(\u03ba\u22122) torque responsible for fibre rotation through the flow-aligned state (see discussion below), leads to trajectories that are no longer closed orbits; in fact, for almost all initial orientations, the slender fibre eventually aligns itself with the flow axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002651_17452759.2018.1442229-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002651_17452759.2018.1442229-Figure4-1.png", + "caption": "Figure 4. Integrated methodology for L-PBF part design.", + "texts": [ + " On the contrary, it is important that datum features are added to the part design in order to provide a reference in the machining setup. Moreover, other additional features, integrated in the design or sacrificial features, may be required to increase the stiffness of the part, in order to avoid deflection or vibration during machining, or to hold the part in the machine. The consideration of finishing requirements in the design process may considerably influence the shape of the final part produced by AM. Integrated design methodology for L-PBF A design approach is here proposed (Figure 4), in which topology optimisation techniques, redesigning for L-PBF, FEM analysis and finishing requirement considerations have been integrated in order to obtain a functional design that meets all the part requirements while exploiting the benefits of AM to a maximum. The full potential of design freedom can be obtained by making effective use of topology optimisation (TO), which is a mathematical approach that can be used to optimise the material layout within a provided design space. The aim is to reach performance targets, and in order to accomplish this, an appropriate set of loads and constraints needs to be provided (Liu and Ma 2016)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.34-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.34-1.png", + "caption": "Fig. 6.34 Calculation model of a belt drive with an elastic tensioning device", + "texts": [ + " If the designer were guided by static considerations, he or she could think of limiting the mandril motion by a strong damping. This could worsen the situation since such stiffening would result in a change of the natural frequencies. Pretensioned belt drives are used to transmit moments. The elasticity of the pretensioning device, together with stiffness differences of the driving and slack strands, causes coupled translational and rotational vibrations. Under the condition of small vibrations, it should be checked for a pretensioned V-belt drive according to Fig. 6.34 with an elastic tensioning device to what extent the dynamic strand forces influence the pretensioning required for moment transfer as a result of rotational and translational vibrations caused by the residual unbalance U = me of the motor armature. The equations of motion and the equations for calculating the two strand forces and the motor torque shall be specified for the case of a constant speed. The belt mass is negligibly small. It is assumed that the change of angle \u03b1, as a result of translational vibrations, as well as slippage are negligible", + " Weak damping can be presupposed so that modal damping is sufficient for calculating the vibration amplitudes. Differences in stiffness between the driving and slack strands result from the nonlinear material behavior. The deformations of the driving and slack strands depend on three coordinates. The following applies: \u0394lZ = r\u03d5M \u2212R\u03d5\u2212 x cos \u03b1; \u0394lL = R\u03d5\u2212 r\u03d5M \u2212 x cos \u03b1. (6.365) The kinetic and potential energy, as well as the virtual work, are formulated as follows using the coordinates defined in Fig. 6.34 (x = 0 and r\u03d5M = R\u03d5 characterizes the pretensioned but vibration-free state): 458 6 Linear Oscillators with Multiple Degrees of Freedom 2Wkin =J\u03d5\u03072+JS M\u03d5\u03072 M + m [ (x\u0307 + e\u03d5\u0307 cos \u03d5M)2 + e2\u03d5\u03072 M sin2 \u03d5M ] =m \u00b7 (x\u03072 + 2ex\u0307\u03d5\u0307M cos \u03d5M) + J\u03d5\u03072 + (JS M + me2)\u03d5\u03072 M (6.366) 2Wpot =cVx2+cZ \u00b7 (r\u03d5M\u2212x cos \u03b1\u2212R\u03d5) 2 +cL \u00b7 (R\u03d5\u2212r\u03d5M\u2212x cos \u03b1) 2 (6.367) \u03b4W = + MM \u00b7 \u03b4\u03d5M\u2212bVx\u0307 \u00b7 \u03b4x \u2212 b \u00b7 (r\u03d5\u0307M\u2212R\u03d5\u0307\u2212x\u0307 cos \u03b1) \u00b7 (r \u00b7 \u03b4\u03d5M\u2212R \u00b7 \u03b4\u03d5\u2212cos \u03b1 \u00b7 \u03b4x) \u2212 b \u00b7 (R\u03d5\u0307\u2212r\u03d5\u0307M\u2212x\u0307 cos \u03b1) \u00b7 (R \u00b7 \u03b4\u03d5\u2212r \u00b7 \u03b4\u03d5M\u2212cos \u03b1 \u00b7 \u03b4x) (6.368) If \u03d5M(t) = \u03a9t, that is \u03d5\u0307M \u2261 \u03a9 = const" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001888_tie.2015.2442519-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001888_tie.2015.2442519-Figure7-1.png", + "caption": "Fig. 7. Flux distributions of 12-slot/8-pole and 12-slot/10-pole SPM machines. (a) 8-pole, (b) 10-pole.", + "texts": [ + " In addition, the torque for 12-slot/8-pole dual three-phase PM machine supplied with optimal 3rd harmonic current is improved by 15% compared with the machine with sinusoidal current, whilst for 12-slot/10-pole dual three-phase PM machines, the additional 3rd harmonic back-EMF can interact with the optimal 3rd harmonic current resulting in more torque improvement, ~18%. This is due to the fact that the 3rd harmonic back-EMF for 12- slot/8-pole machine is zero whilst for 12-slot/10-pole machine the 3rd harmonic is 15% of fundamental one. The 12-slot/8-pole and 12-slot/10-pole PM machines with pole arc to pitch ratio equal to 1 and non-overlapping windings are employed for further analysis in this section, whose outer diameter and active axial length are 90mm and 50mm, respectively. Fig. 7 shows the FE predicted open-circuit field distributions for the 10-slot/8-pole and 12-slot/10-pole SPM machines. Fig. 8 (a) and (b) shows the airgap flux density distributions and harmonic contents. As shown in Fig. 8 (b), 0278-0046 (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. the 3rd harmonic airgap flux density exists for both 12- slot/8-pole and 12-slot/10-pole machines, which shows that the 3rd harmonic airgap flux density are more than 20% of the fundamental one, which is important for the torque improvement utilizing 3rd harmonic current" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.6-1.png", + "caption": "FIGURE 1.6. Illustration of a spherical wrist kinematics.", + "texts": [ + " 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 1.5 schematically illustrat es a 3R manipulator. 1.2.4 Wrist The joints in the kinematic chain of a robot between the forebeam and end effector 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 1.6 shows a schematic illustration of a spherical wrist, which is a Rf--Rf--R mechanism. The spherical wrist greatly simplifies the kinematic analysis effectively, allowing us to decouple the positioning and orienting of the end effector. Therefore, the manipulator will possess three degrees-of-freedom for posi tion, which are produced by three joints in the arm. The numb er of DOF for orientation will then depend on the wrist . We may design a wrist having one, two, or three DOF depending on the application" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure21-1.png", + "caption": "Fig. 21. Measurement of flux density at end shaft. (a) Test setup. (b) No end magnetization.", + "texts": [ + " The platform for testing the static torque is shown in Fig. 20 (a), and it is measured based on the reported method [30]. Fig. 20 (b) shows the dynamic test platform. A DC-motor-based dynamometer is adopted as a variable load. Moreover, an encoder is employed to detect the rotor position of the prototype, whilst a torque transducer is built in the experimental platform to measure the dynamic output torque. Moreover, a tesla meter with hall sensor is adopted to test the leakage flux density at the end shaft, as shown in Fig. 21 (a). Fig. 22 shows the FE predicted and experimental cogging torques with rotor position. It can be seen that the period of the measured result agrees with the FE predicted one. However, there are large difference between FE predicted and measured value. This is due to the fact that the cogging torque in the ideal FE model is small (62 mNm), which is more sensitive to the fabrication tolerances. Although the measured cogging torque of the HPM1 machine is larger than the predicted one, it is still smaller than the predicted one of CPM1-2 machine, as shown in Fig", + " According to both static and dynamic tests, all the results agree with the FE predicted ones. In addition, Fig. 27 shows the FE predicted and measured flux density at 30 mm of the end shaft. It can be seen that the leakage flux of end shaft is bipolar, and hence the proposed machine has no magnetization risks of the mechanical 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. components in the end region. As shown in Fig. 21 (b), the screws and nut cannot be attracted by the bearing. VI. CONCLUSIONS Two novel CPM machines with N-iron-N-iron-N-S-iron-Siron-S and iron-S-iron-S-iron-iron-N-iron-N-iron sequences are presented to eliminate the unipolar leakage flux in the conventional CPM machine. The HPM machines are proposed to suppress the subharmonics of the airgap flux density, and therefore enhance the output torque and reduce the torque ripple. Furthermore, the proposed CPM and HPM machines are compared to the conventional SPM and CPM machines on electromagnetic performance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003538_978-3-319-26106-5_8-Figure8.18-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003538_978-3-319-26106-5_8-Figure8.18-1.png", + "caption": "Fig. 8.18 Schematic illustration of the hybridisation of (a) continuous parallel Fe-based microwire array plus continuous Co-based microwire array and (b) orthogonal Fe-based microwire array plus shortcut Co-based microwire array [102]", + "texts": [ + " It would be also of much scientific interest to investigate the interplay between Co- and Fe-based wires taking into account their different wire alignment, intrinsic microwave properties and geometrical dimensions. Additional magnetic resonances therein would be obtained by means of wire-wire dynamic interactions, which is beneficial to expand DNG operating frequencies and enhance microwave absorptions. Technically, Co-based (Fe4Co68.7Ni1B13Si11Mo2.3) microwires with a total diameter of 15 \u03bcm and a glass coat thickness of 7 \u03bcm are added into the Fe-based wires containing prepregs in two topological arrangements, i.e. parallel Co-based and parallel Fe-based wire array (Fig. 8.18a) and shortcut Co-based and continuous orthogonal Fe-based wire array (Fig. 8.18b) [102]. To avoid excessive reflection loss from direct physical contact, Fe-based and Co-based wires should be integrated in separate prepreg layers. Also as a precaution to prevent microwave noise, the Co-based wire array should be intentionally mismatched to Fe-based wires by approximately 1 mm offset. A routine curing protocol is followed afterwards to fabricate composite samples having an in-plane size of 500 500 mm [2] and thickness of 1 mm. The panel (a) to (i) in Fig. 8.19 describe the transmission, reflection and absorption coefficients of the parallel 10 mm Fe-based, 3 mm Co-based containing composites and their hybrid composite, in the frequency band of 1\u20136 GHz" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure4.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure4.6-1.png", + "caption": "Figure 4.6.1 Body roll, suspension roll and axle roll on a flat, level road, rear view.", + "texts": [ + " This is unambiguous provided that the ground is flat and that front and rear wheel centres have parallel transverse lines (e.g. that wheels and tyres are the same size side-to-side). If the ground is not flat then some mean ground plane must be adopted. The roll angle and roll velocity are in practice fairly clear concepts. Asymmetries, such as the driver, mean that the roll angle is not automatically zero under reference conditions, although it is usual practice to work in terms of the roll relative to the static position. Body roll is accommodated by suspension roll, plus some axle roll from tyre deflection, Figure 4.6.1. fB \u00bc fS \u00fefA For a passenger car, the axle roll is generally fairly small compared with the suspension roll, but this is certainly not true for many racing cars with stiff suspensions, where inclusion of the axle roll angles is essential. For a torsionally-rigid vehicle body, in relation to the torsionalmoments applied, the body torsion angle fBT is negligible. This is applicable to most passenger cars, in which case fBT \u00bc 0 fBf \u00bc fBr fBf \u00bc fSf \u00fe fAf fBr \u00bc fSr \u00fe fAr 90 Suspension Geometry and Computation In the case of most trucks, and some racing cars, the body torsion angle fBT needs to be considered, in which case fBf \u00bc fSf \u00fe fAf fBr \u00bc fSr \u00fe fAr fBT \u00bc fBf fBr The roll gradient is the rate of change of roll angle f with lateral acceleration A: kf \u00bc df dA The body roll gradient is the sum of suspension and axle roll gradients: kBf \u00bc kSf \u00fe kAf Roll is geometrically equivalent to bump of one wheel and droop of the opposite one, relative to the body", + " This is spring jacking. If a droop stop is engaged first, the body may be lowered. There are other jacking effects through the links in cornering and through damper action. Roll speed generally results in a scrub speed of the tyres relative to the ground, causing temporary changes to slip angles and hence to tyre cornering forces. If the road is not flat and level then additional analysis is required. The first case is a flat but non-level road, as for example on a banked high-speed road. At a road bank angle fR, Figure 4.6.2, the body roll relative to the datum plane is fB \u00bc fR \u00fe fA \u00fe fS If the road is not flat, then the road bank angles are different at the two axles. Including the possibility of body torsion, then, fBf \u00bc fRf \u00fe fAf \u00fe fSf fBr \u00bc fRr \u00fe fAr \u00fe fSr The road torsion and body torsion angles are fRT \u00bc fRf fRr fBT \u00bc fBf fBr Ride height is the position of the body (sprung mass) above the basic ground level datum plane. The dynamic ride height is the ride height relative to the static position. In general, during acceleration, braking or cornering and on rough roads, the ride heights vary continuously and have different values at each wheel" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.14-1.png", + "caption": "Fig. 2.14 Gimbal-mounted rotor with input torques about three axes", + "texts": [ + " This is relevant for understanding the range of applicability of such programs, for their proper use, and for evaluating the results of calculations. For most practical problems, the driving forces are given by the motor characteristic, so that it becomes necessary to integrate the equations of motion, see Sect. 2.4.3. A mechanism consists of I links, of which the frame is given the index 1 and the movable bodies are given the indices i = 2, 3, . . . , I , and index I is usually assigned to an output link. Figure 2.12 shows some examples of rigid-body mechanisms with multiple drives. The gyroscope in Fig. 2.14 can also be interpreted in such a way that the position of the rigid body is determined by the three \u201cinput coordinates\u201d q1, q2, and q3. The center-of-gravity coordinates rSi of the ith link of a mechanism show an (often nonlinear) dependence on the so-called kinematic dimensions and the positions of the n input links: rSi(q) = [xSi(q), ySi(q), zSi(q)]T. (2.141) Their velocities can also be calculated according to the chain rule: d(rSi) dt = vSi = n\u2211 k=1 \u2202rSi \u2202qk q\u0307k = n\u2211 k=1 rSi, k q\u0307k; i = 2, 3, ", + "172) by solving the system of linear equations. The time functions of all angles for given moment functions can then be calculated from q1 and q2 and all other angles from (2.163) and (2.164). The same equations can be used for the operating state \u201cinput at the sun gear 2 and the arm 5, output at the ring gear 3\u201d. The expressions for the kinetic energy and the relationships between the moments (Q1 = Mx, Q2 = My\u2217, Q3 = M\u03b6) and the three cardan angles q1, q2, and q3 are to be established for the gyroscope that is supported as shown in Fig. 2.14. The center of gravity is assumed to be at the origin of the body-fixed coordinate system (S = O). Given are all elements of the moment of inertia tensor J S with respect to the center of gravity S and the moments of inertia JA and JB of the two frames with respect to their bearing axes. The kinetic energy of the rotation in (2.57) is used as a starting point and must still be complemented by the kinetic energy of the two frames Wkin frame = 1 2 (JAq\u03072 1 + JBq\u03072 2). (2.175) If one inserts the components of the angular velocity known from (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003236_j.jmapro.2018.06.033-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003236_j.jmapro.2018.06.033-Figure1-1.png", + "caption": "Fig. 1. Schematic visualization of the laser metal deposition (LMD) process. The fixed process parameters where illustrated; these include the flow rate of shielding gas QAr , the shielding gas nozzle angle \u03b3 , the wire feeding nozzle angle \u03b2, the focal spot to wire-feeding nozzle tip distance dN , and the direction of deposition.", + "texts": [ + " A pressure of 8 bar and a particle size between 90 and 150 \u03bcm of the blasting material was used to achieve a surface roughness of Ra =0.20 \u03bcm of the substrate material. An 8-kW continuous wave ytterbium fibre laser YLS-8000-S2-Y12 (IPG Photonics Corporation) integrated with the optical head YW52 Precitec, in a CNC-supported XYZ-machining centre (IXION Corporation), was employed in this study. The optical head was integrated along the Z-axis of the system, which was also equipped with a wire-feeding system along with a local shielding gas supply, as schematically illustrated in Fig. 1. The wire was fed through a nozzle at a fixed angle of \u03b2=35\u00b0, relative to the surface of the substrate. The nozzle for a local shielding gas supply was installed above the wire nozzle with an angle of \u03b3=55\u00b0, a vertical distance of 25mm, and horizontal spacing of 5mm relative to the tip of the wire-feeding nozzle. The shielding gas flow rate was adjusted to 10 l/min, thus providing enough gas to protect the molten material from oxidation with atmospheric gases but not influencing the solidification process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.19-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.19-1.png", + "caption": "FIGURE 2.19. Body and global coordinate frames of Example 28.", + "texts": [ + "129), and noting that IGRBI 'IGR~I IGRBI \u00b7IGRBI IG RB I 2 = 1. (2.135) 66 2. Rot ation Kinematics Using linear algebra and row vectors rHI ' rH 2 , and rH 3 of GRB, we know that (2.136) and because the coordinate syste m is right handed, we have rH2 < i n, = rHI so IGRBI = rk l . rHI = 1. \u2022 Example 28 Elements of transformation matrix. The position vector r of a point P may be expressed in terms of its components with respect to either G(OXYZ) or B(Oxyz) fram es. Body and a global coordinate fram es are shown in Figure 2.19. If G r = 100f 50} + 150K, and we are looking for components of r in the Oxyz fram e, then we have to find the proper rotation matrix B RG first . The row elements of B flG are the direction cosines of the Oxyz axes in the 0 XYZ coordinate frame . The x -axis lies in the X Z plane at 40 deg from the X -axis, and the angle between y and Y is 60deg. Therefore, [ cos ~O )\u00b7I k \u00b7j [ 0.76,6 ) \u00b7 I k \u00b7j (2.137) 2. Rotation Kinematics 67 and by using BRG GRB = BR G BR'[; = I [ 0.766 0 0.643] [0.766 r21 r31] r21 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002410_978-4-431-54400-5-Figure4.17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002410_978-4-431-54400-5-Figure4.17-1.png", + "caption": "Fig. 4.17 Self-heating smart polymer-grafted particles for thermoresponsive chromatography by applying AMF [232]. a Schematic illustration of self-heating system to induce phase transition of thermoreponsive polymer grafted on magnetite nanoparticles, b chemical structure of P(NIPAAmHMAAm)-grafted magnetite nanoparticles, c modulation of steroid elution on self-heating smart column by \u2018on\u2013off\u2019 switching of AMF (chromatogram peaks: 1 hydrocortisone; 2 testosterone)", + "texts": [ + " Such thermally modulated affinity binding/release of target molecules can also be achieved by the incorporation of ligands with affinity into PNIPAAm chains grafted on silica beads, for example, using lactose/galactose-specific lectin [228] and phenylboronic acid (PBA) [229] as ligands for glycoprotein and cis-diol compounds as target molecules, respectively. As described above, thermoresponsive PNIPAAm has been mainly used for the surface modification of chromatographic matrices; thus, their performance is adversely affected by changes in temperature in the entire column or in aqueous mobile phases. We have developed a self-heating system using magnetite nanoparticles as the stationary phase for thermoresponsive chromatography (Fig. 4.17a), which generate heat through magnetic hysteresis following the application of an alternating magnetic field (AMF) [230]. CIPAAm was copolymerized with NIPAAm to modify aminopropylsilane on a magnetite\u2013silica composite via a coupling reaction, and smart polymer-grafted magnetic nanoparticles (MNPs) were packed into a chromatography column and used for the separation of steroids [231]. The retention times of all steroids using the P(NIPAAm-co-CIPAAm)grafted column increased because the surface became hydrophobic owing to AMF-mediated heat generation, whereas these changes were not observed without the application of an AMF", + " [232] also modulated the elution behavior 4.5 Applications of Smart Surfaces 168 4 Smart Surfaces of steroids via the graft architecture of polymers on magnetic surfaces by changing the contents of carboxyl groups in the polymers, which were bound at various points to the aminated surfaces. Techawanitchai et al. [233] investigated the effect of thermal dynamics under an AMF on the retention times of steroids using free-end P(NIPAAm-co-hydroxymethylacrylamide (HMAAm))-grafted magnetite/ silica nanoparticles (Fig. 4.17b). The temperature of MNPs subjected to an AMF rapidly increased to 60 \u00b0C within 15 min, and the retention times of steroids were also significantly increased after 10\u201315 min of AMF irradiation following the selfheating generation of magnetic nanoparticles. On the basis of the elution kinetics under an AMF, the elution process for steroids can be modulated to shorten the total analysis time by turning off the AMF during the elution process, as shown in Fig. 4.17c. In this system, the relationship between the LCST of the grafted polymers and the dynamics of the self-heating generation from the MNPs is important for regulating the elution behavior, and its optimization will enable the more accurate, prompt, and simpler control of biomolecular separation. 169 Since Terry et al. [234] initially proposed the assembly of silicon micromechanical devices for miniaturized gas chromatography in the 1970s, there have been many studies on exploiting the potential benefits of microsize apparatus compared with systems of a conventional size" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000068_s0898-8838(08)60043-4-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000068_s0898-8838(08)60043-4-Figure1-1.png", + "caption": "FIG 1. Cyclic voltammograms of horse heart cytochrome c (5 mgiml) in 0.1 M NaC104/0.02 MP, buffer a t pH 7.0, in the presence of 10 mM 4,4\u2018-bypyridyl in the potential range +0.20 to -0.20 V vs. SCE, at scan rates of (a) 20, (b) 50, and (c) 100 mV sec-I.", + "texts": [], + "surrounding_texts": [ + "(average of the anodic and cathodic peak potentials), El,z = +0.020 V vs. SCE, is identical with potentiometric values. The reagent, 4,4\u2019- bipyridyl, was believed to adsorb on the gold surface, and its coverage was governed by the Langmuir adsorption isotherm ( 1 1 ). Because it is not electroactive in the potential region of interest, it was proposed that the organic adsorbate allowed electron transfer to occur directly by providing the electrode surface with chemical functionalities capable of interacting specifically and reversibly with the protein surface. A more detailed kinetic investigation of the Au/Bipy/cytochrome c system was carried out using the rotating ring-disk technique (12). It was found that rate constants for adsorption and desorption of the protein were 3 x cm sec-\u2019 and 50 sec-l, respectively. The limiting first-order rate constant within the protein-electrode complex was determined as 50 sec-l, a reasonable value as compared to that of longrange electron transfer between or within proteins. Subsequently, Taniguchi and co-workers found (13) that bis(4pyridy1)disulfide (SS-Bipy) adsorbed so strongly on gold that a \u201cpredip\u201d in the SS-Bipy solution for several minutes was sufficient to give excellent electrochemistry of cytochrome c in a \u201cpromoter-free\u201d solution. However, the adsorption behavior of this promoter was interpretated by the Frumkin isotherm rather than by the Langmuir isotherm. As ELECTROCHEMISTRY OF PROTEINS AND ENZYMES 345 addition of SS-Bipy to a solution of cytochrome c did not show any significant change of absorbance at 697 nm, it was unlikely that the promoter bound to the heme iron as an extrinsic ligand. The importance of such a modified electrode lies in the application to a variety of combined optical measurements, because it does not cause any interference. Purine and its derivatives were investigated as possible promoters of cytochrome c electrochemistry at Au electrodes (14 1. It was suggested that the lone-pair electrons of the N atoms at position 1 were important for promotivity, and that the strong adsorptivity of sulfur-containing purines was due to the favorable interaction between gold and sulfur. From the surface-enhanced Raman scattering (SERS) studies (15, 16) a possible model of Bipy and SS-Bipy on a gold electrode was proposed: Bipy adsorbs onto the electrode via one pyridyl nitrogen in a vertical orientation, leaving the other nitrogen directed toward the solution, whereas SS-Bipy adsorbs with a vertical orientation of the pyridine ring as PyS through the S atom with cleavage of the disulfide bond. Furthermore, the SERS spectra of the modified electrode did not change remarkably upon addition of cytochrome c. Presumably, the interaction between the protein and modifier was not so strong as to affect the electronic structure and orientation of the absorbates and hence weak hydrogen bonding is very likely important. These results support the electrode reaction mechanism originally proposed by Hill et al. (1 71, i.e., hydrogen bonding between the lysine residues surrounding the exposed heme edge of cytochrome c and the pyridyl nitrogens a t the electrode surface stabilizes a transient protein-electrode complex oriented so as to allow rapid electron transfer to and from the heme group. The proposed protein-electrode complex can be compared to protein-protein complexes thought to be involved in biological systems. Electron transfer reactions between proteins are believed to involve formation of kinetically detectable precursor protein-protein complexes that are stabilized and oriented by electrostatic and hydrophobic interactions. The large dipole moment arising from the typically asymmetric charge distribution of a metalloprotein has been suggested (18) to be responsible for proper orientation of the protein in the complexes with its physiological partners. The importance of considering this charge distribution is demonstrated (19,201 by studies involving specific lysine modification of cytochrome c and its electron transfer reactions with some protein partners. The general results of these studies show that modification of lysines in a small well-defined region surrounding the exposed heme edge affects electron transfer rates, but 346 LIANG-HONG GUO AND H. ALLEN 0. HILL modification of those outside this region have no effect. Thus, it seems that localized high charge density and resulting dipole moments control the preorientation of the protein reactants as they approach, so that an optimal, rather than a randomly bound, reaction complex is formed. To understand the structural requirements for a molecule to promote cytochrome c electrochemistry at gold electrodes, over 50 bifunctional organic compounds (X - Y, where X is a surface-active functional group, Y is the protein-interactive functionality, and - is the linking structure) were investigated (21 ) to assess their ability to promote cytochrome c electrochemistry at a gold electrode. The results can be summarized as follows: 1. The surface adsorbing groups, X, are most satisfactory when they belong to cr-donor and .rr-acceptor synergic-type ligands such as 4- pyridyl-N, thio-SH, disulfide \u201cS-S,\u201d and phosphine P, which are appropriate for coordination to a Group 11 metal such as Au. 2. The effective Y groups can be divided into two subcategories: (a) neutral groups such as 4-pyridyl-N and an aniline-type amine, ArNH2, which are weakly basic and able to form hydrogen bonds to lysine-NH;; and (b) anionic groups such as carboxylate, sulfonate, phosphonate, or phosphate, which can interact with lysine-NH3 groups through both hydrogen bonding and salt bridging. 3. The link (-1 may be rigid or flexible, aliphatic or aromatic, and of varying length. One crucial role that promoters may play is to prevent adventitious adsorption on an electrode surface of either impurities in the supporting electrolyte or in the protein itself, which usually undergoes denaturation. Obviously, to be compatible with the polar surface amino acid residues of proteins, the hydrophilicity of the electrode surface is important. However, prevention of direct and degradative adsorption of proteins is not the sole function of promoters. It has been shown that diphenyl disulfide, although adsorbing strongly at gold electrodes, did not act as a promoter for cytochrome c. In order that there is a rapid and reversible binding of a protein to the modified electrode surface in a manner that is conducive to electron transfer, it is necessary for promoters to present functional groups at the electrode/electrolyte interface to which protein can bind. A new group of promoters has recently been employed (22) in achieving the direct electrochemistry of cytochrome c and other proteins. Several cysteine-containing peptides for example, (Cys-Glu)z, proved very successful, as they bind tightly to the gold electrode via the sulfur ELECTROCHEMISTRY OF PKO'I'EINS AND ENZYMES 347 atom and interact favorably with the proteins through the charged amino acids." + ] + }, + { + "image_filename": "designv10_3_0000056_s0263574707003530-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000056_s0263574707003530-Figure4-1.png", + "caption": "Fig. 4. Canonical 3R-manipulator.", + "texts": [ + " If the relative position of two rotation axes is described by the usual Denavit\u2013Hartenberg parameters17 (\u03b1i, ai, di), then the coordinate transformation between the coordinate systems attached to the rotation axes is given by G = \u23a1 \u23a2\u23a3 1 0 0 0 ai 1 0 0 0 0 cos \u03b1i \u2212 sin \u03b1i di 0 sin \u03b1i cos \u03b1i \u23a4 \u23a5\u23a6. (13) Using this transformation, we assume the axes of an nRchain being in a canonical start position, where all the axes are parallel to a plane, the first rotation axis is the z-axis of the base coordinate system and the x-axis is the common normal of first and second rotation axis. A simple consideration shows that this is always possible, and there is no restriction of generality.18 As shown in Fig. 4, the rotation axes are always the z-axes of the coordinate systems. Therefore, we can write these rotations as Mi = \u23a1 \u23a2\u23a3 1 0 0 0 0 cos ui \u2212 sin ui 0 0 sin ui cos ui 0 0 0 0 1 \u23a4 \u23a5\u23a6 (14) with ui being the rotation parameters. The forward kinematics of a general 3R chain can be written as D = B \u00b7 M1 \u00b7 G1 \u00b7 M2 \u00b7 G2 \u00b7 M3 \u00b7 G3. The constant matrix B performs the transformation of an arbitrary coordinate system into the canonical base system of Fig. 4. In a step by step procedure, the representation of the 3R in the image space will be derived. At first, we will derive http://journals.cambridge.org Downloaded: 27 Apr 2015 IP address: 169.230.243.252 the representation for the canonical chain for which B is the identity. The transformation that brings the chain into a general position will be performed later in the image space. If one of the three rotation parameters of the 3R chain is fixed for a moment, then a 2R chain remains. The kinematic image of this 2R chain is derived first" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure4-1.png", + "caption": "Fig. 4. Illustration of: (a) reference rack-cutter with straight profiles, (b) shaper parabolic rack-cutter profile, (c) pinion parabolic rackcutter profile.", + "texts": [ + " Two types of face-gear drive geometry with helical pinion are proposed as follows: (i) based on application of a screw involute surface and (ii) a surface of a helicoid determined as the envelope to a parabolic rack-cutter. Two mismatched parabolic rack-cutters are applied for generation of the helical pinion of the gear drive and the helical shaper used for generation of the face-gear. Fig. 3 shows the cross-section of an involute helicoid. The involute screw surface is generated by the screw motion of the cross-section about the axis of the helicoid. Center distance Ews shown in Fig. 3 corresponds to simultaneous meshing of screw involute shaper, grinding worm, and face-gear (see below Figs. 16 and 17). Fig. 4(a) shows in normal section the straight line profiles of a conventional rack-cutter used as a reference one, and shaper and pinion parabolic rack-cutters (Fig. 4(b) and (c)). The analysis of advantages and disadvantages of proposed two types of geometry, and the influence of errors of alignment has been investigated by simulation of meshing and contact of pinion and face-gear tooth surfaces. The algorithm of the computer program developed is based on simulation of continuous tangency of contacting surfaces (Fig. 5). The main results of computerized simulation of meshing and contact are as follows: (i) In the case of a conventional involute geometry, the path of contact on the face-gear tooth surface is directed across the tooth surface", + " Surface Ri (i = 1, s) of the pinion (shaper) is derived as an envelope to the family of surfaces Rc in Si (i = 1, s) [7] and is represented as ri\u00f0ui; li;wi\u00de \u00bc Mic\u00f0wi\u00derc\u00f0ui; li\u00de \u00f0i \u00bc 1; s\u00de; \u00f013\u00de fci\u00f0ui; li;wi\u00de \u00bc nc v\u00f0ci\u00dec \u00bc 0 \u00f0i \u00bc 1; s\u00de: \u00f014\u00de Here, rc(ui, li) and nc represent the rack-cutter surface and its unit normal; vector function ri(ui, li,wi) represents the family of rack-cutter surfaces; fci = 0 is the equation of meshing; matrix Mic(wi) (i = 1, s) is applied for coordinate transformation; vector v\u00f0ci\u00dec of relative velocity and unit normal nc are represented in Sc. The proposed geometry is based on the following ideas: (i) Two imaginary rigidly connected rack-cutters designated as Rc1 and Rcs (Fig. 4) are applied for the generation of the pinion and the shaper, respectively. Notation Rc indicates the conventional reference rack cutter with straight line profiles. (ii) Rack-cutters Rc1 and Rcs are provided by mismatched parabolic profiles that deviate from the straight line profiles of reference rack-cutter Rc. Fig. 4(a) shows schematically an exaggerated deviation of Rc1 and Rcs from Rc. The parabolic profiles of one tooth side of rack-cutters Rc1 and Rcs are shown schematically in Fig. 4(b) and (c). The parabola coefficients for the pinion and the shaper rack cutters are designated by a1 and as, respectively. Rack cutter surfaces Ri (i = c1,cs) are represented in coordinate system Sc (Fig. 9(c)) by vector function rc(ui, li) that yields xc\u00f0ui; li\u00de \u00bc s0 2 cos an sin an \u00fe \u00f0ui uo\u00de cos an \u00fe aiu2i sin an; yc\u00f0ui; li\u00de \u00bc s0 2 cos2an \u00f0ui uo\u00de sin an \u00fe aiu2i cos an cos b li sin b; zc\u00f0ui; li\u00de \u00bc s0 2 cos2an \u00f0ui uo\u00de sin an \u00fe aiu2i cos an sin b\u00fe li cos b: \u00f015\u00de Here, uo indicates the location of the parabola apex wherein parabolic and straight profiles are in tangency (Fig. 4(a)). (iii) The tooth surfaces R1 and Rs of the pinion and the shaper are determined as envelopes to the tooth surfaces of rack-cutters Rc1 and Rcs, respectively. The process is similar to the described one in the previous subsection. In this case, the equation of meshing fci = 0 yields the following value for the generalized parameter of motion wi: wi\u00f0ui; li\u00de \u00bc \u00bd2a2i u3i \u00fe \u00f01\u00fe aiso cos an\u00deui uo cos b\u00fe \u00bdli sin an 2aiuili cos an sin b \u00f0sin an 2aiui cos an\u00derpi : \u00f016\u00de Then, it is possible to represent Ri as Ri\u00f0ui; li\u00de \u00bc ri\u00f0ui; li;wi\u00f0ui; li\u00de\u00de: \u00f017\u00de The normal to Ri is determined as Ni\u00f0ui; li\u00de \u00bc oRi oui oRi oli : \u00f018\u00de The tooth surface R2 of the face-gear is generated as the envelope to the family of tooth surfaces Rs of the shaper", + " Example 1: A conventional face-gear drive with an involute helical pinion has been considered. Correc- tion DE for the drive has not been applied. Examples 2 and 3: A face-gear drive with modified tooth surfaces of the pinion and the shaper is considered. The modification is based on application of parabolic cutters for determination of tooth surfaces. Correction of meshing is provided by application of offset parameter DE (see Fig. 13), variation of relations between parabola coefficients of parabolic rack-cutters, location of the apex of the parabolic profiles (see Fig. 4), and plunging of the disk that generates the helical pinion [14]. Optimization of design parameters in the second type of geometry is an iterative process that enables to obtain: (i) Larger dimensions of the instantaneous contact ellipse and more favorable orientation of the contact ellipse (we remind that the point contact of the pinion and the face-gear tooth surfaces is spread under the load over an elliptical area). (ii) Improvements of contact mentioned above may be accompanied by slight deviation of the path of contact from initially assigned longitudinal orientation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003279_j.ymssp.2020.107325-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003279_j.ymssp.2020.107325-Figure1-1.png", + "caption": "Fig. 1. Planetary gear system and encoder: (1) encoder, (2) graduated disk, (3) ring gear, (4) sun gear, and (5) planet gear.", + "texts": [ + " Section 2 explains the motivation and idea of encoder signal analysis for planetary gearbox fault diagnosis under both constant and time-varying speed conditions. Section 3 introduces the principle and analysis procedure of proposed method. Section 4 illustrates the proposed method via numerical simulation. Section 5 further validates the proposed method via lab experimental signal analysis of a planetary gearbox under both constant and time-varying speed conditions. At last, Section 5 draws conclusions. Fig. 1 shows the typical schematic diagram of planetary gearboxes. A single stage planetary gearbox is often composed of a sun, a ring, and several planet gears. In most cases, the ring gear is fixed, and the sun gear and the planet carrier rotate. All the planet gears not only spin around their own centers, but also revolve with the planet carrier around the co-center of both the sun and the ring gears. Meanwhile, they mesh simultaneously with both the sun and ring gears. Suppose one tooth of a gear is damaged, such as pitting, chipping, spalling, cracking, or even a tooth missing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure7.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure7.3-1.png", + "caption": "Fig. 7.3 Sequence of linear transformations of the feasible activation set in a forward model of static force production by a tendon-driven limb. Using the concepts in Figs. 7.1 and 7.2, we use as neural input a the feasible activation set (a positive unit cube) to produce b the feasible muscle, c feasible joint torque, and d endpoint feasible wrench sets. Adapted with permission from [2]", + "texts": [ + " And any convex polygon can be described and defined equivalently by either its vertices, or the linear equations that define its sides [13]. At this point the ideas of convexity and convex sets become important. Please see Sect. 7.6 where these are developed further. We now apply Eq. 7.3 to tendon-driven limbs to find the set of all feasible mechanical outputs of the system in terms of joint torques and endpoint wrenches. Once again, the nervous system can only produce positive linear combinations of the column vectors of matrix F0, matrix [R F0], and matrix H = [J\u2212T R F0] as shown in Fig. 7.1. Therefore, as shown in Fig. 7.3: \u2022 The set of all possible muscle force vectors is the column space of the matrix F0. This is called the feasible muscle force set. This zonotope (or zonohedron) is produced by the Minkowski sum of all possible muscle force capabilities of the limb. That is, the column vectors of F0 are the generators the nervous system has at its disposal to produce muscle forces. \u2022 The set of all possible joint torque vectors is the column space of the matrix [R F0]. This is called the feasible torque set. This zonotope (or zonohedron) is produced by the Minkowski sum of all possible torque capabilities of the limb", + "16) Likewise, the column vectors wi of matrix [J\u2212T R F0] are the generators of the Minkowski sum in Fig. 7.2. Therefore, the zonotope they create is the feasible wrench set because it describes and contains all possible wrenches the nervous system can produce at the endpoint of the limb in that particular posture. Each generator wi is the wrench vector muscle i produces, and the neural command a defines how the nervous system combines the actions of the N muscles to produce the output wrench w. To summarize, Fig. 7.3 starts with the cube that is the most general feasible activation set, which first creates the parallelepiped of the feasible muscle force set, and then the zonotopes of the feasible joint torque, and feasible output wrench sets. Note that the column vectors \u03c4 i and wi are in the units of joint torques and end- point wrenches, respectively. Their positive linear combinations specify the set of all possible outputs in those spaces. If we consider them as the vi vectors of Fig. 7.2, we can build the zonotopes that correspond to the feasible joint torque set and the feasible output wrench set as shown in Fig. 7.3. In the specific simple case shown in Fig. 7.4, the endpoint wrench is a planar force vector\u2014consisting of fx and fy components only. This zonotope is called the feasible force set, and not the feasible wrench set because the endpoint output contains no torques (see Sect. 2.6). Note that we are studying the general case of the unconstrained feasible torque, wrench, and force sets, as shown in Fig. 7.3. I call these \u2018unconstrained\u2019 feasible sets because they describe what the system can do when you simply combine all possible actions without regard to functional constraints or goals, such as canceling out some elements of the output wrench w while keeping others. The only a priori constraints are that the activation, a, to all muscles be limited to be \u22650 and \u22641. Thus the feasible sets are all zonotopes because they are created by the Minkowski sum of the generator vectors as in Fig. 7.2. For now let us stay with this most general case to discuss the calculation and properties of such convex sets for neuromechanical function", + " Calculating these unconstrained feasible sets is quite straightforward and can be done in two equivalent ways: \u2022 The first is to perform the Minkowski sum of the relevant column vectors, as we saw in Figs. 7.2, 7.3, and 7.4. This produces many points, only a few of which actually become vertices of the convex hull. See Fig. 7.5 for an example that uses a planar 5 muscle system. \u2022 Alternatively, we can think of these unconstrained feasible sets as the mapping of convex sets from one space to another as shown in Fig. 7.3. The second approach hinges on the fact that the neural input to the system\u2014the set of feasible activations\u2014is bounded to the positive octant in activation space. That is, if 0 \u2264 a \u2264 1, then its elements are also bounded as 0 \u2264 ai \u2264 1 for i = 1, . . . , N . This feasible activation space is a unit positive N-cube in R N , as shown in Fig. 7.3. An N-cube is the generalization of a cube to >3 dimensions. It is called an N-cube because it is N-dimensional. And it is a \u2018unit positive\u2019 N-cube because all of its sides have length 1, with values along each dimension ranging from 0 to positive 1. Such a non-negative convex set then lies in the positive octant of RN . An octant is the generalization of a Cartesian quadrant to 3D where there are 8 such regions. The 8 vertices of the cube representing the unit positive octant are, in no particular order, 7", + " Because convex sets remain convex under linear mapping [13, 15], then the feasible muscle force set will be a convex set as well. It is in fact a parallelepiped, which is a cube whose sides are stretched differently by the diagonal elements in the matrix F0. Similarly, mapping the feasible muscle force set by the matrix R will be a convex set in joint torque space: the feasible torque space. And mapping the feasible torque space by the J\u2212T will also produce a convex set in output wrench space: the feasible wrench set. Once again, this sequence is shown in Fig. 7.3. Figure 7.3 merits some explanation as it holds important lessons. The initial mapping from activation space to muscle force space happens within a similar dimensionality, namely R 3. Thus, a diagonal matrix distorts a cube into a parallelepiped. Now consider the mapping from R 3 to R 2. Such mapping is needed in Fig. 7.3 to find the feasible torque set. This is an operation analogous to casting a shadow as shown in Fig. 7.6, and is further described in Sect. 7.6. \u2022 The extreme points of the projected convex set are a function of the extreme points of the original convex set. That is, all edges of the shadow are produced by edges, facets, and vertices of the cube. \u2013 Therefore, every extreme point of the shadow is produced by mapping a unique point on the surface of the original object. See the vertices of the shadow numbered 1, 2, 3, 6, 7, and 8 in Fig", + " But more importantly, it builds foundation for a case, which argues that exploring and exploiting feasible sets in the activation, muscle force, joint torque, or output wrench spaces is a biologically plausible way in which the nervous system may learn and produce the multiple, multifaceted tasks of everyday life in the context of muscle redundancy. 116 8 Feasible Neural Commands with Mechanical Constraints As mentioned above, the feasible sets we are exploring are convex polytopes in their particular multidimensional spaces (e.g., activation, muscle force, joint torque, or output wrench spaces) as shown in Fig. 7.3. These polytopes describe and contain all feasible vectors of a, fm , \u03c4 , and w, respectively. The simplest case is to define the set of feasible activations as the unit positive N-cube, and map it into the feasible muscle force, torque, and wrench sets as shown in Chap.7. This gives us a global view of the raw mechanical capabilities of the limb without any additional constraints. From this, we can find the maximal possible output wrench at the endpoint in every endpoint force and torque direction", + " This can be done with code such as cdd by Avis and Fukuda [15] \u2192 The intersection of all inequality or equality constraints, if it exists, forms a convex polytope. It can be requested in vertex or linear inequality constraints representation (See Sect. 7.6) \u2192 This polytope is the feasible activation set [20, 21] How does one find the feasible output set? As illustrated in Fig. 8.5 the projection of the feasible input set produces a feasible output set\u2014a convex hull that defines the feasible muscle force, joint torque, wrench, or force sets depending on the framing of the problem. Figure7.3 shows this sequence of mappings. Please note that, in general, the feasible input set need not be the feasible activation set. For example, Fig. 7.3 shows that you can be doing your analysis in the feasible torque set, and call that the feasible input set, to produce the feasible endpoint wrench set, which would be your feasible output set. It all depends on the analysis you are doing. Having said this, mapping the feasible input set into the feasible output set translates into the computational geometry problem of finding the convex hull for a cloud of points in the space into which the mapping takes place. This is done as 8.3 Vertex Enumeration in Practice 123 per Algorithm 2. An example of a convex polyhedron representing a feasible output set is shown in Fig. 8.6\u2014the 3D feasible force set for the human index finger [20, 21]. Algorithm 2 Finding the feasible output set Require: Vertices of the feasible input set. These can be obtained as per Algorithm 1 from the matrices F0, R, J\u2212T or their combinations, depending on your definition of what is the input as per Fig. 7.3 \u2192 Project every vertex of the feasible input set by the matrices of interest that produce the desired output. For example, if you consider the feasible activation set as your input then \u2192 Multiply all vertices by F0 to find the feasible muscle force set \u2192 Multiply all vertices by [R F0] to find the feasible joint torque set \u2192 Multiply all vertices by [J\u2212T R F0] to find the feasible endpoint wrench set or feasible endpoint force set depending on the constraints you enforce end if return All pairs of vertices of the feasible activation space and the output they produce \u2192 Apply the convex hull operation to the projected vertices to find the convex polyhedron, polygon, or polytope (depending on the dimensionality of the output space)", + "4 A Definition of Versatility 125 it is trivial to say that paralysis weakens, being able to show exactly how and in which directions the weakening occurs is critical to understand the disability\u2014and to design therapeutic or surgical strategies that restore as much versatility as possible [30]. How does one achieve versatility in tendon-driven limbs? The argument about versatility is often made in the endpoint wrench space where force closure is defined. It makes sense to evaluate the final, most visible mechanical output of the system. However, it is not entirely obvious what properties of the system lead to versatility in the endpoint wrench space because it is the cumulative product of all of the transformations in Fig. 7.3. There are several properties of convex sets that help us establish versatility in a more anatomically intuitive way. As described in [31], it is possible to show that if the feasible joint torque set includes the origin, then the feasible wrench set will also include the origin, and vice versa. Consider Figs. 7.3 and 7.4, which show that the system is versatile because the feasible joint torque and feasible wrench sets both include the origin. The following argument proves this: \u2022 Feasible sets are convex polytopes", + " \u2022 Another way to say this is that internal points of the input convex set can never become extreme points in the output convex set. \u2022 Therefore, if the zero point (i.e., the origin) is an internal point of the feasible joint torque set, then the origin will be an internal point of the feasible wrench set. Thus a system will be versatile in wrench space (i.e., the feasible wrench space will include the origin) if the feasible joint torque set includes the origin in joint torque space. Having a working definition of versatility that can be addressed at the level of the \u2018intermediate\u2019 joint torque space (as shown in Fig. 7.3) has multiple advantages. Most importantly, it is intuitive because the details of the generators that produce the feasible joint torque set come directly from the anatomical routing of the tendons, as shown in Fig. 7.5. Any constraint equations that are added in activation space that modify the initial N-cube can also be readily interpreted at the level of individual muscle actions in torque space. And last, the interactions between neural and anatomical constraints in health and disease can be interpreted at a very intuitive level in torque space", + " That distinction is of course clear and important when we discuss issues of tendon excursions, and muscle fiber lengths and velocities [25], such as muscle work, power, etc., as introduced in Chap. 6. However, we must be careful not to generalize. From the perspective of joint torque production, being a multiarticular muscle simply means that the line of action of that muscle in torque space is not pointing along one of the coordinate axes, as shown in Fig. 7.5 and Chap. 7. But what may be more important functionally is how each muscle contributes to the size and shape of the feasible torque set (or feasible wrench set for that matter, Fig. 7.3). Whether or not the muscle is aligned with the coordinate axes in torque space may or may not matter. In some cases, the line of action of the muscle could be an important evolutionary adaptation for particular tasks that preferentially involve some regions of the torque space [26, 27]. These issues remain relatively unexplored. My hope is that the perspective and techniques presented in this book will enable the study of such co-evolutionary adaptations between brain and body. 166 10 Implications One of the more pernicious consequences of how muscles were named is that they blur the distinction between the neural control of motion versus the neural control of static force", + " The beauty of the link between Euclidean geometry and linear algebra (one of the greatest achievements of mathematics) is that these concepts, and the intuition they provide, extend to any number of dimensions. Hence we can, for example, talk about a vector f \u2208 R 31 that describes the coordination of forces across 31 muscles in the hindlimb of a cat [6]. Moreover, as it becomes clear in several parts of this book, RN is not simply a set of arrays with N entries. Rather, you can think of it as an N-dimensional vector space\u2014be it a physical space, or the \u2018space\u2019 of muscle forces, joint torques, or endpoint forces of a limb as shown in Fig. 7.3. A matrix is also an array of numbers, but with multiple rows and columns. You can think of it as a collection of row or column vectors. Or you can think of a vector as a matrix with only one row or column. When I speak of vectors in this book I often mean column vectors, but discussing the elements of matrices require us to specify whether we are talking about its row or column vectors. I typeset matrices as capital italicized letters. The dimensionality of a matrix A is given as A \u2208 R M\u00d7N for a matrix with M rows and N columns" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000252_1.3085943-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000252_1.3085943-Figure1-1.png", + "caption": "Fig. 1 Definition of oil churning parameters for a gear pair immersed in oil", + "texts": [ + " Similarly, the effect of enclosures in the form of flanges or shrouds in the near vicinity of rotating gears, as reported experimentally by Changenet and Velex 22 , will not be included, as such effects are beyond the scope of this study. 3.1 Power Loss Due to Drag on the Periphery of a Gear. A rotating gear pair that is fully or partially immersed in oil, as Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use s t g f p i t b d t e R t c d l s t S d c a d i o p h l n c t r k e r p a p t s l fl e s a o t a b t d e p c b d f i r h r d o t fl s \u00af \u00af J Downloaded Fr hown in Fig. 1, is subjected to drag forces that are induced along he direction of flow on the periphery circumference and faces sides of the gears, thus, contributing to churning power losses. A ear pair rotating in free air experiences similar drag forces in the orm of air windage. In formulating the drag forces and drag ower losses, each gear is modeled as an equivalent circular cylnder of radius roi the outside radius of the gear . This employs he assumption that, at medium to high speeds of rotation, the ehavior of a gear immersed in oil follows that of a cylindrical isk, as the oil swirling around the gear will not feel the effects of he tooth cavities", + " 5c , the tangential shear stress at the outside radius of gear i, r=roi tangential wall shear stress , is found as dpi w =2 i. Defining the friction drag coefficient as Cdpi=2 dpi w / Ui 2, where Ui= iroi is the freestream velocity of the lubricant near the periphery of the gear i, the drag force acting on the periphery of the gear is found as Fdpi = 1 2 Ui 2AdpiCdpi = Adpi dpi w 6 Here, the wetted surface area of the periphery is given as Adpi =2 iroibi, where bi is face width of gear i and i=cos\u22121 1\u2212 h\u0304i . A dimensionless immersion parameter is defined from Fig. 1 as h\u0304i =hi /roi, where hi is the immersion depth of gear i. Accordingly, hi 0 represents the case of no oil-gear interactions, and h\u0304i 2 corresponds to the case of a gear that is submerged in oil. For hi 2, h\u0304i=2 is used in the above formulation to obtain i= such that the entire periphery of the gear is subject to drag, i.e., Adpi =2 roibi. For h\u0304i 0, it is understood that the gear is submerged in air. Then, the parameters h\u0304i=2 and i= are used together with the properties of air to calculate air windage loss at the periphery of the gear", + " 131, APRIL 2009 om: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms across a flat plate, for which the freestream velocity Ui is constant, the rate of increase in momentum thickness is directly proportional to the wall shear stress, i.e., i x = 1 2 Ci 9 By setting Ci=Ci L and i= i L to represent the laminar regime, and incorporating Eqs. 8b and 8c , Eq. 9 is solved to obtain the boundary layer thickness as i L = 3.46 kx Ui 10 where x is the length parameter, as defined in Fig. 1. At x= i =2roi sin i, the skin friction coefficient is obtained by substituting Eq. 10 into Eq. 8c as C i L = 0.578 k iUi 11 The drag force on the face of the gear in the laminar regime is then given in terms of the skin friction coefficient at x= i as Fdfi L = 1 2 Ui 2AdfiC i L 12a The wetted area of the face is Adfi = roi 2 2 \u2212 sin\u22121 1 \u2212 h\u0304i \u2212 1 \u2212 h\u0304i h\u0304i 2 \u2212 h\u0304i 12b For the case of a fully submerged gear or for air windage , h\u0304i =2 and the wetted surface area of the gear reduces to Adfi= roi 2 , while the length parameter is x= i=2roi", + " The displacement and momentum thicknesses are found from Eqs. 8a and 8b , with the velocity profile defined in Eq. 14a as i T = 1 8 i T and i T = 7 72 i T . Defining the skin friction coefficient for flow over a rough flat plate that is turbulent from the leading edge as 23 Ci T = 0.02 k Ui i T 0.167 14b and substituting the expressions for Ci T , i= i T , and i= i T into the momentum integral equation, the boundary layer thickness is derived as dfi T = 0.142x6/7 k Ui 1/7 15a As in the laminar flow formulation, the value of Ci T at x= i, as shown in Fig. 1, is derived from Eq. 14b as Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use a c S g r F t p t fi r o l c e c s t o d F t J Downloaded Fr C i T = 0.0276 k iUi 1/7 15b nd the drag force on the faces of the gear under turbulent flow onditions is given as Fdfi T = 1 2 Ui 2AdfiC i T 16a ubstituting Eq. 15b and accounting for the both faces of the ear, the drag force on the faces of the gear i in the turbulent flow egime is written as Fdfi T = 0.025 k 0.14 i 1.86roi 1.72Adfi sin i 0", + " This predicted effect of viscosity conflicts the experiments of Luke and Olver 8 and Changenet and Velex 14 , while agrees well with our own experiments 21 . In Fig. 8 b , the influence of the quasistatic oil levels on PT is dem- APRIL 2009, Vol. 131 / 022201-9 of Use: http://www.asme.org/about-asme/terms-of-use o o a r c s d w h p t t s t t F p b s = f a m t = g f h p f i e F f 0 Downloaded Fr nstrated for a gear pair having m\u0303=2.32 mm and b=19.5 mm, perated in lubricant at a temperature of 80\u00b0C =0.0185 Pa s nd =811.3 kg /m3 . Here, the oil levels h\u0304=0.5, 1.0, and 1.5 epresent 25%, 50%, and 75% immersion of the gears in oil, ac- ording to Fig. 1. As all components of PT are dependent on h\u0304, ignificant increases in PT are observed with increased immersion epth, with almost 2.5 times larger PT values at h\u0304=1.5 compared ith those at h\u0304=0.5. Figure 8 c shows the influence of b on PT for a gear pair aving m\u0303=2.32 mm operating at h\u0304=1.0 and 80\u00b0C. Here, the gear air having b=26.7 mm experiences about 2.8 times higher PT han the gear pair with b=14.7 mm. The components of PT for he gear pair with m\u0303=2.32 mm and varying face width values are hown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002987_s00170-016-8543-2-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002987_s00170-016-8543-2-Figure3-1.png", + "caption": "Fig. 3 Schematic diagram of work flat", + "texts": [ + " A gas mixture of Ar (95 %) and CO2 (5 %) with a flow rate of 18 L/min was used as the shielding gas. The deposition experiment was conducted on a mild steel substrate with a dimension of 250 mm\u00d775 mm\u00d79.5 mm. During the additive manufacturing process, the GMAW torch was stationary, thinwalled parts were fabricated by the movement of the work flat, which was driven by three stepping motors, respectively. The work flat is capable of moving along the Y-axis and lifting along the Z-axis. The mechanical part of the work flat is simply presented in Fig. 3. A single layer with a current of 160 A, arc voltage of 22.4 V, and deposit velocity of 5 mm/s is given in Fig. 4a. Point A is in the arc striking area, and point B is in the steady stage. Points C and D are in the arc extinguishing area. Macrophotographs of above 4 points are presented from Fig. 4b\u2013e, respectively. It is seen that the height of point A is larger than that of point B, and the height decreases gradually in the arc extinguishing area. The reason is that the heat dispassion condition in the arc striking area is excellent" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003082_j.jsv.2016.02.021-Figure21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003082_j.jsv.2016.02.021-Figure21-1.png", + "caption": "Fig. 21. The hybrid gear cracks: sun gear Z20 and spur gear Z29.", + "texts": [ + " It can be seen in the figure that the established model for gear crack severity identification fitted the CSD energy features EN and EF well. There was an evident trend of the increasing CSD energy value with the increase of crack severity. The proposed model could correctly identify the gear crack severity. In addition to single crack detection, the proposed SOTBCA method was also applied to detect multiple gear cracks in this work. In addition to the 2.0 mm crack on the spur gear Z29, another crack was also imposed to the sun gear Z20 in the first stage of the planetary gearbox (see Fig. 21). According to the configuration of the test rig (Table 3), the rotating frequency of the sun gear Z20 was fsr \u00bc fm; the fault frequency of the sun gear Z20 was fs \u00bc 10/3 fm; the fault frequency of the planet gear Z40 was fp \u00bc 5/12 fm. Similar to Eq. (15), the following supervising signal was built to track the sun gear crack source in the SOTBCA analysis: f s\u00f0t\u00de \u00bc X8 i \u00bc 1 sin \u00f02\u03c0if st\u00de; (19) and the corresponding AR coefficients were [4.993, 9.97, 9.955, 4.97, 0.9925]. Firstly the hybrid cracks experiment was conducted under fm \u00bc 40 Hz" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001216_tro.2011.2168170-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001216_tro.2011.2168170-Figure3-1.png", + "caption": "Fig. 3. Screw representations of a planar 3R cable-driven open chain.", + "texts": [ + " 1) \u0302$j represents the unit screw for the twist at the jth joint. 2) \u0302$jr represents the unit screw for the reciprocal wrench of the jth joint. 3) \u0302$i:j\u2212k represents the unit screw for the ith cable force acting from the jth link to the kth link, and j = k. 4) $extj represents the screw for the external wrench acting on the jth link. 5) ti represents the tension scalar of the ith cable. In this section, the proposed methodology in Section III is first illustrated using a planar 3R cable-driven \u201cproper\u201d open chain. (Note that R indicates a revolute joint.) Fig. 3 presents a planar 3R cable-driven open chain with four cables. This will be used as an illustrative example to carry out the proposed force-closure analysis. From Fig. 3, the unit screws for the various pure rotation twists (i.e., zero pitch) in the inertial frame are as follows: \u0302$1 = [ 0, 0, 1, 0, 0, 0 ]T (1) \u0302$2 = [ 0, 0, 1, l1s\u03b81 ,\u2212l1c\u03b81 , 0 ]T (2) \u0302$3 = [ 0, 0, 1, l1s\u03b81 + l2s\u03b812 ,\u2212l1c\u03b81 \u2212 l2c\u03b812 , 0 ]T . (3) For planar mechanisms with revolute or prismatic joints, reciprocal screws are easily obtained geometrically. For the case of the 3R planar cable-driven open chain, the wrench that is reciprocal to a zero-pitch twist forms a pencil of screws radiating from the rotation axis and lying in the plane of the rotating joint (i.e., X\u2013Y plane). In order to get the reciprocal wrench for joint 1, its reciprocal wrench \u0302$1r must be reciprocal to joints 2 and 3. \u0302$1r must pass through joint axes 2 and 3. Similarly, \u0302$2r and \u0302$3r can be identified geometrically (see Fig. 3). The unit screws of the various zero-pitch reciprocal wrenches in the inertial frame are described as follows:1 \u0302$1r = [ c\u03b812 , s\u03b812 , l1s\u03b82 ]T (4) \u0302$2r = [ c(\u03b81 + \u03b1), s(\u03b81 + \u03b1), 0 ]T (5) \u0302$3r = [ c\u03b81 , s\u03b81 , 0 ]T (6) where s\u03b8 \u2261 sin\u03b8, c\u03b8 \u2261 cos\u03b8, \u03b812 \u2261 \u03b81 + \u03b82 , and \u03b81 + \u03b1 = atan2 ( l1 sin\u03b81 + l2 sin\u03b81 2 l1 cos\u03b81 + l2 cos\u03b81 2 ) . Based on Proposition 1.1, the external wrenches $extj at each link can be uniquely expressed as a linear combination of the three reciprocal screws, i.e., \u0302$1r , \u0302$2r , and \u0302$3r , and are described as follows: at link 1 : $ext1 = w (1) e1 \u0302$1r + w (2) e1 \u0302$2r + w (3) e1 \u0302$3r (7) at link 2 : $ext2 = w (1) e2 \u0302$1r + w (2) e2 \u0302$2r + w (3) e2 \u0302$3r (8) at link 3 : $ext3 = w (1) e3 \u0302$1r + w (2) e3 \u0302$2r + w (3) e3 \u0302$3r " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000492_0301-679x(81)90058-x-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000492_0301-679x(81)90058-x-Figure10-1.png", + "caption": "Fig 10 Approximate radial profile", + "texts": [ + "5) 2 a o If the pressure distribution was twice as long, the end deflection due to half this longer pressure wouldbe : 8b 5 ( 0 , 1 ) = ~ (ln - - + 0.5) (A1.2) a o TRIBOLOGY international June 1981 135 Johns and Gohar - Roller bearings under radial and eccentric loads which gives the deflect ion at the end of a roller of length 2b. Therefore, f rom Eqs 48), (AI .1 ) and (AI .2) : rr 2b P'(0,1) : - tin - - + 0.5) (A1.3) \"3 -- a O Equating Eqs ( 2 ) a n d (A1.3): a o KI = 1 - 0 .3033 - - ( 3 ) b Appendix 2 Referring to Fig 10, radius RI can describe an arc approxilnate to the Lundberg profile, being exact ly equal to it at point A, of: (b - s ) ~ R1 = - - - (A2.1) 2Pl where P1 is obtained f rom Eq 44) at b-y = S. Pz is also known from Eq 44) and therefore tile fol lowing geometr ical relationships can be used to find Rz : P2 +-R2 s i n c e = P , +R2 cosc~ (A2.2) Rz cos c~ = R2 sin/3 + S (A2.3) remembering that sin 2 ~ + cos 2 c~ = 1, sin/3 = (b-S)/R1, and cos/3 = (R1 -Pl )/R1, Eqs (A2.2) and (A2.3) can be combined to give: [(P2-P~ )~ + s 2 l R 2 = R 1 (A2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure5.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure5.1-1.png", + "caption": "Figure 5.1.1 The front-engined 1894 Panhard-Levassor with tiller steering (uppermost lever) representative of the very early period.", + "texts": [ + " Rear-wheel steering is generally unsafe at high speeds, but because of its convenience in manoeuvring it is sometimes used on specialist low-speed vehicles, such as dumper trucks. This is in contrast to aircraft, which usually have tailplanes and are rear steered by elevators and rudder. Some interest has been shown in variable rear steering for passenger cars, supplementing conventional front steering, and this is has been commercially available. In the early days of motoring, various hand controls were tried for the driver. Tiller steering, as used on boats, for example as on the 1894 Panhard-Levassor in Figure 5.1.1, was satisfactory at low speed, but often dangerously unstable at high speed. Thewheels steered in the same sense as the tiller, so the tillerwas moved to the right tomake a left turn. The driver then tended to fall centrifugally to the right, exaggerating the turn, sometimes leading to an unstable divergencewith disastrous roll-over. Tiller steering was greatly improved by Lanchester who reversed its action to give better stability. It was Benz who introduced the steering wheel, and this was almost universal by 1900" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001154_j.jsv.2012.03.019-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001154_j.jsv.2012.03.019-Figure1-1.png", + "caption": "Fig. 1. Gear pair model. (a) View showing the bearings and the axial positions of bodies. The dashed line is at the center of the active facewidth. (b) View showing the gear plane. (c) View showing the contact plane and the gear mesh model with contact stiffnesses.", + "texts": [ + " The equivalent stiffness representation calculates, from the load distribution at each instant of the vibration, the translational mesh stiffness, the center of stiffness location, and a twist mesh stiffness. Dynamic fluctuations of these two stiffnesses and the center of stiffness location expose the characteristics of the nonlinear vibrations. The system model consists of two gears mounted on shafts. Each gear body is combined with its supporting shaft into a single rigid body. These gear\u2013shaft bodies are each mounted on up to two bearings placed at arbitrary axial locations. Fig. 1 shows the gear model and the bases. The fixed basis is defined as fE1,E2,E3g oriented such that E1 is parallel to the line of action of the gear mesh. The translational (xp,yp,zp) and angular (fp, yp, bp) coordinates of the pinion body are assigned to translations along and rotations about E1, E2, and E3, respectively. The translational and angular coordinates of the gear body follow similarly with subscript g. We refer to rotation about E1 as tilting (fp, fg) and rotation about E2 as twisting (yp, yg)", + " Body-fixed bases fep 1,ep 2,ep 3g and feg 1,eg 2,eg 3g for the pinion and gear are adopted. The pinion translational and angular velocity vectors are _rp \u00bc _xpE1\u00fe _ypE2\u00fe _zpE3, xp \u00bc \u00bd _fp yp\u00f0 _bp\u00feOp\u00de e p 1\u00fe\u00bd _yp\u00fefp\u00f0 _bp\u00feOp\u00de e p 2\u00fe\u00bd _bp\u00feOp fp _yp e p 3, (1) where Op is the specified constant rotation speed of the pinion. The velocity vectors for the gear are identical except with components for the gear. The axial positions of the pinion bearings are measured along E3 by LA p (negative value as shown in Fig. 1(a)) and LB p (positive value). The bearing translational and angular displacement vectors are dA p \u00bc \u00bdyp\u00f0L A p ep\u00de\u00fexp E1\u00fe\u00bdfp\u00f0ep LA p\u00de\u00feyp E2\u00fezpE3, (2) dB p \u00bc \u00bdyp\u00f0L B p ep\u00de\u00fexp E1\u00fe\u00bdfp\u00f0ep LB p\u00de\u00feyp E2\u00fezpE3, (3) CA p \u00bcCB p \u00bcfpE1\u00feypE2\u00febpE3: (4) The bearings are isotropic in the E12E2 plane giving the stiffness matrix for translation as BA p \u00bc diag\u00bdkA p ,kA p ,kAz p , where the equality of stiffness in the two translation directions is evident. The bearing stiffness matrix for rotation is vA p \u00bc diag\u00bdkA p ,kA p ,kAz p . Similar definitions follow for the gear bearings. Distributed gear contact loads are approximated by a discretization scheme [16], similar to a slicing method. The nominal contact lines for no mesh deflection are discretized into n segments with stiffness ki, i\u00bc1,y,n. The discretization of a contact line is shown in Fig. 1(c). Fig. 1(a) and (b) describe the relevant geometry. The radial and axial positions of contact at the center of each segment are, respectively, bi measured from the pinion mass center along E1 (with negative value as shown) and ci measured along E3. The mesh deflection vector at a contact point i is the difference between the position vectors of the contact points on the pinion rpinion i and gear rgear i . The projection of the mesh deflection vector along the tooth surface normal n\u00bc \u00f0cos c,0,sin c\u00de gives the compressive deflection di \u00bc \u00f0r gear i rpinion i \u00de n" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure2.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure2.7-1.png", + "caption": "Figure 2.7.1 Path angle and path radius.", + "texts": [ + " The path shape is defined by the parametric three-dimensional form Road Geometry 53 X X\u00f0s\u00de; Y Y\u00f0s\u00de; Z Z\u00f0s\u00de where (X,Y,Z) are Earth-fixed axes. Much vehicle dynamic analysis is performed in two dimensions, effectively on a flat plane (X,Y). In these two dimensions (road plan view), it is often convenient to express the path shape by Y Y\u00f0X\u00de, that is, Y as a function of X. The path radius of curvature is also dependent on the path position, RP RP\u00f0s\u00de and the path curvature itself is kP kP\u00f0s\u00de \u00bc 1 RP \u00f02:7:1\u00de The path angle n (nu) is defined in Figure 2.7.1. Hence, dX ds \u00bc cos n; dY ds \u00bc sin n; dY dX \u00bc tan n Also n \u00bc atan dY dX but thismust be evaluated into the correct quadrant (BASICAngle(dx,dy), FORTRANAtan2(dy,dx) functions, not the common single-argument Atan(dy/dx) functions). The path curvature and angle are related by kP \u00bc 1 RP \u00bc dn ds \u00f02:7:2\u00de that is, the path curvature is the first spatial derivative of path angle (with the angle expressed in radians, of course). The rate of change of path curvature with path length is the path turn-in tP, expressed by tP dkP ds d ds 1 RP d2n ds2 \u00f02:7:3\u00de 54 Suspension Geometry and Computation Hence the local path parameters include path angle n, path curvature rP and path turn-in tP, with kP \u00bc dn ds tP \u00bc dkP ds \u00bc d2n ds2 \u00f02:7:4\u00de The units arem 1 or rad/m for curvature andm 2 or rad/m2 for turn-in (spatial rate of change of curvature)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003207_s00170-016-9445-z-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003207_s00170-016-9445-z-Figure4-1.png", + "caption": "Fig. 4 Heat source model. a Diagram of heat source. b Finite element model of heat source", + "texts": [ + "00 0.25\u20130.45 Bal. FeCrNiCu 14.05\u201315.10 4.21\u20134.53 4.41\u223c4.45 0.07\u223c0.12 1.20\u223c1.51 0.60\u223c0.72 0.12\u20130.22 Bal. temperatures. Temperature-dependent material properties are given in Table. 3 based on the experiment test. In thermal analysis, the reasonable heat source model can improve simulation precision. In this paper, a Gauss distribution heat sourcemodel which suits for thin-wall impeller blade was chose. The governing equations are shown in Eqs. (1) and (2) [16]. The diagrammatic drawing is shown in Fig. 4a, and FE model of heat source simulated by ANSYS is shown in Fig. 4b. q r; z\u00f0 \u00de \u00bc \u03b7Qe3 \u03c0zi e3\u22121\u00f0 \u00de r2e \u00fe reri \u00fe r2i exp \u2212 3r2 r20 \u00f01\u00de r0 z\u00f0 \u00de \u00bc f z\u00f0 \u00de \u00bc re\u2212 z\u2212ze\u00f0 \u00de zi\u2212ze re\u2212ri\u00f0 \u00de \u00f02\u00de where q(r, z) is heat flux, \u03b7 is average absorptivity of laser cladding material, Q is heat input power, r is heating radius, and z is heat source longitude. During the laser cladding process, the elastic stress-strain relationship of the material is assumed to obey isotropic Hooke\u2019s law. Total strain increment (\u0394\u03b5) can be decomposed into five components, which are elastic (\u0394\u03b5eij ), plastic (\u0394\u03b5pij ), thermal loading (\u0394\u03b5tij ), volumetric change, and transformation plasticity [17]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002996_lra.2017.2654546-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002996_lra.2017.2654546-Figure2-1.png", + "caption": "Fig. 2. The helical robot (inset) is contained inside a catheter (diameter Dch) segment between two rotating permanent magnets (magnetization M). Rotation of the permanent magnets generates a rotating field (B) that exerts a magnetic torque on the dipole of the robot (m). The robot consists of a cylindrical NdFeB magnet with diameter rx, hight ryz , and tail length l.", + "texts": [ + " Second, we control the motion of the robot inside the segments towards clots and compare the removal rate of the rubbing to dissolution rate of lysis using a thrombolytic agent (streptokinase), and investigate the optimal rubbing frequency to achieve maximum removal rate of the clot. The remainder of this paper is organized as follows: Section II provides modeling of the propulsion and the rubbing behaviour against clot. The influence of the lysis and rubbing on the removal of clots is experimentally investigated in Section III. Finally, Section IV concludes and provides directions for future work. The actuation mechanism of the helical robots is based on two rotating permanent magnets placed parallel to a cylindrical catheter segment (Fig. 2) [19]. This segment contains the robot, and is filled with a medium (phosphate buffered saline) with higher viscosity than blood to approach the low Reynolds numbers (< 10\u22122) achieved by microrobots. We calculate the corresponding field and field gradient based on the analysis presented in [20] and [21], and formulate scalar potential for the rotating cylindrical magnets, \u03a6m(r, \u03b8, z). Using the assumptions of azimuthal symmetry, i.e., \u03b8=0, and uniform polarization with respect to radial position, the potential is approximated at the robot position (r) as follows: \u03a6m(r, \u03b8, z) = 1 4\u03c0 \u222b V \u2207 \u00b7M | r\u2212 \u03c1 | dV, (1) where M is the magnetization vector of the permanent magnet, \u03c1 is a position vector to be integrated over the volume of the permanent magnet, and dV signifies the infinitesimal increment in the volume", + " Once the magnetic field (B) is calculated for the two permanent magnets, the magnetic force (Fm) and magnetic torque (Tm) exerted on the robot are calculated using( Fm Tm ) = ( (m \u00b7 \u2207)(R1B1 +R2B2) m\u00d7 (R1B1 +R2B2) ) . (3) In (3), m is the total magnetization vector of the robot, and R1 and R2 are the rotation matrices from frames of the first and second permanent magnets to the frame of the robot, respectively. Further, B1 and B2 are the magnetic fields of the first and second permanent magnets, respectively. The configuration of the rotating permanent magnets (Fig. 2) enables us to apply pure magnetic torque on the robot (when the robot is located at the common centers of the rotating permanent magnets along x-axis) [19]. Any deviation in the position of the robot along x-axis will result in a magnetic force that will contribute to the propulsion force. We calculate the Reynolds number as Re = \u03c1|v|L \u00b5 = 0.089, where \u03c1 is the density of the fluid (995 kg.m\u22123), v is the velocity of the robot before rubbing (20\u00d710\u22123 m.s\u22121) and L is its length (4\u00d710\u22123 m), and \u00b5 is the dynamic viscosity of the fluid (0", + " Furthermore, formation of fluid channels inside the clot is observed after approximately 20 minutes of streptokinase injection. The average dissolution rate is - 0.17\u00b10.032 mm3/min (n=6). Now we turn our attention to the influence of the mechanical rubbing on the removal rate of the blood clot (Fig. 6). The helical robot is propelled along x-axis towards the clot and against similar flow rate to that used in the chemical lysis experiments (10 ml/hr). Two rotating magnets (R750F, Amazing Magnets LLC, California, U.S.A) are used to actuate the robot, as shown in Fig. 2. Each permanent magnet (NdFeB) has diameter and length of 19 mm and 19 mm, respectively, with axial magnetization. The permanent magnet generates magnetic field of 0.552 T on its surface. The two permanent magnets are rotated and the linear speed of the robot is measured to be 15 mm/s, at frequency of 35 Hz. The step-out frequency of the robot is experimentally measured to be 67.3 Hz, and we observe a linear increase of the swimming speed versus the angular frequency of the rotating permanent magnets within this range" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001442_msf.783-786.898-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001442_msf.783-786.898-Figure1-1.png", + "caption": "Fig. 1. Schematic representation of the various orientations of the tensile samples with respect to the building direction (oz).", + "texts": [ + " No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 152.14.136.77, NCSU North Carolina State University, Raleigh, USA-10/04/15,19:57:47) Samples for tensile testing were produced using a MTT SLM 250 laser melting deposition manufacturing system, in an argon purged production chamber, and following three different orientations ox, oy and oz with respect to the building direction (oz), as illustrated in Fig. 1. All samples were processed simultaneously, as parts of one single job, and the processing parameters were kept constant i.e. a laser power of 175 W, a travel speed of 700 mm/s, a focus offset of 1 mm and a powder layer thickness of 60 \u00b5m. The nominal chemical composition of the AISI 316L stainless steel powder was as follows (weight %): Cr \u2013 17.3, Ni \u2013 10.9, Mo \u2013 2.3, Mn \u2013 1.39, Si \u2013 0.46, P \u2013 0.028, N \u2013 0.031, Fe-bal. The substrate was not preheated. Samples for metallographical examinations were embedded in resin and polished following standard practices", + " These grains are elongated following the building direction. Comparison with the optical micrograph of Fig. 4(a) shows that these elongated grains cross over several adjacent melt pools, thus confirming that solidification occurred to some extent through a process of epitaxial growth. Mechanical properties are summarised in Fig. 5 that shows the average values of the yield stress, the ultimate tensile strength and the maximum uniform elongation obtained for the three different processing orientations (Fig. 1). These mechanical properties exhibit a strong anisotropy with respect to the building direction (oz). Samples processed in the ox and oy directions, on the one hand, exhibit very similar properties, along with a typical ductile fracture behaviour. Samples processed with the oz orientation, on the other hand, exhibit significantly lower strengths and elongations. The deterioration of the mechanical properties in the oz samples can be ascribed to their greater volume fraction of defects (Fig. 2(b)), that exhibit moreover a very detrimental orientation (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002162_s10846-013-9813-y-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002162_s10846-013-9813-y-Figure10-1.png", + "caption": "Fig. 10 Avionic components: a main control board with ARM microcontroller, b AHRS, c ultrasonic, d zig-bee receiver/transmitter, e radio control, f brushless DC motor", + "texts": [ + " The control signals are calculated according to the introduced control scheme, and then speed commands are given to the brushless DC motor drivers in PWM form. All sensors data, input commands, and state of controller are stored in the micro-SD RAM for analysis and fault detection after probable crashes. Also, all data are sent to the base station through a wireless network (IEEE 802.11). The base-station is implemented on a PC at core2Due 2.5 GHz with a 3 GB RAM. The system is monitored by a simple Matlab software. The components of avionic system, which are shown in Fig. 10, are as follows; STM32F103RB microcontroller is chosen as flight computer of our quadrotor. It incorporates high performance ARM Cortex-M3 32-bit RISC core operating at a 72 MHz maximum frequency (for our purpose 16 MHz is enough.), high speed embedded memories, an extensive range of enhanced I/Os and peripherals connected to two APB buses, two 12-bit ADCs, and 7 timers plus 9 communication interfaces (I2C, USART, SPI, CAN, USB). This choice enables us to extend the system in a simple way for advanced missions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002976_j.promfg.2015.09.042-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002976_j.promfg.2015.09.042-Figure2-1.png", + "caption": "Fig. 2 Temperature field in the cross-section of laser scanning track.", + "texts": [ + " The laser scanning is symmetric with respect to X-Z plane to decrease the computational time. The initial temperature of powder and substrate is 20 \u00b0C. The powder material was heated by a moving surface heat flux with Gaussian distribution. One single track was scanned to obtain a continuous molten pool. When the molten pool became stable i.e. no dimensional changes in width, depth, and length was observed; the temperature field on the cross-section of the stabilized molten pool was recorded, as shown in Fig. 2. An equivalent heat input was developed from the temperature field and applied to the subsequent meso-scale hatching layer to predict local residual stress. Every point at the same relative spatial location on the cross-section of melt pool along the scanning direction experiences similar temperature history, it is reasonable to extend the molten pool cross-section temperature field to the whole scan track. 3.2 Residual stress field in meso-scale hatch layer In the meso-scale hatch layer, a coupled thermal-mechanical analysis was conducted to predict the local residual stress distribution" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure10.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure10.7-1.png", + "caption": "Fig. 10.7 Waves of magnetic field strength and flux based on the non-linear theory.", + "texts": [ + " fd 2Bs~ d~ Bs d Ho =Hmo sm wI = Jdx = -- \u2022 - = _ . _ (~2) o P dl P dt (10.15) Integrating Eqn. (10.15) and using the boundary conditions of Eqn. (W.14) 2 pHmO ~ =-- (l - cos wt) wBs and wBs Thus ~ = 5 sin(wt/2) over the period Olm = 2wm = v'(8HmoBswp) 1 is the effective flux for unit axial length of the machine (direction z in Fig. 10.6) from which the impedance at any frequency can be found. The result differs from that given by the linear theory in two important respects, (a) The magnitude of 1 m varies as v' Hm 0 and so introduces a non-linear relationship" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001304_j.cirp.2010.03.026-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001304_j.cirp.2010.03.026-Figure2-1.png", + "caption": "Fig. 2. Loads acting on a ball.", + "texts": [ + " In order to determine angles ai, ao more precisely, the simplifying assumption (7) is replaced with relationships connecting these angles with Hertzian deformations in contact points of a ball with raceways. Such approach is presented in paper [11,12] for modelling of a general equilibrium case, described by systems of five equations for a ball and rings. The continuation of such approach can be found in papers [4,14]. The relationship between angles and a deformation is also utilised in a model presented in the paper [13] and [9], reduced to two equilibrium equations. Fig. 2 shows the entire system of forces and moments acting on a ball, as well as a force polygon ensuring the state of equilibrium for a ball. Centrifugal force FC is decomposed to two components: FN in the normal direction and FP in the direction defined by tangents in points of contact with raceways. FN \u00bc FC cos\u00f0\u00f0ai \u00fe ao\u00de=2\u00de cos\u00f0\u00f0ai ao\u00de=2\u00de (8) FP \u00bc FC sin ao cos\u00f0\u00f0ai ao\u00de=2\u00de (9) This makes it possible to describe unequivocally the influence of a centrifugal force. Component FP pushes the ball onto both raceways with force FP/2 sin g, while component FN additionally increases the load of the outer raceway. In this way a simple relationship between pressure values Qo and Qi has been obtained, shown in Fig. 2. Force equilibrium in bearing rings preloaded with a force Fa is shown in Fig. 3. Force acting on the inner ring is counterbalanced by two reaction forces Ri and Ra. The outer ring is kept in equilibrium by: reaction force Ro, preload force Fa and force component To caused by the gyroscopic moment Mg on a ball. In bearings preloaded by means of a spring, force To cos ao is responsible for axial displacements of the outer ring as a self-acting increase of spring force to the value of Fa + To cos ao", + " In case of high friction coefficients, To results directly from the gyroscopic moment. This is decided by a commonly known relationship. Qo \u00fe Q i > 2Mg mD (11) In the presented model it was assumed that, during work, bearing rings keep the parallelism of their axial and radial axes. This made it possible, similarly as in paper [13], to limit the amount of equations from five to two. First of the equations is a commonly known relationship for the equilibrium of forces acting on a ball in radial direction, resulting from the force polygon shown in Fig. 2. Qo cosao Mg D sin ao Q i cos ai \u00fe Mg D sin ai FC \u00bc 0 (12) For the needs of the model it was assumed that the changes of ball position take place while rings remain stationary. Relative movements of this rings, e.g. in solutions with a spring, are possible only after fulfilling force equilibrium conditions in a bearing. Component FP of the centrifugal force FC is responsible for the movement of a ball. It applies identical load of FP/2 sin g to both raceways, forcing the values of angles ao, ai, indispensable for the equilibrium of forces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001909_s00170-013-5449-0-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001909_s00170-013-5449-0-Figure2-1.png", + "caption": "Fig. 2 Process followed in the fabrication of multi-material components using the EBM system", + "texts": [ + " Similarly, tubular copper\u2013titanium joints formed by electrohydropulse have been fabricated to operate as cathode current leads in electrolyzers that are able to withstand a combination of harsh chemical environments and high temperatures [22, 23]. Commercial titanium-clad copper electrodes are available from Anomet Products Inc., USA for various industrial uses including electroplating, chemical processing and recovery of metals. 2.3 Multi-material part fabrication As described previously, the Arcam A2 EBM system is designed to process only one material at a time. A method was implemented to fabricate multi-material parts using discrete runs of the EBM system. The process steps (Fig. 2) for this new method are (1) EBM fabrication and cleaning of bottom halves made of Ti\u20136Al\u20134V; (2) fabrication of copper mask plate using CNC machining; (3) setup of copper mask start plate with the inserted Ti\u20136Al\u20134V components fabricated in the first step; (4) EBM fabrication of upper halves using copper; and (5) cleanup of finished multi-material parts. Specifically, Step 1 consisted of fabricating the bottom halves of the components with their long axis in the X and Z directions and using the material with the highest melting temperature, Ti\u20136Al\u20134V", + " Based on the recorded measurements, the openings in the mask start plate were made with undersized dimensions of 13 \u03bcm and a tolerance of \u00b113 \u03bcm (0.0005 in. in all directions to obtain a press fit of the Ti\u20136Al\u20134V parts, as it is common practice in the fitting of machine alignment components such as metal dowel pins [24]. One of the circular openings in the mask plate was machined to coincide with the geometric center of the plate. This not only offered a fitting place for one of the inserts but also served as a reference for centering the electron beam during the setup. A schematic of the machined mask start plate is shown in Step 2 of Fig. 2. 2.5 Mask plate thermal expansion One concern of the building process described in Section 2.3 was that the Ti\u20136Al\u20134V components would not remain fixed to the copper mask start plate during the copper build because there was a mismatch in coefficient of thermal expansion. Even though powder underneath the mask start plate provided support for the Ti\u20136Al\u20134V inserts, thermal expansion of the openings in the mask start plate could loosen the inserts, allowing them to move and preventing appropriate fabrication" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003253_j.ijfatigue.2019.105236-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003253_j.ijfatigue.2019.105236-Figure2-1.png", + "caption": "Fig. 2. Schematic of substrate and coupons with (a) grind-out and (b) deposit and coupon inlayed.", + "texts": [ + "34 g/min with helium used as the carrier gas and argon as the shielding gas, at 10 L/min and 16 L/min respectively. A 0.8mm grind-out was machined on a flat Ti-6Al-4V substrate, which was subsequently laser deposited with Ti-6Al-4V powder to fill over the grind-out. The top surface of the substrate including the laser deposit layer was machined by 0.2mm to result in a 0.6 mm final grind- out depth to represent a 10% grind-out. A schematic of the substrate, deposit and coupon with the grind-out is shown in Fig. 2. To investigate the effect of the different deposition strategies on the mechanical properties in laser deposit Ti-6Al-4V, two different specimen variations were built as outlined in Table 2. The thermal history of the substrate and deposit area was measured using a FLIR A615 microbolometer. The FLIR A615 has three different temperature ranges that can be measured. For the interest of the final cooling rate, the temperature range set for the FLIR A615 in this investigation was 300\u20132000 \u00b0C. The maximum frame rate of 200 frames per second was used to record the temperature history" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure12.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure12.10-1.png", + "caption": "Figure 12.10 illustrates a 4R planar manipulator with the DH coordinate frames set up for each link . Assume the end-effector force system applied to the environment is measured as", + "texts": [], + "surrounding_texts": [ + "(12.277)\n546 12. Robot Dynamics\nby\n[\nai ]. di sinai .td - i-I i - d, cos ai\n1\nThe backward recursive equations (12.266) and (12.267) allow us to start with a known force system (Fn , M n) at B n, applied from the end-effector to the environment, and calculate the force system at Bn - I .\nOF _ '\" ofn L...J en \u00b0Mn - L OMen + n_~dn X \u00b0Fn\n(12.278)\n(12.279)\nFollowing the same procedure and calculating force system at proximal end by having the force system at distal end of each link, ends up to the force system at the base. In this procedure, the force system applied by the end-effector to the environment is assumed to be known.\nIt is also possible to rearrange the static Equations (12.269) and (12.270) into a forward recursive form\n\u00b0Fi _ 1 +L \u00b0Fei\noM '\" oM \u00b0 of \u00b0 ofi-I + L...J e, + ni X i-I - mi X i \u00b7\n(12.280)\n(12.281)\nTransforming the Euler equation from C, to O, simplifies the forward re cursive equations into the more practical equations\n\u00b0Fi _ 1 + L ofe, \u00b0Mi_ 1 + L \u00b0Mei - i_Pdi X \u00b0Fi_ l .\n(12.282)\n(12.283)\nUsing the forward recursive Equations (12.282) and (12.283) we can start with a known force system (F \u00b0 , M o) at Bo, applied from the base to the link (1), and calculate the force system at B I .\n\u00b0Fo + L \u00b0Fe 1 \u00b0Mo + L \u00b0Me 1 - \u00b0dl X \u00b0Fo\n(12.284)\n(12.285)\nFollowing this procedure and calculating force system at the distal end by having the force system at the proximal end of each link, ends up at the force system applied to the environment by the end-effector. In this procedure, the force system applied by the base actuators to the first link is assumed to be known. \u2022\nExample 292 Statics of a 4R planar manipulator.", + "12. Robot Dynamics 547\nThe manipulator consist s of four RIIR(O) links, therefore their transforma tion matrices i-1Ti are of class (5.32) that because d; = 0 and ai = li, simplifies to\n-sinBi 0 cosBi 0\no 1 o 0\ni, cosBi ] l, sin Bi\n~ . (12.288)", + "548 12. Robot Dynamics\nThe CM position vectors i r i and the relative position vectors i_ pd i are\n(12.289)\n(12.290)\nand therefore,\n(12.291)\n(12.292)\nwhere\nTh e static force at joints 3, 2, and 1 are\n\u00b0F 3 \u00b0F4 - L \u00b0Fe4\n\u00b0F 4 + m4g0jo\n[ ~: ] +m'9 [n [ F,~m49 ]\n(12.293)\n(12.294)\n(12.295)" + ] + }, + { + "image_filename": "designv10_3_0001749_978-3-319-10795-0_4-Figure4.19-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001749_978-3-319-10795-0_4-Figure4.19-1.png", + "caption": "Fig. 4.19 The input force u = F and the output y = x1", + "texts": [], + "surrounding_texts": [ + "Working on hopping [24] juggling [25] etc. illustrates ways in which discontinuous dynamical systems can arise in control and are suggestive of the type of system that can be modelled as hybrid switching systems. However, these applications sometimes involve other complications and for that reason it seems to be worthwhile to consider some simple problems from mechanics that nicely illustrates the depth and breadth of effects what one can expect from this particular class of hybrid systems. To do this, the considered application in this paper is a spring-mass-friction system. The stiction phenomenon, due to the presence of friction force is common in many mechanical systems. The friction force between two surfaces is tied to their instantaneous relative velocity. The continuous trajectory of velocity and position is subject to abrupt changes in acceleration, however, corresponding to transition between the discrete states \u201cstuck\u201d and \u201csliding\u201d. Let us consider the following mechanical spring-mass-friction system [26] which consists in a block sliding surface and compressing a spring under the influence of a user designated input force (Fig. 4.11). In the absence of friction, this behaves like a classical spring-mass system with the study state position proportional to the applied force. When friction between block and surface is taken into account, it tends to resist to the motion. The friction force changes with velocity and tends to be greatest when stationary. This results in a motion with alternately \u201csticks\u201d and \u201cslips\u201d as the overall force balance requires. The equation of motion is Mx\u0308 = F \u2212 Fspring \u2212 Ffriction choosing x = x1 as the position, x\u0307 = x2 is the velocity and x\u0308 = x\u03072 is the acceleration, the system can be written as \u23a7\u23a8 \u23a9 x\u03071 = x2 x\u03072 = 1 M ( F \u2212 Fspring \u2212 Ffriction ) = fq(x1, x2) q = {1, 2, 3} where M is the block mass, F is the input force. The force operated by the spring is given by Fspring = K x with K , the spring rate. The following logic determines Fstationary = F \u2212 Fspring = FsumT ., the instantaneous force such that x\u0307 = 0. Whenever the velocity is nonzero, an impulsive force would be needed to make it zero instantaneously. This always exceeds the capacity, Fsliding, so the latter magnitude is used. When the velocity is already zero, however, Fstationary is the force which maintains this condition by making the acceleration zero. The friction force Ffriction is given as follows: Ffriction = \u23a7\u23a8 \u23a9 sign(x2)Fsliding, x2 = 0 Fsum, |Fsum| < Fstatic, x2 = 0 sign(Fsum)Fstatic, |Fsum| \u2265 Fstatic, x2 = 0 with Fsum = F \u2212 K x1, and Fstatic = Fsliding = 1 N, The observer is designed as follows: { \u02d9\u0302x1 = x\u03022 + \u03bb1 \u2223\u2223x1 \u2212 x\u03021 \u2223\u22231/2 sign(x1 \u2212 x\u03021)\u02d9\u0302x2 = fq(x1, x\u03032) + \u03b11 sign(x1 \u2212 x\u03021) if \u03c3q(x) is verified q = 1, 2, 3. x\u03032 = x\u03022 + \u03bb1 \u2223\u2223x1 \u2212 x\u03021 \u2223\u22231/2 sign(x1 \u2212 x\u03021) sign(e) = \u23a7\u23a8 \u23a9 +1 if e > 0 \u22121 if e < 0 \u2208 [\u22121, 1] if e = 0 Case 1 Simulations were done using the following default parameters: M = 0.001 Kg, K = 1 N/m, Fstatic = 1 N, Fsliding = 1 N. The input force ramps linearly from zero to 5 N and back to zero, with a period of 5 s. The initial conditions are (x10, x20) = (0, 0), while those of the observer are equal to (x\u030210, x\u030220) = (\u22121, 1). In this case, the natural frequency of the system is given by wn =\u221a K M =31.6 rad/s, and both the static Fstatic and sliding Fsliding forces are equal as illustrated in Fig. 4.12. Figures 4.13, 4.14, 4.15, 4.16 and 4.17 illustrate the simulation results. \u2022 In Fig. 4.13, we see that x\u03021 and x\u03022 reaches x1 and x2 respectively in finite time. In fact, a zoom of the error dynamic given in Fig. 4.14 confirms the above result and shows the convergence of e towards zero. \u2022 Fig. 4.15, depicts the time histories of the input force and the resulting position x1of the mass. The input force F must exceed that of static friction in order to begin motion at t = 1. For t \u2208]1s, 5s[, the position tracks the spring force less the kinematic friction force, with small oscillations showing changes in velocity at the natural frequency wn . The input force begins to decrease. The mass immediately comes to a halt and sticks until t = 7. When the input force again exceeds the static friction force, the same movement occur in the inverse direction. \u2022 In Fig. 4.16, one can remark the good results of the identification of the discrete location q and its estimation q\u0303 note qobs in the figure. The discrete location takes values 1, 2, or 3 whether the system is in movement or not and depending on the friction force value. We notice that the system gives a good estimation, except in the transient part where the observer did not converge yet. It is thus important to ensure that the observer must be as fastest as possible. \u2022 In Fig. 4.17, we represent the discrete location q with the switching functions conditions with the friction force Ffriction. One can easily verify the correspondence with the physical behavior of the considered mechanical system with the switching conditions defined by the velocity and the considered friction force values. Case 2 Simulation were done using the following parameters: M = 0.1 Kg, K = 1 N/m, Fstatic = 1 N, Fsliding = 0.14 N. In this case, the static Fstatic and sliding Fsliding forces are not equal and the friction force Ffriction is represented in Fig. 4.18. As in the previous case, Figs. 4.19, 4.20, 4.21, 4.22, and 4.23 illustrate the simulation results. With kinetic friction lower in magnitude than static friction, abrupt discontinuities in acceleration occur at the stuck-to sliding and sliding to stuck state transition. As the velocity reaches zero, the acceleration is often nonzero. If the stuck state in entered, however, the acceleration becomes zero immediately.This highly nonlinear behavior is typical in many systems, making it difficult to precisely control and observer position and velocity design. In this case, also both continuous and discrete observer give good performances and despite the new condition on the static Fstatic and sliding Fsliding forces, the convergence remains ensured and the discrete location well estimated. Thus, one can conclude that in both cases, the hybrid observer works correctly and gives a satisfactory results." + ] + }, + { + "image_filename": "designv10_3_0000888_0278364908091365-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000888_0278364908091365-Figure3-1.png", + "caption": "Fig. 3. Two-dimensional seven-link realistic walking model: (a) the model parameters, the actual parameter values are given in Table 1 (b) the degrees of freedom of the model, the knee of the stance leg is locked which takes away one degree of freedom.", + "texts": [ + " Again, the torque in the stance ankle a st is a controller output, according to the various actuation schemes that are researched in following sections. Depending on the magnitude of the stance ankle torque the heel of the stance foot might lift during the single stance phase. The single stance phase ends when the heel of the swing leg touches the ground at which point the walker goes back into double stance phase and a second step is started. A more realistic model of a walker is the seven-link model depicted in Figure 3. It is modeled after the prototype that is also used in this study and it consists of an upper body, two upper legs, two lower legs and two feet. In the knee joint there is a hyperextension stop and a latching mechanism. The latch is released at the start of the swing phase and locks the knee joint in the stretched position at the end of the swing phase and throughout stance. Owing to this mechanism, there is a maximum number of six degrees of freedom in this model at any instant during gait. The unilateral constraints between the foot and the floor as well as the hyperextension stop in the knee are modeled as rigid constraints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001310_j.ins.2013.12.026-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001310_j.ins.2013.12.026-Figure5-1.png", + "caption": "Fig. 5. Half-car suspension model.", + "texts": [ + " 4c shows the estimated nonlinear function f\u0302 \u00f0g\u0302; h\u00de \u00bc hTw\u00f0g\u0302\u00de with the actual nonlinear function f \u00f0x;u\u00de: It is worth noting that f \u00f0x;u\u00de is only used for simulation purposes, since it is not known by the observer. The norm of the fuzzy parameters is shown in Fig. 4d. Fig. 4a and b clearly show that the observation error is actually vanishing according to the observer dynamics. The parameter adaptation alertness is particularly emphasized in Fig. 4c which shows the estimated function f\u0302 \u00f0g\u0302; h\u00de as well as the actual function f \u00f0x;u\u00de: Example 2. The model of half-car suspension is shown in Fig. 5 [19]. The half-vehicle suspension model is represented by a nonlinear four degree-of-freedom system. It consists in a single sprung mass (car body) connected to two unsprung masses (front and rear wheels) at each corner. The sprung mass is free to heave and pitch, while the unsprung masses are free to bounce vertically with respect to the sprung mass. The suspensions between the sprung mass and unsprung masses are modelled as linear viscous dampers and spring elements, while the tires are modelled as simple linear springs without damping" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001180_tim.2011.2159322-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001180_tim.2011.2159322-Figure2-1.png", + "caption": "Fig. 2. Microphone array for detecting a sound source.", + "texts": [ + " The algorithm for estimating the coordinates of the sound source using three microphones and the arrival time difference among them is described as follows. The received signal by the ith microphone at time tj is denoted as mi(tj) which is composed of the signal and the noise components and is represented as mi(tj) = si(tj) + ni(tj) (1) where si(tj) represents the signal arriving at the ith microphone from the sound source and ni(tj) represents the noise component to the microphone. In this paper, the wind and the bird\u2019s singing are prefiltered so as not to cause unstable operation in the mobile robot. There are three microphones in Fig. 2, namely, M1, M2, and M3, used to receive the sound source S, which are located in a line with the same interval: l12 = l23 = 15 cm. The distances between the sound source and the microphones are represented as d1, d2, and d3. The spacing between the microphones is fixed as 15 cm, which is heuristically determined to provide a high accuracy in measuring distances about 2\u20134 m to the arcing noise source [11]. \u03b8M1 , \u03b8M2 , and \u03b8M3 represent the angles from the microphones to the sound source. The distance from the microphone to the sound source, di, can be represented as di = ti \u00b7 vel (2) where ti represents the time from the sound source to the ith microphone and vel represents the propagation speed of the sound signal at room temperature(= 340 m/s)", + " The denominator normalizes the amplitudes of the two signals by dividing the standard deviations of the two signals. The phase difference between the two signals is converted to the time difference as \u0394tij = \u0394nij \u00d7 cycle (5) where \u0394nij is the phase difference when there is the maximum similarity between the two signals and cycle represents the sampling time of the analog-to-digital (A/D) converter [23] (in the real experiments, cycle = 18.8679 \u03bcs). The m1(n), m2(n), and m3(n) represent the sound signals received at the three microphones M1, M2, and M3 shown in Fig. 2, respectively. The vertical axis is the amplitude of the signal, and the horizontal axis represents the collected time of the signal. To obtain a highly reliable \u0394n12 value, 2000 sets of data are collected and divided into four areas. Therefore, the length of sequence N is set to 500. Notice that the length of the sequence directly affects the processing time for the cross-correlation algorithm, which is carefully considered in the selection of the length. In order to improve the reliability, the four phase differences obtained in the four regions are averaged arithmetically as \u0394nij = \u0394nij,A + \u0394nij,B + \u0394nij,C + \u0394nij,D 4 (6) where \u0394nij,A represents \u0394nij in region A", + " Through the real experiments, it is concluded that the computation time for \u0394nij using four divided blocks and taking the average is shorter than the computation for the whole block at once, along with the reliability being higher than that for the single block operation. Distance Measurement in 2-D Space: The distances between the sound source and the microphones are designated as d1, d2, and d3. From (2) and (3), they can be represented as d1 = vel \u00b7 t1 (7.a) d2 = d1 + vel \u00b7 \u0394t12 (7.b) d3 = d1 + vel \u00b7 \u0394t13. (7.c) When the three microphones are aligned on the line with equal distance (in Fig. 2, l12 = l23), the Pappus centroid theorem provides the following relation: d2 1 + d2 3 = 2 ( d2 2 + l212 ) . (8) Plugging (8) into (7) and deriving for d1 result in d1 = 2 \u00b7 l212 + 2 \u00b7 \u0394d2 12 \u2212 \u0394d2 13 D1 (9) where D1 and \u0394dij are D1 = 2 \u00b7 vel \u00b7 (\u0394t13 \u2212 2 \u00b7 \u0394t12) (10.a) \u0394dij = vel \u00b7 \u0394tij . (10.b) The d1 in (9) represents the distance to the first microphone from the faulty insulator radiating the sound signal. The same procedures are applied for (7.b) and (7.c), so the distances to the second and third microphones are d2 = 2 \u00b7 l212\u22122 \u00b7 \u0394d2 12\u2212\u0394d2 13+2 \u00b7 vel2 \u00b7 \u0394t12 \u00b7 \u0394t13 D1 (11.a) d3 = 2 \u00b7 l212+2 \u00b7 \u0394d2 12+\u0394d2 13\u22124 \u00b7 vel2 \u00b7 \u0394t12 \u00b7 \u0394t13 D1 . (11.b) With the measured distances, the angles to the sound source from the microphones can be also obtained. Fig. 2 illustrates the cosine laws used to obtain the angle from the microphone to the sound source using the triangle \u0394SM1M2. The angle to the first microphone from the sound source \u03b8M1 can be obtained as \u03b8M1 = cos\u22121 d2 1 + l212 \u2212 d2 2 2d1l12 . (12.a) The same procedures are applied for the second and third microphones; the angles are obtained as \u03b8M2 = cos\u22121 d2 2 + l212 \u2212 d2 1 2d2l12 (12.b) \u03b8M3 = cos\u22121 d2 3 + l223 \u2212 d2 2 2d3l23 . (12.c) The inspection robot moves along the overhead ground wire on the top of the electric pole while it is inspecting the insulators and power transmission wires located below the overhead ground wire. Therefore, the angles to the insulators become less than 90\u25e6 since the insulators are on the electric pole as shown in Fig. 4. As shown in Fig. 2, the triangle \u0394SM1M2 is divided into two triangles, and the locations of the three microphones are represented as M1 = (0, 0), M2 = (l12, 0), and M3 = (l12 + l23, 0), respectively, w.r.t. M1. When the coordinates of the sound source is S = (a, b), the Pythagorean theorem provides two equations from the two triangles as a2 + b2 = d2 1 (13.a) (l12 \u2212 a)2 + b2 = d2 2. (13.b) Using these two equations, the coordinates of the sound source S(a, b) can be obtained as S = \u239b \u239dd2 1 \u2212 d2 2 + l212 2l12 , \u221a d2 1 \u2212 ( d2 1 \u2212 d2 2 + l212 2l12 )2 \u239e \u23a0 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure8.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure8.6-1.png", + "caption": "Figure 8.6 illustrates the coordinate frames and velocity vectors of a rigid link (i) . Find", + "texts": [], + "surrounding_texts": [ + "372 8. Velocity Kinematics\n3. Spherical wrist velocity kinematics.\nAssume that we attach a tools coordinate frame, with the following transformatio n matr ix, to the last coordinate frame B6 of a spher ical wrist.\nThe wrist transformation matrices are given in Exercise 3. Assume that the frame B3 is the base frame and find the translational and angular velocities of the tools coordinate frame B7 .\n5. SCARA manipulator velocity kinematics.\nAn RIIR!!RIIP SCARA manipulator is shown in Figure 5.27 with the following transformation matrices . Calculate the Jacobian matrix us ing the Jacobian-generat ing vector technique.\n[ 005B, - sin 8l 0 l,cooO, ]\n\u00b0T1 = sin 81 cos 81 0 h sin81\n0 0 1 0 0 0 0 1\n[ coon, - sin 82 0 l2cos82\n]'T, ~ Si1B2 cos82 0 l2sin 82\n0 1 0 0 0 1\n(8.179)\n(8.180)", + "8. Velocity Kinematics 373\nl cos(h sinB3 o o - sinB3 COSB3 o o\n(8.181)\n(8.182)\n6. Rf-RI IR articulated arm velocity kinematics.\nFigure 5.25 illustrates a 3 DOF Rf-RIIR manipulator with the follow ing transformation matrices. Find the Jacobian matrix using direct differentiating, Jacobian-generating vector methods.\n(a) velocity \"v, of the link at C, in terms of d, and di - l\n(b) angular velocity of the link \u00b0 Wi in terms of di and di - l\n(c) velocity \u00b0Vi of the link at C, in terms of proximal joint i velocity\n(d) velocity \"v, of the link at C, in terms of distal joint i +1 velocity\n(e) velocity of proximal joint i in terms of distal joint i + 1 velocity\n(f) velocity of distal joint i + 1 in terms of proximal joint i velocity\n8. * Jacobian of a PRRR manipulator.\nDetermine the Jacobian matrix for the manipulator shown in Figure 6.5.", + "374 8. Velocity Kinematics\n9. * Spherical robot velocity kinematics.\nA spherical manipulator Rf-Rf-P, equipped with a spherical wrist , is shown in Figure 5.26. The t ransformation matrices of the robot are given in Example 149. Solve the robot's forward and inverse velocity kinemati cs.\n10. * Space station remot e manipulator syst em velocity kinemat ics.\nThe transform ation matrices for the shut t le remote manipulator sys tem (SRMS) , shown in Figure 5.28, are given in the Example 153. Solve the velocity kinematics of the SRMS by calculat ing the Jaco bian matrix." + ] + }, + { + "image_filename": "designv10_3_0002742_s00170-017-0932-7-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002742_s00170-017-0932-7-Figure1-1.png", + "caption": "Fig. 1 The formation of the BCC-type lattice structures based on the feature points of a cube", + "texts": [ + " This section presented an analytical modelling approach that was developed to model the mechanical properties of two types of SLM-built Ti64 lattice structures and to estimate the stress distribution of these structures. The section first introduced the selection of topologies of the structure before presenting in detail the proposed analytical modelling method. Although BCC lattice structures are quite common in the design of SLM-produced lattice structures, few previous studies have explained the rationale of adopting this typical topology. A BCC unit cell may be obtained by connecting a set of feature points on a cube. As Fig. 1a\u2013c shows, the feature points in a cube are categorised as one body-centred point, eight peaks, eight face-centred points and 12 midpoints of 12 edges, as shown in Fig. 1. A strut is then obtained by connecting two feature points, which results in numerous unit cells. Due to the symmetry of the shape, it is reasonable to consider only one-eighth of the previous cube, which yields a new cube with eight peaks in this case, as shown in Fig. 1d. Thus, as Fig. 1e shows, the most complicated unit cells are obtained in cases where all eight feature points are connected to one another as possible struts. All the struts perpendicular to three axes are removed by considering the poor manufacturability of the cantilever beams, then this complicated unit cell is simplified to the more commonly seen BCC unit cell. The BCC lattice structures are obtained using a repeat-and-stack method, as shown in Fig. 1f, g. The BCC structures are isotropic following this process. The equivalent elastic modulus (E*) can then be calculated proximately as shown in Eq. (1), which was obtained based on the beam-theory method proposed in [28]: E* \u00bc 9 ffiffiffi 3 p E\u03c0 4 l . d 2 3\u00fe 8 l . d 2 \u00f01\u00de where E is the elastic modulus of the bulk material, and l and d represent the length and diameter of the strut, respectively. Equation (1) is rewritten as follows when l > > d: E* \u00bc CE d . l 4 \u00f02\u00de where C is a constant. In certain applications that require a large unidirectional bearing capability (which BCC structures cannot provide), some additional struts are superposed on a BCC unit cell to form a so-called unidirectional reinforced lattice structure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000875_j.ins.2011.01.040-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000875_j.ins.2011.01.040-Figure9-1.png", + "caption": "Fig. 9. The trajectories of u \u2018\u2018solid line\u2019\u2019 with p = 0.9, a = 4, d = 20 and u \u2018\u2018dash-dotted\u2019\u2019 with p = 0.9, a = 4, d = 18.", + "texts": [], + "surrounding_texts": [ + "Setting x1 \u00bc q; x2 \u00bc _q and u = s, then the above equation can be rewritten in the following state-space form, including external disturbances:\n_x1 \u00bc x2; _x2 \u00bc u 0:5mgl sin\u00f0x1\u00de\nM ;\ny \u00bc x1;\n\u00f069\u00de\nwhere m = 1 kg, M = 0.5 kg/m2, l = 1 m. Choosing fuzzy membership functions as\nlF1 i \u00f0xi\u00de \u00bc 1 1\u00fe exp\u00bd5 \u00f0xi \u00fe 0:6\u00de ; lF2 i \u00f0xi\u00de \u00bc exp\u00bd \u00f0xi \u00fe 0:4\u00de2 ; lF2 i \u00f0xi\u00de \u00bc exp\u00bd \u00f0xi \u00fe 0:2\u00de2 ; lF4 i \u00f0xi\u00de \u00bc exp x2 i ; lF5 i \u00f0xi\u00de \u00bc exp\u00bd \u00f0xi 0:4\u00de2 ;", + "Using our fuzzy adaptive control method to control (69), the simulation results are shown by Figs. 11\u201314 (solid lines). To further to illustrate the effectiveness of our control method, we apply the fuzzy adaptive control scheme in [31] to the system (69), where fuzzy logic systems and the initial conditions of the variables are chosen the same as our method, the", + "design parameter are chosen k1 = 80, k2 = 800, c1 = 0.5, c2 = 0.05 and qm = 1. The simulation results are also expressed Figs. 11\u201314 (dash-dotted).\nFigs. 11\u201314 show our control scheme can achieve the better control performances than the one in [31]. Moreover, comparing with these two control schemes, one can find that our control scheme has removed the restrictions that the controlled systems satisfy the strictly positive real condition (SPR) and the strict matching conditions imposed on [31].\nExample 3 [5]. Consider the electromechanical system shown by Fig. 15. The dynamics of the electromechanical system is described by the following equation.\nM\u20acq\u00fe B _q\u00fe N sin\u00f0q\u00de \u00bc I;\nL_I \u00bc Ve RI KB _q;\n( \u00f074\u00de" + ] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure6.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure6.12-1.png", + "caption": "Figure 6.12.1 A rigid axle with link location to the body has two location points which define the relative axis of rotation. This position and inclination angle of this axis gives the roll centre and the roll steer coefficient.", + "texts": [ + " This means a small static toe-in for undriven wheels, and a small toe-out for driven ones, so that when the vehicle is running normally the tractive forces and compliances act to bring the toe angles close to zero. Within the allowable band for low wear (a total range of about 1 ), there is only limited scope to use toe angles to tune the handling characteristics. Rigid rear axles can be considered in two groups: thosewith link location and thosewith longitudinal leaf springs. In the case of link location, there are lateral location points A and B according to the particular linkages, defining an axis of rotation of the axle relative to the body. Figure 6.12.1 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 line through the two points is the axis of rotation of the axle relative to the body. The roll centre lies on this line, at the point where it penetrates the transverse vertical 138 Suspension Geometry and Computation plane of the wheel centres. 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)", + " The variation of roll steer with axle suspension bump is kRUZA \u00bc d\u00abRU dzA \u00f06:12:4\u00de This gives the relationship to load (in newtons) according to the total axle suspension stiffness KA: kRUFV \u00bc d\u00abRU dFVA \u00bc 1 KA d\u00abRU dzA \u00f06:12:5\u00de It can be examined easily by considering the change of the axis angle rA from themotion of pointsA andB with increasing load and axle bump deflection. If the points move equally in the same direction then there is a change of roll centre height, but no change of roll steer. In some cases, for example the convergent fourlink suspension of Figure 6.12.1,when the bodymoves down thenAmoves downandBmoves up, giving a small change of roll centre height but a large increase of roll steer coefficient. Some positive sensitivity (i.e. increasing the axis angle rA), may be desirable to help to compensate for the otherwise general trend towards oversteer with increasing load that occurs because of the tyre characteristics. This can help with Bump and Roll Steer 139 primary understeer but does not help with final understeer or oversteer, for which the roll centre height is the dominant factor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001131_j.physd.2010.08.003-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001131_j.physd.2010.08.003-Figure1-1.png", + "caption": "Fig. 1. Illustration of the Cucker\u2013Smale\u2013Povzner-type interaction rule, where a particle located in x with velocity v averages its velocity with a particle located in y with velocityw, according to (16); with e = 1 this leads to v\u2217 1 andw\u2217 1 , while with 0 < e < 1 the result is v\u2217 e andw\u2217 e . Note that v\u2217 \u00b7n = 1\u2212e 2 v \u00b7n+ 1+e 2 w \u00b7n, while v\u2217 \u00b7n\u22a5 = v \u00b7n\u22a5 , where n\u22a5 is a unit vector orthogonal to n = n(x\u2212y) = (x\u2212y)/|x\u2212y|, and analogous relations hold forw. Consequently, for e = 1 we have v\u2217 1 \u00b7n = w \u00b7n andw\u2217 1 \u00b7n = v \u00b7n.", + "texts": [ + " More precisely, let us denote by \u27e8\u00b7, \u00b7\u27e9 the inner product in L2(R3). For all smooth functions\u03c8(v), it holds \u27e8\u03c8, Q\u0304P(f , f )(x, v)\u27e9 = \u222b R3 \u03c8(v)Q\u0304P(f , f )(x, v) dv = 1 \u03f5 \u222b R3 \u222b R3 \u222b R3 B(|x \u2212 y|) \u03c8(v\u2217)\u2212 \u03c8(v) f (x, v)f (y,w)dv dw dy. Let (v\u2032,w\u2032) be the post-interaction velocities in a Povzner elastic interaction with (v,w) as incoming velocities. Denoting by q the relative velocity, q = v \u2212 w, v\u2032 = v \u2212 (q \u00b7 n)n, w\u2032 = w + (q \u00b7 n)n. (21) As before, n = n(x \u2212 y) = x\u2212y |x\u2212y| . Using (16) and (21), one obtains (Fig. 1) v\u2217 = v\u2032 + 1 2 (1 \u2212 e)(q \u00b7 n)n, w\u2217 = w\u2032 \u2212 1 2 (1 \u2212 e)(q \u00b7 n)n. (22) If we assume that the coefficient of restitution has the form (17), then v\u2217 \u2212 v\u2032 = \u03b3 a(|x \u2212 y|)(q \u00b7 n)n. (23) Let us consider a Taylor expansion of \u03c8(v\u2217) around v\u2032. Thanks to (23), we get \u03c8(v\u2217) = \u03c8(v\u2032)+ \u03b3 a(|x \u2212 y|)\u2207\u03c8(v\u2032) \u00b7 (q \u00b7 n)n + 1 2 \u03b3 2a(|x \u2212 y|)2 \u2212 i,j \u22022\u03c8(v\u2032) \u2202v\u2032 i\u2202v \u2032 j (q \u00b7 n)2ninj + \u00b7 \u00b7 \u00b7 . (24) If the interactions are nearly elastic, so that \u03b3 \u226a 1, we can truncate the expansion (24) after the first-order term. Inserting (24) into (21) gives \u27e8\u03c8, Q\u0304P(f , f )\u27e9 \u2248 1 \u03f5 \u222b R3 \u222b R3 \u222b R3 B(|x \u2212 y|) \u03c8(v\u2032)\u2212 \u03c8(v)+ \u03b3\u2207\u03c8(v\u2032) \u00b7 a(|x \u2212 y|)(q \u00b7 n)n f (x, v)f (y,w)dv dw dy = \u27e8\u03c8 ,QP(f , f )\u27e9 + \u03b3 \u27e8\u03c8,I (f , f )\u27e9" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000855_tie.2011.2159357-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000855_tie.2011.2159357-Figure3-1.png", + "caption": "Fig. 3. Distribution of the (a) magnetomotive force and (b) permeance.", + "texts": [ + " The operating principle of this gear is described, and the transmission torque under operation in accordance with the gear ratio is mathematically formulated. In particular, the harmonic order of the cogging torque is described in detail. Moreover, the orders of the cogging torque of both rotors are verified by employing 3-D finite element method (FEM). Furthermore, the computed results are also then further verified by carrying out measurements on a prototype. Assuming that the low-speed rotor is removed, only the high-speed rotor magnet generates the magnetomotive force, as shown in Fig. 3(a). The stationary pole pieces modify the permeance shown in Fig. 3(b), where \u03b8 represents the rotor angle. This distribution of the permeance is due to the difference of the magnetic resistance between the air in the slot and the pole piece made of the magnetic material. The Fourier series expansions of F (\u03b8) and R(\u03b8) are shown in F (\u03b8) = \u221e\u2211 m=1 am sin {(2m \u2212 1)Nh\u03b8} (1) R(\u03b8) = Ro + \u221e\u2211 l=1 al sin {(2l \u2212 1)Ns\u03b8} . (2) Moreover, the magnetic flux distribution \u03c6(\u03b8) can be obtained as follows: \u03c6(\u03b8)= \u221e\u2211 m=1 amR0 sin{(2m\u22121)Nh\u03b8} + \u221e\u2211 l=1 \u221e\u2211 m=1 alam 2 [cos{(2l\u22121)Ns\u2212(2m\u22121)Nh}\u03b8 \u2212 cos{(2l\u22121)Ns+(2m\u22121)Nh}\u03b8] " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure14.19-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure14.19-1.png", + "caption": "FIGURE 14.19. A 2R manipulator moves between two points on a line and a semi-circle.", + "texts": [ + " Find the optimal control command If(t)1 ~ lOON to move the mass m = 1kg rest-to-rest from x(O) = 0 to x(tf) = 10m. The mass is moving on a rough surface with coefficient J.L and is attached to a wall by a linear spring with stiffness k, as shown in Figure 14.18. The value of J.L and k are (a) (b) J.L = 0.1 J.L =0.5 k = 2N/m k = 5N/m. 10. * Convergence conditions. Verify Equations (14.92) to (14.97) for the convergence condition of the floating-time algorithm. 11. * 2R manipulator moving on a line and a circle. Calculate the actuators' torque for the 2R manipulator, shown in Figure 14.19, such that the end-point moves time optimally from P1(1.5m, 0.5m) to P2(0 , 0.5m) . The manipulator has the following characteristics: The path of motion is ml h IP(t)1 IQ(t)1 m2 = 1kg l2 = 1m < 100Nm < 80Nm 640 14. *Time Optimal Control ml = 5kg IQ(t)1 :::; 100Nm mz = 3kg IP(t)1 :::; 80Nm 13. * Control of an articulated manipulator. Find the time optimal control of an articulated manipulator, shown in Figure 5.25, to move from H = (1.1,0.8,0.5) to Pz = (-1,1,0.35) on a straight line. The geometric parameters of the manipulator are given below" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003377_j.addma.2020.101093-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003377_j.addma.2020.101093-Figure8-1.png", + "caption": "Figure 8: AM compression molding mold (Female Side), a) Before machining, and b) After machining", + "texts": [ + " Jo ur l P re -p ro of Table 2: Material properties of individual parts used in the simulation Part Material Young's modulus (GPa) Poisson's ratio Mold Mild Steel 184 0.29 Al 6061 68.9 0.33 Figure 7: Simulation configuration consisting of top and bottom press platens, female and male molds (mild steel or Al 6061), and a molded composite part The MBAAM system was used to fabricate molds for polymer composite parts. The mold consists of a female and male mold which were each printed in approximately 10 hours. ER70S6 welding wire was used to print the mold. The mold size (i.e. each half) was 30 cm x 30 cm x 8 cm in width, length and thickness, respectively. Figure 8 shows the final fabricated mold. It should be noted that this method offers surface quality an order of magnitude worse than laser and electron beam powder beds. Hence, the fabricated parts require post processing (i.e. machining). As the designed part becomes larger Jo rn l P re -p ro of and the printing processes becomes faster, the surface finish of the final part is compromised (Figure 8a). The printed mold was oversized by 3 mm and then was machined to achieve the required final geometry, tolerances and surface quality (Figure 8b). Using a different weld wire size (i.e. smaller) would also enhance the part surface finish significantly. The fabricated AM mold can be used in either sheet molding compound (SCM) or extrusion compression molding (ECM) composite fabrication processes. In this work, we evaluate the use of the mold in an ECM process, in which long fiber thermoplastic (LFT) materials (i.e. fibers with aspect ratio ~ > 100) are used to fabricate complex, cost-effective and short cycle time composite components [26, 27]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002940_j.jcrysgro.2019.05.027-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002940_j.jcrysgro.2019.05.027-Figure12-1.png", + "caption": "Fig. 12. Branching of new dendrites at the diverging boundary of (a) 15\u00b0 oriented stray grain, new branch develops from favorably oriented grain, (b) 25\u00b0 oriented stray grain, new branch develops from unfavorably oriented grain, where SLM parameters are 5m/s and 400W.", + "texts": [ + " As a result, the width of unfavorably oriented Grain B along horizontal direction becomes smaller, representing the suppressive effect for the growth of Grain B. Besides the well accepted promotive or suppresive effect on stray grains, a third type of stray grain growth mechanism, i.e., neutral growth, is discovered. This happens when the orientation of stray grain is significantly deviated from the thermal gradient direction, as shown in Fig. 11 (c). On the diverging boundary, the two adjacent dendrites from each side of the grain boundary form a \u201cvalley\u201d shaped solidification front, as defined by Edge m and Edge n shown in Fig. 12(a). When the angle between the stray grain and the thermal gradient is small, the branching from favorably oriented grain still dominates that from the unfavorably oriented grain, as shown in Fig. 12(a). However, when the angle between the stray grain and the thermal gradient becomes considerably large, as shown in Fig. 12(b), the branching from the stray grain then starts to dominate that from the favorably oriented grain. This is attributed to the larger open angle of the valley, \u03b3. As the \u03b3 increases, more space becomes available for the new dendrites to develop. At a large misorientation angle, the new dendrites of the stray grain are more aligned with the thermal gradient direction as compared to those from the favorably oriented grain, shown by the red arrows. The growth potential for the dendrites emerging from stray grains becomes larger than that from the favorably oriented grain because the former grows into the cooler melt while the latter grows along an isotherm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000491_978-3-540-79029-7-Figure5.20-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000491_978-3-540-79029-7-Figure5.20-1.png", + "caption": "Fig. 5.20 Limitation of control variable: (a) Voltage vector us with arbitrary phase", + "texts": [ + " A better and consistent solution can be provided by reverse-correction of the control deviation (cf. Sch\u00f6nfeld [1985]) which is elaborated on further in this chapter. angle \u03d1u and (b) the maximum modulation ratio maxsu of inverter Treatment of the limitation of control variables 173 Instead of measuring the stator voltage to detect when entering limitation, the stator voltage can be limited intentionally to the maximum modulation ratio. From the chapter 2 is known, that the maximum usable stator voltage lies within a hexagon (fig. 5.20) and furthermore, that only the limitation of the amplitude of the voltage vector is of importance. However, the stator voltage actually exists in components, usd and usq or us\u03b1 und us\u03b2. That means: The voltage limitation must be split into components as well. Suitable methods for this have to be worked out for the chosen coordinate system. The voltage limitation itself is completed with its splitting into components. But as mentioned above: A reverse correction strategy, which prevents the vibrations or oscillations caused by the implicitly existing integral part, must be worked out. The figure 5.20a has pointed to the possibilities of setting the limitation boundaries on the inner circle touched by the hexagon or on the outer hexagon. The limitation most simply works with the circle, but a loss of control reserve (the area between hexagon and circle) would be the result. The phase angle \u03d1u of the stator voltage then is: arctan sq u su sd u u = + (5.71) With the help of (5.71) and fig. 5.20b the maximum amplitude of the voltage vector or the maximum modulation ratio (at normalization with 2UDC/3) depending on the phase angle can be found as: max 3 1 2 sin 3 = + su 1 (5.72) The limitation on the outer hexagon according to (5.72) yields the best actuator utilization with respect to deliverable control voltage, however, causes an additional third harmonic in the current. This is unwanted in the stationary operation where the field and torque forming components represent DC quantities. It is therefore recommended for high-quality servo drives to limit on the inner circle. The maximum modulation ratio then is: 1 After normalizing with 2UDC/3 the voltage is formulated as modulation ratio here; the angle \u03b3 is defined in fig. 5.20b. 174 Dynamic current feedback control in drive systems max 3 2 =su (5.73) In principle the limitation can be implemented on one of the three following levels (fig. 5.21). 1. Level of dq components: This is the mostly applied, most effective variant for the limitation. The decoupling between the dq axes or between torque formation and magnetization can be ensured largely with a correct splitting strategy (cf. chapter 5.5.1). 2. Level of \u03b1\u03b2 components: The application of this variant is only possible if the torque impression is implemented using a current controller in the stator-fixed coordinate system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003857_j.engfailanal.2018.08.028-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003857_j.engfailanal.2018.08.028-Figure15-1.png", + "caption": "Fig. 15. Nephograms of comprehensive deformation: (a) health; (b) l2= 0mm; (c) l2= 3mm; (d) l2= 6mm.", + "texts": [ + " The mesh stiffness at moments D and E is listed in Table 5, and the maximum error is about 3.93%. The increase of l3 leads to the reduction of the healthy part, so the deformation increases (see Fig. 13), and the reduction of the TVMS becomes more significant (see Fig. 12). The TVMS obtained from the proposed method and the FE method under different crack growth distances along tooth depth l2= 0, 3, 6mm and constant q0= 2.5mm, qe= 0.5mm and l1= 2mm is shown in Fig. 14. The comprehensive deformation at moment E under different l2 is shown in Fig. 15. The mesh stiffness at moments D and E is listed in Table 6, and the maximum error is about 5.37%. With the increase of l2, the loss of stiffness decreases slightly (see Fig. 14). When l2= 0, the force lever arm is the longest, the deformation is the largest under this case (see Fig. 15). In this paper, a new analytical method is proposed for calculating the time-varying mesh stiffness (TVMS) of helical gears. Four types of spatial cracks are involved in the analytical model, including addendum non-penetrating crack, addendum penetrating crack, end face non-penetrating crack and end face penetrating crack. The TVMS obtained from the proposed method and the finite element (FE) method is compared under different crack types and crack parameters. The main conclusions can be obtained: (1) The TVMS obtained from the proposed method is in great agreement with that obtained from the FE method, and the maximum error is 6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003497_j.triboint.2019.105960-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003497_j.triboint.2019.105960-Figure1-1.png", + "caption": "Fig. 1. An offshore direct-drive (gearless) wind turbine with the double-row TRB on the main shaft [22].", + "texts": [ + " Moreover, the peak contact pressure can be significantly reduced on the roller with the crowned profile, even if in the case of misaligned bearing. Comparisons of the simulated contact loads and pressure distributions demonstrate the necessity of considering angular misalignment and frictional force in the modelling of large size and heavily loaded double-row TRB. A reliable operation with reduced maintenance cost is one of the critical factors driving the growth of the wind turbine market. Unlike the conventional onshore wind turbines, as shown in Fig. 1, the offshore gearless (also called direct-drive) wind turbine is subjected to additional loading sources acting on the floating platform such as wave, current and buoyant forces. One advantage of the gearless wind turbine design is the replacement of the geared drive-train system commonly used in the conventional wind turbine with a direct-drive generator, to reduce the number of rotating components and thus improve the reliability and stability of generator [1]. A large size double-row TRB and cylindrical roller bearing (CRB) are usually used to carry the rotor assembly and generator shaft" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.9-1.png", + "caption": "FIGURE 1.9. T he RI-Rl.P spherica l configuration of robot ic manipulators.", + "texts": [ + " It is a suit able configurat ion 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 art iculated robot is shown in Figure 1.8 to indicate the name of different components. 1. Introduction 9 10 1. Introduction 3. RI-R..lP The spherical configuration is a suitable configuration for small ro bots. Almost 15% of industrial robots, Stanford arm for instance, are made of this configuration. The Rf-R..lP configurat ion is illustrat ed in Figure 1.9. By replacing the third joint of an art iculate manipulator with a pris matic joint, we obtain the spherical manipulator. The term spherical manipulator derives from the fact that the spherical coordinates de fine the position of the end-effector with respect to its base frame . Figure 1.10 schematically illustrates the Stanford arm, one of the most well-known spherical robots. 1. Introduction 11 4. RIIPf--P The cylindrical configurat ion is a suitable configurat ion for medium load capacity robots" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure10.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure10.5-1.png", + "caption": "Figure 10.5 shows a roller in a circular path . Find t he velocity and acceleration of a point P on the circumference of the roller .", + "texts": [], + "surrounding_texts": [ + "10. Acceleration Kinemat ics 443\nExercises\n1. Notation and symbols.\nDescribe their meaning .\na- GaB b- BaG G d- ~aB B f- ~aGc- GaB e- BaG\ng- gal h- ~a2 . 1 . 2\nk- ~a l 1- k a i1- 2 a l J- 2al J\n0 - 2- 0- GAB G ' q- j r- Xm- 2IXl n- lW2 p- VB\n2. Local position, global acceleration.\nA body is turning about the Z-axis at a constant angular accel eration ii = 2 rad / sec'' . Find th e global velocity of a point, when 0: = 2 rad/ sec, IX = 7f / 3 rad and\n3. Global position , constant angular acceleration.\nA body is turning about th e Z-axis at a constant angular acceleration ii = 2 rad/ sec\". Find the global position of a point at\nafter t = 3sec if t he body and global coordinate frames were coinci dent at t = 0 sec.\n4. Turning about x-axis.\nFind the angular acceleration matrix when the body coordinate frame is turning - 5 deg / sec\", 35 deg / sec at 45deg about the x-axis.\n5. Angular acceleration and Euler angles.\nCalculate the angu lar velocity and accelerat ion vectors in body and global coordinate frames if the Euler angles and their derivatives are :\n'P = .25 rad (} = - .25rad 7/J = .5 rad ep = 2.5 rad / sec e= - 4.5 rad / sec ;p = 3 rad / sec ip = 25 rad / sec2 B= 35 rad / sec2 ~ = 25 rad/ sec2", + "444 10. Acceleration Kinematics\n6. Combined rotation and angu lar acceleration.\nFind the rotation matrix for a body frame after 30 deg rotation about the Z-axis, followed by 30 deg about the X -axis , and then 90deg about the Y-axis. T hen calculate the angu lar velocity of the body if it is turning with a = 20 deg / sec, ~ = - 40 deg / sec, and 1 = 55 deg / sec about the Z, Y , and X axes respectively. Fin ally, cal culate the angular acceleration of the body if it is turning with (i = 2 deg / sec\", $ = 4 deg / sec\", and l' = - 6deg / sec2 about the Z, Y, and X axes.\n9. An RPR manipulator.\nLabel the coordinate frames and find the velocity and acceleration of point P at the endpoint of the manipulator shown in Figure 10.6.", + "10. Acceleration Kinematics 445" + ] + }, + { + "image_filename": "designv10_3_0001539_iciinfs.2013.6731982-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001539_iciinfs.2013.6731982-Figure1-1.png", + "caption": "Fig. 1 The four b", + "texts": [ + " design, ability of table hovering, the urveillance, aerial nd in various other developments in attery technology ators (brushless outrunner motors) it was poss light in weight, powerful to car in flight for a longer duration. II. QUADRO By rotating the two propelle same speed but in opposite direc be cancelled. Since quadrotor controllable actuators, the syste where there are only four controlled directly to achieve these four control variables ha modeling and controlling of th complicated. The four control variables correspond to four basic movem roll movement U2, pitch movem [4][5]. Fig. 1 shows how thes quadrotor are created by ch accordingly. The nominal ho which is deflected by \u2206A, and pitch, yaw, motions. The two th ible to build quadrotors very ry a payload, and able to stay TOR MODELLING r pairs on the two arms with tion, the rotational torque can has only four independently m is an under actuated system degrees of freedoms to be a stable system. Therefore ve to be so selected that the e quadrotor will become less that we selected directly ents, vertical movement U1, ent U3 and yaw movement U4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000657_tmag.2009.2024159-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000657_tmag.2009.2024159-Figure7-1.png", + "caption": "Fig. 7. Reaction field by magnet eddy currents. (a) IPM. (b) SPM.", + "texts": [ + " As a result, the loss increases almost linearly with the number of segmented conductors due to the increase in the total edge length and surface area [3]. On the other hand, when the number of segmentations is larger and the axial length of the conductor is smaller than , the loss decreases with the number of segmentations. The loss characteristics of the IPM motor in Fig. 5 is well expressed by this model. On the other hand, we consider that the differences in the loss-reduction effect due to the rotor types are caused by the differences in reaction fields produced by the magnet eddy currents, as shown in Fig. 7. In the case of the IPM type, the magnet is located inside the rotor core. As a result, the ratio of the reaction field to the total field becomes relatively large and the phenomenon is similar to that of the theoretical infinite model. In this case, the skin effect is relatively strong and the eddy current loss increases with the number of segmentations when the frequency is high and the number of segmentations is small. On the other hand, in the case of the SPM type, the magnet faces to the air gap; thereby, the ratio of the reaction field is smaller than that of the IPM type" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002059_s00466-017-1528-7-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002059_s00466-017-1528-7-Figure2-1.png", + "caption": "Fig. 2 Model material ID switching from powder to solid (background blue color is the base plate). a Predicted temperature; b Material ID with red color for solid and blue color for powder", + "texts": [ + " For each layer, heating lines are automatically created according to the L-PBF process parameters (stripe width and hatch distance). The heating lines were rotated layer by layer with an angle of 67\u25e6. Figure 1 illustrates the created heating lines and the surface observation in a built part. A program modeling material ID switching from powder to solid was developed in this study. A similar approach has been used by other researchers [29,30] tomodel the transition from fresh power to dense solid. The material ID switch is based on the laser-heat source location. Figure 2 shows the laser location and material ID side by side and one at a time on a 2.5 by 2.5 mm built block. In Fig. 2a, gray color shows the melt pool which is the laser location. In Fig. 2b, the red color represents solid material and blue color represents the powder. The base plate is also represented using the blue color. Microstructure and hardness are determined by chemical compositions and thermal history. Thermal history depends on a local geometry, heat convection, and radiation. There- fore, microstructure and hardness can be predicted by simulating the building process in a local interested volume without modeling an entire part. This strategy allows the detailed temperature history duringAMprocesses to bemodeled using the double ellipsoidal heat sourcemodel discussed above in multiple local models" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002751_1.g003201-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002751_1.g003201-Figure2-1.png", + "caption": "Fig. 2 Biplane reference frames.", + "texts": [ + " First, the strategy required for primary control of this UAV is discussed followed by detailed development of the mathematical model that includes flight dynamics, wing aerodynamics, and rotor dynamics. The current tail-sitter UAV operates in three flight regimes: 1) VTOL or quadrotor; 2) transition; and 3) fixed-wing or forward flight. In the quadrotormode, the up/downmotion is easily controlled by collectively increasing or decreasing the collective pitch angles for all the rotors/propellers simultaneously. Forward and side-ward flight can be achieved by controlling pitching and rolling moments. Positive roll of a quadrotor in H-configuration (Fig. 2a) can be achieved by providing higher thrust to rotors 1 and 4, and correspondingly lower thrust to rotors 2 and 3. Similarly, positive pitch can be achieved by providing higher thrust to rotors 1 and 2, and correspondingly lower thrust to rotors 3 and 4. The yaw control is less intuitive. A nonzero net torque along the ZQ axis causes yawing motion that can be generated from the drag force acting on each rotor. The collective pitch of the two diagonal rotors rotating in the same direction is increased and the collective pitch of the other diagonal pair is reduced to generate pure yaw motion", + " The third part, forward flight, is similar to conventional fixed-wing mode. Themechanism to generate pitchingmoment during thismode remains the same as the quadrotor mode. It should be noted that, D ow nl oa de d by U N IV E R SI T Y O F FL O R ID A o n Fe br ua ry 6 , 2 01 8 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .G 00 32 01 after the vehicle maneuvers into the forward flight mode, the yaw and roll degree of freedom during hovering flight becomes the roll and yaw degree of freedom, respectively, as shown in Fig. 2b. The flight control for various motions can be achieved as explained earlier. In addition, the pitching moment contribution from the wings can be compensated by differential thrust generation by the top and bottom rotors, during forward flight. It is important to emphasize that the rotors operate at reduced RPM in forward flight compared with VTOL mode to ensure high efficiency during forward flight. B. Vehicle Equation of Motion A mathematical model of biplane-quadrotor tail-sitter UAV in the body axis can be derived by fixing the right-hand coordinate axis either with respect to conventional wing frame (see Fig 2b) or with respect to conventional quadrotor frame as shown in Fig. 2a. Because most of the flight phases, that is, vertical takeoff, hover, initial transition, and landing, are performed in VTOL mode, the wing aerodynamic forces under this condition are generated primarily due to prop wash because of low translational speeds. Therefore, it is more convenient to describe dynamics of this UAV in the quadrotor frame. In addition, the derivation of control law for all these flight phases becomes relatively simple if reference body frame is chosen to be the quadrotor frame", + " As the forward flight phase is a conventional fixed-wing airplane mode, it is easier to visualize thismode by following the conventional right-hand fixed-wing axes system. However, the variables defining the dynamic model of biplane-quadrotor vehicle in Eqs. (1) and (2) are defined with respect to the quadrotor axes. Hence, the variables that are measured and fed back to the controller are the same quadrotor axes variables. To facilitate control design during the horizontal flight regime, we need to transform the dynamic variables from quadrotor axes to fixed-wing axes. According to Fig. 2, the transformation matrix, which transforms a vector in quadrotor frame to fixed-wing frame, can be defined as 2 4 vx vy vz 3 5 W RW Q 2 4 vx vy vz 3 5 Q (51) where RW Q 2 4 0 0 \u22121 0 1 0 1 0 0 3 5 (52) Note that RW QR WT Q I and RQ W RW\u22121 Q . Hence, the body angular rates, body translational velocities, and inertia matrix in the fixedwing frame can be calculated from the corresponding quantities defined in quadrotor axes using Eq. (51). The quaternion attitude in the fixed-wing frame can be calculated by integrating the quaternion kinematics relation of Eq", + " Similar to the quadrotor mode, the desired body rates in this mode can be computed as follows: _\u03c9W 2G \u03b7eW \u22122\u03b6qwT nq _\u03b7eW \u2212wnqw T nq \u03b7eW \u2212 \u03b7edW _R \u03b7eW T\u03c9dW R \u03b7eW T _\u03c9dW (63) The desired moments in the fixed-wing frame can now be calculated from Eqs. (61) and (63) as \u03c4tW IW _\u03c9W \u03c9W \u00d7 IW\u03c9W \u2212 \u03c4a (64) After the initial transition phase, the remaining transition to the desired trim pitch angle, \u03b8Wtrim , is achieved by the fixed-wing mode controller. The final phase of transition is also commanded to take place at the same altitude. During the quadrotor mode, as shown in Fig. 2, rolling and pitching moments are obtained by the product of differential thrust (left/right and front/back, respectively) and respective moment arms. The yawing moment is obtained from Eq. (15), in which the contribution of blade drag to total torque is independent of thrust and hence remains constant at all times and cancels out for four rotors. The expressions for total forces and moments due to thrust during quadrotor mode are given as T K CT1 CT2 CT3 CT4 (65) Lt Kd CT1 \u2212 CT2 \u2212 CT3 CT4 (66) Mt Kd CT1 CT2 \u2212 CT3 \u2212 CT4 (67) Nt KR 2 p C3\u22152 T1 \u2212 C3\u22152 T2 C3\u22152 T3 \u2212 C3\u22152 T4 (68) The expressions for total forces and moments due to thrust during the fixed-wing mode are given as T K CT1 CT2 CT3 CT4 (69) Lt \u2212 KR 2 p C 3\u22152 T1 \u2212 C 3\u22152 T2 C 3\u22152 T3 \u2212 C 3\u22152 T4 (70) Mt Kd CT1 CT2 \u2212 CT3 \u2212 CT4 (71) Nt Kd CT1 \u2212 CT2 \u2212 CT3 CT4 (72) The control allocation loopworks in similar way for all three flight modes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001458_j.msec.2013.03.050-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001458_j.msec.2013.03.050-Figure3-1.png", + "caption": "Fig. 3. CVs of (a) unmodified CPE in 0.1 M PBS (pH 7.0), (b) unmodified CPE in 0.1 mM NE, (c) 5ADBCNPE in 0.1 M PBS, (d) CNPE in 0.1 mM NE, (e) 5ADBCPE in 0.1 mM NE, and (f) 5ADBCNPE in 0.1 mM NE. In all cases the scan rate was 10 mV s\u22121.", + "texts": [ + " Thus, the electrochemical behavior of 5ADBCNPE was studied at different pHs using CV (Fig. 2). It was observed that the anodic and cathodic peak potentials of 5ADBCNPE shift to less positive values with increasing pH. Inset of Fig. 2 shows potential-pH diagrams constructed by plotting the anodic, cathodic and half-wave potential values as the function of pH. As can be seen the slopes are 47.845, 49.262 and 48.298 mV/pH for Epa, Epc and E1/2 respectively, indicating that the system obeys the Nernst equation for an equal electron and proton transfer reaction [43]. Fig. 3 depicts the CV responses for the electrochemical oxidation of 0.1 mM NE at unmodified CPE (curve b), CNPE (curve d), 5ADBCPE (curve e) and 5ADBCNPE (curve f). As it is seen, while the anodic peak potentials for NE oxidation at the CNPE, and unmodified CPE are 380 and 450 mV, respectively, the corresponding potential at 5ADBCNPE and 5ADBCPE is ~280 mV. These results indicate that the peak potentials for NE oxidation at the 5ADBCNPE and 5ADBCPE electrodes shift by ~100 and 170 mV toward negative values compared to CNPE and unmodified CPE, respectively. However, 5ADBCNPE shows much higher anodic peak current for the oxidation of NE compared to 5ADBCPE, indicating that the combination of CNTs and the mediator (5ADB) has significantly improved the performance of the electrode toward NE oxidation. In fact, 5ADBCNPE in the absence of NE exhibited a well-behaved redox reaction (Fig. 3, curve c) in 0.1 M PBS (pH 7.0). However, there was a drastic increase in the anodic peak current in the presence of 0.1 mM NE (curve f), which can be related to the strong electrocatalytic effect of the 5ADBCNPE towards this compound [43]. The reaction scheme would probably via following mechanistic steps, which NE can be oxidized by product of electrochemical reaction. The effect of scan rate on the electrocatalytic oxidation of NE at the 5ADBCNPE was investigated by CV (Fig. 4). As can be observed in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure14.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure14.10-1.png", + "caption": "Figure 14.10.1 Strut suspension: (a) position diagram; (b) velocity diagram.", + "texts": [ + " The use of a strut at the rear is a little unusual, but has featured in several cases. The usual strut incorporates the damper into the body of the strut, and has a surrounding spring. An alternative design, the damper strut, has only the damper in the strut body,with the spring acting separately on one of the arms. Geometrical considerations are the same, although, of course, in the latter case it is the arm which must be analysed for the spring motion ratio. Overall, the method of analysis is similar to that of the double-wishbone suspension. Figure 14.10.1(a) shows a strut suspension. This is in fact the simpler version where the strut axis passes through the ball joint at B. If the bump camber coefficient is already available, then the vertical velocity VZB of B is given by VZB \u00bc VS\u00f01 e\u00abBC\u00de 286 Suspension Geometry and Computation where e \u00bc XF XB The tangential velocity of B is then VB=A \u00bc VZB cos f1 and the damper compression velocity VD is VD \u00bc VB=A cos\u00f0f1 \u00fe u2\u00de Hence, RD \u00bc VD VS \u00bc \u00f01 e\u00abBC\u00de cos\u00f0f1 \u00fe u2\u00de cosf1 Realistic values may give a motion ratio below 0.9, in contrast to the naive expectation of a value close to 1.0. The velocity diagram is shown in Figure 14.10.1(b). The body is stationary, so A and C are fixed points, appearing as a and c at thevelocity diagramorigin. Construction proceeds by assuming an angular velocity vAB for the bottom link: VB=A \u00bc vABl1 perpendicular to AB, giving point b representing VB in the velocity diagram. Velocity VB/C is the vector sum of longitudinal and tangential components, so construct a line through b perpendicular to CB and through c parallel to CB to intersect, giving point d. Point d represents the velocity of point D, which is a point notionally fixed to the lower part of the strut, and instantaneously coincident with the upper fixture point C" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000081_87.974349-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000081_87.974349-Figure2-1.png", + "caption": "Fig. 2. Backlash model.", + "texts": [ + ", the asymptotic stabilization of the system. With reference to the stabilization of the plant (2.1) in the presence of the backlash nonlinearity (2.3a) and (2.3b) with uncertainties, two different approaches can be followed, depending on the mathematical description used to model backlash. The following model of backlash [3], equivalent to (2.3), will be used for design in the following. Define as the set of states of the backlash model, i.e., the set of all the points in or between the lines of slope (see Fig. 2). For any point at any time define two functions and (4.1a) . (4.1b) The characteristic of backlash can be defined as follows: for any state at any time and for any input monotone over the output is given by (4.2) according to whether is monotonically increasing or decreasing, respectively. Therefore, for any initial state, at any time and for piecewise continuous input , the backlash output is uniquely determined. Define the following quantities: (4.3) Under Assumption II.4, a minimum value for and a maximum value for can be found in the time interval " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.10-1.png", + "caption": "FIGURE 4.10. The SCARA robot of Example 90.", + "texts": [ + " Point P indicates the tip point of the last arm of the robot shown in Figure 4.9. Position vector of P in frame B2 (XZyz zz) is zrp. Frame Bz (XZyz zz) can rotate about zz and slide along Yl . Frame B 1 (XIYl Zd can rotate about the Z -axis of the global frame G(OXYZ) while its origin is at c d l . The position of P in G(OXYZ ) would then be at CR1l Rzzr p + CR11 dz+ c d l 0 for = tan\u22121(d/c + ) \u2212 , tan\u22121(d/c \u2212 ) with sufficiently small > 0, respectively, and d2 /d 2 > 0, i.e., d /d is monotone increasing for \u2208 ( , ) since > \u2212 1 (see Fig. 7). According to the Intermediate value theorem and the monotonicity of d /d , there exists a \u2208 ( , ) such that d /d = 0. These facts indicate the graph of (21) is leftward convex. Now, we set z1 =p1(c+ jd) and z2 =p2(c+ jd), and suppose that contrary to the claim, the maximum of Re(W0(z)) is taken at a middle point z3 =p3(c + jd), p3 \u2208 (p1, p2) when the segment (18) is mapped by W0. Then, W0(z1) and W0(z2) should lie on the left side of W0(z3) in w-plane. Since W0 is homeomorphic (Remark 2), these three points are continuously linked by a single curve" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003153_j.ymssp.2019.106553-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003153_j.ymssp.2019.106553-Figure7-1.png", + "caption": "Fig. 7. The defect profile used in the dynamic model. (a) A flat defect is assumed on the roller and (b) the geometrical property of the flat defect.", + "texts": [ + " m\u20acr \u00bc F \u00f09\u00de J _x \u00bc M \u00f010\u00de where m is the mass, \u20acr is the acceleration vector, J is the principal moment of inertial, _x is the angular acceleration vector. Generally, the translation described by Eq. (9) is calculated in the inertial frame, and the rotation described by Eq. (10) is determined in the body-fixed frame. Therefore, the force and the moment vectors shown in Eqs. (9) and (10) should be described in the inertial frame and the body-fixed frame, respectively. In the dynamic model, it is assumed that a flat defect denoted as AB shown in Fig. 7 is located on the roller. As the curvature radius of the race is larger than the roller, the main impact points between the roller defect and the race are the defect edges A and B, both for the defect profile used in the experiment and that used in the proposed dynamic model. As the main topic of the current investigation is the path of the roller and the vibration patterns as a roller defect rolls through a race, this assumption would be acceptable. The result obtained by the experiment and that obtained based on the flat defect will be discussed in Section 4. In addition, the width and the depth of the flat defect are shown in Fig. 7(b). Besides the coordinate frames discussed in Section 3.1, a new frame called defect frame Odxdydzd is established on the roller (Fig. 8(a)). The origin Od is located at the defect center, and an angle gd is used to locate the defect in the roller. Then, the defect frame can be determined by rotating the roller-fixed frame along the axis xb by gd. Therefore, the transformation matrix from roller-fixed frame to defect frame can be written as Tbd \u00bc T gd;0;0\u00f0 \u00de. Moreover, in Fig. 8, bd is half the angle of the defect in the circumference of the roller, and bdar is the angle between the axis zd and the vector rbr ", + " In this section, the proposed dynamic model is verified with the experiment results given in Section 2. All the parameters of the cylindrical roller bearing in simulation are listed in Table 2. Moreover, as the lubricant characteristics is not the main focus of the current investigation, a simple four-parameter traction model is used to simulate the relationship between the relative sliding velocity and the traction coefficient (i.e., the traction model) as shown in Fig. 12 [54]. The geometrical parameter dd and wd shown in Fig. 7(b) are set as 0.083 mm and 1.5 mm, respectively. In the simulation, these two parameters are equal to those in experiments (See Fig. 3). The bearing housing accelerations in the zi direction obtained by experiment and simulation are shown in Fig. 13. In the experiment and simulation results in time domain (Fig. 13(a) and (c)) it can be found that, the roller defect interacts with both the inner race and the outer race when it rotates around its own axis in the loaded zone, while the roller defect only hits the outer race in the unloaded zone (in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001166_j.bioelechem.2009.02.009-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001166_j.bioelechem.2009.02.009-Figure1-1.png", + "caption": "Fig. 1. A schematic representation of the air diffusion CueO-adsorbed on carbon particle-modified CP electrode.", + "texts": [ + " For the previous O2 reducing biocathodes, which relied on O2 dissolved in the electrolyte solution, the maximum current was thus limited by O2 diffusion, which in turn is determined by the rotating (stirring) rate or flow rate of the electrolyte solution, due to the low solubility and small diffusion coefficient of O2 in water solution [15]. In order to enhance the effectiveness of O2 as electron acceptor, we constructed an air diffusion\u2013type biocathode. In the air diffusion biocathode, O2 is supplied to the electrode surface from the air and protons are supplied from the electrolyte solution (Fig. 1). Important factors for the air diffusion biocathode are porosity, thickness and hydrophobicity of the electrode [16]. The air diffusion biocathode was constructed fromnano-structured carbonparticles, carbonpaper (CP) and a binder to glue the carbonparticles on the carbonpaper.We investigated suitable binders for this biocathode and optimized the buffer solution to improve proton supply. Expression and purification of CueO were carried out as described previously [17]. All other chemicals used in this study were of analytical reagent grade unless otherwise specified and all solutions were prepared with distilled water", + " The weight ratio of PTFE to KB was varied to be 2:8 to 5:5. The KB-modified CP electrodes (KB\u2013 CPE) were created by applying the slurries to the surface of CP and drying in a drying oven at 60 \u00b0C for over 12 h. The KB\u2013CPEs were immersed in CueO solution (5 \u00b5M) to adsorb CueO on the KBmaterials for 5 h, to give CueO-adsorbed KB\u2013CPE, abbreviated as CueO\u2013KB\u2013CPE in this paper. Cyclic voltammograms were recorded with ALS CHI704C electrochemical analyzer using the handmade air diffusion-type electrolysis cell shown in Fig. 1. The projected surface area of the cathode was prepared to be 1.0 cm2 by covering the CP electrode with a cell vessel. The volume of the electrolyte solution was 2 cm3. The scan rate was 20 mV s\u22121. A titanium mesh was used as current collector. Platinum (Pt) wire and Ag|AgCl, KCl(sat.) electrode were used as the counter electrode and reference electrode, respectively. All potentials were referred to the Ag|AgCl, KCl(sat.) reference electrode. Measurements were carried out with a buffer solution of pH 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002280_s12206-012-0627-9-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002280_s12206-012-0627-9-Figure6-1.png", + "caption": "Fig. 6. Forces acting on the cage.", + "texts": [ + " In that illustration, Nij and Noj are contact normal forces acting between the jth rolling element and the races. Fij and Foj are friction forces between the jth rolling element and the races. Nc1j and Nc2j are normal forces at the jth rolling element/pocket contact. Fc1j and Fc2j are friction forces at the jth rolling element/pocket contact. Gr is the force of gravity acting on the rolling element. Fcj is the centrifugal force acting on the jth rolling element due to the cage speed .c\u03c9 Forces acting upon the cage are shown in Fig. 6. For the jth rolling element, the application of the Newton\u2019s second law yields where 2( 1)j j b j N \u03c0\u03b8 \u03c8= \u2212 + (18) 2 .cj r j mF m R\u03c8= & (19) Similarly, for the cage: 1 2 1 ( ) N m c j c j c c i R N N J \u03c8 = \u22c5 \u2212 =\u2211 && (20) with .c c\u03c9 \u03c8= & (21) For the inner race: 1 ( cos sin ) N ij j ij j i i W N F m x\u03b8 \u03b8 = \u2212 \u2212 =\u2211 && (22) 1 ( sin cos ) . N ij j ij j i i N F m y\u03b8 \u03b8 = \u2212 + =\u2211 && (23) The system equations of motion are nonlinear ordinary second order differential equations. They can be solved using a fourth-order Runge-Kutta algorithm with fixed time step" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.40-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.40-1.png", + "caption": "Fig. 2.40 Typical curve of the bearing forces of a rigid rotor for \u03d5\u0307 = \u03a9 = const.; a) Components of the bearing forces due to the static and dynamic unbalances; b) Curve of the bearing forces", + "texts": [ + "324) the components in the fixed reference system result from (2.15) due to the known relation F = AF : FAx = FA\u03be cos \u03d5\u2212 FA\u03b7 sin \u03d5; FBx = FB\u03be cos \u03d5\u2212 FB\u03b7 sin \u03d5 FAy = FA\u03be sin \u03d5 + FA\u03b7 cos \u03d5; FBy = FB\u03be sin \u03d5 + FB\u03b7 cos \u03d5. (2.325) 156 2 Dynamics of Rigid Machines These change harmonically over time with \u03d5(t), and FAx(\u03d5\u2212 \u03c0/2) = FAy; FBx(\u03d5\u2212 \u03c0/2) = FBy. (2.326) For the special case of a constant angular velocity \u03d5\u0307 = \u03a9, the kinetic forces that are exerted by the rotor onto the bearings, see (2.133) and Fig. 2.40, are: FAx = [ (JS \u03be\u03b6 \u2212mb\u03beS) cos \u03a9t\u2212 (JS \u03b7\u03b6 \u2212mb\u03b7S) sin \u03a9t ] \u03a92 a + b FAy = [ (JS \u03be\u03b6 \u2212mb\u03beS) sin \u03a9t + (JS \u03b7\u03b6 \u2212mb\u03b7S) cos \u03a9t ] \u03a92 a + b FBx = [\u2212(JS \u03be\u03b6 + ma\u03beS) cos \u03a9t + (JS \u03b7\u03b6 + ma\u03b7S) sin \u03a9t ] \u03a92 a + b FBy = [\u2212(JS \u03be\u03b6 + ma\u03beS) sin \u03a9t\u2212 (JS \u03b7\u03b6 + ma\u03b7S) cos \u03a9t ] \u03a92 a + b . (2.327) The factors that determine the dynamic bearing forces of a rigid body can be seen from these equations. Any unbalance distribution in a rigid rotor corresponds to a shift in the center of gravity and an inclined orientation of the principal axes of inertia relative to the axis of rotation. It can be recognized from this that the dynamic forces rotate at the angular frequency in the bearings A and B, but are not in phase when the products of inertia do not equal zero. Figure 2.40 shows an example of bearing force curves of an unbalanced rigid rotor where different amplitudes and phases occur at the same angular frequency. A rigid rotor is thus completely balanced if its center of gravity is on the axis of rotation (\u03beS = \u03b7S = 0) and if its central principal axis of inertia coincides with the axis of rotation (JS \u03b6\u03be = JS \u03b6\u03b7 = 0). Then FA = FB \u2261 0. A static unbalance occurs if the center of gravity is not located on the axis of rotation. A dynamic unbalance of the rotor occurs when the central principal axis of inertia (that passes through the center of gravity) does not coincide with the axis of rotation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003778_j.ymssp.2018.06.018-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003778_j.ymssp.2018.06.018-Figure4-1.png", + "caption": "Fig. 4. Schematic view of cryogenic chamber.", + "texts": [ + " The LN2 then accumulated in the chamber and was discharged to the outside through the upper cover of the chamber. The temperature and pressure of the LN2 were measured to determine the phase of the LN2 flow at the inlet and outlet. Furthermore, sight glasses were installed radially on the test chamber to enable the actual LN2 level to be verified with the naked eye. Axial and radial forces were applied by a pneumatic cylinder placed on the test bearing housing using loading arms. Small ball bearings were mounted in the radial and axial directions to increase the DOF of the test bearing housing. Fig. 4 depicts the cryogenic chamber used to measure the traction torque resulting from the outer race. The traction force of the outer race during the rotation of the inner race generated a rotating force on the test bearing housing. To measure the torque of the test bearing, a torque arm of the test bearing housing was placed in contact with the inserted load arm from outside the chamber. The torque of the test ball bearing was measured using a load cell in contact with the inserted load arm. Fig. 5 depicts the test bearing housing and fiber optic displacement sensors used to measure the cage whirling amplitude" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000132_1.1691433-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000132_1.1691433-Figure3-1.png", + "caption": "Fig. 3 Basic involute gear parameters and the coordinate frame", + "texts": [ + " The loaded flanks of the teeth forming the pair are discretized by I11 equally spaced lead lines along the profile direction and rom: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Term J11 equally spaced profile lines along the lead direction. Hence, nodes of a fixed surface grid are defined at discrete locations ij where i50,1,2, . . . ,I and j50,1,2, . . . ,J resulting in (I11) 3(J11) number of points representing the tooth contact surface of each gear. If the i th grid line of the tooth on the driving gear in profile direction has radius Ri p , then angle invf i p defined in Fig. 3 can be described by using the relationships of involute gear geometry as invf i p5tanF cos21S Rb p Ri pD G2cos21S Rb p Ri pD (3) where invf i p is the involute angle and Rb p is the base circle radius. Position vector of a point Ri p on the side edge of gear p ( j50) at the starting rotational position r50 is given by ~Xi0!r50 p 5F Ri p sin~ invf i p! Ri p cos~ invf i p! 0 G . (4) As one moves away from this edge keeping the radius constant, the profile is rotated due to the helix angle only. The amount of this rotation at a distance zp5 jDzp along the gear face from the edge is given by Dw i j p 5 jDzp tan c i p Ri p (5) JULY 2004, Vol" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure1.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure1.4-1.png", + "caption": "Fig. 1.4 Diagram of an idealized cross-field d.c. machine.", + "texts": [ + " The term winding, on the other hand, may refer to a single coil - for example, the field coil F - or it may refer to several coils, as in the three-phase armature winding represented by the three coils A, Band C. Often it is necessary to make approximations. The cage damper winding of a practical synchronous machine consists of many circuits carrying different currents and would require a large number of coils for its exact representation. For many purposes it is sufficiently accurate to represent the damper winding by only two coils KD and KQ, which afford an example of the kind of approximation that is necessary in order to obtain a workable theory. As a second example, Fig. 1.4 is the diagram of an idealized cross-field direct-current machine having salient poles on the stator and a commutator winding with main brushes on the direct axis and cross brushes on the quadrature axis. In the diagrams of commutator machines the convention is adopted that a brush is shown at the position occupied by the armature conductor to which the segment under the brush is connected. The circuits through the brushes are labelled D and Q respectively. The machine represented also has a main field winding F and a quadrature field winding G acting along the direct and quadrature axes respectively. The machine may be represented alternatively by the four coils of Fig. l.5, corresponding to the four separate circuits of Fig. 1.4. The general theory given hereafter is developed to cover a wide range of machines in a unified manner. A very important part of this generalization applies to the two-axis theory in which, by means of an appropriate transformation, any machine can be represented by coils on the axes. However, other forms are possible, for example the phase equations of an a.c. machine or those of a commutator machine with brushes displaced from the axis. Kron called the two-axis idealized machine, from which many others can be derived, a primiti]", + " In order that the effects of rotation in a practical machine may be representable in an equivalent primitive machine, it is necessary, as shown later, that the coils D and Q representing the winding on the moving element of the primitive machine should possess special properties. The properties are the same as those possessed by a commutator winding, in which the current passes between a pair of brushes, viz., Such a coil, located on a moving element but with its axis stationary, and so possessing the above two properties, may be termed a pseudo-stationary coil. The commutator machine of Fig. 1.4 may be either a d.c. machine or an a.c. commutator machine depending on the nature of the supply voltage. The actual circuits D and Q through the commutator winding not only form pseudo-stationary coils like the coils D and Q of the primitive machine of Fig. 1.5, but have the same axes as these coils. There is thus an exact correspondence between Figs. 1.4 and 1.5, and as a result the two-axis equations derived for the primitive machine of Fig. 1.5 apply directly to the commutator machine of Fig. 1.4. On the other hand, the three moving coils on the armature of the synchronous machine of Fig. 1.3b do not directly correspond to the coils D and Q of Fig. 1.5. In developing the two-axis theory of the synchronous machine, the three-phase coils A, Band C are replaced by equivalent axis coils D and Q, like those of Fig. 1.5, or in other words, the variables of the (a,b,c) reference frame are replaced mathemat- ically by variables of the (d,q) reference frame. The transfonn ation involved in the conversion, which depends on the fact that the same m", + " Since a The Basis of the General Theory 17 stationary coil on one axis is mutually non-inductive with a stationary coil on the other axis, there would, if the machine were at rest, be no voltages induced in any coil on one axis due to currents in coils on the other axis. Hence the equations of each pair separately would be similar to those of the transformer. When the machine rotates, however, there are additional terms in the equations because, as a result of the rotation, voltages are induced in the pseudo-stationary coils D and Q by fluxes set up by currents on the other axis (see p. 9). For the commutator machine of Fig. 1.4, or the alternative representation by four coils as shown in Fig. 1.5, the equations relating the voltages and currents in the four circuits are derived in Section 2.1 and stated in Eqn. 0.5). Parameters in Eqn. (l.5) may be either in actual units or in per-unit. R f + Lffp LdfP ir LdfP Rd +LdP Lrqw Lrgw -LrfW -Lrd W Rq +LqP LqgP LqgP Rg + LggP . ig (l.5) The constants in the equations are resistances R, self-inductances Lff, L d, L q, Lgg and mutual inductances Ldf, Lqg with suffixes indicating the coils to which they refer", + " machine is a special case, is included here because of the clear physical separation of the two axes. The variables in the primitive machine are identical with those in the practical machine and no transformation is needed. The theory applies directly to a.c. commutator machines, with or without a transformation. The two-axis theory of a.c. machines without commutators in later chapters will be followed more easily if the reader has a sound understanding of the material in the present chapter. The voltage equations of the cross-field d.c. machine repre sented in Fig. 1.4 were stated without full proof in Eqns. 0.5). The result can be justified by considering each term separately as being the voltage which would arise in the circuit concerned if there were current in only one of the four circuits. The terms for resistance drops or voltages induced in stator windings need no further explanation, but the armature voltages, already discussed on p. 18, are considered in more detail in the following pages. The sign convention used has been explained in Section 1.2. The transformer voltage induced between the brushes on either axis is proportional to the rate of change of the flux on the axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003607_s11071-020-05671-x-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003607_s11071-020-05671-x-Figure1-1.png", + "caption": "Fig. 1 Quadrotor configuration", + "texts": [ + " The quadrotor is considered as one of themost complex UAVs dynamic considering its six-degree-of-freedom (6-DOF) nonlinearities (i.e., nonlinear system, strong coupling system and underactuated system), whose mathematical dynamic model is derived via Newton\u2013 Euler formalism. To understand its movement, we have to place two coordinates: The first is a static Galilei coordinate of the earth frame E(xe, ye, ze) and the other one is B(xb, yb, zb) body-fixed frame placed on the structure coincident to the vehicle inertia axes as shown in Fig. 1. The solid structure of the quadrotor is assumed to be symmetrical; also, the thrust and drag are proportional to the square of the propellers speed. 2.1 System model The position of the quadrotor in the earth frame is represented by \u2118 = [x, y, z]T and \u03be = [x\u0307 y\u0307 z\u0307]T is the translation velocity vector, where x , y and z denote the position of the quadrotor with respect to E(xe, ye, ze), \u03a6 = [\u03c6 \u03b8 \u03c8]T is the attitude quadrotor vector and \u03c9 = [\u03c6\u0307 \u03b8\u0307 \u03c8\u0307]T is the angular velocity vector, where \u03c6, \u03b8 , \u03c8 called the Euler angles (roll angle, pitch angle and yaw angle) in E(xe, ye, ze) and \u03c6\u0307, \u03b8\u0307 , \u03c8\u0307 are the angular velocity of roll, pitch and yaw with respect to B(xb, yb, zb)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002059_s00466-017-1528-7-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002059_s00466-017-1528-7-Figure3-1.png", + "caption": "Fig. 3 Hexagonal prisms (12 \u00d7 12 \u00d7 10mm) were built for screening process parameters", + "texts": [ + " A coupled thermal, metallurgical, and mechanical analysis can be conducted to predict microstructure, residual stress, and distortion in a built part. This will be the future direction for this study. Experiments were conducted to validate the predicted hardness by sequentially coupled thermal and metallurgical analysis and the predicted deformation by sequentially coupled thermal and mechanical analysis. Test samples were built with L-PBF in an EOS M280 machine which has a 400 W laser. Hexagonal prisms (12 \u00d7 12 \u00d7 10 mm), as shown in Fig. 3, were built with 4140 steel powder using L-PBF process with the parameters shown in Table 1. The steel powder chemical compositions are shown in Table 2. Macrographs were prepared by cutting the prisms along the height, as shown in Fig. 4. Vickers hardness was measured with a load 0.5 kgf along the height direction, as indicated with a red line in Fig. 4. A bridge sample, as shown in Fig. 5, was built using L-PBF process with the process parameters shown in Table 3. The stripe overlap was 0.08 mm and layer neat thickness was 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000526_tmag.1977.1059627-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000526_tmag.1977.1059627-Figure1-1.png", + "caption": "Figure 1. Polar and rectangular coordinate systems for gapped wedges. (a) semiinfinite head, (b) zero width head.", + "texts": [], + "surrounding_texts": [ + "Recently van Herk and Tjaden [ l ] have derived the potential of an infinite permeability, zero gap wedge having an exterior angle a. With the two sections of the wedge charged at magnetostatic potentials +V0/2, the potential at any point in space outside the wedge is given in cylindrical coordinates by - V(p,'p,x) = -(Vo/r)tan-l { csc(r'p/a)sinh[(r/a)~inh-~(x/p)]} (1) In (1) the x-axis runs along the corner of the wedge and the polar angle 'p and radius p lie in planes normal to x. One surface of the wedge originates at 'p = 0. The solution (1) for zero gap length can be extended to finite gap length, g, if the potential inside the wedge is assumed to drop linearly across the gap, as in the two-dimensional Karlqvist head theory [2]. The finite gap potential, V, is then related to (1) by a convolution integral V(P,'pP,X) = ( l / g ) l g / 2 V(P,'p,x-x')dx' g/2 - (2) For certain values of a, (2) can be integrated in closed forms. The magnetic field is obtained from (2) via H = -VV (3) The wedges of most importance to magnetic heads are discussed in the next section. Each field component ( 3 ) was found by differentiating under the integral in (2) and integrating the result." + ] + }, + { + "image_filename": "designv10_3_0000301_physrevlett.92.065502-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000301_physrevlett.92.065502-Figure4-1.png", + "caption": "FIG. 4. Schematic of the suggested mechanism of pinned nanotube bending by a moving receding front of a drying droplet.", + "texts": [ + " Overall, this results in one-dimensional roughness along the nanotube of 0.2\u20130.3 nm, a characteristic of atomic scale corrugation of the nanotube walls caused by sharp wrinkles of the graphitic layers during bending as was already observed [18]. No single point buckling is found for the bent nanotubes indicating a uniform bending stress distributed over the entire nanotube length. Considering the features of the phenomenon observed, we suggest the moving contact line to be responsible for the formation of woven or looped nanotubes (Fig. 4). In fact, the liquid drying under the unidirectional gravitational force inevitably leads to the directional flow within relatively thick layers followed by the formation of a gradient molecularly thick microfluidic layer, which is a subject of the contact line instability [6,19,20]. Such instabilities cause the formation of an array of periodically spaced microdroplets left behind the moving triple contact line [21]. To envision how this process could interact with carbon nanotubes, we should emphasize that the carbon nanotubes adsorbed from solution should be tethered to the hydrophilic surface [22]. The pinned nanotubes can be trapped by the moving contact line of drying microdroplets and initially align themselves along the droplet circumference in straight form (Fig. 4). At the next stage of drying, the decreasing of the overall length of the contact line along with increasing of its curvature force the trapped carbon nanotubes to follow the overall diminishing shape of the droplets by gradual bending (Fig. 4). The nanotube loops are fixed in this strained state by strong interactions with functionalized substrate and van der Waals interaction between the two portions of the nanotube in a close contact. The variation of the initial trapping scenario and size/location of a microdroplet causes a variety of looped shapes observed under different prepa- 065502-3 ration conditions. In addition, preorientation of carbon nanotubes along the hydrophilic stripes caused by hydrodynamic forces should play a significant role in the texture formation as will be discussed in a separate publication [23]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001831_j.mechmachtheory.2011.08.009-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001831_j.mechmachtheory.2011.08.009-Figure6-1.png", + "caption": "Fig. 6. Deviations between the modulated tooth surface Rg (M, j) and theoretical tooth surface Rg (T).", + "texts": [ + " (5) yields a wheel surface locus that consists of only three variables \u2013 u, \u03b2, and \u03d51 \u2013 which allows the theoretical tooth surface R T\u00f0 \u00de g and its surface normal n T\u00f0 \u00de g to be solved through the equation of meshing (Eq. (10)) plus two boundary equations of the gear blank (a plane grid of gear blank). Each coefficient in the original five-axis kinematic positions will be added by a small amount one by one, and then, the corresponding tooth surfaceR M;j\u00f0 \u00de g can be similarly determined. The flank sensitivity matrix is obtained by comparing the each modulated tooth surface R M;j\u00f0 \u00de g with the theoretical tooth surface R T\u00f0 \u00de g . As shown in Fig. 6, before calculating the deviations between the modulated tooth surface R M;j\u00f0 \u00de g and the theoretical tooth surface R T\u00f0 \u00de g , the backlash must be eliminated by rotating the surface R M;j\u00f0 \u00de g into R M0 ;j\u00f0 \u00de g until its mean point coincides with the theoretical surface's mean point. The normal deviations of the surface points between the modulated and theoretical surfaces can then be represented as following: \u2202R j\u00f0 \u00de i \u00bc R M0 ; j\u00f0 \u00de g;i R T\u00f0 \u00de g;i \u22c5n T\u00f0 \u00de g;i \u00f0i \u00bc 1;\u2026p\u22122; and j \u00bc 1;\u2026; q\u00de: \u00f017\u00de By the added small amount \u2202\u03b6j in the polynomial coefficients and their corresponding normal deviations \u2202Ri(j) of the surface points, the sensitivity matrix can be constructed by Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000320_ip-b.1988.0042-Figure39-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000320_ip-b.1988.0042-Figure39-1.png", + "caption": "Fig. 39 Emsland Transrapid test track", + "texts": [ + " To achieve an acceptable inverter rating the stator winding is therefore divided into sections with only those sections coupled to the secondary excited at a given time [43]. This is achieved as shown in Fig. 38 with two inverters supplying two supply cables, 1 and 2, running the length of the track (31.5 km at Emsland). The sections are connected alternately to feeders 1 and 2 through switches which are then sequentially operated in a leapfrog manner to ensure a smooth transition as the secondary moves from one section to another. The layout of motor sections at the Emsland Track is shown in Fig. 39 with 58 feeder sections between 300 m in length in the high speed area, and 2,000 m in the reversing loops. The 3-phase stator windings are positioned in slotted, laminated, cores approximately 1 m long and 220 mm wide laid end to end along the track [44]. Fig. 40 shows details of the winding which consists, very simply, of three insulated cables laid into the stator slots in a wavelike manner, forming a 1 turn per coil, one slot per pole per phase, fully pitched winding of 150 mm2 copper cross-sectional area", + " 40 Stator winding arrangement for Emsland track One advantage of an active track is that the on-board power requirements are much less than a short-stator equivalent, where the primary winding, inverter, and conditioner, are often mounted on the vehicle, and supplied by means of current collectors. The design balance of this advantage against the impedance of an active track is IEE PROCEEDINGS, Vol. 135, Pt. B, No. 6, NOVEMBER 1988 395 shown in Fig. 41 for the Emsland test track. The section numbers correspond to those of Fig. 39 and it can be 2 000r facing downwards to attract the vehicle mounted poles upward, as shown in the TR 06 cross-section of Fig. 42. 298m min. length stator ^wind ing feeder cable output trans 57 former stator inding feeder cable output .trans former 5710 20 30 A0 50 number of motorsection c Fig. 41 Data of Emsland test track stator sections a Length of sections b Resistance of sections c Inductance of sections seen that those sections on the high speed straight, which operate at high frequency, have been reduced in length to keep the section impedance to an acceptable value", + " A similar mechanism for providing excitation to a synchronous motor excitation winding was proposed by Chalmers [49] for cylindrical machines in 1972. The rectified output of the pole-face generator winding supplies a 440 V battery required for low speed operation. At a velocity of 110 km/h the generator is capable of supplying all on-board requirements, and above this speed the batteries are recharged. Table 11 gives some basic data of the Transrapid 06. Initial tests have been performed using sections 11 to 57 (Fig. 39) which were the first to be built. Figs. 45 and 46 show some of the characteristics during acceleration to 355 km/h. F, in these Figures is the load force including gradients, windage and drag force. The discontinuity at DT/SB on Fig. 45 is due to the change from direct inverter supply to sypply via the output transformers. Evaluation of these graphs shows the following performance data: Maximum motor active power 11.5 MW Maximum motor apparent power 15 MVA Power factor 300 km/h constant) 0.6-0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000457_s0006-3495(78)85431-9-FigureI-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000457_s0006-3495(78)85431-9-FigureI-1.png", + "caption": "FIGURE I FIGURE 2", + "texts": [ + " If we introduce the angle, a(s, t) between the flagellum and the x axis, then dx = cos ads and dy = sin ads. Then x(s, t) = x(O, t) + cos (a(s', t)) ds', (2a) s y(s, t) = y(O, t) + sin (a(s', t)) ds' (2b) where (x(O, t), y(O, t)) is the motion of the proximal end of the flagellum. We now introduce a local coordinate system defined by the unit tangent and normal vectors at a point on the flagellum (see Fig. 1). T(s, t) = = (cos (a(s, t)), sin (a(s, t))), (3a) as N(s, t) =(sin a(s, t), cos (a(s, t))) (3b) HINES AND BLUM Bend Propagation in Flagella 43 FIGURE I The vector r(s, t) describes the position of point s on the flagellum (O < s < L) at time t. Normal, N, and tangential, T, unit vectors are also shown. The variable a(s, t) measures the angle between T and the x-axis. Viscous Forces We next use the Gray-Hancock approximation to relate the normal, XN(5, t), and tangential, T(S, t), forces to the normal and tangential velocities, respectively, on an element ds. ON(S, t)ds = -CN VNds (10) 0T(S, t)ds = -CT VTds (11) The normal viscous drag coefficient, CN, is taken in this paper to be twice that of the tangential drag coefficient, CT, although a ratio of CN/CT = 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000491_978-3-540-79029-7-Figure6.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000491_978-3-540-79029-7-Figure6.11-1.png", + "caption": "Fig. 6.11 Vector diagram of the IM in the stationary operation", + "texts": [ + " r NR s Z 2 3 r sqNN RP I s 2 3 N sqN N PI Z 2 cosPhase Phase sqN N U II Z Parameter estimation from name plate data 207 2. Calculation of the torque-forming current component isq 222sqN sdNNI I I (6.62) 3. Calculation of \u03c9r 2 60 p N rN N z n f= (6.63) 4. Calculation of the rotor time constant Tr sqN r sdNrN IT I = (6.64) 5. Calculation of the leakage reactance s sX L= The voltage drop over the stator resistance is neglected, which is justified for the nominal working point, compared to the voltage drop over the leakage inductance in the vector diagram in the figure 6.11. The simplified vector diagram of the figure 6.12 can be obtained then. 208 Equivalent circuits and methods to determine the system parameters (5) Inserting (2) into (4): =s in s in cossqN sdN N N I I I I (6) From fig. 6.12 it will be obtained: s in N sqN UX I (7) Inserting (5) into (6): s in cos sdN N sqN N I UX I I With these results the formula for the calculation of X\u03c3 is obtained: sin cos 3 sdN N sqN N UIX II (6.65) 6. Calculation of the main reactance Xh: The main reactance ( )1h s s s sX L L= is the reactance of the EMF eg" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003943_j.msea.2019.04.108-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003943_j.msea.2019.04.108-Figure5-1.png", + "caption": "Fig. 5. (a) 3D schematic and (b) specimen.", + "texts": [ + " All specimens were fabricated under the same combination of the process parameters so that the specimens had the similar density and mechanical properties. The specimens were designed according to Chinese GB/T228-2002 standard [27] which was nearly similar to ISO 6892\u20131998 [28]. The dimensions of the specimen are shown as Fig. 4. According to the literature [23,29], the mechanical properties of the specimens which were parallel to the deposition direction were lower than those of the specimens which were perpendicular to the deposition direction. As shown in Fig. 5(a), the rod is perpendicular to the deposition direction. The rods were subjected to subsequent machining and polishing to form the experimental specimens, which are shown in Fig. 5(b). The microstructure of the LMDed specimen was different from that of the specimen manufactured by the traditional manufacturing process [30,31]. In order to observe the microstructure of the specimen, nitrohydrochloric acid was applied to corrode the surface. The optical microscopy (OM) was employed to observe the microstructure of the LMDed SS304 specimen. ImageJ software was applied to measure the grain size. Electron backscattered diffraction (EBSD) was applied to ensure the phase compositions of the LMDed specimen" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure15-1.png", + "caption": "Figure 15. Monitor locations.", + "texts": [ + " According to the previous analysis, gearbox resonance occurs with increasing vehicle velocity due to the 20th-order polygon wheel wear. Moreover, vibration of the monitoring points increases sharply relative to the normal condition. To validate the accuracy of the dynamics model and the simulation results, rig tests in the laboratory and field experiments on the Beijing\u2013Shanghai high-speed rail line, respectively, were carried out. Acceleration was measured on the gearbox housing and axle box. Figure 15 shows the locations of the accelerometers. The acceleration data were collected both in the lateral and the vertical directions with a sampling frequency of 5000Hz. The rig consisted of one full-scale bogie with a scaled roller (Figure 16), and the roller was designed to be replaceable to simulate all types of wheel defects, such as wheel flat, wheel tread peeling, and polygonal wheel wear. During the rig tests, the motor of the rig drove the roller via the transmission system, and the wheelset was driven by the roller" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000888_0278364908091365-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000888_0278364908091365-Figure2-1.png", + "caption": "Fig. 2. A typical walking step of our simple point mass model. The double stance phase starts when the heel of the leading leg has just made contact with the ground. In this phase torques in both ankles and actuate the walker. The effect of this actuation is studied in this paper. When the foot of the trailing leg loses contact with the ground, the single stance phase starts in which the actuated ( ) swing leg (thin line) swings forward past the stance leg (thick line). Foot scuffing at the midstance is ignored. The stance leg is still actuated by the ankle torque . A step is completed when the heel of the swing leg touches the ground. Here is the angle between the stance leg and the ground normal, h is the angle between the two legs, a st is the angle between the stance/leading leg and foot, a sw is the angle between the swing/trailing leg and foot, ll is the leg length, lh is the distance from ankle to heel, lt is the distance from ankle to toe, M is the hip mass, m is the leg mass and g is the gravitational acceleration. Adapted from Garcia et al. (1998).", + "texts": [ + " The contribution of ankle actuation to energy use, disturbance rejection and versatility is studied through the use of two models and one physical prototype walker. The first model is a generalistic and fast computable simple point mass model, the second model is a more realistic model closely resembling the actual dynamic properties of a real prototype. The model findings will be verified by measurements on a real 2D prototype walker called \u201cMeta\u201d. The two models and the prototype are described in the following. Simple straight legged point mass models of bipeds (Figure 2) have been studied thoroughly (Garcia et al. 1998 Goswami at UNIV OF COLORADO LIBRARIES on December 22, 2014ijr.sagepub.comDownloaded from et al. 1998 Kuo 2002 Kajita et al. 2003). Owing to the fact that the dynamics of these models are well understood and that their simulation time is relatively short, we use such a point mass model as the start of our research into ankle actuation for Limit Cycle Walkers. Our simple point mass model is based on the simplest walking model by Garcia et al. (1998). Our model is a 2D model consisting of four rigid links, two legs with unit length ll connected at the hip and two feet connected to each leg at the ankle, extending forward over a distance of lt (ankle\u2013toe) and backward over a distance of lh (ankle\u2013heel). There are three point masses in the model, one in the hip with unit mass M and two infinitesimally small masses m at the ankle joint as shown in Figure 2. The model walks in a gravity field with unit magnitude g. Torques are applied in the hip joint ( h) and in the two ankle joints ( a st and a sw). The unilateral constraints between the model\u2019s feet and the ground are modeled as rigid constraints. A typical step of this model starts when the heel of the leading leg has just made contact with the ground. The model is in double stance as long as both feet are touching the ground. During this phase the effect of the infinitesimally small masses m is negligible" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002905_s11665-017-2874-5-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002905_s11665-017-2874-5-Figure13-1.png", + "caption": "Fig. 13 CAD model of the engine mount", + "texts": [ + " Numerical results with power reduced to 300 W show a reducing of ball height to 60 lm\u2014just enough to enable successful build of the specimen with minimal interaction between the material and the coater blade. Forster et al. (Ref 18) reported a similar problem pertaining to the interaction of the coater arm with the distorted surface of the build. During the build process the upper layers might deform or delaminate causing the build process to terminate. An engine mount is used to study the ability of macromodels to predict the distortions during the build process (Fig. 13). The process parameters used were chosen based on coupon experiment series 1 and simulation results showing high density and no balling. Figure 14 shows the state of the build after the build process was interrupted. The build height achieved is approximately 6 mm. The actual region where the coater arm collided with the build could not be identified exactly\u2014the support structure is thought to be the region with most interaction. Residual stress modeling was pursued (Ref 36). Taking the process parameters and the deposition strategy into account the macromodel results indicate a distortion of 15 lm after 2 mm and 102 lm after 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003636_j.wear.2016.09.020-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003636_j.wear.2016.09.020-Figure5-1.png", + "caption": "Fig. 5. A schematic of the end-face friction tester.", + "texts": [ + " Metallographic examination was performed using optical microscopy, scanning electron microscopy (SEM), and energydispersive x-ray spectroscopy (EDS) on polished and etched cross sections. The surface topography after friction and wear testing was observed using confocal laser scanning microscopy (CLSM). Friction and wear tests were performed on a ring-on-disc rig (Jinan YiHua Tribology Testing Technology Co., Ltd., Jinan, China), which was used in the previous studies for simulating the contact between the port plate and cylinder barrel in an axial piston pump [25,29]. As shown in Fig. 5, the upper sample is mounted on the main shaft driven by a servo motor and rotated at a constant speed. A force is applied to the lower sample by a load cell via a hydraulic cylinder which raises the normal force to contact surfaces between the port plate and the cylinder barrel. In this way, the rig creates a sliding contact which can measure the coefficient of friction and wear rate between the port plate and cylinder barrel. The upper and lower samples are sealed in an oil box through which oil flows in and out" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002576_tie.2019.2952786-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002576_tie.2019.2952786-Figure1-1.png", + "caption": "Fig. 1. Earth-fixed frame XOY and the body-fixed frame XBFBYB .", + "texts": [ + " Eventually, a dynamics-level finitetime fuzzy monocular visual servo (DFFMVS) scheme for a USV is created, and thereby achieving a completely modelfree visual servo which can also be readily extended to other mobile vehicles. The rest of this paper is organized as follows. The visual servo problem for a USV is formulated in Section II. Visual servo error dynamics are derived in Section III. The FVO for scaled velocity is developed in Section IV. The DFFMVS scheme together with stability analysis is presented in Section V. Simulation studies are conducted in Section VI, and conclusions are drawn in Section VII. As illustrated in Fig. 1, the USV kinematics and dynamics can be described within earth- and body-fixed coordinate frames, i.e., XOY and XBFBYB , respectively, and are modeled as follows [44]: \u03b7\u0307 = Rz(\u03c8)\u03bd (1a) M(t)\u03bd\u0307 = f(\u03bd, t) + \u03c4 (1b) where \u03b7 = [x, y, \u03c8]T and \u03bd = [u, v, r]T are kinematics and dynamics vectors, \u03c4 := [\u03c4u, \u03c4v, \u03c4r] T is the control input vector, f(\u03bd, t) := [fu, fv, fr] T is the vector of completely unknown dynamics including both internal dynamics and external dis- turbances, inertia matrix M(t) = [ m11(t) 0 0 0 m22(t) m23(t) 0 m32(t) m33(t) ] > 0 \u2200t, includes the mass of the USV and added moment of inertia arising from complex hydrodynamics, Rz(\u03c8) =[ cos\u03c8 \u2212 sin\u03c8 0 sin\u03c8 cos\u03c8 0 0 0 1 ] is the rotation matrix" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000449_0278364907080423-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000449_0278364907080423-Figure4-1.png", + "caption": "Fig. 4. The robot on the stairs with the defined frames shown: the global frame G fixed to the stairs, the local frame L , attached to the robot, and the camera frame C . The width of the stairs is denoted by .", + "texts": [ + " The main reasons for this are: (i) dynamic modeling is dependent on robot and stair parameters, and would thus require calibration for every new stair, and (ii) dynamic model-based observers require a large number of states that increase the computational needs without producing superior results. This has been documented in the literature before the interested reader is referred to Lefferts and Markley (1976), Roumeliotis et al. (1999), and Maybeck (1979) for a detailed discussion. The robot\u2019s attitude describes the relationship between the global coordinate frame G and the robot-fixed local coordinate frame L . As shown in Figure 4, G is affixed to the stairs, such that the y-axis is parallel to the edges of the steps and the z-axis is pointing upwards. Additionally, we define a camera-fixed coordinate frame C , whose relationship to the local frame L is known and constant. The Euler angles yaw, pitch, and roll, which are the most commonly used attitude representation (Shuster 1993), are subject to singularities. The direction-cosine matrix, another at TEXAS SOUTHERN UNIVERSITY on November 5, 2014ijr.sagepub.comDownloaded from popular representation, suffers from redundancy, comprising nine elements of which only three are independent", + " We note that this ratio will in general differ from the ratio of the distances of the robot\u2019s center from the ends of the stairs. However, for small steering angles this difference is not significant, and we found that it does not hinder the controller\u2019s performance. The 3D coordinates of two points that lie on the left and right ends of a stair edge are given respectively by: GpL xo zo and GpR xo 0 zo (52) where the width of the stairs is denoted by , and the coordinates xo and zo can be arbitrary (cf. Figure 4). The projective image coordinates of the projection of the left endpoint on the image are determined by: at TEXAS SOUTHERN UNIVERSITY on November 5, 2014ijr.sagepub.comDownloaded from pLp 1 cL C CG qs C pG GpL 1 1 cL C CG qs C CG qs GpC GpL 1 1 cL C CG qs GpL GpC (53) where the vector GpC [xc yc zc]T denotes the position of the camera in the global coordinate frame, and cL is an arbitrary nonzero scalar. From the last expression we obtain: xo xc yc zo zc cLCT CG qs pLp (54) By employing similar derivations for the right endpoint of the stair edge, we obtain xo xc yc zo zc cRCT CG qs pRp (55) for some nonzero multiplicative constant cR " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000619_00207178408933260-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000619_00207178408933260-Figure4-1.png", + "caption": "Figure 4. Five-link model of CW-I.", + "texts": [ + " Coordinate transformer and analogue switches : R when grounding foot is right one; L when grounding foot is left one. 3.2. Modelling for the attitude control We assume that the above mentioned foot controller is perfectly executed and that the foot of the supporting leg is fixed to the floor until the swinging leg is transferred to the forward direction. Also we assume that the floor is located at the level of the ankle of the supporting leg (to simplify the problem). Then the seven-link model is reduced to a five-link model, illust.ratcd by Fig. 4. In this model, the parameters of the lower part of the swinging leg are obtained such that the lower leg is assumed to include the foot. If the origin of the sagittal plane is placed at the ankle of the supporting leg, the eentre of mass (3:,., y,.) of each link can be described by .7:1=a1 sin (}1' x. = II sin (}1 +G. sin ()., x3 = 11 sin (}1 + l. sin (),+a3 sin (}3' x4=ll sin (}1+l. sin (}.-b. sin e; x. = II sin (}1 + l. sin ().-l. sin (). - b. sin (). Yl = a1 cos (}1 Y. = II eos (}1 +G. eos ()" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000665_800905-FigureA-4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000665_800905-FigureA-4-1.png", + "caption": "Fig. A-4 - One spring from a four-spring suspension with torque leaves (see Fig. 6)", + "texts": [], + "surrounding_texts": [ + "8 0 0 9 0 5 9\nand (b) the effective spring rate decreases if either the amplitude of stroking is increased or the nominal static load is descreased. Since truck leaf springs are complicated nonlinear devices, involving hysteretic damp ing, their representation in detailed analyses of vehicle dynamics studies of ride, braking, or handling is not easily accomplished using linear approximations or simplified models. Accordingly, a mathematical method for repre senting the force-deflection properties of truck leaf springs has been presented and discussed herein.\nREFERENCES 1. R.W. Murphy, J.E. Bernard, and C.B. Winkler, \"A Computer-Based Mathematical Method for Predicting the Braking Performance of Trucks and Tractor-Trailers.\" Phase I Report:\nMotor Truck Braking and Handling Performance Study, Highway Safety Research Institute, University of Michigan, Ann Arbor, September 15, 1972. 2. P.S. Fancher, Jr., \"Pitching and Bouncing Dynamics Excited During Antilock Braking of a Heavy Truck.\" Proceedings, 5th VSD-2nd IUTAM Symposium, Vienna, Austria, September 19-23, 1977, pp. 203-221.\n3. C.C. MacAdam, \"Computer Simulation and Parameter Sensitivity Study of a Commercial Vehicle During Antiskid Braking.\" 6th VSD3rd IUTAM Symposium, Berlin, Germany, September 1979. APPENDIX A\nFigures A-l through A-4 plus Figure 8 illustrate the overall force versus deflection characteristics of the leaf springs examined in this research investigation.\n1000 lbs\nDEFLECTION-\nFig. A-l - Tapered-leaf front spring", + "10 800905", + "8 0 0 9 0 5\nAPPENDIX B The figures in this appendix ( B - l through B-5) provide comparisons between test results obtained at 0.5 and 6.0 Hz. Four sets of data (at two amplitudes of deflection and two nominal loads) are presented for each of the springs\ntested. Although the data measured at 6.0 Hz contain high frequency fluctuations, examina tion of the data presented in this appendix indicates that the force-deflection charac teristics measured at 6.0 Hz are practically the same as the results obtained at 0.5 Hz." + ] + }, + { + "image_filename": "designv10_3_0003886_j.mechmachtheory.2019.103693-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003886_j.mechmachtheory.2019.103693-Figure1-1.png", + "caption": "Fig. 1. Structure of high-speed CDPR \u201cT-Bot\u201d.", + "texts": [ + " In Section 4 , force transmission of CDPRs is analyzed, and indices for evaluating the performance are defined based on matrix orthogonal degree. In Section 5 , the geometric parameters of T-Bot are optimized. The spring parameters are determined based on the acceleration and cable tension requirements. Section 6 presents the experimental verifications of the robot on performances of workspace, dynamics, and high-speed pick-and-place motion. Finally, the conclusions and prospects are provided in Section 7 . The prototype of the designed translational CDPR is displayed in Fig. 1 , and named T-Bot. The T-Bot includes a base, actuation units, guiding pulleys, three sets of parallel cables, passive telescopic rod, and end effector. The end effector is connected to the base through six cables and the spring-mounted telescopic rod. The six cables are divided into three sets of parallel cables. Each set of parallel cables is driven by a servomotor through a reducer and drum. The three groups of actuation units and parallel cables are distributed circularly symmetrically. The tensioned parallel cables ensure that the end effector does not rotate during motion, therefore achieving three DOFs of translational motion. The spring-mounted telescopic rod consists of a rigid rod and a compressed spring, which are coaxially installed, as indicated in Fig. 1 (b). The rigid rod is attached to the base by a hybrid hinge that is composed of a universal (U) joint and prismatic (P) joint. The other end of the rigid rod is connected to the center of the end effector through the other universal joint. The telescopic rod can be regarded as a UPU branch that can swing around point O and move along the axial direction of the prismatic joint. The spring is compressed during the motion, and a reasonable downward pressure is applied on the end effector to meet the requirements of cable tension and acceleration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001539_iciinfs.2013.6731982-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001539_iciinfs.2013.6731982-Figure4-1.png", + "caption": "Fig. 4. Full assembled flight ready quadr", + "texts": [ + "32 \u00d7 1 Motor constant 1050 Propeller parameters Thrust coefficient 2.06 \u00d7 1 Torque coefficient 1.01 \u00d7 1 Pitch 4.5 V. IMPLEMENTATIO Implementation of the quadrotor was m software implementation of the controller and fabrication of a hardware platform. A. Design and fabrication of hardwa m 0-2 kgm2 0-2 kgm2 0-2 kgm2 rpm/V 0-7 Ns2 0-10 Nms2 N ainly focused on as well as design re platform shaped base structure due to weight. BLDC motors of 1050k blade propellers were used as Lithium Polymer battery, which used. Fig. 4 shows the fully asse The controller board was controller board which was us remote controller. Microcontro Microchip PIC 32MX795L512H were designed for GPS, Com sensors. The controller board RS232 interfaces, one USB inte (OTG) interface for communi sensor was used as the IMU wh attitude data at a speed of 5 quadrotor were taken from LS 2.4GHZ XBee-PRO 63mW rad data transferring allowed to communication protocol. Fig. 5 board. Mechanical vibrations motor-propeller assembly affec readings. Mechanical vibration the propellers and using dam sponge) to get a less noisy feedb B" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure9.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure9.7-1.png", + "caption": "Fig. 9.7 Phasor diagram.", + "texts": [ + " l) is an important variable because it is the mechanical angle which determines the inertia torque in the equation of motion. The transformation for the ith machine in an m-machine system is or UDQi = Udqi\u20ac-ioj The current transformation is IDQi =ldqi\u20ac-ioj (9.1 ) Thus the transformation for anyone machine is independent of those for all the other machines. The network equation relating the set of voltages UD Q and currents ID Q are (9.2) where ZD Q is the matrix of self and transfer complex impedances of the system and LD Q is the matrix of network inductances. Fig. 9.7 is a phasor diagram to illustrate, at any general operating condition, the position of the network voltage U in the common reference frame (D,Q) for either of two individual machines having reference frames (d l ,ql ) and (d2 ,Q2). The angles by which the two rotors lag behind the synchronously rotating reference frame are l) land l) 2 . 9.S.1 Solution neglecting -J; d, -J; q' and iD Q With this simplification the axis currents and voltages in a machine are slowly changing quantities and the three-phase armature currents, and hence also the network currents, may therefore be represented by slowly changing phasors" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003507_j.apmt.2020.100611-Figure27-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003507_j.apmt.2020.100611-Figure27-1.png", + "caption": "Fig. 27. Laminar actuator preparation scheme. (a) Printing and curing. (b) Activation by applied current [146]. Reproduced by permission of The Royal Society of Chemistry.", + "texts": [ + " This work represents a great and innovative contribution to the study of LCEs for 4D printing applied to new fields. The same research team also used three monomers combined in a printable material: RM257, EDDET and 3-mercaptopropionate, used as crosslinker [146]. They also created current responsive shapes printed in TangoBlackTM or VeroWhiteTM. Moreover, silver nanoparticles printed on the top of the LCE based shapes added the electric conductive properties to the final materials. A laminar actuator prepared with the described process is represented in Fig. 27. The shape morphing of the samples is due to the heating induced by the applied current (conductive Joule heating effect), leading the component to contract due to polymeric chain relaxation. These studies contributed to the establishment of LCE base materials as good candidates for 4D applications. 3.2.6. Other polymers As previously stated, some of the chosen polymeric materials needed to be modified. The present sub-section presents the reported work with polymeric materials not included in any of the previous classifications" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002779_s00170-015-7609-x-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002779_s00170-015-7609-x-Figure3-1.png", + "caption": "Fig. 3 The entire model and extracted model of the finite element model for numerical simulation", + "texts": [ + " Moreover, in contrast to the modeling SLS processing, the element size of the powder bed should be much smaller and was taken as 10 \u03bcm in our model. The \u03bcMKS (termed as \u03bcm, kg, s) system of units was employed for the micro-scale modeling and turns out to be efficient [26]. Taking account of the computational precision as well as the elapsed time cost of iterations, the finite element meshes with 175,200 hexahedral elements and about 190,776 nodes have been used for this simulation, which is shown in Fig. 3. In the scanning process of a track, the movement heat source was considered to occur in discrete time steps, and each time period is dictated by the element size and laser flight speed; moreover, the laser beam moves stepwise by one element in the x-direction. The stepping sequence begins at the starting spot and continues until the designated number of tracks is reached. Table 1 summarizes the parameters used in the finite element model. In order to determine the dimensions of the volumetric heat source, the radius and depth of the laser powder interaction zone are assumed to be equal to the laser beam radius x = 10 \u03bcm) and the optical penetration depth, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure23-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure23-1.png", + "caption": "Fig. 23 contac", + "texts": [ + " The generation of a face-gear that is conjugated to a helical involute pinion is traditionally performed by a helical shaper. The authors have developed the generation of a face-gear conjugated to a helical pinion by a worm of a special shape. The proposed approach is based on simultaneous meshing of the worm, the sha- per, and the face-gear (Fig. 18) taking into account the following: the shaper surface Rs is in line contact with the face-gear tooth surface R2 and with the worm surface Rw as well. Designations Ls2 and Lsw indicate the lines of tangency of surfaces Rs and R2 and of tangency of Rs and Rw (Fig. 23(a) and (b)). However, the worm and the face-gear surfaces Rw and R2 are in point contact at every instant since contact lines Ls2 and Lsw do not coincide but intersect each other (Fig. 23(c)). Consider now that the worm and the face-gear perform rotations about their axes related by equation ww w2 \u00bc N 2 Nw : \u00f041\u00de Usually, Nw = 1 since a one-thread worm is applied. Due to the point tangency of surfaces Rw and R2, the worm may generate on surface R2 only a strip. The generation by the worm of the whole surface R2 (instead of a strip), requires application of two- parameter enveloping process that is based on the following ideas: (1) Assume that the worm, the shaper, and the face-gear are in simultaneous meshing as it is represented in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002517_1.4033662-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002517_1.4033662-Figure5-1.png", + "caption": "Fig. 5 The mesh used to verify the heat input model, displacement boundary conditions (markers on the 2x face), and heat source scans (lines on the 1z face, not to scale). The hatch spacing between scans is 0.1 mm.", + "texts": [], + "surrounding_texts": [ + "4.1 Numerical Implementation. In order to verify the accuracy and efficiency of the proposed heat input models, simulations are performed for the same process with Goldak\u2019s model and each of the new models with various time increment sizes. An 18 18 1.5 mm3 Ti\u20136Al\u20134V substrate is heated by five heat source passes, each proceeding in the \u00fex direction (see Figs. 5 and 6). The substrate\u2019s density is 4430 kg/m3, its Young\u2019s modulus is 200 GPa, its Poisson\u2019s ratio is 0.3, and its coefficient of thermal expansion is 9 lm/m K. The temperature-dependent conductivity, specific heat, and yield strength are shown in Fig. 7. Outside the illustrated range of properties, the closest value is used. The complete stress relaxation is simulated at 690 C [42]. The heat source parameters are efficiency g\u00bc 0.45, width a\u00bc 0.1 mm, depth b\u00bc 0.06 mm, and length c\u00bc 0.1 mm. The power is P\u00bc 100 W, the length of each scan is 10 mm, and the scan velocity is vs\u00bc 450 mm/s. These values are taken from Ref. [7], which investigates a selective laser-melting process. For the thermal model, a uniform natural convection of 10 W/m2 K and radiation with emissivity 0.5 are applied to all the free surfaces. The ambient temperature and initial temperature for the substrate are both 30.5 C. For the mechanical model, six displacement constraints are applied to prevent the rigid body translations and rotations. A nonconforming mesh is automatically generated with the eight-node linear hexahedral elements for both thermal and mechanical analysis. The analysis code is CUBES by Pan Computing LLC, State College, PA, described in Ref. [13]. The lengths of the finest elements are 0.047 mm, roughly half the heat source radius. The time increment size is set such that the heat source moves approximately one fine element length each increment. 4.2 Results. The final temperature and displacement contours are shown in Figs. 8 and 9 for Goldak\u2019s model. The remainder of 111004-4 / Vol. 138, NOVEMBER 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935392/ on 02/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use this section compares Goldak\u2019s model to the two new models. The temperature results are compared along a line in the middle of the substrate. The displacement results are compared along a free edge of the substrate and are compared at node 1 on the free corner. These verification locations are illustrated in Fig. 10. Temperature versus x location is compared with the Goldak\u2019s model in Fig. 2(a) for LI and Fig. 2(b) for EE. The Ds\u00bc 0.5 curves in Figs. 2 and 11 are the results of the Goldak\u2019s model (Eq. (12)), while the other curves are the results of the new heat source models. As expected, the results for both models converge monotonically toward that of the Goldak\u2019s model as the time increment decreases. To facilitate comparison of different models, a dimensionless time increment size Ds is introduced Ds \u00bc vsDt c (19) Because Goldak\u2019s model requires Ds 1, this parameter provides a measure of how large the time increments used for the new models are relative to those used for the Goldak\u2019s model. Equivalently, it also measures the length of the segments in terms of the heat source radius. Note the stairsteps in the temperature profiles of LI, which motivate the use of EE. The longitudinal distortion is shown in Fig. 11. As expected, the results for LI converge monotonically toward that of Goldak\u2019s as Ds decreases. However, the EE models do not converge monotonically. Specifically, the largest time increment size Ds\u00bc 100 yields more accurate longitudinal distortion results than Ds\u00bc 25. Simulation wall times and percent errors are shown in Table 1. The percent errors for mechanical results are calculated as enode 1 \u00bc 100 uz u\u0302z uz (20) eRMS \u00bc 100 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 L \u00f0L 0 uz u\u0302z uz 2 dx s (21) where uz and u\u0302z are the z displacements calculated from the Goldak\u2019s model and one of the new models, respectively, and L\u00bc 18 mm is the length of the part. Equation (20) represents the error at the point of maximum displacement, while Eq. (21) averages errors along the displacement profile shown in Fig. 11. The error in residual stress is evaluated as estress \u00bc 100 j\u00f0rmax r\u0302max\u00de=rmaxj, where rmax and r\u0302max are the maximum von Mises stresses calculated from the Goldak\u2019s model and one of the new models, respectively. Percent errors for the thermal results are averaged over the heated region shown in Fig. 2 etherm% \u00bc 100 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Dx \u00f0x0\u00feDx x0 T T\u0302 T 2 dx vuut (22) Journal of Manufacturing Science and Engineering NOVEMBER 2016, Vol. 138 / 111004-5 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935392/ on 02/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use where T and T\u0302 are the temperatures calculated from the Goldak\u2019s model and one of the new models, respectively, x0 4.03 mm, and Dx 9.94 mm. These values of x correspond to the nodes closest to the beginning and end of the scan path. As expected, the simulations run faster as Ds increases. Even the slowest of the new models (LI with Ds\u00bc 10) runs nearly eight times faster than the Goldak\u2019s model. The percent errors generally increase as Ds increases. An LI usually gives more accurate mechanical results, likely because of the consistency with the Goldak\u2019s model as shown in Eq. (15). Despite its smoother and more accurate thermal results, EE gives less accurate displacements for small Ds. A convenient feature of LI is that each point in space receives the same incident energy as in Goldak\u2019s model, although distributed differently in time. However, EE differs from Goldak\u2019s model in both time and space, giving only the same total energy integrated over the volume of the part. These observations suggest that the 111004-6 / Vol. 138, NOVEMBER 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935392/ on 02/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use displacement is more sensitive to where heat is added to the part and less sensitive to when heat is added." + ] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.15-1.png", + "caption": "FIGURE 5.15. A Pf-R(90) link.", + "texts": [ + " Therefore, the transformation matrix -2. Tn place of the usual electrical equivalent (Fig. 4a), in which two electrical circuits with well defined terminals are linked magnetically, we may use a magnetic circuit (Fig. 4b) in which the coupling is electric. The current Equivalent circuits for rotating machines a Electric terminals b Magnetic terminals density everywhere in the rotor due to >< >: \u00f01\u00de _p \u00bc c1r \u00fe c2p\u00f0 \u00deq\u00fe c3L\u00fe c4N _q \u00bc c5pr c6 p2 r2 \u00fe c7M _r \u00bc c8p c2r\u00f0 \u00deq\u00fe c4L\u00fe c9N 8>< >: \u00f02\u00de where the dynamics of _v and _c are expressed as _v \u00bc L sinl\u00feY cosl mV cos c \u00fe T sina sinl cosa sinb cosl\u00f0 \u00de mV cos c _c \u00bc L cosl Y sinl mV \u00fe T cosa sin b sinl\u00fesina cosl\u00f0 \u00de mV g cos c V ( \u00f03\u00de The aerodynamic forces L;D;Y , and the moments L;M ;N are expressed as [33] L \u00bc qsCL; D \u00bc qsCD; Y \u00bc qsCY ; L \u00bc qsbCl; M \u00bc qscCm; N \u00bc qsbCn CL \u00bc CL0 \u00fe CLaa; CD \u00bc CD0 \u00fe CDaa\u00fe CDa2a2; CY \u00bc CY0 \u00fe CYbb Cl \u00bc Cl0 \u00fe Clbb\u00fe Cldada \u00fe Cldrdr \u00fe Clpbp 2V \u00fe Clrbr 2V Cm \u00bc Cm0 \u00fe Cmaa\u00fe Cmdede \u00fe Cmqcq 2V Cn \u00bc Cn0 \u00fe Cnbb\u00fe Cndada \u00fe Cndrdr \u00fe Cnpbp 2V \u00fe Cnrbr 2V 8>>>>< >>>>: \u00f04\u00de where q \u00bc 1 2q0V 2 is the dynamic pressure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000320_ip-b.1988.0042-Figure19-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000320_ip-b.1988.0042-Figure19-1.png", + "caption": "Fig. 19 Linear stepper motor arrangement", + "texts": [ + " By supplying the primary windings with a 2-phase current, the primary will step to the right in a synchronised motion. Fig. 18 shows the sequence of steps to move the slider over a tooth pitch in quarter pitch steps. At each step, the slider moves to the position of minimum reluctance for the current pattern selected. The current into each phase is a simple square wave and can be achieved by a bipolar chopper drive. Either the primary or secondary can be made the moving member. The motor shown in Fig. 19 is manufactured by TKK of IEE PROCEEDINGS, Vol. 135, Pt. B, No. 6, NOVEMBER 1988 387 Japan and distributed in the UK by Astrosyn International Technology. Resolution values (i.e. incremental movement of one step) of 0.2 mm and 0.4 mm are offered with a maximum load weight of 3 or 5 kg if the primary moves along a fixed secondary. Speeds of over 500 mm/s are possible. Obvious uses for these motors are high speed accurate positioning applications such as typewriters, printer and XY plotter drives, robot manipulator arms and machine tool positioning" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.5-1.png", + "caption": "Fig. 1.5 Designations on the physical pendulum; a) Internal center of gravity b) External center of gravity", + "texts": [ + " The accuracy of the result is determined by the difference (F2 \u2212 F1). The height h should therefore be selected as large as possible. 1.2 Determination of Mass Parameters 17 In a simple pendulum test, the body is suspended as a physical pendulum on an edge in a hole and can perform weakly attenuated oscillations about the contact point. The equation for its small-angle approximation of the natural frequency contains the moment of inertia about the axis of the suspension point and the centroidal distance. Thus, the period of vibration of the pendulum, see Fig. 1.5, for oscillations about A and B,respectively, is: TA = 2\u03c0 \u221a JA mga ; TB = 2\u03c0 \u221a JB mgb . (1.9) The distances a and b extend from the center of gravity to the suspension points A and B. Furthermore, according to the parallel-axes theorem (Steiner\u2019s theorem:), the following applies: JA = JS + ma2; JB = JS + mb2, (1.10) where JS is the moment of inertia with regard to the center of gravity in S. Taking into account the distance of the pendulum points e = b\u00b1 a, it follows that: b = e 4\u03c02e g \u2213 TA 2 2 4\u03c02e g \u2213 T 2 A \u2212 T 2 B ; JS = T 2 B 4\u03c02 mgb\u2212mb2. (1.11) The upper sign (\u2212) applies if S is located between A and B (Fig. 1.5a), the lower sign (+) applies if S falls outside of AB (Fig. 1.5b). It should be noted that (1.11) only applies when the center of gravity is located on the connecting line of the two suspension points. If this is not the case, one must first determine the center of gravity using a static method, and then determine the moment of inertia according to (1.9) and (1.10). 18 1 Model Generation and Parameter Identification An example will be used to compare the result determined by an experiment with a rough calculation. The following has been determined for the connecting rod shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure3.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure3.6-1.png", + "caption": "Figure 3.6.2 Rectangular-roughness cornering test.", + "texts": [ + " the pair of paths)maybe considered as a total symmetrical road partZS on the centreline plus an antisymmetrical banking part ZB, half of the path height difference, ZS \u00bc 1 2 \u00f0ZL \u00fe ZR\u00de ZB \u00bc 1 2 \u00f0ZL ZR\u00de and in reverse, ZL \u00bc ZS \u00fe ZB ZR \u00bc ZS ZB The centreline road elevation is therefore ZS \u00bc 1 2 \u00f0SL \u00fe SR\u00de sin\u00f0vSRX\u00de\u00fe 1 2 \u00f0CL \u00feCR\u00de cos\u00f0vSRX\u00de \u00bc SS sin\u00f0vSRX\u00de\u00feCS cos\u00f0vSRX\u00de The banking component is ZB \u00bc 1 2 \u00f0SL SR\u00de sin\u00f0vSRX\u00de\u00fe 1 2 \u00f0CL CR\u00decos\u00f0vSRX\u00de \u00bc SB sin\u00f0vSRX\u00de\u00feCB cos\u00f0vSRX\u00de The amplitudes are therefore related simply by SS \u00bc 1 2 \u00f0SL \u00fe SR\u00de CS \u00bc 1 2 \u00f0CL \u00fe CR\u00de SB \u00bc 1 2 \u00f0SL SR\u00de CB \u00bc 1 2 \u00f0CL CR\u00de These may in turn be combined into total amplitudes and phases: ZS \u00bc ZS0 sin\u00f0vSRX\u00fefS\u00de ZB \u00bc ZB0 sin\u00f0vSRX\u00fefB\u00de ZS0 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S2S \u00feC2 S q ZB0 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S2B \u00feC2 B q The phase angles are tan fS \u00bc CS=SS; fS \u00bc atan2\u00f0CS; SS\u00de tan fB \u00bc CB=SB; fB \u00bc atan2\u00f0CB; SB\u00de The antisymmetrical part may be considered to be due to a road bank angle fRB: tan fRB \u00bc 2ZB T \u00bc ZL ZR T ; 90 0 is arbitrarily small (see Fig. 2). 266 A. V. Bolsinov, A.V. Borisov, and I. S. Mamaev By the property of continuous dependence of solutions on the initial data (see [52]), the orbital stability of a solution x0(t), a < t <\u221e, is independent of the choice of the initial moment t0 \u2208 (a,\u221e); therefore, one can speak about the orbital stability of the whole trajectory. First of all we point out that, in contrast to the case of general Hamiltonian systems, in the integrable situation we have much more information about the system due to the presence of an additional structure: the integral and the foliation defined by it of the phase space into invariant integral submanifolds" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003053_978-0-8176-4962-3-Figure4.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003053_978-0-8176-4962-3-Figure4.1-1.png", + "caption": "Fig. 4.1. Inverted cart\u2013pendulum.", + "texts": [ + "7 Example 37 The proposed OISM algorithm can be summarized as follows: (1) design matrix L such that the eigenvalues of A\u0302 := (A\u0303\u2212LC) have negative real part; (2) compute the scalar gain \u03b2 (t) as in (4.8); (3) design the auxiliary systems x (k) a as in (4.19) with the sliding surfaces s(k) as in (4.21) and compute the constants Mk, k = 1, .., l\u2212 1; (4) run simultaneously the observer x\u0302 according to (4.23) and the controllers u0, u1 according to (4.27) and (4.8), respectively. To illustrate the procedure given above, let us take again the linearized model of an inverted pendulum over an inverted cart\u2013pendulum (see Fig. 4.1).The control problem is to maintain the inverted pendulum in a vertical line. The control law is the force applied to the trolley. The motion equations are as follows: x\u0307 (t) = Ax (t) +B (u0 + u1) +B\u03b3 (x, t) y (t) = Cx (t) (4.28) A = \u23a1 \u23a2 \u23a2 \u23a3 0 0 1 0 0 0 0 1 0 1.2586 0 0 0 7.5514 0 0 \u23a4 \u23a5 \u23a5 \u23a6 , B = \u23a1 \u23a2 \u23a2 \u23a3 0 0 0.1905 0.1429 \u23a4 \u23a5 \u23a5 \u23a6 , C = [ 1 0 0 0 0 0 0 1 ] \u03b3 (t) = {\u22120.4 n\u2212 5 \u2264 t < n\u2212 2.5 0.4 n\u2212 2.5 \u2264 t < n , n = 5, 10, . . . The state vector x consists of four state variables: x1 is the distance between a reference point and the center of inertia of the trolley; x2 represents the angle between the vertical and the pendulum; x3 represents the linear velocity of the trolley; finally, we have that x4 is equal to the angular velocity of the pendulum" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.8-1.png", + "caption": "FIGURE 5.8. Two coordinate frames based on Denevit-H art enberg rules.", + "texts": [ + " _ 1 1 1 - 0 1 (5.12) where and [ COS Bi i - I .u, = sl~Bi - sin Bi cos ai cos Bi cos o , sin a i sin Bi sin ai ] - cos Bi sin a i cos o, (5.13) [ ai cos Bi ] i - 1di = aisinBi . di The inverse of the homogeneous transformation matrix (5.11) is (5.14) i - 1r.- 1 1 [ COs Bi - sin Bi cos ai sin Bi sinai o sin Bi cos Bi cos o , - cos Bi sin a i o o sin a i cos o , o (5.15) - ai ]-di sin a i - di cos a i . 1 210 5. Forward Kinemat ics Proof. 1 Assume that the coordinate frames B 2(X2,Y2, Z2) and Bl(Xl ,Yl , Zt} in Figure 5.8 are set up based on Denavit-Hartenberg rules. The position vector of point P can be found in frame B, (Xl, Yl , Zl) using 2 r p and 18 2 lrp = lR2 2 r p + 18 2 which, in homogeneous coordinate representation , is equal to (5.16) cos(k2 , i t} cos(k2 , j t} cos(1\"2 , 1,, l ) o . (5.17) Using the parameters introduced in Figure 5.8, Equation (5.17) becomes - Se2ca2 Ce2ca 2 sa2 o Se2sa2 -Ce2sa2 ca2 o (5.18) If we subst it ute the coordinat e frame B, by Bi-l(Xi-l ,Yi-l , Zi-t} , and B2 by Bi(Xi ,Yi, Zi) , then we may rewrite the above equation in the requir ed form [ Xi_I ] [ ce i Yi-l _ sei Zi-l - 0 1 0 -Seicai Ceicai so; o Seisai - Ceisai cai o aiCei aiSei di 1 (5.19) 5. Forward Kinematics 211 Following the inversion rule of homogeneous transformation matrix i- 1Ti [ G~B ~S ] (5.20) i-ly- l [ G~~ _ G~~ Gs ] (5.21)z we also find the required inverse transformation (5", + " [~ ] [ COi SOi 0 - ai ][ x,_, ]-SOicai cOicai sai -disa i Y , -1 (5.22) SOisai - cOisa i cai -dicai Zi-l 0 0 0 1 1 \u2022 Proof. 2 An alternat ive met hod to find iTi_ 1 is to follow t he sequence of t ransla tions and rotations that brings the frame Bi - 1 to t he present configuration starting from a coincident posit ion with the frame Bi. Note that work ing with two frames can also be equivalent ly described by B == B, and G == B i - 1 , so all the following rotations and translations are about and along t he local coordinate frame axes. Inspect ing Figure 5.8 shows that: 1. Frame B i - 1 is translated along the local zi-axis by distance - di , 2. The displaced frame B i- 1 is rotated through - Oi about the local zi-axis, 3. The displaced frame B i - 1 is translated along t he local xi-axis by distance - ai , and 4. The displaced frame B i- 1 is rotated through - a i about the local xi-axis . Following these disp lacement sequences, the transformation matrix iTi_1 would be iTi_ 1 R Xi ,-o. i D x i ,-ai RZi ,-Oi DZi, -d i (5.23) [ cos Oi sin Oi 0 - ai ]- sin Bi cos ai cos Oi cos ai sinai - di sinai sin Bi sin a i - cos Oi sin a i cos a i - di cos a i 0 0 0 1 where D\",,-d, ~ [ ~ 0 0 0 ]1 0 0 (5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure3.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure3.1-1.png", + "caption": "Fig. 3.1 Rotary offset press with foundation; a) Schematic, b) FEM model and calculated third mode shape at f3 = 5.01 Hz (Source: Doctoral thesis Xingliang Gao, TU Chemnitz, 2001)", + "texts": [ + " The compensation amounts involved are often substantial since foundations do not just weigh a few dozen but hundreds (forging hammers, printing machines) or thousands of metric tons (groups of buildings) [25], [33]. This chapter discusses only some issues from the vast field of machine foundations [15], [19], [25], [31]: foundation blocks. It should be noted that many dynamic problems arise when configuring machine platforms as they are used, for example, for turbogenerators and printing machines, see the example shown in Fig. 3.1. Such large foundation designs require comprehensive calculations in advance using models with many degrees of freedom, see Chap. 6. The steel structure that carries the actual machine sub-assemblies is connected with a concrete foundation, which in turn rests on the subsoil, the characteristic values of which depend on the geological conditions at the mounting site. Sometimes a huge effort must be made to install a large machine, the foundation of which weighs several hundred tons, in such a way that it is operationally safe and isolated against vibrations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000902_0959651812455293-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000902_0959651812455293-Figure2-1.png", + "caption": "Figure 2. Definition of the Qball-X4 attitude.", + "texts": [ + " One frame is the body-fixed frame in which the origin is located at the centre of the mass of the Qball-X4. The other reference frame is the earth-fixed frame (known as the global frame) in which the origin can be chosen as desired. The coordinates xq, yq, zq are defined in body-fixed frame, and x, y, z are defined in the earth-fixed frame. Qball-X4 can be considered as a local frame rotating and translating in the global coordination. The Euler rotation and translation matrix has been introduced here to generate the general transformation. Figure 2 shows the Qball-X4\u2019s pitch, roll and yaw attitudes along the body-fixed axes x\u2013y. The general rotation matrix of all three axes, x\u2013y\u2013z, can be written as R=RzRyRx = cosc cos u cosc sin u sinf cosf sinc cosc sin u cosf+ sinf sinc sinc cos u sinc sin u sinf+ cosf cosc sinc sin u cosf sinf cosc sin u sinf cos u cos u cosf 2 4 3 5 \u00f01\u00de where c is the yaw angle about the z axis, u is the pitch angle along the y axis and f is the roll angle along the x axis. In the body-fixed frame, due to the alignment of propellers, all four forces generated by the four propellers are along the z axis, which are in the following form Fxq Fyq Fzq 2 4 3 5= 0 0 F1 +F2 +F3 +F4 2 4 3 5 \u00f02\u00de where Fi, i=1, ", + " Using the rotation matrix, equation (1), forces in the earth-fixed frame can be found as Fx Fy Fz 2 4 3 5=R Fxq Fyq Fzq 2 4 3 5 \u00f03\u00de By Newton\u2019s second law of motion, F=ma, and taking the friction factor f into consideration, the acceleration of each axis in the earth-fixed frame can be extracted as a=(F f)=m, or \u20acx \u20acy \u20acz 2 4 3 5= 1 m Fx fx Fy fy Fz G fz 2 4 3 5 = Fzq m cosc sin u cosf+ sinf sinc sinc sin u cosf sinf cosc cos u cosf 2 4 3 5 1 m fx fy G+ fz 2 4 3 5 \u00f04\u00de where m is the mass of the Qball-X4 and G=mg represents the gravity of the Qball-X4. The drag forces fx, fy and fz are defined according to aerodynamics19 as fx = dx _x, fy = dy _y and fz = dz _z. Positions, velocities and accelerations are variables governing the motion of the Qball-X4, which are caused by the change of the attitude of the Qball-X4 through pitch, roll and yaw angles. Attitude is determined directly from the force generated by each propeller. For instance, as shown in Figure 2, if forces F1 and F2 change, the torque of the x axis in the body-fixed frame will change accordingly with respect to the difference F1 F2, so as to the change of pitch angle, u. Similarly, the roll angle, f, will be changed by the difference F3 F4 and the yaw angle, c, will be changed by F1 +F2 F3 F4. A translational momentum M of the Qball-X4 rigid body can be written as19 M= _H= _Hq +vq 3H = Jq _vq + vq 3H \u00f05\u00de and in terms of Mq in a body-fixed frame, one has _vq = J 1q (Mq vq 3Hq)= J 1q \u00bdMq vq 3 (Jqvq) \u00f06\u00de where H is the matrix of the angular momentums in the earth-fixed frame, Hq is the matrix of the same momentums in the body-fixed frame, vq contains all of the angular velocities of the body-fixed frame and Jq is the at LAURENTIAN UNIV LIBRARY on November 25, 2014pii" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000428_jp7111457-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000428_jp7111457-Figure1-1.png", + "caption": "Figure 1. (a) Scheme of a single camphor-soaked, 1 mm agarose disk floating at an interface between water and air. The bottom picture is a side-view of the particle and illustrates the three major processes occurring in the system: camphor transport into the water, convection currents generated by surface tension, and sublimation of camphor at the water-air interface. WB and WS denote the bottom and the side walls of the particle, respectively. (b) An example of dynamically selfassembled array of 41 disks interacting via repulsive hydrodynamic interactions discussed in the text.", + "texts": [ + " Dynamic self-assembly (DySA),1,2 that is, self-assembly in systems organizing only when dissipating energy, is of fundamental interest in the context of life,3\u20135and can have practical applications in new classes of smart/adaptive systems and materials.6\u20138 Despite recent progress in the applications of DySA,9\u201311 the study of its underlying principles1,12,13 is often hampered by the lack of suitable model systems that would exhibit DySA under well-defined experimental conditions. Here, we describe one such system, in which surface-tension effects give rise to dynamic forces between the components and mediate their DySA into extended patterns (Figure 1). This system is based on the well-known camphor \u201cboats\u201d (i.e., millimeter-sized particles made from agarose and filled with camphor) floating at the interface between water and air. Such particles have been studied extensively by others,14\u201316 mostly for their ability to move autonomously15,17 and/or to synchronize their motions in constrained geometries.18,19 Although some of these works quantified the nature of the flow-fields around individual particles,15,17 they did not investigate whether such flows give rise to interparticle interactions", + " Particle trajectories and/or configurations were analyzed by image recognition software downloaded from http://physics.georgetown.edu/matlab/.* Corresponding author. E-mail: grzybor@northwestern.edu. 10.1021/jp7111457 CCC: $40.75 2008 American Chemical Society Published on Web 08/08/2008 1. Flows and Forces between Particles. 1.1. Flows around Isolated Particles. We first discuss the flows generated by an isolated and stationary, camphor-filled particle placed at the interface between water and air (Figure 1a). In doing so, we extend the previous models of the Marangoni convection around camphor boats by accounting for shear stress due to surface tension and sublimation of camphor as boundary conditions on the liquid-air interface. Previous studies17 have approximated these boundary conditions as volumetric effects occurring only within a thin layer of thickness \u03b4 near the interface. This approximation becomes increasingly inaccurate as \u03b4 increases. It also does not account for the transport of camphor in the bulk of the fluid which, through Marangoni convection, affects the interfacial camphor concentration and, as we will see later in the text, the forces between camphor-emitting particles", + ", particle and the surrounding fluid) is always maintained out of equilibrium by continuous delivery of camphor from the particle onto the interface and by camphor evaporation. The dynamics of this system has three major components: (i) flows generated by gradients of surface tension in the plane of the interface (i.e., Marangoni convection); (ii) camphor transport via both diffusion and convection; and (iii) sublimation of camphor from the liquid-air interface. It is important to note that these processes are mutually related (cf. Figure 1a). For example, gradients in the concentration of camphor at the interface give rise to gradients of surface tension which, ultimately, induce fluid flows. These flows, in turn, alter the distribution of camphor within the fluid and at the interface, and thus influence surface tension gradients that drive the flows. The fluid flows within the system are governed by the Navier-Stokes equations combined with the continuity equation for an incompressible fluid: F(\u2202Vb\u2202t +Vb \u00b7 \u2207 Vb))- \u2207 P+ \u00b5\u22072Vb and \u2207 \u00b7 Vb) 0 (1) Here, Vb is the fluid velocity, F is the density, \u00b5 is the viscosity, and P is the pressure", + " The boundary conditions are such that there is \u201cno slip\u201d both at the walls of the Petri dish and at the fluid-particle interface. At the fluid-air interface, S, camphor- induced gradients in the surface tension create shearing stresses on the liquid surface. The Cartesian components of these stresses in the plane of the interface (x-y) are related to the gradients of surface tension, \u03b3, by \u03c3bzx ) \u2202\u03b3/\u2202x|Sebx and \u03c3bzy ) \u2202\u03b3/\u2202y|Seby, where ebx and eby are the unit vectors in, respectively, the x and y directions, and the z-axis is normal to S and pointing upward (cf. Figure 1). Because camphor is only sparingly soluble in water and its solute-solute interactions are negligible, the variation of surface tension with concentration can be approximated as linear:22 \u03b3 ) \u03b3o - bc, where \u03b3o denotes the surface tension of pure water (72 mN/m), b is a constant of proportionality (henceforth, \u201cshear constant\u201d), and c stands for the concentration of camphor. With this simplification and using the well-known relation between shearing stresses and velocity gradients for a Newtonian fluid, the effects of surface tension to the flow fields can be related by \u03c3zx ) \u00b5[\u2202Vz \u2202x + \u2202Vx \u2202z ]S ) \u2202\u03b3 \u2202x S)-b \u2202c \u2202xS and \u03c3zy ) \u00b5[\u2202Vy \u2202z + \u2202Vz \u2202y ]S ) \u2202\u03b3 \u2202y S)-b \u2202c \u2202yS (2) Next, the equation governing the transport of camphor is \u2202c \u2202t +Vb \u00b7 \u2207 c)D\u22072c (3) where D is the diffusion coefficient of camphor in water. For the boundary conditions, there is no flux of camphor through the walls of the dish, nb\u00b7 (D\u2207c - Vbc)W ) 0 (nb is the unit vector normal to the walls, and W indicates the lower and side walls of the dish; see Figure 1a). The boundary condition at the liquid/ air interface accounting for the flux of camphor due to sublimation can be approximated as17 \u2202cS/\u2202t ) -kcS, where k is the rate constant of sublimation and cS is the camphor concentration at the interface. Because the z-component of velocity in the plane of the interface is zero, the sublimation flux through this interface is equal to diffusive flux of camphor from the fluid\u2019s bulk: -D\u2202c/\u2202z|S ) kcS. Because of the existence of the so-called Gibbs layer, the surface concentration of camphor, cS, may be larger than the concentration in the bulk, and can be approximated as23,24 cS ) Rc, where R is the adsorption equilibrium constant" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.34-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.34-1.png", + "caption": "Fig. 2.34 Nomenclature for the drive system of a processing machine with multiple linkages that operate in parallel", + "texts": [ + " It is not only the maximum value of the periodic forces and moments transmitted by a machine, but the size of each Fourier coefficient that is of interest in conjunction with vibration analyses for foundations, see 3.2.1.3. In multilink mechanisms, even the higher harmonics of the inertia forces are relevant. Often the task is to keep the inertia forces and specific excitation harmonics that are transmitted onto the foundation as small as possible. The respective methods for balancing of mechanisms and balancing of rotors are discussed in 2.6. Consider a multilink mechanism whose links move in parallel planes that can be offset in the z direction, see, for example, Fig. 2.34. The goal is to determine the resultant forces and moments that are transmitted from the moving machine parts via the frame onto the foundation. Internal static and kinetostatic forces and moments of the machine, such as spring forces between individual links, processing forces (e. g. cutting and pressing forces in forming machines and polygraphic machines, gas forces in internal combustion engines and compressors), have no influence on the foundation forces since they always occur in pairs and cancel each other out" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002174_s00170-012-4560-y-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002174_s00170-012-4560-y-Figure2-1.png", + "caption": "Fig. 2 The planetary gearbox test rig [1]", + "texts": [ + ", Newton\u2019s method [28] with the following iterative equation: \u03c3k\u00fe1 \u00bc \u03c3k J \u03c3\u00f0 \u00de J \u03c3\u00f0 \u00de \u00bc \u03c3k B \u03c3\u00f0 \u00de W \u03c3\u00f0 \u00de B \u03c3\u00f0 \u00de W \u03c3\u00f0 \u00de \u00f022\u00de where J and J are the first derivative and the second derivative of J with respect to \u03c3, respectively; and B \u03c3\u00f0 \u00de \u00bc 1PL i\u00bc1 P j\u00bc1 j 6\u00bc i L NiNj PL i\u00bc1 P j\u00bc1 j 6\u00bc i L PNi t\u00bc1 PNj k\u00bc1 k x\u00f0i\u00de t ; x\u00f0j\u00de k x\u00f0i\u00de t x\u00f0j\u00de k 2 \u03c33 h i ; W \u03c3\u00f0 \u00de \u00bc 1PL i\u00bc1 N2 i XL i\u00bc1 XNi t\u00bc1 XNi k\u00bc1 k x\u00f0i\u00de t ; x\u00f0i\u00de k x\u00f0i\u00de t x\u00f0i\u00de k 2 \u03c33 h i ; B \u03c3\u00f0 \u00de \u00bc 1PL i\u00bc1 P j\u00bc1 j 6\u00bc i L NiNj XL i\u00bc1 X j\u00bc1 j 6\u00bc i L XNi t\u00bc1 XNj k\u00bc1 k x\u00f0i\u00de t ; x\u00f0j\u00de k x\u00f0i\u00de t x\u00f0j\u00de k 4 3\u03c32 x\u00f0i\u00de t x\u00f0j\u00de k 2 \u03c36 h i ; W \u03c3\u00f0 \u00de \u00bc 1PL i\u00bc1 N2 i XL i\u00bc1 XNi t\u00bc1 XNi k\u00bc1 k x\u00f0i\u00de t ; x\u00f0i\u00de k x\u00f0i\u00de t x\u00f0i\u00de k 4 3\u03c32 x\u00f0i\u00de t x\u00f0i\u00de k 2 \u03c36 h i : The kernel feature selection and KFDA use the same parameter selection algorithm in different feature spaces, namely, the original feature space (n) and the reduced feature space (n\u2032), respectively. 3.1 Planetary gearbox test rig Figure 2 shows a planetary gearbox test rig designed to perform fully controlled experiments for developing a reliable diagnostic system. The planetary gearbox test rig has an over-hung floating configuration that can mimic the operation of field mining. It mainly includes a 20-HP drive motor, a one-stage bevel gearbox, a two-stage planetary gearbox, a two-stage speed-up gearbox, and a 40-HP load motor. Table 1 lists the number of teeth and transmission ratio achieved by each stage. The study object in this paper is the two-stage planetary gearbox diagramed in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002454_j.isatra.2016.01.017-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002454_j.isatra.2016.01.017-Figure1-1.png", + "caption": "Fig. 1. Reference frames.", + "texts": [ + " Body frame F tb is considered to be coincide with the LVLH frame, i.e., xtb is parallel to the vector rt and points to the radial direction; ytb is along the opposite direction of docking port, and ztb is perpendicular to the target orbit and three mutually perpendicular axes complete the right hand system; likewise, in frame F pb, ypb points toward the docking port on the pursuer spacecraft and three mutually perpendicular axes coincident with the principle axis of inertia. All the frames are shown in Fig. 1, where rt is the inertial position of the target spacecraft represented in the frame F tb, while rp is the inertial position of the target spacecraft represented in the frame F pb. Please cite this article as: Xia K, Huo W. Robust adaptive backsteppin with input saturation. ISA Transactions (2016), http://dx.doi.org/10.10 Suppose the target spacecraft is flying in an elliptical orbit. According to [20], the target position signals are governed by _v t \u00bc \u03bc r3t rt ; rt \u00bc \u00bdrt ;0;0 T ; rt \u00bc a\u00f01 e2\u00de 1\u00fee cos \u03bd ; where vt is the velocity of the target spacecraft with respect to F i expressed in F tb, \u03bc is the geocentric gravitational constant, a\u00bc rpa =\u00f01 e\u00de is the semimajor axis, rpa is the perigee altitude, e is the eccentricity of the elliptical orbit, \u03bd is the true anomaly, and the rate of the true anomaly is given by [21] _\u03bd \u00bc n\u00f01\u00fee cos \u03bd\u00de2 \u00f01 e2\u00de32 ; where n\u00bc ffiffiffiffiffiffiffiffiffiffi \u03bc=a3 p is the mean motion of the target" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000845_j.jbiomech.2008.02.031-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000845_j.jbiomech.2008.02.031-Figure1-1.png", + "caption": "Fig. 1. Illustration of human walking with arm swing on one foot stance. The torsional effect of the out-of-phase arm swing motion about the vertical axis is the same as that of the ground reaction moment about the vertical axis of the stance foot. Out-of-phase arm swing motion, therefore, reduces the reaction moment of the stance foot.", + "texts": [ + " There has also been analysis of arm swing in the sagittal plane using pendulum models (Wagenaar and Van Emmerik, 2000; Kubo et al., 2004). These studies correlate the magnitude and phase of arm swing with the speed of walking. Popovic et al. (2004) demonstrate that spin angular momentum is regulated during human walking and this idea is used in control. Building upon past work, in this paper we attempt to gain further insight into why and how out-of-phase arm swing motion is generated. We focus on the effect of reaction moment about the vertical axis of the foot (Fig. 1). It is believed that further study of arm motion will greatly aid in the understanding of the walking pattern overall. This understanding could prove useful in biomechanics, particularly with regard to the relation between leg muscle activation and upper body motion (Ferris et al., 2006). For humanoid robots, implicit, online generation of natural arm swing during walking could replace pre-planned joint trajectories to resolve problems of potential instability. The relationship between arm swing and reaction moment about the vertical axis of the foot is explained in Section 2 using an articulated multi-body system model", + " However, the subject may naturally compensate for lack of arm swing with head, torso, and pelvic motion that produce similar effects on the foot moment. Additionally, the behaviors of male and female subjects can be very different due to cultural influences (Li et al., 2001). Simulation allows the human motion to be consistently controlled, with the flexibility to introduce or remove constraints at will. Out-of-phase arm swing is a common pattern during human bipedal walking. The left arm moves forward when the right leg and torso move forward, and vice versa for the opposing leg and arm (Fig. 1). This arm motion, though natural, is not required for walking motion. For example, we are able to walk even while executing certain manual tasks which constrain the arms from swinging (e.g., holding an object with two hands or carrying a suitcase). However, without any special manual objectives the arm movements follow a consistent pattern. In this section, the reason for this natural arm motion is analyzed qualitatively from a dynamics perspective. Based on the conclusions obtained, ARTICLE IN PRESS J" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.17-1.png", + "caption": "FIGURE 4.17. A line indicated by two points.", + "texts": [ + " Th ey are: 1 - s (hx\" , i) s(hy , jJ, J) s (hz , 0:, K) 2 - s(hy , jJ, J) s(hz, 0:, K) s(hx , 'Y, i) 3 - s (hz, 0: , K)S(hx , 'Y, i) s(hy , jJ, J) 4 - s (hz, 0:, K) s (hy, jJ, J) s (hx, 'Y , i) 5 - s(hy, jJ, J) s(hx, 'Y, i) s(hz, 0: , K) 6 - s(hx, 'Y, i) s(hz , 0: , K) s (hy , jJ, J) Th e expanded form of the six com binations of prin cipal central screws are present ed in Appendix C. 4.8 * The Plucker Line Coordinate The most common coordinate set for showing a line is t he Plucker coordi nates. An alytical representation of a line in space ca n be found if we have t he position of two different po ints of that line . Assume PI (XI, YI , ZI) and P2(X2 , Y2 , Z 2) at rl and r 2 ar e two different points on the line l as shown in Figure 4.17 . Using the position vectors rl and r 2, the equation of line l can be defined by six elements of two vectors l=[~]= L M N p Q R (4.22 3) 174 4. Motion Kinematics referred to as Pliicker coordinates of the directed line, where, (4.224) is a uni t vector along the line referred to as direction vector, and (4.225) is the mom ent vector of uabout t he origin . The Plucker method is a canonical representation of line definition and therefore is more efficient than the ot her methods such as parametric form l(t) = rj + til , point and direction form (rj ,u), or two-point representation (rj,r2) " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.21-1.png", + "caption": "FIGURE 4.21. Illustration of two skew lines.", + "texts": [ + "248) [ ~: ] = G r B [ ~: ] by a 6 x 6 transformation matrix defined as G [ GRB 0]r \u00bb = GSoG R B GR B where (4.249) (4.250) (4.251) 180 4. Motion Kinematics S2 r32 - S3 r22 -Slr32 + S3r12 Slr22 - S2r12 (4.252) S2 r33 - S3 r23 ] -Slr33 + S3r13 . Slr23 - S2 r13 (4.253) (4.254) 4.9 * The Geometry of Plane and Line Plucker coordinates introduces a suitable method to define the moment be tween two lines, shortest distance between two lines, and the angle between two lines. 4.9.1 ~ A1o~ent Consider two arbitrary lines h = [Ul PI] T and l2 = [U2 P2] T as shown in Figure 4.21. Points PI and P2 on II and l2 are indicated by vectors rl and r2 respectively. Direction vectors of the lines are Ul and U2' The moment of the line l2 about PI is (r2 - rd x U2 and we can define the moment of the line l2 about h by l2 X h = Ul . (r2 - rd x U2 which, because of Ul . rl x U2 = U2 . Ul x rl , simplifies to (4.255) 4. Motion Kinematics 181 The reciprocal product or virtual product of two lines described by Plucker coordinates is defined as (4.256) The reciprocal product is commutative and gives th e moment between two directed lines" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000537_j.automatica.2006.05.008-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000537_j.automatica.2006.05.008-Figure2-1.png", + "caption": "Fig. 2. Mapping by W0: the bold line represents the argument + of the branch cut, while the dotted line represents the argument \u2212 of it.", + "texts": [ + " Since W0 is homeomorphic (Remark 2), these three points are continuously linked by a single curve. However, due to the leftward convexity of (21), i.e., the right side of the graph is open, the curve must be overlapped in a certain interval. This is contradictory to the fact that the mapping is homeomorphic. Namely, the maximum of Re(W0(z)) is taken at either z1 or z2. In the other cases where c = 0 or d = 0, which are the extreme cases of the previous one, we can show the similar properties from (19) that the \u2013 graph is leftward convex (see also Fig. 2) and W0 is proven to be a homeomorphism. Therefore, we can repeat the above argument in these cases, leading to the conclusion. The above discussion yields the following lemma, which elucidates a property of SW( , ) with respect to r . Lemma 6. Let and be constant. Then, max{SW( , )| r \u2208 [ r , r ]} = max{SW( , rej ), SW ( , r ej )}. Proof. As r varies in [ r , r ], zw moves along a segment similar to (18) and the extreme points of its locus correspond to r and r . The lemma follows from the above discussion", + " WR 0 (r, ) is a monotone increasing function with respect to \u2208 (\u2212 , 0] and a monotone decreasing function with respect to \u2208 [0, ]. WR k (r, ), k=\u22121, . . . ,\u2212\u221e are monotone increasing functions with respect to \u2208 (\u2212 , ]. WR k (r, ), k = 1, . . . ,\u221e are monotone decreasing functions with respect to \u2208 (\u2212 , ]. Proof. Let = . Since z /\u2208 BC0, W0(z) is analytic from Lemma 11. We thus obtain Re ( dW0(z) d ) = Re ( W0(z) 1 + W0(z) j ) . (A.2) Setting W0(z) = 0 + j 0, (A.2) is written as \u2212 0 (1 + 0) 2 + 2 0 . (A.3) Since 0 < 0 for \u2208 (\u2212 , 0) and 0 > 0 for \u2208 (0, ) (see Fig. 2), (A.3) > 0 and (A.3) < 0 is satisfied, respectively. This shows that WR 0 (r, ) is monotone increasing with respect to \u2208 (\u2212 , 0) and monotone decreasing with respect to \u2208 (0, ). Moreover, as WR 0 (r, ) is continuous at = 0 and , monotonicity is preserved at these points. In the same way, Wk(z), k = \u00b11, . . . ,\u00b1\u221e are analytic in z /\u2208 BC by Lemma 11 and we obtain Re ( dWk(z) d ) = \u2212 k (1 + k) 2 + 2 k , k = \u00b11, . . . ,\u00b1\u221e (A.4) with Wk(z) = k + j k , k = \u00b11, . . . ,\u00b1\u221e. Since k < 0 for Wk , k = \u22121, ", + " As C does not cross the branch cut of W0, W0(C), the mapping of C by W0, is separated from the other branches (see also Fig. 5) and we cannot follow the above discussion. To reach the conclusion, note that WR\u22121(1/e, ) = \u22121 and lim \u2192\u2212 WR 1 (1/e, ) = \u22121. Due to Lemma 12, we have WR\u00b11(1/e, ) \u2212 1 for \u2208 (\u2212 , ] (WR\u00b11 represents WR 1 and WR\u22121) and Lemma 13 leads to the fact that WR\u00b11(r, ) < \u2212 1 is true for r < 1/e and \u2208 (\u2212 , ]. On the other hand, it should be noticed that when r < 1/e, WR 0 (r, ) > \u2212 1 is satisfied for \u2208 (\u2212 , ] (see Fig. 2). Consequently, WR\u00b11(r, ) < WR 0 (r, ) (A.12) follows for r < 1/e and \u2208 (\u2212 , ]. Lemma 3 can now be concluded from the inequalities (A.8)\u2013(A.12). The proof is complete. Ahlfors, L. V. (1979). Complex analysis. (3rd ed.), New York: McGraw-Hill. Asl, F. M. & Ulsoy, A. G. (2000). Analytical solution of a system of homogeneous delay differential equations via the Lambert function Proceedings of the American control conference, Chicago, IL (pp. 2496\u20132500). Chen, J. & Niculescu, S.-I. (2004). Robust stability of quasi-polynomials with commensurate delays" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000308_s0006-3495(76)85672-x-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000308_s0006-3495(76)85672-x-Figure5-1.png", + "caption": "FIGURE 5 The body-fixed coordinate system of a sperm with a spherical head of radius R, a thick midpiece of length 6, and a tail which is executing helical motion about the z axis. The amplitude of the helical motion is p, and the thickness of the tail is 2b. The z coordinates of the beginning and end of the tail are 0 and z1, respectively. The end of the tail is not shown.", + "texts": [ + " 3 and 5 or 22 we see that the z component of r is essentially periodic in t with angular frequency 2w. Thus each point of the flagellum performs a figure eight motion in the xz plane. This kinematic effect is in agreement with Gray's (1958) observation of the motion of the tip of the flagellum in the planar case. 4. TRAJECTORY OF ORGANISM WITH HELICAL FLAGELLAR MOTION Let r = (x, y, z) be the cartesian coordinate vector in a system fixed in an organism with a helically waving flagellum. The z axis is along the axis of the helix, with the positive direction from head to tail (see Fig. 5). In this coordinate system G, F' and T', which were defined in section 1, are constants independent of t. This is shown in section 6 and Appendix B. Therefore from Eq. 2 it follows that w and 0 are also constants in this coordinate system. We denote their components by w,, w2, w3 and 2lQ2, Q3, respectively. The equation of the helix is r(s) = [pcos(kscosf#), psin(kscos,B), scosf]. (8) BIoPHYSICAL JOURNAL VOLUME 16 1976156 Here p is the amplitude, k is the wavenumber, and (3 is the pitch angle of the helix, while s is arclength along it", + "36k2p2)(3R/L)log(b/aL) When R = 0 and kp = 1, this formula yields the result -W3/c = 0.209, which is the same value as that determined from Eq. 27. BIoPHYSICAL JOURNAL VOLUME 16 1976162 We have used Eq. 30 to calculate the velocities Wi3 for six bull sperm whose motions were observed by Rikmenspoel et al. (1960). From their data we took b = 0.4 jm and R = 4Mgm, the latter being an effective radius of an ellipsoidal head with axes 8, 4, and 1 ,um, together with an attached thick midpiece. From supplementary data in Fig. 5 of Rikmenspoel (1965), we inferred that z, = 45 Mm. In Table I he gave the values of p, w/2ir, and 2w/k for each sperm cell. Then Eq. 28 and the approximation sin2O = 0.36 yielded L for each sperm. We also used Gray and Hancock's (1955) estimate aL = 4w/ke'l/2, and the relation c = w/k. With these data we computed - W3 for each sperm cell. The results are shown in Table I, together with the observed velocities. We see that the calculated values are in error by about 30%. This discrepancy is much less than the factor of five reported by Rikmenspoel et al. (1960). 6. FORCE, TORQUE AND VELOCITIES FOR HELICAL MOTION We choose as a model of a swimming microorganism with a helically moving flagellum that shown in Fig. 5. It consists of a spherical head of radius R attached to a flagellum of length L + 6 and circular cross section of radius b. The tail or distal segment of length L forms a helix of radius p and wavelength X. Thus its wavenumber is k = 27r/X, its pitch angle j is given by cos# = [1 + (kp)2]-/2 and its equation is given in Eq. 8. It is connected to the head by a midpiece or proximal segment of length 6. The whole organism is translating with a velocity w, the flagellum is rotating about the origin with an angular velocity Q, and the head is rotating with the angular velocity OH We assume that H,, differs from Q only in the z component, so we write l - (ll, %2, %3) and QH = (Q,, %2, WH)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure1.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure1.3-1.png", + "caption": "Fig. 1.3 Diagram of an idealized synchronous machine", + "texts": [ + " For the purpose of analysis it is immaterial which of the two elements of the machine rotates and which is stationary, since its operation depends only on the relative motion between them. In a practical machine with salient poles, for example, either element may carry the salient poles. For a machine with a commutator, however, the commutator winding is always on the rotor, and the element carrying it is always indicated on the diagram of the idealized machine as the inner rotating member. As an example, two alternative arrangements of an idealized three-phase salient-pole synchronous machine are shown in Fig. 1.3. A practical machine of this type usually has its three-phase armature winding on the stator and the field winding on the rotor as shown in Fig. 1.3a, but machines with the reverse arrangement as shown in Fig. 1.3b are often built. It is convenient when representing and analysing such a machine to use the fonn in Fig. 1.3b, but it is understood that the theory applies to either arrangement. Only one of the two salient poles is indicated. The outer member in Fig. l.3b carries a field coil F and damper coils KD and KQ. The axis of the pole round which the field coil F is wound is called the direct axis of the machine, while the axis 90\u00b0 away from it is called the quadrature axis. At the instant considered, the axis of the coil representing the armature phase A makes an angle 0 in a counter-clockwise direction with the direct axis", + " The positive direction of the current in any coil is into the coil in the conductor nearer to tht< centre of the diagram, as indicated by an arrow in Fig. l3b. The positive direction of the flux linking a coil is radially outwards, as indicated by an arrow-head along the axis in the middle of the loop representing the coil. The loops of The Basis of the General Theory 7 the coils are not intended to show the direction round the pole, but the convention is adopted that a current in a positive direction in a coil on any axis sets up a flux in the positive direction of that axis. In referring to the diagrams of idealized machines, such as Fig. 1.3, the term coil is used to indicate a separate circuit in the machine which carries a single current. In the practical machine such a coil may consist of many turns, distributed over many poles and often in several slots on each pole. The term winding, on the other hand, may refer to a single coil - for example, the field coil F - or it may refer to several coils, as in the three-phase armature winding represented by the three coils A, Band C. Often it is necessary to make approximations. The cage damper winding of a practical synchronous machine consists of many circuits carrying different currents and would require a large number of coils for its exact representation", + " commutator machine depending on the nature of the supply voltage. The actual circuits D and Q through the commutator winding not only form pseudo-stationary coils like the coils D and Q of the primitive machine of Fig. 1.5, but have the same axes as these coils. There is thus an exact correspondence between Figs. 1.4 and 1.5, and as a result the two-axis equations derived for the primitive machine of Fig. 1.5 apply directly to the commutator machine of Fig. 1.4. On the other hand, the three moving coils on the armature of the synchronous machine of Fig. 1.3b do not directly correspond to the coils D and Q of Fig. 1.5. In developing the two-axis theory of the synchronous machine, the three-phase coils A, Band C are replaced by equivalent axis coils D and Q, like those of Fig. 1.5, or in other words, the variables of the (a,b,c) reference frame are replaced mathemat- ically by variables of the (d,q) reference frame. The transfonn ation involved in the conversion, which depends on the fact that the same m.m.f. is set up in the machine by the currents of either reference frame, is explained and justified in Section 4", + "4. It may be noted that the direction of h is opposite to that usually shown in textbooks. Fig. 3.5 is a diagram of a two-pole synchronous machine having a field winding F on the outer member and a three-phase winding on the inner rotating member. In a practical machine, particularly in a large generator, the field system is almost always on the rotor, but in the diagram of the idealized machine it is indicated on the stator and its axis is taken as the direct axis. The damper windings shown on Fig. 1.3 are omitted in Fig. 3.5 because they do not affect the operation under steady conditions. I Quadrature aXIs --_ -=----. Dire.ct --- Fi aXIs Fig. 3.5 Diagram of a synchronous generator. Fig. 3.5, as well as Figs. 3.6 to 3.10, apply for steady operation of the machine as a generator at lagging power factor. The rotor runs at the constant synchronous speed Wo and it is assumed that the direction of rotation is clockwise, so that w = -Wo. The armature winding carries balanced polyphase currents, the phase sequence of which must be A-C-B", + " The coefficients in the Fourier series can be calculated from the design or determined by test. It is evident however that the determination of the parameters and the solution of equations in this form is a complicated process, but is quite possible with a digital computer. For many purposes the equations can be simplified by neglecting the Fourier terms of order 3 and higher, thus assuming that all of the inductances vary sinusoidally, with an additional constant term in some cases. The equations relating the terminal voltages to the currents in the six circuits of Fig. 1.3 are then expressed by the matrix equation u =Zi (4.1) where Z is given by Eqn. (4.2). For a two-phase machine having two armature phases ex and {3 located at 90 degrees, as shown in Fig. 4.1, the self-inductances of a b c f kd kq Z = a R a + p [ - B o + p [ -B o + p( A o + A 2 co s 20 ) B 2 co s ( 20 - 231T ) ] B c os (2 0 _ ~1T )] p C I c os 8 p D I co s 0 p D I si n 8 I b P [- B o + R a + P [A o p (- B o + B 2 co s (2 8 _ ~1T )] + A 2 co s (2 8 _ ~1T )] B 2 co s 28 ) p C I c os (o - 231T ) p D I C OS (8 - 231T ) p D I s in (8 - 231T ) P [- B o + p (- B o + R a + P [A o B 2 co s ( 20 _ ~1 T)] + A 2 co s (2 8 - 231T )] , 4) p D I CO s ( 8 _ ~1T ) P D IS in (o - ~1T ) B 2 co s 20 ) p C I co s (0 - 31T c f p C I co s 8 p C I co s (0 -2 31T ) p C I co s (8 _ ~1 T) R f + L ff p L fk d P kd p D I c os 0 p D I co s (0 _ ~1 T) p D I co s (0 _ ~ 1T) L fk d P R kd + L kk d P kq p D I si n 8 p D t si n (0 - 231T ) p D t si n (0 _ ~1 T) R kq + L kk q P - - - - - - - - - (4 ", + " i c \u2022 Because the three actual coils are replaced by a system of two axis coils, it is advantageous to change the base value of current in the axis coils to a value one and a half times the base current in the phase coils. It is shown later that as a result of this choice of base values, and of the transformation Eqns. (4.4) and (4.6), which define the new variables, the circuit Eqns. (4.15) relating axis quantities are obtained in a form which does not introduce a numerical factor. Assuming that the m.m.f. wave due to the current ia in the phase coil A of Fig. 1.3 is sinusoidal, the maximum m.m.f. is proportional to ia and occurs at the axis of the coil; that is, at the angular position o. The m.m.f. wave due to ia may be resolved into two components, one along each of the direct and quadrature axes. The amplitude of the direct-axis component is: kmiacos 0 where km is a constant. The direct-axis component of the resultant m.m. f. wave, due to the combined action of the three-phase currents, is therefore of amplitude km {ia cos 0 + ib cos (0 - 231T ) + ic cos (0 _ ~1T)} The amplitude of the m", + " The quantities U z and iz are related to each other independently of the others, and for many problems only the axis voltages and currents need to be considered. Thus the transformation brings about a great simplification. The two equations for the axis quantities in Eqn. (4.15) are identical with Eqns. (2.5) for the d.c. machine. It follows that, for the a.c. machine, the voltages Ud and uq , which were defined arbitrarily by Eqns. (4.6), can be interpreted as the impressed voltages on the direct and quadrature axis coils, provided that these coils possess the pseudo-stationary property defined on p. 9. The synchronous machine of Fig. 1.3 can then be replaced by the primitive machine of Fig. 4.2, in which the coils D and Q are pseudo-stationary coils located on the axes. Thus the same primitive machine diagram applies to both the d.c. machine and the a.c. machine and the primitive equations can be regarded as generalized equations applicable to all the principal machine types. The General Equations of A.C. Machines 73 The form of the armature voltage equations leads to a simple method of writing down the complete equations of a synchronous machine", + " Methods of calculating the performance are explained in Section 10.4. The design of a machine has to allow for many side effects, of which saturation and eddy currents are important ones. In the present chapter the emphasis is on the performance characteristics rather than on design details. A complete determination of the effect of saturation would require, for any set of currents in the windings at any instant, a mapping of the flux over the whole region occupied by the machine. The six by six matrix for a machine with six circuits (c.f. Fig. 1.3 and Eqn. 4.1) contains nineteen independent inductances, each of which is a function of all six currents as well as of the rotor position. The determination by measurement or design calculation of such a mass of data and its organisation for computation would be almost impossible. To calculate the voltage induced by each flux linkage, six partial derivatives of each inductance function would be needed. As an example, the interaction between the direct and quadrature-axis magnetizing inductances is illustrated by Fig", + " In a winding consisting of conductors in series, which \u00b7are of small section with negligible eddy currents, the current is determined by summating the electric field strength over the area occupied by the conductors, assuming them to be distributed over the slot area. Effects of Saturation and Eddy Currents 219 The above method can be applied directly to the field winding but there would be great complication in applying it exactly to an armature winding, which is in motion relative to the field. The following approximate method is proposed. Assume that the field structure is stationary (c.f. Fig. 1.3b) and that the armature structure moves relative to it at the instantaneous speed w. Then replace the armature by a magnetic part which has infinite permeability and a uniform cylindrical surface with no slots. The three-phase armature winding is replaced by a current sheath at the surface having a sinusoidal distribution of linear current density. The current density distribution is defined completely by the two-axis currents id and iq , which are calculated by summating the electric field strength in the conductors, having regard to the winding distribution, and the externally applied voltage" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003820_tits.2020.2987637-Figure26-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003820_tits.2020.2987637-Figure26-1.png", + "caption": "Fig. 26. Prototype and Experiment setup.", + "texts": [ + " When the fault resistance R f \u2264 R1turn , the short-circuit current increase sharply, and the generated heat causes the temperature at the short-circuit fault to rise sharply. The temperature reaches over 130\u25e6 C, which is much higher than the ambient temperature, but still within the safe operating range of the motor. It is indicated that if the ITSC fault is found and shut off in 30s, serious results to the EVs can be avoided. In order to verify the simulation results aforementioned, the PMSM prototype is manufactured and a test platform is prepared, as shown in Fig. 26. Several PT100s are placed in the windings to detect the temperature. The lines for short circuit is added during the manufacturing the prototype to test the short circuit currents. The performances of PMSM are tested. The no-load back EMF at speed of 6000 rpm and line voltage at load current IL = 12A (n = 5500 rpm) are test and compared with the simulation results, as shown in Fig. 27. It is obvious that simulation results are in good agreement with the experiment results. Besides, the resistances are measured: the resistance of phase A is 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.27-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.27-1.png", + "caption": "FIGURE 5.27. An RIIRIIRIIP SCARA manipulator robot.", + "texts": [ + " However, since we are attaching the wrist at point P of the frame B3, the transformation matrix 3T4 in (5.68) must include this joint distance. So, we substitute matrix (5.68) with 3T, ~ l~1:: ~1 to find Twrist 3T6 [ -SB4SB6 + cB4cB5cB6 -cB6sB4 - cB4cB5sB6 cB4sB6 +cB5cB6sB4 cB4cB6 -cB5sB4sB6 -cB6sB5 sB5sB6 o 0 The rest position of the robot can be checked to be at 0T7 = l~ ~ ~ d2 l~ b ] o 0 1 dl + d6 o 0 0 1 (5.122) 5. Forward Kinematics 239 because [ 1 0 0 0 ] 6 0 1 0 0 T7 = 0 0 1 d 6 . o 0 0 1 (5.123) Example 152 SCARA robot forward kinematics. Consider the RIIRIIRIIP robot shown in Figure 5.27. The forward kin e matics of the robot can be solved by obtaining individual transformation matrices i - 1Ti. The first link is an R IIR(O) link, which has the following transformation matrix: [ 00,0, - sin ()1 0 II cos ()1 ]\u00b0T, ~ '1\u00b0' cos ()1 0 t, sin ()1 0 1 0 0 0 1 Th e second link is also an RIIR(O) link [ =0 2 - sin ()2 0 l, COSO, 1 'T, ~ 'ir' cos ()2 0 l2 sin ()2 0 1 o . 0 0 1 (5.124) (5.125) (5.126) (5.127) 240 5. Forward Kinematics Th e third link is an R IIR(O) with zero length [ cos (h - sin 03 0 2r", + " In inverse transformation technique , we extract equat ions with only one unknown from the following matrix equations, step by step. (6.188) (6.189) (6.190) (6.191) (6.192) (6.193) The iterat ive technique is a numerical method seeking to find the joint variable vector q for a set of equations T (q ) = O. [ 0058, 0 - sin B4 ~ j 3T 4 = sin B4 0 cosB4 0 -1 0 0 0 0 [ cos 85 0 sin B5 ~ j 4T 5 = sin B5 0 - cos B5 0 1 0 0 0 0 [ 00586 - sin B6 0 n5T, ~ 8186 cos B6 0 0 1 0 0 294 6. Inverse Kinematics 4. SCARA robot inverse kinematics. Consider the R IIRIIRIIP robot shown in Figure 5.27 with the following forward kinematics solution. Solve the inverse kinematics and find 81, 82 , 83 , d. lcooO, - sin8 l 0 II COS0 1 ] \u00bbr, = sin 81 cos 81 0 h sin8 l 0 0 1 0 0 0 0 1lCOO02 - sin 82 0 l 2 cos 82 ]lT2 = sin 82 cos 82 0 l2 sin 82 0 0 1 0 0 0 0 1lCOO03 - sin 83 0 ~ ]2T3 = sin 83 cos 83 0 0 0 1 0 0 0 l~ 0 0 ~ ]3T4 = 1 0 0 1 0 0 \u00bbr, lT2 2T3 3T 4 [ cOn, -S8l 23 0 i.\u00bb, + I,din ] S8l 23 C8123 0 u\u00bb. + hs812 0 0 1 d 0 0 0 1 81 + 82 + 83 81 + 82 5. m-RIIR articulated arm inverse kinematics. Figure 5", + " 81 56deg 82 - 28 deg 83 - lOdeg h 100cm l2 55cm b 30cm ih 30deg / sec 82 10deg / sec 83 - 10 deg / sec 372 8. Velocity Kinematics 3. Spherical wrist velocity kinematics. Assume that we attach a tools coordinate frame, with the following transformatio n matr ix, to the last coordinate frame B6 of a spher ical wrist. The wrist transformation matrices are given in Exercise 3. Assume that the frame B3 is the base frame and find the translational and angular velocities of the tools coordinate frame B7 . 5. SCARA manipulator velocity kinematics. An RIIR!!RIIP SCARA manipulator is shown in Figure 5.27 with the following transformation matrices . Calculate the Jacobian matrix us ing the Jacobian-generat ing vector technique. [ 005B, - sin 8l 0 l,cooO, ] \u00b0T1 = sin 81 cos 81 0 h sin81 0 0 1 0 0 0 0 1 [ coon, - sin 82 0 l2cos82 ]'T, ~ Si1B2 cos82 0 l2sin 82 0 1 0 0 0 1 (8.179) (8.180) 8. Velocity Kinematics 373 l cos(h sinB3 o o - sinB3 COSB3 o o (8.181) (8.182) 6. Rf-RI IR articulated arm velocity kinematics. Figure 5.25 illustrates a 3 DOF Rf-RIIR manipulator with the follow ing transformation matrices", + " Choose a set of sample data for the dimen sions and kinematics of the manipulator and find the inverse of the J acobian matrix. 6. J acobian matrix for a spherical wrist . Use the Jacobian matrix technique from links' tr ansformation ma tri ces and find the Jacobian matrix of the spherical wrist shown in Figure 5.22. Assume that the frame B3 is the base frame. 7. J acobian mat rix for a SCARA manipulator. Use t he Jacobian matrix technique from links' transformat ion matri ces and find the Jacobian matrix of the RIIRIIRIIP robot shown in Figure 5.27. 8. Jacobian matrix for an m -R IIR art iculated manipulator . Figure 5.25 illustrates a 3 DOF m -RIIR manipulator. Use the Jaco bian matri x technique from links' t ransformat ion matrices and find the Jacobian matrix for the manipulator . 9. * Partitioning inverse method. Calculate the matrix inversion for t he matrices in Exercise 2 using the partitioning inverse method. 10. * Analytic matrix inversion. Use the analyt ic and LU factorization methods and find the inverse of or an arbitrary 3 x 3 matrix", + " Robot Dynamics (a) Find the equations of motion for the manipulator utilizing the backward recursive Newton-Euler technique. (b) * Find the equations of motion for the manipulator utilizing the forward recursive Newton-Euler technique. 19. * Recursive dynamics of an articulated manipulator. Figure 5.25 illustrates an articulated manipulator Rf-RIIR. Use g = gOko and find the manipulator's equations of motion (a) utilizing the backward recursive Newton-Euler technique. (b) utilizing the forward recursive Newton-Euler technique . 20. * Recursive dynamics of a SCARA robot. A SCARA robot RIIRIIRIIP is shown in Figure 5.27. If g = gOkO determine the dynamic equations of motion by (a) utilizing the backward recursive Newton-Euler technique. (b) utilizing the forward recursive Newton-Euler technique . 21. * Recursive dynamics of an SRMS manipulator. Figure 5.28 shows a model of the Shuttle remote manipulator system (SRMS). (a) Derive the equations of motion for the SRMS utilizing the back ward recursive Newton-Euler technique for g = O. (b) Derive the equations of motion for the SRMS utilizing the for ward recursive Newton-Euler technique for g = O", + " The manipulator is attached to a wall and therefore , g = 9 \u00b0io. 23. Polar planar manipulator Lagrange dynamics. Find the equations of motion for the polar planar manipulator, shown in Figure 5.37, utilizing the Lagrange technique. 24. * Lagrange dynamics of an articulated manipulator. Figure 5.25 illustrates an articulated manipulator Rf-RIIR. Use g = gOko and find the manipulator's equations of motion utilizing the Lagrange technique . 12. Robot Dynamics 561 25. * Lagrange dynamics of a SCARA robot. A SCARA robot RIIRIIRIIP is shown in Figure 5.27. If g = gOko determine the dynamic equations of motion by applying the Lagrange technique . 26. * Lagrange dynamics of an SRMS manipulator. Figure 5.28 shows a model of the Shuttle remote manipulator system (SRMS). Derive the equations of motion for the SRMS utilizing the Lagrange technique for (a) g = 0 (b) g = gOko. 27. * Work done by actuators. Consider a 2R planar manipulator moving on a given path. Assume that the endpoint of a 2R manipulator moves with constant speed v = 1m/ sec from PI to P2 , on a path made of two semi-circles as shown in Figure 13", + " In Exercise 28 keep O2 = 45 deg and calculate the static moments Q1 and Q2 as functions of 01. Plot Q1 and Q2 versus 01 and find the configuration that minimizes Q1, Q21 Q1 + Q21 and the potential energyV. 12. Robot Dynamics 563 31. * Statics of an articulated manipulator. An articulated manipulator Rf-RIIRis shown in Figure 5.25. Find the static force and moment at joints for g = gOko. The end-effector is carrying a 20kg mass. Calculate the maximum base force moment. 32. * Statics of a SCARA robot . Calculate the static joints ' force system for the SCARA robot RIIRIIRIIP shown in Figure 5.27 if g = gOko and the end-effector is carrying a 10kg mass. 33. * Statics of a spherical manipulator. A model of the Shuttle remote manipulator system (SRMS) is shown in Figure 5.28. Analyze the static configuration of the SRMS and calculate the joints' force system for g = s\"ko. Assume the links are made of a uniform cylinder with radius r = .25m and m = 12kg/ m. Use the characteristics indicated in Table 5.11 and find the maximum value of the base force system for a 24kg mass held by the end-effector" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002905_s11665-017-2874-5-Figure16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002905_s11665-017-2874-5-Figure16-1.png", + "caption": "Fig. 16 Predicted vertical distortion for horizontal build ( 1:1 mm UZ 0:4 mm)", + "texts": [ + " 15), which is much larger than the gap between the coater arm and the build upper surface. The termination of experiment 2 is therefore attributed to distortion of deposited layers. Macromodels predicted the termination at a build height of 4.8 mm as compared to 6 mm in the experiment. Journal of Materials Engineering and Performance In search for a build strategy for the engine mount, the build orientation was varied numerically (experiment 2). The engine mount built using on a horizontal orientation failed to build due a maximum distortion of 1.1 to 0.4 mm as shown in Fig. 16. Foster et al. (Ref 18) added supports to enable the horizontal build, but the sides broke off due to the excessive residual stresses. The numerical vertical distortions of the sides correlate very well with the breaking reported in Ref 18. Numerical parameter studies indicated that rotating the build direction reduces distortion. Figure 17 shows that when rotated 45 degrees the maximal final vertical distortions (along Z+) are reduced to 0.4 mm being almost negligible (only the size of a layer thickness)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003925_access.2018.2846554-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003925_access.2018.2846554-Figure5-1.png", + "caption": "FIGURE 5. Representation of the paths (A) 1, (B) 2, (C) 3 e (D) 4 traveled by the robot.", + "texts": [ + " Thus, whenever the robot arrives at a card, a transition of Petri Net is enabled and the place that received the token determines the action that must VOLUME 4, 2016 7 2169-3536 (c) 2018 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. be performed by the robot. The paths traveled by the robot during the tests are shown in Figure 5. The maps to be followed can be represented in two ways. In the first, mathematically, the map is represented by the incidence matrix of a Petri Net. Thus, for each path there is a specific matrix that needs to be loaded on the Arduino board before the robot initiates the movement through that path. Adapted incidence matrices are shown in Figure 6 and are, respectively, the PNs shown in Figure 7. It is important to note that due to reasons of algorithm implementation, matrices A are the transpose of the incidence matrices", + " When the robot passes over the card, the future marking matrix of the RP is updated, that is, the token is moved to the next place in the RP. Thus, the algorithm determines which card the robot should go to. The robot was previously programmed and placed it at the starting point P1. When the robot arrived at its destination, a buzzer sounded. It is carried out the tests on the four trajectories mentioned above. The four paths chosen have specific characteristics to make the robot more robust, overcoming different situations. Path 1 is the most basic. All its curves are to the left, as shown in Figure 5 (a). Path 2 presents curves to the left and to the right, as shown in Figure 5 (b), whereas path 3, according to Figure 5 (c), also includes curves to the left and to the right. Nevertheless, its incidence matrix is not square, which means that the number of transitions of the PN that defines this map is different from the number of places. At last, path 4, as shown in Figure 5 (d), represents a peculiarity. The robot passes through the place P4 twice and follows different ways according to the path defined by the PN. The results and considerations for the tests performed are presented bellow. The results are compiled in Table 3. The movement control of the robot is essential for the execution of the task of following the map. The rows 1 and 2 of Table 3 present satisfactory results for this action, since the robot can identify the black line and perform the movements necessary to remain on the path without deviations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002783_1.4030676-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002783_1.4030676-Figure7-1.png", + "caption": "Fig. 7 Quadrotor model and reference frames. Superscript i denotes the inertial frame and superscript b denotes the body frame.", + "texts": [ + " The increased thrust rate of change and the availability of negative thrust coming from the addition of variable-pitch propellers are utilized in this section to develop trajectory generation and control algorithms. The control algorithms developed are nonlinear and are not based on near-hover assumptions, allowing for control of aggressive and aerobatic maneuvers. Algorithms generating attitude-specific trajectories that account for actuator saturation levels are also presented. While these algorithms are implemented on a variable-pitch quadrotor, they are general and can be applied to quadrotors with fixed-pitch propellers as well. 4.1 Dynamic Model. Consider the quadrotor helicopter depicted in Fig. 7 with mass, m, and mass moment of inertia, J, where J is aligned with the body x, y, and z axes. Let the position of the center of mass of the quadrotor with respect to an inertial frame, i, be defined by ri. The attitude of the vehicle in the inertial frame is described by the quaternion q with the rotational velocities of the vehicle in the body frame, b, being Xb. The quaternion convention, q \u00bc q0 qT T , is used where q0 is the scalar portion and q is the vector portion of the quaternion. In particular, the quaternion rotation operation that rotates the vector v in R3 from the body frame to the inertial frame is defined as 0 vi \u00bc q 0 vb q (12) where q* is the quaternion conjugate of q, and is the quaternion multiplication operator [33]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure6.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure6.4-1.png", + "caption": "Fig. 6.4 Nominal length and velocity properties of maximally activated muscle tissue. These properties are often described in normalized muscle fiber length and velocity, where the maximal isometric (i.e., static and constant length) force a muscle can produce is F0. Note how the directions of contraction are traditionally indicated in the abscissa of the figures, which define concentric and eccentric contractions. a Isometric force\u2013length (f\u2013l) properties of a tendon-less muscle when fully activated. The passive force is generated by the muscle\u2019s connective tissue when stretched. Active forces are produce by the sarcomeres, the molecular motors that are the foundation of neurallycontrolled muscle activity [15, 16]. The active force is assumed to scale linearly with activation, whereas the passive force is assumed to be independent of activation. By definition, peak active isometric force, F0, is developed when fibers are at their optimal length (i.e., when lm = l0). b Force\u2013velocity (f\u2013v) relation of maximally activated muscle tissue. The force at zero normalized fiber velocity is F0. An applied constant force less (greater) than F0 causes muscle tissue to shorten (lengthen). Limits exist to force generation (<1.8 F0) and active shortening velocity (vmax = \u22125 lm s , maximal shortening velocity). These relationships are assumed to scale linearly for less than fully-activated muscle tissue [9, 15]. Adding a tendon will affect these properties due to its compliance [9]", + "texts": [ + " Thus, if the lengthening of a given muscle is not forthcoming, the required postures will not be attainable or the movement will be disrupted. For a single joint movement, the DOF can cease if even one muscle that needs to lengthen fails to do so. Of the muscles that need to shorten to accomplish the motion, those that are not controlled properly will simply go slack. But at least some of those muscles need to produce the necessary forces to move the limb. A muscle\u2019s ability to produce a force depends critically on the length and velocity of its fibers. Figure 6.4 describes nominal force\u2013length and force\u2013velocity properties as per current thinking [9, 15, 16]. Given that muscle fibers have a length and a velocity at any given point in time, these properties are best visualized as a 3D surface that contains all combinations of muscle fiber lengths and muscle fiber velocities, Fig. 6.5. However, despite decades of research, it is not known if these force\u2013length and force\u2013velocity properties in fact combine and superimpose in such a linear way. These properties need to be treated with caution, and some skepticism [5, 17\u201322], and remain active fields of research [16, 18, 23\u201326]", + ", inject kinetic and potential energy into the limbs and environment) in concentric contractions because muscle force and tendon excursion are in the same direction, and produce negative work (i.e., operate as breaks, or energy sinks, removing kinetic and potential energy from the limbs and environment) in eccentric contractions as the force and displacement are in opposite directions [28]. When calculating mechanical work, it is important to know how external work is related to the definition of positive and negative tendon excursion in Sect. 4.6. Active shortening of the musculotendon (i.e., negative tendon excursion during a concentric contraction, Fig. 6.4b) while under tension means the muscle is producing positive work. This is because the force in the tendon is in the same direction as the movement of the tendon. Conversely, a positive tendon excursion is one that lengthens the musculotendon,1 Fig. 6.4b. In such eccentric contractions, the muscle serves as a break that absorbs energy (i.e., produces negative work as the force and displacement are in opposite directions). Understanding how the nervous system regulates the exchange of mechanical energy among the body, limbs, and environment is central to our understanding of all behavior and the reader is referred to that body of work (e.g., [5, 28\u201331], and references therein). 1Recall that tendon excursions do not obligatorily define muscle fiber length changes", + " But in the case of anatomical tendon-driven limbs, this built-in tolerance to excursion errors may be a critical complement to, and enabler of, the neural control of smooth movements [5]. In addition, several authors have highlighted the tradeoffs for stiff versus compliant tendons in terms of neural control versus energy dissipation and regulation. For example, Zajac [9, 49] has highlighted the fact that the elasticity of the tendon modifies the force\u2013length properties of muscle\u2014which are usually given for tendonless muscles as in Fig. 6.4. Others have highlighted and debated the importance of tendons to locomotor function from the mechanical, shock-absorption, and energetic perspectives (e.g. [50\u201354]). This continues to be an active area of research in neural control, muscle mechanics, biomechanics, and evolutionary biology. Exercises and computer code for this chapter in various languages can be found at http://extras.springer.com or found by searching the World Wide Web by title and author. 1. R.M. Murray, Z. Li, S.S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC Press, 1994) 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.2-1.png", + "caption": "FIGURE 4.2. A translating and rot atin g body in a global coordinate frame.", + "texts": [ + " \u2022 Example 67 Translation and rotation of a body coordinate frame. A body coordinate frame B (oxy z) , that is originally coincident with global coordinate frame G(OXYZ), rotates 45 deg about the X -axis and translates to [3 5 7 r. Then, the global position of a point at B r = [ x y z r is G r GRBBr+Gd [ ~ .:45 - s~ 45 ] [~z ]+ [ ;7 ] o sin 45 cos 45 (x + 3) j + (O .707y - O.707z + 5) j + (O .707y+ O.707z + 7) k. 4. Motion Kinematics 129 Z z \u2022 \u2022 cf: p Gr Example 68 Moving body coordinate frame. Figure 4.2 shows a point P at B r p = O.li + 0.33+ 0.3k in a body frame B , which is rotat ed 50 deg about the Z-axis, and tran slat ed - 1 along X, 0.5 along Y , and 0.2 along the Z axes. Th e position of P in global coordinate fram e is G RBB r p + Gd [ COS 50 - sin 50 sin 50 cos 50 o 0 [ - 1.166 ] 0.769 . 0.5 0] [0.1 ] [-1 ]o 0.3 + 0.5 1 0.3 0.2 Example 69 Rotation of a translated rigid body. Point P of a rigid body B has an ini tial position vector B r p . T B r p = [ 1 2 3] If the body rotates 45 deg about the x -axis, and then translates to G d = [4 5 6] T, the final position of P would be B R T B r + Gdx ,45 p [ 1 0 0 ]o cos 45 - sin 45 o sin 45 cos 45 [ 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.37-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.37-1.png", + "caption": "Figure 5.37 depicts a polar planar manipulator with 2 DOF.", + "texts": [ + " A one-link RI-R( -90) arm. 256 5. Forward Kinematics For the one-link Rf-R( -90) manipulator shown in Figure 5.35 (a) and (b) , find the transformation matrices \u00b0T1 , ITz, and \u00b0Tz. Compare the transformation matrix ITz for both frame installations. 4. A 2R planar manipulator. Determine the link 's transformation matrices \u00b0T1, ITz, and \u00b0Tz for the 2R planar manipulator shown in Figure 5.36. 5. A polar manipulator. Determine the link 's transformation matrices ITz, zT3 , and IT3 for the polar manipulator shown in Figure 5.37. 6. A planar Cartesian manipulator. Determine the link 's transformation matrices ITz, zT3 , and IT3 for the planar Cartesian manipulator shown in Figure 5.38. 7. Modular articulated manipulators. Most of the industrial robots are modular. Some of them are manu factured by attaching a 2 DOF manipulator to a one-link Rf-R( -90) arm. Articulated manipulators are made by attaching a 2R planar manipulator, such as the one shown in Figure 5.36, to a one-link Rf-R( -90) manipulator shown in Figure 5.35 (a) . Attach the 2R ma nipulator to the one-link Rf-R( -90) arm and make an articulated manipulator. Make the required changes into the coordinate frames of Exercises 3 and 4 to find the link 's transformation matrices of the articulated manipulator. Examine the rest position of the manipula tor. 5. Forward Kinematics 257 258 5. Forward Kinematics 8. Modular spherical manipulators. Spherical manipulators are made by attaching a polar manipulator shown in Figure 5.37, to a one-link Rf--R( -90) manipulator shown in Figure 5.35 (b) . Attach th e polar manipulator to the one-link Rf--R( -90) arm and make a spherical man ipulator. Make the required changes to the coordinate frames Exercises 3 and 5 to find the link 's transformation matrices of the spherical manipulator. Examine the rest position of t he manipulator. 9. Modular cylindrical manipulators. Cylind rical manipulators are made by at taching a 2 DOF Car tesian manipulato r shown in Figure 5.38, to a one-link RI-R(-90) manip ulator shown in Figure 5", + " Find an equation to relate the angular acceleration of link (i) to the angular acceleration of link (i - 2), and the angular acceleration of link (i) to the angular acceleration of link (i + 2). 6. Acceleration in different frames. For the 2R planar manipulator shown in Figure 12.5, find ~az, &az, \u00b0 z z dOzaI, oal, oaz, an laI \u00b7 7. Slider-crank mechanism dynamics. A planar slider-crank mechanism is shown in Figure 12.11. 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 5.37. Eliminate the joints' constraint force and moment to derive the equations for the actuators' force or moment. 558 12. Robot Dynamics 9. Global differential of a link momentum. In recursive Newton-Euler equations of motion , why we do not use the following Newton equation? . cd . cd . .. . 'F = -'F = -m'v = m'v + 'w ' x m':v dt dt 0 \u2022 10. 3R planar manipulator dynamics. A 3R planar manipulator is shown in Figure 12.13. The manipulator is attached to a wall and therefore, g = 9 \u00b0io. (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. 11. A planar Cartesian manipulator dynamics. Determine the Newton-Euler equations of motion for the planar Carte sian manipulator shown in Figure 5.38. 12. Polar planar manipulator dynamics. A polar planar manipulator with 2 DOF is shown in Figure 5.37. (a) Determine the Newton-Euler equations of motion for the ma nipulator. (b) Reduce the number of equations to two, for moments at the base joint and force at the P joint. 12. Robot Dynamics 559 (c) Substitute the vectorial quantities and calculate the action force and moment in terms of geometry and angular variables of the manipulator. 13. * Dynamics of a spherical manipulator. (d) Assume the links are made of a uniform cylinder with radius r = .25 m and m = 12kg/ m. Use the characteristics indicated in Table 5", + " (a) Derive the equations of motion for the SRMS utilizing the back ward recursive Newton-Euler technique for g = O. (b) Derive the equations of motion for the SRMS utilizing the for ward recursive Newton-Euler technique for g = O. 22. 3R planar manipulator Lagrange dynamics . Find the equations of motion for the 3R planar manipulator shown in Figure 12.13 utilizing the Lagrange technique . The manipulator is attached to a wall and therefore , g = 9 \u00b0io. 23. Polar planar manipulator Lagrange dynamics. Find the equations of motion for the polar planar manipulator, shown in Figure 5.37, utilizing the Lagrange technique. 24. * Lagrange dynamics of an articulated manipulator. Figure 5.25 illustrates an articulated manipulator Rf-RIIR. Use g = gOko and find the manipulator's equations of motion utilizing the Lagrange technique . 12. Robot Dynamics 561 25. * Lagrange dynamics of a SCARA robot. A SCARA robot RIIRIIRIIP is shown in Figure 5.27. If g = gOko determine the dynamic equations of motion by applying the Lagrange technique . 26. * Lagrange dynamics of an SRMS manipulator. Figure 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003637_j.mechmachtheory.2016.09.017-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003637_j.mechmachtheory.2016.09.017-Figure2-1.png", + "caption": "Fig. 2. The 3D cylindrical gear mesh model: (a) The local (U-V-W) and global (X-Y-Z) coordinate systems (b) The 3D gear mesh model (c) Projection drawing in Wdirection (d) Projection drawing in V-direction.", + "texts": [ + " Typically, each shaft is supported by at least two rolling element bearings of varying types and parameters. Normally, they are modeled as stiffness only and the cross terms and damping are ignored [12,16], i.e. six spring stiffnesses in the x, y, z, \u03b8x, \u03b8y, \u03b8z directions: \u23a1 \u23a3 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2 \u23a4 \u23a6 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5 K k k k k k k =b xx yy zz \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 x x y y z z (3) These bearing stiffness matrices are then assembled into the overall shaft stiffness matrix Ks at the nodes corresponding to their locations on the shafts. A general three dimensional (3D) model of a cylindrical gear pair is shown in Fig. 2. In this model, the mesh behaviour of the gear pair is represented by two rigid cylinders whose radii are the gear base circles Rb1 and Rb2, connected by a series of stiffness cells kj along the contact line in the direction of the tooth normal determined by the helix angle \u03b2. \u03a91 and \u03a92 are the nominal rotating speeds of the driving gear and driven gear, respectively. T1 and T2 are the torques applied on the driving gear and driven gear, respectively. X-Y-Z is the global Cartesian coordinate system as defined in the shaft model. The helix angle \u03b2 of the cylindrical gear pair is defined as: \u23a7 \u23a8\u23aa \u23a9\u23aa \u03b2 = > 0 If the driving gear has left hand teeth = 0 If the driving gear is a spur gear < 0 If the driving gear has right hand teeth (4) For the purpose of illustration, a localized Cartesian coordinate system (U-V-W) is established (as shown in Fig. 2(a)). The origin is at the driving gear center O1. The U-axis is in the direction of the line of action (LOA) and positive from the driving gear to the driven gear. The V-axis points from the driving gear center O1 to the tangent point A at the base circle of the driving gear, i.e. off line of action (OLOA). The W-axis is along the axial direction (same with the Z-axis) and can be determined by following the right-hand rule. It should be noted that the U-V plane is in the same plane with the X-Y plane. Therefore, the dynamic motions of the two gear centers consist of three translations and three rotations such that [14,17]: \u23aa \u23aa \u23aa \u23aa \u23a7 \u23a8 \u23a9 \u23ab \u23ac \u23ad D \u03b7 O u U v V w W \u03c9 \u03b8 U \u03b8 V \u03b8 W i{ }= \u23af\u2192( ) = \u23af\u2192 + \u23af\u2192 + \u23af\u2192 \u23af\u2192= \u23af\u2192 + \u23af\u2192 + \u23af\u2192 , = 1, 2i i i i i i i ui vi wi (5) In Fig. 2(c), the mounting angle \u03b1 ( \u03b1 \u03c00 \u2264 < 2 ) describes the relative position of the gears, which is defined as the angle that the line connecting the gear centers makes with the positive X-axis. Therefore, the angle between the positive U-axis and positive Y-axis becomes\u03c8. Since the plane of action changes direction depending on the rotation direction of driving gear, \u03c8 is defined as: \u23aa \u23aa\u23a7\u23a8 \u23a9 \u03c8 \u03b1 \u03c6 \u03b1 \u03c6 \u03c0 = \u2212 \u03a9 : positive Z \u23af\u2192 direction + \u2212 \u03a9 : negative Z \u23af\u2192 direction 1 1 (6) where \u03c6 is the transverse operating pressure angle of the gear pair", + " With \u03c8 defined, the transform matrix T between the global coordinate system X-Y-Z and the local coordinate system U-V-W can be determined as: \u23a7 \u23a8 \u23aa\u23aa\u23aa \u23a9 \u23aa\u23aa\u23aa T sin\u03c8 cos\u03c8 cos\u03c8 sin\u03c8 sin\u03c8 cos\u03c8 cos\u03c8 sin\u03c8 = \u2212 0 0 0 0 \u22121 \u03a9 : positive Z \u23af\u2192 direction \u2212 0 \u2212 \u2212 0 0 0 1 \u03a9 : negative Z \u23af\u2192 direction 1 1 (7) For a contact point Mj with local coordinates (uj, Rb1, wj), the dynamic motions of the two gear centers will give a normal approach on the base plane relative to rigid body positions: \u2211 \u2211\u03b4 M \u03b7 M n \u03b7 O \u03c9 O M n( )= \u23af\u2192( )*\u23af\u2192 = {\u23af\u2192( )+\u23af\u2192\u00d7 \u23af \u2192\u23af\u23af\u23af\u23af }*\u23af\u2192 j i i j ij i i i i i j ij =1 2 =1 2 (8) where n\u23af\u2192ij is the outer unit vector normal to gear i at contact point Mj. It is assumed that the base plane is unchanged and the outer normal vector n\u23af\u2192ij is not modified by defects, thus n n\u23af\u2192 =\u23af\u2192 ij i. Besides, O M u U Rb V w W O M u u U Rb V w W \u23af \u2192\u23af\u23af\u23af\u23af\u23af = \u23af\u2192 + \u23af\u2192 + \u23af\u2192 , \u23af \u2192\u23af\u23af\u23af\u23af\u23af =\u2212( \u2212 ) \u23af\u2192 \u2212 \u23af\u2192 + \u23af\u2192 j j j j g j j1 1 2 2 (9 - a, b) where ug is the length of LOA as shown in Fig. 2(d). Eq. (8) can be rewritten in matrix form: \u0395 q\u03b4 M M( )= ( )j j T (10) where qT = {u1, v1, w1, \u03b8u1, \u03b8v1, \u03b8w1, u2, v2, w2, \u03b8u2, \u03b8v2, \u03b8w2} is the local degree of freedom vector of the gear pair considered, and \u0395(Mj) is the so-called structure vector which relates the local degree of freedom vector q to normal approach \u03b4(Mj), which depends on gear geometry and the position of Mj on the base plane: namely, \u23a7 \u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa \u23a9 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa \u23ab \u23ac \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa \u23ad \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa E M \u03b2 \u03b2 Rb \u03b2 w \u03b2 u \u03b2 Rb \u03b2 \u03b2 \u03b2 Rb \u03b2 w \u03b2 u u \u03b2 Rb \u03b2 ( )= \u2212 cos 0 sin sin \u2212 cos \u2212 sin cos cos 0 \u2212 sin sin cos \u2212( \u2212 )sin cos j j j j g j 1 1 2 2 (11) The normal approach \u03b4(Mj) can also be expressed in terms of the global degree of freedom vector: E \u039eu\u03b4 M M( )= ( )j j T (12) where uT = {x1, y1, z1, \u03b8x1, \u03b8y1, \u03b8z1, x2, y2, z2, \u03b8x2, \u03b8y2, \u03b8z2} is the global degree of freedom vector of the gear pair considered", + " In most of the previous research work employing a 2-dimensional gear model, gear unloaded static transmission error excitation e is expressed as a simple harmonic excitation as a function of time. However, for a 3D model, it is a function of the contact pointMj which depends not only on time but also on the contact position along the tooth face-width direction. A detailed discussion can be found in [14]. In this paper, gear tooth local scale errors are denoted as ef1(Mj) and ef2(Mj) for the driving gear and driven gear, respectively (as shown in Fig. 2(d)). The overall profile error of the gear pair ef(Mj) is defined as the sum of ef1(Mj) and ef2(Mj). (b) Global scale errors Two typical types of mounting errors of a gear pair are misalignments and eccentricities. Misalignments of the gears are modeled by small constant angles of \u03b8 \u03b8,xi m yi m relative to the X-axis and the Y-axis [14] as shown in Fig. 3. Therefore, the corresponding normal deviations in Mj due to misalignments can be expressed as: V ue M M( )= ( )m j m j mT (15) where Vm(Mj) is a subset of V(Mj) which includes only the components related to bending slopes \u03b8xi and \u03b8yi, and um is the misalignment vector: u \u03b8 \u03b8 \u03b8 \u03b8={ }m x m y m x m y m 1 1 2 2 T (16) Eccentricity of a gear i is defined as the distance ei between the center of rotation and the center of inertia (as shown in Fig", + " Their influence is usually disregarded especially for narrow-faced gears [18]. Besides, in order to get a constant structure vector V0, the contributions of bending angles are usually averaged over one mesh period [19,20]. In a word, \u2211 \u2211K u V V V V V V ut k M M k k t( , ) = ( ) ( ) \u2248 = ( , )g u u i N t i j j i N t j g T =1 ( , ) 0 0 T =1 ( , ) 0 0 Tc c (25) where \u222cV V T W M dtdz= 1 * ( ) s j0 0 (26) is the averaged structural vector, Ts is the mesh period andW0 is the length of tooth face width along the axial direction (as shown in Fig. 2); Nc(t, u) is the number of stiffness cells kj considered; kg(t, u) is the time-varying, nonlinear, mesh stiffness of the gear pair, which can be acquired either by finite element analysis (FEA) method or by analytical method [18,21\u201323]. In this paper, a much more simple method to predict gear mesh stiffness based on the ISO standard 6336 will be used. An important simplification brought by the ISO formulae is that the mesh stiffness per unit contact length k0 is considered as approximately constant so that the following approximation can be used: u uk t k L t( , )= ( , )g 0 (27) where L(t, u) is the time-varying (possibly non-linear) contact length [24]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000641_1.4004683-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000641_1.4004683-Figure1-1.png", + "caption": "Fig. 1 The crack growth model in the pinion", + "texts": [ + " Because the dynamic modeling of gear systems not only provides us the vibration signatures in gear transmissions, but also furthers our understanding of the dynamic behavior when the transmission suffers from various types of gear tooth damage, a great deal of research has been done to study the dynamic modeling of gear systems and the vibration response when there is a local fault on the gear teeth [4\u20138], pitting, spalling, or a local crack of a specific size, while Wu [9,10] studied the effects of a tooth crack growth on the vibration response of a 6DOF one-stage gearbox with spur gears. They simplified that crack growth path model (according to Refs. [11,12], the gear tooth root crack propagation path is a slight curve extending from the tooth root), by considering the crack growth path to be a straight line (the broken straight line A-B as shown in Fig. 1), with a intersection angle, t, which is between the crack path and the central line of the tooth is set at a constant angle, v\u00bc 45 deg. It started at the root of the pinion, and it provided the formulas for the time varying meshing stiffness of the meshing pairs when there are different levels of crack in the pinion, with the assumption that the tooth with a crack is still a cantilevered beam, and the boundary condition is that the root of this tooth does not experience any deflection when there is a crack in the pinion", + " The algorithm combined AR modeling method and demodulation method is proposed to analysis the response signal from the 16DOF dynamic model; (3) give the relationship between the indicators of the residual signal, the demodulated signal and the crack growth level, and a comparison of the evolution of the indicators as the crack level increases when different dynamics models are used and different meshing stiffness calculation methods are used. 2.1 Crack Path Assumption. The shape of the crack can be described in three dimensions: length, width, and thickness. Here, to simplify the model, we focus only on the crack\u2019s development in one dimension, so the crack is assumed to be along the whole width of the tooth from the point of its initiation, and the influence of the crack\u2019s thickness is ignored. In this paper, the crack path is simplified as the straight line A-B as shown in Fig. 1, which is the crack growth path studied in Refs. [9,10]. To study the early crack growth effect when there is an axle hole in the pinion, the maximum value of the crack length, qm, is define as the length of line A-B, with a intersection angle, t. In later reference of the crack 1Corresponding author. Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL of VIBRATION and ACOUSTICS. Manuscript received June 8, 2010; final manuscript received May 27, 2011; published online December 28, 2011. Assoc. Editor: Cheng-Kuo Sung. Journal of Vibration and Acoustics FEBRUARY 2012, Vol. 134 / 011011-1Copyright VC 2012 by ASME Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use growth, a relative length, 100% qc/qm, will be used, where qc and qm are illustrated in Fig. 1. From the geometry of a tooth shown in Fig. 1, the max crack length, qm, can be given by qm \u00bc Rb1 sina2=sint (1) where Rb1 is the radius of the base circle of the pinion, a2 is the half of the base tooth angle of pinion, and t is the intersection angle of the crack growth path. The length of qf, which is related to where the elastic contact force, F, is on the crack path as shown in Figure 1, can be given by qf \u00bc abs a1\u00fe a2\u00f0 \u00de cosa1\u00fe sina1\u00fe sina2\u00f0 \u00de Rb1=sintf g (2) where abs is the absolute value, a1 is the angle of the force point on the base circle. And qf will be used to determine how to do the time-varying meshing stiffness calculation when the force moved from the tooth root to tooth crest with the different level cracks in the pinion in a later paragraph. 2.2 Time-Varying Meshing Stiffness Formulas Derivation. Since the main source of vibration in a gear transmission system is usually the meshing action of the gears, we focus on the effects of the time-vary meshing stiffness with the crack growth on the vibration response" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure8.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure8.2-1.png", + "caption": "FIGURE 8.2. A 2R planar manipulator.", + "texts": [ + " \u00b0T2 = \u00bbr, lT2 [ cosO - sin () 0 ~ ][ ~ 0 0 ~ ] sin () cos () 0 1 0 0 0 1 0 1 0 0 0 0 0 [ NS O - sin () 0 rcoo O ] sin e cos () 0 r sin () (8.38) 0 0 1 0 0 0 0 1 The tip point of the manipulator is at [ X ] =[ r C?S e ] (8.39)Y rsm () and therefore, its velocity is [ ~] =[ C?S () - r sin () ] [ ~ ] (8.40 )Y sm() r cos () () 348 8. Velocity Kinematics which shows that J = [ cos 8 - r sin 8 ] D sin 8 r cos 8 . (8.41) Example 212 Jacobian matrix for the 2R planar manipulator. A 2R planar manipulator with two RII R links was illustrated in Figure 5.9 and is shown in Figure 8.2 again. The manipulator has been analyzed in Example 132 for forward kinematics, and in Examp le 168 for inverse kinematics. The angular velocity of links (1) and (2) are . 0 A (8.42)OWl 81 ko 0 . 0 A (8.43)l W2 82 kl 0OW2 OWl + l W2 (01+ 02) oko (8.44) and 0OW2 OWl + l W2 (01+02) \u00b0ko (8.45) 8. Velocity Kinematics 349 and the global velocity of the tip position of the manipulator is O\u00b7 O \u00b7 d 1 + 1d 2 OWl X \u00b0d1 + OW2 X 7d2 . 0 ' 0 ( . .) 0 ' 001 ko X h 21+ 01+ O2 ko X 12 22 h ih 0)1 X 12 (ih + (h) 0h (8", + " The two columns of the Jacobian matrix become parallel because the Equation (8.145) becomes (8.153) In this situation, the endpoint can only move in the direction perpendicular to the arm links . 366 8. Velocity Kinematics Example 220 Analytic method for inverse velocity kinematics. Theoretically, we must be able to calculate the joint velocities from the equations describing the forward velocities, however, such a calculation is not easy in a general case. As an example , consider a 2R planar manipulator shown in Figure 8.2. The endpoint velocity of the 2R manipulator was expressed in Equation (8.58) as O\u00b7 . 0' 0 , 0, . 0' 0, d2 = fh ko x (h 21 + h 22) + O2 kl X l2 22\u00b7 A dot product of this equation with \u00b0i2 , gives (8.154) (8.155) and therefore, o; 0'. d2 \u00b7 22 01 = ....,....-\"-\"\"\"\";:'h sin O2 . Now a dot product of (8.154) with Oil reduces to (8.156) and therefore, (8.158) Example 221 * Inverse Jacobian matrix for a robot with spherical wrist . The Jacobian matrix for an articulated robot with a spherical wrist is calculated in Example 215" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002029_1077546311431270-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002029_1077546311431270-Figure1-1.png", + "caption": "Figure 1. Quadrotor aircraft concept.", + "texts": [ + " Sections 3 and 4 present an adaptive trajectory tracking control design algorithm. In Section 5 numerical simulation results of a quadrotor trajectory tracking are discussed. Finally the conclusion of the proposed trajectory tracking control design algorithm is presented in Section 6. The quadrotor is a typical under-actuated, nonlinear coupled system in control terms. In order to compensate for the effect of the reaction torques, the four rotors are divided into two pairs of (1, 3) and (2, 4) turning in the opposite directions, as depicted in Figure 1. Hence, the quadrotor is suitable for hovering and quasi-static flight conditions. The quadrotor flight mechanism is that: 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\u2013rear set or the left\u2013right set of rotors, coupled with lateral motion; yaw motion is realized by the different reaction torques between the (1, 3) and (2, 4) rotors. So the number of individual manipulating variables cannot instantaneously set the accelerations in all directions of the configuration space. at UNIV OF MICHIGAN on March 1, 2013jvc.sagepub.comDownloaded from Let I \u00bc {Oexeyeze} denote an Earth-fixed inertial frame and A\u00bc {Oxyz} denote a body-fixed frame whose origin O is located at the center of mass of the quadrotor, as shown in Figure 1. The quadrotor attitude is defined by three Euler angles ?\u00bc ( , , )T, and R2SO(3) denotes the orthogonal rotation matrix to orient the quadrotor: R \u00bc C C S C S S C S C C \u00fe S S C S S S S \u00fe C C S S C C S S C S C C 0 @ 1 A where S( ) X sin( ), C( ) X cos( ). The quadrotor kinematic equations (Zuo 2010a,b) can be expressed as _p \u00bc t \u00f01\u00de _? \u00bcW: \u00f02\u00de where p denotes the absolute position of the origin of frame A, t the linear velocity of the center of mass expressed in frame I , : the three rotations, the matrix W is defined as follows: W \u00bc 1 S T C T 0 C S 0 S =C C =C 0 @ 1 A where Ty X tan " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003434_1.4033525-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003434_1.4033525-Figure9-1.png", + "caption": "Fig. 9 a lath width (lm) after the part has cooled (a) 0 s dwell and (b) 4 s dwell", + "texts": [ + " The values of the material properties, before and after optimization, are shown in Table 1. Note that the properties that govern a growth and dissolution (a, b, and n) do not change significantly from the published values. On the other hand, kw and Tact, which govern equilibrium a lath widths, are both reduced by several orders of magnitude. The optimized values are physically justified because they are much closer to the length scales and temperatures relevant to the microstructural transformation, respectively, micron and hundreds of K. Lath widths are calculated at all points in Fig. 9 and compared to experiments in Fig. 10. Plots of phase fractions, lath width, and temperature are shown in Fig. 11 as functions of time for a single point in the middle of the three-bead leg. Error bars on the experimental results are 6 one standard deviation of the three measurements taken at each location. Out of a total 24 experimental data points at different locations and builds, 12 of the points were used for the inverse simulation (Figs. 10(b) and 10(d)), while the other 12 were kept hidden from ANMS for validation of the model (Figs", + " Predicted colony-a phase fractions after the part has cooled are shown in Fig. 12. The total a and b phase fractions return to their room temperature equilibrium values after cooling, fa \u00bc 0:91 and fb \u00bc 0:09. It can be seen that the 4 s dwell time between layers is 111007-8 / Vol. 138, NOVEMBER 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935392/ on 02/19/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use expected to result in less colony-a and finer laths (Fig. 9) compared to 0 s dwell. Using Fig. 12(a) as an example, several observations can be drawn in parallel with what Kelly found: (1) The large thermal mass of the substrate has an effect on the lowest layers, in this case, roughly layers 1\u201332 (0\u20135.7 mm above substrate) (2) The middle characteristic layers all have essentially the same microstructure, layers 33\u2013235 (5.7\u201342.0 mm above substrate) (3) The top layers have not yet undergone as much thermal cycling as the characteristic layers and show differing amounts of colony alpha, layers 236\u2013286 (42" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure14.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure14.9-1.png", + "caption": "Figure 14.9.1 Double-wishbone suspension: (a) position diagram; (b) velocity diagram.", + "texts": [ + " For example, a bump deflection zs of, say, 100mm on an effective arm length l, which may be as much as 1.3 m for a transverse arm or swing axle, gives an angular bump motion of the arm of about 4\u20135 . For a trailing arm of length 0.4m, the angle is 15 . The double wishbone or double A-arm suspension is a little more difficult to solve than the simple rigid arm. As before, it is necessary to establish a motion ratio between the suspension bump velocity and the angular velocity of the armwhich operates the spring or damper, or operates the pushrod to the rocker for a racing car. Figure 14.9.1(a) shows the basic configuration. 284 Suspension Geometry and Computation If the linear bump camber coefficient of the suspension is already known, then a particularly simple method is possible. The linear bump camber coefficient \u00abBC1 is the rate of change of wheel camber angle g with suspension bump, arising from suspension geometry: \u00abBC1 \u00bc dg dzS \u00f0rad=m\u00de For a suspension bumpvelocityVS, and for a reasonably constant \u00abBC1, usually an adequate approximation for the present purpose, the wheel camber angular velocity is dg dt \u00bc \u00abBC1 dzS dt \u00bc \u00abBC1VS gBC \u00bc \u00abBC1zS \u00fe \u00abBC2z 2 S \u00abBC \u00bc dg dzS \u00bc \u00abBC1 \u00fe 2\u00abBC2zS From Figure 14.9.1, the vertical velocity of B differs from the vertical velocity of F by the camber angular velocity multiplied by the lateral difference of position e, where e \u00bc XF XB The vertical velocity of B is therefore VB \u00bc VS e\u00abBCVS \u00bc VS\u00f01 e\u00abBC\u00de Hence, the motion ratio RB/S of ball joint B to suspension bump is RB=S \u00bc 1 e\u00abBC Realistic values are e\u00bc 0.1m and \u00abBC\u00bc 1 rad/m, which will give RB/S a value of 0.9, a substantial deviation from 1.0 which should certainly be included in the analysis. In the absence of prior information on the bump camber coefficient, a velocity diagram may be considered, as in Figure 14.9.1(b). This is more easily constructed by initially assuming an angular velocity vAB for the lower link, rather than a bump velocity of the wheel. The body is deemed to be stationary, so points A and C are fixed points, with zero velocity, and therefore appear as a and c at the origin of the velocity diagram. The tangential velocity of B relative to A is vABlAB, and the line ab in the velocity diagram is perpendicular to link AB, the length of ab being the tangential velocity at the diagram scale" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003507_j.apmt.2020.100611-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003507_j.apmt.2020.100611-Figure9-1.png", + "caption": "Fig. 9. Scheme of the printing design and actuation of", + "texts": [ + " Method B, however, offered a quicker response and greater control regarding the direction of folding and angle precision [54]. Baker et al. developed trilayered multi-material with hydrophobic passive polyurethane (Ninjaflex\u00ae) top and bottom layers and a hydrophilic active polyurethane core (TecophilicTM) [55]. The resulting constructs were able to switch from flat 2D parts to 3D structures through moisture action. After drying, the printed parts recovered the original configuration as schematically represented in Fig. 9. The article reported the conduction of multiple actuation cycles to confirm the shape change reversibility. However, there was no reference to the number of cycles performed. In 2017, Kang and co-workers created a shape memory composite (SMC) using three different components: Nylon\u00ae 12 (SMP), NitinolTM as a shape memory alloy (SMA) and PLA to increase flexibility [56]. After printing the polymers using an FDM system, the NitinolTM wires went between the two polymeric layers. By applying current to the metallic wires, the shape change occurred due to the transferred heat to the SMP layers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001907_j.1550-7408.1964.tb01756.x-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001907_j.1550-7408.1964.tb01756.x-Figure5-1.png", + "caption": "Fig. 5 . Diagram oi the effect of different mastigoneme arrangements on efficiency of reverse water movement. a. The 90\u201d fixed arrangement assumed for Ochrontonas. b. A theoretical hinged system in which the mastigonemes may swing between 0\u201d and 90\u2019.", + "texts": [ + " Fig. 4 shows that a flagellum with rigid lateral mastigonemes. and beating with a planar sine wave, may exert a net force in either direction. dependent upon the relative values of amplitude ( B ) and wavelength ( A ) and also upon the relative values of two force coefficients, which in turn depend upon the dimensions and the roughness of the flagellum. The longitudinal force coefficient can be increased greatly if lateral projections appear only on the outer side of the sine wave as shown in Fig. 5b. This would be possible if semi-rigid mastigonemes were attached to the flagellum in such a manner that, like hair on a cat\u2019s fur. they stood up when opposed by water in one direction, but lay down when water exerted a force in the opposite direction. In this way, mastigonemes contributing to the transverse force coefficient would be passively raised by the water while those which would tend to work against it would be passively \u201claid down\u201d by the action of the water. However, all available electron micrographs( 23) show an arrangement generally similar to ja, but with about equal numbers of mastigonemes showing more than 90\u2019 and less than 90\u201c angle with the flagellum" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002024_j.jfranklin.2013.09.009-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002024_j.jfranklin.2013.09.009-Figure5-1.png", + "caption": "Fig. 5. Quanser 3-DOF Hover plant.", + "texts": [ + " But as time goes on, the tracking errors go to zero asymptotically. Because the pitch motion is controlled only by u1,u2 and the roll motion is controlled by u3, u4. Whenu1fails, we can see from Fig. 2 that only the yaw angle and pitch angle are affected. When u3 fails, it can be seen from Fig. 3 that only the yaw angel and roll angle are affected. Fig. 4 shows that the disturbance observer can estimate the real interference terms quickly and accurately. Here, we applied the control scheme proposed in this paper to a Quanser 3-DOF hover platform (Fig. 5), where u1 \u00bc 1:3\u00f0V\u00de for tZ10\u00f0sec\u00de, d\u00f0t\u00de \u00bc \u00bd0; 0; 0; 0:8; 1:4; 2:2 T for tZ0\u00f0sec\u00de. The semi-physical simulations are shown in Fig. 6. The hover system consists of a frame with four propellers. The frame is mounted on a three degree of freedom pivot joint that enables the body to rotate about the roll, pitch and yaw axes. Each propeller generates a lift force and the lift forces are used to control the pitch and roll angles. The total torque generated by the propeller motors causes the body to move about the yaw axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003775_j.ijheatmasstransfer.2018.04.092-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003775_j.ijheatmasstransfer.2018.04.092-Figure2-1.png", + "caption": "Fig. 2. Computational domain and subdomains.", + "texts": [ + " The rate of energy loss, q8; is assumed to be distributed uniformly through the liquid domain with a negative value. The reduction of the WP energy reduces the weld penetration. The rate of volumetric energy loss is computed as follow: q8 \u00bc qw\u00bdcpw\u00f0Tlw T0\u00de \u00fe Lw UwAw 8 \u00f012\u00de where qw, cpw and Lw are the density, specific heat capacity and latent heat of the wire, respectively. Tlw and T0 are liquidous and ambient temperatures of the wire. Uw and Aw are wire feed rate and wire cross sectional area. 8 is the volume of the fluid domain Xl (see Fig. 2). The mass transfer is important to investigate the final distribution of chemical compositions in the weld zone after two dissimilar alloys are mixed. In this study, the substrate material is stainless steel and wire is made of Inconel 718. The mass transport equation is: \u00f0 u\u00fe Ut\u00de \u00f0 rCi\u00de \u00bc r \u00f0Di rCi\u00de \u00f013\u00de where Ci is the concentration of the ith alloying element; and, Di is the diffusion coefficient of that element in the molten pool. The computational domain is divided into two subdomains. Fig. 2 illustrates the computational domain and subdomains. The molten pool occurs in the smaller subdomain Xl. The fluid flow is restricted to the subdomain Xl to save calculation time. The material properties of the liquid domain are calculated using mass fraction of alloying elements like iron concentration (CFe) as follows: MF \u00bc CFe CFeclad CFesubstrate CFeclad \u00f014\u00de al \u00bc MFal clad \u00fe \u00f01 MF\u00deal substrate \u00f015\u00de where MF denotes mass fraction, CFeclad and CFesubstrate are concentration of iron in the clad layer and the substrate, respectively, and al represents the material property of the liquid phase" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001680_j.triboint.2011.11.025-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001680_j.triboint.2011.11.025-Figure1-1.png", + "caption": "Fig. 1. Geometric condition", + "texts": [ + " Mass conserving cavitation, non-Newtonian flow and the real involute characteristics of the tooth flanks are incorporated. States of mixed friction and microhydrodynamic effects are ascertained integrally based on realmeasured surface topographies. Straight spur gear pairs serve as an example to present the results of calculating the influence of surface roughness asperities and gearing geometry. & 2011 Elsevier Ltd. All rights reserved. Spur gears are implemented in a transmission to transmit and gear torques and rotary motions between parallel shafts (see Fig. 1). The involute has been established to be a common tooth profile. The rolling contact between the tooth flanks has a curvature that varies with the direction of the addendum. A combined sliding and rolling motion always exists on the tooth flanks, with the exception of the pitch point. The amounts of sliding motion reach their maximums in the regions of the addendum and root. The lubricated tooth flank contact constitutes a thermal elastohydrodynamic line contact that expands finitely in the direction of the width of the tooth flanks" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure8.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure8.12-1.png", + "caption": "Figure 8.12.2 Rolled vehicle showing swing arm angles uSA in vehicle coordinates and uSAR in road coordinates.", + "texts": [ + " To obtain this in terms of the actual roll angle, in radians, eB1;Roll \u00bc 1 2 TeB1;Roll;ZB \u00f08:11:7\u00de This has units m/rad, lateral motion of the GRC per radian of suspension roll angle. The preceding analysis has been performed in the vehicle-body-fixed coordinates (B, H) because this is much clearer than a suspension analysis in Earth-fixed road coordinates (Y, Z). However, for application, it is desired to know the values in the Earth-fixed system, so a transformation of coordinates must be applied, as seen in Figure 8.12.1. Thevehicle body position is defined by a heaveZB (a negative suspension bump) followed by a suspension roll fS. The order of this sequence is significant; if the movement is defined in the other order then the transformation equations are altered. Previous to the displacement, the two axis systems (B, H) and (Y, Z) are coincident. A general point P is at vehicle-fixed (B, H) and at Earth-fixed (Y, Z). By simple geometry, Y \u00bc B cosfS H sinfS Z \u00bc B sinfS \u00fe H cosfS \u00fe ZB \u00f08:12:1\u00de This may be arranged as two simultaneous equations in B andH, and solved by the usual methods, giving B \u00bc Y cos fS \u00fe\u00f0Z ZB\u00desinfS H \u00bc \u00f0Z ZB\u00decos fS Y sinfS \u00f08:12:2\u00de The vehicle also heaves on the tyres because of changing total normal force and because of variation of the effective tyre normal stiffness with lateral force, and the axle rolls on the tyres because of the lateral transfer of normal force in cornering combined with the tyre vertical compliance. An additional transformation, similar to the above, may be applied for this. Roll Centres 175 When roll is applied before heave, the equations are Y \u00bc \u00f0H \u00fe ZBf\u00desinfS \u00fe B cosfS Z \u00bc \u00f0H \u00fe ZBf\u00decos fS \u00fe B sinfS \u00f08:12:3\u00de with B \u00bc Y cosfS \u00fe Z sinfS H \u00bc Y sinfS \u00fe Z cosfS ZBf \u00f08:12:4\u00de Figure 8.12.2 shows the rolled vehicle, with swing arm angles in vehicle coordinates uSA,L and uSA,R. Relative to the road, the swing arm angles are uSAR;L \u00bc uSA;L fS uSAR;R \u00bc uSA;R \u00fe fS \u00f08:12:5\u00de By this means, the GRC may be solved directly in road coordinates, if desired. The bump scrub rate coefficients may be expressed easily in road coordinates for small angles: eBScdR;R \u00bc eBScd;R \u00fe fS eBScdR;L \u00bc eBScd;L fS \u00f08:12:6\u00de Using this method, all vehicles become asymmetrical. For steady-state handling analysis, the roll centre height may be represented approximately by H \u00bc H0 \u00fe kH1AY \u00fe kH2A 2 Y B \u00bc B0 \u00fe kB1AY \u00fe kB2A 2 Y \u00f08:13:1\u00de In a linear model, the suspension double bump (axle bump zA) and suspension roll angle fS are related to the lateral acceleration (latac) by zA \u00bc kZAAY fS \u00bc kfSAY \u00f08:13:2\u00de H \u00bc H0 \u00fe eH1;RollkfSAY \u00fe eH2;Rollk2fSA 2 Y B \u00bc eB1;RollkfSAY \u00fe eB2;Rollk2fSA 2 Y \u00f08:13:3\u00de The linear effect on GRC height is usually quite small, being the result of vehicle asymmetries, so kH1 is small" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002751_1.g003201-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002751_1.g003201-Figure3-1.png", + "caption": "Fig. 3 Transition from hover (vertical) to forward flight (horizontal) mode.", + "texts": [ + " A nonzero net torque along the ZQ axis causes yawing motion that can be generated from the drag force acting on each rotor. The collective pitch of the two diagonal rotors rotating in the same direction is increased and the collective pitch of the other diagonal pair is reduced to generate pure yaw motion. The control of transition is crucial and challenging as the vehicle does not have enough forward speed to generate adequate lift for supporting the entire weight of the UAV. A conceptual idea of transition is demonstrated in Fig. 3. The vehicle is initially commanded to change its pitch orientation by 90\u00b0 from the vertical orientation of rotors and wings to the orientation for the horizontal flight where both rotors and wings are nearly horizontal. Because no conventional control surfaces are present, the control moments need to be generated by the four rotors. When aerodynamic forces contributed by the wing become significant, the fixed-wing aerodynamics becomes prominent, but the UAV translational and rotational motions are still controlled using the forces and moments generated by the rotors for this tailless configuration having no control surfaces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001151_j.mechmachtheory.2014.08.006-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001151_j.mechmachtheory.2014.08.006-Figure1-1.png", + "caption": "Fig. 1. Ball orbital and spinning angular speed and pitch angle.", + "texts": [ + " In this paper, a quasi-static analysismodel is developed in order to analyze the performance of angular contact ball bearings, such as the ball-raceway contact angle, contact force and spin-to-roll ratio, under the combined action of radial, axial loads and the shaft tilting moment along with the consideration of the effects of centrifugal force and gyroscopic moments. The present model has removed the assumption of raceway control; the balls contacting both outer and inner raceways roll and spin simultaneously. Thus, the spin-to-roll ratio at both ball-outer and ball-inner raceway contacts can be obtained simultaneously, which is more close to real conditions. In order to investigate the dynamic characteristics of ball bearing, the ball angular speed and pitch angle should be determined first. Fig. 1 illustrates the angular speed vector for a single ball in a bearing. The coordinate system O0-xyz with the x axis collinear with bearing axis is defined. In the present model, it is assumed that the outer ring is fixed in housing while the inner ring is fixed rigidly to the shaft which rotates at angular speed \u03c9i about the x axis. As shown in Fig. 1, the ball not only orbits around the bearing axis at angular speed\u03c9c, but also rotates at angular speed\u03c9b around its own axis O1O, inclined by ball pitch angle \u03b2 from x axis. Therefore, based on the rules of vector addition, the ball absolute angular speed \u03c9b\u204e can be obtained as: \u03c9 b ! \u00bc \u03c9b !\u00fe \u03c9c ! : \u00f01\u00de During operation, the ball contacts outer and inner raceways at point Ce and Ci, respectively. At the ball-inner raceway contact point Ci, the linear speed of the inner ring relative to the cage can be determined as: viCi \u00bc 1 2 \u03c9i\u2212\u03c9c\u00f0 \u00dedm 1\u2212\u03b3i\u00f0 \u00de: \u00f02\u00de Similarly, the linear speed of the ball relative to the cage can be determined as: vbCi \u00bc 1 2 \u03c9bD cos \u03b1i\u2212\u03b2\u00f0 \u00de: \u00f03\u00de It is usually assumed that there is no sliding at ball-raceway contact, therefore, viCi \u00bc vbCi : \u00f04\u00de Thus, the ball spinning speed around its own axis can be obtained as: \u03c9b \u00bc \u03c9i\u2212\u03c9c\u00f0 \u00de dm 1\u2212\u03b3i\u00f0 \u00de D cos \u03b1i\u2212\u03b2\u00f0 \u00de : \u00f05\u00de The same way is applied to the ball-outer raceway contact, one can get: \u03c9b \u00bc \u2212\u03c9c\u00f0 \u00de dm 1\u00fe \u03b3e\u00f0 \u00de D cos \u03b1e\u2212\u03b2\u00f0 \u00de : \u00f06\u00de Based on Eqs", + " (5) and (6), one can get the ball orbital speed and spinning speed, respectively: \u03c9c \u00bc \u03c9i 1\u2212\u03b3i\u00f0 \u00de cos \u03b1e\u2212\u03b2\u00f0 \u00de 1\u00fe \u03b3e\u00f0 \u00de cos \u03b1i\u2212\u03b2\u00f0 \u00de \u00fe 1\u2212\u03b3i\u00f0 \u00de cos \u03b1e\u2212\u03b2\u00f0 \u00de \u03c9b \u00bc \u03c9i dm D 1\u2212\u03b3i\u00f0 \u00de 1\u00fe \u03b3e\u00f0 \u00de 1\u00fe \u03b3e\u00f0 \u00de cos \u03b1i\u2212\u03b2\u00f0 \u00de \u00fe 1\u2212\u03b3i\u00f0 \u00de cos \u03b1e\u2212\u03b2\u00f0 \u00de 8>< >: : \u00f07\u00de Assume that the angular speed of the ball relative to the inner ring is \u03c9bi, it is collinear with CiO1, where O1 is the relative instantaneous center of velocity.\u03c9bi should be equal to the difference between the ball and inner ring angular speeds relative to the cage at contact point Ci, which can be written as: \u03c9bi ! \u00bc \u03c9b !\u2212 \u03c9i !\u2212\u03c9c ! : \u00f08\u00de Similarly, at the contact point Ce, the angular speed of the ball relative to the outer ring can be written as: \u03c9be ! \u00bc \u03c9b !\u2212 \u2212\u03c9c ! : \u00f09\u00de Angular velocity\u03c9bi can be divided into rolling and spinningmotions as shown in Fig. 1, the component\u03c9bi S acts normal to the surface indicating a spinning motion in the contact zone while the component \u03c9bi R acts tangential to the surface standing for a purely rolling motion. They can be determined as follows, respectively, \u03c9S bi \u00bc \u03c9i\u2212\u03c9c\u00f0 \u00de sin\u03b1i \u00fe\u03c9b sin \u03b1i\u2212\u03b2\u00f0 \u00de \u00f010\u00de \u03c9R bi \u00bc \u03c9i\u2212\u03c9c\u00f0 \u00de cos\u03b1i \u00fe\u03c9b cos \u03b1i\u2212\u03b2\u00f0 \u00de: \u00f011\u00de Similarly, for ball-outer raceway contact, \u03c9S be \u00bc \u03c9e\u2212\u03c9c\u00f0 \u00de sin\u03b1e\u2212\u03c9b sin \u03b1e\u2212\u03b2\u00f0 \u00de \u00f012\u00de \u03c9R be \u00bc \u2212 \u03c9e\u2212\u03c9c\u00f0 \u00de cos\u03b1e \u00fe\u03c9b cos \u03b1e\u2212\u03b2\u00f0 \u00de: \u00f013\u00de From Eqs. (10)\u2013(13), spin-to-roll ratios for a ball contacting with raceways are obtained by: SRi \u00bc \u03c9S bi=\u03c9 R bi \u00bc \u03b30 sin\u03b1i \u00fe 1\u2212\u03b3i\u00f0 \u00de tan \u03b1i\u2212\u03b2\u00f0 \u00de \u00f014\u00de SRe \u00bc \u03c9S be=\u03c9 R be \u00bc \u03b30 sin\u03b1e\u2212 1\u00fe \u03b3e\u00f0 \u00de tan \u03b1e\u2212\u03b2\u00f0 \u00de: \u00f015\u00de Based on the D'Alember's inertia force principle, the power conducted by all the forces applied on the ball including inertial force should be zero. The following deduction in this section is based on reference [23]. As illustrated in Fig. 1, Mbi S andMbe S are defined as spinning friction moment between ball and inner, outer raceway, respectively, it can be found that: P \u00feMS bi\u03c9 S bi3\u2212MS be\u03c9 S be3 \u00bc 0 \u00f016\u00de where \u03c9bi S ' and\u03c9be S ' are the inner and outer raceway spinning angular speeds relative to the ball, whose magnitudes are equal to \u03c9bi S and \u03c9be S , respectively. P* is the power of external force conducted to the ball, except for Mbi S and Mbe S . Since the outer raceway keeps fixed in space and inner raceway connects rigidly to the shaft, positive work is done by the inner ring while negative work is done by the outer ring for ball" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure7.14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure7.14-1.png", + "caption": "Fig. 7.14 Kinematic variables during a stick-slip vibration (\u03bc0 = 0.25; \u03bc = 0.14; \u03c90v/g = 0.2); a) Time functions, dashed/dotted line: displacement x\u03c92 0/g, solid line: \u03c90x\u0307/g; dotted line: x\u0308/g b) Phase curves", + "texts": [ + " a) b) It is assumed that the mass initially sticks to the support that moves at a constant velocity v and that the slipping motion starts at the moment when the mass breaks away from the support. The equation of motion then becomes (without damping) mx\u0308 + cx = \u03bcmg; x\u0307 v. (7.77) The initial conditions describe the fact that initially the spring force c x0 is as large as the maximum adhesive force and the velocity of the mass m is equal to that of the support: t = 0: x(0) = x0 = \u03bc0mg c ; x\u0307(0) = v0 = v. (7.78) The solution obtained for the first interval (0 t t1) is \u03c92 0 = c/m, see Fig. 7.14a: x(t) = \u03bcmg c + (\u03bc0 \u2212 \u03bc) mg c cos \u03c90t + v \u03c90 sin \u03c90t = \u03bcg \u03c92 0 + s\u0302 cos \u03c90(t\u2212 t\u2217) (7.79) x\u0307(t) = \u2212\u03c90s\u0302 sin \u03c90(t\u2212 t\u2217) The following applies in the range 0 < \u03c90t \u2217 = arctan v\u03c90/g \u03bc0 \u2212 \u03bc < \u03c0/2 sin \u03c90t \u2217 = v s\u0302\u03c90 ; cos \u03c90t \u2217 = (\u03bc0 \u2212 \u03bc)g s\u0302\u03c92 0 (7.80) and the amplitude is 7.3 Self-Excited Oscillators 493 s\u0302 = \u221a[ (\u03bc0 \u2212 \u03bc)2 mg c ]2 + ( v \u03c90 )2 = mg c \u221a (\u03bc0 \u2212 \u03bc)2 + ( v\u03c90 g )2 . (7.81) 494 7 Simple Nonlinear and Self-Excited Oscillators The velocity of the mass at first drops as a result of the braking friction force before it increases and once again reaches the velocity of the belt at the time t1, see Fig. 7.14a. The condition x\u0307(t1) = v = \u2212\u03c90s\u0302 sin \u03c90(t1 \u2212 t\u2217) (7.82) results in \u03c90t1 = \u03c90t \u2217 + arcsin[v/(\u03c90s\u0302)] + \u03c0. (7.83) The first interval is completed at the time t1 and the displacement x(t1) = \u03bcmg c + s\u0302 cos \u03c90(t1 \u2212 t\u2217) = \u03bcmg c + s\u0302 \u221a 1\u2212 sin2 \u03c90(t1 \u2212 t\u2217) (7.84) = \u03bcmg c + \u221a s\u03022 \u2212 ( v \u03c90 )2 = \u03bcmg c \u2212 (\u03bc0 \u2212 \u03bc) mg c = (2\u03bc\u2212 \u03bc0) mg c is reached as follows from (7.79) with (7.81) and (7.82). At this moment, the second interval starts, in which the mass is carried along by the adhesive force. The velocities of mass and belt are constant and equal while the displacement and the spring force are increasing: x(t) = x(t1) + v(t\u2212 t1) = (2\u03bc\u2212 \u03bc0) mg c + v(t\u2212 t1); t1 t T", + " This occurs after a full cycle of motion at the time T , which is why the initial values have to be valid again (period of oscillation T ). Inserting the values from (7.78) results in: Fmax = cx(T ) = (2\u03bc\u2212 \u03bc0)mg + cv(T \u2212 t1) = \u03bc0mg. (7.86) In this equation, only the period of oscillation of the steady-state vibration considered is unknown. It is derived from it as follows T = t1 + 2(\u03bc0 \u2212 \u03bc) mg cv = t1 + 2(\u03bc0 \u2212 \u03bc) g v\u03c92 0 . (7.87) The curves for displacement, velocity and acceleration are shown in Fig. 7.14a. This calculation was used to demonstrate the stable motion that develops on the so-called limit cycle, the closed curve in the phase plane (Fig. 7.14b). The curves run into this periodic motion for all initial conditions outside of the limit cycle. Studies with various other friction characteristics show that such a limit cycle exists for all descending characteristics (and taking damping into account). The connection of the (interfering) amplitude with the system parameters is quite interesting, see (7.81). This problem was solved using SimulationX R\u00a9 [34], taking into account additional viscous damping. The calculated phase plot for the model in Fig. 7.13 is shown in Fig. 7.15. One can see that damped vibrations occur for initial conditions that describe a state inside of the limit cycle since all phase curves project spirally 7.3 Self-Excited Oscillators 495 from there towards a vortex point. The motions that start outside of the limit cycle converge to the same limit cycle that is known from Fig. 7.14. One can reduce or prevent the stick-slip vibrations by \u2022 Reduction of the normal force FN acting onto the surfaces with friction \u2022 Increase of damping or friction \u2022 Interference with the time function of the normal force, e. g. additional vibrations \u2022 Lower slope of the descending friction characteristic, e. g. by another material \u2022 Increase of the natural frequency (smaller mass, stiffer spring). The critical speed for the severely simplified calculation model of an elastically supported plate that is exposed to an incident flow parallel to the plate plane is to be determined, see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure7.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure7.1-1.png", + "caption": "Fig. 7.1 Amplitude frequency response of the first harmonic and the third subharmonic of the Duffing oscillator", + "texts": [ + " Typical nonlinear effects are that: \u2022 the period of undamped oscillations depends on the initial conditions (initial energy), that is, on the oscillation amplitude; \u2022 the time functions of undamped oscillations are not harmonic but periodic, e. g. the free vibration of mechanisms, see Sect. 2.4.4. \u2022 in the case of harmonic excitation, the amplitude of the motion (steady-state response) is not proportional to the excitation amplitude \u2022 the amplitude and phase of forced steady-state vibrations may change abruptly depending on the excitation frequency, see Fig. 7.1 \u2022 under certain conditions energy that is supplied at a frequency f1 is also transferred into vibrations with another frequency f2 and that self-synchronization and a rectifying effect may occur, see Sect. 7.2.3.3 \u2022 when passing through resonance, the response amplitude at an increasing excitation frequency differs from the one occurring at decreasing excitation frequency, see Figures 7.1 and 7.8 \u2022 combined vibrations at the frequencies mf1 +nf2 and mf1\u2212nf2 (m and n very small integer numbers) may occur when the system is simultaneously excited with two different frequencies f1 and f2", + "24) provides the following quadratic equation for \u03b72 = (\u03a9/\u03c90) 2: \u03b74 + 2\u03b72 [ 2D2 \u2212 1\u2212 3 4 \u03b5\u2217V 2 ] + [ 1 + 3 4 \u03b5\u2217V 2 ]2 \u2212 ( 1 V )2 = 0. (7.26) It has the following two solutions: \u03b72 1,2 = 1 + 3\u03b5\u2217 4 V 2 \u2212 2D2 \u00b1 \u221a 1 V 2 \u2212 4D2 [ 1 + 3 4 \u03b5\u2217V 2 \u2212D2 ] . (7.27) One obtains one or two values of \u03b7 for each given value of the nondimensionalized amplitude function V (only the real roots have physical relevance) so that the desired resonance curve V (\u03b7, D, \u03b5\u2217) is obtained as the inverse function of \u03b7(D, V, \u03b5\u2217). Vice versa, one, two or three different amplitudes can be associated with an \u03b7 value, see Fig. 7.1. This amplitude frequency response for the first harmonic differs significantly from that of a linear oscillator. The dashed line in the center is the so-called skeleton line. It describes the dependence of the natural frequency on the amplitude. The skeleton line is bent to the right for progressive restoring forces because the natural frequency increases with the amplitude in this case. The skeleton line is bent to the left for degressive characteristics. There are unique amplitude values for low (left of D) and for high excitation frequencies (right of B)", + " This is the case if the following condition is satisfied for a progressive characteristic (\u03b5 > 0), see also (7.17): 7.2 Nonlinear Oscillators 475 \u03a9 > 3\u03c90 \u221a 1 + 21\u03b5q\u03022 16 > 3\u03c90 \u221a 1 + 3\u03b5q\u03022 4 = 3\u03c9. (7.39) The inequality sign has to be reversed for \u03b5 < 0. The amplitudes of the subharmonics are large when the excitation frequency is over triple the fundamental frequency. The forced vibrations then oscillate at a frequency that is approximately equal to the natural frequency, that is about one third of the excitation frequency. Figure 7.1 also shows the skeleton line for the third subharmonic. It turns out that the amplitudes of the subharmonic considerably exceed those of the fundamental harmonic in the area \u03a9 > 3\u03c90. There is also a combination of parameter values at which only the subharmonic occurs (q\u0302 = 0). From the first pair of brackets in (7.35), one first finds the relation \u03b5\u03c92 0a3 1/3 = 4F\u0302 /m (the displacement amplitude is proportional to the cubic root of the force amplitude). The second pair of brackets leads to the circular frequency of the excitation at which this motion may occur: \u03a9\u2217 = 3\u03c90 \u221a 1 + 3\u03b5a2 1/3 4 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000882_j.rcim.2010.08.007-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000882_j.rcim.2010.08.007-Figure5-1.png", + "caption": "Fig. 5. Category 2.2.", + "texts": [ + " Without loss of generality, let r1\u00bcr2\u00bcr3\u00bcr, as shown in Fig. 3. Substituting these parameters into (14), (16), and (17), we have f\u00bc arctan sincsiny cosc\u00fecosy \u00f018\u00de x\u00bc \u00f0cysf scsycf\u00der \u00f019\u00de y\u00bc r 2 \u00f0 ffiffiffi 3 p ccsf\u00fecccf\u00fe ffiffiffi 3 p cysf ffiffiffi 3 p scsycf cycf scsysf\u00de \u00f020\u00de The parasitic motion of the 3-PRS PM in subcategory 2.1 is depicted in Fig. 4. Carretero presented the equations of the three parasitic motion of this kind of 3-PRS PM in [20], and the parasitic motion was drawn with the scope of c, y being ( 0.2,0.2), radian. As shown in Fig. 5, three LPs intersect at a line with noncolinear spherical centers, and two LPs are coincident and perpendicular to the other LP. Note that this architecture was disclosed by Carretero [20]. Substituting a\u00bc1801, b\u00bc01into (14), (16), and (17), we can obtain the three parasitic motion fuction as following: x\u00bc rscsy, y\u00bc 0, f\u00bc 0 Hence, the 3-PRS PM in subcategory 2.2 has only one parasitic motion and it is depicted in Fig. 6. The three LPs of the 3-PRS PMs in this category intersect at a line with collinear spherical centers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003645_tie.2017.2698358-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003645_tie.2017.2698358-Figure1-1.png", + "caption": "Fig. 1. Architecture of the heavy towing equipment with HAHC", + "texts": [ + " In Section II, detailed nonlinear mathematical model is presented. The prediction algorithm, adaptive extended disturbance observer and nonlinear cascade controller are given in Section III. Then, the experimental setup and results are presented in Section IV. Finally, conclusions are drawn in Section V. 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. II. DYNAMIC MODEL OF HAHC SYSTEM As shown in Fig. 1, the towed payload is attached to a heavily armored cable which is driven by a storage winch and two auxiliary tension winches. The HAHC system is placed between the frame and the tension winches. The vessel motions are measured with a motion reference unit (MRU) which has three accelerometers for detecting surge, sway, and heave and three rotation rate sensors for measuring roll, pitch, and yaw. The acceleration signals are double integrated in order to obtain the desired relative position of the ship as the feedback signal of HAHC" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003082_j.jsv.2016.02.021-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003082_j.jsv.2016.02.021-Figure7-1.png", + "caption": "Fig. 7. The cracked gears with different crack depths.", + "texts": [ + " To further evaluate the performance of the proposed method in a practical application, experiment tests were conducted in a wind turbine transmission system shown in Fig. 6. From left to right in the figure, the components of the test system are a data acquisition module, a 3HP driving motor, a two-stage planetary gearbox, a two-stage spur gearbox, and a controllable magnetic brake. The numbers of the gear teeth of the two gearboxes are shown in Table 3. In this work, a crack fault was imposed to the tooth root of gear Z29 (gear teeth number is 29) in the intermediate shaft of the spur gearbox. Fig. 7 shows a picture of the normal and cracked Z29 gears. Three different crack depths were tested, including 0.5, 1.25 and 2.0 mm, respectively. The most recent research in [55] concluded that the vibration response of the gear crack propagating through the rim (CPR) was greater than the crack propagating through the tooth (CPT) under the same crack level. In order to examine the proposed detection method in a harsh condition, in this work the CPT was processed on the Z29 gears by wire electrical discharge machining" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002359_j.engappai.2011.12.006-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002359_j.engappai.2011.12.006-Figure1-1.png", + "caption": "Fig. 1. Twin rotor MIMO system.", + "texts": [ + " In certain aspects, its behaviour resembles the dynamics of a helicopter (Ahmad et al., 2003; Rahideh et al., 2008). For example, it possesses a strong cross-couplings between the collective (main) and tail rotors. The TRMS is characterised by its complex and highly nonlinear dynamics. Some of its states and outputs are also inaccessible for measurements. All these typify TRMS as a challenging engineering problem. The control objective is to make the beam of the TRMS tracks a predetermine trajectory. Fig. 1 shows the TRMS considered in this investigation. The dynamic model as supplied by the manufacturer has been improved in this study and the electric motors are modelled with respect to the corresponding equations. The TRMS possesses two permanent magnet DC motors; one for the main and the other for the tail propelling. The motors are identical with different mechanical loads. The mathematical model of the main motor (Rahideh et al., 2008), as shown in Fig. 2, is presented in: diav dt \u00bc 1 Lav \u00f0Vv Eav Raviav\u00de \u00f01\u00de Eav \u00bc kavfvov \u00f02\u00de dov dt \u00bc 1 Jmr \u00f0Tev TLv Bmrov\u00de \u00f03\u00de Tev \u00bc kavfviav \u00f04\u00de TLv \u00bc ktv9ov9ov \u00f05\u00de where Vv is the voltage control input of the vertical channel, Eav, Rav, Lav and iav are, respectively, the electromotive force, armature resistance, armature inductance and armature current of the main motor, kav and ktv are constants, jv is the magnetic flux, ov is the rotational velocity, Tev is the electromagnetic torque, TLv is the load torque, Jmr is the rotor moment of inertia and Bmr is the rotor damping coefficient all of the main motor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001796_978-3-319-32156-1-Figure10.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001796_978-3-319-32156-1-Figure10.4-1.png", + "caption": "Fig. 10.4 Effect of overconstraint of PCB and housing. a Original design. b Redesign", + "texts": [ + " In an additional publication [17], 15 strategies for variation reduction are laid out. However, only two of these strategies (Quality Control and Shielding) are possible in the electronics industry. All electrical components have a mechanical interface to them. Mounting and fitting of PCBs is notorious for throwing up late stage issues and failures especially during the high volume ramp-up. There are two common errors here. First it seems to be a common mistake to overconstrain the PCB within the housing. An example 156 P. Hehenberger et al. of this can be seen in Fig. 10.4a where it is clear that there are too many surfaces responsible for the positioning of the PCB within the housing (the outer edge, the four pins, the inner edge, the notch at the top and the bottom). As a consequence the PCB had to be reworked in various areas before the assembly process\u2014the areas of rework can be seen in Fig. 10.4b. In the case above where a PCB is unable to fit correctly in its housing, the worst case will be time and money spent on rework before assembly. In some cases it may also lead to a potential distortion of the PCB during mounting, causing it some damage. When it comes to mounting of sensors, the positioning of the sensor can have a huge consequence on the performance of the product, this is a case of cross-domain robustness, dealt with in the next section. With reference to mechatronics, cross-domain robustness arises where a variation in the mechanical domain leads to performance change in the electrical domain, or variation in the electrical domain affects the mechanical performance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002280_s12206-012-0627-9-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002280_s12206-012-0627-9-Figure5-1.png", + "caption": "Fig. 5. Forces acting on the jth rolling element.", + "texts": [ + "oj ojF uN= (12) The friction force at the front interface between the rolling element and the race pocket at the jth rolling element can be expressed as 1 1 .c j c jF uN= (13) The friction force at the rear interface between the rolling element and the pocket at the jth rolling element can be expressed as 2 2 .c j c jF uN= (14) The equations of motion that describe bearing dynamic behavior can be derived from Newton\u2019s laws. To derive these equations of motion it is first necessary to analyze the forces acting upon the separate rolling elements, the cage and the inner race. Forces acting upon the jth rolling element are shown in Fig. 5. In that illustration, Nij and Noj are contact normal forces acting between the jth rolling element and the races. Fij and Foj are friction forces between the jth rolling element and the races. Nc1j and Nc2j are normal forces at the jth rolling element/pocket contact. Fc1j and Fc2j are friction forces at the jth rolling element/pocket contact. Gr is the force of gravity acting on the rolling element. Fcj is the centrifugal force acting on the jth rolling element due to the cage speed .c\u03c9 Forces acting upon the cage are shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure2-1.png", + "caption": "Figure 2. Model of vehicle dynamics. (a) Dynamics model of the motor car and (b) dynamics model of the bogie.", + "texts": [ + " The modal superposition method is used to evaluate the dynamic responses of the flexible gearbox housing with polygonal wear of wheels. At the same time, rig tests in the laboratory and field tests on the Beijing\u2013Shanghai high-speed rail line are carried out. Furthermore, the dynamic responses of the gearbox housing with polygonal wear of wheels and the damage it causes to the gearbox housing are analysed. In this paper, a vehicle dynamics model is established, considering the flexible gearbox, gear transmission system, and the vehicle. Figure 2 illustrates the finite element (FE) model of the flexible gearbox housing, gear meshing model, and wheel polygon model in the SIMPACK environment. The FE model of the gearbox housing is used to determine its modal properties via eigen analysis. The modal vectors are subsequently integrated with the vehicle model by using the finite element multibody system (FEMBS) interface in SIMPACK.14 As for the gear transmission system, the mesh stiffness presents significant changes periodically. The mesh stiffness is calculated using the FE model of the gear pair and applied to the vehicle dynamics model via SIMPACK\u2019s expression force element" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000789_s00170-010-2641-3-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000789_s00170-010-2641-3-Figure3-1.png", + "caption": "Fig. 3 Temperature distribution at different times for P=100 W and V=30 mm/s. a 0.075 s, b 0.08 s, c 0.365 s", + "texts": [ + " The inclusion of temperature-dependent thermo-physical properties and a radiation term in the boundary condition makes the simulation highly nonlinear. The focus of the current research lies in establishing a FEA 3D model for the selective laser melting W\u2013Ni\u2013Fe powder system. To get a further understanding about the influences of processing parameters (laser power, scan velocity, scan interval, and preheating temperature, etc.) on temperature field, the established model was applied to simulate the temperature field in powder bed under a successive scan mode. Figure 3 shows the typical temperature field with fixed parameters (laser power 100 W, scan velocity 20 mm/s, scan interval 0.05 mm, scan thickness 0.05 mm). As shown in Fig. 3, the isotherm curve formed by moving laser beam seems to be a series of ellipses. Specifically, the isotherm curves that occur at the front-end of molten pool are denser by comparison with the back-end. There are two main causes for this significant difference: the accumulated heat by the melted zone and the higher coefficient of heat conductivity in the melted zone which is a benefit to heat transmission. In the W\u2013Ni\u2013Fe powder system, the melting points of W, Ni, and Fe are 3,420\u00b0C, 1,453\u00b0C, and 1,535\u00b0C, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003703_j.mechmachtheory.2020.103889-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003703_j.mechmachtheory.2020.103889-Figure2-1.png", + "caption": "Fig. 2. The mechanical and deformation states for ball bearing with the ring misalignment error: (1) The coordinate system of ball bearing; (b) The geometry and displacements in the ball-raceway contacts.", + "texts": [ + " Besides, by further comparing the two types of misalignment errors in rotor systems as shown in Fig. 1 (a) and (b), one can find that the directions of the ring angular misalignment of the rear bearing are significantly different, which may further leads to the difference in the dynamic performance of the rotor system. In order to reveal the influence of the ring misalignment on the service characteristics of the rotor systems, the theoretical model of the single-row ball bearing with any given misalignment error should be presented first. As shown in Fig. 2 , without loss of generality, it is assumed that the outer ring of ball bearing is fixed and the angular misalignment of bearing inner ring is \u03b8 , it can be further decomposed as: \u03b8 = [ \u03b8y , \u03b8z ] (1) where \u03b8 y and \u03b8 z are the angular misalignment around Y -axis and Z -axis of bearing inner ring, respectively. It can be seen from Fig. 2 (a), the displacement vector d = { \u03b4x , \u03b4y , \u03b4z } of the inner ring relative to the fixed outer ring for ball bearing subjected to the external load vector F = { F x , F y , F z } is generated. In order to further determine the relation between the local deformations of the ball-raceway contacts and the global displacements of the inner ring, the center position changes of the ball and inner raceway curvature are presented in Fig. 2 (b), and the ball center and inner raceway curvature center respectively shift from point O b to O \u2032 b and point O i to O \u2032 i under the combined action of the external forces and inertia forces. So the final curvature center distances in horizontal and vertical directions are written as: { A 1 k = ( r i + r o \u2212 D ) sin \u03b10 + \u03b4ak A 2 k = ( r i + r o \u2212 D ) cos \u03b10 + \u03b4rk (2) where r i and r o are the inner and outer raceway curvature radii (unless otherwise stated, the subscripts i and o denote the variables of the inner and outer raceway contacts, respectively), and D is the ball diameter. \u03b10 is the ball-raceway initial contact angle. Besides, the local relative displacements at any position angle \u03c8 k ( \u03c8 k = 2 \u03c0(k \u2212 1) /Z , k denotes the k th ball and Z is the number of balls) are given as: [ \u03b4ak \u03b4rk ] = [ 1 0 0 0 . 5 d m sin \u03c8 k \u22120 . 5 d m cos \u03c8 k 0 cos \u03c8 k sin \u03c8 k 0 0 ] \u00d7 [ \u03b4x \u03b4y \u03b4z \u03b8y \u03b8z ]T (3) where d m denotes the pitch diameter of ball bearing. As shown in Fig. 2 (b), the following equilibrium equations can be obtained according to the Pythagorean theorem: { ik sin \u03b1ik + ok sin \u03b1ok \u2212 A 1 k = 0 ik cos \u03b1ik + ok cos \u03b1ok \u2212 A 2 k = 0 (4) where \u03b1ik and \u03b1ok are the ball-inner raceway and ball-outer raceway contact angles, respectively. Different from the previous studies of ball bearing [ 14\u201318 , 30 ] the ball-raceway contact angles \u03b1ik and \u03b1ok are selected as the intermediate unknown variables in the subsequent derivation. Besides, the center distances between ball and inner/outer raceway curvature are given as: { ik = r i \u2212 0 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.15-1.png", + "caption": "FIGURE 4.15. Screw motion of a rigid body.", + "texts": [ + " When the screw is not central and il is not passing through the origin, a screw motion to move p to p\" is denoted by p\" = (p-s)cos\u00a2+(l-cos\u00a2)(il\u00b7(p-s))il + (il x (p - s)) sin \u00a2 + s + hil or p\" = G RB (p - s) + s + hil G RB p + s - G RB S + hil and therefore, p\" = s(h,\u00a2, il, s)p = [T] p where (4.112) (4.113) (4.114) [T] G s - G R f G s + hil ] Gd ] 1 . (4.115) The vector Gs , called location vector, is the global position of the body frame before screw motion. The vectors p\" and p are global positions of a point P after and before screw, as shown in Figure 4.15. The screw axis is indicated by the unit vector ii. Now a body point P moves from its first position to its second position pi by a rotation about il . Then it moves to P\" by a translation h parallel to ii. The initial position of P is pointed by p and its final position is pointed by p\" . 4. Motion Kinematics 157 In some references, screw is defined as a line with a pitch. To indicate a motion, they need to add the angle of twist . So, screw is the helical path of motion, and twist is the actual motion ", + "204) [ G~l so- GR\\ SO+ hOUO ] [1~2 Sl- lR2;1+hlUl] [ G~2 GRl (Sl - lR2Sl + hlU{) + SO- GRl SO+ hOUO ] [ G~2 GRl (l - lR2)Sl+(I- ~Rt}SO+hlGRlUl+hOUO] where G R2 = G R l 1R2 . (4.205) To find the screw parameters of the equivalent screw G 82(h,\u00a2, U, s) , we start obtaining U and \u00a2 from G R2 based on (4.131) and (4.129). Th en, utili zing (4.172) and (4.173) we can find h and S h= u \u00b7 Gd (4.206) (4.207) where Gd GRl (l- lR2)Sl+(I- GRt} so+ hlGRlUl + houo (GRl - GR2) Sl + GRl (hlUl - so) + So + houo. (4.208) \u2022 Example 108 * Exponential representation of a screw. To compute a rigid body motion associated with a screw, consider the motion of point P in Figure 4.15. The final position of the point can be given by p\" S + e 0 , kp > 0 and transform the equation of motion to mx+(c+kD)x+(k+kp)x=O. (15.11) (15.12) (15.13) By comparison with the open-loop equation (15.11), the closed loop equation shows that the oscillator acts as a free vibrating system under the action of new stiffness k + kp and damping c + ko - Hence, the control law has changed the apparent stiffness and damping of the actual system", + " The second term , Qfb, is the f eedback command, which is the correct ion torques to reduce the errors in the path of the robot . Computed torque cont rol is also called feedback lin earizat ion , which is an applied technique for robots' nonlinear cont rol design. To apply the feedback linearization technique, we develop a control law to eliminate all nonlinearities and reduce the problem to the linear second-order equat ion of error signal (15.38) \u2022 Example 330 Comp ut ed force control for an oscillator. Figure 15.2 depicts a lin ear ma ss-spring-damper oscillator under the ac tion of a control force. Th e equation of motion for the oscillator is m /i + ex + kx = f. Applying a computed force control law (15.43) f e m (Xd - kDe - kpe) + ex + kx X -Xd (15.44) (15.45) reduces the error differential equation to e+ kDe + kpe = O. Th e solution of the error equation is (15.46) e AeA1t + BeA2t -kD \u00b1 Jk'b - 4k p (15.47) (15.48) where A and B are fun ctions of initial conditions, and ), 1,2 are solutions of the characteri stic equation (15" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000720_0278364910394392-Figure28-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000720_0278364910394392-Figure28-1.png", + "caption": "Fig. 28. Kinematic model for a rolling disk. The disk\u2019s position is the ( x, y) location of its contact point on the plane, and its \u2018shape\u2019 is the roll angle \u03b1a and the heading angle \u03b1b.", + "texts": [ + " The pointer is implemented mechanically with a differential gear set that takes the difference between the two wheels\u2019 axle angles; for unit wheel spacing and radius, the pointer angle is \u03b2p = \u03b11 \u2212 \u03b12. (40) at Ondokuz Mayis Universitesi on May 8, 2014ijr.sagepub.comDownloaded from A comparison of Equation (39) with Equation (40) clearly shows that \u03b2\u03b8 = \u03b2p, and, thus, that optimizing the coordinates for the differential-drive car produces a mathematical description of the south-pointing chariot. The rolling disk is an elementary non-holonomic system, often used in tutorial examples. Its kinematic model is depicted in Figure 28, with position g =( x, y) \u2208 R 2 and \u2018shape\u2019 r =(\u03b1a,\u03b1b) \u2208 S \u00d7 S. The connection vector fields and height functions for the rolling disk are the same as for the optimized differential-drive, but rotated clockwise by 45 degrees; the reason for this becomes immediately clear when we consider that rolling the disk forward is equivalent to driving both wheels of the car together, while changing the disk\u2019s heading corresponds to driving the wheels in opposite directions to each other. This relationship between the \u03b1 parameters for the disk and car is illustrated in Figure 29" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001207_s10846-010-9395-x-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001207_s10846-010-9395-x-Figure6-1.png", + "caption": "Fig. 6 CFLC input (Ze and w) and output (\u03b4s) membership functions", + "texts": [ + " Two system state variables Ze (depth error) and w (heave velocity) are selected as the feedback signals. The input to the SIFLC is the distance d which is obtained using the signed distance method, i.e.: d = w + Z e\u03bb\u221a 1 + \u03bb2 (17) Variable \u03bb represents the slope of diagonal line LZ . The computed input d is then fed into the control surface block \u03c8 . The output from the control surface is denoted as u\u03070. The scaled output u\u0307 is obtained by multiplying u\u03070 with output scaling factor, denoted as r: u\u0307 = u\u03070. r (18) Figure 6 shows the \u201cequivalent\u201d membership functions for input and output for CFLC which is obtained by trial and error approach. Table 4 is the corresponding rule table for this CFLC. This is to be compared to the SIFLC rule table shown in Table 5 The reduced SIFLC rule table d \u22120.7 \u22120.466 \u22120.23 0 0.233 0.466 0.7 u\u0307o \u22120.99 \u22120.66 \u22120.33 0 0.33 0.66 0.99 Table 5. In order to derive Table 5, the input \u201cd\u201d calculated from the seven diagonal lines shown in Table 4. To validate the proposed work, the Marine Systems Simulator (MSS) is utilized" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002038_physrevlett.110.048103-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002038_physrevlett.110.048103-Figure1-1.png", + "caption": "FIG. 1. Examples of active torque dipoles. Black arrows indicate the torques. (a) A swimming bacterium with rotating flagella. (b) Cytoskeletal torque dipole consisting of two actin filaments and myosin motors. (c) Idealized chiral motor consisting of two counterrotating spheres at distance d.", + "texts": [ + " Further examples are rotating motors on a surface [17\u201319] and carpets of beating cilia used for fluid transport along surfaces [20,21]. Many microorganisms possess carpets of cilia on their outer surface, which are used for selfpropulsion. Various beating patterns of cilia exist, which in general are chiral and often exhibit rotating movements resulting in helical trajectories of microswimmers [21]. The interaction of microswimmers with surfaces can lead to interesting effects [22]. Recently, flagellated E. coli bacteria [see Fig. 1(a)] close to a solid surface were reported to generate large scale chiral flow patterns [23]. The cell cytoskeleton and suspensions of active swimmers have been described as active fluids and gels and studied in the framework of hydrodynamic theories [24\u201329]. Such approaches are based on liquid crystal hydrodynamics [30\u201335] driven out of equilibrium by internal active processes. It has been shown that stresses generated by active processes can give rise to a rich variety of dynamic patterns and flows [10,36\u201341]. Similar approaches have also been used for the study of granular systems [42,43]. Recently, we proposed a systematic extension of the theory of active gels to active chiral fluids [44], in which active contributions to the antisymmetric stress and active angular momentum fluxes are generated by microscopic torque dipoles which arise in situations where interacting objects counterrotate. Examples of torque dipoles are the counterrotation of cell body and flagella of swimming bacteria, see Fig. 1(a), helical actin filaments interacting via clusters of myosin motors; see Fig. 1(b). Thus, in general suspensions of chiral swimmers as well as the cell cytoskeleton can be considered to be active chiral fluids. Many of the most striking active chiral effects, including the biological examples mentioned above, have been observed at interfaces and close to boundaries [2,3,45]. It PRL 110, 048103 (2013) P HY S I CA L R EV I EW LE T T E R S week ending 25 JANUARY 2013 0031-9007=13=110(4)=048103(5) 048103-1 2013 American Physical Society is the aim of the present work to derive a generic theory for active chiral films", + " Note that the spin angular momentum density l and the spin angular momentum flux M do not depend on the choice of the coordinate system. We define an effective rate of spin rotation of local volume elements via l \u00bc I , where I is the moment of inertia tensor per unit volume [35]. The spin angular momentum then obeys @tl \u00bc 2 a \u00fe @ M \u00fe ext ; (3) which shows that spin and orbital angular momentum are not individually conserved but can be exchanged through antisymmetric stress. We discuss the effects of an active chiral process by considering a torque dipole \u00f0r\u00de in a fluid, located at r \u00bc 0, see Fig. 1(c). This torque dipole is built from two torque monopoles q p , of strength q separated by a small distance d in the direction of the torque axis given by the unit vector p: \u00bc q p r d 2 p r\u00fe d 2 p \u2019 qd p p @ \u00f0r\u00de: (4) Note that is invariant under the transformation p ! p, which implies a nematic character. From Eq. (3) the torque dipole can be interpreted as an active contribution Mact \u00bc qd p p \u00f0r\u00de to the spin angular momentum flux, which obeys @ M act \u00bc . In a suspension of many identical torque dipoles at positions r\u00f0i\u00de and with orientations p\u00f0i\u00de, the active angular momentum fluxes are Mact \u00bc qd X i p \u00f0i\u00de p\u00f0i\u00de \u00f0r r\u00f0i\u00de\u00de \u2019 p p \u00fe 0 ; (5) where \u00bc Sqdn and 0 \u00bc \u00f0S 1\u00deqdn=3 describe the strength of a nematic and an isotropic active contribution to M , respectively, and n is the dipole density" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003532_j.conengprac.2015.05.008-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003532_j.conengprac.2015.05.008-Figure8-1.png", + "caption": "Fig. 8. Over-steering.", + "texts": [ + " Due to the slippage phenomena, the measured yaw velocity will be different from the theoretical one. At high velocities, a robot moving on a slippery terrain begins to slip, so that the assumption of rolling without slipping and of no lateral slip become inapplicable. In that case, two kinds of situations have to be avoided: A vehicle under-steers (Fig. 7) when the front wheels are outside of the curvature, i.e. when the front wheels are slipping more than the rear ones. In that case, there is an accident hazard with a roadway exit. In the opposite way, a vehicle over-steers (Fig. 8) when the rear wheels are outside of the curvature, i.e. when the rear wheels are slipping more than the front ones. In that case, there is a hazard of harsh swing-around. Considering that the steering control laws are used to regulate the lateral deviation and the heading error, the introduction of a stabilization algorithm is proposed to avoid the two phenomena of under- and over-steering and to improve the controllability of the robot motion. The objective of the controller can be specified as follows: given a theoretical yaw rate rt that assumes the non-slippage constraint and measuring the real yaw rate r with a gyrometer determine a control law on the traction torque of the wheels \u03c4i that improves the controllability of the vehicle when turning" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure6.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure6.2-1.png", + "caption": "Fig. 6.2 Example 6.2. Two trucks in relative motion", + "texts": [ + "k q : (6.25) Thus, j k QB D j k O j k q 2j\u02dbk j!k q j!k j\u02dbk q j!k j!k j!k q : (6.26) Afterward, substituting Eqs. (6.26) and (6.24) into Eq. (6.23) and reducing terms, we obtain Eq. (6.18). \u02d8 Postulate 2. Some vectors of Eq. (6.18) may be grouped as follows: jcor D 3j\u02dbk kvm O C 3j!k kam O C 3j!k j!k kvm O ; (6.27) where jcor is termed the Coriolis jerk. Example 6.2. Truck B is traveling at the speed of 50 km/h and accelerates at the constant rate 2 m=s2 over a circular curve of radius r D 325 m (see Fig. 6.2). At the same time, truck A is traveling at the speed 80 km/h and accelerates in the direction of its motion at the constant rate of 3 m=s2. Determine the jerk of truck B as observed from truck A when D 30\u0131. Solution. Let XY be a reference frame attached to the center of the curve with associated unit vectors OiOj. In this example it is possible to observe three bodies in relative motion. To apply Eq. (6.17), let us consider body j as the Earth, while body k is truck A and body m is truck B; for example, j D 0, k D A, and m D B" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000802_j.mechmachtheory.2010.03.010-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000802_j.mechmachtheory.2010.03.010-Figure3-1.png", + "caption": "Fig. 3. Coordinate systems between the virtual pinion cutter and the work gear.", + "texts": [ + " (2) yields a cutter surface locus consisting of only three variables \u2013 two surface coordinates (u, \u03b2) and one motion parameter \u03d5c \u2013 which allows the tooth surface to be solved by the following equation of meshing and two boundary equations of the gear blank: f1 u; \u03b2;\u03d5c\u00f0 \u00de = N1\u22c5v 12\u00f0 \u00de 1 = \u2202r1 \u2202u \u00d7 \u2202r1 \u2202\u03b2 \u22c5 \u2202r1 \u2202\u03d5c \u03d5c \u22c5 = 0 \u00f06\u00de Here, modulating the polynomial coefficients (ai1\u223cai6) of the six-axis motion facilitates approximation of the optimal tooth flank geometry. 3. Definition of optimal ease-off According to the definition given in Ref. [10], the ease-off topography represents the normal deviations between the fully conjugated and mated flanks at sampling points. In theory, fully conjugated tooth flanks can be obtained by using a pinion as a virtual cutter to produce the ring gear as shown in Fig. 3. It means that such mating gear set is in line contact with zero transmission error. The mated gear is the ring gear derived from either the mathematical model outlined above or from the CMM data. Although the ease-off technique is recognized as an effective intuitive approach for gear design, it does not answer one important question: what is the optimal ease-off topography? Because industrial applications use a lapping process in gear finishing to achieve better running characteristics (e.g., smooth, quiet running), it is extremely important that the ease-off for a lapped gear pair be selected as the optimization goal for flank modification by reverse engineering (see Ref" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001186_j.1749-6632.1968.tb20346.x-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001186_j.1749-6632.1968.tb20346.x-Figure5-1.png", + "caption": "FIGURE 5 . Oxygen electrode for measuring glucose. A layer of glucose oxidase (solid black area) is held between the end of a conventional oxygen electrode (E) having a polypropylene or Teflon membrane and a membrane of dialysis material, such as Cellophane, Visking casing, or Cuprophane. The cap (A) stabilizes and protects the enzyme layer. The cap (B) bears against the electrode so as to hold it in position and seal it, by compression of the \u201c0\u201d rings, against the end of the jacket (J). The assembly is mounted in a thermostated, flow-through cuvette.", + "texts": [], + "surrounding_texts": [ + "centration, which may affect the characteristics of many tissues, is very low. For example, gastric mucosa in vitro gives low secretory rates in the absence of bicarbonate. Because the oxygen electrode current is not affected by carbon dioxide tension when the correct voltage is used, studies can be conducted using gas mixtures containing sufficient C 0 2 to maintain normal bicarbonate concentrations. High carbon dioxide tensions lower the pH of the oxygen probe electrolyte layer and hence shift the polarogram to the left (FIGURE 1 ) , but this will not increase the oxygen current reading unless an unusually high voltage is applied. Between 0.6 and 0.8 volt, the carbon dioxide 'has no influence on the electrode and will only affect the reading to the extent that it has actually affected the oxygen tension. Many designs for oxygen consumption and oxygen release chambers suitable for tissue and enzyme studies have been described in the literature and some are now available commercially. They consist essentially of stirred sealed chamber^,'.^ made of materials, such as glass or Kel-F, which do not dissolve oxygen, in which the oxygen tension can be continuously monitored. Provision is made for the intermittent addition of reagents, drugs, etc. or for the continuous mixing of two or more streams. Such systems for respirometers may be made with microliter capacities or adapted to production scale tanksg It has been possible to design systems with drifts of less than 1% per hour. FIGURE 2 is a diagram of a respirometer, designed for studying the metabolism of gastric mucosa, which has proven useful both for direct oxygen consumption studies, where the oxygen tension falls as the oxygen is consumed and for an oxystat procedure where the oxygen tension is held constant and oxygen-rich fluid is automatically added and recorded. The respirometer is designed so as to accept electrodes for imposing a constant current, for measuring potential difference, pH, pC0, and p02. It could be adapted for use with other flat tissues, such as diaphragm. In FIGURE 3, the components used in the oxystat have been diagrammed. FIGURE 4 is presented to illustrate the stability of the system, the APPLIED VOLTAGE FIGURE 1. The effect of carbon dioxide on the oxygen polarogram. An oxygen electrode having a platinum cathode, silver reference, and a polypropylene membrane was exposed directly to the gases. The scan rate was 200 millivolts per minute. response time, and the fact that amytal does not completely inhibit respiration, as\u2019has been previously reported by others using Warburg technique. Note that cyanide stopped respiration and that there was no electrochemical interference with the membrane electrode. Although exposed metallic electrodes (such as the vibrating and rotating electrodes) are undoubtedly useful in measuring changes in oxygen tension, one must be sure that no polarographically reducible substances are added or formed, or serious errors may result. There are a large number of inorganic and organic substances which are cathodically reduced\u2019 and which otherwise influence the characteristics of the exposed metal surface. Similar precautions must be used when the platinum anode is used; more than one investigator has been misled by assuming that only one component of the enzyme system under study was oxidized by the metallic anode. The oxygen consumed by the isolated tissue may be replaced by exposing the solution to gaseous oxygen, as by bubbling, or by adding oxygen-saturated sohtion under manual or automatic control. Presumably, electrochemical methods 136 Annals New York Academy of Sciences b Radiometer T T T Ic and SBR 2c High 0 Recording stOt I Beckmon Model Physiological Gos Analyzer cretory Solution Hlgh 0 G Secretory + Nutrient SBR2c Recording PH stat Btckman Model Physiological Gas Analyzer L E G E N D G * Gastric Mucosa C = Clark Oxygen Electrode K = K e l - F Chamber A = Solution Reservoir Clark & Sachs: Tissue Metabolism 137 could also be devised. Perhaps the most generally useful method for equilibrating flowing solutions to known oxygen tensions depends upon utilizing the high gas permeability of silicone elastomers in the form of tubing. It is possible, for example, to completely degas fluid, at a rate of 6 cc per minute by pumping it through eight feet of silicone rubber tubing encased in a chamber evacuated by an ordinary vacuum pump. This gas-fluid separation or equilibration technique has been used to measure nitrous oxide in blood,lOJ1 to record changes in tissue gas tensions,12 and in the continuous measurement of blood oxygen content.*JsJ4 It has recently been applied in equilibrating blood microdialysate streams to a fixed PO, before contacting an oxygen electrode having an enzyme layer (FIG-" + ] + }, + { + "image_filename": "designv10_3_0002966_j.jsv.2015.02.021-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002966_j.jsv.2015.02.021-Figure1-1.png", + "caption": "Fig. 1. Simplified model of the linear guide under preload.", + "texts": [ + " preload, initial contact angle, the diameter and number of balls to discuss the effects of those. Finally we will present our conclusions briefly. The linear guide is a type of transmission assembly unit widely used in machine tools due to the low wear and friction for the ball bearings compared with the traditional guide. The transmission function is implemented based on the interactions of rail, carriage and balls. To analyze the dynamic behaviors of the linear guide, the stiffness should be obtained firstly. A simplified contact model is constructed as shown in Fig. 1, where the accessories are neglected for their few effects on its behaviors. To calculate the stiffness of the linear guide, we presume that (1) when analyzing the interactions between balls and grooves, the contact of ball bearings is regarded as elastic contact; and (2) when calculating the displacement of carriage relative to rail, the carriage and rail are viewed as rigid. In view of Fig. 1 again, the linear guide has four grooves expressed as i\u00bc1, 2, 3, and 4. \u03b80 is the initial nominal contact angle, Oci and Ori are the groove curvature centers and rc and rr are the curvature radiuses of the carriage and rail respectively, usually rc\u00bcrr is represented with r, and \u03b40 is the initial oversize of balls under preload P0. The initial distance s0 between Oc and Or is s0 \u00bc rr\u00ferc \u00bc 2r\u00bc d0\u00fe\u03b40; \u03b4040; (1) where d0 is the initial diameter of ball. Under preload P0, the balls will generate the elastic deformation", + " Then, we can obtain the threshold displacement vc as follows: vc \u00bc s0 sin \u03b80 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r d0\u00f0 \u00de2 s0 cos \u03b80 2q : (11) When v4vc, the relationship between Fv and v is transformed into Fv \u00bc 2Nb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s0 sin \u03b80\u00fev 2\u00fe s0 cos \u03b80 2q 2r d0\u00f0 \u00de 2\u03b7 0 @ 1 A 3=2 s0 sin \u03b80\u00fevffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s0 sin \u03b80\u00fev 2\u00fe s0 cos \u03b80 2q : (12) Accordingly, the expression of vertical stiffness is transformed into K2(v) as K2\u00f0v\u00de \u00bc Nbffiffiffi 2 p \u03b73=2 \u03ba1\u00fe\u03ba2\u00fe\u03ba3\u00f0 \u00de: (13) As demonstrated in Fig. 1, the structure of the linear guide is symmetrical. Therefore, when vcovo0, the stiffness of the linear guide K3(v) is equal to K2(v); and when vo vc, the balls in upper grooves lose contact and the stiffness K4(v) is equal to Nb= ffiffiffi 2 p \u03b73=2\u00f0\u03ba4\u00fe\u03ba5\u00fe\u03ba6\u00de. Thus, the vertical stiffness of the linear guide is a piece-nonlinear function about the displacement as follows: f \u00f0v\u00de \u00bc Nbffiffiffi 2 p \u03b73=2 \u03ba1\u00fe\u03ba2\u00fe\u03ba3\u00fe\u03ba4\u00fe\u03ba5\u00fe\u03ba6; vj jrvc; \u03ba1\u00fe\u03ba2\u00fe\u03ba3; v4vc; \u03ba4\u00fe\u03ba5\u00fe\u03ba6; vo vc: 8>< >: (14) To verify the static model, we use the same parameters in Ref" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002642_j.jmapro.2017.06.010-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002642_j.jmapro.2017.06.010-Figure15-1.png", + "caption": "Fig. 15. Simulation for K in work zone 2 (Green circle). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)", + "texts": [], + "surrounding_texts": [ + "L. Cen, S.N. Melkote / Journal of Manufacturing Processes 29 (2017) 50\u201361 57\nt 8, Te\nr f r (\na c f t F s a\nt f s t f t 1 e w\nT f (\nt ( T c b ( h\nanging from 0.7 to 1.3 mm/s, while Fig. 12a\u2013c shows the resultant orces for Case 2 at feed rates ranging from 0.9 to 1.5 mm/s. Typical esults for the force components under unstable (Test 1) and stable Test 7) conditions are shown in Appendix C.\nIt can be seen from Fig. 11a (Test 1) and Fig. 11b (Test 3) that significant reduction in the resultant cutting force occurs at the ritical feed rate. For Case 1, the average resultant force is reduced rom 147.6 N to 69.5 N, a 52.9% reduction. Similarly, a 46.9% reducion in the average resultant force is observed in Case 2, as seen in ig. 12a (Test 8) and Fig. 12b (Test 10). A significant reduction in the urface roughness was observed between the unstable (\u223c0.03 mm) nd the stable cases (\u223c0.01 mm).\nFor the robot configurations used in Cases 1 and 2, there is a ransition from an unstable (chatter) cut to a more stable cut as the eed rate increases. This is consistent with the simulation results hown in Figs. 9a and 10, respectively. In the experiments, the ransition occurs at a feed rate of \u223c0.9 mm/s for Case 1 and at a eed rate of \u223c1.1 mm/s for Case 2, both of which are slightly less han the simulated transition feed rates of 1.02 mm/s for Case 1 and .23 mm/s for Case 2. This discrepancy is attributed to the damping ffect present in the actual process (but ignored in the simulation), hich increases the stability of the system.\nIn order to further analyze the experimental results, Fast Fourier ransform (FFT) of the resultant forces in three representative tests or Case 1 are shown in Fig. 13a (unstable), b (transition), and c stable).\nAs seen in Fig. 13a (Test 1), the mode coupling chatter vibraion frequency is close to the natural frequency of the robot arm \u223c11.44 Hz), which was identified through a modal hammer test. he vibration of the robot arm adversely impacts the undeformed hip thickness, which acts as an additional 11 Hz input that is fed ack to the system. Therefore, the cutter tooth passing frequency \u223c33 Hz), the chatter frequency (\u223c11 Hz), and their corresponding armonics are visible in the FFT. CNC milling experiments per-\nst 10, and Test 14).\nformed under the same cutting conditions confirm that \u201csize effect\u201d is not a significant factor in the robotic milling experiments.\nAs the feed rate increases to the transition point (Test #3, Fig. 13b), the dominant frequency becomes the tooth passing frequency (\u223c33.33 Hz), and the chatter frequency is largely suppressed. When the feed rate increases to 1.3 mm/s, the system is further stabilized in Test 7. It can be seen from Fig. 13c that the chatter frequency is almost negligible compared to the tooth passing frequency. However, there is still some residual vibration in Test 7, as seen in Figs. 11c and 13c. This can be explained by the magnitude of the robot arm stiffness (on the order of 105\u2013106 N/m), which is much smaller than the stiffness of a typical CNC milling machine (on the order of 108 N/m).\nComparing Tests 1, 3 and 7 (see Fig. 13a\u2013c), it can be seen that the tooth passing frequency (\u223c33.33 Hz) is more significant than the chatter frequency (\u223c11 Hz). The system therefore becomes more stable as the feed rate increases from 0.7 to 1.3 mm/s, which is consistent with the trend shown in the simulation (see Fig. 9a).\n5.3. Applicability to different arm configurations\nIn order to further assess the applicability of the mode coupling chatter avoidance method for robotic milling presented in the previous sections, the stability of robotic milling for different arm configurations needs to be evaluated. It is well known from previous work [11\u201316] that there are two important factors in mode coupling chatter evaluation. One is the angle between Kmax and the average cutting force direction, while the other is the difference between the two principal stiffnesses of the robot arm ( K = Kmax \u2212 Kmin). Mode coupling chatter is more likely to happen when K is small, which, as shown elsewhere [11\u201316], can be derived from the eigenvalue analysis of matrix [A] (see Eq. (14)).\nSimilar to [41,42,45], only the translations of the robot end effector in the XZ plane are analyzed for simplicity. As shown in Figs. 14\u201316, the joint coordinates, indicated on the robot arm,", + "58 L. Cen, S.N. Melkote / Journal of Manufacturing Processes 29 (2017) 50\u201361\nrotate about the Z axis for each joint. Because the 2nd, 3rd, and 5th revolute joins are the three most influential joints as far as the translations of the robot end effector in the XZ plane are concerned, the rest of the joints are set to 0 in the simulations to simplify the analysis and to assist in more easily visualizing the arm configurations.\nAssuming the same workpiece orientation and cutting conditions (Kp, \u02db, \u02c7), mode coupling chatter is more likely to occur when K is small. In order to assess the stability in robotic milling for different arm configurations, the magnitude of K in the XZ plane was calculated.\nAs shown in Figs. 14\u201316, K decreases from work zone #3 to #1 as the end effector moves farther away from the robot base. As the magnitude of K decreases from work zone #3 to #1, [KC ] plays an increasingly important role in CCT-based robotic arm stiffness modeling (see Eq. (16)), which is consistent with previous findings [41,42]. Therefore, the CCT-based method is more effective in the weak stiffness work zones, where mode coupling chatter is more likely to occur.", + "nufac\n6\nf p m t c s t m i r t m f m p t\nA\np t\nA\n(\ni ( i\nF\nF\nF\n|\nw t\nL. Cen, S.N. Melkote / Journal of Ma\n. Conclusions\nIn this paper, a new mode coupling chatter avoidance method or robotic milling using the CCT-based stiffness model is proosed. Robotic milling experiments were conducted to validate the ethod. The experimental results demonstrated significant reducion (> 45%) in the average resultant force when the proposed hatter avoidance strategy was implemented. Simulations demontrated that the proposed CCT-based method is more effective in he weak stiffness work zones, where mode coupling chatter is\nore likely to occur. Distinct from the previous methods reported n the literature, the new method presented in this paper does not equire changing the tool feed direction or the workpiece orientaion, which preserves the versatility of robotic milling and thereby\nakes it more practical for industrial applications. Future work will ocus on developing a more comprehensive robotic milling chatter\nodel which takes into account both regenerative and mode couling chatter effects, and on extending this work to more complex ool paths.\ncknowledgment\nThe authors would like to thank the Boeing Strategic Universities rogram for supporting this work. The authors would also like to hank Dr. James Castle and Mr. Howard Appelman for their support.\nppendix A. Milling force model details.\n1) Mechanistic average milling force model\nThe mechanistically derived average milling force components n the Xo (the radial depth of cut), Yo (axial depth of cut), and Zo feed) directions are given by [32]: (Coordinate o is shown in Fig. 1 n Section 2.1)\n\u00afxo = { Na 8\n[cKtc(2\u2205 \u2212 sin2\u2205) + cKrccos2\u2205 \u2212 4Ktecos\u2205 \u2212 4Kresin\u2205]} \u2205ex\n\u2205st (23)\n\u00afyo = {Na 2\n[\u2212cKaccos\u2205 + Kae\u2205]} \u2205ex\n\u2205st (24)\n\u00afzo = { Na 8\n[cKtccos2\u2205 \u2212 cKrc(2\u2205 \u2212 sin2\u2205) \u2212 4Ktesin\u2205 + 4Krecos\u2205]} \u2205ex\n\u2205st (25)\u221a\nF\u0304 | = (F\u0304xo ) 2 + (F\u0304yo ) 2 + (F\u0304zo ) 2\n(26)\nhere (F\u0304xo , F\u0304yo , F\u0304zo ) are the average milling force components in he XoYoZo directions of coordinate o, a is the axial depth of cut,\nFig. A1. Typical results for force com\nturing Processes 29 (2017) 50\u201361 59\nN is the number of cutter teeth, c is the feed, and \u2205st and \u2205ex are the cutter entry and exit angles. (Ktc,Krc, Kac) are the cutting force coefficients contributed by the shearing action in the tangential, radial, and axial directions, respectively, and (Kte, Kre, Kae) are the edge force coefficients, which can be obtained experimentally as discussed in [32]. In the present work, (Krc , Ktc , Kac) are 2.94 \u00d7 108, 9.04 \u00d7 108, and 2.78 \u00d7 108 N/m2, respectively, while (Kre, Kte, Kae) are 6.6 \u00d7 103, 6.09 \u00d7 103, and 1.12 \u00d7 103 N/m, respectively.\n(2) Calculation of Kpxo\nKpxo = \u2202|F\u0304 | \u2202xo is the sensitivity of d|F\u0304 | due to small deflections dxo from the nominal position xm during milling in coordinate system o. (R is the radius of the cutter)\nThe corresponding cutting coefficients can be derived as shown below:\nKXpxo = \u2202F\u0304xo \u2202xo = ( Na 8R \u2217 sin\u2205ex )[cKtc(2 \u2212 2cos2\u2205ex) \u2212 2cKrcsin2\u2205ex\n+4Ktesin\u2205ex \u2212 4Krecos\u2205ex] (27)\nKYpxo = \u2202F\u0304yo \u2202xo = ( Na 2R \u2217 sin\u2205ex )(cKacsin\u2205ex + Kae) (28)\nKZpxo = \u2202F\u0304zo \u2202xo = ( Na 8R \u2217 sin\u2205ex )[\u22122cKtcsin2\u2205ex \u2212 cKrc(2 \u2212 2cos2\u2205ex)\n\u22124Ktecos\u2205ex \u2212 4Kresin\u2205ex] (29)\nTherefore, Kpxo = \u2202|F\u0304 | \u2202xo\n= \u221a\n(KXpxo )2 + (KYpxo )2 + (KZpxo )2 (30)\n(3) Calculation of Kpyo\nKpyo = \u2202|F\u0304 | \u2202yo is the sensitivity of d|F\u0304 | due to small deflections dyo from the nominal position ym during milling in coordinate system o.\nThe corresponding cutting coefficients can be derived as shown below:\nKXpyo = \u2202F\u0304xo \u2202yo = { N 8\n[cKtc(2\u2205 \u2212 sin2\u2205) + cKrccos2\u2205 \u2212 4Ktecos\u2205 \u2212 4Kresin\u2205]} \u2205ex\n\u2205st (31)\nponents for Test 1 and Test 7." + ] + }, + { + "image_filename": "designv10_3_0001457_j.optlastec.2012.09.014-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001457_j.optlastec.2012.09.014-Figure4-1.png", + "caption": "Fig. 4. Finite element modeling: (a) Preplaced powder layer and substrate, (b) Detail of substrate mesh, (c) Detail of preplaced powder layer mesh.", + "texts": [ + " These material data were collected in the material properties resources of SYSWELD [11] software package. The scanning speed of the laser beam was varied from 30 mm/min to 360 mm/ min. At a scanning speed of 120 mm/min, completing a singlepass laser cladding with a bead length of 75 mm took 37.5 s. The computation was completed when 2000 s of cooling had been numerically experienced. Single-pass laser cladding of a preplaced cobalt-based powder layer on a rectangular steel plate was analyzed using a finite element model with dimensions of 75 mm (L) 30 mm (W) 15 mm (H), as shown in Fig. 4(a). The model was meshed into 54494 elements and 48944 nodes. The powder layer on the substrate surface had dimensions of 75 mm (L) 2 mm (W) 0.3 mm (T). The desired width of 2 mm is based on the preplaced layer width of 2 mm given in the FE model. The range of the desired depth from 0.3 mm to 0.6 mm is based on the layer depth of 0.3 mm in the FE model on one hand, and Laser beam Direction of moving work Fig. 5. Laser cladding of preplaced powd should not exceed twice the preplaced layer depth to guarantee a dilution less than 50% in the cladding practice on the other hand", + "1 mm 1.0 mm, (54494 elements); 0.05 mm 0.05 mm 1.0 mm, (127808 elements) and 0.025 mm 0.025 mm 1.0 mm, (368926 elements) were considered. The variation in peak temperatures obtained using these mesh sizes did not exceed 1%. Hence, a mesh size of 0.1 mm 0.1 mm 1.0 mm is chosen for sufficient computation accuracy and reduced computation time. The clad bead and its vicinity were treated as three layers whose meshes comprised of finer linear tetrahedral elements of size 0.1 mm 0.1 mm 1.0 mm, as shown in Fig. 4(b) and (c). The substrate was treated as 18 meshed layers with increasingly thick elements, starting from 0.1 mm adjacent to the clad layer to 1.7 mm at the middle bottom of the substrate. In practice, the substrate was fixed on the work bench, so the substrate model was constrained in the z-direction. To consider the boundary conditions, including those associated with radiation and convection, on the surface of the workpiece, a surface layer consisting of threedimensional elements with zero thickness was attached to the threedimensional model with an identical mesh pattern to ensure nodal continuity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.1-1.png", + "caption": "FIGURE 1.1. A two-loop planar linkage with 7 links and 8 revolute joints.", + "texts": [ + " Introduction 3 of a manipulator or rover, a wrist , an end-effector, actuators, sensors, con trollers, processors, and software . 1.2.1 Link The individual rigid bodies that make up a robot are called links . In robotics we sometimes use arm to mean link. A robot arm or a robot link is a rigid member that may have relative motion with respect to all other links . From the kinematic point of view, two or more members connected together such that no relative motion can occur among them are considered a single link. Example 1 Number of links . Figure 1.1 shows a mechanism with 7 links. There can not be any relative motion among bars 3, 10, and 11. Hence, they are counted as one link, say link 3. Bars 6, 12, and 13 have the same situation and are counted as one link, say link 6. Bars 2 and 8 are rigidly attached, making one link only, say link 2. Bars 3 and 9 have the same relationship as bars 2 and 8, and they are also one link, say link 3. 1.2.2 Joint Two links are connected by contact at a joint where their relative mo tion can be expressed by a single coordinate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003153_j.ymssp.2019.106553-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003153_j.ymssp.2019.106553-Figure8-1.png", + "caption": "Fig. 8. Roller defect model. (a) bdarj j > bdj j, and (b) bdarj j < bdj j.", + "texts": [ + " As the main topic of the current investigation is the path of the roller and the vibration patterns as a roller defect rolls through a race, this assumption would be acceptable. The result obtained by the experiment and that obtained based on the flat defect will be discussed in Section 4. In addition, the width and the depth of the flat defect are shown in Fig. 7(b). Besides the coordinate frames discussed in Section 3.1, a new frame called defect frame Odxdydzd is established on the roller (Fig. 8(a)). The origin Od is located at the defect center, and an angle gd is used to locate the defect in the roller. Then, the defect frame can be determined by rotating the roller-fixed frame along the axis xb by gd. Therefore, the transformation matrix from roller-fixed frame to defect frame can be written as Tbd \u00bc T gd;0;0\u00f0 \u00de. Moreover, in Fig. 8, bd is half the angle of the defect in the circumference of the roller, and bdar is the angle between the axis zd and the vector rbr . The interaction between the race and the defect is checked based on bd and bdar . The angles bd and bdar can be respectively given as bd \u00bc arcsin wd D \u00f011\u00de and bdar \u00bc arctan rdbr2 rdbr3 ! \u00f012\u00de where wd is the width of the defect, D is the roller diameter, the superscript d indicates that the relative position vector rbr is written in frame Odxdydzd, and subscripts 2 and 3 indicate the second and the third components of vector rdbr ", + " Generally, in the beginning of each numerical integration time-step, the position vectors of the roller and the race (i.e., rb and rr) are known, and these two vectors and the corresponding relative position vector (ribr \u00bc rib rir) are all written in the inertial frame. Then, vector rdbr in Eq. (12) can be determined as rdbr \u00bc Tidribr \u00f013\u00de where Tid \u00bc TbdTib is the transformation matrix from the inertial frame to the defect frame. The defect potentially contacts with the race if bdarj j is smaller than bdj j, as shown in Fig. 8(b). The interaction between a race and a roller defect when bdarj j < bdj j can be determined as follows. The geometrical interaction between a defect and a race should be calculated for every point on the defect, and the maximum one is the defect-race geometric interaction. For any point p on the defect (refer to Fig. 8(b)), the position locates the point relative to the roller center is rpb which can be descried in the defect frame as rdpb \u00bc 0 yp wd 2tanbd n oT \u00f014\u00de where yp is the position of the point p in the yd axis (Fig. 8(b)). Then, the vector locates the point p relative to the race center is given as rdpr \u00bc rdbr \u00fe rdpb \u00f015\u00de The vector rpr can be described in the roller-race-azimuth frame by vector transformation: rarpr \u00bc Tdarrdpr \u00f016\u00de where superscript ar means that the vector rpr is written in the roller-race-azimuth frame, and Tdar is the transformation matrix form the defect frame to the roller-race-azimuth frame: Tdar \u00bc TrarTirT 1 ib T 1 bd \u00f017\u00de where the superscript 1 means the inverse of the transformation matrix" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure4.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure4.1-1.png", + "caption": "Fig. 4.1 Anatomy of a 1 muscle, 1 DOF tendon-driven limb. a The force produced by the muscle is transmitted by the tendon to induce a rotation of the joint. b This can be analyzed as a muscle force fm acting at a distance r from the joint center to produce a torque \u03c4 at the joint, where r is the moment arm of that muscle at that joint", + "texts": [ + " Note that throughout this book, I use the terms muscle when relating specifically to the behavior, forces, or state of the muscle tissue, musculotendon when relating to issues that involve the muscle and its tendons of origin and insertion, and tendon when relating specifically to the behavior, forces, or state of the tendon of insertion of the muscle. For most mathematical and mechanical analyses, however, the term tendon suffices as it applies to both robots and vertebrates. When the analysis continues on to consider muscle mechanics and its neural control, I will prefer to use the term musculotendon. \u00a9 Springer-Verlag London 2016 F.J. Valero-Cuevas, Fundamentals of Neuromechanics, Biosystems & Biorobotics 8, DOI 10.1007/978-1-4471-6747-1_4 37 Figure4.1 shows the simplest tendon-driven limb: 1 muscle acting on a planar hinge joint. The muscle is idealized as a linear actuator attached to the proximal link (or bone), which projects its tendon distally across the joint and attaches to the distal link. As discussed earlier, this is a reasonable description because many joints in vertebrate limbs can be treated, as a first approximation, as hinge joints. The muscle force fm transmitted by the tendon produces a torque \u03c4 at the DOF because the tendon crosses the joint at a distance r from its joint center", + "3) which is easy to illustrate for joints idealized as pulleys that enforce constant or nearly constant moment arms. I will present a more formal definition in Sect. 4.3. \u2022 Constant moment arms Whenever an articulation can be modeled as a circular pulley, the scalar equation 4.3 can be used to calculate joint torque. There are precious few anatomical joints with such geometry, but this is an assumption that is often used as a first approximation in musculoskeletal models [1]. Such joints can be represented as shown in Fig. 4.1. \u2022 Posture-dependent moment arms Consider the more common case where the bone contours cannot be considered a circular pulley, the moment arm is created by a system of ligamentous pulleys (Fig. 4.2), or the tendons bow-string away from the joint (Fig. 4.3). In these cases it is clear that r(q) needs to be calculated for each joint angle. In the case of the non-circular pulley (Fig. 4.2a), the shape of the cam defines r(q). In the case of Fig. 4.3 Anatomy of posture-dependent moment arms where the tendon can bowstring away from the bones r q r q a b c A B C tendon pulleys (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure6.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure6.4-1.png", + "caption": "Fig. 6.4 Planar two-degree-of-freedom parallel manipulator", + "texts": [ + "m m 1$m C : : :C 2 m 2!m 1 m 2$m 1 m 1\u02dbm m 1$m C j\u02dbjC1 j$jC1 jC1!jC2 jC1$jC2 C : : :C m 2!m 1 m 2$m 1 C m 1!m m 1$m C jC1\u02dbjC2 jC1$jC2 jC2!jC3 jC2$jC3 C : : :C m 1!m m 1$m C : : :C m 2\u02dbm 1 m 2$m 1 m 1!m m 1$m C j!jC1 j$jC1 j!jC1 j$jC1 jC1!jC2 jC1$jC2 C : : :C m 1!m m 1$m 150 6 Jerk Analysis C jC1!jC2 jC1$jC2 jC1!jC2 jC1$jC2 jC2!jC3 jC2$jC3 C : : :C m 1!m m 1$m C : : :C m 2!m 1 m 2$m 1 m 2!m 1 m 2$m 1 m 1!m m 1$m (6.78) is termed the Lie screw of jerk of body m as observed from body j. Example 6.4. Figure 6.4 shows a planar two-degree-of-freedom parallel manipulator where the position of point P is controlled by two generalized coordinates notated as q1 and q2. The exercise consists of finding the input\u2013output equations of velocity, acceleration, and jerk of the robot related with the control point P. Note that the primal parts of the velocity state, the accelerator and the jerkor, vanish. Thus, the dimension of the Lie algebra must be properly taken into account. Solution. Using the geometry of the mechanism, it is straightforward to demonstrate that b D q2 1 q2 2 C a2 2a ; h D q q2 1 b2; \u02c7 D tan 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003216_physrevfluids.2.044202-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003216_physrevfluids.2.044202-Figure2-1.png", + "caption": "FIG. 2. Low-frequency tumbling (a); tumbling-to-wobbling transition (b), and dual wobbling solution (c), (d) of the cylinder-like object. For frequencies 0 < \u03c9\u0303 < c the magnetization components m\u2016 and m\u22a5 and the net magnetic moment m = m\u2016 + m\u22a5 rotate in the field plane with m\u22a5 running ahead of m\u2016 (a). At the transition frequency \u03c9\u0303t-w = c , the magnetic field H aligns with m\u22a5 and tumbling regime bifurcates into wobbling (b). There is multiplicity of wobbling dynamical states at \u03c9\u0303t-w < \u03c9\u0303 < \u03c9\u0303s-o corresponding to two complementary precession angles \u03b81 < \u03c0/2 (c) and \u03b82 = \u03c0 \u2212 \u03b81 > \u03c0/2 (d).", + "texts": [ + " Since driven in-sync rotation of the cylinder-like object is important towards the understanding of the rotational dynamics of an arbitrary shaped propeller, we provide here a brief overview of the solution. Two distinct regimes of in-sync rotation of a cylinder-like object\u2014tumbling and wobbling\u2014can be identified. In the low-frequency tumbling regime the net magnetic moment m = m\u2016 + m\u22a5 (with m\u22a5 and m\u2016 being the components parallel and transverse to the rotation easy axis, respectively) rotates in the plane of the applied magnetic field H in an attempt to catch up with it minimizing the magnetic energy Em = \u2212m \u00b7 H [see Fig. 2(a)]. Note that m\u22a5 is running ahead of m\u2016 [29] and elevating the driving frequency increases the angle between the magnetic field H and the magnetic moment m. At the critical frequency, \u03c9\u0303t-w = c , when the magnetic field H aligns with m\u22a5 [see Fig. 2(b)] the tumbling regime bifurcates into two high-frequency wobbling states, whereas the long x3 axis of the object goes off the field rotation plane resulting in the precession of x3 around Z [see Figs. 2(c) and 2(d)]. The tumbling-to-wobbling transition can be explained by energy arguments as the disadvantageous orientation of the longitudinal component m\u2016 is compensated by the energy gain due to reduced viscous friction associated with rotation about the long x3 axis as compared to rotation about the short axis in the tumbling regime [15]", + " Above the step-out frequency, \u03c9\u0303s-o = \u221a c2 + s2 p2, the viscous torque can no longer be balanced by the magnetic torque and the propeller cannot keep up turning in-sync with the fast rotating magnetic field. Thus, for \u03c9\u0303 > \u03c9\u0303s-o the wobbling solution breaks down and the synchronous regime switches into an asynchronous one [9,15]. As was first mentioned in Ref. [9] there are two stable wobbling solutions for a magnetized cylinder corresponding to a pair of (complementary to \u03c0 ) precession angles: \u03b81 < \u03c0/2 [see Fig. 2(c)] and \u03b82 = \u03c0 \u2212 \u03b81 > \u03c0/2 [see Fig. 2(d)]. The cylinder rotates synchronously with the field, the precession 044202-5 angle \u03b81 between its long axis, and the Z axis of the field rotation diminishes with the growth of frequency, whereas the angle \u03b82 increases. These dynamical states correspond to the same value of the magnetic energy, so that the tumbling-to-wobbling transition pertains to a symmetric pitchfork bifurcation [30]. The explicit form of the tumbling solution at low frequencies, 0 < \u03c9\u0303 < \u03c9\u0303t-w, is \u03b8 = \u03c0/2, \u03c8 = \u2212\u03b1, \u03d5\u0303 = \u2212 + arccos \u03c9\u0303" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001776_tia.2016.2533598-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001776_tia.2016.2533598-Figure5-1.png", + "caption": "Fig. 5. Configuration of winding I and winding II of the calculated motor on 12-slot 10-pole concentrated winding permanent magnet motor.", + "texts": [ + " See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. To take advantage of the two conclusions in section III, carrier harmonic iron loss reduction motor is proposed in this section. The proposed motor utilizes two sets of three phase windings that are each wound around different teeth. As an example, a concentrated winding PMSM with 12-slot 10- pole is applied. Two sets of three phase windings (windings I and II) are alternately set on teeth as shown in Fig. 5. The motor can be driven with both windings I and II (operation mode I: conventional), or with only winding I or II (operation mode II: proposed). This structure can be realized by using winding changeover techniques [21]-[25] or multi-inverter drive techniques [26]. The proposed motor drive system is operated in operation mode I when the required shaft torque is medium or higher. Operation mode II is utilized in the low torque region. When the motor is driven in operation mode II, six windings and six teeth are not exited" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000378_j.jsv.2005.04.033-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000378_j.jsv.2005.04.033-Figure2-1.png", + "caption": "Fig. 2. Basic torsional model.", + "texts": [ + " (5)), (ii) Ipi=Rb2 at all the torsional dof of the gear shaft as a consequence of the non-steady rotational speed when no-load transmission error is not nil (Ipi is the polar moment of inertia attached to node i). ~F W\u00f0 \u00deT \u00bc 0; 0; 0; 0; 0; 0; 0; 2m2 e2 Rb2 Rb1 Rb2 cos O2t l2\u00f0 \u00de; 2m2 e2 Rb2 Rb1 Rb2 sin O2t l2\u00f0 \u00de; 0; 0; 0 , ~G W\u00f0 \u00deT \u00bc 0; m1e1 cos\u00f0 O1t l1\u00f0 \u00de; m1e1 sin O1t l1\u00f0 \u00de; 0; 0; 0; 0, m2e2 Rb1 Rb2 2 cos O2t l2\u00f0 \u00de; m2e2 Rb1 Rb2 2 sin O2t l2\u00f0 \u00de; 0; 0; 0\u00de, 0 d a \u00bc dW a. In the interest of clarity, the analysis of transmission errors as excitation terms is first conducted by using the classical torsional model shown in Fig. 2, in order to privilege the methodological approach as opposed to the mathematical manipulations required by a 3D model. In such conditions, the differential system (14) reduces to O2 1 J1 0 0 J2 \" # y001 y002 \" # \u00fe X i ki ! cos2 bb Rb21 Rb1Rb2 Rb1Rb2 Rb22 2 4 3 5 y1 y2 \" # \u00bc Cm0 Cr \" # J2 Rb1 Rb22 O2 1 NLTE00 1 0 \" # J2 Rb2 O2 1 NLTE00 0 1 \" # \u00fe X i kide Mi\u00f0 \u00de ! cos bb Rb1 Rb2 \" # . \u00f015\u00de After multiplying the first line in Eq. (15) by Rb1J2, the second line by Rb2J1, adding the two equations and dividing all terms by (J1Rb22+J2Rb21), the semi-definite system (15) is transformed into the differential equation O2 1meqx00 \u00fe X i ki " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.11-1.png", + "caption": "Fig. 4.11 Four-bar linkage mechanism", + "texts": [ + " One of the most popular examples of a constrained linkage is the four-bar linkage mechanism. In spite of its simple topology, this planar closed kinematic chain is commonly applied in aerospace mechanical linkages as well in robot manipulators. For instance, the celebrated Delta robot (Clavel 1991) is considered a spatial generalization of a four-bar linkage mechanism. In this example the position and velocity analyses of the famous four-bar linkage mechanism are presented. Solution. As shown in Fig. 4.11, the input angle or generalized coordinate q denotes the orientation of the input crank a1 measured counterclockwise from the X-axis, whereas the orientation of the coupler bar a2 is indicated by the angle \u02c7 measured counterclockwise from the X-axis. Furthermore, the angle denotes the orientation of the output crank a3 measured clockwise from the X-axis. To approach the displacement analysis of the four-bar linkage, we consider it a parallel manipulator where the coupler bar is assumed to be the moving platform, body 2, while the crank a0 is assumed to be the fixed platform, body 0", + " vO ; may be expressed through any of the two connector chains as 0V2 O D 0! i 1 0$1 i C 1! i 2 1$2 i ; i D 1; 2; (4.87) where 0!1 1 D Pq. Meanwhile, the screws in Eq. (4.87) are given in Pl\u00fccker coordinates by 4.3 Equations of Velocity in Screw Form 87 0$1 1 D 2 66666664 0 0 1 0 0 0 3 77777775 ; 1$2 1 D 2 66666664 0 0 1 a1 sin q a1 cos q 0 3 77777775 ; 0$1 2 D 2 66666664 0 0 1 0 a0 0 3 77777775 ; 1$2 2 D 2 66666664 0 0 1 a3 sin a1 cos q a2 cos \u02c7 0 3 77777775 : (4.88) On the other hand, referring to Fig. 4.11, consider three lines L1, L2, and L3 whose Pl\u00fccker coordinates are given by L1 D 2 66666664 1 0 0 0 0 a1 sin q 3 77777775 ; L2 D 2 66666664 0 1 0 0 0 a1 cos q 3 77777775 ; L3 D 2 66666664 cos sin 0 0 0 a0 sin 3 77777775 : (4.89) Later on, by systematically applying the Klein form of the lines Li.i D 1; 2; 3/ to both sides of Eq. (4.87) and reducing terms, we obtain\u02da L1I 0V2 O D a1 Pq sin q; \u02da L2I 0V2 O D a1 Pq cos q; \u02da L3I 0V2 O D 0: (4.90) Finally, casting Eq. (4.90) into matrix-vector form, we find that the input\u2013output equation of velocity of the four-bar linkage results in JT 0V2 O D q; (4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003653_j.measurement.2017.07.034-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003653_j.measurement.2017.07.034-Figure12-1.png", + "caption": "Fig. 12. Geometrical parameters for the fillet-foundation deflection [9,60].", + "texts": [ + "2(1 )( ) ( ) [ ( ) ]s \u03b1 \u03b1 2 1 2 21 2 (31) \u222b= \u2212 + \u2212\u2212k \u03b1 \u03b1 \u03b1 \u03b1 EL \u03b1 \u03b1 \u03b1 \u03b1 d\u03b11 ( )cos sin 2 [sin ( )cos ]a \u03b1 \u03b1 2 2 1 21 2 (32) \u239c \u239f \u239c \u239f= \u23a7 \u23a8 \u23a9 \u239b \u239d \u239e \u23a0 + \u239b \u239d \u239e \u23a0 + + \u23ab \u23ac \u23ad \u2217 \u2217 \u2217 \u2217 k \u03b1 EL L u S M u S P Q \u03b11 cos (1 tan ) f m f f f f m 2 2 2 (33) where, E is the modulus of elasticity, L is the tooth width, and \u03c5 is the Poison\u2019s ratio. The detailed notations and expressions are given in Ref. [9,60]. The coefficients L\u2217, M\u2217, P\u2217, Q\u2217 can be calculated by following polynomial functions as given in Eq. (34). = + + + + +\u2217X 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 (34) where Xi \u2217denotes the coefficients L\u2217, M\u2217, P\u2217, Q\u2217; hfi = rf/rint; rf, rint, hfi, and \u03b1m are described in Fig. 12, the values of Ai, Bi, Ci, Di, Ei, and Fi are listed in Table 2. The description of remaining parameters of Eq. (33) and Eq. (34) are Fig. 9. Displacement image before loading at 26-degree rotation angle during DTCP. shown in Fig. 12. The analytical formulations for calculating the gear mesh stiffness with cracked tooth are given below. Gear tooth crack has the effect of reducing the mesh stiffness value. In the case of tooth crack, the Hertzian stiffness, axial compressive stiffness and fillet foundation stiffness remain the same [9,61]. However, the bending stiffness and shear stiffness are changed due to the presence of a crack. The bending stiffness and the shear stiffness for crack tooth can be calculated as [9,61]; \u222b= + \u2212 \u2212 \u2212 \u2212 + + \u2212\u2212k cos\u03b1 \u03b1 \u03b1 sin\u03b1 cos\u03b1 \u03b1 \u03b1 cos\u03b1 EL sin\u03b1 sin\u03c5 sin\u03b1 \u03b1 \u03b1 cos\u03b1 d\u03b11 12{1 [( ) ]} ( ) [ ( ) ]b \u03b1 \u03b1 q r 1 2 2 2 2 2 3 crack p 2 2 1 (35) \u222b= + \u2212 \u2212 + + \u2212\u2212k \u03bd \u03b1 \u03b1 cos\u03b1 cos\u03b1 EL sin\u03b1 sin\u03c5 sin\u03b1 \u03b1 \u03b1 cos\u03b1 d\u03b11 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002286_j.isatra.2015.11.024-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002286_j.isatra.2015.11.024-Figure2-1.png", + "caption": "Fig. 2. Coaxial-rotor structure with the associated forces and frames.", + "texts": [ + " This system is an underactuated mechanical system with six degrees of freedom, but only four degrees of freedom can be controlled independently with four control inputs, which are the thrust T and the three control torque \u0393 \u00bc \u00f0\u03c4\u03d5; \u03c4\u03b8 ; \u03c4\u03c8 \u00deT produced by both rotors and Swashplate incidence angles. The main thrust is used to compensate the gravity force and to control the vertical movement. The horizontal movements are controlled by directing the force vector in the appropriate direction (thrust vectoring control) through the cyclic swashplate. Control moments are used to control the aircraft body orientation which controls the rotorcraft horizontal movement. Consider the coaxial-rotor depicted in Fig. 2 as a solid body incorporating a force and moment generation process [3,6]. Let B\u2254 \u00f0G; xb; yb; zb\u00de be the body-fixed frame attached to the center of gravity of the aerial vehicle, where xb is the longitudinal axis, yb is the lateral axis and zb is the vertical direction in hover conditions and I\u2254\u00f0O; xI ; yI ; zI\u00de is the Earth frame. The generalized coordinates describing the rotorcraft position and orientation are q\u00bc \u00bd\u03be;\u03b7 T , where \u03be\u00bc \u00f0x; y; z\u00deT AR3 represents the translation coordinates relative to the inertial frame and \u03b7\u00bc \u00f0\u03d5;\u03b8;\u03c8 \u00deT AR3 are the Euler angles representing the orientation of the rotorcraft in frame I , where \u03d5 is the Roll angle (rotation around the x-axis), \u03b8 is the Pitch angle (rotation around the y-axis), and \u03c8 the Yaw angle (rotation around the z-axis)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000566_tro.2006.889485-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000566_tro.2006.889485-Figure2-1.png", + "caption": "Fig. 2. Illustration of the swimming microrobot\u2019s tail.", + "texts": [ + " The solution of the fluidic problem provides the velocity field around the tail, from which one is able to calculate the force exerted on the beam and the maximal stroke. The actuator is modeled by three 1-D elastic domains designated by the distributed parameters . 1552-3098/$25.00 \u00a9 2007 IEEE A different voltage is applied to each one of the three segments, so that each exhibits a distinct curvature. The beam is a general piezoelectric beam, i.e., for each elastic domain, one can define different elastic and piezoelectric layers with different geometry (see Fig. 2). The field equations of the tail are as follows: (1) where is the distributed mass of each elastic domain. In each domain, designated by index , there are layers. Each layer, designated by index , has a different cross-sectional area (in the case of a rectangular cross-section ), and density . is the distributed force applied by the fluid on each elastic domain. is the stiffness of each elastic domain, . The stiffness depends on the Young modulus , the cross-coupling coefficient of the piezoelectric layers (see [15] for further details on this coefficient), the cross-section inertia (in the case of a rectangular cross-section ), the cross-section area and the distance from neutral axis . The neutral axis position is fixed if no voltage is applied to the piezoelectric layers, and its value is when measured from an arbitrary point (see Fig. 2). The BCs are linear and angular spring at and free at . Spring BC conditions were chosen because of the difficulty of creating clamped BCs in an experimental setup. The BCs are defined as follows: (2) where is the angular spring coefficient and is the linear spring coefficient. In order to solve the model, continuity conditions (CCs) between the different elastic subdomains must be defined (3) The elastic moment along a piezoelectric beam based on Euler\u2013Bernoulli beam assumptions is (4) where ; is the effective piezoelectric coefficient of the th layer, and is the electric domain on the th layer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.12-1.png", + "caption": "FIGURE 2.12. Arm of Example 12.", + "texts": [ + " If a local coordinate fram e Oxyz has been rotated 60deg about the z axis and a point P in the global coordinate fram e 0 XYZ is at (4,3,2) , its coordinates in the local coordin ate fram e Oxyz are cos 60 sin 60 - sin 60 cos 60 o 0 46 2. Rotation Kinematics Example 11 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) , it s position in the global coordinate frame 0 XY Z is at [ X] [COS 60 sin 60 0] T [ 4 ] [ -0.60 ] ~ = -S~60 CO~60 ~ ~ = ~~06 Example 12 Successive local rotation, global position. The arm shown in Figure 2.12 has two actuators. The first actuator ro tates the arm -90 deg about y-axis and then the second actuator rotates the arm90degaboutx-axis. If the endpointP is at Br p = [9.5 -10.1 10.1 f , then its position in the global coordinate frame is at G r 2 [Ax ,9o Ay ,_ 90 r l B r p A- I A-I B y ,-90 x ,90 r p AT AT B y ,-90 x,90 rp [ 10.1 ] -10.1 . 9.5 (2.53) 2. Rotation Kinematics 47 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 Al , A2 , A3, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001118_0301-679x(79)90001-x-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001118_0301-679x(79)90001-x-Figure6-1.png", + "caption": "Fig 6 Kurtosis profiles at various stages through the second life test f l = 3Hz-5kHz, a = 329h; f2 = 5 - 1 0 kHz, b = 454h; f3 = 10-15kHz, c = 637h; f4 = 1 5 - 2 0 kHz, d = 657h", + "texts": [ + " In addition to the primary emissions from propagating fatigue cracks, the secondary emissions produced by rubbing of the crack faces, grinding of metal fragments in the bearing and impacts between the rolling elements and the damaged parts of the bearing in the load zone, will be a function of the overall condition of the bearing. *There is no implication in this paper that the Taperex slew ring has performed unsatisfactorily 54 T R I B O L O G Y internat ional Apr i l 1979 is to support the upper rotating part of the structure on the lower, fixed base. The drive for the rotating part is housed on a geared ring acting on the fixed race of the slew ring itself. Fig 6 shows such a gear in the inner ring version, similar to the slew ring of the platform crane on which the acoustic emission measurements reported below were made. An exploratory exercise was undertaken on a platform crane to determine the background noise level during slewing under different loading conditions and the suitability of using a simple linear array for emission source location. The sensors, $1 and $2, were positioned diametrically opposite to each other on the fixed inside face of the slew ring 2cm below the gear teeth (Fig 7)", + " TRIBOLOGY international Apri l 1979 57 Severe d a m a g e In a test lasting a total of 658h, incipient damage was detected after 444h. At this stage the bearing was removed and inspected: an inner race fatigue crack 3ram long was found. The bearing was then reassembled and the test continued for a further 214h. Severe damage was sustained by the original bearing (Figs 3 and 4) and this damage caused primary and secondary damage on the other three bearings. Fig 5 again highlights the early warning capabil i ty of kurtosis, while Fig 6 shows the variation of kurtosis in various frequency bands as damage propagates. In general, init ial signs of damage are indicated by an increase in kurtosis values in the low frequency band: as damage becomes more severe, the kurtosis values increase in the higher frequency bands. When damage becomes very advanced, kurtosis values peak above 20 kHz but fall in the lower frequency bands: it is the distr ibution, not the absolute value of kurtosis, that is important. F ie ld t r ia ls Several hundred bearings were monitored during the field evaluation of the kurtosis meter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002757_s40815-018-0576-2-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002757_s40815-018-0576-2-Figure1-1.png", + "caption": "Fig. 1 Inertial reference frame and body coordinate system", + "texts": [ + " Further, adaption laws and fuzzy rules are described. Schematic structures of designed FPID and AFPID controllers are presented in the next section. In Sect. 4, simulation results and comprehensive discussion on them are presented in detail. The final section concludes the paper. Regarding an observer on the satellite, the body-fixed frame is used to derive the equations that describe the motion of the satellites. The center of gravity of the satellite is considered as the origin of this frame. As shown in Fig. 1, the motion of the satellite in x-axis that represents the roll is aligned tangent to circular orbit, the y-axis that represents the pitch is normal to the orbit plane, and the zaxis that represents the yaw satisfies the right-hand rule. In Fig. 1, the x y z and XE YE ZE frames represent the body-fixed frame and earth-fixed frame, respectively. Just like the satellite body-fixed frame, the earth-fixed frame is defined as right-handed and orthogonal, and rotates at the orbit rate of one revolution per day (x0 \u00bc 7:272 10 5 rad/s). This frame is used to derive the governing equations of the system. Assuming that the center of mass coincides with the center of gravity, the angular momentum of a rigid body around its center of mass is determined as: H~ \u00bc Z r~ r~ x~\u00f0 \u00dedm \u00f01\u00de in which r~ and x~ represent the location vector of an element inside the body and the angular velocity vector of the body, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002553_j.jclepro.2018.07.185-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002553_j.jclepro.2018.07.185-Figure2-1.png", + "caption": "Fig. 2. Schematic of the Selective Laser Sintering Process with polymers.", + "texts": [ + " Therefore, a multi-objective optimization model based on energy consumption, material cost, and machine constraints has been proposed in this present study. A framework for the energy consumption of the SLS is conducted and NSGA-II genetic algorithm is applied for optimization. Nowadays, SLS is widely used for the Direct Manufacturing of parts. SLS has been well received due to its increased freedom of design and its relatively rapid production process (Wohlers et al., 2013). As such, it is possible to manufacture cost-efficient, individual parts in small series production (Thomas and Gilbert, 2014). In Fig. 2, the general major components of SLS are shown. To model the SLS process, an integrated computer\uff0daided manufacturing definition function modeling (IDEF0) is created for the material, energy and information flow, as shown in Fig. 3. The inputs and outputs of the material and energy are fully defined. Furthermore, with the IDEF0 model, the process of powder form to the product can be realized. In the building stage, the electric power for the furnace is the main energy consumption. Besides, the SLS typically consist of a high CO2 power laser, heating insulation system, powder conveying system and auxiliary systems, such as: computer system, cooling system, lighting system, air compressor system and powder circulating filtration system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001243_elan.201000708-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001243_elan.201000708-Figure4-1.png", + "caption": "Fig. 4. Cyclic voltammetric profiles recorded for 1 mM acetaminophen (Ap) in a pH 7 phosphate buffer solution using a 0.5 mg graphene modified electrode (thick line) and in the absence of acetaminophen (dotted line) and the response of an unmodified basal plane-like screen printed electrode in the presence (thin line) and absence (solid line) of acetaminophen. Also shown is the response of a surfactant modified (dashed line) electrode in the presence of acetaminophen. Scan rate: 200 mV s 1 (vs. Ag/AgCl).", + "texts": [ + " The effect of surfactants on electrochemical processes are not completely understood [32,33] and more work is needed to elucidate the exact mechanism, but in the case of the electrochemical oxidation of NADH it is likely there is no favourable interaction between the electrochemical formed product with that of the surfactant. We now consider the electrochemical oxidation of 1 mM acetaminophen in a pH 7 phosphate buffer solution at a basal plane-like screen printed electrode. A typical cyclic voltammetric profile is depicted in Figure 4 exhibiting an oxidation wave at ca. +0.45 V and a reduction wave at ca. 0.25 V (vs. Ag/AgCl). The effect of scan rate on the voltammetric response was explored with a plot of peak height against square root of scan rate found to be linear (Ip (A)=2.41 10 6 A/(V s 1)1/2 +2.68 10 6 ; R2 =0.99), indicating a diffusion process as opposed to a Fig. 1. A) Cyclic voltammetric profiles recorded for 1 mM NADH in a pH 7 phosphate buffer solution using an edge plane pyrolytic graphite electrode (thin line), basal plane-like screen printed electrode (dotted line), 0", + "5 mV/pH which is deviated from the typical Nernstian response for a two-electron, two-proton process (59 mV/pH) as observed on a glassy carbon electrode [36], yet is in agreement with 45 mV/pH reported by Fanjul-Bolado et al. [37] using commercially available screen printed electrodes, and also agrees with other previously reported results of 37, 46.5, and 42 mV/pH [35,38, 39] indicating a complex oxidation mechanism for acetaminophen. We now turn to exploring the voltammetric response of graphene modified electrodes for the electrochemical sensing of acetaminophen. Figure 4 shows a typical voltammetric response obtained after graphene modification, which is distinctively different to that observed at the underlying electrode substrate. It is interesting to note that in comparison to the underlying basal plane-like screen printed electrode, the oxidation wave has shifted to a higher potential at ca. +0.69 V (vs. Ag/AgCl) however exhibits a large increase in the magnitude of the voltammetric wave due to the increase in the electrode surface area; additionally the reduction wave is significantly reduced in magnitude and has shifted to ca", + " Note that this is in distinct contrast to that observed above for the underlying electrode and with that reported previously for the electrochemical detection of acetaminophen using graphene, which was found to exhibit a surface confined process rather than a diffusional one as observed here, and additionally a gradient of 59 mV/pH was observed indicating a two-proton, two-electron electrochemical process [29]. A surfactant modified electrode was consequently explored towards the sensing of acetaminophen where as depicted in Figure 4 an electrochemical wave is observed at ca. +0.56 V (vs. Ag/AgCl) and when comparison between the surfactant and graphene response is sought, it is clear that a similar electrochemical response is observed, which can be attributed to the surfactant and not graphene, usually assumed in the absence of appropriate control experiments. Note that increasing the amount of surfactant immobilised onto the electrode surface results in an increase to the magnitude of the voltammetric peak height but has no effect on the peak potential" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure2.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure2.2-1.png", + "caption": "Fig. 2.2 Pollard\u2019s spray painting machine (U.S. Patent No. 2,286,571)", + "texts": [ + " One of the first well-documented parallel manipulators was precisely a lowermobility mechanism. After World War I, the cinematography industry became one of the most lucrative businesses in America. Hence, Gwinnet (1931) proposed a spherical parallel manipulator as a cinema motion simulator, the Oxymoron, and was granted the corresponding patent (Fig. 2.1). However, at that time the industry was not ready for Gwinnett\u2019s invention. Several years later, a more practical application of a parallel manipulator was introduced by Pollard (1940): a spray painting machine (Fig. 2.2). Pollard\u2019s creative invention, a simple five-bar parallel robot, for which he was granted the corresponding patent, is considered the first industrial application of 2.1 Typical Parallel Manipulators 21 a parallel robot. Although Gwinnett and Pollard had pioneering contributions, undoubtedly the most celebrated parallel manipulator is the universal tyre testing machine credited to Dr. Eric Gough, an automotive engineer at Dunlop Rubber Company. As Gough noted, this mechanical device had been glimpsed in 1947 and its construction was finished in 1955 to respond to problems of aero-landing loads and to determine the properties of tyre under combined loads" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000056_s0263574707003530-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000056_s0263574707003530-Figure7-1.png", + "caption": "Fig. 7. Symbolic sketch of SM1.", + "texts": [ + " The transformation from canonical form to general position will not change the geometric properties. The one parameter sets of 3-spaces T (v1), T (v2), and T (v3) are well known in geometry. Geometrically, they can be obtained by the following algorithm: Take two 3-spaces in P 7 and define a linear relation between the points in these spaces, which means that each point of one space is joined by a line with exactly one corresponding point of the other three space. The manifold of all these lines is called a Segre manifold. A symbolic sketch of a Segre manifold is depicted in Fig. 7. In this figure, 3-spaces corresponding to discrete http://journals.cambridge.org Downloaded: 27 Apr 2015 IP address: 169.230.243.252 values of v1, are drawn as boxes. Through every point of such a 3-space, there is exactly one line that belongs to the manifold. A lower dimensional example of a Segre manifold is a hyperboloid in E3, where one has to take two lines instead of the 3-spaces in P 7 and a linear relation between the points on both lines. The lines connecting the corresponding points determine a regulus of a hyperboloid, a Segre manifold in P 3", + " As stated above, all three manifolds have the same intersection with S2 6 and therefore describe the same set of displacements. Note that the difference between the three manifolds are points outside of S2 6 . It has turned out that one has to switch between the different descriptions when special layouts like parallelism of rotation axes occur. Parametric representation, span of points: Specify one arbitrary 3-space of T (v1) by fixing the parameter v1 = v10. Choose four linearly independent points pk (k = 1, . . . , 4) of this space and then let v1 vary again (compare Fig. 7). Because of Theorem 1, this results in four straight lines lk and pk(v1) = T (v1) \u2229 lk . Now the points of SMi are described by x = 4\u2211 k=1 \u03bbkpk(v1) where (\u03bb1, \u03bb2, \u03bb3, \u03bb4)T is a homogeneous quadruple. In this representation, the algebraic degree of SMi is easily computed. It is defined as the number of intersection points of SMi and a generic 3-space U \u2282 P 7 (see Harris20). Let U be the span of four points described by u1, . . . , u4. U and T (v1) intersect if and only if det[p1(v1), p2(v1), p3(v1), p4(v1), u1, u2, u3, u4] = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000765_978-3-540-30301-5_15-Figure14.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000765_978-3-540-30301-5_15-Figure14.10-1.png", + "caption": "Fig. 14.10 Dynamics of the last link", + "texts": [ + " It is as- sumed that there is a wrist-mounted six-axis force/torque sensor, and that suitable filters have been designed to estimate the velocity \u03b8\u0307i and acceleration \u03b8\u0308i at each joint i. The procedure involves 1. formulating the Newton\u2013Euler equations of the load dynamics to reveal a linear dependence on the inertial parameters, and 2. estimating the parameters using ordinary least squares. Load Dynamics Kinematically, the force-torque sensor is part of the last link n, mounted near the joint axis zn and origin On . The Part B 1 4 .3 sensor provides readings relative to its own coordinate system, called n +1 (Fig. 14.10). The remainder of the last link is attached to the shaft of the force-torque sensor, and so the force-torque sensor is measuring the loads on the last link excluding itself. The acceleration of the force-torque sensor reference frame would have to be calculated based on the amount of offset from On , but we will ignore that complication here and assume that the sensor origin On+1 is coincident with On . The center of mass of link n is defined as Cn , located relative to the base origin O0 by rn = Cn \u2212 O0 and relative to link n\u2019s origin On by cn = Cn \u2212 On " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002924_j.optlastec.2018.08.003-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002924_j.optlastec.2018.08.003-Figure9-1.png", + "caption": "Fig. 9. Images from the high-speed camera record, showing the stable phases of both processes.", + "texts": [ + " 8. According to the evaluation of both processes, in the stable phase, the images obtained from the camera does hardly change over time \u2013 quasi-stationary. By comparison of the stable phases, it can be observed: the bright area of IN718 is larger than that of IN625; the shape of the bright areas of processes with IN718 and IN625 are different. Based on the observations, the two processes will be characterized in this part. Two images of the stable phase from the high-speed camera are shown in Fig. 9. Different sizes and shapes of the bright areas recognized by the camera at the stable phase between IN718 and IN625 can be clearly recognized in Fig. 9: the bright area of IN718 is larger than that of IN625; for IN718, a droplet form can be observed, for IN625, a droplet form with a crescent-shaped backside. The droplet form of the bright area of IN718 is plausible since this is the typical form of melt for LMD processes. In comparison, the shape of the bright area of IN625 is unusual. However, this observation can be well used to explain the results obtained from the microstructure analysis \u2013 there is a stronger convection in the melt pool of IN625 \u2013 because of the convection, the heat could be transferred from the middle of the melt pool to both sides, which leads to temperature increase at the edges. As a result, a crescent-shaped backside is formed in the process with IN625. Furthermore, different glow colours can be observed in Fig. 9. According to the differences between these glow colours, the bright areas can be divided into three zones: the yellow-white zone, the light-yellow zone and the bright-yellow-red zone. The different glow colours, which can be recognized by the high-speed camera, are related to the temperatures: from yellow-white decreasing to bright-yellow-red. The yellow-white zone must consist of liquid metal because it is located at the centre of the melt pool. Based on the following two facts, the bright-yellow-red zone is supposed to be solidified metal with high temperature: laser is a fast cooling energy source, and this zone lies relative far behind the laser spot; the glow colour of this zone is much deeper than the other glow colours", + " According to the following reasons, the light-yellow zone could be liquid metal: the glow colour is similar to yellow-white, which indicates small temperature difference; the light- yellow zone locates right next to where the laser beam locates. Actually, these assumptions for the state of the metal do not have crucial effects on the following discussions since it regards the comparison of both processes \u2013 important is that the same glow colour represents the same state of material. In order to more intuitively represent these observations, the bright areas for stable phases for both processes have been schematically drawn and shown in Fig. 9, where the size, the shape and the different zones of the bright areas have been demonstrated. By using these schematics, both processes can be schematically presented and compared, as shown in Fig. 10. In Fig. 10, t0 represents the start time for both processes, and t1 is a point in time. that lies in the stable phases of both processes. As shown in Fig. 10, point A of IN718 and point M of IN625 melt at timet1. With the progress of both processes, point A of IN718 will solidify at time pointt2, and point M of IN625 at time point \u2032t2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000470_978-1-4613-2937-4_6-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000470_978-1-4613-2937-4_6-Figure2-1.png", + "caption": "Fig. 2. Spectral densities of different codes.", + "texts": [ + " As we will see later (and as has been mentioned in a previous course), several types of light sources are available with respect to current/light power curve, linearity spectrum width, and speed of response, leading to totally different aspects of the system (pulse width modulation, pulse position modu lation, etc.). Among many \"two state\" (light and dark) modulations proposed earlier in many contributions and publications, we have shown some of the simplest ones in Fig. 1. Their spectral densities are shown in Fig. 2. Thus far we have surveyed the fundamentals of digital and PCM techniques. We will discuss analog transmissions along optical fibers later in this course. Since this aspect is very much depen dent upon component linearity and fiber frequency response, let me first introduce these in the frame of pulse transmission which pre sently seems to be of great interest. The next section will be devoted to the fiber itself, the ways systems people are working with fiber today; the receiver design will be developed in Section III and we will discuss transmitter design in Section IV" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000124_iros.2005.1544969-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000124_iros.2005.1544969-Figure4-1.png", + "caption": "Fig. 4. The needle, currently in the b = 0 bevel-left direction, is tracing the solid control circle with radius r in the counter-clockwise direction. The needle orientation \u03b8 is the tangent angle of the control circle. If the bevel direction is changed to the b = 1 bevel-right direction, the needle will begin to trace the dashed control circle in the clockwise direction at a tangent point 180\u25e6 from its tangent point on the solid control circle.", + "texts": [ + " Each point c on the control circle represents an orientation \u03b8 of the needle, where \u03b8 is the angle of the tangent of the circle at c with respect to the z-axis. If b = 0, the needle will trace an arc of length \u03b4 along the control circle in a counter-clockwise direction. If b = 1, the needle will trace an arc in a clockwise direction. If control u = 1, the needle is rotated 180\u25e6 to change bevel direction. On the control circle, this action corresponds to rotating the point c representing the needle tip by 180\u25e6 to the other side of the circle and tracing subsequent insertions on the control circle in the opposite direction, as shown in Fig. 4. We subdivide the control circle into Nc equally sized arcs of length \u03b4 = 2\u03c0r/Nc, the needle insertion distance between controls. The endpoints of the arcs generate a set of Nc control circle points, ci, i = 0, . . . , Nc\u22121, each representing a discrete orientation state, as shown in Fig. 5(a). We require that Nc is a multiple of 4 to facilitate the orientation state change after a bevel direction change. We overlay the control circle on a regular grid of spacing \u2206 and round the positions of the control circle points ci to the nearest grid point, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.5-1.png", + "caption": "Fig. 2.5 Geometrical and kinematic quantities at a roller of the edge mill", + "texts": [ + "4 Rotor in a pivotable frame Frame dimensions l and h Distance of a point P in the rotor \u03b7P Pivoting angle \u03b1(t) Angle of rotation of the rotor \u03b3(t) 1.Components of the angular velocity \u03c9 and angular acceleration \u03c9\u0307 of the rotor in the co-rotating \u03be-\u03b7-\u03b6 coordinate system 2.Components of the absolute velocity vP of point P . 2.2 Kinematics of a Rigid Body 77 An edge mill is a machine for comminuting, grinding, or mixing, (e. g. ores, coal, clay, corn, etc.) in which rollers are guided along an angular path that compress and comminute the material to be ground. Figure 2.5 shows the grindstone modeled as a homogeneous cylinder with a center of gravity that is guided at a distance \u03beS along a planar circular path around the fixed vertical z axis. The \u03be axis of the grindstone is pivoted horizontally at the angular speed \u03d5\u0307(t). Pure rolling of the center plane of the roller at the grinding level is assumed. Roller radius R Distance to the center of gravity \u03beS Angular velocity of the axle \u03d5\u0307(t) Find: 1.Rotational transformation matrix A 2.Angular velocity vector both in fixed (\u03c9) and in body-fixed (\u03c9) coordinate directions 3", + "42) The first expression results from the differentiation of rO from (2.39). The second expression is either obtained by differentiation of A and lP from (2.39), or by multiplying A from (2.40) and \u03c9\u0303 from (2.36) and lP . The acceleration aP could be determined by another differentiation of vP with respect to time. This involves terms with the factors \u03b1\u0308, \u03b3\u0308, \u03b1\u03072, \u03b3\u03072, and \u03b1\u0307\u03b3\u0307. S2.2 A body-fixed \u03be-\u03b7-\u03b6 system with its origin in the bearing O was introduced in addition to the fixed x-y-z reference system, see Fig. 2.5. In the initial position, the \u03be axis is parallel to the x axis, the \u03b7 axis is parallel to the y axis, and the \u03b6 axis is parallel to the z axis. Pure rolling of a circular cone would be possible if there were a conic support surface. However, a planar 2.2 Kinematics of a Rigid Body 79 support surface and a circular cylinder are used in the calculations here, assuming that the circle rolls off at the distance \u03beS on the z = 0 plane. The stipulation \u03c8(\u03d5 = 0) = 0 means for the angles (when pure rolling takes place at the distance \u03beS) that the constraint \u03beS\u03d5 = R\u03c8; \u03c8 = \u03beS\u03d5 R ", + "10), the rotation matrix A can be determined using the sequence of the two elementary rotations \u03d5 and \u03c8:\u23a1\u23a3x y z \u23a4\u23a6= \u23a1\u23a3cos \u03d5\u2212 sin \u03d5 0 sin \u03d5 cos \u03d5 0 0 0 1 \u23a4\u23a6 \ufe38 \ufe37\ufe37 \ufe38 =A\u03d5 \u23a1\u23a3x\u2217 y\u2217 z\u2217 \u23a4\u23a6, \u23a1\u23a3x\u2217 y\u2217 z\u2217 \u23a4\u23a6= \u23a1\u23a31 0 0 0 cos \u03c8 sin \u03c8 0\u2212 sin \u03c8 cos \u03c8 \u23a4\u23a6 \ufe38 \ufe37\ufe37 \ufe38 =A\u03c8 \u23a1\u23a3 \u03be \u03b7 \u03b6 \u23a4\u23a6 (2.44) If these equations are combined, the rotational transformation relations between the fixed x, y, z\u201d= coordinates and the co-rotating \u03be, \u03b7, \u03b6 coordinates are obtained: A = A\u03d5 \u00b7A\u03c8 = \u23a1\u23a3 cos \u03d5 \u2212 sin \u03d5 cos \u03c8 \u2212 sin \u03d5 sin \u03c8 sin \u03d5 cos \u03d5 cos \u03c8 cos \u03d5 sin \u03c8 0 \u2212 sin \u03c8 cos \u03c8 \u23a4\u23a6 (2.45) The components of the angular velocity vector with respect to the body-fixed coordinate directions can be read from Fig. 2.5, keeping in mind that the angular velocity \u03c8\u0307 opposes the positive \u03be-direction, and if the angular velocity \u03d5\u0307 pointing in the z-direction is decomposed into its components in the directions of \u03b7 and \u03b6 using the angle of rotation \u03c8: \u03c9\u0304 = \u23a1\u23a3 \u03c9\u03be \u03c9\u03b7 \u03c9\u03b6 \u23a4\u23a6 = \u23a1\u23a3 \u2212\u03c8\u0307 \u2212\u03d5\u0307 sin \u03c8 \u03d5\u0307 cos \u03c8 \u23a4\u23a6 = \u03d5\u0307 \u23a1\u23a2\u23a2\u23a3 \u2212\u03beS/R \u2212 sin ( \u03beS\u03d5 R ) cos ( \u03beS\u03d5 R ) \u23a4\u23a5\u23a5\u23a6 (2.46) The result specified last in (2.46) was obtained by inserting the constraint (2.43) (also in differentiated form). Using the rotation matrix A, the following is obtained for the fixed directions: \u03c9 = [\u03c9x, \u03c9y , \u03c9z ]T = A\u03c9 = \u03d5\u0307 [ \u2212 \u03beS R cos \u03d5, \u2212 \u03beS R sin \u03d5, 1 ]T (2", + "47), due to the special property \u03c9\u0307 = \u03c9\u0307, provides the components of the angular acceleration vector, with respect to the body-fixed directions: \u03c9\u0307 = \u03c9\u0307 = \u03d5\u0308 \u23a1\u23a2\u23a2\u23a2\u23a3 \u2212\u03beS/R \u2212 sin ( \u03beS\u03d5 R ) cos ( \u03beS\u03d5 R ) \u23a4\u23a5\u23a5\u23a5\u23a6 \u2212 \u03d5\u03072 \u03beS R \u23a1\u23a2\u23a2\u23a2\u23a3 0 cos ( \u03beS\u03d5 R ) sin ( \u03beS\u03d5 R ) \u23a4\u23a5\u23a5\u23a5\u23a6 (2.50) For the velocity and acceleration distributions, which are most appropriately determined using Euler\u2019s kinematic equations, the coordinates of the points located on the line segment AB are required, to which r = [x, y, z]T = [\u03beS cos \u03d5, \u03beS sin \u03d5, z]T (2.51) applies according to Fig. 2.5. If the center of gravity S of the roller (and not O!) with rS = \u23a1\u23a2\u23a2\u23a2\u23a3 \u03beS cos \u03d5 \u03beS sin \u03d5 R \u23a4\u23a5\u23a5\u23a5\u23a6 , r\u0307S = \u03beS\u03d5\u0307 \u23a1\u23a2\u23a2\u23a2\u23a3 \u2212 sin \u03d5 cos \u03d5 0 \u23a4\u23a5\u23a5\u23a5\u23a6 , r\u0308S = \u03beS\u03d5\u0308 \u23a1\u23a2\u23a2\u23a2\u23a3 \u2212 sin \u03d5 cos \u03d5 0 \u23a4\u23a5\u23a5\u23a5\u23a6 \u2212 \u03beS\u03d5\u03072 \u23a1\u23a2\u23a2\u23a2\u23a3 cos \u03d5 sin \u03d5 0 \u23a4\u23a5\u23a5\u23a5\u23a6 (2.52) is selected as reference point, the following applies to the velocity distribution according to (2.25) with \u03c9\u0303 according to (2.48): r\u0307 = r\u0307S + \u03c9\u0303 (r\u2212 rS) = \u03beS\u03d5\u0307 \u23a1\u23a3\u2212 sin \u03d5 cos \u03d5 0 \u23a4\u23a6 + \u03beS\u03d5\u0307 \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 0 \u2212 1 \u03beS \u2212 sin \u03d5 R 1 \u03beS 0 cos \u03d5 R sin \u03d5 R \u2212 cos \u03d5 R 0 \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 \u23a1\u23a3 0 0 z \u2212R \u23a4\u23a6 (2.53) = \u03beS\u03d5\u0307 \u23a1\u23a2\u23a2\u23a2\u23a3 \u2212 sin \u03d5 cos \u03d5 0 \u23a4\u23a5\u23a5\u23a5\u23a6 z R ", + "87) for |\u03c9\u03be| \u03a9 and |\u03c9\u03b7| \u03a9 when neglecting the products of the small components of the angular velocity: MS kin \u03be \u2261 JS \u03be\u03be\u03c9\u0307\u03be+ JS \u03be\u03b7\u03c9\u0307\u03b7\u2212 [JS \u03be\u03b7\u03c9\u03be+ (JS \u03b7\u03b7 \u2212 JS \u03b6\u03b6)\u03c9\u03b7]\u03a9 \u2212 JS \u03b7\u03b6\u03a9 2 = MS \u03be MS kin \u03b7 \u2261 JS \u03b7\u03be\u03c9\u0307\u03be+ JS \u03b7\u03b7\u03c9\u0307\u03b7+ [JS \u03be\u03b7\u03c9\u03b7+ (JS \u03be\u03be \u2212 JS \u03b6\u03b6)\u03c9\u03be]\u03a9 + JS \u03be\u03b6\u03a9 2 = MS \u03b7 MS kin \u03b6 \u2261 JS \u03b6\u03be\u03c9\u0307\u03be+ JS \u03b6\u03b7\u03c9\u0307\u03b7+ (JS \u03b7\u03b6\u03c9\u03be\u2212 JS \u03be\u03b6\u03c9\u03b7)\u03a9 = MS \u03b6 . (2.93) The principle of conservation of angular momentum is often used in the form of (2.92) or (2.93) if a rigid body is part of a vibration system, see also Sects. 3.2.2 and 5.2.3. For more detailed information on the theory of gyroscopes and its applications, see [23]. The kinematics of edge mills were discussed in Sect. 2.2.4 in the solution of problem P2.2 so that this discussion refers to the results obtained there. The rotating body (grindstone) according to Fig. 2.5, which rolls off along a circular path, exerts a force in addition to its own weight on its base that is due to the gyroscopic effect. The problem is to calculate the required input torque, the normal force and the horizontal force on the grindstone for pure rolling motion for a given function of the pivoting angle \u03d5(t). Given: Gravitational acceleration g Roller radius R Roller length L Distance to the center of gravity \u03beS Time function of the pivoting angle \u03d5(t) Mass of the roller (grindstone) m Moments of inertia of the roller with respect to S JS \u03b6\u03b6 = JS \u03b7\u03b7 = m(3R2 + L2) 12 , JS \u03be\u03be = 1 2mR2 Since it is assumed here as in S2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure8.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure8.9-1.png", + "caption": "Figure 8.9.1 A vehicle with rolled suspension, rear view, in vehicle coordinates, shown with positive B.", + "texts": [ + " However, the above results are very general, and can be used to obtain results for specific cases of combined heave and roll, expressed as equivalent bumps. In the case of a symmetrical vehicle, equation (8.8.2) for the GRC lateral position becomes B \u00bc \u00f0zL zR\u00de 1\u00fe 1 2 TeBScd1 2eBScd0 \u00fe\u00f0zL \u00fe zR\u00deeBScd1 \u00f0symmetrical vehicle\u00de \u00f08:8:4\u00de Equation (8.8.3) for the GRC height does not simplify usefully, so it is better to evaluate the bump scrub rates at the two bump positions and use equation (8.8.3) as it is. Figure 8.9.1 shows the geometry for movement of the GRC relative to the body when the vehicle is rolled with no heave, just a positive suspension roll angle. Positive suspension roll is clockwise in the figure, looking along the positive longitudinal axis, so the corresponding suspension bumps are zR \u00bc \u00fe 1 2 TfS; zL \u00bc 1 2 TfS \u00bc zR \u00f08:9:1\u00de For convenience, it is easier to work initially in terms of zR and zR rather than the actual roll angle expressions, in other words to analyse an antisymmetrical double bump", + "3) gives B \u00bc 2zR \u00fe 1 2 T\u00f0 2eBScd1zR\u00de 2eBScd0 so B \u00bc \u00f01\u00fe 1 2 TeBScd1\u00de eBScd0 zR \u00f08:9:7\u00de and, in terms of the suspension roll angle fS, B \u00bc 1 2 T \u00f01\u00fe 1 2 TeBScd1\u00de eBScd0 fS \u00f08:9:8\u00de By differentiation, the lateral GRC movement coefficient in roll is eB1;Roll \u00bc 1 2 T 1\u00fe 1 2 TeBScd1 eBScd0 \u00f08:9:9\u00de If desired, this can be made zero by designing the suspension such that eBScd1 \u00bc 2 T \u00f08:9:10\u00de With positive initial roll centre height, for eBScd1> 2/T (e.g. zero), theGRCmoves towards the outside of the curve. For eBScd1< 2/T, the GRC moves towards the inside of the curve, left in Figure 8.9.1. The GRC height, from equation (8.9.4), by substitution of the linear symmetrical bump scrub rates, becomes H \u00bc zR2eBScd1zR \u00fe T\u00f0e2BScd0 e2BScd1z 2 R\u00de 2eBScd0 \u00bc 1 2 TeBScd0 eBScd1 eBScd0 1\u00fe 1 2 TeBScd1 z2R \u00f08:9:11\u00de 172 Suspension Geometry and Computation so, in terms of the suspension roll angle fS, H \u00bc 1 2 TeBScd0 1 4 T2 eBScd1 eBScd0 1\u00fe 1 2 TeBScd1 f2 S \u00f08:9:12\u00de The linear bump scrub variation, therefore, does not produce a linear factor in the GRC height, but a quadratic effect: H \u00bc H0 \u00fe eH1;RollfS \u00fe eH2;Rollf2 S H0 \u00bc 1 2 TeBScd0 eH1;Roll \u00bc 0 eH2;Roll \u00bc 1 4 T2 eBScd1 eBScd0 1\u00fe 1 2 TeBScd1 \u00f08:9:13\u00de with the quadratic coefficient having units m/rad2", + "1 shows the geometry for movement of the GRC relative to the body when the asymmetricalsuspension-geometry vehicle is rolledwith no heave. The small track variation is neglected. Vehicle bump scrub asymmetry is now included, although this does not show in the diagram. The simultaneous equations for B and H in general form are as in the previous section, and the solution is the same: B \u00bc 2zR \u00fe 1 2 TeBScd;L R eBScd;R\u00feL \u00f08:11:1\u00de Figure 8.11.1 An asymmetrical suspension geometry vehicle with rolled suspension, rear view, in vehicle coordinates, but still with zero heave, the same diagram as Figure 8.9.1. 174 Suspension Geometry and Computation H \u00bc zReBScd;L R \u00fe TeBScd;R L eBScd;R\u00feL \u00f08:11:2\u00de Now consider asymmetrical linear bump scrub variation (still with equal and opposite bumps, zL\u00bc zR): eBScd;R \u00bc eBScd0;R \u00fe eBScd1;RzR eBScd;L \u00bc eBScd0;L eBScd1;LzR \u00f08:11:3\u00de with further relationships eBScd;R\u00feL \u00bc eBScd0;R\u00feL \u00fe eBScd1;R LzR eBScd;R L \u00bc eBScd0;R L \u00fe eBScd1;R\u00feLzR \u00f08:11:4\u00de Inserting the linear variations into equation (8.10.1), B \u00bc 2zR 1 2 TeBScd0;R L 1 2 TeBscd1;R\u00feLzR eBScd0;R\u00feL \u00fe eBScd1;R LzR \u00f08:11:5\u00de Taking the derivative of the quotient, and substituting zR\u00bc 0 gives the GRC lateral position variation in roll as a function of the associated suspension bump deflection: eB1;Roll;ZB \u00bc 2eBScd0;R\u00feL \u00fe 1 2 T\u00f0eBScd0;R\u00feLeBScd1;R\u00feL eBScd0;R LeBScd1;R L\u00de e2BScd0;R\u00feL \u00f08:11:6\u00de This coefficient has units m/m, that is, no dimensions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure10-1.png", + "caption": "Fig. 10 (b) illu", + "texts": [ + " In this case, the equation of meshing fci = 0 yields the following value for the generalized parameter of motion wi: wi\u00f0ui; li\u00de \u00bc \u00bd2a2i u3i \u00fe \u00f01\u00fe aiso cos an\u00deui uo cos b\u00fe \u00bdli sin an 2aiuili cos an sin b \u00f0sin an 2aiui cos an\u00derpi : \u00f016\u00de Then, it is possible to represent Ri as Ri\u00f0ui; li\u00de \u00bc ri\u00f0ui; li;wi\u00f0ui; li\u00de\u00de: \u00f017\u00de The normal to Ri is determined as Ni\u00f0ui; li\u00de \u00bc oRi oui oRi oli : \u00f018\u00de The tooth surface R2 of the face-gear is generated as the envelope to the family of tooth surfaces Rs of the shaper. Since two types of geometry have been developed, surface Rs may be represented: (i) by equations (8) or (13) and (14) for the case of an involute screw surface, or (ii) by Eq. (17). In both cases, index i = s has to be taken. We apply for derivations the fixed coordinate systems Sm and Sa (Fig. 10(a)) and movable coordinate systems S2 and Ss (Fig. 10(b)). Parameter L0 for distance jO0 2Oaj is chosen as the distance to the mid section of the shaper. Parameters L2 and L1 determine the outer and inner dimensions of the face-gear and can be obtained from the conditions of avoidance of undercutting and pointing (see below). Angle cm is formed by the axes of the face-gear and the shaper. Parameter rps is the radius of the pitch cylinder of the shaper. Parameter af is the addendum of the face-gear. The shaper and the face-gear perform related rotations about the za and zm axes", + " 11(b)) is formed: (i) as the working part (generated by the involute or modified involute surface of the shaper) and (ii) as the fillet part (generated by rounded top of the shaper tooth). The rounded top of the shaper is defined by an arc of radius q that is in tangency with the profile and the addendum circle of the shaper. Application of a rounded top of the shaper reduces the bending stresses of the face-gear [14]. The length of the face-gear teeth has to be limited by dimensions L1 and L2 (Fig. 10) to avoid undercutting in plane A and pointing in the plane B (Fig. 11(b)). Avoidance of undercutting is based on the following ideas [6\u20138]: (i) Appearance of singular points on the generated surface R2 is the warning that the surface might be undercut in the process of generation. (ii) Singular points on surface R2 are generated by regular points of the generating surface Rs when the velocity of a contact point in its motion over R2 becomes equal to zero: v\u00f02\u00der \u00bc v\u00f0s\u00der \u00fe v\u00f0s2\u00de \u00bc 0: \u00f023\u00de (iii) Eq", + " The coefficient c has been obtained taking into account that the undercutting conditions of the concave side of the face-gear limits the inner radius L1. Undercutting conditions of the convex side give smaller values of L1. The considered input data are: an = 27.5 , kc = 1.0, mn = 3.175mm, cm = 90 . Comparison of a face-gear and a spiral bevel gear drive shows that a substantial larger gear ratio (up to m12 = 7 or greater) and a larger tooth length can be obtained by application of a face-gear drive instead of a spiral bevel gear drive. However, the design of a face-gear drive requires limitations of the tooth length by L1 and L2 (Fig. 10(a)) to avoid undercutting and pointing. TCA is designated for simulation of meshing and contact of surfaces R1 and R2 of helical pinion and face-gear and provides a way to investigate the influence of errors of alignment on transmission errors and shift of bearing contact. The TCA algorithm is based on observation of continuous tangency of pinion and face-gear tooth surfaces R1 and R2 in the process of meshing (Fig. 5). Face gear drives with helical pinions of two types of geometry have been investigated (Section 4): (a) of screw involute pinions, and (b) pinion tooth surface determined as an envelope to a parabolic rack-cutter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002096_j.mechmachtheory.2014.10.011-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002096_j.mechmachtheory.2014.10.011-Figure7-1.png", + "caption": "Fig. 7. Three operation modes of a variable-DOF single-loop mechanism with 1 to 2 DOF: Mechanism 2.", + "texts": [ + " The fourth ideal, J 4, yields only complex solutions (v1 =\u00b1 I), which has no physical meaning from the perspective of Euclidean motion. The first ideal, J 1, has the solution fv1 \u00bc v1; v7 \u00bc 0; x0 \u00bc \u2212 1 40 75v21x3 \u00fe v21y2 \u00fe 35x3 \u00fe y2 v1 ; x1 \u00bc 0; x2 \u00bc 0; x3 \u00bc x3; y0 \u00bc 0; y1 \u00bc 1 8 525v21x3 \u00fe 7v21y2 \u00fe 525x3 \u00fe 15y2 v1 ; y2 \u00bc y2; y3 \u00bc 0g: \u00f016\u00de The vanishing set of this ideal has dimension 3, therefore the mechanism has 2 DOF. Since v7 = 0, we have \u03b87 = 0, which leads to configurations where the axes of joints 6 and 1 are parallel. Therefore, Eq. (16) represents a 2-DOF planar 5R operation mode of Mechanism 2 (Fig. 7a), in which the axes of R joints 1, 2, 4, 5 and 6 are parallel. The second ideal, J 2, in Eq. (15) has the solution fv1 \u00bc v1; v7 \u00bc \u22121 2 ffiffiffi 2 p v21\u22121 v1 ; x0 \u00bc 0; x1 \u00bc 2v1x2 v21\u22121 ; x2 \u00bc x2; x3 \u00bc \u2212 x2 v41 \u00fe 2v21 \u00fe 1 v41\u22122v21 \u00fe 1 ; y0 \u00bc 10v1x2 v21\u22121 ; y1 \u00bc \u2212 20 3v21\u22127 v1x2 v41\u22122v21 \u00fe 1 ; y2 \u00bc 5 5v41 \u00fe 42v21\u22123 x2 v41\u22122v21 \u00fe 1 ; y3 \u00bc 5x2 5v21 \u00fe 3 v21\u22121 g \u00f017\u00de and the third one, J 3, has the solution fv1 \u00bc v1; v7 \u00bc 1 4 ffiffiffi 2 p 3v21 \u00fe 7 v1 ; x0 \u00bc \u2212 4v1x3 3v21 \u00fe 7 ; x1 \u00bc 0; x2 \u00bc \u2212x3; x3 \u00bc x3; y0 \u00bc \u221240v1x3 v21 \u00fe 1 ; y1 \u00bc 20v1x3 3v21 \u00fe 7 ; y2 \u00bc \u2212 15x3 5v21\u22127 3v21 \u00fe 7 ; y3 \u00bc \u2212 5x3 5v21\u22123 v21 \u00fe 1 g: \u00f018\u00de Eqs. (17) and (18) correspond to different one-DOF spatial 7R operation modes of the mechanism (Figs. 7b and 7c). In these operation modes, the axes of R joints 1 and 2 are usually not parallel to those of R joints 4, 5 and 6. 3.3.2. Transition configurations Following the procedure for the reconfiguration analysis of Mechanism 1 in Section 3.2.2, the transition configurations between the planar 5R operation mode (Eq. (16) and Fig. 7a) and the first 7R-mode (Eq. (17) and Fig. 7b) are obtained as (Figs. 8a and 8b): fv1 \u00bc 1; v7 \u00bc 0; x0 \u00bc 0; x1 \u00bc 0; x2 \u00bc 0; x3 \u00bc \u2212 1 55 y2; y0 \u00bc 0; y1 \u00bc 4 11 y2; y2 \u00bc y2; y3 \u00bc 0g: \u00f019\u00de A transition configuration between the planar 5R operation mode (Eq. (16) and Fig. 7a) and the second 7R-mode (Eq. (18) and Fig. 7c) is not possible in real space. Aminor drawback of the tangent-half-angle substitution should be noted in calculating the transition configurations between the first spatial 7R operation mode (Eq. (17) and Fig. 7b) and the second spatial 7R operation mode (Eq. (18) and Fig. 7c). The potential solutionwith \u03b87= 180\u00b0, which corresponds to v7=\u221e, could bemissing. To overcome this problem, one can substitute v7 \u00bc 1=v7 into Eqs. (17) and (18). Then the solutions with v7 \u00bc 0 correspond to the solutions with v7 = \u221e. Using this substitution, one obtains the transition configuration (Fig. 8c) between the two spatial 7R operation modes as: v1 \u00bc 0; v7 \u00bc 0; x0 \u00bc 0; x1 \u00bc 0; x2 \u00bc \u2212x3; x3 \u00bc x3; y0 \u00bc 0; y1 \u00bc 0; y2 \u00bc 15x3; y3 \u00bc 15x3f g: \u00f020\u00de The above analysis shows that Mechanism 2 has three operation modes, including one 2-DOF planar 5R operation mode (Eq. (16) and Fig. 7a) and two 1-DOF spatial 7R operation modes (Eq. (17) and Fig. 7b as well as Eq. (18) and Fig. 7c). It can switch from the 5R operation mode to the first spatial 7R operation mode at two transition configurations (Eq. (19) and Figs. 8a and 8b), between the two spatial 7R operation modes at one transition configuration (Eq. (20) and Fig. 8c). However, Mechanism 2 cannot switch directly between the 5R operation mode and the second spatial 7R operation mode without passing through the first spatial 7R operation mode. A new method has been proposed to the type synthesis of variable-DOF single-loop mechanisms" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure13.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure13.3-1.png", + "caption": "Figure 13.3.1 Roll and steer angles of an axle defined, taken in that order, AB being the line between the wheel centres, AD parallel to the Y axis, CD parallel to the X axis, BC parallel to the Z axis. Subsequent pitch is about the axle centreline AB.", + "texts": [ + " In the case of an axle, the roll angle is an independent variable, and best taken first, followed by the steer angle and then the pitch angle. Note that the axle heave steer angle is not the same as a rigid axlewith steeredwheels, which has independent wheel steer rotation relative to the axle. The latter also involves the steering mechanism. The roll angle, taken first, is about an axis parallel to the longitudinal reference X axis, through the axle centre. The steer angle is then about the vertical Z axis. The pitch angle is last, performed most conveniently about the axis line between the wheel centres. Figure 13.3.1 shows the axle centreline AB (the line between the twowheel centres) with roll and steer angles applied in that order. In the context of a computer analysis, the angles must be related to the coordinates of the wheel centres A and B, with the angles taken in the correct order. The axle length between centres is LAx\u00bc LAB. AD is parallel to the Y axis, CD is parallel to theX axis and BC is parallel to the Z axis. Then LBC \u00bc LAx sin f \u00bc zB zC LCD \u00bc LAx cos f sin d \u00bc \u00f0xC xD\u00de \u00bc \u00f0xB xD\u00de LAD \u00bc LAx cosf cos d \u00bc yD yA \u00bc yC yA \u00bc yB yA For given wheel centre coordinates, the angles may be deduced from sinf \u00bc zB zC LAx and, with the steer angle positive for right-hand rotation about the Z axis, tan d \u00bc xC xD yD yA \u00bc xB xA yB yA The axle pitch angle does not arise directly in the above, being applied subsequently about the axle centreline AB" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure8.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure8.2-1.png", + "caption": "Fig. 8.2 Infinitesimal screws of the 3R2T parallel manipulator", + "texts": [ + "9) where is the position vector of point S4 while xi, yi, and zi are the coordinates of the centers of the spherical joints expressed in the moving reference frame xyz. Once the points Si are computed, the generalized coordinates qi.i D 1; 2; 3/ are obtained as q2 i D .si bi/ .si bi/; i D 1; 2; 3; (8.10) whereas, taking into account that S4 D .X4; Y4; Z4/, we calculate the generalized coordinates q4 and q5 directly as q4 D Y4 and q5 D X4. In this section the velocity and acceleration analyses of the 3R2T parallel manipulator are addressed using screw theory. The model of the infinitesimal screws is depicted in Fig. 8.2. Let VC D ! vC be the velocity state of the moving platform, with respect to the fixed platform, where the primal part, P.VC/ D !, is the angular velocity vector of the moving 194 8 3R2T Parallel Manipulator platform with respect to the fixed platform, and the dual part, D.VC/ D vC, is the linear velocity of point C D S4 embedded in the moving platform as measured from the fixed platform. The velocity state of the moving platform with respect to the fixed platform, the six-dimensional vector VC, may be expressed in screw form through any of the UPS-type limbs as follows: 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000737_00368791111101830-Figure19-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000737_00368791111101830-Figure19-1.png", + "caption": "Figure 19 Model of wind turbine gear system in WTplus", + "texts": [ + "3 KS7: T1 = 188 Nm Load dependent gear losses Load dependent bearing losses No-load gear and bearing losses Type C Low loss \u201374% \u201373% \u201352% \u201332% \u201368% \u201370% \u201354% \u201340% \u201365% \u201367% \u201357% \u201342% Pitch line velocity (m/s) Source: Wimmer et al. (2005) 20 0.5 2 8.3 KS9: T1 = 302 Nm 20 D ow nl oa de d by U N IV E R SI T A E T O SN A B R U C K A t 2 0: 59 3 0 Ja nu ar y 20 16 ( PT ) a planetary low-speed first stage and an intermediate- andhigh-speed cylindrical gear stage was modelled in the computer program WTplus (Kurth, 2008) (Figure 19). The program calculates the expected power loss of gears, bearings and seals for any gearing system. The influence of the lubricant can be introduced into the calculation with the evaluation of the friction coefficient of the lubricant according to Doleschel (2002). From the results of the FZG-FVA efficiency test for the candidate oil at different operating conditions, an empirical equation is derived for the calculation of the mesh friction in gears and bearings. The friction coefficient mM in a gear mesh consists of a portion of solid body friction mF and a portion of fluid film friction mEHD: mM \u00bc \u00f012 z\u00de \u00b7mF \u00fe z \u00b7mEHD \u00f07\u00de with: mM mixed friction coefficient (-)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001623_tro.2012.2226382-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001623_tro.2012.2226382-Figure2-1.png", + "caption": "Fig. 2. Schematic illustration of the robot showing the articulated joint structure.", + "texts": [ + " The importance of flexible access also becomes evident in the context of emerging surgical techniques, such as natural orifice transluminal endoscopic surgery (NOTES), which aims to accomplish scarless surgical operations through transluminal pathways. One key requirement for NOTES instrumentation is adequate articulation to ensure no tissue damage during insertion and a wide visual exploration angle of the operative site including retroflection [1]. In order to meet these requirements, we developed a lightweight universal-joint-based articulated flexible access platform [2], which has been tested in in vivo trials, as shown in Fig. 1. Fig. 2 illustrates the structure of our snake-like robot prototype that comprises a series of identical link units. Each link embeds two micromotors, which provide angular actuation between two adjacent joints generating relative rotations along perpendicular axes. Hence, the rigid robot links are connected by universal joints, each providing two-degree-of-freedom (DoF) rotational movement within \u00b1qmax = \u00b145\u25e6. Independent actuation of each joint provides typical hyper-redundant kinematic structure [3]", + " In order to meet the clinical demand, as stated in Section II, detailed technical approaches to address the engineering challenges mentioned earlier will be provided in this section. More specifically, they will address 1) shape conformance and realtime PQs; 2) motion modeling, parameterization, and control of the snake robot; 3) visual-motor and haptic interaction of the robot under DACs. 1) Shape Conformance to Parametric Curve: Given a snake robot with the generic configuration, as shown in Fig. 2, the homogeneous transformation of link i relative to link i \u2212 1 is determined by a joint-angle pair qi := [q2i\u22121 , q2i ]T . This can be expressed as i\u22121 i T (qi) \u2200i = {1, . . . , L}, where L is the total number of links forming the robot. To position the robot in the safest region inside a constraint pathway, the robot configuration in joint space has to be computed so that all the joint centers are aligned along the centerline [24], [25]. This is particularly important for transluminal navigation so that the robot is able to kinematically conform to the curvature of the channel to ensure accurate path following", + " Provided with a serial kinematic structure, such a configuration can be mathematically characterized by the gradual change of joint values from proximal to distal joints. We consider that only a certain number of distal joints L are directly manipulated by the user, while the proximal joint values are determined through the shape conformance algorithm introduced in Section III-A as q\u0303 L\u2212 L +1...L . The optimal configuration of the distal joints is instead denoted by \u0394q := [\u0394q1 , . . . ,\u0394q L ]T \u2208 2 L \u00d71 , where \u0394qi = [\u0394q2i\u22121 ,\u0394q2i ]T and L \u2265 L. As shown in Fig. 2, each universal joint comprises two DoFs with odd and even joint indices. Since the corresponding joint axes are parallel to each other when the robot is in a straight configuration, actuation of either odd or even joint angles along the robot structure yields a planar motion, as shown in Fig. 4(a) and (b). These two motion planes are orthogonal to each other, as shown in Fig. 4(c). For panoramic exploration, the linear combination of such independent odd- and even-joint angles actuation can generate a wide range of configurations in different bending directions, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001333_j.ijsolstr.2014.09.014-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001333_j.ijsolstr.2014.09.014-Figure8-1.png", + "caption": "Fig. 8. Cross-section view of a gel (Nm = 0.005, e = 0.78) subjected to irradiation of different intensities at 308 K. The contour plots show the deformation in the radial direction.", + "texts": [ + " Although an analytical approach is possible by solving the governing equations (Eshelby, 1956) for temperature sensitive hydrogels (Cai and Suo, 2011), the phenomenon of coexistence within a gel is a complex one and often requires numerical methods to predict the overall self-consistent behavior. Here we will attempt to employ the developed FE formulation to study this phenomenon. Consider a hydrogel rod immersed in water (ls,0 = 0), fixed at both ends and originally unexposed to irradiation. As light is being irradiated on the middle portion of the rod, the exposed portion starts to undergo phase transition. The process takes place under an isothermal condition of 308 K. Axisymmetric four-node CAX4 elements were used for the mesh. Fig. 8 shows the simulation results which successfully captures the state of deformation when the gel is subjected to light with different intensities. Under increasing intensities, the extent of deswelling of the exposed rod increases. As the middle portion shrinks, the interface between the two phases experiences tension, which changes the proportion of the radial dimensions of the two phases. It should be noted, however, that the parameters used in this simulation causes continuous phase transition, thus allowing the simulation to be completed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001355_17452751003703894-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001355_17452751003703894-Figure3-1.png", + "caption": "Figure 3. (a) Three-part designs produced by SLM to be used in Charpy tests; (b) Orientation of a standard part manufactured with the building axis coinciding with the x-direction.", + "texts": [ + " The experimental layout for all the batches produced is given in Table 2, where the number of produced samples from each material and specimen design is shown. Three batches of specimens from two materials (Ti alloy and the maraging steel 300) were produced in order to investigate different factors that may influence the toughness of SLM parts. Only one batch was produced in AISI 316L. In the first batch, two-part designs were used to study whether high roughness values encountered in SLM cause any notch- effect influencing toughness results. Different part designs used in the experiments are shown in Figure 3a. A part Table 2. The experimental layout. AISI 316 L Ti-6AI-4V Maraging Steel BATCH 1 S P E C IM E N D E S IG N Standard specimen 3 3 3 Non notch specimen 3 3 3 EDM-notch specimen no no no Building axis x-axis x-axis x-axis Heat Treatment none none none Sand Blasting yes yes yes Number of replicates 3 3 3 BATCH 2 S P E C IM E N D E S IG N Standard specimen 3 3 Non notch specimen 3 3 EDM-notch specimen 3 3 Building axis x,y and z x,y and z Heat Treatment none yes Sand Blasting yes yes Number of replicates 1 1 BATCH 3 S P E C IM E N D E S IG N Standard specimen 6 6 Non notch specimen no no EDM-notch specimen no no Building axis x-axis x-axis Heat Treatment 2-types 2-types Sand Blasting Yes yes Number of replicates 3 3 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 0 2: 47 2 8 N ov em be r 20 13 Figure 4. Micrographs of etched SLM parts. D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 0 2: 47 2 8 N ov em be r 20 13 design without a notch (design: \u2018no notch\u2019) but with an equal cross-section area was utilized as well as a standard Charpy test specimen (design: \u2018standard\u2019). In the second batch, the influence of the building axis was taken under investigation with three-part designs: the coordinate system attached to the part is shown in Figure 3b. In addition to the two designs explained above, a bar without any groove or notch was made, in which the notch defined by the standard was made afterwards by EDM (design: \u2018notch to be made by EDM\u2019). Finally, in the third batch, standard specimens were produced along the x-axis to test how different heat treatments may influence the toughness of SLM materials. For each material, different heating cycles were applied. The details of the heating cycles are explained in Section 3.3. 3. Experimental results 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001933_tia.2015.2448065-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001933_tia.2015.2448065-Figure1-1.png", + "caption": "Figure 1. Cross sectional view of test motor and location of attached acceleration sensors.", + "texts": [ + " The DC-bus voltage varying from 0 to 750V is supplied from the battery simulator installed on the dynamo system. Since the tested SR motor is in torque control mode, the dynamo system keeps the motor speed constant at 1500r/min in following experiments. The experimental measurements are conducted at the operating condition as mentioned in the foregoing section, that is, at approximately 1/3 of the rated torque and a half of the rated speed which corresponding to the frequent urban driving situation of a target electric vehicle. As can be seen in Fig. 1, acceleration of vibration is measured by two acceleration sensors attached. As space of manuscript is limited, the vibration measured at P1 is only demonstrated in following experimental results. Note that the vibration measured by P2 has a tendency similar to that measured by P1. Usually, acoustic noise measurement should be implemented in anechoic chamber. Even so, since the anechoic chamber is unavailable, the measurement in this study is conducted for a purpose of relative comparison of acoustic noise at the almost same operating condition under the different types of voltage PWM control" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure9.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure9.1-1.png", + "caption": "Fig. 9.1 The RR + RRR spherical parallel manipulator", + "texts": [ + " 185 Fig. 8.1 3R2T parallel manipulator and its geometric scheme . . . . . . . . . . . . . 190 Fig. 8.2 Infinitesimal screws of the 3R2T parallel manipulator . . . . . . . . . . . . 194 Fig. 8.3 Example 8.1. Time history of the angular and linear velocities of the center of the moving platform . . . . . . . . . . . . . . . . . . . . 201 List of Figures xxi Fig. 8.4 Example 8.1. Time history of the angular and linear accelerations of the center of the moving platform . . . . . . . . . . . . . . . . 201 Fig. 9.1 The RR + RRR spherical parallel manipulator . . . . . . . . . . . . . . . . . . . . 206 Fig. 9.2 Geometric scheme of the RR + RRR parallel wrist. . . . . . . . . . . . . . . . 207 Fig. 9.3 Infinitesimal screws of the RR + RRR parallel wrist . . . . . . . . . . . . . . 211 Fig. 9.4 Example 9.3. Time history of the angular quantities of the knob as measured from the base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Fig. 10.1 The 3-RRPS parallel manipulator . . . . . . . . . ", + " Gallardo-Alvarado, Kinematic Analysis of Parallel Manipulators by Algebraic Screw Theory, DOI 10.1007/978-3-319-31126-5_9 205 206 9 Two-Degree-of-Freedom Parallel Wrist a 2-DOF wrist is carried out by combining screw theory and the so-called firstorder coefficients. None of the above-mentioned contributions approached the jerk analysis. This chapter reports on the position, velocity, acceleration, and jerk analyses of a simple 2-DOF parallel manipulator. The parallel wrist considered for analysis is depicted in Fig. 9.1. The spatial mechanism consists of a moving platform, named the knob, and a fixed platform, named the base, connected to each other by two distinct kinematic chains, RR and RRR, where the active revolute joints or actuators are conveniently mounted on the fixed platform and are indicated with underlines. All the axes of the revolute joints are concurrent, and the linear infinitesimal kinematic properties of the intersecting point therefore vanish, yielding spherical motions of the knob as observed from the base" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000883_j.bios.2013.10.069-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000883_j.bios.2013.10.069-Figure1-1.png", + "caption": "Fig. 1. Schematic representation of electrochemical magnetoimmunosensing system for ApoE detection: (A) components of the microfluidic platform with integrated screen-printed electrodes (SPEs) and (B) picture of the set-up.", + "texts": [ + " Finally, the PDMS channel and the PC substrate were assembled using a previously reported protocol (Tang and Lee, 2010). The PC substrate was treated by air-plasma for 1 min and then immersed into a 2% (v/v) 3-aminopropyltriethoxylane (APTES) (Sigma Aldrich) solution in water for 1 h. The surface of the PDMS channel was also activated for 1 min by plasma, and put into contact with the PC sheet to achieve irreversible bonding (Medina-S\u00e1nchez et al., 2012a, 2012b). Finally, a homemade connector was used for the electrical connection (see Fig. 1). The morphology of streptavidin-QD655 was checked through high resolution transmission electron microscope (TEM). A 2 \u03bcL drop of QD solution (12.5 nM in milli-Q water) was deposited onto a holey carbon layer copper grid and then air-dried. A Tecnai TEM (USA) operating at 200 kV was used to obtain the images for posterior analysis. Magneto-immunoassay was also checked by MAGELLAN scanning electron microscopy (SEM), operating at 2 kV. A Leica TCS SP5 AOBS spectral confocal microscope (Leica Microsystems, Germany) was employed to evaluate the effect of blocking step into the microfluidic channel" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001018_j.cirp.2010.03.131-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001018_j.cirp.2010.03.131-Figure4-1.png", + "caption": "Fig. 4. Geometry of the machined samples.", + "texts": [ + " Besides the influence of machining processes, more and more attention is paid on surface coatings [21]. To allow for a comprehensive comparison of the surface integrity, in this study, milling and grinding experiments were performed, machining SLM-samples made of 18 Maraging 300 (1.2709, X3NiCoMoTi18-9-5) with both, vertical and horizontal layer orientation, as well as conventional samples made of AISI 52100 (100Cr6). An overview of the presented investigations is given in Fig. 3. Cylindrical samples with a diameter of 45 mm and a height of 15 mm (Fig. 4) were prepared within the CIRP collaborative work by the IWT Bremen and the irpd St. Gallen, Switzerland. They showed two grooves of 5 mm width and 6 mm height at the bottom side to allow proper clamping during the machining process. In their soft state the AISI 52100 samples were pre-machined by turning and milling, whereas the SLM-samples were produced using the parameters shown in Table 2. The SLM scan strategy and further environmental processing parameters are described in more detail in [5]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001118_0301-679x(79)90001-x-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001118_0301-679x(79)90001-x-Figure7-1.png", + "caption": "Fig 7 Kurtosis profiles f l = 3 H z - 5 kHz, f2 = 5 -10kHz , f3 = 1 O- 15kHz, f4 = 15-20kHz, f s = 20kHz, f6 = 20kHz", + "texts": [ + " Fig 6 shows such a gear in the inner ring version, similar to the slew ring of the platform crane on which the acoustic emission measurements reported below were made. An exploratory exercise was undertaken on a platform crane to determine the background noise level during slewing under different loading conditions and the suitability of using a simple linear array for emission source location. The sensors, $1 and $2, were positioned diametrically opposite to each other on the fixed inside face of the slew ring 2cm below the gear teeth (Fig 7). Large amplitude emissions were observed when the crane was in motion. Fig 8a shows the distribution of signal amplitudes on sensor $1 for a sample time of 2\u00bd min, during which time the crane was rotated through 180 \u00b0 and back to its starting point. A total of 10 000 events were recorded, of which ten had amplitudes in excess of 25 dB above the electronic noise level. There was little difference between the amplitude distributions recorded when the crane was off load and when it carried a four tonne load (boom at 56 degrees to vertical)", + " Kurtosis evaluation of this type of bearing was only partially successful and further information is being obtained to establish the usefulness of the technique for this type of bearing. The instrument successfully predicted damage on a wide variety of bearing types. The rms values were found useful in diagnosing very advanced damage and the combination of kurtosis and rms values give a success rate of 96% when the predicted damage was compared with visual inspection of the bearings. Three examples are presented in Fig 7. Fig 7(a) shows the kurtosis profile of a 55mm double self-aligning ball bearing supporting a cooling fan running at 1400 rev/min. There had been no increases in rms values, but the kurtosis profile indicated medium to advanced damage. Inspection revealed that the balls were pitted from corrosion, with one ball in particular being badly spalled. The inner track was discoloured and fretting had commenced. Fig 7(b) shows the kurtosis profile from an 85ram double row spherical bearing supporting an exhaust fan running at 1500 rev/min. The bearing was running hot, but there was no significant increase in the rms levels. The kurtosis profile, however, indicated medium to advanced damage: inspection showed that the cage was severely deformed, but there was no roller damage. Fig 7(c) is for a bearing in a similar application. This kurtosis profile would not normally warrant removal of the bearing. In this case, however, it was convenient to remove the bearing and close examination revealed a fine crack across the contact surface of one of the rollers, confirming the kurtosis prediction of early damage. *This data has been abstracted from an article by A.A. Rush published . in the February 1979 issue o f lron and Steel lnternational {pp 23-27). The article gives a full definition o f kurtosis, a description o f the kurtosis meter, fuller data, detail on accelerometer attachment, etc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000855_tie.2011.2159357-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000855_tie.2011.2159357-Figure11-1.png", + "caption": "Fig. 11. Prototype of the SPM-type magnetic gear.", + "texts": [ + " The expected orders shown in Table I can be seen; however, the 14th, 16th, and 28th orders also stand out in Fig. 9. The cogging torque on the high-speed rotor due to the stationary part contains 14th, 16th, and 28th components. This is due to the disrupted magnetic flux density of the high-speed rotor and stationary part by the low-speed rotor. The orders of 14th, 20th, 28th, and 40th stand out in Fig. 10 as well. Thus, Table I is verified through 3-D FEM. In order to verify the order shown in Table I and the computed order, a prototype shown in Fig. 11 was manufactured. This prototype was set to the torque measuring system shown in Fig. 12, and a constant rotation speed was given to both rotors in accordance with the gear ratio by the ac servo motors [55]\u2013[65]. Both ac servo motors operate synchronously by the signal from the function generator, and the torque signal is collected to the PC via the strain amplifiers, as shown in Fig. 13. A mechanical gear with a ratio of 1:9 was used to connect the high-speed rotor torque transducer to the ac servo motor, and a mechanical gear with a ratio of 1:80 was used to connect the low-speed rotor torque transducer to the ac servo motor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure11.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure11.1-1.png", + "caption": "Fig. 11.1 Six-legged parallel manipulator provided with linear and rotary actuators", + "texts": [ + " This chapter uses screw theory to address the kinematics of a six-degree-of-freedom (DOF) parallel manipulator equipped with three rotary and three linear actuators. For the sake of completeness the displacement analysis of the robot at hand is also investigated. The finite kinematics of the chosen parallel manipulator is precisely where the benefits of using mixed schemes of actuation are evident when compared with the Gough\u2013Stewart platform. 11.2 Description of the 3RRRSC3RRPS Parallel Manipulator In Fig. 11.1 a 6-DOF parallel manipulator equipped with a mixed scheme of actuation is outlined. Referring to Fig. 11.1, the robot under study consists of a moving platform (m) and a fixed platform (0), connected to each other by three RRP S-type and three R RRS-type kinematic chains, where superscript asterisks denote active kinematic pairs while R, P, and S stand for revolute, prismatic, and spherical joints, respectively. Thus, the limbs of the parallel manipulator are in touch with the moving and fixed platforms through spherical and revolute joints, respectively. According to the Chebychev\u2013Gr\u00fcbler\u2013Kutzbach criterion, the mobility F of a spatial mechanism formed from N links, including the fixed link, and j kinematic pairs each one with freedom fi" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003309_978-3-319-24729-8-Figure6.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003309_978-3-319-24729-8-Figure6.7-1.png", + "caption": "Fig. 6.7 3D flying robot", + "texts": [ + "6, and we define the rotation matrix of frame B with respect to the inertial frame as R := [r s] = [ cos(\u03b8) \u2212 sin(\u03b8) sin(\u03b8) cos(\u03b8) ] . Then, as in Chap.2, we have R\u0307 = R [ 0 \u2212\u03c9 \u03c9 0 ] = RS(\u03c9). The thrust vector f is parallel to the body frame axis r and has magnitude u, f = u Re1, where e1 = [1 0]T . In conclusion, we can rewrite model (6.1) as follows: mx\u0308 = u Re1 R\u0307 = RS(\u03c9) J \u03c9\u0307 = \u03c4 . (6.2) 74 6 Introduction to Flying Robots We will now see that this model has a straightforward generalization to the threedimensional setting. Consider now the setup of Fig. 6.7, in which the robot flies in the three-dimensional Euclidean space. As before, we fix an inertial frame I and a body frame B = {b1, b2, b3}, both orthonormal and right-handed. We denote by x = (x1, x2, x3) the coordinates of the robot\u2019s centre of mass in frame I. The body is propelled by a thrust vector f that is now assumed to point opposite to the body axis b3. There are four control inputs: the magnitude u of the thrust vector and three torques \u03c41, \u03c42, \u03c43 about the three body axes. As in the planar case, we define the rotation matrix of frame B with respect to frame I, R = [b1 b2 b3]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002943_rpj-03-2019-0065-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002943_rpj-03-2019-0065-Figure2-1.png", + "caption": "Figure 2 Dimensions of (a) cantilever beams and (b) cubes for residual stress measurements", + "texts": [ + " An X-ray diffraction (XRD) instrument and a coordinate measuring machine (CMM) are used for residual stress and part distortion measurements, respectively. ANSYS\u00a9 19.2 Workbench Additive, coupled thermal-mechanical FE module, is used to predict residual stresses and part distortions during SLM as shown in Figure 1. The main contribution of the present study is to analyze and quantify the residual stresses induced in Ti-6Al-4V, SS 316L and Invar 36 during the SLM process and investigate their relationship with thematerial thermal properties. A cantilever beam, Figure 2a, was designed to assess the part distortions, and a cube, Figure 2b, was designed to measure the residual stress evolution. The cantilever beam method is commonly used in the literature (Papadakis et al., 2014a; Papadakis et al., 2014b, Li et al., 2017;Mugwagwa et al., 2018) to assess distortions of SLMparts. Influence of thermal properties Mostafa Yakout, M.A. Elbestawi, S.C. Veldhuis and S. Nangle-Smith Rapid Prototyping Journal Volume 26 \u00b7 Number 1 \u00b7 2020 \u00b7 213\u2013222 Table I shows the optimal SLM process conditions for Ti-6Al-4V, SS 316L and Invar 36 parts for minimal defect evolution as reported in the literature (Liu et al", + " The model was able to illustrate the relative differences in the deflection trends observed for the three materials. Both experimental and numerical results showed that the deformation because of residual stress of Ti-6Al-4V cantilever was more than twice that of SS 316L. Invar 36 cantilever had the lowest deformation and accordingly the lowest residual stresses. The directional residual stress wasmeasured on the cubes using the XRD method, which determines the stress tensor based on lattice strain measurements. The measurements were taken on the top and lateral surfaces of each cube, as shown in Figure 2b. Two directional stresses were measured in ten sub-surfaces for each point. The top surface measurements represent the horizontal residual stresses (sx, s y), and the lateral surface measurement represents the vertical residual stress (s z). Figure 12a shows the evolution of residual stresses as measured using the XRDmethod, and Figure 12b shows the evolution of residual stresses as predicted using the ANSYS\u00a9 model. The trends seen in the numerical results agreed with the experimental results, but the prediction accuracy for the simulations was found to be better for the vertical residual stresses rather than the horizontal residual stresses" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.25-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.25-1.png", + "caption": "Fig. 2.25 Kinematic schematic of a belt-type stacker for strip mining 1 swivel axis; 2 motor; 3 coupling; 4, 5 gear mechanism; 6 top section", + "texts": [ + "242), the effective work during the operating cycle due to the pressing action is WN = \u2212 8\u03c0\u222b 0 Mt(\u03d52)d\u03d52 = F0r4 \u03beS5 l5 r2 r3 4\u03c0\u222b 0 sin \u03d52 4 d\u03d52 + 8\u03c0\u222b 4\u03c0 0d\u03d52 = 8F0r4 \u03beS5 l5 r2 r3 = 3420 N \u00b7m. (2.266) 2.4 Kinetics of Multibody Systems 133 At the mean angular velocity of \u03c92m = 76, 4 s\u22121, the effective mechanical power is Pm = WN/T = 3420 N \u00b7m/0, 329 s = 10, 4 kW. The mean input torque Man = 272 N \u00b7m that results from all four moment components yields a total power of Pm + Pv = Man\u03c92m = 272 \u00b7 76, 4 W = 20, 8 kW. According to (2.237), the efficiency of this press drive is only about \u03b7 = 0.5. The grossly simplified calculation model shown in Fig. 2.25 reflects the drive system of a belt-type stacker used for dumping overburden in strip mining. The slewing gear, which consists of a motor, a coupling, and two gear mechanisms, sets the top section into motion. Given: moments of inertia of the motor: J2 = 2, 14 kg \u00b7m2; coupling: J3 = 1, 12 kg \u00b7m2; gear mechanism 1: J4 = 22, 6 kg \u00b7m2; referred to gear mechanism 2: J5 = 4540 kg \u00b7m2; transmission output engine room: J6 = 1, 185 \u00b7 108 kg \u00b7m2; Top section masses: m7 = 2, 05 \u00b7 104 kg; m8 = 1, 85 \u00b7 105 kg; Top section lengths: l7 = 110 m; l8 = 61 m; Gear ratios: u42 = u43 = 627; u54 = u64 = 36, 2 Note that the sequence of indices is relevant for the gear ratio (\u03d5\u2032 k = u2k = 1/uk2) and that it is defined as the ratio of input to output angular velocities, see (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002517_1.4033662-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002517_1.4033662-Figure15-1.png", + "caption": "Fig. 15 Sectioned view of the mesh, showing how the element sizes vary in the z direction", + "texts": [ + "org/about-asme/terms-of-use with Inconel VR 625 (a\u00bc 2.87 mm2/s), a heat source speed vs\u00bc 650 mm/s, and a source radius c\u00bc 0.1 mm. Because this particular speed has not been investigated previously, it is not obvious what time increment Dt would be appropriate for an LI model of the process. Substituting these parameters as well as A\u00bc 1.92 and B\u00bc 0.500 into Eq. (25) yields Dt\u00bc 0.00136 s or Ds\u00bc 8.82. This time increment could then be used as an initial guess before performing a full convergence study to determine the optimal increment (Fig. 15). While powder bed processes are capable of producing parts with smaller dimensional tolerances than those produced by other AM processes, they are difficult to model because of their small heat source radii. Adaptive meshing can be used to reduce the number of necessary elements, but not the number of time increments. The heat input models proposed here can significantly reduce the number of increments while giving the displacement results within 10% of Goldak\u2019s model or to any desired level of accuracy" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.23-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.23-1.png", + "caption": "FIGURE 4.23. A pyramid.", + "texts": [ + " What is th e final position of a point at B r p = [10 0 0 r after the central screw s(4, 30 deg, J) followed by s(2,30 deg,i) and s(-6,120 deg, K)? 22. * Screw composit ion. Find the final posit ion of a point at B r p = [ 10 0 0 r afte r a screw followed by 23. * Plucker line coordinat e. Find th e missing numb ers l = [1 /3 1/ 5 ? ? 2 -1 r. 4. Motion Kinematics 197 24. * Plucker lines. Find the Plucker lines for AE, BE, GE, DE in the local coordinate B , and calculate the angle between AE, and the Z-axis in the pyramid shown in Figure 4.23. The local coordinate of the edges are A(l , 1, 0) B(-l ,l ,O) G(-l ,-l ,O) D( l , -1, 0) E(O,0, 3). Transforms the Plucker lines AE, B E , GE, DE to the global coor dinate G. The global position of 0 is at 0(1,10 ,2 ). 25. * Angle between two lines. Find the angle between 0 E , 0 D, of the pyramid shown in Figure 4.23. The coordinates of the points are D(l , -1, 0) E(O,0, 3). 26. * Dist ance from the origin. The equat ion of a plane is given as 4X - 5Y - 12Z - 1 = O. Determine th e perp endicular distance of the plane from the origin . 5 Forward Kinematics 5.1 Denavit-Hartenberg Notation A series robot with n joints will have n + 1 links. Numbering of links starts from (0) for the immobile grounded base link and increases sequentially up to (n) for the end-effector link. Numbering of joints starts from 1, for the joint connecting the first movable link to the base link, and increases sequentially up to n " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001078_j.ijheatmasstransfer.2013.04.050-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001078_j.ijheatmasstransfer.2013.04.050-Figure1-1.png", + "caption": "Fig. 1. Configuration of coaxial laser cladding process.", + "texts": [ + " It is found that it has potential to be applied in the thermal simulation of laser cladding with varying process parameters, considering the variation of the characteristic dimensions of deposition bead and the heat source. 2013 Elsevier Ltd. All rights reserved. As an advanced technology of material processing, Laser cladding has been applied in many aspects of industry such as surface treatment, surface modification [1], component repairing [2] and even metal rapid manufacturing [3\u20135]. As is seen from Fig. 1 that illustrates the fundamental of coaxial laser cladding, it is actually a process of depositing powder material on substrate using laser beam as a moving heat source. Due to intensive heating and rapid cool rate during laser cladding, the heat affected zone (HAZ) and melt pool are so small that a thin metallurgical bonded coating is produced between the cladding layer and substrate. Meanwhile, the temperature-dependent thermo-physical properties of material vary rapidly and phase transformation generally exists during laser cladding" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003216_physrevfluids.2.044202-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003216_physrevfluids.2.044202-Figure5-1.png", + "caption": "FIG. 5. Principal axes of the rotational mobility for a three-bead cluster.", + "texts": [ + " The following analysis based on the theory developed above is able to fill this gap. The geometry of three interconnected beads is very simple and can be characterized by a single parameter\u2014the angle of the vertex formed by the lines of centers connecting the spheres. This angle takes the values from 60\u25e6 (equilateral triangle) and 180\u25e6 (straight chain). We calculated numerically the mobility tensors of the cluster using the particle-based multipole expansion method (see, e.g., [34] for a detailed description). The principal axes of the rotational mobility F are depicted in Fig. 5 and their order is in accord with the intuitive expectations\u2014the unit vector e3 (easy axis of rotation) is oriented along the base of triangle formed by beads, e2 is parallel to the symmetry axes, and e1 (hard axis of rotation) is normal to the plane of bead centers. This order is invariant to the value of the vertex angle. The computed values of the rotational anisotropy parameters \u03b5 and p\u22121 are depicted in Fig. 6 as a function of the vertex angle. It can be readily seen that transverse rotational anisotropy is quite weak, \u03b5 0", + " It is well known that every object irrespective of shape possesses a unique geometric point (center of hydrodynamic reaction) at which the coupling resistance tensor becomes symmetric [22]. It can be shown that in a complete analogy to the coupling resistance, the coupling mobility G can always be symmetrized at the center of hydrodynamic mobility (see 044202-10 Supplemental Material [21], Sec. I), so that in particular for the three-bead cluster G13 = G31. Note that in the frame of axes shown in Fig. 5 the coupling coefficient is negative, G13 < 0. Rotation of the frame of axes in Fig. 5 about e3 by \u03c0 (i.e., e1 \u2192 \u2212e1,e2 \u2192 \u2212e2) would result in G13 \u2192 \u2212G13. Thus, it follows from Eqs. (17) and (18) that the propulsion velocity of the three-bead cluster is given by UZ \u03c9a = C\u0303h s\u03c8s2\u03b8 , (19) where a is the radius of a single bead and C\u0303h \u2261 Ch13 = 1 2a G13(F1 \u22121 + F3 \u22121) < 0 is the pseudochirality coefficient. C\u0303h is determined solely by the cluster geometry, i.e., by the vertex angle as shown by the solid (green) line in Fig. 6. It takes zero values for limiting angles of 60\u25e6 (equilateral triangle) to 180\u25e6 (straight chain) as can be anticipated from symmetry arguments and attains its extreme value C\u0303h \u2248 \u22120", + " Roughly speaking, to achieve such values of precession angles one can use magnetization along an axis inclined by = 45\u25e6 relative to the e3 axis of easy rotations. Such magnetization corresponds to equal magnitudes of the longitudinal m\u2016 and transverse m\u22a5 components of the magnetization, m\u2016 \u2248 m\u22a5. Below we vary (rotate) the orientation of the transverse magnetization component m\u22a5 while keeping m\u2016 fixed. Let us consider a few particular cases. Assume that m\u22a5 belongs to the plane of the cluster, i.e., oriented along the symmetry axis e2 (see Fig. 5) so that \u03b1 = \u03c0/2. Such magnetization results in the degenerate rotational dynamics depicted in Fig. 3 (see Supplemental Material [21], Sec. IV B for details). Similarly to a cylindrical object there are well-distinguished tumbling and wobbling regimes; in the wobbling frequency domain 044202-11 there are two symmetric solution branches with the same magnetic energy. For tumbling motion \u03b8 = \u03c0/2 and the propulsive velocity (19) vanishes. In the wobbling state, the two symmetric solution branches yield propulsion with the same speed in the opposite directions", + "615 the net propulsion is along the Z axis (movie 1), while for \u03b82 = 2.52 the cluster moves in the negative Z direction with the same speed (movie 2). In all movies, the red arrow attached to the cluster marks the orientation of the magnetic moment and the blue arrow illustrates the driving magnetic field. Notice the similarity between the animations here and the experimental video in Ref. [20]. Now assume that m\u22a5 is orthogonal to the cluster plane, i.e., directed along the hard axis of rotation, e1 (see Fig. 5), so that \u03b1 = 0 or \u03b1 = \u03c0 . As in the previous subsection, this magnetization also corresponds to a symmetric rotational pitchfork bifurcation shown in Fig. 3 (see Supplemental Material [21], Sec. IV B for details). The dependence of the cluster propulsion velocity on actuating frequency proves to be essentially different from the case of \u03b1 = \u03c0/2, since now the three-bead achiral cluster possesses the same propulsion velocity (along the Z axis) in the two wobbling regimes, as the two solutions [red and blue curves in Fig", + " 8), which is here equivalent to the transformation m\u22a5 \u2192 \u2212m\u22a5. Space inversion reverses the sign of the propulsion velocity, UZ \u2192 \u2212UZ , as discussed in Sec. IV. In other words, the direction of propulsion of the geometrically achiral cluster in rotating magnetic field depends on the mutual orientation of three vectors\u2014the longitudinal m\u2016 and transverse m\u22a5 components of the magnetic 044202-13 moment and the vector e2 pointing away from the vertex formed by the three spheres of the cluster (as shown in Fig. 5). For clusters with a right-handed triad of vectors {m\u2016,m\u22a5,e2} taken in the indicated order, the object would propel in the positive Z direction similarly to a right-handed helix [as in Fig. 7(b)], whereas the cluster with left-handed triad would move in the negative Z direction similarly to a left-handed helix [mirror-symmetric image of the velocity dependence in Fig. 7(b) about the frequency axis]. Under space inversion the geometrically achiral shape in Fig. 8 and its mirror image are superimposable on each other by applying extra rotation", + " Like the three-bead cluster, the propulsion of the arc-shaped magnetic particle in a rotating magnetic field is governed by a single pseudochirality coefficient C\u0303h, which is a function of a single parameter\u2014the arc central angle \u03b2 (see Fig. 14). However, there is a difference in rotational anisotropy between the arc and three-bead cluster: for the arc with a central angle \u03b2 100\u25e6 the principal rotation axes e1 and e2 interchange, so that the symmetry axis becomes the hard axis of rotations, e1, as shown in Fig. 14 (compare to Fig. 5). As a result of that, the nontrivial coefficients of the coupling mobility matrix G are G23 = G32. Note that in the axes frame shown in Fig. 14 the value of the coupling mobility coefficient proves to be positive, G23 > 0. 044202-20 The velocity of the arc propulsion is [cf. with Eq. (19) of the speed for three bead cluster] U arc Z \u03c9a = C\u0303h c\u03c8s2\u03b8 , (26) where C\u0303h \u2261 Ch23 = 1 2a G23(F2 \u22121 + F3 \u22121) > 0. The search for the optimal achiral arc propeller involves geometry and magnetization optimization" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000770_j.jmps.2012.09.017-Figure16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000770_j.jmps.2012.09.017-Figure16-1.png", + "caption": "Fig. 16. Setup of the buckling of a straight rod on a foundation. A rod with elliptical cross section is attached to a foundation, the z-axis. An increase in length leads to a buckling instability.", + "texts": [ + " Note also that the linear analysis presented here can also be completed by a general weakly nonlinear analysis to obtain the amplitude as a function of the load (see for instance Lange and Newell, 1971; Goriely and Tabor, 1997b). In the previous section, the rod was assumed to remain planar. This is a very typical assumption in models of rods on foundations. However, the question remains whether a planar deformation is a valid assumption. Here we explore this issue in the context of a rod with non-circular cross section. The setup is pictured in Fig. 16. We assume an infinite, extensible, naturally straight rod that is positioned in its initial configuration parallel to the z-axis and take the foundation to be the z-axis. The cross section is assumed elliptical, with antipodal points at distances a1 and a2 from the centre of the ellipse, and aligned along the x and y directions, respectively, in the initial configuration. As in the previous section, we compute the critical growth at which the rod buckles to a non-straight configuration, but here we allow for a fully general three-dimensional deformation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.13-1.png", + "caption": "FIGURE 4.13. Spherical coordinates of a point P.", + "texts": [ + " Motion Kinemat ics 153 drical coordinates C(Onpz) to Cart esian coordinates G(OXYZ) is GTc \u00bb., Rz,'P Dx ,r [ 1 0 0 0 1 ['~ ~ - sin e 0 ~ 1l ~ 0 0 ~ 1 o 1 0 0 sin c cos cp 0 1 0 001 z 0 0 1 0 1 000 1 0 0 0 0 0 [ 'OO ~ - sin

0. Figs. 9\u201311 represent the results for the tooth segment of m \u00bc 1 defined in Fig. 6. As the contact moves from the SAP to the tip, the histories of the multi-axial stress state are recorded for every material point considered. Using these stress histories, the fatigue fracture plane that is assumed to be the plane experiencing the maximum normal stress amplitude is searched with an angle increment of 1 . Rotating from the fracture plane by the angle h (Eq (19a)), the characteristic plane is then arrived [8], on which the fatigue damage is evaluated according to the fatigue criterion of Eq. (18) and the fully reversed axial and torsional fatigue strength of the steel to determine the fatigue life K\u00f0/;Y; Zm\u00de for point \u00f0/;Y ; Zm\u00de as defined in Fig. 6. The micro-pit crack nucleation life distribution for the tooth segment of m \u00bc 1 is plotted in Fig. 12. The fatigue lives of the material points are seen to range between 106 and 1010 cycles within the depth of 4 lm. Comparing the fatigue lives along Y, the crack nucleation sites are observed to be on the surface for most of the asperity highlands where asperity contacts take place to induce large local stress concentrations, agreeing with the experimental observations [4]. For the locations where no severe asperity interaction occurs (roughness valleys for instance), the cracks are mostly initiated below the surface while still in a very shallow location of about 2 lm in depth" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001971_s00339-018-1737-8-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001971_s00339-018-1737-8-Figure5-1.png", + "caption": "Fig. 5 The schematic diagram of the focusing of F \u2212 \u03b8 lens", + "texts": [ + " [30, 36, 37]: (8) T z = Aq(x, y, z, t) \u2212 hc ( T \u2212 T0 ) \u2212 r s ( T4 \u2212 T4 0 ) \u2212 qev, (9)q(x, y, z) = 2AP 2 exp ( \u22122 r2 2 ) , Thermal dynamic behavior during\u00a0selective laser melting of\u00a0K418 superalloy: numerical\u2026 1 3 Page 5 of 16 313 where P is the laser rated power, is the radius of the Gaussian laser beam, q(r) means the heat flux at a distance r from the center of the circle where |x| and |y| denote the distance along the X and Y axes, respectively, and v is the laser scanning speed. The absorptivity of the material to the laser beam is relative to the thermal physical parameters of the material, material porosity, the laser wavelength, and laser incident angle. Due to the smaller laser scanning area of 100\u00a0mm \u00d7 100\u00a0mm and the larger focal length (H = 330\u00a0mm) of the F \u2212 \u03b8 lens as seen in Fig.\u00a05, the laser beam can be approximately considered as perpendicularly irradiate on a substrate pass through an F \u2212 \u03b8 lens, i.e., the incident angle is 90\u00b0in simulation. In this work, the absorptivity A of the fiber laser beam by nickel-based alloy powder bed was settled as 0.6 according to Gusarov et\u00a0al. [38]. The full heat-flux boundary condition at the free surface is given by where the Stefan\u2013Boltzmann constant s is 5.67 \u00d7 10\u2212 8\u00a0W/ (m2\u00a0K4). During the SLM process, at higher energy inputs, some liquid metal evaporates and accumulates above the molten pool, forming a so-called Knudsen layer [39, 40]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure8.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure8.5-1.png", + "caption": "FIGURE 8.5. Singular configurations of a 2R planar manipulator.", + "texts": [ + " Velocity Kinematics 365 locity kin ematics are also found in Example 212 as Jq [ -hS01 - 12s (01+O2) h C01 + 12 c (01+ O2) The inverse velocity kinematics needs to find the inverse of the Jacobian . Therefore, J - 1 X [ -h S01 - 12s (01+ O2) hC01 +12C(01 +02) where, and hence, ih = Xc(01 + O2 ) + Ys (01 + O2 ) hS02 8 2 = X(hC01 + 12C(01 + O2)) + Y(hS01 + bs (01+ O2)) . -h12s02 Singularity occurs when the determinant of the Jacobian is zero. Therefore, the singular configurations of the manipulator are O2 = 180deg (8.149) (8.150) (8.151) (8.152) corresponding to the fully extended or fully contracted configurations, as shown in Figure 8.5. At the singular configurations, the value of 01 is inde terminate and may have any real value. The two columns of the Jacobian matrix become parallel because the Equation (8.145) becomes (8.153) In this situation, the endpoint can only move in the direction perpendicular to the arm links . 366 8. Velocity Kinematics Example 220 Analytic method for inverse velocity kinematics. Theoretically, we must be able to calculate the joint velocities from the equations describing the forward velocities, however, such a calculation is not easy in a general case" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002212_s00170-016-9510-7-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002212_s00170-016-9510-7-Figure11-1.png", + "caption": "Fig. 11 Fixture dimensions a two-dimensional drawing and b substrate fitted in fixture", + "texts": [ + "0 m/min, the corresponding\u0394t value will be 0.015 s. Based on these and the material thermal diffusivity (obtained from Fig. 7(a)), the Courant number, C will be 0.4758 which satisfies the convergence and stability criteria as mentioned above. To validate the FE analysis presented above, multi-pass welddeposition was carried on a C45 substrate plate with dimensions 160 \u00d7 160 \u00d7 10 mm and the residual stresses generated in the same was compared with that obtained from simulations. The fixture design for the same is shown in Fig. 11. Design of fixture is important while conducting experiments: if the specimen is allowed to cool down without end constraints, the residual stress induced within the material will try to relieve in the form of warping of the substrate plate. However, in FE analysis, residual stresses are quantified rather than warping deformations. Hence, the clamped conditions in the experiments are maintained till the residual stresses are measured in the completely cooled condition, as explained in the subsequent part of this section. The clamping of the substrate is done with the help of two center-cut square plates encompassing the edges of the substrate as shown in the Fig. 11a. The substrate is sandwiched between these plates, along with heat insulation strips between them, to constraint and insulate the substrate, respectively (Fig. 11b). The following are other considerations to be taken into account for the fixture design: & Equal and uniform force should be exerted throughout the boundary of the plate. & Proper clearance should be provided for the movement of the weld torch and for the movement of the XRD probe for residual stress measurement. & Deposited area of the substrate plate and its bottom surface should not be in contact with any other material (i.e., heat loss is through convection and radiation only). & The fixture should be able to withstand the force exerted due to the induced residual stress. The experiments were performed using twin-wire welding setup consisting of two TransPuls Synergic (TPS) power units integrated with the robotic position manipulator, shown in Fig. 12. These experiments were conducted on substrate as shown in Fig. 11b. The weld- deposition was carried out on an area of 80 \u00d7 31.5 mm at the center of the substrate plate with a step-over increment of 3 mm between the passes. The process parameters used are listed in the Table 1. Figure 13a shows the fixture before deposition and Fig. 13b, c shows the top and bottom view of the substrate after deposition obtained using spiral-in pattern. Residual stresses were measured using pro-XRD residual stress measuring instrument shown in Fig. 14. Residual stress was measured on top and bottom of the substrate along diagonal and axial directions (represented by yellow and green lines, respectively) as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure13-1.png", + "caption": "Figure 13. Displacement mode of the gearbox housing.", + "texts": [ + " From Figure 11(c), it can be seen that the vibration of the gearbox housing is induced mainly by the 20thorder polygonal wear. Compared to the vibration at the frequency of 672Hz, the vibration is obviously at a high level at the frequency of 573Hz. To understand the effects of polygonal wear on the dynamic performance of the gearbox housing, the responses of the gearbox housing are simulated at different speeds. Figure 12 shows the variation of the acceleration responses of the gearbox housing with increasing velocity. Figure 13 shows the displacement mode of the gearbox housing at the frequency of 580Hz and the locations of monitors 1\u20133. It can be seen from Figure 12 that the trends of the maximum amplitude and RMS acceleration increase as the vehicle velocity increases. In addition, at the speeds of 150 and 300 km/h, the maximum amplitude and RMS acceleration are relatively higher. According to the results of the modal analysis of the gearbox housing, the excitation frequency of the 20th-order polygonal wear is 576Hz at the speed of 300 km/h, which is close to the natural frequency of 580Hz of the gearbox housing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001693_1.4003595-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001693_1.4003595-Figure1-1.png", + "caption": "Fig. 1 The global contact patch in the elastic microcontact model consists of a certain number of statistically distributed similar contacts at summits \u202017\u2021", + "texts": [ + " 3 Single summit deforms elastically corresponding to the Hertzian contact theory as follows: single contact area:Ai = ri i 2 single contact force:Fi = 4 3 E ri 1/2 i 3/2 3 where i is the average summit height reduction and E is reduced Young\u2019s modulus, 1 /E = 1\u2212v1 2 /E1+ 1\u2212v2 2 /E2, E and are the Young modulus and Poisson ratio, respectively, and indices 1 and 2 refer to bodies 1 and 2. 4 Summit heights expressed as a deviation from the mean plane of the summits are a random variable with a standard deviation s and surface density of summits . 5 The contact of two rough surfaces depends on the relative profile of two surfaces and can be considered as a contact of an elastic rough surface having effective modulus of elasticity E and relative profile of two surfaces with a smooth rigid surface. Figure 1 shows an elastic microcontact model; the global conact patch consists of a certain number of statistically distributed imilar contacts. The classical Hertzian theory is assumed to hold t each single microcontact, and the applied load is carried out on ontacting summits. When a rough elastic cylinder or a sphere rolls over a rough lastic surface, the global static load has to be supported by a ertain number of summits within the nominal contact patch durng any time increment. The number of contact points can be stimated by the product of summit density and contact area obained from the classic Hertz theory: n = Ac 4 uring rolling, a single summit comes into the contact area and ontributes in load carrying for a small span of time and then goes ut of the contact area" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure9.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure9.3-1.png", + "caption": "Figure 9.3.1 Compliance steer and compliance inclination angles for a single wheel: (a) steer angle in plan view; (b) inclination angle in rear view; (c) hub pitch angle in side view.", + "texts": [ + "4 The total wrench at the base of a wheel, exerted by the ground on the wheel, analysed as six force\u2013moment components, SAE system. Figure 9.2.3 The total wrench at the base of a wheel, exerted by the ground on the wheel, analysed as six force\u2013moment components, ISO system. Compliance Steer 181 Apart from the ride-improving properties of the suspension compliance, the most important compliance effects are those directly affecting the handling qualities, specifically the compliance steer angle and the compliance camber angle or compliance inclination angle, Figure 9.3.1. Considering these angles, for a given design of suspension location system with its rubber bushes, reveals the critical aspects of the suspension in this regard. The steer angles are measured from a line parallel to the vehicle centreline, with a total steer angle which is simply the sum of the geometric and compliance angles: d \u00bc dG \u00fe dC \u00f09:3:1\u00de Similarly, the inclination or camber angles may be measured from the perpendicular to the road surface, with g \u00bc gG \u00fe gC \u00f09:3:2\u00de Also, for pitch angle (caster angle) of the wheel hub, u \u00bc uG \u00fe uC \u00f09:3:3\u00de The pitch angle variation changes the caster angle of the wheel upright. With positive rotation as righthand about the Y-axis, the static caster angle would be negative, so this sign convention is rarely applied. Figure 9.3.1(c) shows positive values of uG and uC, caster being simply taken as positivewhen the steering axis leans backwards.. Thewheel hub pitch angle is not necessarily identical to the caster angle, the former possibly being defined as zero in the static position, although the difference will be constant at the static caster minus static hub pitch angle. The total force and moment wrench at each independent wheel contact patch is considered as three force and three moment components: FX, FY, FZ, MX, MY, MZ" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001150_physrevlett.103.138103-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001150_physrevlett.103.138103-Figure1-1.png", + "caption": "FIG. 1 (color online). Schematic representation of the experimental setup and a summary of observations. (a) E. coli were subjected to shear flow just over the bottom surface in a singleinlet single-outlet microfluidic device. (b) The position, orientation, and projected dimensions of the imaged cells were tracked as they drifted within the field of view of a 40 phase-contrast objective. Here, this composite image incorporates the minimum pixel value in every third frame within a 1.5 s observation window (scale bar: 5 m). (c) Within the resolution of our experiment, a given bacterium\u2019s center appeared to follow a straight line along the downstream direction and parallel to the bottom surface. (d) Cells exhibited modified Jeffery orbits within the relative coordinate system that drifts with a given bacterium\u2019s center.", + "texts": [ + " Although it may be presumed that nonflagellated, rodshaped bacteria will also be subject to modified Jeffery orbits in shear flow near a boundary, we are aware of no prior experimental work characterizing this phenomenon. To investigate the hydrodynamic interactions between bacteria cell bodies and a bounding wall in shear flow, we fabricated single-inlet/single-outlet microfluidic devices using soft lithography [15], and subjected nonflagellated E. coli K12 derivatives (YK4116 [16]) to various laminar flow regimes. A glass slide was coated with a 30 m layer of polydimethylsiloxane prior to attachment of the top mold to create an all polydimethylsiloxane microchannel [Fig. 1(a)]. In experiments, bacteria were harvested during their log phase, suspended in Luria-Bertani broth at room temperature and allowed to precipitate to the bottom surface of the channel. A sterile, equal-part mixture of LuriaBertani broth and glycerol was then pumped into the microchannel with a calibrated syringe pump at flows ranging from 100 l=min up to 3:5 ml=min (see supplementary information [17]). A Navier-Stokes solver in COMSOL MULTIPHYSICS was used to calibrate the vertical gradient of flow (henceforth called \u2018\u2018shear rate,\u2019\u2019 or ) along the bottom surface (see supplementary information [17], Figs. S1 and S2). The mixture\u2019s high viscosity (10 mPa s) partly suppressed both translational and rotational Brownian motion, enabling an easier observation of hydrodynamic effects as the cells drifted through the field of view [typically, within a few seconds at lowest flow rates; Fig. 1(b)]. In addition, we observed no noticeable sedimentation of bacteria within the short observation window, owing, in part, to the high viscosity of this mixture. Cells were imaged from below through a 40 phase-contrast objective (numerical aperture \u00bc 0:65; depth of focus \u00bc 2 m) via a high-speed, highresolution video camera at 60 frames=second. Resulting image sequences were analyzed offline in MATLAB. Positions of bacteria body centers did not change appreciably along either the x or z direction during observation PRL 103, 138103 (2009) P HY S I CA L R EV I EW LE T T E R S week ending 25 SEPTEMBER 2009 0031-9007=09=103(13)=138103(4) 138103-1 2009 The American Physical Society [Fig. 1(c)]. Within a coordinate system that drifts with a given bacterium\u2019s center, the cells executed closed orbits [such as in Fig. 1(d)], as expected (see supplementary movies [17]). Bacteria images obtained through phase-contrast light microscopy were inherently subject to diffraction effects. To accurately calibrate bacterial dimensions, we used transmission electron microscopy (TEM) images of cells harvested simultaneously with those imaged via light microscopy. Observed bacterial widths were narrowly Gaussian; cell body lengths displayed a log-normal distribution [Fig. 2(a)]. Cells suspended in Luria-Bertani broth at room temperature were sampled and characterized with TEM periodically, and their size distribution remained unchanged over the course of the experiment (up to six hours)", + " 3(d)] between the xy plane and the bacterium\u2019s principal axis. As a cell follows a particular Jeffery orbit with constant drift velocity [v in Fig. 3(c)], it invariably passes through an orientation parallel to the bottom surface [ \u00bc 0 in Fig. 3(d)]. In that instant, the apparent length of its image projected onto the xy plane is at its maximum (Lmax). Hence, the ratio L=Lmax can be used to reasonably estimate through the inverse cosine of the ratio L=Lmax. Jeffery\u2019s original analysis may be adapted to include the axes defined in Fig. 1 and the angles c and depicted in Fig. 3 through a simple coordinate transformation (see supplementary information [17]). For a closed Jeffery orbit, equals zero when the value of c is at either extreme. By simply using either c extremum (when \u00bc 0) as an initial condition to a Jeffery\u2019s orbit, the orbital trajectory of that cell can be fit rather well [Fig. 3(d) and 3(e)]. In Fig. 3, we have deliberately chosen to depict a slightly asymmetrical cell, which displays a corresponding mismatch in the length of any two consecutive half periods of its Jeffery orbit" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000641_1.4004683-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000641_1.4004683-Figure2-1.png", + "caption": "Fig. 2 Three-dimensional FE model of the pinion with a 100% crack", + "texts": [ + " According to the above analysis and hypothesis, the Hertzian stiffness and the axial compressive stiffness between meshing teeth are constant when the crack length grows, while the bending stiffness and the shearing stiffness of the pinion vary with the growth of the crack length. We will label the stiffness calculation method proposed in Ref. [14] as \u201cTian\u2019s method\u201d (with the additional shear energy taken into account), and the calculation method used in this paper as \u201cProposed method\u201d (considering that the gear body is no longer a rigid body). To confirm the accuracy of the proposed gear pair meshing stiffness calculation method when there is a crack in the pinion, the meshing stiffness calculated from software (ROMAX and ANSYS) are used. Figure 2 shows the 3D finite element model of the pinion with a 100% crack used in the FEA with the same parameters. According to the Ref. [20], the internal diameter of pinion and gear are clamped, and the uniform distributed force which stand for the action of the meshing tooth of gear pair are applied along the action line at the appropriate mesh angle to the involute profile, so we can get the deflections of the pinion and the gear, and then get the meshing stiffness between the meshing teeth at this mesh point" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000658_tcom.1977.1093835-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000658_tcom.1977.1093835-Figure2-1.png", + "caption": "Fig. 2. Resolution into data pulses, n = 2, @ = n/2. (a) In-phase Fig. 3. Resolution into data pulses, n = 2, @ = 0. (a) Quadrature pulses. (b) Quadrature pulses. (c) Transmitted total. pulses. (b) In-phase pulses. (c) Transmitted total.", + "texts": [ + " For some selected integer I 2 n + l f2 =- 2 T n 2 T f1=- . (1) Paper approved by the Editor for Communication Theory of the IEEE Communications Society for publication without oral presentation. Manuscript received August 18, 1976; revised December 17, 1976. CA 92634. The authors are with the Hughes Aircraft Company, Fullerton, In random data transmission, the resulting spectrum will be centered on an apparent carrier located at f, = (211 + 1)/4T. The frequencies fl and f2 have been referred to [3 I as mark and space frequencies, respectively. Fig. 2 shows the MSK wave synthesized as the sum of a stream of modulated pulses at the bit rate 1/T for the choice n = 2. Strictly for graphical clarity, the successive pulses are shown alternately in Fig. 2(a) and (b). Note that all pulses are identical except for sign and time displacement. There is a regular time overlap between the pulses in Fig. 2(a) and those in Fig. 2(b), and the MSK wave of Fig. 2(c) is at all times the sum of two such overlapping pulses. Note that the frequency turns out to be constant over each interval of duration T, as prescribed in the MSK format. A distinct, but equally legitimate MSK wave for IZ = 2 is given in Fig. 3. The transitions between fi and f2 take place at the peaks of the wave rather than at the zero crossings, which was the case in the more familiar form of Fig. 2. The enhanced waveform continuity in Fig. 3 is the result of the different forms of basic pulses shown in Fig. 3(a) and (b). Here the pulses have zero slope at the bit boundaries, a property not found in Fig.2. The signs and time placements of pulses in This expression for p(t) is consistent with the prevailing concept of MSK pulse structure. The factor sin nt/2T is the individual pulse modulation envelope, shown as dashed lines in Figs. 2 and 3. The factor sin [ ( ( ~ I z -t l ) /%T)nt + @ I represents the apparent carrier at f,. To confirm that overlapping pulses appear to derive from \u201cin-phase\u2019\u2019 and \u201cquadrature\u201d sources of f,, it is only necessary to note that which means that from pulse to pulse the phase off, appearing in the pulse is, with respect to some reference phase, shifted by some odd multiple of n/2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure4.22-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure4.22-1.png", + "caption": "Fig. 4.22 Motorbike engine; a) Schematic of the power unit, 1 Piston, 2 Generator armature, 3 Crank mechanism, 4 Clutch, b) Vibration model", + "texts": [ + "126) with the Fourier coefficients Am = (1\u2212m2\u03b72)am \u2212 2Dm\u03b7bm (1\u2212m2\u03b72)2 + (2Dm\u03b7)2 m2\u03b72; Bm = 2Dm\u03b7am + (1\u2212m2\u03b72)bm (1\u2212m2\u03b72)2 + (2Dm\u03b7)2 m2\u03b72. (4.127) The frequency ratio \u03b7 = \u03a9/\u03c90 was introduced here. The following applies for the amplitude of the mth harmonic: Cm = \u221a A2 m + B2 m = m2\u03b72 \u221a a2 m + b2 m\u221a (1\u2212m2\u03b72)2 + (2Dm\u03b7)2 . (4.128) If the circular frequency of the excitation m\u03a9 of the mth harmonic coincides with the natural circular frequency \u03c90 , m\u03b7 = 1 and the following estimate applies to the resonance amplitude: |q|max Cm max \u2248 Cm(\u03b7 = 1/m) = \u221a a2 m + b2 m 2D . (4.129) 4.3 Forced Vibrations of Discrete Torsional Oscillators 263 Figure 4.22 shows the power unit of a motorbike engine and its calculation model. The engine is a two-stroke engine. Periodic excitation with four harmonics occurs: M2 = 4\u2211 m=1 M\u03022m sin(m\u03a9t + \u03b1m). (4.130) Based on the given mass and spring parameters J1 = 1.027 \u00b7 10\u22122 kg \u00b7m2; cT1 = 25.9 \u00b7 103 N \u00b7m J2 = 0.835 \u00b7 10\u22122 kg \u00b7m2; cT2 = 20.6 \u00b7 103 N \u00b7m J3 = 0.079 \u00b7 10\u22122 kg \u00b7m2, (4.131) the natural frequencies of the undamped system are derived from (4.12): f1 = 0; f2 = 366 Hz; f3 = 853 Hz. (4.132) With the help of known software, the steady-state periodic vibrations are calculated from (4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure11-1.png", + "caption": "Fig. 11. Schematic illustrations of: (a) boundary conditions for the pinion and the gear, and (b) reference node of the rigid surface of the pinion.", + "texts": [ + " This establishes the number of elements in the sensitive-contact region as (2Nb+6) \u22c5Na \u22c5Nd. (vi) Size of the elements located out of the sensitive-contact region increase exponentially from such a region towards the borders or the intermediate surfaces of the tooth model. Number of elements in profile, longitudinal, and inner directions are controlled by numbers Np, Nl, and Ns, respectively. A summary of the set of variables for mesh refinement control is shown in Table 1. Step 6 Setting of boundary conditions are accomplished as follows (Fig. 11): (i) Nodes on the two sides and bottom part of the gear rim are encastred (Fig. 11(a)). (ii) Nodes on the two sides and bottom part of the pinion rim form a rigid surface (Fig. 11(a)). (iii) A reference node N located on the axis of the pinion is used as the reference point of the previously defined rigid surface (Fig. 11(b)). Reference point N and rigid surface constitute a rigid body. (iv) Only one degree of freedom is defined as free at the reference point N\u2014rotation about the pinion axis\u2014while all other degrees of freedom are fixed. Application of a torque T1 in rotational motion at the reference pointN allows to apply such a torque to the pinion model while the gear model is held at rest. Step 7 Elements of first order have been considered in the finite elementmesh. This type of elements is recommended for contact simulations [15]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000360_13506501jet656-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000360_13506501jet656-Figure3-1.png", + "caption": "Fig. 3 The contact of an ideally smooth elastic sphere with an ideally smooth (broken line and contact radius rs) and a randomly rough (solid line and contact radius rr) flat surface, and the respective normal pressures [10]", + "texts": [ + " Engineering Tribology JET656 at TOBB Ekonomi ve Teknoloji \u00dcniversitesi on April 26, 2014pij.sagepub.comDownloaded from occur in spherical roller bearings but not in cylindrical roller bearings. Real bodies have form errors, surface waviness, and surface roughness due to the surface manufacturing and previous operation. In contacts between rolling elements and raceways, the real contact area is smaller than the apparent one and the border of the real contact area may expand outside that of the theoretical one (see Fig. 3) [10, 14]. Rolling contacts comprise dynamically varying stress fields from surface roughness and contaminant particles. A wave motion initiated from any point of dynamic stress propagates as spherical fronts of pressure and shear waves [10, 15]. The interaction of pressure and shear waves with the free surface gives rise to the Rayleigh wave, which is a surface wave. In rolling contact, fatigue crack formation and contaminant particle crushing introduce high-frequency vibrations. Figure 4 shows the principle for the propagation of high-frequency vibration waves" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000701_ichr.2010.5686316-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000701_ichr.2010.5686316-Figure4-1.png", + "caption": "Fig. 4. Layout of the muscles. The symbols are, Gmin: gluteus minimus muscle, ADD: adductor muscles, Gmax: gluteus maximus muscle, IL: iliopsoas muscle, HAM: hamstrings, RF: rectus femoris muscle, VAS: vastus muscles, SOL: soleus muscle, TA: tibialis anterior muscle, respectively.", + "texts": [ + " In use of pneumatic actuator driven by pressured air is not suitable for the precise position/angle control application. In contrast, we can control force/torque with relatively ease by the control of the air pressure. We employ custom-made proportional pressure control valve to control the inner pressure of the muscles. The robot with musculoskeletal mechanisms and the controller of the muscle tension force is an appropriate platform for bipedal running with the force control. The artificial musculoskeletal system of the robot is based on the anatomical structure of the human (Fig.4). We carefully chose the parameters of mono-articular and bi-articular muscles, such as diameter, length, and moment arm of the tendon-pulley unit for each muscles (Fig.5). The parameters of muscle configuration are decided by consideration of both mathematically obtained parameters using model of musculoskeletal leg and anatomical data of the human. The physiological cross-sectional area: PCSA and mass of the human muscles are reported in the literature in biomechanics [13], [14]. The lower leg of the human behaves like a non-linear spring during dynamic locomotion [15], [16]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure13.17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure13.17-1.png", + "caption": "FIGURE 13.17. An obstacle in the Cartesian space of motion for a 2R manipu lator.", + "texts": [ + " Assume that the endpoint of a 2R manipulator moves with constant speed v = 1m/ sec from PI to P2 , on a path made of two semi circles, as shown in Figure 13.16. Calculate and plot the joints' path if h = l2 = 1 m. Calculate the value and position of the maximum angular acceleration and jerk in joint variables. The center of the circles are at (0.75m, 0.5m) and (-0.75m, 0.5m). 17. * Obstacle avoidance and path planning. Find a path between PI = (1.5,1) and P2 = (-1 ,1) to avoid the obstacle shown in Figure 13.17. The path may be made of two straight lines with a transition circular path in the middle . The radius of the 13. Path Planning 605 circle is r = 0.5 m and the center of the circle is at a point that makes the total length of the path minimum. The lines connect to the circle smoothly. The endpoint of a 2R manipulator, with h = l2 = 1 m, starts at rest from PI and moves along the first line with constant acceleration. The endpoint keeps its speed constant v = 1 tu] sec on the circular path and then moves with constant acceleration on the final line segment to stop at P2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001863_j.optlaseng.2017.07.008-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001863_j.optlaseng.2017.07.008-Figure9-1.png", + "caption": "Fig. 9. Schematic diagram of the cross-section of STC.", + "texts": [ + " The ndex of P and V both are less than zero, which indicates the P and V has negative effect on H c . However, the index of T which is more than 1 hows that T is the most main effect on the H c . These results are also in greement with the analysis of Section 3.1.2 . The fitting model is also onfirmed by the residuals diagram depicted in Fig. 8 (b). .3. Geometry modeling of the sectional profile for STC In order to describe the contour profile of the cross-section for STC, circular form curve was adopted in this study. The equation of the ircular curve will be derived in detail as follows. Fig. 9 shows the schematic diagram of the cross-section of the STC. t is assumed that the cross-section could be described in a circular arc. fter measuring the cladding width ( W c ) and height ( H c ), the equation f the circular arc will be determined by three points which do not lies n a straight line. The circular arc can be expressed by Eq. (2) . 2 + ( \ud835\udc66 + \u210e ) 2 = \ud835\udc45 2 , \u2212 \ud835\udc64 \ud835\udc50 \u22152 \u2264 \ud835\udc65 \u2264 \ud835\udc64 \ud835\udc50 \u22152 (2) here x, y is the x -coordinate and y -coordinate of the circular arc, repectively. h is the distance between the center of the circle O s and the rigin of the coordinate system O . And R is the radius of the circular arc. According to the geometrical relationship presented in Fig. 9 , in the riangle of the ONO S , \ud835\udc42\ud835\udc41 \ud835\udc42 \ud835\udc60 = 90 \u25e6 \u2212 ( 180 \u25e6 \u2212 \ud835\udf03) = \ud835\udf03 \u2212 90 \u25e6 (3) = \ud835\udc42\ud835\udc41\u2215 cos ( \ud835\udf03 \u2212 90 \u25e6) = 0 . 5 \ud835\udc4a \ud835\udc50 \u2215 sin \ud835\udf03 (4) 2 = \u210e 2 + ( \ud835\udc4a \u22152) 2 = ( \ud835\udc45 \u2212 \ud835\udc3b ) 2 + ( \ud835\udc4a \u22152) 2 (5) \ud835\udc50 \ud835\udc50 \ud835\udc50 According Eqs. (4) and (5) , = 180 \u25e6 \u2212 arcsin [4 \ud835\udc4a \ud835\udc50 \ud835\udc3b \ud835\udc50 \u2215(4 \ud835\udc3b \ud835\udc50 2 + \ud835\udc4a \ud835\udc50 2 )] (6) = (4 \ud835\udc3b 2 \ud835\udc50 + \ud835\udc4a 2 \ud835\udc50 )\u2215(8 \ud835\udc3b \ud835\udc50 ) (7) = 360 \u25e6 \u2212 2 \ud835\udf03 = 2 arcsin [4 \ud835\udc4a \ud835\udc50 \ud835\udc3b \ud835\udc50 \u2215(4 \ud835\udc3b 2 + \ud835\udc4a 2 )] (8) \ud835\udc50 \ud835\udc50 \ud835\udc66 c \ud835\udc66 E \ud835\udc34 3 m Based on Eqs. (2) \u2013(4) , = \u2212 \u210e + \u221a \ud835\udc45 2 \u2212 \ud835\udc65 2 = \ud835\udc3b \ud835\udc50 \u2212 0 . 5 \ud835\udc4a \ud835\udc50 \u2215 sin \ud835\udf03 + \u221a (0 . 5 \ud835\udc4a \ud835\udc50 \u2215 sin \ud835\udf03) 2 \u2212 \ud835\udc65 2 (9) By substituting the Eq. (6) into the Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure24-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure24-1.png", + "caption": "Fig. 24. Coordinate systems applied in the generation of a helical face gear by a worm.", + "texts": [ + " The feed motion means that the installment of the worm with respect to the face-gear has to be varied in the process of generation. The worm will generate at each installment a strip on the face-gear tooth surface. In the following discussions, we initially interpret the feed motion as a discrete process. (3) New installments of the worm, the shaper, and the face-gear are performed as follows: (i) The worm is translated in the direction of the axis of the shaper on Dlw and, simultaneously, the shaper is turned on angle Dws (Fig. 24). The magnitudes of Dlw and Dws are components of screw motion of the worm about the axis of the shaper related as . Contact lines on shaper surface Rs: (a) contact lines Ls2 between Rs and R2, (b) contact lines Lsw between Rs and Rw, and (c) t lines Ls2 and Lsw for a chosen value of the parameter of motion. Dlw Dws \u00bc ps: \u00f042\u00de Here, ps is the screw parameter of the shaper. Observation of Eq. (42) allows us to provide tangency of Rw and Rs at each installment. (ii) Simultaneous tangency of three surfaces at each installment requires that the face-gear will be turned for an additional angle Dw2 determined as Dw2 \u00bc Dws Ns N 2 \u00bc Dlw ps Ns N 2 : \u00f043\u00de (4) The derivation of the face-gear tooth surface generated by the worm may be now represented as a con- tinuous two-parameter enveloping process based on application of two independent set of parameters: (i) set one formed by (ww,w2) related by Eq", + " (45) and (46) are two equations of meshing; (us,ws) are the worm surface parameters; generalized independent parameters of motion are designated as ww and Dlw and the two independent set of parameters are: (ww,w2) and (Dlw,Dw2); Nw is the normal to the worm surface at the current point of contact and is represented in system Sw; vector v \u00f0w2;ww\u00de w represents the relative sliding velocity between the worm and the face-gear determined under the condition that generalized parameter ww of motion is varied and the other generalized parameter Dlw is held at rest; similarly, vector v\u00f0w2;Dlw\u00dew represents the relative sliding velocity between the worm and the face-gear, but it is determined under the condition that the generalized parameter Dlw is varied and the other generalized parameter of motion ww is held at rest. Both vectors of relative velocity are represented in system Sw. Vector equations (44)\u2013(46), if considered simultaneously, determine surface R2 as the envelope of two-parameter enveloping process. Applied coordinate systems are shown in Fig. 24. Vector function r2(us,ws,ww,Dlw) and equations of meshing f \u00f01\u00de w2 \u00bc 0 and f \u00f02\u00de w2 \u00bc 0 represent surface R2 generated by the worm by four related parameters. The computations have been performed for determination of surface R2 twice, wherein R2 is generated by a shaper and by a worm. Comparison of the results obtained confirms the identity of the surfaces. The goals of stress analysis represented in this section are: (i) Determination of contact and bending stresses and investigation of formation of the bearing contact in a face-gear drive with a helical pinion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001994_i2mtc.2013.6555507-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001994_i2mtc.2013.6555507-Figure2-1.png", + "caption": "Fig. 2. Lighting setup. Three light sources are used independently based on the current detection scheme. Contrast between adjacent weld seams is enhanced by illumination from the right side for bead angles from 45\u00b0 to 135\u00b0 and illumination from the front for angles from 0\u00b0 to 45\u00b0 and 135\u00b0 to 180\u00b0 . Reflectors enable diffuse lighting on the work plane. Separate dark field lighting uses parallel lighting to highlight elevations .", + "texts": [ + " caused by process gas residues on optics and camera, we chose an external position. Since most LBM systems are equipped with a process window, we developed a camera mount for the machine door (Figure 1 ) , which allows flexible positioning of the camera. A geared head (Junior Geared Head by Manfrotto, Italy) enables three-axis rotations for precise alignment of camera and build platform. Two orthogonally positioned LED line lights (A = 470 nm) provide lighting for the build platform. Matt reflectors on machine back and coater (Figure 2) are used to obtain diffuse lighting from a close distance, which was found to yield the best surface images [8] . The orthogonal position was selected to deal with rotating scan patterns, which change the weld seam orientation after each layer, e .g. by 66\u00b0 , and allows to choose the optimum lighting direction which maximizes con trast. Additionally, a LED stripe with slit aperture is mounted directly above the build platform and provides parallel dark field lighting which emphasizes elevated structures " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003780_j.optlastec.2018.06.042-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003780_j.optlastec.2018.06.042-Figure1-1.png", + "caption": "Fig. 1. The established three-dimensional finite element model and multi-track scan strategy during LMD process.", + "texts": [ + " and e is the emissivity of the substrate material which can be expressed as; e \u00bc AHeH \u00fe 1 AH\u00f0 \u00deeS \u00f010\u00de where eS is the emissivity of the powder, AH and eH are the area fraction of the surface that is occupied by the radiation-emitting holes and the emissivity of the hole, respectively. The FEM was constructed as a deposition layer with shape of circular arc placed on a block as the substrate, which was based on real deposition geometry in LMD process. In transient thermal analysis, the thermal conduction element SOLID70 was utilized to mesh entire FEM. The mesh density affects the calculation accuracy and the calculation time directly, so a non-uniform mesh was used to assure the accuracy of the simulation and reduce the computational cost. The FEM model is shown in Fig. 1 During LMD process, laser beam was directed onto substrate surface to create a moving molten pool, which contributed to the formation of strong temperature gradient in the whole molten pool. Hence, fine mesh was utilized in deposited layer and the contact area with substrate [14]. Multi-track laser melting deposition process with laser power of 800 W, scanning speed of 500 mm/s, and powder flow rate of 2.4 g/min was used in this simulation. In order to depict the process of mass transfer due to powder deposition on substrate, the technique of element birth and death was applied to the threedimension thermal model" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000491_978-3-540-79029-7-Figure2.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000491_978-3-540-79029-7-Figure2.1-1.png", + "caption": "Fig. 2.1a Principle circuit of a VSI inverter-fed 3-phase AC motor", + "texts": [ + " erweiterte Auflage, expert Verlag Quang NP, Dittrich A, Lan PN (2005) Doubly-Fed Induction Machine as Generator in Wind Power Plant: Nonlinear Control Algorithms with Direct Decoupling. CD Proc. of 11th European Conference on Power Electronics and Applications, 11-14 September, EPE Dresden 2005 Quang NP, Dittrich A, Thieme A (1997) Doubly-fed induction machine as generator: control algorithms with decoupling of torque and power factor. Electrical Engineering / Archiv f\u00fcr Elektrotechnik, 10.1997, pp. 325-335 Sch\u00f6nfeld R (1990) Digitale Regelung elektrischer Antriebe. H\u00fcthig Verlag, Heidelberg The figure 2.1a shows the principle circuit of an inverter fed 3-phase AC motor with three phase windings u, v and w. The three phase voltages are applied by three pairs of semiconductor switches vu+/vu-, vv+/vv- and vw+/vw- with amplitude, frequency and phase angle defined by microcontroller calculated pulse patterns. The inverter is fed by the DC link voltage UDC. In our example, a transistor inverter is used, which is today realized preferably with IGBTs. Figure 2.1b shows the spacial assignment of the stator-fixed \u03b1\u03b2 coordinate system, which is discussed in the chapter 1, to the three windings u, v and w. The logical position of the three windings is defined as: 0, if the winding is connected to the negative potential, or as 1, if the winding is connected to the positive potential of the DC link voltage. Because of the three windings eight possible logical states and accordingly eight standard voltage vectors u0, u1 ... u7 are obtained, of which the two vectors u0 - all windings are on the negative 2 Inverter control with space vector modulation potential - and u7 - all windings are on the positive potential - are the so called zero vectors. The spacial positions of the standard voltage vectors in stator-fixed \u03b1\u03b2 coordinates in relation to the three windings u, v and w are illustrated in figure 2.1b as well. The vectors divide the vector space into six sectors S1 ... S6 and respectively into four quadrants Q1 ... Q4. The table 2.1 shows the logical switching states of the three transistor pairs. The following example will show how an arbitrary stator voltage vector can be produced from the eight standard vectors. 18 Inverter control with space vector modulation Let us assume that the vector to be realized, us is located in the sector S1, the area between the standard vectors u1 and u2 (fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.12-1.png", + "caption": "Fig. 1.12 Stiffness curve with engaged teeth; a) Contact ratio \u03b5 = 2.5, b) Contact ratio \u03b5 = 4.1", + "texts": [ + " In this model, all internal moments occur at the same time, there are no oscillations, and the time-variant moments are based on the kinetostatic moment distribution (see also Fig. 4.1). The model of level 2a represents a classical model of a torsional vibration system with forced excitation, which can be used to determine the natural frequencies, mode shapes and dynamic moments (see Sections 4.2 through 4.4). In such models, the determination of the real torsional stiffnesses can be problematic (see Table 1.5). Parameter excitation, which occurs in cases of temporally varying tooth stiffnesses, is considered in model level 2b (see Fig. 1.12 and Sect. 4.5.3.2). The model shown at the bottom of Table 1.2 includes the coupling of torsional and bending vibrations of the shafts with the elastic bearings. This is still part of the linear theory (see Problem P6.6). In this model, the masses of the gears also play a role. In a calculation model of level 3, the nonlinear characteristics of the driving and output torques, as well as bearing springs, are taken into consideration (see also Sect. 4.5.3.2). Even more sophisticated calculation models for gear mechanisms have been developed, in which, for instance, the characteristics of the bearings and gears, as well as the vibrations of the housing walls in the acoustic frequency range, are included", + "00182x2 2] N/(\u03bcm \u00b7mm) where zn1,2 = z1,2/(cos \u03b2)3, b tooth width, z1, z2 tooth numbers, x1, x2 addendum modification coefficients, \u03b2 helix angle. In (1.41), plain disk wheels and the standard reference profile (DIN 867) are assumed for the gearing. In DIN 3990, correction factors are given for using studded wheels and profiles that deviate from the standard profile to take the resulting influences on tooth stiffness into account. A variable number of tooth pairs are engaged due to the contact ratio, which causes the effective tooth stiffness during an engagement period to vary as well. Figure 1.12 shows the stiffness curve for mating gears for two different contact ratios [4]. It can be seen how the resulting stiffness is composed of the stiffnesses of the individual teeth. There is a large jump in the variation of the contact ratio for spur gears. It will be shwon in Sect. 4.5.3.2, how the the position-dependent stiffness influences parametrically excited vibrations in gear mechanisms. In the case of helical gears, there is naturally a larger number of teeth in engagement so that the stiffness jumps are smaller, which has an effect on the excitation of vibrations", + " The internal excitation causes include variations of the gearing stiffness c(t) that occur when the tooth flanks roll off and when switching from single to double meshing. Deviations from the optimum gearing geometry or pitch errors and radial runout can result in vibration excitation not only in the event of gear damage, but also in intact gear mechanisms. The periodic function of the gearing stiffness can be described as follows by the mean value cm, the Fourier coefficients c\u0302k and the meshing frequency fz: c(t) = cm + \u2211 k c\u0302k cos(2\u03c0kfzt + \u03d5k). (4.236) Figure 1.12 shows a typical curve of the variable tooth stiffness, see Sect. 1.3. In a helical gear mechanism, the variations are small as compared to spur gear mechanisms, which means that a few Fourier coefficients suffice to describe them. The meshing frequency is the product of the angular velocity and the number of teeth. The meshing frequency occurs at the contact point of two gear wheels (shaft 304 4 Torsional Oscillators and Longitudinal Oscillators 1: angular velocity \u03a91, number of teeth z1 and shaft 2: angular velocity \u03a92, number of teeth z2) fz = zf = z1\u03a91 2\u03c0 = z2\u03a92 2\u03c0 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000882_j.rcim.2010.08.007-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000882_j.rcim.2010.08.007-Figure9-1.png", + "caption": "Fig. 9. Category 3.2.", + "texts": [ + " Because the attachment point Ci can only move in the limb plane, we have the following Fig. 6. Parasitic motion (x) for r\u00bc0.1, c, yA( 60,60)deg. three constraint equations for each leg: l3x \u00bc 0, l1y \u00bc \u00f0l1x\u00fer\u00detan\u00f0a\u00de, l2y \u00bc \u00f0l2x r\u00detan\u00f0b\u00de \u00f021\u00de As shown in Fig. 7, we have li \u00bc ai\u00feP\u00bc Taui\u00feP and it can be rewritten as lix \u00bc x\u00feT11auix, liy \u00bc y\u00feT21auix, liz \u00bc z\u00feT11auix \u00f022\u00de Substituting aui into (22) yeilds l1x \u00bc x\u00feT11\u00f0 r\u00de, l2x \u00bc x\u00feT11\u00f0r\u00de l1y \u00bc y\u00feT21\u00f0 r\u00de, l2y \u00bc y\u00feT21\u00f0r\u00de \u00f023\u00de Substituting Eq. (23) into constraint equations in Eq. (21) yields x\u00bc 0 \u00f024\u00de As shown in Fig. 9, three LPs intersect at a line with three spherical joint centers being colinear, and two LPs are coincident and perpendicular to the other LP. Obviously, we havea\u00bc1801,b\u00bc01,r1\u00bcr2\u00bcr, r3\u00bc0. Substituting them into Eq. (14), (16), and (17), we can obtain x\u00bcy\u00bcf\u00bc0. Therefore, the 3-PRS PM belonging to subcategory 3.2 has no parasitic motion. The three LPs of the 3-PRS PM in this category are parallel to one another. As shown in Fig. 10, the three LPs of the 3-PRS PM belonging to subcategory 4.1 are parallel and the three spherical joint centers are noncolinear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001025_1.3005147-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001025_1.3005147-Figure1-1.png", + "caption": "Fig. 1 Each limb was represented by a translational spring, with stiffness K and slack length L0, that was rigidly coupled to a roller of radius R on one side and pinned to a point mass M on the other side. The point mass was assumed to be at the height H of the center of mass of the body with the limb spring in an unstretched upright configuration. Simulations were performed assuming normative values of H=1 m and M=80 kg. Roller radii of 0.0 m, 0.1 m, 0.2 m, 0.3 m, and 0.4 m were considered.", + "texts": [ + " Our second purpose was to evaluate the effect of roller radius, limb impact angle, and limb stiffness on cadence, step length, walking speed, and induced ground reactions. The third purpose was to determine if modulation of limb stiffness and impact angle is sufficient to induce the speed-dependent changes in cadence, step length, ground reactions, and center-of-pressure excursions seen in normal human walking. Methods The model consisted of a point mass M , two massless limb springs of stiffness K, and massless circular roller feet of radius R Fig. 1 . The base of each limb spring was rigidly fixed to its roller foot, such that a single angle defined the orientation of a limb and a foot with respect to a vertical upright. The proximal end of the limb spring was pinned to the point mass. Thus, the configuration of each limb was described by a limb angle and spring length L. Equations of motion Eq. 1 for the model were derived in terms of the trailing limb denoted by subscript 1 using a Lagrangian approach Appendix A , JANUARY 2009, Vol. 131 / 011013-109 by ASME erms of Use: http://www" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure16.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure16.1-1.png", + "caption": "Fig. 16.1 Parameters of the rotation matrix", + "texts": [ + " Time history of the displacement of the center of the moving platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Fig. 14.6 Example 14.4. Time history of the velocity of the moving platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Fig. 14.7 Example 14.4. Time history of the acceleration of the moving platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Fig. 16.1 Parameters of the rotation matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 Part I General Introduction Chapter 1 The geometry of lines plays a central role in three-dimensional mechanics. In fact, lines can be used to represent the screw axes of spatial motions and also to represent the action of forces. With this assumption in mind, a screw may be understood as two concatenated vectors: The first vector, namely the primal part of the screw, is a unit vector along the axis of the screw, while the second vector, namely the dual part, is the moment produced by the primal part about a reference point named the reference pole", + " However, such methods require a little experience dealing with the handling of two related reference frames through the introduction of a wide class of orientation angles, such as Euler angles, Tait\u2013Bryan angles (roll, pitch, and yaw), XYZ angles, and so on. This appendix provides a simple method for computing the rotation matrix. The method is based on the fact that the coordinates of three points of a rigid body are sufficient to determine the pose of the rigid body as observed from another body or reference frame. With reference to Fig. 16.1, let us consider two identical triangles A1A2A3, body labeled 0, and a1a2a3, body labeled 1, where the coordinates of the vertices of both triangles are expressed in accordance with the reference frame XYZ attached to body 0. The rotation matrix R of body 1 with respect to body 0 may be expressed as R D \u0152 OuX OuY OuZ ; (16.1) where the unit vector OuX is given by OuX D . a2/C .a3 a2/ j . a2/C .a3 a2/ j : (16.2) Here is the position vector of point o with respect to point O. Meanwhile, taking into account that d D r sin = sin" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000594_s0022-0728(83)80244-7-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000594_s0022-0728(83)80244-7-Figure1-1.png", + "caption": "Fig. 1. Computer-s imulated current -potent ia l curves of the ec catalytic m e c h a n i s m plotted as normal ized current (i,~\u00a2/i~,\u00a2 o) vs. normal ized potential (E - E ~ ) [7]. Kinetic parameters for curve A were: ks, M = 0, ks . s=5X~10-~cm s -1, k f = 0 , for curves B; ks, M = l . 0 cm s -1, ks, s = 5 \u00d7 1 0 -9, kt values; (1) 0.0, (2) 2\u00d7 102, (3) 6\u00d7 102, (4) 2X 103, (5) 2\u00d7 104 M -1 s - k Other parameters in text.", + "texts": [ + " Thermodynamically, Sox should be reduced prior to Mox at E~', which is more negative in potential than E~'. However, in the presence of a large overpotential due to the heterogeneous rate constant, ks, s, being much less in magnitude than ks, M, the reduction of Mox proceeds prior to So~, and hence the turnover of Sox to S R via reaction (2). The cyclic voltammetric (CV) current-potent ial (i-E) curves for a simple ec catalytic mechanism have been digitally simulated [7]. The results are illustrated graphically in Fig. 1. The simulation parameters are: n s = n M ----- 1; D s = D M = 1.0 \u00d7 10 -5 c m 2 / s ; c s = c M = 1.0 \u00d7 10 - 3 mol/1; ks, M = 1.0 cm/ s ; ks. s = 5 X 10 -9 cm/ s ; kf varied from 0.0 to 2 \u00d7 10 4 M - 1 s - l ; scan rate, v, = 100 m V / s ; and E~' = - 2 0 0 mV and is referenced to E~' which is assigned a value of 0.00 V. As expected the peak current, ip, S, of the irreversible wave for the electrochemical conversion of species S at E - - 0 . 6 V, decreases in magnitude while the ec coupled wave increases as the rate constant, k f , for reaction (2) increases in value", + " The peak potential of the catalytic w a v e , Ep,ca t , is closely related to the E~' value. How closely the Ep,ca t tracks the E~' depends on experimental parameters such as concentrations and kinetic rates of reactions (1-3). Nonetheless, Ep,ca t wi l l be within about 50 mV of E~' when ks. M >~ 10 - 3 c m / s and kf>~ 10 4 M - 1 s - 1 in the normal CV scan range of ca. 100 mV/s . As the value of ks, M decreases, Ep,ca t m o v e s toward negative potentials and k f primarily affects the current function; ie. ip,cat a s already seen in Fig. 1. It is interesting to note that the maximum value of the peak current, ip, cat' is attained when the Ep,ca t coincides with the Ep, M. That is, the maximum peak current occurs at the potential determined by the reduction of Mo~ in the absence of Sox. The ip,cat under such circumstances is given by [7] ip,cat = 2.67 X 105(1.09) . . . . ~a:b~M__Mn'/Z,,'/2,~ + 'p.M\" (4) where ip, M is the peak current given by the Randles-Sevcik equation [10] for a reversible electrode reaction of species Mox in the absence of Sox" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003620_s00466-015-1243-1-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003620_s00466-015-1243-1-Figure1-1.png", + "caption": "Fig. 1 Model setup for the powder bed FEA study", + "texts": [ + " In the ideal case, the specific heat outputs and the change in enthalpy due to phase transformation, as obtained fromCALPHAD,would be fitted to smooth functions and could be directly implemented in Eq. 9. The strong nonlinearity in the outputs is prohibitive for curve fitting the data, which is the reason for use of the much simpler piecewise constant model for the thermodynamic properties. To compare the CALPHAD-derived properties with standard handbook properties the authors have developed a FE model of the EBM process. The model used for the present work is shown in Fig. 1. As can be seen in the figure, the model consists of 150,000 linear heat transfer hexahedral elements with 164,016 nodes. The plane of symmetry shown in the figure is located at the midpoint of the axis of the beam, which scans the domain parallel to the plane of symmetry. This model is indicative of a single track AM process for simplicity but there is no limitation of the proposed methodologies to such simplifications. The dimension Lx , Ly, and Lz are the length, width, and height of the domain, respectively, while the dimension Lt represents the thickness of the current layer in the EBM process. The parameters P and V x are the beam power and velocity, respectively. The dimensions and process parameters used for the present work are shown in Table 1. All simulations were conducted using an in-house FE software that was developed by the first author. The average simulation time for the model shown in Fig. 1 for the CALPHAD-based solution was around 25 minutes using a single processor. The handbook-based solution was completed in around 7 minutes using a single processor. It should be noted that powder bed based AM processes have an added complexity over thedirect depositionprocesses in that the powder bed itself has dynamic thermal properties. In particular, the powder bed initially has a low conductivity compared with that of the bulk material or substrate. The powder bed properties must be accounted for in analysis because the thermal history in the heat affected zone is strongly dependent on the surrounding thermal influences, e", + "175 The thermal history and heating/cooling rates based on the thermodynamically consistent properties, which were derivedusing theCALPHADmethod, are the primaryquantities of interest; both the temperature and cooling rate govern the evolution of the microstructural phases of the material during solidification. Therefore, the present section provides a comparison between the handbook-obtained and the thermodynamically consistent properties for the temperature and the rate of change of temperature as a function of time. The FE model for the EBM process shown in Fig. 1 was used for the study. The heat source model parameters (see Eq. 4) are shown in Table 6, followed by the radiation boundary condition parameters (see Eq. 5) in Table 7. m \u03b8 (K) k ( W/mm K) 0 0.0 0.0003 m \u03b8 (K) k (W/mm K) 0 0.0 0.0003 The thermodynamic properties obtained from the handbook are shown in Table 8. It should be noted that thematerial density (shown in Table 8) is assumed to be the same for both the handbook-based and CALPHAD-based solution. The density is further assumed to be constant in temperature dependence, despite the fact that the material switches from powder form, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002066_j.ymssp.2018.06.054-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002066_j.ymssp.2018.06.054-Figure10-1.png", + "caption": "Fig. 10. Twin RIP.", + "texts": [ + " The proposed observer is used to approximate the pendulum\u2019s velocities. Some studies have introduced additional complexity to the common single RIP. This is to test the effectiveness and robustness of the proposed controllers on more complex RIP. For example, Fujita et al. [96] investigated the swinging up and stabilizing control for twin RIP pendulums. The arm of twin RIP pendulums is connected to the motor shaft at its center and the pendulum is positioned at each ends of the arm, as shown in Fig. 10. Energy-based controller was used for swing up control while the LQR was used for stabilization when the two pendulums simultaneously reach the neighborhood of upright position. The energy-based controller was also proposed in Ref. [125], which concurrently achieves the swing up of the twin RIP and the minimum of the mechanical energy when the rotary pendulums are in their respective vertical positions. ANN was used in system identification of twin RIP in Ref. [16]. Some researchers implement their controllers on another type of double RIP, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001749_978-3-319-10795-0_4-Figure4.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001749_978-3-319-10795-0_4-Figure4.5-1.png", + "caption": "Fig. 4.5 Finite time convergence observer", + "texts": [ + " For any bounded initial conditions x(0), x\u0302(0), there exists a choice of \u03bbi and \u03b1i such that the state observer x\u0302 converges in finite time T f s \u03c4q to x and \u03b8\u0303 converge also in finit time to fq(x). Proof The proof is given in [3] for the case of n = 2. Figure 4.4 illustrates the finite time convergence behavior of the proposed observer. The demonstration is based on the error trajectory for each quadrant in the worst cases. In the case of n > 2, the convergence is ensured step by step following this order: (e\u03071 = e2, e1) \u2192 (0, 0) in finite time T1 in the first step (Fig. 4.5). (e\u03072 = e3, e2) \u2192 (0, 0) in finite time T2 in the second step. And (e\u0307i = ei + 1, ei ) \u2192 (0, 0) in finite time Ti in the step i . Finally, (e\u0307n\u22121 = en, en\u22121) \u2192 (0, 0) in finite time Tn\u22121 in the step (n \u2212 1). The finite time of convergence of the full state x is: T f s = n\u22121\u2211 j=1 Tj (4.12) The choice of \u03b1i and \u03bbi are such that T f s \u03c4q and then we have the time to converge before the next jump. In this section, we design a discrete part of the proposed observer. Let us consider the system (4.4), the task of the discrete time observer is to locate which dynamic of the system is in evolution" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003601_s13738-020-01876-4-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003601_s13738-020-01876-4-Figure2-1.png", + "caption": "Fig. 2 Graph of the oxidative peak current of 1.0 mM HLD in 0.1\u00a0M PBS (pH 7.0) versus the number of polymerization cycles of HLD", + "texts": [ + " The peaks frequently travelled downwards with respect to time for each cycle with the decline of peak currents; this information confirms that monomer HLD films got converted into polymer HLD films, and these films were established on the less active surface of the BCPE. The most probable mechanism of electrochemical polymerization of HLD on the surface of CPE is shown in Scheme\u00a01 [59]. 1 3 Impact of\u00a0the\u00a0number of\u00a0cycles on\u00a0the\u00a0construction of\u00a0PHLDMCPE The thicknesses of the polymer layer of HLD modify the electrocatalytic activity of the CPE. The covering of the HLD film on BCPE was hindered by alternating the number of scan cycles from 2 to 14 by taking 1 \u00d7 10\u22124\u00a0M RL in 0.1\u00a0M PBS of pH 7.0 at the sweep rate of 0.1\u00a0V/s. Figure\u00a02 shows that the peak current was boosted till the 10th cycle, but after the 10th cycle, the peak current got reduced, because of the inactive proportion of electron transfer of the RL at PHLDMCPE, and hence, the number of scan cycles for electropolymerization of HLD was fixed to ten. Detection of\u00a0the\u00a0electrochemical surface area of\u00a0PHLDMCPE and\u00a0BCPE The CV exploration was done for the assessment of the available active surface areas of PHLDMCPE and BCPE through the utilization of 0.05\u00a0mM potassium ferrocyanide solution and was taken in an electrochemical compartment with 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002162_s10846-013-9813-y-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002162_s10846-013-9813-y-Figure8-1.png", + "caption": "Fig. 8 The quadrotor platform", + "texts": [ + " The values of control signal change between 0 to 214(16384), so the control signal equal to 0 means duty cycle of PWM is 1 ms, and if the control signal equals to 16384, its corresponding duty cycle is 2 ms. This section describes our quadrotor platform briefly at first. In the following subsection, an efficient algorithm has been proposed to simplify the implementation of feasible controllers. The experimental results are illustrated in the last part of this section. 5.1 Hardware Description The structure of our platform is made of carbon fiber (65 cm \u00d7 65 cm \u00d7 25 cm). Its total weight is 1,210 gr with payload capacity about 250 gr permits 15 min flight duration (see Fig. 8). Its avionic architectures as shown in Fig. 9 is completely modular. The Arm microcontroller gathers data of Attitude and Heading Reference System (AHRS) and ultra-sonic sensor. Four control signals are transmitted by a radio control transmitter to an ARM microcontroller. In order to simplify tuning of the controller and for flight security reasons, we have introduced some switches in remote control. The control signals are calculated according to the introduced control scheme, and then speed commands are given to the brushless DC motor drivers in PWM form" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003857_j.engfailanal.2018.08.028-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003857_j.engfailanal.2018.08.028-Figure2-1.png", + "caption": "Fig. 2. Helical gears with identical slice profile: (a) crack; (b) spalling; (c) wear.", + "texts": [ + " For the helical gears with identical slice profile, the mesh stiffness of helical gears can be obtained by the idea of \u2018offset and superposition\u2019, and the calculation efficiency can be improved significantly. For the helical gears without identical slice profile, the proposed method is also applicable but the improvement of the calculation efficiency of the proposed method is not evident. It is obvious that the slice profile of the healthy helical gears is identical, and some fault gears also satisfy this situation, such as the uniform penetrating crack (see Fig. 2a), uniform penetrating spalling (see Fig. 2b) and uniform wear (see Fig. 2c). The slice profile of the healthy helical gears is identical, so the healthy helical gear is taken as an example to illustrate the idea of \u2018offset and superposition\u2019. According to the property of the involute, the arc length of SnHn in Fig. 3a is equal to the length of \u2032 \u2032S Hn n in Fig. 3b. The offset angle of the nth sliced gear relative to the first sliced gear \u03b8n can be expressed as: = \u2032 \u2032 =\u03b8 S H \u03b2 r nL \u03b2 Nr tan tan n n 1 b b1 b b1 (1) where rb1 is the radius of base circle of driving gear; \u03b2b is the helix angle of base circle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001796_978-3-319-32156-1-Figure9.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001796_978-3-319-32156-1-Figure9.4-1.png", + "caption": "Fig. 9.4 A shape converter is assembled with the insert, converting the geometry to vertical sides and horizontal top, removing collisions", + "texts": [ + " Existing 3D printers are designed to work with planar horizontal layers, so the top of the part being built must always be flat to avoid collisions with the print head or recoating wiper arm (see in Fig. 9.3a). This requirement prevents the insert from being embedded until the build level is as high as it is. However, if the upper geometry of the part is convex, then the cavity will be enclosed by the time the build level is high enough to shield the component (Fig. 9.3b). To overcome these issues, Shape Converters can be used (Fig. 9.4). These are additional parts that fit around the component, converting its geometry into one with vertical sides and a horizontal top that can be inserted without protruding [15]. These allow embedding but remove some of the possible advantages by adding extra process planning and assembly steps. The shape converter must be designed (it could have a complex shape) and manufactured, before being manually attached to the component for insertion into the main build. In more recent work, the ability to print using transparent materials has enabled printing around embedded optical elements to create displays and illumination, or even customised optoelectronic sensors [16]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure7-1.png", + "caption": "Fig. 7. For determination of main and secondary contact points: (a) contact at the main contact point, and (b) function of transmission errors.", + "texts": [ + " \u2013 F1 e\u00f0 \u00de = 4 \u03c0e2 1=3 b a 1=2 a b 2 E e\u00f0 \u00de\u2212K e\u00f0 \u00de K e\u00f0 \u00de\u2212E e\u00f0 \u00de\u00bd 1=6 is a function that depends on the relation a/b. (vii) Contact area Ac, maximum contact pressure po, and compression \u03b4, are obtained as [10] Ac = \u03c0ab \u00f06\u00de po = 3 2 F \u03c0ab \u00f07\u00de \u03b4 = 3 2 F \u03c0ab 1 E\u204e bK e\u00f0 \u00de \u00f08\u00de (i) Two types of contact point are defined: (1) the main contact point and (2) the secondary contact point. The assignation of themain and secondary contact points depends on the angle of rotation of the pinion, \u03d51, and the corresponding function of transmission errors. Fig. 7 shows the two types of contact point, P1 and P2, wherein the main one, P1, is that of lower transmission error. (ii) The main contact point, P1, is determined by application of the algorithm explained in detail in [5]. Angle of rotation of the pinion, \u03d51, and angle of rotation of the gear, \u03d52, are then determined, for pinion and gear tooth surfaces to be in contact at point P1. (iii) The secondary contact point, P2, is determined by application of a similar algorithm, but considering as fixed the previously determined angle \u03d52" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003082_j.jsv.2016.02.021-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003082_j.jsv.2016.02.021-Figure6-1.png", + "caption": "Fig. 6. The experimental platform for the wind turbine transmission system.", + "texts": [ + " Hence it can infer that the independent assumption limits the applications of the ICA based methods. The BCA-PM performed better than the E-BCA by comparing the index values. Consequently, the recovery performance of the proposed BCA approach was superior to the E-BCA, JADE and FastICA in the separation of the correlated sources simulated in Fig. 5. To further evaluate the performance of the proposed method in a practical application, experiment tests were conducted in a wind turbine transmission system shown in Fig. 6. From left to right in the figure, the components of the test system are a data acquisition module, a 3HP driving motor, a two-stage planetary gearbox, a two-stage spur gearbox, and a controllable magnetic brake. The numbers of the gear teeth of the two gearboxes are shown in Table 3. In this work, a crack fault was imposed to the tooth root of gear Z29 (gear teeth number is 29) in the intermediate shaft of the spur gearbox. Fig. 7 shows a picture of the normal and cracked Z29 gears. Three different crack depths were tested, including 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000108_i2008-10388-1-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000108_i2008-10388-1-Figure1-1.png", + "caption": "Fig. 1. Filament attached perpendicular to a bounding wall. The first three bonds t\u22121, t0 and t1 are shown. The actual filament starts with the bead at r0, whereas the virtual beads drawn as dotted lines are kept at fixed positions to anchor the filament perpendicular to the (x, y)-plane through their elastic force contributions. The actuating magnetic field oscillating around the z-axis is also sketched.", + "texts": [ + " The superparamagnetic filament is modeled by a beadspring configuration, which additionally resists bending like a worm-like chain [32]. Consequently, each bead of the filament is subject to stretching and bending forces, for which the chemical linkers are responsible, and to dipolar interaction forces due to the induced magnetic dipoles of the beads. We completely ignore the contributions of the chemical linkers to hydrodynamic friction, so the filament interacts with the fluid surrounding solely via the hydrodynamic friction of the beads. As illustrated in Figure 1, the filament is attached to a planar surface with the help of two virtual beads that fix its position and give it an orientation orthogonal to the surface. These virtual beads contribute to elastic forces but do not participate in hydrodynamic or dipolar interactions. In the following, we will summarize the forces, acting on each bead within the filament, and the equations of motion. Details of the derivations are given in reference [18]. The equations of motion contain hydrodynamic mobilities which we construct up to Rotne-Prager level based on the appropriate Green function commonly called Blake\u2019s tensor [33,34]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure9.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure9.7-1.png", + "caption": "Figure 9.7.1 Equivalent force systems for tractive force generated by driveshaft torque.", + "texts": [ + " Because the lateral force effective in creating distortions is the sprung mass force rather than the total lateral force, the Compliance Steer 185 compliance gradients are as follows: kd;C \u00bc kd;FY \u00fe kd;MZ kd;FY \u00bc mBfCd;FY;f \u00femBrCd;FY;r kd;MZ \u00bc mBftfCd;MZ;f \u00femBrtrCd;MZ;r \u00f09:6:3\u00de where mB is the body mass (sprung mass) and t is the tyre pneumatic trail. Similar equations can be written for the camber. Typical values of compliance understeer gradient are 1.0 deg/g at the front and 0.2 deg/g at the rear. For a driven wheel, or with inboard brakes, the driveshaft transmits a moment MD which, for constant wheel angular speed, generates a longitudinal force FX \u00bc MD RL \u00f09:7:1\u00de where RL is the loaded radius of the wheel. As shown in Figure 9.7.1, this combination of force and moment is equivalent to a force only, atwheel centre height. It is also equivalent to a forceFX at the contact patch plus a pitching momentMY there, whereMY\u00bcMD. Comparing Figure 9.7.1(a) and (c), the moment has been moved. This is permissible, as the application point, or axis, of a moment has no effect on the influence of the moment on a rigid body. The configuration of Figure 9.7.1(c) can then be used with the compliance matrix to obtain the compliance deflections for the hub-height force. This illustrates the principle, although, of course, in a practical case there may be complications; for example, with an inclined driveshaft there will be an additional moment MZ. It is also of interest to obtain the coefficients for the force FX applied directly at the wheel centre. The compliance steer angle is dC \u00bc Cd;FXFX \u00feCd;MYFXRL \u00f09:7:2\u00de so the compliance steer coefficient for the wheel-centre-height force is Cd;FX;WCH \u00bc Cd;FX \u00feCd;MYRL \u00f09:7:3\u00de This may be elaborated to include other effects such as an inclined driveshaft" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure13.16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure13.16-1.png", + "caption": "FIGURE 13.16. A 2R manipulator moves on a path made of two semi-circles.", + "texts": [ + " If g = gOko determine the dynamic equations of motion by applying the Lagrange technique . 26. * Lagrange dynamics of an SRMS manipulator. Figure 5.28 shows a model of the Shuttle remote manipulator system (SRMS). Derive the equations of motion for the SRMS utilizing the Lagrange technique for (a) g = 0 (b) g = gOko. 27. * Work done by actuators. Consider a 2R planar manipulator moving on a given path. Assume that the endpoint of a 2R manipulator moves with constant speed v = 1m/ sec from PI to P2 , on a path made of two semi-circles as shown in Figure 13.16. Calculate the work done by the actuators if h = l2 = 1 m and the manipulator is carrying a 12kg mass. The center of the circles are at (0.75m, 0.5 m) and (-0.75 m, 0.5 m). 562 12. Robot Dynamics The links are uniform with 24kg 18kg 1m 1m 0, -g Jo \u00b7 There is a load Fe = -14g 030 N at the endpoint. Calculate the static moments Q1 and Q2 for 01 = 30 deg and O2 = 45 deg. 29. Statics of a 2R planar manipulator at a different base angle. In Exercise 28 keep O2 = 45 deg and calculate the static moments Q1 and Q2 as functions of 01", + " Calculate a cubic rest-to-rest path in Cartesian space to join the following points with a straight line. PI (1.5,1) P2 (-0.5,1.5) . Then calculate and plot the joint coordinates of a 2R manipulator, with h = l2 = 1 m, that follows the Cartesian path. What is the maximum angular acceleration of the joints' variable? 16. * Joint path for a given Cartesian path. Assume that the endpoint of a 2R manipulator moves with constant speed v = 1m/ sec from PI to P2 , on a path made of two semi circles, as shown in Figure 13.16. Calculate and plot the joints' path if h = l2 = 1 m. Calculate the value and position of the maximum angular acceleration and jerk in joint variables. The center of the circles are at (0.75m, 0.5m) and (-0.75m, 0.5m). 17. * Obstacle avoidance and path planning. Find a path between PI = (1.5,1) and P2 = (-1 ,1) to avoid the obstacle shown in Figure 13.17. The path may be made of two straight lines with a transition circular path in the middle . The radius of the 13. Path Planning 605 circle is r = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001290_1.3607699-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001290_1.3607699-Figure2-1.png", + "caption": "Fig. 2 Successive links of a mechanism: (a) Before deformation; (b) after deformation", + "texts": [ + "\\N> P\\I = the constraint torques exerted by link i + 1 on link i counterclockwise about the positive xt, y;, and z,-axes, respectively. A,.,-, A v 0 A2i = the translation from the true position of the coordinate system O.-Xji/.-Zj to its deformed position O^y,-^ taken along the positive x,-, iji and zraxes, respectively. A !A , A v i , AiVi = the rotation from the true position of the coordinate system 0ixiyizi to its deformed position 0 f t a k e n counterclockwise about the positive xi: yit and z,~axes, respectively. Thus a tj-pical variation, Axf along the ,1,-axis, is shown in Fig. 2. Certain characteristics of the chosen deformations are evident in this figure: (a) Only one constraint is varied at one time. When the 6 Throughout this paper, the term \"force\" is used in a general sense and meant to include torques. corresponding constraint force has been found, then this constraint is restored and another is varied. (6) The dependent pair variables are in general a function of both the input variable qx and the deformation A. Thus they will change as the deformation takes place", + " Aj-iq,^ a = 1 j- 1 + Yj AlA* \u2022 \u2022 \u2022 Aa-lQaAa \u2022 \u2022 \u2022 Ai-,Q&A( . . . A j-iqabAuji (1 = 1 + Au42 . . . Ai.iQAAj.iUjf. (30) QA is defined as in equation (7) and QA as in equation (20). 1 This masking function plays the same role in indexed variables as the step function plays in a continuous system. where P is the unknown force, the bearing reaction in the direction of the varying constraint due to the inertia of the moving links. To produce a positive variation A, work must be done by the s3'steni against the force P (see Fig. 2); thus the negative sign. Of course, to find the true value of P, equation (33) must be evaluated with the conditions A = A = A = 0. When the expression for kinetic energy, equation (31), is substituted into equation (33), the differentiation performed and terms in A and A set equal to zero, the result is as follows: 7 7 5/7 P = -Tr Y UaiJaUaA'qi- Tr V \u2014^JaUaA'?I2 ^ ^ i>qi o = 2 a = 2 7 dUaA1 . 1 7 dUaL -Tr Y2 U\u00b0>J\u00b0 V \" Tr Y a = 2 dA + -Tr Y qi>. A a = 2 &A (34) Noticing that the trace of a matrix is equal to the trace of its transpose, the last two terms combine to give 7 7 bU P = -Tr Y UalJaUaA'q, -Tr Y JaUaA'qS \u0394t because FS = 0 and the modal force hi = 0, pi = hi \u03bci\u03c9i \u0394t\u222b 0 sin \u03c9i(t\u2212t\u2032)dt\u2032 + t\u222b \u0394t 0dt\u2032 = hi \u03b3i [cos \u03c9i(t\u2212\u0394t)\u2212cos \u03c9it] (6.296) and after a few trigonometric transformations pi = 2hi \u03b3i \u00b7 sin \u03c9i\u0394t 2 sin \u03c9i ( t\u2212 \u0394t 2 ) (6.297) is obtained. If one sets \u03c9i = 2\u03c0/Ti, one can represent pi using (6.295) for 0 \u2264 t/\u0394t \u2264 1 and (6.297) for t/\u0394t > 1. Figure 6.25c shows this for various ratios \u0394t/Ti. One can see that the maximum value is pi max = 2hi \u03b3i \u2223\u2223\u2223\u2223sin \u03c9i\u0394t 2 \u2223\u2223\u2223\u2223 = 2hi \u03b3i \u2223\u2223\u2223\u2223sin \u03c0\u0394t Ti \u2223\u2223\u2223\u2223 . (6.298) Each principal coordinate thus deforms as a result of a sudden load at most twice as much as for a static load of the same magnitude. The maximum value depends on the ratio of excitation time \u0394t to period Ti of the respective natural vibration. The peak value of the force generated in the system, the so-called maximum impulse response is often used to compare impulse excitations and to simulate laboratory tests. One distinguishes between the initial impulse response that takes into account the highest amplitude during the impulse period (0 < t < \u0394t) and the 6.5 Forced Undamped Vibrations 435 436 6 Linear Oscillators with Multiple Degrees of Freedom residual impulse response that expresses the highest amplitude after the excitation time (t > \u0394t). Figure 6.25c illustrates the impulse response for a rectangular and a half-sine load pattern. The solid curve matches the solution obtained using (6.295) and (6.296) while results from the literature were used for the half-sine impulse. If the excitation time is an integer multiple of the oscillation period (\u0394t = nTi), the respective mode shape remains at rest after the force subsides, see (6.297). This extinction of the residual oscillation (rectangular impulse: \u0394t = Ti +nTi, half-sine impulse: \u0394t = 1, 5Ti + nTi) is an interesting dynamic effect, see Fig. 6.25c. For a modal hammer, it can result in a mode shape not being excited despite the impulse. The energy supplied in the first half period is removed by the \u201csource of energy\u201d in the second half period. If the excitation time is small as compared to the period of oscillation, a series expansion for \u0394t/Ti 1 results from (6.297) because of sin(\u03c0\u0394t/Ti) \u2248 \u03c0\u0394t/Ti in the following form pi max = 2\u03c0hi\u0394t \u03b3iTi = \u03c9i \u03b3i hi\u0394t = hi\u0394t\u221a \u03b3i\u03bci . (6.299) The coordinates qk are derived from (6.108), (6.294), and (6.297) for t > \u0394t : qk = n\u2211 i=1 vki 2hi \u03b3i sin \u03c9i\u0394t 2 sin \u03c9i ( t\u2212 \u0394t 2 ) = 2Fs n\u2211 i=1 vkivsi \u03b3i sin \u03c9i\u0394t 2 sin \u03c9i ( t\u2212 \u0394t 2 ) " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000960_j.conengprac.2010.02.007-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000960_j.conengprac.2010.02.007-Figure5-1.png", + "caption": "Fig. 5. The prototype of the ducted-fan micro-aerial vehicle used for the experiments with avionics and control hardware: the fuselage ((a) and (c)) containing the MNAV sensor (b), the embedded computer (e), the brushless motor regulator (f) and the LiPo batteries (d).", + "texts": [ + " To this aim this layer is designed in order to allow two different kinds of interaction: the first allows the operator to remotely govern the aircraft dynamics in realtime, and for this reason is denoted by ROV Mode (remotely operated vehicle), while the second allows to program a certain set of trajectories (trajectory mode) to be executed. Section 5.3 will point out the main characteristics of these communication and interaction algorithms. The design of the prototype has been strongly influenced by the estimation of the overall weight obtained considering the payload, the desired flight endurance and the aircraft mechanical layout. The payload has been estimated by considering the avionics and a wireless miniature camera. The avionics is composed of the following components (see also Fig. 5): IMU/GPS sensor board; embedded computer board; wireless communication board and wireless antenna; serial communication interface to connect the sensor board with the processor board and eventually other peripheries; power system with a LiPo (lithium polymer) battery and voltage regulator. The overall weight is approximately 150 g. As far as the mechanical layout is concerned, as previously mentioned in Section 2, a system with two levels of control vanes and with the avionics box positioned above the propeller disk (see also Figs", + " The total mass, inertia, and the other aerodynamical parameters which characterize system dynamics have been accurately estimated by the CAD model, and are shown in Table 1. The lift coefficient cL and the drag coefficient cD of the flaps can be estimated by choosing a known NACA airfoil profile (see Abbott & von Doenhoff, 1959). In particular, following a design pattern frequently adopted for small R/C aircrafts, laminar airfoils have been employed for which, according to thin airfoils theory (see for example Jones, 1990), the lift coefficient for small angles of attack is approximately 2p and the drag coefficient is close to zero. Fig. 5 shows the layout of the avionics box. It is worth noting that the pressure sensors and magnetometers have been kept sufficiently far, respectively, from the propeller (which create a pressure disturbance) and the brushless motor (which, being driven by continuous current load of approx. 20 A at hover, generates a magnetic disturbance). Flight tests revealed a hovering flight endurance of about 14 min. The avionics is composed of two main hardware components, the IMU/GPS sensor and the embedded computer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003820_tits.2020.2987637-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003820_tits.2020.2987637-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of ITSC fault: (a) one branch of phase C has ITSC faults, (b) fault winding in series.", + "texts": [ + " As the wheel traction motor of EVs, the power/torque density is usually high while the working condition is always poor. Overheat, material defects or mechanical compressing can cause insulation failure easily and then the ITSC faults. In this paper, the 16-pole 18-slot outer rotor PMSM with surface mounted PMs and its characteristics of ITSC faults are investigated. As to this machine, the windings are concentrated around the stator teeth, and the number of parallel branches of each phase winding is 2. Fig. 1 is a schematic diagram of ITSC fault, assuming one branch of phase C has ITSC faults and the fault winding in series. Table I shows the main parameters of the PMSM. A 2D FEM of the PMSM without considering control method is carried out and simulated, which focuses on the intrinsic characteristics of ITSC fault. ITSC fault occurs in the bottom of the slot, shown as Fig. 2. The external circuit model of the inter-turn short circuit is shown in Fig. 3. A contact resistance R f is adopted in this model to represent the fault path, whose value R f depends on many factors, such as heating caused by fault current, duration of the short circuit and property of insulation material" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000960_j.conengprac.2010.02.007-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000960_j.conengprac.2010.02.007-Figure1-1.png", + "caption": "Fig. 1. The ducted-fan micro-aerial vehicle. On the right it is possible to see", + "texts": [ + " Sections 3 and 4 present, respectively, the control problem and the design of the control law, focusing on the properties of the closed loop system and illustrating a tuning procedure for the control parameters. Section 5 describes the experimental framework, focusing on the ducted-fan prototype, which has been realized to test the control law, and on the software architecture. Finally Section 6 presents the experimental results, showing the effectiveness of the overall design. The ducted-fan aerial vehicle presented in this paper is composed of three different subsystems. The first consists of a fixed-pitch propeller driven by an electric motor (see (b) in Fig. 1). This subsystem has the fundamental role of generating the main thrust required to counteract the gravity force. The second subsystem consists of a set of control vanes which are positioned below the propeller (see (c1) and (c2) in Fig. 1) in order to properly deviate its airflow. The vanes are governed to achieve full controllability of the attitude of the vehicle, playing the role that the tail rotor and the cyclic pitches have in a standard helicopter. The third and last subsystem is composed of the duct and the fuselage which contains all the avionics and applicationpurpose hardware ((c1) and (a) in Fig. 1, respectively); the role of the duct, in particular, is to protect the environment from the propeller and, if suitably designed, to even improve the efficiency of the thrust generation increasing the flight endurance or the payload. In order to derive a mathematical model for the system, the Newton\u2013Euler equations of motion of a rigid body in the configuration space SE\u00f03\u00de \u00bcR3 SO\u00f03\u00de have been employed. In particular, by considering an inertial coordinate frame Fi \u00bc fOi; i ! i; j ! i; k ! ig and a coordinate frame Fb \u00bc fOb; i ", + " By considering each control vane as a wing immersed into a relative wind Vi, see for example Stengel (2004), the aerodynamic lift and drag forces, L and D, can be computed as L\u00bc 1 2 rSCLV2 i ; D\u00bc 1 2rSCDV2 i ; \u00f03\u00de where S is the vane\u2019s surface and CL, CD are, respectively, the lift and drag coefficients (see also Fig. 2). For reasonably small angles of attack, it turns out that CL \u00bc cLa; CD \u00bc cDa2\u00fecD0 \u00f04\u00de with cL, cD, cD 0 constant parameters which depend on the airfoil profile (which in this case is the same for all the control surfaces) and a the vane\u2019s angle of attack. The configuration considered in this paper has been built as a cascade of two different levels of control vanes, respectively, (c1) and (c2) in Fig. 1. In the first level, depicted on top of Fig. 2, the vanes are disposed radially around the propeller spin axis and are constrained to have the same angle of attack c with respect to the airflow. In this way, recalling (3) and (4), the aerodynamic lift forces turn out to generate a torque contribution Nc \u00bc \u00f01=2\u00dercLSL1V2 i c\u00f0dT=2\u00de, with dT/2 the lever arm of the lift, which is applied by definition in the so-called center of pressure of the vane, and SL 1 the overall surface. The role of the first level is to control the yaw attitude dynamics and, in turn, to counteract the aerodynamic torque N. The second level, at the bottom of Fig. 2, is composed of two independent control vanes, whose angles of attack are denoted, respectively, by a and b. By construction the resultant lift forces, denoted by FL x and FL y, are directed, respectively, along the body x- and y-axes of the vehicle and their points of applications form, with respect to the center of mass of the vehicle, a lever arm of length d (see also Fig. 1). In this way two torques are generated to control the roll and pitch attitude dynamics. In summary, by considering the contributions of the control vanes and of the propeller, the forces and torques which govern the system dynamics are given by f b \u00bc Fx L Fy L T\u00feFD 2 64 3 75\u00feRT 0 0 Mg 2 64 3 75; tb \u00bc Fy L d Fx L d N\u00feNc 2 64 3 75\u00feRT wPGo; \u00f05\u00de where g is the gravity acceleration, Fx L \u00bc \u00f01=2\u00dercLSL2 a V2 i and Fy L \u00bc \u00f01=2\u00dercLSL2bV2 i , in which SL2 is the surface of each independent control vane in the second level, FD denotes the sum of all the drag forces of the control vanes in both levels, which can be obtained by using (3) and (4), and finally G = Skew(col(0, 0, Irot)) with Irot the inertia of the propeller with respect to its spin axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure12.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure12.3-1.png", + "caption": "FIGURE 12.3. One link manipulator.", + "texts": [], + "surrounding_texts": [ + "12. Robot Dynamics 511\nthe environment are extra exte rn al force syst ems on the base and end effect or links . The force and moment that the base act uator applies to the first link are Fo and M o, and the force and moment that the end-effector applies to the environment are F n and M n . If weight is the only extern al load on link (i) and it is in - \u00b0ko direction, then we have\n\u00b0 \u00b0Ami g = -mig ko\n\"r , x m ; 0g = - or i x m igOkO\n(12.28)\n(12.29)\nwhere g is the grav itat ional acceleration vector. As shown in Figure 12.2, we indicate the global position of the mass center of the link by \u00b0ri , and the global position of the origin of body fram es B, and Bi - 1 by \u00b0di and \u00b0d i_ 1 respecti vely. The link 's velociti es \u00b0Vi ' OWi and accelerations \u00b0ai , OQi are measured and shown at Gi . The physical properties of the link (i) are specified by its moment of inerti a \u00b0I, about the link 's mass cent er Gi , and its mass m i .\nThe Newton's equation of motion determines that the sum of forces ap plied t o the link (i) is equal to the mass of the link times its accelera t ion at c;\n(12.30)\nFor t he Euler equat ion , in addit ion to the action and reaction moment s, we must add th e moments of the action and reaction forces about Gi . The moment of -Fi and F i- 1 are equa l to -mi x F, and n, x F i- 1 where m, is the posit ion vector of o, from C, and n , is the position vector of 0i-l from C i . Therefore, the link 's Euler equation of mot ion is\n\u00b0Mi _ 1 - \u00b0M i + L \u00b0Me i\n+ \u00b0lli X \u00b0Fi_1 - ami x \u00b0Fi = \u00b0I, OQi\nhowever , n, and m , can be expressed by\n\u00b0d i _ 1 - \"r,\n\u00b0d i - \"r,\n(12.31)\n(12.32)\n(12.33)\nto derive Equat ion (12.27). Since t here is one t ranslationa l and one rotational equation of motion for each link of a rob ot , there are 2n vectorial equations of motion for an t i link robot . However , t here are 2(n + 1) forces and moments involved . Therefore, one set of force systems (usually F n and M n ) must be specified to solve t he equa t ions and find th e joints' force and moment . \u2022\nExample 280 One-link manipulator. Figu re 12.;] depict s a link atta ched to the ground via a jo int at O . Th e free body diagram of the link is m ade of an extern al force and moment at", + "512 12. Robot Dynamics\nthe endpoint, gravity , and the driving force and moment at the joint. The Newton-Eul er equations for the link are\nFo +Fe +mgK\nMo + Me + n X F\u00b0 + m X Fe\nma\n/0. .\n(12 .34)\n(12.35)\nExample 281 A four-bar linkag e dynamics. Figu re 12.4(a) illustrates a closed loop four-b ar linkag e along with the free body diagrams of the links , shown in Figure 12.4(b). Th e position of the mass centers are given, and therefore the vectors ani and ami for each link are also kno wn. Th e Newton-Euler equations for the link (i) are\n\u00b0 \u00b0 'F i - I - F , +mig J \u00b0Mi_I - \u00b0Mi + ani X \u00b0Fi_ I - ami x F,\nm , \"a, (12.36)\nt, Oo. i (12 .37)\nand therefore, we have three sets of equations.\n\u00b0 \u00b0 'F o - F I +mIgJ\n\u00b0Mo - \u00b0MI + \u00b0nI x \u00b0Fo - \"m, x F I\n\u00b0 \u00b0 'F I - Fz + mzgJ\n\u00b0MI - \u00b0Mz + \u00b0nz x \u00b0FI - \u00b0mz x Fz\n\u00b0 \u00b0 'Fz - F3 + m 3g J\n\u00b0Mz - \u00b0M3 + \u00b0n3 x \u00b0Fz - \u00b0m3 x F3\n(12.38)\n(12.39)\n(12.40)\n(12.41)\n(12.42)\n(12.43)\nWe assume that there is no fr-iction in joints and the m echanism is planar. Th erefore, the force vectors are in the XY plan e, and the moments are", + "12. Robot Dynamics 513\nparallel to the Z-axis. In this condition, the equations of motion simplify to,\na a A\n\u00b0aI (12.44)F a - F I + mIgJ mi \u00b0M o + anI x \u00b0Fo - \"m, x F I It Oal (12.45)\na a A\nm2 \u00b0a2 (12.46)F I- F2+ m2g J\n\u00b0n2 x \u00b0F I - \u00b0m2 x F 2 12 Oa2 (12.47)\na a A\nm2 \u00b0a2 (12.48)F 2 - F 3+ m3g J\n\u00b0n3 x \u00b0F 2 - \u00b0m3 x F 3 13 Oa3 (12.49)\nwhere \u00b0M o is the driving torque of the mechanism. The number of equations reduces to 9 and the unknowns of the mechanism are\nE\"ox,E\"Oy ,E\"Ix ,E\"Iy,E\"2x,E\"2y,E\"3x,E\"3y,AiO.\nThe set of equations can be arranged in a matrix form\n[A] x= b (12 .50)" + ] + }, + { + "image_filename": "designv10_3_0000023_j.mechmachtheory.2006.01.003-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000023_j.mechmachtheory.2006.01.003-Figure3-1.png", + "caption": "Fig. 3. The equilateral end effector platform projected into the x\u2013y plane.", + "texts": [ + " As developed in the following section, these equations relate the independent variables Aiz to the remaining, dependent variables Aix and Aiy where i = 1, 2, and 3 for the three spherical joints. The end effector platform may be modeled as a triangle whose vertices are the centres of the three spherical joints. Recalling that the end effector radius is represented by rp, the magnitude of each side of such a triangle is k \u00bc 2rp cos p a 2 \u00f017\u00de The projection of the chosen points Ai into the xy plane is denoted by corners A0i of the triangle depicted in Fig. 3. The magnitude of any side of this projected triangle dij, can be obtained: dij \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2 \u00f0Aiz Ajz \u00de2 q \u00f018\u00de Using the sine law: sin\u00f0a\u00de d12 \u00bc sin\u00f0h1\u00de A1x \u00f019a\u00de sin\u00f0b\u00de d13 \u00bc sin\u00f0x2\u00de A1x \u00f019b\u00de Eqs. (19a) and (19b) may be equated in terms of A1x and reduced as d12 d13 \u00bc sin\u00f0x2\u00de sin\u00f0a\u00de sin\u00f0h1\u00de sin\u00f0b\u00de \u00f020\u00de By observation of Fig. 3, angle h1 can be written in terms of x2 as follows: h1 \u00bc h h2 \u00bc h \u00f0p x1 \u00f02p a b\u00de\u00de \u00bc h a b\u00fe p\u00fe x x2 \u00f021\u00de where, using the cosine law, angles h and x are h \u00bc cos 1 d2 12 \u00fe d2 23 d2 13 2d12d23 \u00f022a\u00de x \u00bc cos 1 d2 23 \u00fe d2 13 d2 12 2d23d13 \u00f022b\u00de Two solutions exist for angles h and x from Eqs. (22a) and (22b). However, recalling that these angles refer to the inside angles of a triangle, they must lie within the range 0 6 h, x 6 180 for which only one solution may be obtained from Eqs. (22a) and (22b)", + " (27) and (29), two solutions for each A2x and A3x are possible. Consider the segment d12, where \u00bdA1x ;A1y is known as the starting point. When constrained to lie on the x\u2013y plane, the end point on the line segment lies on a circle of radius d12 in that plane. This circle intersects the plane defined by the second limb in two possible locations, corresponding to the two solutions for A2x . The first solution for A2x may lie in the second quadrant corresponding to a negative A2x value, as depicted in Fig. 3. The alternate solution corresponds to a positive A2x value, where the line segment d12 would intersect the plane defined by the second limb, in the fourth quadrant. As depicted in Fig. 3, the former solution is preferred. To this point, the three elevations of the spherical joints have been chosen to be independent variables which may be used to define the remainder of the system\u2019s pose. It is now possible to relate the first time derivative of these variables ( _A1z , _A2z , and _A3z ) to the actuator rates by a 3 \u00b7 3 Jacobian matrix. Consider the following equation: J0 _x0 \u00bc _q \u00f030\u00de where for the considered example: _x0 \u00bc \u00bd _A1 _A2 _A3 T 9 1 \u00f031\u00de _q \u00bc \u00bd _b1 _b2 _b3 T 3 1 \u00f032\u00de As a result, although J0 \u00bc oq ox is found using the first derivative of a closed vector loop, its numerical result is known and is equivalent to J0 \u00bc ob1 oA1x ob1 oA1y ob1 oA1z ob1 oA2x ob1 oA2y ob1 oA2z ob1 oA3x ob1 oA3y ob1 oA3z ob2 oA1x ob2 oA1y ob2 oA1z ob2 oA2x ob2 oA2y ob2 oA2z ob2 oA3x ob2 oA3y ob2 oA3z ob3 oA1x ob3 oA1y ob3 oA1z ob3 oA2x ob3 oA2y ob3 oA2z ob3 oA3x ob3 oA3y ob3 oA3z 2 6666664 3 7777775 \u00f033\u00de Then, expressing all the dependent terms Aix and Aiy as functions of the selected independent terms Aiz , Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000086_0167-6911(94)00061-y-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000086_0167-6911(94)00061-y-Figure1-1.png", + "caption": "Fig. 1. Configuration space of the fire truck.", + "texts": [ + " Note that if we view the state of the system as (e, ~), the equations will look like ~ = g(~)Ud(\u00a2, t) + g(~)e. The linearly stable coordinates will then contain not only the terms due to Ud(~, t) as before, but also the entire vector e. In the center manifold, e -- 0. Consequently the equations for the dynamics on the center manifold are exactly the same as in the kinematic case. We conclude stability. 4. An e x a m p l e The stabilization method presented in this paper will be illustrated b.y a simple three-input example: the fire truck. The state ~ = (x, y, ~bo, 00, ~bl, 01 ) (see Fig. 1 ) has dynamics [2] ~ = go(~)uo + gl(~)Ul + g2(~)u2, where go(e) = ( l , tan Oo, O,(1/Lo)tan C~o see O0,O,(-1/Ll)sin(q~l- 00+01)see ~bl sec 0o) a', g l ( ~ ) = (0,0, 1,0,0,0) r, and g2(~) = (0, 0, 0, 0, 1, 0) r. A modification of the transformation given in [2] puts the system directly into power form: yo = x, tan ~b0 Y l - - Lo cos 3 00' zl0 = - tan 00 + X L F C~o COS 3 00 ' sin(q~l - 00 + 01 ) z20 = - y - x L1 cos ~bl cos 0o\" -- sin(q~l -- 0o + 01 ) Y2 = L1 c o s ~bl c o s 0o ' t an t~O q- IX2 tan ~0 Z~o = 01 - x j ~ \u00b0 cos3 00 2 Lo cos 3 0 0 ' We skip the steps leading to its derivation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003696_ab6e60-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003696_ab6e60-Figure3-1.png", + "caption": "Figure 3. (a) Computer-aided design model of hydrogel valve. Labels indicate components to be printed with (i) alginate/PNIPAAm ICE hydrogel ink, (ii) Emax, (iii) alginate/polyacrylamide ICE hydrogel ink, and (iv) alginate-based ink for printing sacrificial support structures. (b) the Bioplotter printing the valve; (c) the 4D printed valve swollen in water at 20 \u00b0C; and (d) the 4D printed valve swollen in water at 60 \u00b0C. Reproduced with permission.38 Copyright 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.", + "texts": [ + "38 It worked as the reinforcing agent and provide actuation through reversible volume alterations at critical temperature (TC = 32 \u223c 35 \u00b0C). They designed a new mechanically robust and thermoresponsive gel ink for 3D printing and printed a smart valve with full control of water using alginate/PNIPAAm based-ionic covalent entanglement (ICE) gel ink alongside other static materials. The valve automatically closed when exposed to hot water, dropping the flow rate by 99%, and reverse in cold water (Fig. 3). The alginate portion of the ICE gel resists the contraction of the thermally responsive PNIPAAm phase, so the contraction ratio decreased as the alginate fraction increased. The alginate/PNIPAAm ICE gels can be promising materials for developing soft-actuators because they can repetitively achieve a large free strain and blocked stress. Naficy et al.62 printed a hydrogel 3D architecture capable of reversible shape deformation in response to both hydration and temperature change. Polyether-based polyurethane (PEO-PU) has been incorporated into the matrix of a thermoresponsive poly(Npropylacrylamide) (NIPAm) and a non-responsive poly(2-hydroxyethyl methacrylate) (HEMA) based hydrogels where PEO-PU acted both as a rheology modifier and a swelling modifier" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001472_iros.2011.6094526-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001472_iros.2011.6094526-Figure7-1.png", + "caption": "Fig. 7. The applied tip force continually increases in a direction in which the robot is relatively stiff. This leads to poor convergence when the sensor accuracy is not high enough.", + "texts": [ + " 5 shows the result when the sensor accuracy is that of (18). In Fig. 6, a more accurate sensor was simulated by averaging the previous ten measurements at each time step, and the Q from (18) was accordingly replaced with Q/10 (since the variance of the sample mean of a Gaussian scales inversely with the number of samples). The result in Fig. 6 is higher accuracy, but the accuracy is more dependent on the direction, as shown by the smaller, yet flatter ellipses. The second test case is shown in Fig. 7, and 8. The actuators remain at fixed values, and the force was increased from 0 to [100 \u2212100]T mN in increments of [20 \u221220]T mN at each time step. This represents a difficult scenario for force estimation, since the force is applied in a direction in which the robot is much stiffer (corresponding to the short axis of the ellipse in Fig. 4). In this case, Fig. 7 shows that the measurement accuracy (Q in (18)) is insufficient for quick convergence of the EKF algorithm. In Fig. 8, convergence is achieved by increasing the sensor accuracy (by averaging the previous 100 measurements), and using Q/100 in the EKF, indicating that high measurement accuracy may be needed for good performance in some cases. The results in Section IV show that using an Extended Kalman Filter approach is feasible for deflection-based force sensing using continuum robots, which, as we showed in Section II, often have illconditioned compliance matrices and Jacobians" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002273_tmag.2011.2175714-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002273_tmag.2011.2175714-Figure5-1.png", + "caption": "Fig. 5. Structural dynamic model of the motor.", + "texts": [ + " For example, if we have to apply forces on 30 000 nodes the time needed to create the load files (defined on RLOAD cards) is about 4 min for an extruded regular mesh whereas it grows to 4 h for an automatic non-regular mesh. The same kind of economy will be achieved in the reading process during problem resolution. Reading the RLOAD files will take 1 min as compared to 1 h for the automatic non-regular mesh. The vibratory spectrogram realization is got using a modal superposition resolution method (Sol111 with NASTRAN\u00ae) for each motor speed. The model used is presented in Fig. 5. It is made of 497 455 elements (and 19 200 shell elements), it has 2 305 182 DOF and 7056 nodes in which we apply magnetic forces. Note that the stator is embedded through four fixations on the shaft side. The realized spectrograms, presented Fig. 6, represent the evolution with speed of the vibratory response on the motor housing surface (average level of the radial acceleration on 12 calculation points). They are made of 75 different engine speeds (600 rpm to 8000 rpm by 100 rpm steps). The calculation time is about 45 min by engine speed (12 calculation points) or 56 h for a spectrogram" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000566_tro.2006.889485-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000566_tro.2006.889485-Figure10-1.png", + "caption": "Fig. 10. Illustration of a piezoelectric unimorph actuator.", + "texts": [ + " The moment created by the piezoelectric layer is related linearly to the layer thickness, , and is related by the third power to the stiffness of the beam, . In general, in a piezoelectric bimorph, the thinner the piezoelectric layer\u2019s thickness, the larger is the actuator\u2019s stroke. In a unimorph or any other composite piezoelectric beam, one can find what is the optimal combination of thicknesses to get maximal stroke. For example, for a unimorph actuator made of a PZT layer and an Si layer (see Fig. 10), the stroke of the actuator is proportional to the term (24) where , is the electric field on the piezoelectric layer, is the piezoelectric coefficient, and is the cross-coupling coefficient. For the physical properties given in Table I, the optimal thickness ratio is . Fig. 11 illustrates the dependence of the stiffness on the parameter and the single maxima. An additional parameter that influences the propulsion velocity is the length of each actuator in the tail, i.e., the parameters and . Previously [21], the actuators were divided equally, , . For the tail defined in Fig. 10 with an Si layer thickness of 20 m and PZT layer thickness of 1 m (electrode thickness is neglected), the propulsive velocity was 7.4 mm/s. Fig. 12 shows the propulsive velocity for parameter range ; . One can observe that there is a local maxima at , . The propulsive velocity at the maxima is 98.5 mm/s. The reason for such a dramatic increase in the propulsive velocity is the voltages that are applied to each actuator. In the case of even distribution of actuator lengths, the voltages on each actuator are V", + " For example, changing the BCs from clamped to spring at the base ( ) alters the optimal swimming configuration to (see Fig. 13). The maximal propulsive velocity at the maxima is 67.9 mm/s. From the point of view of electrical circuitry, the swimming tail is a resistance-capacitance (RC) circuit with several capacitors (the total capacitance depends on the number of piezoelectric layers and the electrode setup) and negligible resistance. Assuming that the swimming tail is optimized (i.e., all the magnitudes of the input voltages are equal), the apparent power consumed by capacitors of the unimorph in Fig. 10 is W (25) The reactance of the capacitors is (26) Thus, the supply current to the actuators is mA (27) A standard hearing aid battery, such as Renata No. ZA 10 [22], (the battery\u2019s diameter is 5.8 mm, height 3.5 mm, nominal voltage of 1.4 V, and capacity of 95 mAh) connected with the proper electric circuitry enables a constant operation period of 24 min, assuming the power needed for the electrical circuitry is very small. The swimming tail is able cover a distance of approximately 100 m during this operation period" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure4.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure4.10-1.png", + "caption": "Fig. 4.10 Diagram of an induction motor with the reference axes attached to the primary member.", + "texts": [ + " The voltage and torque equations, if zero sequence equations are omitted, are The General Equations of A.C. Machines 95 R d2 +L22P LmP LmP R d1 +LllP LllW Lm w = Uql -Lm w -LIIW Rq1+LllP LmP iq 1 Uq 2 LmP Rq2 + L22P iq2 M Wo (L .. L\u00b7\u00b7) e = - m ld 2lq I - m ld Ilq 2 2 (4.44) (4.45) where Lm is the magnetizing inductance and LII and L22 are the self-inductances. secondary member. The alternative arrangement in which the reference frame is attached to the primary member with the direct axis chosen to coincide with the primary phase AI, is shown in Fig. 4.10. The only essential difference compared with Fig. 4.9 is that the primary and secondary applied voltages are changed over. The form of the equations is therefore exactly as before with the suffixes interchanged. The voltage and torque equations are: Rdl +LIIP LmP Ud2 LmP Rd2 + L22P L22W Lm w = Uq 2 -Lm w -L22W Rq2 + L22P LmP Uql LmP Rql +LllP M WO (L .. L\u00b7\u00b7) e = 2 m ld 1 lq 2 - m ld 21q 1 (4.46) (4.47) The primary current transformations are obtained from Eqns. (4.10) with suffix I, and the secondary current transformations from Eqns", + " These components are similar to the quantities obtained when resolving an m-phase system into symmetrical components, and are determined by independent equations. The practical cage winding consists of many coupled circuits interconnected through the end-rings, each circuit being strictly a mesh in a network and each current being the current in a bar. Since the impressed voltage in every circuit is zero, all the symmetrical component voltages are also zero. Consequently all the current components except id and iq are also zero. Hence the cage is equivalent to the two-phase winding formed by coils D2 and Q2 in Fig. 4.10 and for most purposes it is not necessary to introduce the actual currents at all. The equations of a double-cage induction motor can be written down by including an additional pair of two-phase coils in Fig. 4.9 or 4.10 and adding two more voltage equations (see Section II. 2). Chapter Five Types of Problem and Methods of Solution and Computation For a machine represented in the primitive diagram by n coils there are n voltage equations and a torque Eqn. (1.6). If the n applied voltages and the applied torque are known, as well as initial conditions, the (n + 1) equations are sufficient to determine the n currents and the speed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001506_s00170-012-4721-z-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001506_s00170-012-4721-z-Figure2-1.png", + "caption": "Fig. 2 SLM equipment", + "texts": [ + " They found that the laser melted pool stabilizes the TIG arc and a laser trailing arrangement allows welding speeds until 15 m/min. Moreover, the full penetration joints can be successfully produced minimizing the TIG current and using argon as a shielding gas. A significant improvement of the melting efficiency was achieved with the combined action of plasma arc and laser beam [19]. The SLM technology creates fully functional parts directly from metal powders without using any intermediate binders or any additional processing step after the laser sintering operation [20]. The equipment consists (Fig. 2) of a control system, a coater or roller, a laser source, a scanning system, a working chamber, a powder chamber which is the reservoir for the powder, a controlled atmosphere chamber, and some rooms filled with excess powder. The working chamber is filled with a gas (Ar or N2 depending on the processed materials), to minimize both the oxidation and degradation of the molten metal. The coater deposits, in uniform way, the powder on the building chamber. The laser beam selectively scans and melts the surface of the powder" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002702_1.4029988-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002702_1.4029988-Figure5-1.png", + "caption": "Fig. 5 Ball\u2019s motion while rolling out from the defect", + "texts": [ + "3 Exit Event: Restressing Phase (III). In this phase the ball resumes contact with the nondefective part of the outer raceway. During this phase it is assumed that the ball rolls out of the compressed trailing edge of the defect with fixed center of rotation Journal of Vibration and Acoustics OCTOBER 2015, Vol. 137 / 051002-5 Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/22/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use PTR by rotating by an angle b as shown in Fig. 5. In this process, the center of the ball moves from O0 to D in Fig. 5 and from C2 to C3 in Fig. 2. In order to find the time taken by the ball to accomplish the restressing phase, rate of roll out dx0/dt, initial angular velocity xTEi and final angular velocity xTEf with which ball rolls out of the defect is needed. The initial angular velocity xTEi may be obtained by applying principle of conservation of angular momentum at point PTR, which the ball strikes at an angular velocity xf and starts moving out with angular velocity xTEi, as rb mv0 \u00bc rb cos hb mvc ) xTEi \u00bc xf cos hb (21) where rb is the ball radius" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001990_j.phpro.2014.08.100-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001990_j.phpro.2014.08.100-Figure1-1.png", + "caption": "Fig. 1. Integration of the interferometry sensor into the optical setup of the SLM machine.", + "texts": [ + " For deflection and focusing of the laser beam a SCANLAB intelliSCAN 30 and a varioSCAN 40 with a focal length of 639 mm \u2212 712 mm are being used. The scanner has a working distance of 520 mm. The control of these units happens via a SCANLAB RTC5 PCI controller board. Besides of the standard mirror coating for the processing wavelength \u03bbp of 1070 nm the deflection mirrors of the scanner have an additional coating for the sensor wavelength \u03bbs of 880 nm. A beam splitter couples the sensor light onto the axis of the processing laser as displayed in figure 1. 3.2. Sensor setup The optical sensor is based on the PRECITEC IDM sensor (www.precitec.de). The maximum scan rate of the device is 70 kHz and complies with the requirements in SLM. The measuring principle is based on the low coherence interferometry principle. The topology to be captured is actively exposed to the radiation of a broadband light source. The acquired signals are transferred to a distance information which can be accessed either at the analog output (16-bit resolution), via USB or via a serial connection in real-time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.10-1.png", + "caption": "Fig. 4.10 Example 4.4. Actuating mechanism for a telescoping antenna on a spacecraft, infinitesimal screws", + "texts": [ + "3 Equations of Velocity in Screw Form 83 Proof. The proof is immediate by a recursive application of Eqs. (4.56) and (4.63). \u02d8 Example 4.4. The velocity analysis of the actuating mechanism for a telescoping antenna on a spacecraft of Example 4.3 is investigated again here. It is necessary to determine the equation of velocity in screw form of body m as measured from body 0. After, we must apply that equation to compute the angular velocity of m with respect to body 0 as well as the velocity of point P. With reference to Fig. 4.10 to simplify the computation of the Pl\u00fccker coordinates of the involved infinitesimal screws, the origin O of the fixed reference frame XYZ is chosen as the reference pole. The velocity state of body m with respect to body 0, the vector 0Vm O, is given by P 0$j C P j$k C P\u030ck$m C Plk$ m D 0Vm O; (4.79) 84 4 Velocity Analysis where k$m is the screw representing the revolute joint associated to the revolute joint connecting the bodies m and k while k$ m represents the screw associated to the translational motion of body m as observed from body k" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002786_j.optlastec.2014.06.002-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002786_j.optlastec.2014.06.002-Figure1-1.png", + "caption": "Fig. 1. (a) Experimental setup and (b) laser head installed with powder nozzles [21].", + "texts": [ + " In this study, a comprehensive monitoring of the mass- and heat-transfer phenomena during the HPDDL cladding process was performed by optical diagnostics. A CCD camera was used to detect the particle-in-flight behavior. A pyrometer and an infrared camera were used to visualize the interaction of laser beam and powder flow and to measure the molten pool temperature. The influences of the main processing parameters such as laser power (P), powder feeding rate ( _m), carrier-gas flow rate (CG), and scanning speed (V) on the powder feeding behavior and the thermal behavior of molten pool were investigated. The experimental setup shown in Fig. 1 is comprised of an 8-kW Coherent HPDDL, a 6-axis KUKA robot, an AT-1200 highpressure rotary powder feeding system, and two powder feeding nozzles installed symmetrically with the laser head at an angle of 351 with respect to the vertical axis of the laser head. The exit of the powder feeding nozzle had a rectangular shape with the dimensions of 10 mm 1 mm. In order to protect the lens from the reflection of light and ricochet particles, the entire laser head tilted 101 with respect to the vertical axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002647_s40964-018-0039-1-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002647_s40964-018-0039-1-Figure10-1.png", + "caption": "Fig. 10 Points of interest with numbered labels", + "texts": [ + " The predicted maximum temperature rise from room temperature was approximately 250\u00a0\u00b0C. Figure\u00a09b, c show the predicted temperature history of all 14 points (at the end of layer deposition). The plot illustrates the influence of the overall energy input, geometric features, and fabrication time on the overall temperature increase. For example, Fig.\u00a09b shows a sudden layer temperature drop around 300\u00a0min, when building of a thin region at the lefthand\u00a0side of the geometry was completed, with no further direct heat input above points 1 and 2 (refer to Fig.\u00a010). The sudden layer temperature increase around 500\u00a0min was caused by a reduction in scanning time for one layer from 70 to 50\u00a0s because of a smaller scanning area.Table\u00a02 summarizes the predicted temperature increase from room temperature when the points of interest were built. 1 3 While the large-scale perspective shows the gradual temperature increase during the build, the temperature profile on a local scale is essential for microstructural prediction. As examples, the calculated transient temperatures of points 7 and 14 are shown in Fig", + " Obviously, this is speculative since measurements of pool temperatures under these conditions are extremely difficult, but based on prior measurements for the powder bed fusion process [25], it is realistic to believe that peak temperatures within the melt pool were no greater that approximately 1500\u00a0\u00b0C, which would have resulted in over prediction of temperatures by approximately 100\u00a0\u00b0C. Nevertheless, according to the comparison with the temperature measurement, the thermal simulation has shown a reasonably accurate prediction, which provides great confidence in the numerical model. 1 3 Figure\u00a013a shows melt pools on a polished cross-section. The melt pool width and depth at points 7 and 8 (refer to Fig.\u00a010) were measured, taking 20 width and depth measurements in the vicinity of each point of interest. Figure\u00a013b, c compare the measurements and calculations, showing that the melt pool width was slightly over-predicted and the melt pool depth slightly underpredicted. Two possible reasons for the differences are onset of keyholing and measurement difficulties. For process conditions close to the onset of keyholing, the melt pool is deeper and narrower than expected [35]. Second, overlapping from adjacent and overlying tracks can lead to measurement uncertainty" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003721_s11665-020-05125-w-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003721_s11665-020-05125-w-Figure7-1.png", + "caption": "Fig. 7 Principle of acoustic emission", + "texts": [ + " Acoustic emission (AE) can be used for finding internal structural defects using the acoustic signals generated by internal defects. An AE testing can be done mainly by two integrated components, a defect, which is mainly the source of energy release in the material and transducers which collect the information from the generated source (Ref 38). Thus, the technique is mainly based on the generation of a signal, data acquisition, comparison of data, and finally, making the decision. The schematic shown in Fig. 7 represents the general working principle of an acoustic emission system, and Fig. 8 shows a typical characteristic of AE signals where defects limits and threshold limit are shown. A fault spread its Journal of Materials Engineering and Performance signal in the form of high-frequency sound waves that are received by sensors. Amplitude, rising time, energy, duration, and count are the main characteristic features of the emitted AE waves (Fig. 8a) which can be used for evaluation and characterization of the AE signals" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003309_978-3-319-24729-8-Figure2.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003309_978-3-319-24729-8-Figure2.8-1.png", + "caption": "Fig. 2.8 Variables used to describe the bicycle: z1 and z2 are the positions of the two wheels; r1 and r2 are the normalized velocity vectors", + "texts": [ + "7 Schematic: (x, y) is the location of the rear wheel, B is the wheelbase, \u03b8 is the angle of the frame with respect to the x-axis, \u03b3 is the angle of the front wheel with respect to the frame contact of the rear wheel with the ground. We let \u03b8 be the angle that the frame makes with the x axis, and \u03b3 the steering angle, as in the figure. While this model might not be a faithful representation of a real bicycle, it turns out to be quite useful because it captures the essential features of a car with four wheels, only the front two being steerable. Since the bicycle is assumed to be perpendicular to the ground, we may represent it on the complex plane as in Fig. 2.8. In the figure, z1 is the position of the rear wheel, i.e., z1 = x + jy, and z2 the position of the front wheel. The vector r1 is the normalized difference z2 \u2212 z1, while r2, also a unit vector, represents the heading of the front wheel. In terms of the angles \u03b8 and \u03b3, we have r1 = ej\u03b8 and r2 = ej(\u03b8+\u03b3). We see that the bicycle has four degrees of freedom: x, y, \u03b8, \u03b3. We take as control inputs the speed of the point z1 and the steering rate \u03b3\u0307. We denote them by v and \u03c9, respectively. 14 2 Models of Mobile Robots in the Plane Lemma 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002466_tmag.2017.2656178-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002466_tmag.2017.2656178-Figure2-1.png", + "caption": "Fig. 2. Phasor diagram of end cogging forces.", + "texts": [ + " 1) can be given as [10]: 1_ 1 sin 2 ( , ) slot nn s r x F F n Z LCM Z P (3) and the end cogging force of module 1 can be written as [10]: 1_ 1 sin 2end m pm F F m x (4) As the length of the flux barrier is set as \u0394, the end cogging force of module 2 and module 3 can be given as: 2_ 1 sin 2end mm p x F F m (5) 3_ 1 2 sin 2end mm p x F F m (6) Generally, if the primary mover is composed of k modules, the end cogging force of module k can be derived as: 1 2 sin 1k mm p m F F x k (7) Thus, if the end cogging force of each module is regarded as a vector, the phase difference between the end cogging forces of the adjacent two modules is 2m\u03c0\u0394/\u03c4p. So, the phasor diagram of the end cogging forces of the k modules can be illustrated as Fig. 2. Then, the total end cogging force by the k modules can be written as: total_end 1 2 kF F F F 1 sin 2 sin sin p mm p p k m m x F m (8) Therefore, the total end cogging force would be zero if the following equation is satisfied: sin sin 0 p p k m m (9) In this paper, k equals 3. Hence, Eqn. 9 can be rewritten as: 24cos 1 0 p m (10) Since the fundamental component (m=1) takes the majority of the total end cogging force, the optimal length of the flux barrier can be given as: 1 3 ph (11) where h is an integer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure12.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure12.5-1.png", + "caption": "Figure 12.5.1 Angled parallel equal-length arms.", + "texts": [], + "surrounding_texts": [ + "The earliest double-transverse-arm suspensions, seen in front view, had arms that were simply of equal length and horizontal when in the static position, Figure 12.4.1. The basic properties are easily found by inspection, and are shown in Table 12.4.1. The camber is unchanging. The initial bump scrub rate is zero, implying that the roll centre is initially at ground level. The bump scrub rate variation and associated roll centre movement depend on the lateral arm length LY." + ] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure13.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure13.9-1.png", + "caption": "Figure 13.9.1 ExampleAxle 1,with convergent link location: (a) sideview; (b) front view; (c) planview; (d) axometric three-quarter view.", + "texts": [ + " In the case of the numerical evaluation of sensitivities, the question arises as to the size of increment to use. This is not highly critical, but in practice a linear displacement in metres or angular displacement in radians of 10 4 to 10 11 works well, using 8-byte variables, with 10 7 being near the centre of the range. Outside that range, convergence is inferior. The similarity of values for displacement and angle relates to the fact that a suspension has a scale of about 1 metre. Actual example values of sensitivity matrices are given in subsequent sections. The first example axle is shown in Figure 13.9.1. It is a conventional four-link type similar to that in Figure 13.2.1. Table 13.9.1 presents the numerical values for initialisation of the iteration process, beginningwith the actual unmoved position coordinates. Also given are thevalues of the sensitivitymatrix in the static position,where, for example, the first column is the response toX displacement of the axle, that is, the X direction cosines. Then the interpolation values f2 and f3 followwith the normal displacements of points relative to the reference triangle, as specified earlier" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002721_0278364916640102-Figure33-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002721_0278364916640102-Figure33-1.png", + "caption": "Fig. 33. 12 Control points of B\u00e8zier curve for front legs\u2019 swing trajectory, and a sinusoidal wave with a magnitude \u03b4 for stance foot-end trajectory which is designed to penetrate into the ground for ground-robot interaction according to Equilibriumpoint hypothesis.", + "texts": [ + " ( s)k ( 1 \u2212 s)j\u2212k \u2022 psw i |Ssw i =0 = c0, p\u0307sw|Ssw i =0 = n( c1 \u2212 c0) /T\u0302sw \u2022 psw i |Ssw i =1 = cn, p\u0307sw|Ssw i =1 = n( c11 \u2212 c10) /T\u0302sw \u2022 Double-overlapped control points generate zero velocity. \u2022 Triple-overlapped control points generate zero acceleration. The leg angle of attack at the touchdown (See Figure 34 in Appendix 4) is, as a default, set to be 68\u25e6 with Lspan = at THOR Data Center ehf on June 17, 2016ijr.sagepub.comDownloaded from [Lspan,F , Lspan,B]T = ( 200, 200)T (mm) for front/back legs, referring to the observation on the running-dog kinematics data (Gross et al., 2009). Figure 33 shows 12 control points of the B\u00e9zier curve used for the designed swing phase trajectory. The control points are determined by utilizing the properties of B\u00e9zier curve as follows. 1. Double-overlapped control points in the y-axis, (c0,y, c1,y) and (c11,y, c12,y), are used for zero vertical velocity with respect to a shoulder/hip joint at legs\u2019 liftoff and touchdown. 2. For the transition of force exertion from \u201cfollowthrough\u201d to \u201cprotraction\u201d, the direction of force is intended to be changed by triple-overlapped control points, c2, c3, c4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002193_j.measurement.2014.04.024-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002193_j.measurement.2014.04.024-Figure4-1.png", + "caption": "Fig. 4. The gear-box mounted with a tri-axial accelerometer.", + "texts": [ + " In the MFS, a 3-phase induction motor was connected to a rotor that in turn was coupled to the gear box through a pulley and belt device. The gear box and its assemblage are illustrated in Fig. 2. In the analysis of faults in gears, three different types of faulty pinion gears to be precise the ND, CT, MT and WT were considered and are depicted in Fig. 3. The online data in time domain were captured with a tri-axial accelerometer (with a sensitivity of 100.3 mV/g in the x-axis direction, 100.7 mV/g in the y-axis direction and 101.4 mV/g in the z-axis direction) that was fixed on the gearbox as illustrated in Fig. 4. With the dataacquisition hardware and a computer the data were stored for further processing. Signals were captured for the rotational speed of 10\u201330 Hz in the interval of 2.5 Hz for each of four fault conditions. For each measurement set, 300 cycles of data with 2000 samples each were taken and data were collected at the rate of 20,000 samples per second. Total 2000 300 data points were collected for each of three directions (i.e., x, y and z directions). The collected data points were processed further for the machine fault diagnosis as explained in the flow chart in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.8-1.png", + "caption": "Fig. 4.8 Example 4.3. Decomposition of the velocity analysis", + "texts": [ + "k OuP=O; \u2022 kvm P D Pl OuP=O. Next, the velocity state of point P fixed to body m as measured from the Earth .0/, the vector 0Vm P D 0!m 0vm P ; 4.2 Fundamental Equations of Velocity 79 may be expressed as 0Vm P D 0Vj P C jVk P C kVm P D 0!j 0v j P C j!k jvk P C k!m kvm P D 2 66666664 P sin. /C P\u030c sin. / cos. / P C P\u030c cos. / P cos. / P\u030c sin. / sin. / l P sin. / sin. / l P cos. / cos. /C Pl sin. / cos. / l P sin. /C Pl cos. / l P sin. / cos. /C l P sin. / cos. / Pl sin. / sin. / 3 77777775 : (4.60) For clarity, Fig. 4.8 shows the decomposition of the velocity analysis of the open kinematic chain at hand. After, the angular velocity of body m as measured from body 0 is obtained as the primal part of the six-dimensional vector 0Vm P as follows: 0!m D P sin. /C P\u030c sin. / cos. / OiC 80 4 Velocity Analysis P C P\u030c cos. / OjC P cos. / P\u030c sin. / sin. / Ok: (4.61) Meanwhile, the velocity of point P is precisely the dual part of 0Vm P . Indeed, 0vm P D l P sin. / sin. / l P cos. / cos. /C Pl sin. / cos. / OiC l P sin. /C Pl cos" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001888_tie.2015.2442519-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001888_tie.2015.2442519-Figure11-1.png", + "caption": "Fig. 11. Prototype of 12-slot/10-pole dual 3-phase SPM machine. (a) Stator, (b) Rotor.", + "texts": [ + " However, the cooling requirement for the inverter should be improved due to the increase of the fundamental current and additional 3rd harmonic current, resulting in increased inverter losses. In addition, when the machine is supplied with the same rms current, the peak current has reduced from 15A to 13A and this will decrease the power inverter VA rating by injecting 3rd harmonic current with the same rms value current. The 12-slot/10-pole SPM machines with SPM rotor have been prototyped and tested for validation. Fig. 11 (a) and (b) shows the pictures of the 12-slot stator together with the SPM rotor, respectively. The static torque with current angle of the prototypes is measured according to the test method reported in [22]. The steady-state dynamic experiments on dual-three phase 12-slot/10-pole SPM machine are carried out on a dSPACE DS1005 platform. The dual-three phase machine is coupled with a permanent magnet dc motor, which is connected with an adjustable power resistor used as load. The phase currents are measured by the current transducer whilst a model which combines the voltage model and the current model is employed to estimate the torque" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001222_ac900790m-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001222_ac900790m-Figure1-1.png", + "caption": "Figure 1. PPF microelectrode array. (a) SEM image taken of the PPF microelectrode array after dicing. Each of the four electrodes is 10 \u00b5m wide and 50 \u00b5m long. The white dots indicate the four electrodes, while the arrow indicates the insulation layer. (b) Drawing of the device (not to scale).", + "texts": [ + " To address this problem, the arrays were cleaned with an air plasma for 1 min after pyrolysis and again after insulation. Subjecting the wafers to this cleaning step improves the success of fabrication and improves the performance of the sensors. Plasma treatment of carbon surfaces has also been shown to increase the amount of oxygen functional groups on carbon surfaces.25 Interestingly, these functional groups have been shown to increase the sensitivity to dopamine.5 An SEM image of a PPF microarray is shown in Figure 1a. This image confirms that only nominal reflow occurs during pyrolysis of the photoresist. A qualitative measure of the film thickness was obtained by dicing and subsequent polishing of the PPF and substrate. This revealed a thickness of around 400 nm, an 80% reduction, consistent with a previously reported value of 81.60% at 1000 \u00b0C.14 The small thickness of the electrodes compared to their length (50 \u00b5m) and width (10 \u00b5m) makes the electrodes essentially planar with a band geometry.26,27 The bands are spaced 100 \u00b5m apart, avoiding diffusive cross talk between the bands" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001025_1.3005147-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001025_1.3005147-Figure8-1.png", + "caption": "Fig. 8 The velocity of the mass M can be decomposed by components in the forward \u201ex\u2026 direction and both along and perpendicular to the trailing limb", + "texts": [ + " omenclature M point mass g gravitational acceleration R roller radius K limb stiffness limb impact angle H center of mass height in an upright unstretched configuration TE total system energy L0 spring resting length Li limb length trailing limb i=1; leading limb i =2 i limb angle L\u0307i limb linear velocity \u0307i limb angular velocity L\u0308i limb linear acceleration \u0308i limb angular acceleration v point mass velocity V potential energy T kinetic energy L Lagrangian ournal of Biomechanical Engineering om: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 T Appendix A: Lagrangian Formulation of Equations of Motion The equations of motion of the conservative mass-spring model Fig. 8 were derived using a Lagrangian formulation. The total potential energy, V, in the system includes the elastic energy stored in the springs and the gravitational energy associated with the height of the mass M, V = 1 2K L0 \u2212 L1 2 + 1 2K L0 \u2212 L2 2 + R + Li cos i Mg A1 where K represents the spring stiffness, L0 represents the unstretched spring lengths, L1 represents the trailing spring length, L2 represents the leading spring length, R represents the roller radius, M represents the point mass, g is the gravitational constant, and Li and i refer to a limb currently in contact" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.39-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.39-1.png", + "caption": "FIGURE 5.39. Disassembled links of a spherical wrist.", + "texts": [ + " Attach the 2 DOF Cartesian ma nipulator to the one-link Rf--R( -90) arm and make a cylindrical ma nipul ator. Make the required changes into the coordinate frames of Exercises 3 and 6 to find t he link 's t ransformation matrices of the cylindrical manipulator. Examin e the rest position of the manipula tor. 10. Disassembled spherical wrist. A spherical wrist has three revolute joints in such a way that their joint axes inte rsect at a common point, called the wrist point. Each revolute joint of the wrist at taches two links. Disassembled links of a spherical wrist are shown in Figure 5.39. Define the required DR coordinat e frames to the links in (a) , (b) , and (c) consistentl y. Find the transformation matrices 3T4 for (a) , 4Ts for (b) , and sT6 for (c) . 11. Assembled spherical wrist . 5. Forward Kinematics 259 Lab el the coordinat e frames attached to the spherical wrist in Fig ure 5.40 according to the frames that you inst alled in Exercise 10. Determine the transformation matrices 3T6 and 3T7 for the wrist. 12. Articulat ed robots . Attach the spherical wrist of Exercise 11 to the articulated manip ulator of Exercise 7 and make a 6 DOF art iculated robot " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.6-1.png", + "caption": "Fig. 1.6 Connecting rod; a) Drawing, b) Division into elementary bodies", + "texts": [ + "1 Classification of Calculation Models 13 14 1 Model Generation and Parameter Identification Knowledge of a rigid body\u2019s ten mass parameters is required to describe the dynamic behavior of that rigid body: Mass (m), position of its center of gravity (\u03beS, \u03b7S, \u03b6S), position of the principal axes of inertia and principal moments of inertia or the moment of inertia tensor (J\u03be\u03be, J\u03be\u03b7, J\u03be\u03b6 , J\u03b7\u03b7, J\u03b7\u03b6 , J\u03b6\u03b6). Various methods of determining the parameters are used depending on whether the body is available through design documents, or as a real object (see Table 1.3). The analytical methods of determining parameters from design documents are always based on breaking the body down into elementary bodies (ring, disk, cuboid, sphere, example: see Fig. 1.6). For example, cylindrical sections with the reference axis of the moment of inertia are used as the cylinder\u2019s axis for determining the moments of inertia. Mass parameters of the rigid bodies are required as input data for computer programs. The accuracy of these parameter values (input data) is of great importance, since the accuracy of the force and motion variables to be calculated depends on it. The mass parameters cannot always be calculated with sufficient accuracy from the data of the structural description in a CAD program (and the specified material density data)", + " It should be noted that (1.11) only applies when the center of gravity is located on the connecting line of the two suspension points. If this is not the case, one must first determine the center of gravity using a static method, and then determine the moment of inertia according to (1.9) and (1.10). 18 1 Model Generation and Parameter Identification An example will be used to compare the result determined by an experiment with a rough calculation. The following has been determined for the connecting rod shown in Fig. 1.6b: e = 156 mm; m = 0.225 kg; TA = 0.681 s; TB = 0.709 s. (1.12) According to (1.11), these values can be used to determine the centroidal distance b = 89 mm and the moment of inertia JS = 7.25 \u00b7 10\u22124 kg \u00b7m2. For the rough calculation, the body is broken down into elementary bodies, as shown in Fig. 1.6b. It suffices to approximate the shaft as a prismatic rod with the dimensions lSt = 129.5 mm\u2212 46 + 27 2 mm = 93 mm f = 18 + 20 2 mm = 19 mm; c = 5 mm (1.13) . 1.2 Determination of Mass Parameters 19 Starting from axis 0, the centroidal distance \u03beS is: \u03beS = lStfc(lSt + dA1) 2 + \u03c0(d2 B1 \u2212 d2 B2)hBl 4 lStfc + \u03c0(d2 B1 \u2212 d2 B2)hB 4 + \u03c0(d2 A1 \u2212 d2 A2)hA 4 . (1.14) Substituting the numbers from Fig. 1.6, one finds \u03beS = 50.0 mm; b = l \u2212 \u03beS + dB2 2 ; b = 88.5 mm. (1.15) If a density of = 7.85 g/cm 3 is assumed, the moment of inertia about the center of gravity can be calculated from: JS = {\u03c0hA(d4 A1 \u2212 d4 A2)/32 + \u03c0(d2 A1 \u2212 d2 A2)hA\u03be2 S/4 + cf3lst/12 +fcl3St/12 + cflSt[(lSt + dA1)/2\u2212 \u03beS]2 +\u03c0hB(d4 B1 \u2212 d4 B2)/32 + \u03c0(d2 B1 \u2212 d2 B2)hB(l \u2212 \u03beS)2/4} (1.16) The result using the given numbers is JS = 7.37 \u00b7 10\u22124 kg \u00b7m2. If the shaft is approximated as a trapezoidal rod, one finds that \u03beS = 49.85 mm. The method of the rolling pendulum can be used to determine the moment of inertia JS for large cylinders or crankshafts" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.11-1.png", + "caption": "FIGURE 5.11. A R .1R(90) link.", + "texts": [ + " Therefore, the transformation matrix i- 1T i for a link with Cti = 0 and RIIR or RIIP joints, known as RIIR(O) or RIIP(O) , is r COSOi - sinOi 0 ai COS Oi j i-IT = sinOi COS Oi 0 a; sinOi , 0 0 1 di o 0 0 1 while for a link with Cti 180 deg and RIIR or RIIP joints, known as (5.33) (5.34) 214 5. Forward Kinematics RIIR(180) or RIIP(180), is [ COS o sin ei 0 ;-' T; ~ 'ir:-r;~1 Example 134 Link with K1R or KiP jo ints. Wh en the proximal j oin t of link (i) is revolute and the distal join t is either revolute or prismatic, and the joint axes at two ends are perpendicular as shown in Figure 5.11, then (}:i = 90 deg (or (}:i = -90 deg), a; is the distance between the j oin t axes on Xi, and ei is the only variable param eter. Th e joint distance di = cte is the distance between the origin of B , and Bi - I along Zi. However we usually set XiYi and Xi- IYi- I coplanar to have d; = O. The R.lR link is made by twist ing the RIIR link about its center line Xi-I -axis by 90 deg. Th e Xi and Xi- I are parallel for an R.lR link at rest position . Th erefore, the transformation matrix i- ITi for a link with (}:i = 90deg and R" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure1-1.png", + "caption": "Fig. 1. Cross-section of 9-slot/10-pole machines with different rotors. (a) Stator. (b) Configurations of the PM and iron. (c) Conventional SPM rotor. (d) Conventional CPM rotor (CPM1). (e) Proposed CPM rotor (CPM2). (f) Proposed CPM rotor (CPM3). (g) CPM2 with tangential magnetized PMs (HPM1). (h) CPM3 with tangential magnetized PMs (HPM2).", + "texts": [ + " In Section IV, the electromagnetic performance of the proposed CPM and HPM machines, including the open-circuit airgap flux density, average torque, torque ripple, loss, efficiency, unbalanced magnetic force (UMF), demagnetization withstand capability and unipolar leakage flux, are investigated and compared to those of the conventional SPM and CPM machines. A 9- slot/10-pole HPM machine is prototyped to validate the foregoing analyses in Section V, whilst Section VI is the conclusion. II. PM MACHINE WITH DIFFERENT ROTORS In order to investigate the electromagnetic performance of the machines with the conventional and proposed rotors, the 9- slot/10-pole PM machine with double-layer non-overlapping winding is employed. Fig. 1 (a) shows the 9-slot stator and winding distribution, whilst Fig. 1 (b) gives the PM and iron sequences of all the CPM rotors. Fig. 1 (c) shows the conventional SPM rotor, whilst Fig. 1 (d) shows the conventional CPM rotor (CPM1). Figs. 1 (e) and (f) show the proposed CPM rotors with N-iron-N-iron-N-S-iron-S-iron-S and iron-S-iron-S-iron-iron-N-iron-N-iron sequences, i.e, CPM2 and CPM3, respectively. Furthermore, the tangential magnetized PMs are embedded into the proposed CPM2 and CPM3 to form the HPM rotors, i.e., HPM1 and HPM2, as shown in Figs. 1 (g) and (h) In the conventional SPM machine, the adjacent PMs have opposite polarities, which constitute one pole-pair. In the CPM1, all the N pole or S pole PMs are replaced by salient irons, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003358_j.ymssp.2019.04.058-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003358_j.ymssp.2019.04.058-Figure7-1.png", + "caption": "Fig. 7. Developed experimental setup with different sensors position.", + "texts": [ + " (c) The SAE 20W-50 lubricant oil is used which doesn\u2019t have anti-wear properties. Several works in the past used similar considerations [3,9,12]. Table 2 shows the specifications of the gear used in the experiment. The gearbox health condition in the present work is monitored using the multiple sensors, namely, accelerometer, torque and temperature sensor. A flexible miniature inspection camera is also used to access the actual physical damage on the tooth. In addition, a proximity sensor is used to obtain the reference shaft rotation (key phasor) signal. Fig. 7 shows the position of the all the sensors mounted on the gearbox. The purpose and details of the sensors used are: Table 2 Gear specifications. Parameter Module No of teeth Face width Contact ratio Pressure angle Driver Gear (Pinion) 2 mm 27 10 mm 1.697 20 Driven Gear 2 mm 53 10 mm 1.697 20 (a) Accelerometer: B&K make 4514 ICP type accelerometer is used for measuring the vibration acceleration from the gearbox casing. The effectiveness and sensitivity of the sensor for early fault detection depend on the position and direction of measurement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000671_j.matdes.2012.03.011-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000671_j.matdes.2012.03.011-Figure1-1.png", + "caption": "Fig. 1. Schematic of experimental set-up.", + "texts": [ + " As LRM process, due to associated directional solidification, introduces some texture in the fabricated structure, an attempt has also been made in this work to compare corrosion resistance on three mutually perpendicular sections. The output of this study would provide valuable input regarding the suitability of laser rapid manufactured components of type 316L SS (particularly with respect to wrought products) for service in corrosive environments. The experimental setup for LRM comprised of an indigenously developed 3.5 kW CO2 laser system, integrated with a beam delivery system, co-axial powder-feeding nozzle and a 3-axis CNC work station, as shown schematically in Fig. 1. Raw laser beam, emanating out of the laser system, was folded with a 45 water-cooled gold-coated plane copper mirror and the folded laser beam was subsequently focused with a ZnSe lens (focal length = 127 mm), housed in a water-cooled co-axial copper nozzle. Laser deposition process involved scanning the substrate with a defocused laser beam of about 3 mm diameter along with simultaneous injection of type 316L SS powder into the resultant melt pool through a co-axial copper nozzle. During the course of LRM, argon gas was used as the shroud and powder carrier gas" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure12.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure12.2-1.png", + "caption": "Figure 12.2.1 Basic layouts of double-arm suspension: (a) double transverse; (b) double trailing; (c) lower transverse, upper leading; (d) lower leading, upper trailing; (e) lower trailing, upper leading.", + "texts": [ + " To control the eight variables as desired, the system must have at least eight suitable degrees of design freedom, four in the transverse properties and four in the longitudinal ones. Basically, these are the two arm lengths and the two arm angles to the horizontal. As seen in front view, this gives the first four factors, and in side view the second four. Strictly speaking, every coordinate affects every coefficient, but in practice the individual coefficients can be quite closely related to particular individual geometric features. Figure 12.2.1 shows a range of basic possibilities for the double-arm suspension. The pivot axis of each arm may be at almost any angle in plan view, although always approximately horizontal. Also, the arm lengths may vary considerably. The double transverse arm may have the pivot axes substantially parallel with the vehicle centreline, as shown, but to obtain certain characteristics one or other arm axis may be inclined in side view, or even more so in plan view. The double-trailing-arm suspension seen in Figure 12.2.1(b) is simply a particular type of double arm with the pivot axes transverse to the vehicle centreline. Figure 12.2.1(c) shows a rarer type, in which the 228 Suspension Geometry and Computation lower arm is a conventional transverse arm, but the upper arm is leading and has its axis transverse. This is geometrically, in front view, somewhat like a strut. This is a particularly extreme case of crossed axes. In Figure 12.2.1(d,e) are seen types with one leading and one trailing arm. These are unusual, but have the advantage that there is a Watt\u2019s linkage effect which minimises the fore and aft movement of the wheel centre, so these configurations are sometimes used for driven rear independent suspensions. The three-dimensional system can be approached as two separate problems, each in two dimensions only, one problem being the front (or rear) view controlling the transverse properties, the other being the side view controlling the longitudinal properties", + " This point then, with the axis direction cosines, defines the ideal rack-end axis. In the above investigation the arc of the steering arm end is not strictly in a perfect plane. Therefore, it may be preferred to obtain track-rod coordinates for more bump positions, and to fit a plane by statistical error minimisation techniques. Also, if the two arm pivot axes are not parallel, then the ideal axis is not really a straight line. In particular, this occurs with the crossed axes of the one-leading-arm one-transverse-arm suspension, shown in Figure 12.2.1(c). In that case it may be worthwhile to obtain the ideal rack end position directly for various rack longitudinal positions. The purpose of these investigations is, of course, to see the implications for rack length and ideal rack vertical position if it is moved longitudinally to alter the Ackermann factor. The strut-and-arm suspension, commonly just called a strut suspension, typically uses a basically transverse lower arm, with the upper arm and wheel carrier (wheel upright) replaced by an integrated unit of wheel carrier, slider and spring\u2013damper unit, acting on an upper trunnion where it connects to the inner part of the bodywork" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure4.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure4.6-1.png", + "caption": "Fig. 4.6 Measurement of tendon excursion for a simple tendon path. Note that a negative (as per the right hand rule) rotation of the joint \u2212\u03b4q induces a positive (rightward) tendon excursion \u03b4s that lengthens the musculotendon, and vice versa. See Sect. 4.6 for a definition of this sign covention", + "texts": [ + "4) Given that the DOF of the joint is the angle q defined from the vertical, we obtain C = 180 \u2212 q c = \u221a (a + b cos(q))2 + (b sin(q))2 Law of sines: sin(C) c = sin(A) a (4.5) \u21d2 sin(A) = a c sin(C) which leads to r = ab c sin(C) \u21d2 r = ab\u221a (a + b cos(q))2 + (b sin(q))2 sin(180 \u2212 q) (4.6) The geometry of tendon actuation also has important implications to muscle force production. This comes from the fact that the force a muscle can produce depends on its length and velocity [2, 3]. Thus it is important to calculate the length and velocity of a muscle for any posture of the limb. Consider Fig. 4.6 where we see that the change in angle \u03b4q induces an excursion, or travel, of the tendon. Call this tendon excursion \u03b4s. The question is, what is \u03b4s as a function of \u03b4q? We start with the simple example of a circular cam that produces a constant moment arm. Figure4.4 shows from first principles that Circumference = 2\u03c0r (4.7) \u03b4s = r\u03b4q (4.8) r = \u03b4s \u03b4q (4.9) These equations imply several important facts: \u2022 If \u03b4q is in radians, for a tendon with a constant moment arm r , then \u03b4s = r\u03b4q in the units of the moment arm", + " \u2022 The instantaneous moment arm, r(q), is equal to the partial derivative of the measured excursion with respect to the measured angle, Fig. 4.5. This is the formal definition of the moment arm r(q). This geometric definition is used experimentally to extract moment arm values for complex tendon paths [4, 5]. \u2022 It is critical that a sign convention be defined to specify positive and negative excursions. I used a convention based on the definition of a positive rotation as per the right hand rule. See Fig. 4.6 and Sect. 4.6. Fig. 4.7 A planar 1 DOF limb driven by 6 tendons r 3 r 2 r 1 m 1 m 3 m 2 m 4 m 6 m 5 Consider Fig. 4.7, where 6 muscles cross a planar joint. In this case we can sum the scalar equation 4.3 for each muscle to find the net joint torque at the joint, and also begin to use the notation of vector multiplication1 \u03c4 = 6\u2211 i=1 r(q)i fi (4.10) or \u03c4 = ( r(q)1, r(q)2, r(q)3, \u2212 r(q)4, \u2212 r(q)5, \u2212 r(q)6 )T \u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239d f1 f2 f3 f4 f5 f6 \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u23a0 (4.11) following the conventions that forces fi are positive values because muscles cannot push, but only pull; and moment arms r(q)i are absolute distances where their signs depend on whether their torque would induce a positive or negative rotation as per the right hand rule", + "7\u2014which is not as well highlighted in the literature [8]\u2014concerns the tendon excursions of the N muscles that cross the joint. In this case of a single DOF q \u03b4si = \u2212r(q)i\u03b4q for i = 1, . . . , N (4.17)\u239b \u239c\u239c\u239c\u239d \u03b4s1 \u03b4s2 ... \u03b4sN \u239e \u239f\u239f\u239f\u23a0 = \u239b \u239c\u239c\u239c\u239d r(q)1 r(q)2 ... r(q)N \u239e \u239f\u239f\u239f\u23a0 \u03b4q (4.18) which in vector form is \u03b4s = \u2212r(q) \u03b4q (4.19) 2Note that the letter M need not stand for muscles, nor N be used only for kinematic DOFs of a limb. They are simply letters to indicate indices and dimensions. See Appendix A. The negative sign before the moment arm vector r(q) comes from the sign convention shown in Fig. 4.6. This vector multiplication represents a mapping from the scalar value of change in joint angle (of dimension 1, or q \u2208 R 1), to the high-dimensional vector space of tendon excursions (of dimension N , or \u03b4s \u2208 R N ). R 1 \u2192 R N (4.20) Equations4.17 and 4.19 are overdetermined in that they equivalently express that a change in a single DOF \u03b4q determines the excursions \u03b4s of all N tendons. Said differently, if for some reason any of the muscles fail to stretch to keep up with the joint rotation, the single joint will lock up", + " This is the opposite of redundancy\u2014and begs the question of how the nervous system controls the excursions of all muscles so that the limb can move smoothly. We have raised this issue in [8], and we will discuss this in detail in Chap. 6. The concepts of moment arms and tendon excursions presented above extend to the case of multiple muscles crossing multiple joints. Consider the planar system with can be compiled as a moment arm matrix, R(q) \u2208 R M\u00d7N , with M rows and N columns, Eq.4.21. The entries of the R(q) matrix are the r(q)i, j values, which are signed scalars (as per the convention shown in Fig. 4.6), i is the index indicating the DOF and ranges from 1 to M , and j is the index indicating the tendon (or muscle or musculotendon) and ranges from 1 to N . R(q) = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 r(q)1,1 r(q)1,2 r(q)1,3 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 r(q)1,N r(q)2,1 r(q)2,2 r(q)2,3 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 r(q)2,N ... ... ... ... ... ... r(q)M,1 r(q)M,2 r(q)M,3 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 r(q)M,N \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (4.21) (a) The moment arm matrix can be used to transform the vector of muscle forces fm transmitted by their tendons into the vector of joint torques \u03c4 using the following vector-matrix equation \u239b \u239c\u239c\u239c\u239d \u03c41 \u03c42 ", + " Once again, by convention, the moment arm values are entries of a matrix r(q)i, j , where, i is the joint number and ranges from 1 to M , and j is the tendon (or muscle or musculotendon) number, which ranges from 1 to N , as in Eq.4.21. By convention, a moment arm is defined with positive values indicatingpositive rotationor torquegenerated at a jointwhen tension is applied to the tendon, and vice versa. However, in this case wemust consider that when a muscle induces a positive joint rotation or produces a positive torque, it must shorten or try to shorten as shown in Fig. 4.6. Therefore, a positive rotationwith a positive moment arm induces a musculotendon shortening and therefore a negative tendon excursion\u2014and vice versa. Thus if the entries r(q)i, j are arranged to represent the effect of a positive rotation of joint i on the excursion of tendon j , we obtain \u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d \u03b4s1 \u03b4s2 \u03b4s3 ... ... \u03b4sN \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u2212r(q)1,1 \u2212r(q)2,1 \u00b7 \u00b7 \u00b7 \u2212r(q)M,1 \u2212r(q)1,2 \u2212r(q)2,2 \u00b7 \u00b7 \u00b7 \u2212r(q)M,2 \u2212r(q)1,3 \u2212r(q)2,3 \u00b7 \u00b7 \u00b7 \u2212r(q)M,3 ... ... ... ... ... ... ... ... \u2212r(q)1,N \u2212r(q)2,N \u00b7 \u00b7 \u00b7 \u2212r(q)M,N \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 \u239b \u239c\u239c\u239c\u239d \u03b4q1 \u03b4q2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002702_1.4029988-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002702_1.4029988-Figure1-1.png", + "caption": "Fig. 1 Motion of the ball around the defect greater than the contact area", + "texts": [ + " The presence of defect (howsoever small) creates an obstacle in the regular motion of contact patch and this causes excitation to the bearing and the surrounding system in different forms depending on the size of the defect. Generation of only impact [16\u201323] is the widely known theory for defects greater than the contact patch but recent studies report the existence of multiple events during the passage of ball over the defect. In order to explain the number of events generated, it is important to know the relation between the defect geometry (width and depth) and the ball geometry (diameter) as explained in Fig. 1. Figure 1 illustrates the motion of the ball around the defect greater than the contact area; curvature effect of the race is assumed to be small in the vicinity of the defect and is therefore neglected. In the given figure, db is the ball diameter, ddef and hdef are the width and depth of the defect (represented with subscript \u201cdef\u201d), x1 is the angular velocity with which the ball rolls and x2 is the angular velocity with which ball hits the trailing edge of the defect, the dotted line shows the ball on the verge of entry into the defect and the solid line shows the ball into the defect. The shape of the defect is just a representative shape to illustrate a small defect where there is a two point contact. From Fig. 1 it is seen that the center of the ball sinks by an amount Dh while bridging the defect/gap and is expressed as Dh \u00bc db 2 \u00f01 cos g\u00de; g sin g \u00bc ddef =2 db=2 \u00bc ddef db (1) where g is the angle turned by the ball to hit the trailing edge and is expressed in terms of ball and defect geometry. It is assumed that the angle is small enough for the approximation. The expression for Dh may be reduced to the following equation by using the power reducing formula for (1 cosg) as sin2g/2\u00bc (1 cosg)/2: Dhapprox \u00bc d2 def 4db (2) Two events (entry and impact at the trailing edge) may be generated when the combination given in Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002193_j.measurement.2014.04.024-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002193_j.measurement.2014.04.024-Figure3-1.png", + "caption": "Fig. 3. Pinion with (a) chipped tooth, (b) missing tooth and (c) worn tooth faults.", + "texts": [ + " This setup could be considered for the replication of a variety of machine faults, for example in the gearbox, shaft misalignments, rolling element bearing damages, resonances, reciprocating mechanism effects, motor faults, pump faults, etc. In the MFS, a 3-phase induction motor was connected to a rotor that in turn was coupled to the gear box through a pulley and belt device. The gear box and its assemblage are illustrated in Fig. 2. In the analysis of faults in gears, three different types of faulty pinion gears to be precise the ND, CT, MT and WT were considered and are depicted in Fig. 3. The online data in time domain were captured with a tri-axial accelerometer (with a sensitivity of 100.3 mV/g in the x-axis direction, 100.7 mV/g in the y-axis direction and 101.4 mV/g in the z-axis direction) that was fixed on the gearbox as illustrated in Fig. 4. With the dataacquisition hardware and a computer the data were stored for further processing. Signals were captured for the rotational speed of 10\u201330 Hz in the interval of 2.5 Hz for each of four fault conditions. For each measurement set, 300 cycles of data with 2000 samples each were taken and data were collected at the rate of 20,000 samples per second" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000721_j.ymssp.2008.08.015-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000721_j.ymssp.2008.08.015-Figure4-1.png", + "caption": "Fig. 4. HyGears simulation results: contact stress patterns around a spall.", + "texts": [ + " It is worthwhile noting that the bucket profiles in RTE in smaller spalls (Fig. 3, (1)\u2013(4)) are consequence of the bridging rather than the contacting of the spall bottom. The shapes of the spalls in different stages of development shown in Fig. 3, (1)\u2013(5) were determined based on the understanding of the high contact stress positions which occur around the fault. Occurrence of a small seed spall in the mid-face of the gear tooth in the pitch line area was assumed initially. Contact stress patterns of the spall shown in Fig. 4, (a)\u2013(d) shows that very high contact stresses in the spall occur at the entry and exit ends of the spall, as contacting tooth rolls into and out of the crater, Fig. 4, (b) and (d). Somewhat higher stress on the side edges of the spall is also observed when the contacting tooth bridges across the width of the spall as it rolls over the crater, see Fig. 4, (c). The high contact stress on the entry and exit ends of the spall initially drives the rapid expansion the spall in the direction of tooth rolling. The spall expands up to where the zone of single tooth contact ends. Beyond the single tooth zone loads are shared by two tooth pairs and thus halved. The spall then continues to grow across the width of the tooth face. The first and second derivatives of the RTEs of a TFC and a spall estimate the difference between undamaged and faulty gearmesh velocity (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002302_j.ymssp.2017.01.032-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002302_j.ymssp.2017.01.032-Figure4-1.png", + "caption": "Fig. 4. Decomposition of the gear force Fri\u00f0t\u00de into the sensor direction.", + "texts": [ + " It considers the ring gear and planet gears vibrations, as opposed to the function proposed by Liang et al. [16], that only considers the planet vibrations. Notice that even though sun-planet interactions are not explicitly included in the proposed formulation, it is con- sidered since the response of planet movements are determined in part by these interactions. This is in agreement with the work of Inalpolat and Kahraman [21]. The last term of Eq. (2), sin\u00f0Xct \u00fe ar \u00fe wi\u00de, performs the decomposition of the gear force in the sensor direction (Fig. 4), and solves the issues of the other solutions found in literature [21\u201323]. In order to find the spectral composition of the theoretical sensor measurements, an analytical procedure is carried out. For this we assume that Fri\u00f0t\u00de is a function with fundamental frequency equal to f g . The spectral structure of sensor measurement yr\u00f0t\u00de is thus obtained by taking the Fourier transform (F ) of yr\u00f0t\u00de as follows: yr\u00f0t\u00de$FT Yr\u00f0f \u00de \u00bc XN i\u00bc1 Yr i \u00f0f \u00de \u00bc XN i\u00bc1 Ffsri\u00f0t\u00deg FfFri\u00f0t\u00deg Ffsin\u00f0Xct \u00fe ar \u00fe wi\u00deg \u00f04\u00de where is the convolution product" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002156_978-3-642-27482-4_8-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002156_978-3-642-27482-4_8-Figure7-1.png", + "caption": "Fig. 7 Electronic diagram", + "texts": [ + " Itwas previously designed for fitting into the Y1 modules for controlling the modular robots used for research purposes[7]. It is a minimal design with only the necessary components for controlling the robot. It includes an 8-bit pic16f876amicro-controller, headers for connecting the servos, an I2C bus for the sensors, serial connection to the PC, a test led and a switch for powering the circuit (figure 6). 13 http://www.iearobotics.com/wiki/index.php?title=Skycube An electric connection diagram is shown in figure 7, where the servos are connected directly to the board. The speed is set by means of two PWM signals. The two ultrasound sensors in the robot\u2019s front are connected thought the I2C bus. Robot version 1.0 have two ultrasound sensors, but as they are connected to the I2C bus, more sensors can be easily added. For the power supply four AAA type standard batteries are used. The board can be connected to the PC by a serial RS232 connection for downloading the firmware. The PCB has been designed with the open source Kicad tool" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000620_ac60371a025-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000620_ac60371a025-Figure3-1.png", + "caption": "Figure 3. A plot of '/*the signal-to-noise ratio obtained for 2.5 X M peroxide vs. the pH of the peroxide solutions.", + "texts": [ + " The noise a t higher Et3N levels arises primarily from fluctuations in background CL as reagents flow through the cell in the absence of added peroxide. Since the noise level was proportional to the magnitude of background CL, variations in noise re,flect the background intensity. The nature of the background CL is not presently known. One possible approach to improving signal-to-noise ratios would be to mix the C1 reagents before entering the flow cell and measure intensity a t some time after mixing. This was not tried. pH. The next parameter to be investigated was the effect of the pH of the aqueous solution on CL intensity. Figure 3 is a plot of the signal-to-noise ratios-observed as a function of pH. Optimum response is observed a t pH 8; however, sensitive peroxide analysis is possible from pH 4 to 10. Table I1 lists the relative values of signal and noise obtained for the various buffers used to encompass the pH range from 4 to 10. I t can be seen that the buffer appears to have an effect other than just a pH effect. If noise and/or signal is plotted vs. pH, discontinuities occur when a shift is made to another buffer system, particularly when the buffer is changed from phosphate to borax" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.12-1.png", + "caption": "FIGURE 5.12. An Rf-R(90) link.", + "texts": [ + " Th erefore, the transformation matrix i- ITi for a link with (}:i = 90deg and R.lR or R.lP j oin ts, kno wn as R.lR(90) or R.lP(90) , is [ COS e. 0 sin ei a; cos ei ] i- IT i = sin~e: 0 - cosei a; sin ei 1 0 di 001 5. Forward Kinematics 215 while for a link with (Xi = -90 deg and R-lR or R-lP jo ints, known as R-lR( - 90) or R-lP( -90) , is (5.35) Ex ample 135 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 (Xi = 90deg (or (Xi = -90deg), a; = 0, di = ete is the distance between the coordinates origin on z. , and Oi is the only variable parameter. Note that it is possible to have or assume d; = O. The Xi and Xi - I of an R~R link at rest position are coincident (when d, = 0) or parallel (when d; =J 0). Therefore, the transformation matrix i-I T i for a link with (Xi = 90 deg and R~R or R~P joints, kno wn as R~R( 90) or R~P(90) , is [ COO0; 0 sinOi i - I T i = sinOi 0 - COS Oi 0 1 0 0 0 0 (5.36) 216 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure4.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure4.1-1.png", + "caption": "Fig. 4.1 Diagram of an idealized two-phase machine.", + "texts": [ + " It is evident however that the determination of the parameters and the solution of equations in this form is a complicated process, but is quite possible with a digital computer. For many purposes the equations can be simplified by neglecting the Fourier terms of order 3 and higher, thus assuming that all of the inductances vary sinusoidally, with an additional constant term in some cases. The equations relating the terminal voltages to the currents in the six circuits of Fig. 1.3 are then expressed by the matrix equation u =Zi (4.1) where Z is given by Eqn. (4.2). For a two-phase machine having two armature phases ex and {3 located at 90 degrees, as shown in Fig. 4.1, the self-inductances of a b c f kd kq Z = a R a + p [ - B o + p [ -B o + p( A o + A 2 co s 20 ) B 2 co s ( 20 - 231T ) ] B c os (2 0 _ ~1T )] p C I c os 8 p D I co s 0 p D I si n 8 I b P [- B o + R a + P [A o p (- B o + B 2 co s (2 8 _ ~1T )] + A 2 co s (2 8 _ ~1T )] B 2 co s 28 ) p C I c os (o - 231T ) p D I C OS (8 - 231T ) p D I s in (8 - 231T ) P [- B o + p (- B o + R a + P [A o B 2 co s ( 20 _ ~1 T)] + A 2 co s (2 8 - 231T )] , 4) p D I CO s ( 8 _ ~1T ) P D IS in (o - ~1T ) B 2 co s 20 ) p C I co s (0 - 31T c f p C I co s 8 p C I co s (0 -2 31T ) p C I co s (8 _ ~1 T) R f + L ff p L fk d P kd p D I c os 0 p D I co s (0 _ ~1 T) p D I co s (0 _ ~ 1T) L fk d P R kd + L kk d P kq p D I si n 8 p D t si n (0 - 231T ) p D t si n (0 _ ~1 T) R kq + L kk q P - - - - - - - - - (4 ", + " Machines 61 the field and damper coils and the mutual inductance between F and KD are constant as before [26]. The inductances of a salient-poie machine vary periodically as follows when the Fourier terms of order 3 and higher are neglected: - L(i(i = Ao + A2 cos 2(J L(i(3 = B2sin 2(J L(if = C1 cos (J L(ikd = Dl cos (J L(i kq = Dl sin (J The remaining inductances involving coil (3 are obtained by replacing (J by ((J - 1f /2) in the appropriate expressions. The equations for the terminal voltage of the five coils in Fig. 4.1 are expressed by Eqn. (4.1), where Z is given by Eqn. (4.3). functions of (J, are difficult to handle directly. Subject to some Z = a (j f kd kq a R a+ p( A o + A 2 co s 28 ) pB 2 si n 28 pC l c os 8 pD l c os 8 pD t sin 8 - - - - - ~ pB 2 sin 2 8 Re t + p( A o - A 2 co s 28 ) pC l s in 8 pD t sin 8 -p D l c os 8 f kd kq i pC l c os 8 pD l co s 8 pD l si n 8 pC l s in 8 pD l sin 8 -p D l co s 8 R f + L ff P Lf kd P I L fk dP R kd + L kk d P R kq + L kk qP - - - - - - - - (4 .3 ) The General Equations of A" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure2.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure2.4-1.png", + "caption": "Fig. 2.4 The Delta robot (U.S. Patent No. 4,976,582)", + "texts": [ + " After these seminal works, in the subsequent two decades most significant efforts of the kinematician community devoted to the study of parallel manipulators focused on elucidating the forward kinematics of the Gough\u2013Stewart platform as well as introducing lower-mobility parallel manipulators. In the 1980s, at \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, EPFL, Professor Reymond Clavel revealed the original idea to design a lower-parallel manipulator to realize three translations and one rotation between the moving and fixed platforms (Fig. 2.4). Clavel\u2019s invention, named the Delta robot, was based on the use of parallelograms to constrain the rotations of the moving platform and culminated in his doctoral dissertation (Clavel 1991); Dr. Clavel had been granted the associated patent one year before (Clavel 1990). As the Delta robot was well appreciated by engineers and scientists, Clavel was honored with the prestigious Golden Robot Award, an event sponsored by ABB Flexible Automation, for his innovative work. The Delta robot is one of the most successful parallel robot designs because the original design is capable of achieving accelerations of up to 50 G and 12 G in experimental and industrial environments, respectively, in a wide workspace", + " Forward displacement analysis of general six-in-parallel SPS (Stewart) platform manipulators using SOMA coordinates. Mechanism and Machine Theory, 31(3), 331\u2013337. Wang, Y. (2007). A direct numerical solution to forward kinematics of general Stewart\u2013Gough platforms. Robotica, 25(1), 121\u2013128. Zuo, A., Wu, Q. M. J., & Gruver, W. A. (2002). Stereo vision guided control of a Stewart platform. In Proceedings IEEE International Symposium on Intelligent Control, Vancouver (pp. 27\u201330). Chapter 14 Delta Robot The Delta robot (see Fig. 2.4), a limited-degree-of-freedom (DOF) parallel manipulator invented by Clavel (1990, 1991), is one of the most emblematic and celebrated machines with parallel kinematic structures successfully introduced in both academia and industry. With the reflection of Prof. Clavel\u2014\u201c: : : why use robots with multi-kilowatt motors to handle products of only a few grams?\u201d\u2014 began an intensive and prolific research field of modern robotics. The Delta robot was designed to serve in the electronic, food, and pharmaceutical industries, which require a high level of hygiene and reliable standards for products" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002073_978-3-319-06698-1-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002073_978-3-319-06698-1-Figure8-1.png", + "caption": "Fig. 8 Finite element model of the 2-SBF chain", + "texts": [ + " 7 A deployable mechanism with a rectangular outline can be used to assemble a DM with an approximate elliptical or circular boundary. Moreover, the values of a and b are controlled independently by the two dof, each varying between rmin and rmax. Unlike the parallelogram DM, all used DUs are not exactly identical: the ones at the periphery are smaller. Amodel of such a mechanism with 14 DUs has been designed and simulated. During the deployment process, the angle between each two edges of the approximating polygon varies, so some additional revolute joints are introduced into the system to solve this problem, Fig. 8. Figure 9 shows the shape change of the DM viewed from the top. Similar designs allow to approximate and control the shape of other two-parameter curves. An example is the mechanism in Fig. 10, in which the boundary points always lie on a hyperbola, x2 a2 \u2212 y2 b2 = 1, whose parameters a and b vary when the configuration changes. As in the elliptical case, some revolute joints are added in the simulated model. The CAD model of this mechanism is built, and the simulations are performed as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure12.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure12.10-1.png", + "caption": "Figure 12.10.1 Double transverse arm, equivalent linkage mechanism for numerical solution.", + "texts": [ + "3 can then be used to obtain the coefficients of the proposed geometry, as a check, to compare the specified coefficients with the calculated ones for the derived design. This check shows that the equations are consistent. However, it does not prove them physically accurate, because of themodelling approximations, for example, the neglect of the lateral position of the ball joints, and small-angle approximations. Nevertheless, these equations are useful for design purposes, and the design may subsequently be refined by accurate numerical computer analysis in three dimensions. Given a two-dimensional equivalent front-view linkagemechanism, as in Figure 12.10.1, there are several possible solution methods for a precise solution. In general, there is no explicit solution for a specified bump of the wheel-to-road contact point E. Therefore the practical approach is to move one arm (e.g. the lower arm AB) by an angle, and solve all points from that, including the suspension bump zS\u00bc zE and scrub s\u00bcDyE. Using a suitable range of arm angles, quadratic curves can be fitted to g(zS) and s(zS) to obtain the bump camber and bump scrub coefficients, and thence the bump scrub rate coefficients" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.5-1.png", + "caption": "Fig. 4.5 Bodies j, k, and m in relative motion", + "texts": [ + "34) 74 4 Velocity Analysis Hence, expression (4.32) can be rewritten as kd dt \u02c7 D ld\u02c71 dt b1 C ld\u02c72 dt b2 C ld\u02c73 dt b3 C \u02c71 k!l b1 C \u02c72 k!l b2 C \u02c73 k!l b3: (4.35) On the other hand, note that ld dt bi D 0: (4.36) Thus, kd dt \u02c7 D ld dt .\u02c71b1 C \u02c72b2 C \u02c73b3/C k!l .\u02c71b1 C \u02c72b2 C \u02c73b3/ ; (4.37) which implies that in fact kd dt \u02c7 D ld dt \u02c7 C k!l \u02c7: \u02d8 In what follows Propositions 4.2 and 4.3 are used to determine the angular and linear velocities of several bodies in relative motion. With reference to Fig. 4.5, consider a multibody system formed by three rigid bodies labeled j, k, and m. Furthermore, let \u02c7 be an arbitrary vector. We are required to find the angular and linear velocities of point O in body m as observed from body j considering the existence of body k. To accomplish this, the time derivatives of \u02c7 as observed from bodies j and k are expressed, respectively, as 4.2 Fundamental Equations of Velocity 75 and kd dt \u02c7 D k!m \u02c7: (4.39) However, clearly jd dt \u02c7 D kd dt \u02c7 C j!k \u02c7: (4.40) Therefore, substituting Eqs", + "k D j; jC 1; : : : ; m 2; m 1/ of intermediate bodies between m and j (see Fig. 4.6). In fact, in general, j\u02dbm 6D j\u02dbjC1 C jC1\u02dbjC2 C : : :C m 2\u02dbm 1 C m 1\u02dbm: (5.4) In order to clarify this point, the next proposition investigates the relationship between the joint-acceleration rates of a multibody mechanical system formed with three rigid bodies. Then the obtained results are extended to multibody mechanical systems where the number of bodies is not a limitation. Proposition 5.1. Let j, k, and m be three rigid bodies or reference frames (see Fig. 4.5). If Om is a point embedded in body m that is instantaneously coincident with 5.2 Fundamental Equations of Acceleration 101 the point Ok of body k, then the angular and linear accelerations of body m, with point O chosen as the reference pole, with respect to body j are given respectively by j\u02dbm D j\u02dbk C k\u02dbm C j!k k!m (5.5) and jam O D jak O C kam O C 2j!k kvm O: (5.6) Proof. Taking into account that j!m D j!k C k!m [see Eq. (4.43)], according to Definition 5.1 we have j\u02dbm jd dt .j!m/ D jd dt .j", + " The Coriolis acceleration, notated as acor, is given by the following terms contained in Eq. (5.11): acor D 2j!k kvm O C kam O: (5.13) Example 5.1. Truck B is traveling at the constant speed of 50 km/h over a circular curve of radius r D 325 m (see Fig. 5.1). At the same time, truck A is accelerating in the direction of its motion at the rate 3 m/s2 and passes the center of the circle. Determine the acceleration of truck B as observed from truck A considering D 30\u0131. Hint: As an initial step identify bodies j, k, and m (see Fig. 4.5). Solution. Let XY be a reference frame attached to the center of the curve with associated unit vectors OiOj. In this example one can observe three bodies in relative motion. To apply Eq. (5.6), consider that body j D 0 is the Earth while k D A and m D B denote the labels of the trucks. Hence, 0aB D 0aA C AaB C 20!A AvB; (5.14) 5.3 Equations of Acceleration in Screw Form 103 where, because of the translational motion of body A as observed from body 0, the vector 0!A vanishes. Furthermore, 0aA D 3Oi while 0aB D v2 B r \u0152cos", + "12) Furthermore, the acceleration vector a of the rocket is obtained as a D d dt v D d dt h Pr sin. /C r P cos. / i Oj D h .Rr r P 2/ sin. /C .r R C 2Pr P / cos. / i Oj; (6.13) where Rr D r P 2 tan2. /C h .Pr P C r R / i tan. /C r P 2: (6.14) Finally, the jerk vector of the rocket results in D d dt a D d dt h .Rr r P 2/ sin. /C .r R C 2Pr P / cos. / i Oj D h .\u00abr 3r P R 3Pr P 2/ sin. /C .3Pr R r P 3 C 3Rr P C r\u00ab / cos. / i Oj; (6.15) where \u00abr D 2r P 3 tan3. /C .3r P R C 2Pr P 2/.1C tan2. //C .2r P 3C Rr P C 2Pr R C r\u00ab / tan. /: (6.16) 138 6 Jerk Analysis Proposition 6.1. With reference to Fig. 4.5, let j, k, and m be three rigid bodies or reference frames. Furthermore, let Om and Ok be two points, the first one fixed to body m and the second one attached to body k, where point Om is instantaneously coincident with point Ok. The angular and linear jerks notated as j m and j m O, respectively, of body m with respect to body j are given by j m D j k C k m C 2j!k k\u02dbm C j\u02dbk k!m C j!k j!k k!m (6.17) and j m O D j k O C k m O C 3j\u02dbk kvm O C 3j!k kam O C 3j!k j!k kvm O : (6.18) Proof. From the acceleration analysis it is known that j\u02dbm D j\u02dbk C k\u02dbm C j", + "m j!m rP=Q D j\u02dbm j!m j!m rP=Q C j!m \u02da j\u02dbm j!m rP=Q C j!m j\u02dbm rP=Q C j!m j!m rP=Q 9>>>>>>>>>>>>>>>>>>>>>= >>>>>>>>>>>>>>>>>>>>>; : (7.6) Substituting Eqs. (7.6) into Eq. (7.5) and reducing terms, one obtains j m P D j m Q C j m rP=Q C 3j m j!m rP=Q C 3j\u02dbm j\u02dbm rP=Q C3j\u02dbm j!m j!m rP=Q C 2j!m j\u02dbm j!m rP=Q Cj!m j m rP=Q C j!m j!m j\u02dbm rP=Q Cj!m \u02da j!m j!m j!m rP=Q : (7.7) Expression (7.7) provides the means to study the hyper-jerk of three bodies in relative motion. Proposition 7.1. With reference to Fig. 4.5, let j, k, and m be three rigid bodies or reference frames. Furthermore, let Om and Ok be two points, the first one fixed to body m and the second one attached to body k, where point Om is instantaneously coincident with point Ok. The angular and linear hyper-jerks, the vectors j m and j m O, of body m with respect to body j are given, respectively, by j m D j k C k m C 3j!k k m C 3j\u02dbm k\u02dbm C 3j!m j!k k\u02dbm C 2j\u02dbk j!k k!m C 162 7 Hyper-Jerk Analysis j k k!m C j!k j\u02dbk k!m C j!k j!k j!k k!m (7.8) and j m O D j k O C k m O C 4j", + "41) can equate separately to an arbitrary vector C without affecting the meaning of Eq. (7.41). For example, we have FP C 3j m jvm P C 3j\u02dbm jam P C j!m j m P D FQ C 3j m jvm Q C 3j\u02dbm jam Q C j!m j m Q D C; (7.44) where in general C 6D 0. However, the simplest representation of the reduced hyper-jerk state arises precisely when C D 0. The correctness of the representation of the hyper-jerk state of a rigid body through Eq. (7.31) has been proven; now let us consider three rigid bodies j, k, and m in relative motion (see Fig. 4.5). The reduced hyper-jerk state of body m as measured from body j, based on Eqs. (4.63), (4.43), (4.55), (5.5), (5.6), (5.30), (5.36), (6.17), (6.18), (6.43), (6.44), (7.8), and (7.9), may be determined as follows: 170 7 Hyper-Jerk Analysis jHm O D j m j m O 3j m jvm O 3j\u02dbm jam O j!m j m O D \" j k j k O 3j k jvk Q 3j\u02dbk jak O j!k j k O # C k m k m O 3k m kvm O 3k\u02dbm kam O k!m k m O C3 j!k k m j!k .k m O 2k\u02dbm kvm O k!m kam O/ k m jvk O C3 j\u02dbk k\u02dbm j\u02dbk .kam O k!m kvm O/ k\u02dbm .jak O j!k jvk O/ C3 2 4 j" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003703_j.mechmachtheory.2020.103889-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003703_j.mechmachtheory.2020.103889-Figure4-1.png", + "caption": "Fig. 4. The ball-raceway contact state determination.", + "texts": [ + " In addition, according to the results of the previous studies [12\u201330] part of balls may separate from the inner raceway when ball bearing is subjected to a large external load (The ball is always in contact with the outer ring due to the action of ball centrifugal force). This phenomenon also can be generated for ball bearing with a larger angular misalignment of the inner ring. Therefore, in order to guarantee the smooth progress of iteration calculation, the contact state between ball and inner raceway needed be judged in each iteration calculation. The geometry relationship in the ball-inner raceway contact at the critical contact/separation state is given in Fig. 4 . One can find that the ball and inner raceway curvature centers respectively shift from point O bk to O \u2032 bk and point O ik to O \u2032 ik under the combined action of the inertia forces and external loads. Therefore, the elastic deformation in ball-inner raceway contact can be written as: \u03b4ik = O \u2032 ik O \u2032 bk \u2212 ( r i \u2212 0 . 5 D ) (19) If the ball separates from the inner raceway, the following inequality can be written: O \u2032 bk O \u2032 ik = \u221a ( P O \u2032 bk )2 + ( P O \u2032 ik )2 \u2264 r i \u2212 0 . 5 D (20) { P O \u2032 bk = ( r i + r o \u2212 D ) cos \u03b10 + \u03b4rk \u2212 ok P O \u2032 ik = ( r i + r o \u2212 D ) sin \u03b10 + \u03b4ak (21) Based on the above analysis, one can find that only two unknown variables \u03b1ik and \u03b1ok are introduced in mechanical analysis of local balls, and other variables can be explicitly expressed by the variables \u03b1ik and \u03b1ok " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001007_1.4025219-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001007_1.4025219-Figure1-1.png", + "caption": "Fig. 1 Representation of planar motion pattern: E virtual chain", + "texts": [ + " Although the type synthesis of planar PMs can be carried out using different approaches and is thought to be well-solved, this section will present a systematic study of this problem using the virtual-chain approach to the type synthesis of PMs [10] and reveal planar PMs, especially those with a Bennett CU, that have not been presented in the literature. 2.1 Virtual-Chain Approach. Using the virtual-chain approach to the type synthesis of PMs [10], planar PMs can be constructed using several classes of CUs [10,14]. One of the key ideas underlying this approach is to represent each motion pattern using a virtual chain, which helps reduce the type synthesis of PMs to the type synthesis of single-loop kinematic chains using CUs. A planar motion can be represented by a planar virtual chain (also E virtual chain, Fig. 1). An E virtual chain may take different forms such as a planar kinematic chain composed of two prismatic (P) joints and one R joint or a planar kinematic chain composed of three R joints. The latter, denoted by either E or (RRR)E, will be used in this paper as it facilitates the type synthesis of planar PMs composed of only R joints. Here and throughout this paper, both the moving platform and base are represented using a ring with extra holes to facilitate creating the CAD models for different PMs. The wrench system of the E virtual chain is a 2 f1 1 f0 - system (Fig. 1). A basis of the 2 f1 1 f0-system is composed of two basis wrenches of 1-pitch (f11 and f12) and one basis wrench of 0-pitch (f03). The axis of f1j is parallel to the plane of motion of the E virtual chain or is perpendicular to the axes of the R joints within the E virtual chain. The axis of f03 is perpendicular to the plane of motion of the E virtual chain. For clarity, s denotes a unit vector parallel to the axes of the R joints within the E virtual chain. f1 and f0 are represented by a dotted square arrow and a dotted round arrow, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000904_tmech.2009.2013943-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000904_tmech.2009.2013943-Figure1-1.png", + "caption": "Fig. 1. Robot pose using conventional versus cluster space representations. A conventional description of a cluster of robots provides individual robot frame descriptions with respect to a global frame, typically in the form of a homogeneous transform T . The cluster space description establishes a cluster reference frame; references to individual robots in the cluster are made with respect to this cluster frame.", + "texts": [ + " Overall, the cluster space approach allows the pilot to specify and monitor motions from the cluster space perspective, with automated kinematic transformations converting this point of view to and from robot-specific drive commands and sensor data. The first step in the development of the cluster space control architecture is the selection of an appropriate set of cluster space state variables. To do this, we introduce a cluster reference frame and select a set of state variables that capture key pose and geometry elements of the cluster. A. Introduction of a Cluster Reference Frame Consider the simplified, general case of an n-robot system where each robot has the same m DOF and an attached body frame, as depicted in Fig. 1. Let m = p + r, where p is the number of translational DOFs and r is the number of rotational DOFs for each robot. Typical robot-oriented representations of pose use (nm) variables to represent the position and orientation of each of the robot body frames, {1}, {2}, . . ., {n}, with respect to a global frame {G}. These may be formalized as n robot-specific homogeneous transforms, G 1 T, G 2 T, . . . , G n T , where for robot i G i T = ( G i R GPio r g [ 0 0 0 ] 1 ) (1) where G i R is a rotation matrix denoting the orientation of the {i} frame with respect to {G}, and GPio r g is a vector specifying the translation of the origin of frame {i} with respect to {G}" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure6-1.png", + "caption": "Fig. 6. Dimensions of contact ellipse and area of interference in: (a) pinion and gear tooth surfaces, and (b) reference surface \u03a3r.", + "texts": [ + " (v) Ratio a/b of the lengths of major and minor semi-axis of the contact ellipse given by the Hertz theory is related with principal curvature radii RI and RII as [10]: RI RII = a b 2 E e\u00f0 \u00de\u2212K e\u00f0 \u00de K e\u00f0 \u00de\u2212E e\u00f0 \u00de : \u00f04\u00de Here, e = ffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u2212 b2 a2 r is the eccentricity of the ellipse; K e\u00f0 \u00de = \u222b\u03c0 = 2 0 1\u2212e sin2\u03b8 \u22121=2 d\u03b8 is the complete elliptic integral of the first kind [13]; E e\u00f0 \u00de = \u222b\u03c0 = 2 0 1\u2212e sin2\u03b8 1=2 d\u03b8 is the complete elliptic integral of the second kind [13]. For the solution of Eq. (4), the ratio a/b is considered as unknown. During the iterative process for solution of Eq. (4), elliptic integrals K(e) and E(e) are determined numerically as a function of values a/b. The dimensions of the semi-major and semi-minor axes of the contact ellipse, a and b, are quite different from the dimensions of the semi-major and semiminor axes of the contact area of interference, A and B, as shown schematically in Fig. 6 for a given compression \u03b4. (vi) The dimensions of the contact ellipse, a and b, may be obtained by consideration of an additional relation between a and b [10], a \u22c5 b = 3FRe 4E\u204e 2=3 F1 e\u00f0 \u00de\u00bd 2: \u00f05\u00de Here, \u2013 F is the transmitted load between the pair of teeth and can be obtained from T1=r1(P)\u00d7Fn1 (P) wherein T1 is the applied torque to the pinion.ffiffiffiffiffiffiffiffiffiffip \u2013 Re = RIRII is the equivalent radius of curvature at the contact point. \u2013 ET = 1 1\u2212\u03bd2 1 E1 + 1\u2212\u03bd2 2 E2 is the equivalent elastic modulus, that is a function of elastic modules E1 and E2 and Poisson's ratios \u03bd1 and \u03bd2 of pinion and gear materials" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure15.16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure15.16-1.png", + "caption": "Figure 15.16.1 Factors f2 and f3 for PointITinit and PointIT.", + "texts": [ + " Purpose: \u2018Point In a Triangle initialisation\u2019 \u2013 to obtain the factors for location of a point in the plane of a triangle, in terms of the triangle corner point coordinates. This is for later use by PointIT, after the triangle has moved, carrying the point P with it. The point P must be accurately in the plane of the triangle, but not necessarily within the bounding sides of the triangle. Inputs: Coordinates of the three triangle-defining points P1, P2 and P3, and of the in-plane point to be analysed P 310 Suspension Geometry and Computation Outputs: The factors f2 and f3, Figure 15.16.1 Notes: The coordinates of a point P in the plane of a triangle may be expressed symmetrically by xP \u00bc f1x1 \u00fe f2x2 \u00fe f3x3 yP \u00bc f1y1 \u00fe f2y2 \u00fe f3y3 zP \u00bc f1z1 \u00fe f2z2 \u00fe f3z3 \u00f015:16:1\u00de The additional factor f1 is f1 \u00bc 1 f2 f3 \u00f015:16:2\u00de Slightly more simply, using only two factors, it may be represented by xP \u00bc x1 \u00fe f2\u00f0x2 x1\u00de\u00fe f3\u00f0x3 x1\u00de yP \u00bc y1 \u00fe f2\u00f0y2 y1\u00de\u00fe f3\u00f0y3 y1\u00de zP \u00bc z1 \u00fe f2\u00f0z2 z1\u00de\u00fe f3\u00f0z3 z1\u00de \u00f015:16:3\u00de Using local coordinates u\u00bc x x1, v\u00bc y y1 and w\u00bc z z1, uP \u00bc f2u2 \u00fe f3u3 vP \u00bc f2v2 \u00fe f3v3 wP \u00bc f2w2 \u00fe f3w3 \u00f015:16:4\u00de The local coordinates have origin at P1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001076_j.wear.2013.11.016-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001076_j.wear.2013.11.016-Figure4-1.png", + "caption": "Fig. 4. Test gears.", + "texts": [ + " In the AB and DE regions the theoretical tooth load is half of the total tooth load. Accordingly, distribution of the tooth load that is formed by tooth force on the surface along line of action is as shown in Fig. 3(a). This distribution is valid if gears are totally rigid. In practice, distribution of the load is as shown in Fig. 3(b) since gear are not totally rigid and thus deform under load [21,22]. The pinion and internal gear which were used in experimental studies were St50 steel with a surface hardness of 160\u2013170 HB (Fig. 4). The geometrical properties of gears are given in Table 1. In Table 1 subscript 1 and 2 shows the pinion and the internal gear respectively. For experimental studies, a pinion-internal gear fatigue and wear test apparatus which has the same working principle with FZG closed circuit power circulation system [23,24] is manufactured and wear experiments are performed (Fig. 5). The apparatus which is shown in Fig. 5 consists of two gear boxes providing the same contact ratio. One of the gear boxes transmits power coming from the electromotor to the shafts" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002899_joe.2017.2651242-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002899_joe.2017.2651242-Figure1-1.png", + "caption": "Fig. 1. Earth-fixed and body-fixed coordinate frames [20].", + "texts": [ + " Section V draws the conclusions. Notations: R denotes the set of all real numbers, Rn denotes the set of all n-dimensional real vectors, and Rn\u00d7m denotes the set of all n\u00d7m real matrices. \u03bbmin(\u00b7) denotes the minimum eigenvalue of a matrix. || \u00b7 || denotes the 2-norm of a vector or a matrix, i.e., for a vector \u03d5 = [\u03d51 , . . . , \u03d5n ]T \u2208 Rn , ||\u03d5|| = \u221a \u03d52 1 + \u00b7 \u00b7 \u00b7 + \u03d52 n and for a matrix \u03a5 \u2208 Rn\u00d7m , ||\u03a5|| =\u221a \u03bbmin(\u03a5T \u03a5). To describe ship motions, the two right-hand coordinate frames are defined as indicated in Fig. 1.OX0Y0Z0 is the earthfixed frame, which is an inertial frame. The origin O is taken as any point on the earth\u2019s surface. The axis OX0 is directed to the north, OY0 is directed to the east, and OZ0 points toward the center of the earth. AXY Z is the body-fixed frame, which is fixed to the moving ship. When the ship is port-starboard symmetric, the origin A is taken as the center of ship gravity. The axis AX is directed from aft to fore, AY is directed to starboard, and AZ is directed from top to bottom" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002751_1.g003201-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002751_1.g003201-Figure1-1.png", + "caption": "Fig. 1 Vertical and forward mode of the biplane-quadrotor UAV.", + "texts": [ + " The control of tail-sitter UAVs with one or two propellers relies on controlling the thrust of the propeller and deflection of control surface in the prop wash. The attitude control is thus largely dependent on the slipstream of the propellers and the vehicle airspeed, and special care is needed to ensure sufficient control authority from the control surfaces such as elevator, ailerons, and canards [22]. Therefore, the control approaches developed for single-propeller tail-sitter UAVs cannot be employed for quadrotor tail-sitter [14,16]. The schematic of the vehicle is shown in Fig. 1. Although significant work has been done on the design and aerodynamic analysis of the quadrotor biplane tail-sitter configuration, systematic development of flight dynamics model and control design has not been carried out. A detailed flight dynamics model of tail-sitter UAVs with longitudinal and lateraldirectional coefficients is sparse in the literature. In this paper, a complete flight dynamics model is developed with description of geometric and aerodynamics parameters along with prop wash modeling" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.20-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.20-1.png", + "caption": "Fig. 2.20 Cutting machine as an example of a machine with multiple mechanisms a) schematic of mechanism, b) motion programs of the three sequences of motion; six stages: 1 eject, 2 take up, 3 feed, 4 hold down, 5 press, 6 release", + "texts": [ + " Electric motors are typically selected based on their driving power and heating up, taking into account their duty cycle. The input torque, however, is more meaningful than the driving power when characterizing the mechanical loads on machine elements. In most machines, multiple drive mechanisms interact in an accurately coordinated sequence of motions. Designers use motion programs that describe the coordinated sequences of motions of all drives of a machine to make major decisions in the blueprint phase that also affect dynamic behavior. Figure 2.20 shows an example of a motion program. Starting from the minimum engineering requirements, a designer has to determine all sequences of motions with consideration to the dynamic aspects to ensure stable a operation even at high operating speeds. Since each mechanism involves a different set of inertia forces, the one that is most dynamically demanding should be designed, for example, such that the unsteady stages of motion are stretched over a longer periods of time. In the example shown in Fig. 2.20, the motion stages 1, 3, 4 and 6 exhibit the greatest accelerations. The reduced moment of inertia changes most in these sec- 124 2 Dynamics of Rigid Machines tions. The designer also has to take into account the influence on the excitation of torsional vibrations, see Sect. 4.3. The treatment of starting and braking processes involves the mathematical problem of integrating the differential (2.209) under the initial conditions t = 0 : \u03d5(0) = \u03d50, \u03d5\u0307(0) = \u03c90 (2.238) (angle of rotation \u03d5 = q). In physical terms, this means that the sequence of motions \u03d5(t) must be determined if an initial position \u03d50 and an initial angular velocity \u03c90 are given at a specific time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000824_iros.2007.4399407-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000824_iros.2007.4399407-Figure12-1.png", + "caption": "Fig. 12. A double pendulum model fitted to a full planar biped robot", + "texts": [ + " To realize the balance task being performed by the model, which is using the controller from the previous section, we use the acceleration induced by its control, P\u0308 d r = P\u0308m = J\u0307m\u03b8\u0307m + JmM\u22121 m (\u03c4m \u2212Nm) (13) Since the robot may have a center of mass slightly to the side due to its bent legs, we also need to feed in the CM of the robot to a slow integrator that adjusts the desired CM of the model, CMd model = \u2212Ki \u222b t 0 CMrobotdt. (14) To summarize, the full state of the system is X = \u03b8r \u03b8\u0307r \u03b8m \u03b8\u0307m \u03c4m CMd model and the full controller is \u03c4r = Nr + MrJ\u0304r(J\u0307m\u03b8\u0307m + JmM\u22121 m (\u03c4m \u2212Nm) \u2212J\u0307r \u03b8\u0307r + Kpe + Kde\u0307), (15) where \u03c4m is the torque found by simultaneous forward simulation of the model and the integral of Eq.(7). To illustrate the use of this control algorithm, we control the 3-link planar biped using the same double inverted pendulum controller from above. The two systems can be seen in Fig. 12. At the start of the simulation, the double inverted pendulum is fit to the biped using a mapping created by setting the operating points of the two models equal, \u03b8m = X\u22121 m (Xr(\u03b8r)) \u03b8\u0307m = J\u0304mJr \u03b8\u0307r The parameters of the robot and model are taken from a biped robot in our lab and are displayed in Table III. Fitting the model to the robot is an important step. We want the dynamics of the model to match the dynamics of the robot as closely as possible. So to do this, the following relationships were used: Lm 1 = 0.95(Lr 1 + Lr 2) Lm 2 = Lr 3 mm 1 = mr 1 + mr 2 mm 2 = mr 3 where these variables are described in Fig. 12. The bottom link is purposely set to a slightly shorter length than the sum of the lengths of the femur and tibia to prevent the knees straightening out. Such a condition would be problematic as a singularity exists when the knees are straight and we do not currently have constraints that would keep the knees from bending in the opposite direction. The tracking controller uses PD gains to follow the operational points. The Cartesian positions of these points are shown in Fig. 13. The gains used for this simulation were Kp = diag[10, 10, 10, 10] Kd = diag[10, 10, 10, 10] Ki = 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure6-1.png", + "caption": "Figure 6. Torsional vibration model of the gear transmission system.", + "texts": [ + " In addition, the pinion is hinged to the marker located at the centre of the pinion bearing hole. Hence, the method incorporates the forces and moments arising from gear meshing, motor driven torque, bracket suspension, and wheel\u2013rail impacts. High-speed trains adopt a single-stage helical gear transmission that offers the advantages of easy operation, simple structure, reliable running, and easy maintenance. In the present dynamics model, it is simplified as a torsional vibration model, as shown in Figure 6. In the torsional multibody model, all bodies have exactly one DOF that is rotation around their axis of symmetry. Moreover, the coupling of two bodies involves only two DOFs. A pair of gears can be modelled as two disks coupled by a nonlinear mesh stiffness and mesh damping. The corresponding equations of motion can be written as follows16 Ip \u20ac p \u00fe cmRp\u00bdRp _ p Rg _ g \u00fe kmRp\u00f0Rp p Rg g\u00de \u00bc Tp \u00f03\u00de Ig \u20ac g cmRg\u00bdRp _ p Rg _ g kmRg\u00f0Rp p Rg g\u00de \u00bc Tg \u00f04\u00de where p and g are the angle displacements of the pinion and gear wheel, Ip and Ig are the moments of inertia of the pinion and gear wheel, Rp and Rg are the base circle radii of the pinion and gear wheel, cm is the mesh damping, Tp and Tg are the driving torque and driven torque of the system, and km is the mesh stiffness" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000887_am100244x-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000887_am100244x-Figure2-1.png", + "caption": "FIGURE 2. Illustrations of magnetic field configurations used in the experiment. Dots and adjacent numbers represent the measured vertical magnetic field strength (in mT). The light-gray area denotes the volume occupied by the magnetic suspension, and the horizontal dashed line indicates the location of the substrate: (A) a relatively homogeneous magnetic field created by the electromagnet with circular poles; (B) a strongly inhomogeneous field created by the cubic NdFeB magnet. Notice that the third dimension of the permanent magnet is the same as the other two and that the magnetic suspension is placed in the center of the upper square plane of the magnet.", + "texts": [ + " The magnetic field gradient played an important role in the structure formation during phase separation. Its effect was studied by using two magnets to create a 450 mT vertical magnetic field with different vertical gradients on the substrate surface: an electromagnet with a circular-pole cross section (GMW 5403) and a permanent magnet with a square cross section (NdFeB, Neorem Magnets 495a). There was only a small field gradient along the axis of the electromagnet from the magnet center toward the poles (approximately 0.1 T/m; Figure 2A). More important was the transverse gradient (0.4 T/m), which in the central plane of the electromagnet (equal distances from the both poles) pointed toward the center and at the pole surfaces from the www.acsami.org VOL. 2 \u2022 NO. 8 \u2022 2226\u20132230 \u2022 2010 2227 center toward the pole edge. Approximately in the middle between the central plane and the pole planes was a region in which the transverse magnetic field gradient was negligible. If the substrate was placed on this plane, growth of the cilia mimics took place equally at all distances from the central axis of the magnet. On the other hand, if the substrate was placed on the lower pole, the transverse component pulled all of the formed structures to the edges of the dish, and if placed in the central plane, the structures migrated toward the axis of the magnet. In the case of the permanent magnet (Figure 2B), there was both a large vertical gradient (20 T/m) toward the magnet surface and a smaller gradient toward the central axis of the magnet (4 T/m). Being dominated by the vertical gradient, the magnetic structures did not show a tendency to migrate toward the central axis. The length and aspect ratio of the magnetic cilia depended strongly on the vertical magnetic field gradient. The cilia mimics made under a small vertical gradient of 0.1 T/m (electromagnet) were approximately 6 mm long and had an aspect ratio of 120 on average (Figure 3, left)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001193_j.rcim.2012.09.007-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001193_j.rcim.2012.09.007-Figure1-1.png", + "caption": "Fig. 1. Data capture for parameter identification accor", + "texts": [ + " From the points that are measured in the linear- or circularshaped paths that are independent of the axis type, this methods first determines both the joint axis direction and a point that belongs to that axis. Once path points are captured with the measuring system, the line normal to the best-fit plane that contains these points is considered to be the joint link direction. In the case of rotary joints, the circle centre that best fits the path points that are projected onto the plane is considered an axis point (Fig. 1). A characteristic of circle point analysis (CPA) is that joints located ahead of the joint that is being measured as it moving through its path must remain still, and it is preferred that the stationary joints be blocked by joint breaks as this can be an important error source for axis placement during the procedure. Thus, the CPA method obtains the spatial localisation of the joint axis for a specific robot configuration. From the algebraic analysis of two consecutive axes, it is possible to extract the parameters that form the geometric transformation between the two joints", + " However, in this case the uncertainty is not obtained analytically but by analysing the influence of the input variables covering their maximum possible range of values and analysing the possible outputs that can be determined. This process will give the most probable output value with a confidence interval, which will allow for the establishment of the related uncertainty (Fig. 5). In the CPA method, it is possible to capture the geometric information about the rotation of each joint by means of several capture methods that are generally based on the large scale coordinate measuring systems, such as laser trackers, total stations or indoor GPS (Fig. 1). Using a reflector placed on a point in a forward location of the robot structure regarding the current rotary joint, besides the capacity of tracking this reflector, makes these types of techniques simple and accurate for this task. The proposed method generates synthetic measurement points from the definition of the variables that influence the result. The variables coming from the measurement uncertainty of the measurement system used and the sampling process definition parameters will affect, in an indirect way, the final uncertainty because they cause a change in the best-fit calculations of the CPA method" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000904_tmech.2009.2013943-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000904_tmech.2009.2013943-Figure3-1.png", + "caption": "Fig. 3. Pose reference frames for the planar two-robot system.", + "texts": [ + " This work has included experiments with two-, three-, and four-robot planar land rover clusters [39]\u2013[41], with two-boat surface vessel systems [42], and for robots that are both holonomic and nonholonomic. To demonstrate the simple application of this framework, we have applied it to the specification and control of two-robot and three-robot clusters of wheeled differential drive rovers operating in a plane. This section reviews the selection of cluster space variables for each of these examples; the resulting kinematic transforms are provided in the Appendix. Fig. 3 depicts the relevant reference frames for the planar two-robot problem. Because of the sensor data used in experimentation, the global frame conventions were selected as follows: yG points to the north, xG points to the east, and \u03b8G is the compass-measured heading. For our paper, we have chosen to locate the cluster frame {C} at the cluster\u2019s centroid, oriented with xc pointing toward robot 1. Based on this, Table II summarizes the variables of interest, the applicable DOFs, and the acting constraints, following the protocol presented in Section II" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003168_s11356-020-10045-2-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003168_s11356-020-10045-2-Figure5-1.png", + "caption": "Fig. 5 Contour plots for MB dye removal efficiency as a function of process variables using RSM", + "texts": [ + " From these numerical runs, it was observed that four Gaussian membership functions resulted in lower RMSE (indicated in bold values in Table 2) for a linear output function. Hence, this topology is considered as the best or optimal network. Therefore, this optimal ANFIS topology is used in further analysis. Evaluation of the effect of process parameters on MB dye removal efficiency via RSM and ANFIS approaches For a better understanding of the influence of two independent variables and their interactions on the MB dye removal efficiency in the multi-stage vertical column, the contour plots are produced, as shown in Fig. 5. The combined effect of the influent flow rate and the ratio of H2O2/dye concentrations on dye removal efficiency were illustrated in Fig. 5a. Notably, the influent flow rate is one of the major factors that can affect the performance of MB dye removal process (Ravikumar et al. 2020). This is because the influent flow rate controls the contact time between the MB dye and the immobilized JP membrane. To understand the non-linearity of the removal process, the surface plots are produced, which gives a clear picture of the shape of non-linearity. The surface plots from the RSM and ANFIS analyses are shown in Fig. 6 a\u2013c and d\u2013f, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001007_1.4025219-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001007_1.4025219-Figure5-1.png", + "caption": "Fig. 5 Some legs for E/PPP 5 PMs: (a) 00 R 00 R 00 R R R and (b) \u00f0~R\u00de0( 00R)\u2018( 00 R)\u2018( 00 R)\u2018\u00f0~R\u00de0", + "texts": [ + " 6\u201312 in Table 1) have a 1-f1-system. In each of these legs (see the No. 6 00 R 00 R 00 R R R leg in Fig. 4(a)), for example), the axes of two or three successive R joints are parallel, and the axes of the other R joints are also parallel. These legs all satisfy the conditions for translational PMs. Therefore, the Nos. 6\u201312 legs for planar PMs are legs for E/ PPP\u00bc PMs, as listed in Nos. 2\u20138 legs in Table 3. The No. 6 00 R 00 R 00 R R R leg for planar PMs (Fig. 4(a)) is the No. 2 00 R 00 R 00 R R R leg for E/PPP\u00bc PMs (Fig. 5(a)). The legs for planar PMs of subclasses 2\u20134 (Nos. 13\u201332 in Table 1) usually have a 1-f0-system. In each of these legs, all the axes of the 00 R joints remain parallel when the moving platform undergoes planar motion. However, they do not satisfy directly the conditions for legs for translational PMs. Following the above steps 2\u20135, we can obtain legs for E/PPP\u00bc PMs by rendering each leg so that all the R joints except the 00 R joints have parallel axes that are not parallel to the axes of the 00 R joints, if possible", + " If we render all the axes of the _R joints to be parallel, all the successive _R joints are coaxial and degenerate to one R joint. Therefore, no leg for E/ PPP\u00bc PMs can be obtained from the above seven types of legs. The legs for planar PMs of subclass 3 (Nos. 20\u201329 in Table 1) are each composed of three 00 R joints and two inactive ~R joints. If we render each of these legs so that the axes of the two ~R joints are parallel, no two successive R joints become coaxial. From the ~R 00 R 00 R 00 R ~R leg (No. 29 in Table 1 as shown in Fig. 4(c)) for planar PMs, we can obtain a rendered ~R 00 R 00 R 00 R ~R (Fig. 5(b)) leg. In this rendered leg, all the 00 R joints are successive R joints with parallel axes, and the rendered ~R joints also have parallel axes. Therefore, the rendered ~R 00 R 00 R 00 R ~R leg for planar PMs is a leg for E/ Table 3 Legs for E/PPP 5 PMs in a transition configuration ci Class No. Type Description Leg-wrench system 1 5R 1 \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 The axes of two or three successive R (or ( 00 R )\u2018) joints within a leg are parallel, while the axes of the 00 R (or \u00f0~R\u00de0) joints within a PM are parallel", + " \u00f0~R\u00de0 denotes an R joint in a transition configuration which acts as an ~R joint in the planar motion mode or an R joint in both the spatial translation mode and a transition configuration. ( 00 R )\u2018 denotes an R joint in a transition configuration which acts as an 00 R joint in both the planar motion mode and a transition configuration or an R joint in the spatial translation mode. Using these two notations, the above leg for E/PPP\u00bcPMs is denoted by \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 (No. 1 leg in Table 3 as shown in Fig. 5(b)). In the transition configuration, the leg-wrench system of an \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 leg is a 1-f1-system in which the axis of the basis f1 is perpendicular to all the axes of the R joints. No leg for E/PPP\u00bc PMs can be obtained from the Nos. 22\u201323 and 26\u201328 legs in Table 1 for planar PMs, since in the associated rendered legs, there is no one group of R joints with parallel axes in which all the R joints are successive. Although legs for E/ PPP\u00bc PMs can be obtained from the Nos", + " Therefore, no leg for E/PPP\u00bc PMs can be obtained from these three types of legs. In summary, eight types of legs with a 1-f1-system have been obtained for E/PPP\u00bcPMs (Table 3) in a transition configuration. It is noted that each of the Nos. 2\u20138 legs in Table 3 has a 1-f1system in a regular configuration no matter whether the leg is in a transition configuration, the planar mode or spatial translational mode. That is why these legs can be represented using the same notations for PMs with a mono-operation mode. In the 00 R 00 R 00 R R R (Fig. 5(a)), R R 00 R 00 R 00 R , 00 R 00 R R R 00 R , and 00 R R R 00 R 00 R legs (Nos. 2\u20135 in Table 3), the R joints are inactive if the E/PPP\u00bc PM works in the planar mode, and no joint is inactive joint if the E/PPP\u00bcPM works in the spatial translational mode. In the 00 R R R R 00 R , 00 R 00 R R R R, and R R R 00 R 00 R legs (Nos. 6\u20138 in Table 3) legs, no joint is inactive no matter which mode an E/PPP\u00bcPM works in. However, the leg-wrench system of the \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 leg (Fig. 5(b), No. 1 in Table 3) changes from a 1-f0-system in the planar mode to a 1-f1-system in the spatial translational mode and vice versa. In the planar mode of the E/PPP\u00bc PM, the \u00f0~R\u00de0 joints become inactive ~R joints whose axes are not parallel anymore, and the ( 00 R )\u2018joints become 00 R joints. In the spatial translational mode of the E/PPP\u00bc PM, the ( 00 R )\u2018joints become R joints whose axes are parallel but are not parallel to the axes of the 00 R joints, and \u00f0~R\u00de0 joints become R joints with parallel axes (For details, see the example at the end of Sec", + " To guarantee that the DOF of the E/PPP\u00bcPM is three and not greater than three at a regular configuration, the linear combination of all its leg-wrench systems should be a 2-f1-1-f0-system if the PM works in the planar mode or a 3-f1-system if the PM works in the spatial translational mode. From section 3.2, it is found that a leg for E/PPP\u00bc PMs has a 1-f-system in a regular configuration (Table 3). Since the leg-wrench system of each leg varies with the change of its configuration, we make the assumption that such conditions are met as long as a 3-DOF E/PPP\u00bcPM is composed of at least three legs with a 1-f-system, including at least one \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 leg (Fig. 5(b)) that has a 1-f0-system in the planar mode, listed in Table 3. By assembling the legs listed in Table 3 and their variations, a large number of E/PPP\u00bcPMs can be obtained. The geometric constraints among legs of a PM can be clearly shown in a transition configuration of the PM by the notation of R joints: All the axes of ( 00 R )\u2018 and 00 R joints within the PM are parallel, and all the axes of R joints denoted by the same notation, \u00f0~R\u00de0, R or R, within the same leg are parallel. For example, one can obtain an \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0\u20132- 00 R 00 R 00 R R R PM by assembling one \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 leg (Fig. 5(b)) and two 00 R 00 R 00 R R R legs (Fig. 5(a)). Figure 6(b) shows a transition configuration of this PM. In this transition configuration, all the axes of the 00 R and ( 00 R )\u2018joints in the PM are parallel, the axes of the two \u00f0~R\u00de0 joints within the \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 leg are parallel, and axes of the two R joints within the same 00 R 00 R 00 R R R leg are parallel. The wrench system of each leg is a 1-f1-system in which the axis of the basis fi 11 (i\u00bc 1, 2, and 3) is perpendicular to all the axes of the R joints within the same leg" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003280_j.ijfatigue.2020.106008-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003280_j.ijfatigue.2020.106008-Figure1-1.png", + "caption": "Fig. 1. In-situ fatigue and RBF samples: (a), (d) 90\u25e6 samples; (b), (e) 45\u25e6 samples; (c), (f) 0\u25e6 samples; (g), (h) Geometries of RBF bar and in-situ fatigue samples.", + "texts": [ + " Finally, the SEM and transmission electron microscope (TEM) are applied to study the fatigue crack propagation behaviour and failure mechanism. In the present SLM processes, the Ti6Al4V powder particles whose powder size ranged from 20 to 60 \u03bcm were used. To study the effect of SLM building directions on the fatigue properties of Ti6Al4V alloys, the in-situ fatigue and rotating bending fatigue (RBF) bar samples in 0\u25e6, 45\u25e6 and 90\u25e6 building directions were fabricated by the SLM M280 equipment, as shown in Fig. 1. The material chemical composition, static mechanical properties and SLM process parameters provided by TSC Laser Technology Development (Beijing) Co., Ltd are shown in Table 1\u20133, respectively. Moreover, to reduce the negative effect of residual stress and improve the specimen ductility, the SRA process at 850 \u25e6C (2 h) was conducted for the specimens with furnace cooling. To study quantitatively the effect of AM defects on the SLM Ti alloy fatigue performance, the AM defects were preserved. No HIP process was carried out for the materials" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure14-1.png", + "caption": "Fig. 14. Function of transmission errors.", + "texts": [ + " (i) The effect of asymmetry of bearing contact (see Fig. 6) exists indeed and may be recognized wherein the helix angle is of larger magnitude. (ii) The bearing contact for the convex side is directed longitudinally and this is an advantage of the second type of geometry in comparison with the first one. (iii) The formation of the bearing contact (performed in Section 10 for stress analysis) shows that edge con- tact (that existed for the first type of geometry) is avoided. (iv) The new geometry causes a function of transmission errors (Fig. 14) of a parabolic type of a limited magnitude (up to 8 arcsec). (v) Optimization of meshing and contact is achieved by variation of the difference of parabola coefficients of the profiles for the rack-cutters of the pinion and the shaper. Fig. 15(a) shows the longitudinal bearing contact on the face-gear tooth surface that has been obtained using the following values of the parabola coefficients: as = 0.003mm 1 for the rack-cutter of the shaper and a1 = 0.002mm 1 for the rack-cutter of the pinion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002819_j.mechmachtheory.2016.11.006-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002819_j.mechmachtheory.2016.11.006-Figure2-1.png", + "caption": "Fig. 2. Displacement increment along the line of action with driven gear eccentricity.", + "texts": [ + " The NLTE is expressed as \u0394F e \u03c6 \u03b1 \u03b8 e \u03b1 \u03b8= sin( + \u00b1 ) \u2212 sin( \u00b1 )1 1 1 1 1 1 (1) where \u03c61 is the angular displacement of driving gear;e1and\u03b81are the driving gear eccentricity and its initial phase, respectively;\u03b1is the pressure angle. The upper symbols are available when the driving gear rotates counterclockwise, otherwise the under symbols are available. The time-varying backlash is generated accordingly for the reason of eccentricity, and its formula can be written as \u0394b e \u03b8 \u03c6 tan\u03b1= \u22122 cos( \u00b1 )1 1 1 1 (2) The analysis model with driven gear eccentricity is shown in Fig. 2. In this case, the formulas of NLTE and time-varying backlash are written as \u0394F e \u03c6 \u03b1 \u03b8 e \u03b1 \u03b8= sin( \u2212 \u2213 ) \u2212 sin(\u2212 \u2213 )2 2 2 2 2 2 (3) \u0394b e \u03b8 \u03c6 tan\u03b1= 2 cos( \u2213 )2 2 2 2 (4) where meanings of these symbols are same as above, and the subscript 2 denotes driven gear. Since the transmission error due to driving and driven gear eccentricities can be described by the displacement increment along the line of action and unified positive direction is given as well, the NLTE of the gear pair with double gear eccentricities can be achieved by adding the NLTE in both cases together" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001680_j.triboint.2011.11.025-Figure17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001680_j.triboint.2011.11.025-Figure17-1.png", + "caption": "Fig. 17. Alternative tooth trace corrections in the", + "texts": [ + " The higher sliding velocity between the tooth flanks is primarily responsible for this difference in temperature. The accompanying decrease in the hydrodynamic load capacity, which is due to temperature, leads to smaller minimum film thicknesses and larger solid body contact load ratios. Calculations of the \u2018\u2018rough\u2019\u2019 V-plus gearing with alternative tooth trace corrections in the direction of the width of the tooth flanks were performed at another stage of analysis. Specifically, the influence of fillets and chamfers on these calculations was studied (see Fig. 17). Unlike crowning, as is seen in Fig. 8, these tooth trace corrections alter the gap characteristic only at the edges of the teeth. Within a reduced width b0, the gap characteristic corresponds to a parallel gap. For the calculations, peak values at the edges of dfil\u00bcdcha\u00bc5 mm and a reduced width of b0 \u00bc12 mm were defined for both alternative corrections. Fig. 18 presents the most important results for the different tooth trace corrections, which are plotted along the length of action. Only slight differences are detectable within the curves of the minimum film thickness and the solid body contact load ratio" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure10.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure10.6-1.png", + "caption": "FIGURE 10.6. A planar RPR manipulator.", + "texts": [ + " Find the rotation matrix for a body frame after 30 deg rotation about the Z-axis, followed by 30 deg about the X -axis , and then 90deg about the Y-axis. T hen calculate the angu lar velocity of the body if it is turning with a = 20 deg / sec, ~ = - 40 deg / sec, and 1 = 55 deg / sec about the Z, Y , and X axes respectively. Fin ally, cal culate the angular acceleration of the body if it is turning with (i = 2 deg / sec\", $ = 4 deg / sec\", and l' = - 6deg / sec2 about the Z, Y, and X axes. 9. An RPR manipulator. Label the coordinate frames and find the velocity and acceleration of point P at the endpoint of the manipulator shown in Figure 10.6. 10. Acceleration Kinematics 445 446 10. Acceleration Kinematics 11 Motion Dynamics 11.1 Force and Moment From a Newtonian viewpoint , the forces act ing on a rigid body are divided into in tern al and exte rn al forces. Internal forces are act ing between par ti cles of the body, and exte rnal forces are act ing from outside th e body. An external force is either contact force, such as actuat ing force at a joint of a robot , or body force, such as gravitational force on th e links of a robot " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003218_tpel.2017.2710137-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003218_tpel.2017.2710137-Figure15-1.png", + "caption": "Fig. 15 Simple i-\u03a8 loci curves at high speed and large torque", + "texts": [ + " With an advance angle, the phase current at magnetization area and the chopping area is nearly the same. However, the r.m.s of phase current is reduced with advance angle at the demagnetization area. 0885-8993 (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. (c) High speed and large torque When the given torque gets larger, the chopping area is reduced and the phase current is fully conductive finally. As shown in Fig.15, without advance angle, the magnetic curve during operation looks like a soft diamond. The peak current around turn-on angle is small and peak current around turn-off angle is large, which leads to high r.m.s of phase current. So an advance angle will change the shape of magnetic curve. It increases current around turn-on angle and decreases the current around turn-off angle. S1 is the area where fully conductive current changes into chopping current around turn-on angle. In area S2, the linkage and current spikes around the advance turn-off angle are effectively reduced, which improves motor performance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001304_j.cirp.2010.03.026-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001304_j.cirp.2010.03.026-Figure8-1.png", + "caption": "Fig. 8. Approach of front and rear spindle bearing sets DA and contraction of its tip DB.", + "texts": [ + " Prior to comparing simulation results with the experiment it was necessary to define the displacement of a sleeve caused by the contraction of the spindle itself under the influence of centrifugal forces. A solid line in Fig. 7 is a sum of sleeve displacements \u2013 both forced by a set of bearings (excess of forces acting on the outer ring over the force exerted by springs) and forced by a spindle (contraction of a spindle). The result of simulations was only little diverged from the sleeve displacements measured for different rotational speeds in the range up to 45 000 rpm after subtracting the thermal component. The contribution of a spindle in the total sleeve displacement can be read from Fig. 8. It amounted, for a speed of 45 000 rpm, in about 20%. As a result of this sleeve displacement the spring force rose from 500 to 507 N. In measurements realised by means of two displacement sensors it was observed that the sleeve loses its coaxiality with the spindle. The increase of friction caused by such phenomenon can be accounted for the fact that most of measurement points are located below the curve acquired from calculations (Fig. 7). With the increased resistance to motion, a sleeve can move less than it theoretically should" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003167_j.promfg.2020.05.158-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003167_j.promfg.2020.05.158-Figure2-1.png", + "caption": "Fig. 2. Deposition strategy: (a) linear, (b) zigzag, (c) chessboard and (d) contour.", + "texts": [ + "5 mm) around the laser focal point does not significantly change the laser spot size and bead geometry, even when considering the variation of stepover within our narrow range. The optimum focal distance for both powder and laser was 3.5 mm. Deposition was carried out in ambient atmosphere with local argon shielding delivered by a coaxial nozzle at the rate of 6 L/min. Argon was also used as nozzle and carrier gas, set at the rate of 3 L/min and 5 L/min, respectively. Four different deposition strategies were considered as pathways, labeled A, B, C and D with respect to linear, zigzag, chessboard and contour raster strategies, respectively, as shown in Figure 2. These deposition paths were performed with bead stepovers of 0.44 mm and 0.55 mm through each single layer, as shown in Figure 3. Such values were defined based on previous tests, which revealed that below 0.44 mm there was no significant gain in density and above 0.55 mm the above layer profile could induce porous between layers. It can be noted that the overleaping area reduces as the stepover increases, and that may lead to deeper critical valleys in larger than 0.55 mm stepover. The trajectory rotates layer by layer in 67\u00ba for strategies A and B, and 90\u00ba for strategy C, whilst D did not use any raster rotation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003572_j.optlastec.2018.07.037-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003572_j.optlastec.2018.07.037-Figure1-1.png", + "caption": "Fig. 1. LAM-DED. (a) Experimental setup. (b) Scanning strategy.", + "texts": [ + " Although conventional processing and LAM-PBF are previously investigated and reported [6,7], there is a need to study the process development and characterization of Hast-X using LAM-DED. With significant differences in cooling pattern and solidification between two LAM processes, different material properties are expected and there is knowledge gap about properties of LAMDED Hast-X components. This motivated the current investigation. In the present study, a 2 kW continuous wave fibre laser based LAM-DED system is used (refer Fig. 1a) and the details of system are reported in our previous work [5]. The LAM-DED is set to deliver a beam spot diameter of 2.5 mm on the top surface of SS304L substrate. Gas atomized Hast-X powder conforming to AMS standard with particle size 45\u2013106 \u00b5m and spherical morphology is deposited using LAM-DED. Table 1 presents the composition of Hast-X powder used for LAM-DED. Argon gas with a 6 L per minute flow rate is used for powder feeding. Initial trials are performed by laying tracks as per full factorial design varying the laser power (600\u20131600 W), scan speed (0.3\u20130.7 m/min) and powder feed rate (5\u20138 g/min) in three, three and two levels, respectively. Process parameters are identified for defect free deposition yielding maximum deposition rate. Identified parameters with 50% overlap are used for deposition of rectangular block using LAM scanning strategy as shown in Fig. 1b. Samples are cut in the plane transverse to direction of laying, epoxy mounted and prepared using standard metallographic procedure. Subsequently, electrolytic etching is Table 1 Composition of Hast-X powder used for LAM-DED. Element Ni Cr Fe Mo C Mn Si W N O C P S Composition (%) 47 20.5 18.9 9.2 1.32 1 0.75 0.65 0.08 0.06 0.03 0.01 0.005 carried out in a solution of 10 g of oxalic acid in 100 ml distilled water at 12 V for 10\u201315 s. These etched samples are studied under optical microscope (Make: Olympus)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002066_j.ymssp.2018.06.054-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002066_j.ymssp.2018.06.054-Figure2-1.png", + "caption": "Fig. 2. Free body diagram of RIP.", + "texts": [ + " But in actual sense, the rotary motion of the arm should be considered together with the pendulum. The frictional force effect in the pendulum and arm joint are normally neglected in previous works. However, the effect of friction in RIP is clearly visible. It has been shown in Ref. [14] that the friction in the driven arm might cause LCs with high amplitude. This can have a significant impact on the performance of the proposed controllers. The RIP consists of two connected rigid bodies actuated by a servomotor system as shown in Fig. 2. These bodies are the rotational arm and the pendulum. Both the arm and pendulum have one degree of freedom (DOF). The arm is attached to the output gear of the motor, and it can rotate around the fixed point B. As shown in Ref. Fig. 2, the angle /1 is the generalized coordinate for arm, which is the angle between the arm and the horizontal x-axis (arm angle). The vectors b\u03021; b\u03022; b\u03023 are the inertial earth fixed reference frame, in which b\u03023 is away and perpendicular to the earth surface. The vectors b\u0302r ; b\u0302/1 ; b\u03023 are the arm fixed reference in which br is away from fixed point B along the arm length. The pendulum is attached to the free end of the rotating arm and has its mass center at point C. The angle /2 is the generalized coordinate for the pendulum, which is the angle between the pendulum and the vertical z-axis (pendulum angle)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure4.49-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure4.49-1.png", + "caption": "Fig. 4.49 Longitudinal lifting mechanism of a transfer manipulator; a) Mechanism schematic, b) Calculation model, 1 Drive from the press, 2 Articulated shaft (cT; bT), 3 Cam mechanism (r1 \u2212 r2 = Umax), 4 Gripper rails and workpieces", + "texts": [ + " On modern presses, workpieces are transported using so-called transfer manipulators that operate in sync with the press stroke and have to keep the workpiece immobile during the forming process. Due to the large distance between the press drive and the output link (the gripper rails), which is bridged by an articulated shaft of several meters in length, the drive cannot have a torsionally stiff design. There is a risk with fast-running manipulators that the vibrations of the grippers result in inaccurate workpiece placement and collisions in the dwell phase. Figure 4.49a shows the grossly simplified mechanism schematic and Fig. 4.49b the associated minimal model. The cam mechanism, which is characterized by its motion program U(\u03d5), is a major element of the drive system. The motion program represents the connection between the input motion \u03d5 and the output motion, in the example on hand the motion of the gripper rails x; x = U(\u03d5). This motion is characterized by two dwell phases, the transitions of which are described by a \u201cmotion program of the 5th power\u201d (VDI Guideline 2143 [36]). The following applies outside of the dwell phases: x = U(\u03d5) = Umax(10z3 \u2212 15z4 + 6z5); z = z(\u03d5) (4", + "229) 300 4 Torsional Oscillators and Longitudinal Oscillators The variable z is connected to the input angle \u03d5 in the following way: \u221270\u03c0 180 \u2264 \u03d5 \u2264 70\u03c0 180 : z = 9 7\u03c0 \u03d5 + 1 2 (rise); z\u2032 = 9 7\u03c0 70\u03c0 180 \u2264 \u03d5 \u2264 110\u03c0 180 : z = 1 (front dwell) 110\u03c0 180 \u2264 \u03d5 \u2264 250\u03c0 180 : z = \u2212 9 7\u03c0 \u03d5 + 25 14 (return); z\u2032 = \u2212 9 7\u03c0 250\u03c0 180 \u2264 \u03d5 \u2264\u221270\u03c0 180 : z = 0 (rear dwell). (4.230) The reduced moment of inertia is determined by the rotating masses of the drive (J0), the mass m of the output and the motion program. The following applies according to (2.199) J(\u03d5) = J0\u03d5 \u20322 + mx\u20322 = J0 + mU \u20322. (4.231) The equation of motion of the calculation model in Fig. 4.49b is derived from (4.223). One finds 4.5 Parameter-Excited Vibrations 301 (J0 + mU \u20322)q\u0308 + (bT + 2mU \u2032U \u2032\u2032\u03a9)q\u0307 + [cT + m\u03a92(U \u2032\u20322 + U \u2032U \u2032\u2032\u2032)]q = \u2212m\u03a92U \u2032U \u2032\u2032. (4.232) The following applies for the various derivatives of the motion program with U \u2032 = dU/d(\u03a9t) and z\u2032 according to (4.230): 0th order: U = Umax(10z3 \u2212 15z4 + 6z5) 1st order: U \u2032 = Umax30z\u2032(z2 \u2212 2z3 + z4) 2nd order: U \u2032\u2032 = Umax60z\u20322(z \u2212 3z2 + 2z3) 3rd order: U \u2032\u2032\u2032 = Umax60z\u20323(1\u2212 6z + 6z2) . (4.233) Figure 4.50a shows the various derivatives of the motion program" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000720_0278364910394392-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000720_0278364910394392-Figure1-1.png", + "caption": "Fig. 1. Two representations of the velocity of a robot. The robot, represented by the triangle, is translating up and to the right, while spinning counterclockwise. In (a), the world velocity, g\u0307, is measured with respect to the global frame. The body velocity, \u03be , in (b) is the velocity represented in the robot\u2019s instantaneous local coordinate frame.", + "texts": [ + " 2007a) has addressed this question with the development of the reconstruction equation and the local connection, tools for relating the body velocity of the system, \u03be , to its shape velocity r\u0307, and accumulated momentum p. The general reconstruction equation is of the form \u03be = \u2212A( r) r\u0307 + ( r) p, (1) where \u03be is the body velocity of the system, A( r) is the local connection, a matrix that relates joint to body velocity, ( r) is the momentum distribution function, and p is the generalized non-holonomic momentum, which captures how much the system is \u2018coasting\u2019 at any given time (Bloch et al. 2003). The body velocity, illustrated for a planar system in Figure 1(b), is the position velocity as expressed in the instantaneous local coordinate frame of the system, that is its forward, lateral, and turning velocities. For systems that translate and rotate in the plane, with an SE( 2) position space, the body and world velocities are related to each other as \u03be = \u23a1 \u23a3\u03bex \u03bey \u03be\u03b8 \u23a4 \u23a6 = \u23a1 \u23a3 cos \u03b8 sin \u03b8 0 \u2212 sin \u03b8 cos \u03b8 0 0 0 1 \u23a4 \u23a6 g\u0307, (2) where \u03b8 is the system\u2019s orientation. For systems that have as many velocity or momentum constraints as dimensions in the position space, the generalized momentum disappears (Shammas et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002483_s00170-018-2207-3-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002483_s00170-018-2207-3-Figure4-1.png", + "caption": "Fig. 4 The evolution of residual stress during the SIM process", + "texts": [ + " Because the rapid scanning speed of laser causes the short interaction between laser and material, the region irradiated by laser undergoes rapid heating, melting, rapid cooling, and solidification. This part of the material is inflated by heat, but the low-temperature region limits the expansion of the material, which leads to thermal stress. In the meantime, the yield limit of the material in the laser area is decreased with the increase of temperature. As a result, the thermal stress of partial region is greater than the yield limit of the material, and the plastic thermal compression deformation occurs. Under the constraint by cooling in surrounding area, residual stress occurs. In Fig. 4, the heated material and the solid surrounding material can be assimilated to a structural unbalance that effectively restrains the movement of the heated metallic material when the latter changes in state. During the cooling, a complex contraction of the irradiated region takes place that is a tension state, while the material that surrounds the irradiated zone undergoes an expansion that results in a compression state. The volumetric shrinking of the material melted during the cooling induces compression stresses in the surrounding material, which is under the influence of the temperature gradient" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure2.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure2.2-1.png", + "caption": "Fig. 2.2 Diagram of a simple d.c. machine:", + "texts": [ + " The voltage equations of the machine are thus R f + Lffp LdfP LdfP Rd + LdP Lqw Lqgw Uq -LdfW -Ld W Rq +Lqp LqgP Ug LqgP Rg + LggP (2.7) They are of the same form as Eqns. (1.5) but some of the coefficients in Eqns. 0.5) are now equal in pairs because of the sinusoidal flux density distribution. Hence if Lrq = Lq , are substituted into Eqns. 0.5) they become Eqns. (2.7). (2.8) The Primitive Machine 33 The torque (Eqn. (1.10\u00bb can now be expressed in terms of the flux linkages. (2.9) As a practical example of the primitive machine, consider the simplest possible d.c. machine illustrated by Fig. 2.2. The machine has only two windings. The stator has a field winding on the vertical axis (which is now the pole axis of the d.c. machine) and the rotor has a commutator winding with brushes located so that an armature current sets up a field on the horizontal axis. The vertical axis is chosen as the pole axis in order to avoid having a negative sign in the voltage equations. The diagram represents a separately excited d.c. machine with its brushes in the neutral position. As in Fig. 1.5, the armature circuit through the brushes can be replaced by an axis coil on the direct axis. The coil A then has the pseudo-stationary property discussed on p. 9. The coils F and A of Fig. 2.2 correspond to the coils G and Din the primitive machine of Fig. 1.5 and the equations can be found from Eqns. (1.5) by omitting the first and third rows and columns of the impedance matrix. R = I--R_f_+_L_f_fP----i ____ ---i G LafW Ra + LaP (2.10) These two equations do not depend on any assumption that the flux wave is sinusoidal, since both the rotational voltage Lafwir in the armature winding and the voltage Lffpif in the field winding depend on the total flux regardless of its distribution. Eqns", + "13) The curve relating the armature voltage to armature current under steady conditions with a constant field current and speed, is shown in Fig. 2.3. The positive value of fa, corresponding to motoring action, is plotted to the left in Fig. 2.3 in order to show the characteristic for a separately excited d.c. generator in the form usual in textbooks. For the idealized machine the curve is a straight line. The effects of brush shift, series windings, interpole and compensating windings can be allowed for by addition of suitable coils to the primitive machine of Fig. 2.2. However the treatment of such phenomena is not within the scope of this book. See [20]. The Primitive Machine 35 The last two types of problem covered by Table 5.1, p. 99, arise when a machine operating under steady conditions is subjected to a small disturbance. If the changes in the variables are small, so that their squares or products can be neglected, the differential equations relating the changes are linear even when the general equations are non-linear. Such equations can be used for studying steady-state stability, which depends on the effect of making a small change relative to a steady condition, or for calculating the magnitude of small oscillations which may be superimposed on a condition of steady operation. In the present section the method of analysing small changes or small oscillations is explained in detail for the simple d.c. machine represented in Fig. 2.2 for which the equations are Eqns. (2.10) and (2.12). When w is variable, these equations are non-linear because they contain the products wir and iria \u2022 However, they can be linearized by neglecting the products or squares of the small changes. The technique of linearization is explained here in relation to the simple d.c. machine. The method is applied in Section 7.6 to the more complicated synchronous machine. Assume that the field voltage changes from a steady value Uro to a slightly different value Uro + ilUf, and that all the other variables change similarly" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001835_med.2011.5983144-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001835_med.2011.5983144-Figure2-1.png", + "caption": "Fig. 2. Quadrotor helicopter configuration frame system", + "texts": [ + " Experimental results in position and velocity control are presented in order to show the overall efficacy of the proposed controller in Section V, followed by conclusions in Section V. The model of the quadrotor utilized in this article, assumes that the structure is rigid and symmetrical, the center of gravity and the body fixed frame origin coincide, the propellers are rigid and the thrust and drag forces are proportional to the square of propeller\u2019s speed. Two coordinate systems have been utilized, i.e. the Body\u2013fixed frame (BFF) 978-1-4577-0123-8/11/$26.00 \u00a92011 IEEE 1247 B = [B1, B2, B3]T and the Earth\u2013fixed frame (EFF) E = [Ex, Ey, Ez]T as presented in Figure 2. The Euler\u2013Lagrange formulation [3] of the quadrotor dynamics that takes under consideration the additive effects of the atmospheric disturbances, results in a nonlinear system, described by the following set of twelve ODEs of the form: X\u0307= f (X,U)+W\u0303 (1) with U \u2208 \u211c5 the input vector, and X \u2208 \u211c12 the state vector that consists of the translational components \u03be = [x, x\u0307, y, y\u0307, z, z\u0307]T , and the rotational components of the quadrotor, with respect to the ground, defined by \u03b7 = [\u03c6 , \u03c6\u0307 , \u03b8 , \u03b8\u0307 , \u03c8 , \u03c8\u0307]T , where \u03be , \u03b7 \u2208 \u211c6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000023_j.mechmachtheory.2006.01.003-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000023_j.mechmachtheory.2006.01.003-Figure2-1.png", + "caption": "Fig. 2. Vector model of the 3-PRS manipulator.", + "texts": [ + " Each limb contains an actuated prismatic joint inclined from the base platform by angle c (in [7] c = 0 ), followed by a passive revolute joint, a fixed length link, and a passive spherical joint. The Gru\u0308bler\u2013Kutzbach mobility criterion may be easily used to demonstrate the mechanism has three dof. In many works [7,14,17\u201319], the independent dof for this manipulator are defined as a translation along the z-axis and rotations around the x and y-axes (angles h and w, respectively, as depicted in Fig. 2). A vector model of the manipulator\u2019s first limb is depicted in Fig. 2. Two frames of reference also depicted in Fig. 2, are used to describe the manipulator and its motion. The base, or inertial frame of reference is {O} (where {*} indicates frame *) and is coincident with the centre of the base platform. Unit vectors x, y, and z denote this frame\u2019s axes. The origin of frame {P} is coincident with the centre of the moving platform and is therefore a moving reference frame with respect to the global frame {O}. The axes of frame {P} are denoted by unit vectors u, v, and w. The planes containing the second and third limbs of the manipulator make angles a and b, respectively with the first limb", + " Point Bi (i = 1,2,3) corresponds to the intersection of joint axes P and R, and points Ai are coincident with the centre of the spherical joints. Four vectors are sufficient for geometrically analyzing each limb. Vector bi \u00bc \u00bdbix ; biy ; biz T describes the position of the point Bi with respect to the inertial frame {O}. The vector li \u00bc \u00bdlix ; liy ; liz T is the vector between point Bi and a point on the moving platform. Since vector li is used to point to the spherical joint at Ai, as depicted in Fig. 2, li represents the fixed length link vector. Finally the position of the spherical joint is modelled by vectors ri \u00bc \u00bdrix ; riy ; riz T and ai \u00bc \u00bdaix ; aiy ; aiz T in reference to frames {O} and {P}, respectively. The radius of the moving platform is denoted by rp. As previously mentioned, this manipulator is capable of 3-dof motion. However, motion in these 3-dof occurs at the expense of what Carretero et al. [7] defined as \u2018parasitic motion\u2019, meaning that although only 3-dof motion is desired, the manipulator may be forced to move in other directions as well", + " Due to the complex motion of the manipulator, in addition to the existence of parasitic motions as introduced in [7], no constrained set of three Cartesian velocities in the moving frame may be used throughout the manipulator\u2019s workspace to represent the end effector velocity. Therefore, the method of constraining the Jacobian matrix as introduced in [12] is not possible. The end effector velocity must be represented using a set of Cartesian velocities in the base frame. Based on the method introduced by Kim and Ryu in [13], a dimensionally homogeneous Jacobian may be developed. This Jacobian is developed from the vectors depicted in Fig. 2 representing the manipulator. For the inclined 3-PRS manipulator, any point vi (with respect to the base frame {O}) on the plane defined by the three spherical joints (points A1, A2 and A3) may be found using the following parametric equation of the plane, where ki,j are dimensionless constants: vi \u00bc OA3 \u00fe ki;1\u00f0OA1 OA3\u00de \u00fe ki;2\u00f0OA2 OA3\u00de \u00f04\u00de It should be noted that the plane on which the end effector platform lies may be defined by any three points on that plane, not necessarily points Ai representing the spherical joints. These points are chosen here only as a matter of convenience. As depicted in Fig. 2, vectors OAi are denoted by ri. Therefore, any point vi on the plane may be defined by vi r3 \u00bc ki;1\u00f0r1 r3\u00de \u00fe ki;2\u00f0r2 r3\u00de \u00f05\u00de If in fact, the points vi were to correspond to one of three points on the end effector platform (denoted by vector ri with respect to the base frame for i = 1,2,3), then ri r3 \u00bc ki;1\u00f0r1 r3\u00de \u00fe ki;2\u00f0r2 r3\u00de \u00f06\u00de This vector loop may now be rewritten as ri \u00bc ki;1r1 \u00fe ki;2r2 \u00fe ki;3r3 \u00f07\u00de from which, values for ki,1, ki,2, and ki,3 may be easily found, where ki,1 + ki,2 + ki,3 = 1. For the most trivial case, where points ri correspond to the spherical joints, ki,j = 1 when i = j and ki,j = 0 otherwise. The vector ri may also be defined using the following closed loop vector equation: ri \u00bc bi \u00fe li \u00bc sbi jbij \u00fe sli jlij \u00f08\u00de where unit vectors sli and sbi are in the direction of li and bi, respectively. As depicted in Fig. 2, vector li represents the constant length link, and vector bi, the actuated prismatic joint. Equating expressions (7) and (8) yields ki;1r1 \u00fe ki;2r2 \u00fe ki;3r3 \u00bc sbi jbij \u00fe sli jlij \u00f09\u00de Next, taking the first time derivative of Eq. (9) yields: ki;1 _r1 \u00fe ki;2 _r2 \u00fe ki;3 _r3 \u00bc sbi j _bij \u00fe xi sli jlij \u00f010\u00de where xi is the angular velocity of the constant length limb represented by vector li. Next, projecting all elements of Eq. (10) onto the vector sli , i.e., dot-multiplying Eq. (10) by sli simplifies the equation: ki;1sT li _r1 \u00fe ki;2sT li _r2 \u00fe ki;3sT li _r3 \u00bc j _bijsT bi sli \u00f011\u00de Finally, writing Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001657_icra.2015.7139508-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001657_icra.2015.7139508-Figure1-1.png", + "caption": "Fig. 1. Independent position and attitude control by a quad tilt rotor UAV.", + "texts": [ + "jp concept could arbitrarily determine the directions of propeller thrust, it required rather complex control calculations, and was difficult to use to achieve stable flight and led to frequent flight failure. Further, the tilting propeller mechanism also improves the yaw control performance [6]. Although the previous studies could achieve independent position and attitude control, the flight performance in wide range of attitude has not been discussed yet, e.g. the UAV flies and hovers with 90 [\u25e6] pitch angle (Fig. 1(c)) and even the UAV can flip over when the range of the tilting motor is wide enough. Such flight conditions allow the UAV to fly easier in narrow space or provide possibility to work on vertical wall surfaces etc. In this paper, we focus on the attitude transition flight control system for pitch angles from 0 [\u25e6] to 90 [\u25e6] (perpendicularly-oriented flight, as shown in Fig. 1(c)) since the flight condition at a 90 [\u25e6] pitch angle significantly differs from that in a conventional quadrotor UAVs. An adequate control system and sufficient experimental validation are necessary for stable flight in a wide range of attitude conditions. Section II describes a developed quadrotor UAV with 4 tilting mechanisms for 4 propeller units. Section III explains dynamics modeling for the quad tilt rotor UAV. 978-1-4799-6923-4/15/$31.00 \u00a92015 IEEE 2326 Section IV proposes control system with low calculation cost for on-board calculation on the basis of PID control" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001489_j.snb.2015.08.013-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001489_j.snb.2015.08.013-Figure1-1.png", + "caption": "Fig. 1. Fabrication sequences of 3D micro-needle array with Pt black c", + "texts": [ + " After the in vitro test, we carried out animal test. We obtained the interstitial glucose values and measured electrochemically every 5 min. We administered the glucose solution three times a week, and checked the glucose levels four times in subcutaneous tissue. At the same time, we also took the blood samples, and analyzed by using a glucose analyzer (YSI 2300 STAT). 2.3. Electromechanical model ymatic biosensor based on 3D SUS micro-needle electrode array s B: Chem. (2015), http://dx.doi.org/10.1016/j.snb.2015.08.013 Fig. 1 shows the fabrication process of the 3D micro-needle array with Pt black catalytic layer. We patterned the proposed microneedles from 316L grade stainless steel by using jet of ferric chloride atalytic layer for the patch type non-enzymatic glucose sensor. ARTICLE IN PRESSG Model SNB-18868; No. of Pages 8 S.J. Lee et al. / Sensors and Actuators B xxx (2015) xxx\u2013xxx 3 Fig. 2. (a) A photograph of the fabricated patch type biosensor using a 3D micro-needle array with Au/Pt black-nafion working electrode and Au/Ag/AgCl-nafion counter/reference electrode; (b) Cyclic voltammogram of the fabricated 3D micro-needle array with Pt black before nafion coating (scan rate of 200 mV s\u22121, in 1 M H2SO4 solution); (c) FE-SEM image of the 3D micro-needle array with Au/Pt black on stainless steel before nafion coating; (d) FE-SEM image of Pt black formed at the tip of the micro-needle before nafion coating; (e) and (f) FE-SEM images after nafion coating; (g) Cyclic voltammograms of Pt black after and before nafion coating (scan rate of 2 w n a s p f 00 mV s\u22121, in 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001888_tie.2015.2442519-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001888_tie.2015.2442519-Figure1-1.png", + "caption": "Fig. 1. 12-slot/8-pole dual three-phase SPM machines with different winding configurations. (a) DL-1, (b) DL-2, (c) DL-3, (d) 8-pole rotor.", + "texts": [ + " can improve the torque by 3rd harmonic current injection. Meanwhile, in order to implement the 3rd harmonic current injection, the neutral point of the two sets windings should be connected, as given in [15]. Two dual three-phase 12-slot/8-pole (two sets of winding in phase) and 12-slot/10-pole (two sets of winding displaced in space by 30 elec.deg.) surface-mounted PM (SPM) machines with double-layer non-overlapping winding is employed. The winding configurations can be determined by the star slots [3]-[4]. Fig. 1 and 2 (a), (b) and (c) show the stator together with the winding connections used for the dual three-phase winding configurations of 12-slot/8-pole and 12-slot/10-pole machines. The 8-pole and 10-pole PM rotors are shown in Fig. 1 and 2 (d), respectively. These winding configurations are designated as DL-1, DL-2, and DL-3. For DL-1 configuration, the machine is split in two parts, and for DL-2 configuration, the phases of the winding are alternated along the stator circumference. The single coils are alternated in terms of the same phase order and different windings in DL-3 configuration. For the 12-slot/8pole PM machines, the fundamental winding factor Kdp1 of the winding configuration DL-1, DL-2, and DL-3 is 0.833, and the 3rd harmonic winding factor Kdp3 is 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure15.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure15.7-1.png", + "caption": "Figure 15.7.1 Triangles for the sine rule, alternative notations.", + "texts": [ + " A generally non-unit vectorN with the normal direction to the plane of A and B is given by the easily remembered form N \u00bc A B \u00bc i\u0302 j\u0302 k\u0302 xA yA zA xB yB zB where (\u0302i; j\u0302; k\u0302) with circumflex marks are unit vectors of the (x, y, z) axes respectively. Expanding the determinant in the usual way, with alternating signs, N \u00bc i\u0302\u00f0yAzB yBzA\u00de j\u0302\u00f0xAzB xBzA\u00de\u00fe k\u0302\u00f0xAyB xByA\u00de \u00bc i\u0302Nx \u00fe j\u0302Ny \u00fe k\u0302Nz This calculation of the vector normal to a plane is frequently required in suspension geometry analysis. The sine rule is occasionally useful in suspension analysis, and applies to three-dimensional triangles as well as to two-dimensional ones, both being of necessity in a single plane, Figure 15.7.1. However, it is expressed in terms of the two-dimensional properties of the triangle rather than in direct three-dimensional terms. For a triangle with sides a, b and c, with opposing angles A, B and C, sin A a \u00bc sin B b \u00bc sinC c It is easily proved by dropping a perpendicular. It can equally well be expressed in reciprocal form, a/sinA\u00bc b/sinB\u00bc c/sinC. In three dimensions, considering the cross product of various pairs of sides, in each case the magnitude of the product is equal to twice the area of the triangle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000288_jes.0b013e31803eafa8-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000288_jes.0b013e31803eafa8-Figure1-1.png", + "caption": "Figure 1. Schematic representation of the inverted pendulum mechanism of walking in adults: the hip vaults over the stance limb resulting in mechanical energy fluctuations of the center of body mass (COM). Based on this inverted pendulum model, animals cannot walk faster than the speed at which the centripetal force (ma = mV2/R, where m is the mass, V is the speed, a is the acceleration and R is the radius of curvature) required to keep the COM moving along the curved path exceeded the force provided by gravity (mg) (V2 G gL, where L is a characteristic leg length and g is the acceleration of gravity) (1).", + "texts": [ + " The obvious example of bipedal movement is among the birds and their ancestors, the theropod dinosaurs. Bipedal movement is less common among mammals, most being quadrupedal, although examples of bipedalism can be found (e.g., bears and monkeys). Erect posture and bipedal walking entail several advantages including higher viewing perspective for distant dangers or resources and free forelimbs for manipulation, flight, or combat. The dominant hypothesis regarding templates for bipedal walking in the gravity field is a process of vaulting over an inverted pendulum of the stance limb (Fig. 1) while simultaneously swinging the contralateral limb in a synchronized fashion. The literature on the pendulum mechanism of walking in different animals has been growing rapidly in recent years (5,20). The inverted pendulum model accurately predicts the general pattern of mechanical energy fluctuations of the body during walking and an optimal walking speed. Kinetic energy of forward motion of the center of mass in the first half of the stance phase is transformed into gravitational potential energy, which is partially recovered as the center of body mass (COM) falls forward and downward in the second half of the stance phase (Fig. 1). Recovery of mechanical energy by the pendulum mechanism depends on speed, amounting to a 67 ARTICLE Address for correspondence: Yuri P. Ivanenko, Ph.D., Department of Neuromotor Physiology, Scientific Institute Foundation Santa Lucia, 306 via Ardeatina, 00179 Rome, Italy (E-mail: y.ivanenko@hsantalucia.it). Accepted for publication: November 8, 2006. Associate Editor: E. Paul Zehr, Ph.D. 0091-6331/3502/67Y73 Exercise and Sport Sciences Reviews Copyright * 2007 by the American College of Sports Medicine Copyright @ 2007 by the American College of Sports Medicine", + " Dynamic similarity implies that the recovery of mechanical energy in subjects of short height, such as children, pygmies, and dwarfs, is not different from that of normal-sized adults at the same Fr. At Fr = 0.25, an optimal exchange between potential and kinetic energies of the COM occurs. Other reference Froude numbers having a biomechanical meaning are (1,20): Fr = 0.5 (walk-to-run transition speed) and Fr = 1 (upper speed limit at which the body takes off from the ground and thus walking is no longer feasible, (Fig. 1)). The pendulum mechanism has been demonstrated not only in humans but also in a wide variety of animals that differ in body size, shape, mass, leg number, posture, or skeleton type, including birds, monkeys, kangaroos, elephants, dogs, lizards, frogs, crabs, and cockroaches, and it was even applied to estimate how fast dinosaurs were moving or the size of a dinosaur from the size of its footprint (1,5). Bipedalism of hominids represents a fundamental evolutionary adaptation. Extraordinary paleoanthropological discoveries during the 20th century revealed that bipedalism was present at least a million years before stone tools and the development of a large brain (16,26)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure7.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure7.9-1.png", + "caption": "Fig. 7.9 Problem 2. Hyper-jerk analysis", + "texts": [ + "8 rotates about a fixed axis passing through point O with angular velocity ! D 5 rad=s, angular acceleration \u02db D 2 rad=s2, angular jerk D 3 rad=s3, and angular hyper-jerk D 2 rad=s4 in the indicated directions. On the other hand, the small sphere A moves in the slot undergoing relative motions with respect to the slot as follows: Pu D 2 m=s, Ru D 1:5 m=s2, \u00abu D 0:5 m=s3, and\u00acu D 3 m=s4 in the indicated directions. We must compute the instantaneous velocity, acceleration, jerk, and hyper-jerk of sphere A considering x D 0:75 m and y D 0:5 m. 2. Figure 7.9 shows an actuating mechanism for a telescoping antenna on a spacecraft. The supporting shaft j rotates about the fixed Y-axis while the orientation of the telescoping antenna is determined according to the angles .t/ D 9 C 6 sin.t/ and .t/ D 6 C 9 sin.t/. At the same time, the antenna extends according to the variable length l.t/ D 1C 18 sin.t/ while body m rotates freely with respect to body k along the unit axis OuP=O according to the angle \u02c7.t/ D 4 C 12 sin.t/. Determine the velocity, acceleration, jerk, and hyper-jerk of P as measured from the fixed body at time t D 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000466_tie.2008.2005019-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000466_tie.2008.2005019-Figure7-1.png", + "caption": "Fig. 7. Experimental setup. (a) Test rig. (b) Stator of the prototype machine.", + "texts": [ + " 6 also agree with the phenomena described in [14], which indicates that applying a terminal short circuit as a remedial action to limit the current in partially shortcircuited turns might not be suitable. As will be evident in Fig. 6, the resulting short-circuit current reaches 1.7 times the rated value of 6 A when the short-circuited turn is located in the innermost position. Experiments have been carried out in order to validate the analytical prediction using the prototype fault-tolerant PM machine. The test setup is shown in Fig. 7(a), where a dynamometer is used to control the speed and the faulttolerant PM machine operates at torque/current control mode with each phase driven by a separate H-bridge converter (not shown). Since the phase winding of the prototype machine is wire wound, it is difficult to control the exact locations of a few turns. Instead, one phase winding is divided into two separate coils connected in series, each having 42 and 20 turns, respectively. A 20-turn short-circuit fault is generated by closing a mechanical switch (relay) that is connected in parallel with the 20-turn coil, as shown in Fig. 7(b). For comparison, the analytically predicted and FE-predicted self-inductance and mutual inductance with 20 short-circuited turns in the innermost of the slot area are shown in Table II. The resulting peak phase currents at no load and rated speed of 3000 r/min are also shown in Table II. A good agreement can be observed between the FE and analytical calculation. Fig. 8 compares the analytically predicted and measured variations of the steady-state peak short-circuit current with rotor speed at no load (I1 = 0)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure11.14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure11.14-1.png", + "caption": "Figure 11.14.1 The single-arm suspension with a kingpin axis for steering.", + "texts": [ + " The dependence of these on suspension bump can be represented by quadratic expressions in the usual way: uKI \u00bc uKI0 \u00fe \u00abBKI1zS \u00fe \u00abBKI2z 2 S uKC \u00bc uKC0 \u00fe \u00abBKC1zS \u00fe \u00abBKC2z 2 S The kingpin inclination angle is generally taken as positive when it slopes inwards at the top, that is, analogous to thewheel camber angle but of reversed sign. The caster angle is positivewhen the axis slopes to the rear as it rises. The kingpin axis is fixed relative to the single arm, so the bump kingpin inclination coefficients are essentially the same as the bump camber coefficients. The kingpin axis is approximately vertical, Figure 11.14.1, specified typically by two points, the ball joints, easily giving the parametric form of the steer axis line. Numerical solution of the moved axis then follows by the same principles as for the wheel axis. It is apparent that in the case of the transverse arm there will be large changes of inclination angle, which is undesirable, with small changes of caster angle. In contrast, the trailing and semi-trailing arms have small changes of kingpin inclination angle but large changes of caster angle: \u00abBKI1 \u00bc cos uAx RA \u00abBKC1 \u00bc sin uAx RA \u00bc cos cAx RA This large caster angle variation of the steered trailing arm, over 10 in each direction, is a serious difficulty, and contributed to the early demise of the type in favour of the double-wishbone suspension" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001095_rm2010v065n02abeh004672-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001095_rm2010v065n02abeh004672-Figure1-1.png", + "caption": "Figure 1. Liouville tori and a singular manifold adjoining an unstable periodic solution.", + "texts": [ + " However, globally we discover two possible situations by moving the transversal along the trajectory and watching the behaviour of the \u2018cross\u2019: the \u2018cross\u2019 may return back to the previous position (in this case the multipliers are positive), and it may be turned through the angle \u03c0 (then the multipliers are negative). In the first case the singular integral manifold Mh0,f0 is locally the direct product of a cross by a circle, while in the second case it is a skew product (which can be thought of as a pair of Mo\u0308bius bands transversally intersecting along the common middle line); see the corresponding singular integral manifolds Mh0,f0 in Fig. 1 and Fig. 4, respectively. Following Fomenko [14], we say that the trajectory has an orientable separatrix diagram in the first case and a non-orientable separatrix diagram in the second case. The behavior of the system in this case is described as follows. Topology and stability of integrable systems 277 Theorem 3. In a neighbourhood of a non-degenerate hyperbolic trajectory \u03b3 there exist canonical coordinates I , \u03d5, p, q ({\u03d5, I} = {q, p} = 1) such that H = H(I, pq), F = F (I, pq). Here the angular coordinate \u03d5 (mod 2\u03c0) along the curve \u03b3 is defined so that \u2013 points with coordinates (I, \u03d5, p, q) and (I, \u03d5 + 2\u03c0, p, q) are identified in the case of an orientable separatrix diagram, \u2013 (I, \u03d5, p, q) and (I, \u03d5+2\u03c0,\u2212p,\u2212q) are identified in the case of a non-orientable separatrix diagram, while the original trajectory \u03b3 is defined by the equations I = 0, p = q = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.35-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.35-1.png", + "caption": "Fig. 2.35 Inertia forces and moments on a link in the fixed and body-fixed reference systems", + "texts": [], + "surrounding_texts": [ + "It is of great practical significance to know the dynamic excitation forces and moments that a machine transmits onto the frame, since these can excite undesirable vibrations in the subsoil or the buildings. The problems of machine foundations and vibration isolation that arise in this respect are discussed in more detail in Sect. 3. It is not only the maximum value of the periodic forces and moments transmitted by a machine, but the size of each Fourier coefficient that is of interest in conjunction with vibration analyses for foundations, see 3.2.1.3. In multilink mechanisms, even the higher harmonics of the inertia forces are relevant. Often the task is to keep the inertia forces and specific excitation harmonics that are transmitted onto the foundation as small as possible. The respective methods for balancing of mechanisms and balancing of rotors are discussed in 2.6. Consider a multilink mechanism whose links move in parallel planes that can be offset in the z direction, see, for example, Fig. 2.34. The goal is to determine the resultant forces and moments that are transmitted from the moving machine parts via the frame onto the foundation. Internal static and kinetostatic forces and moments of the machine, such as spring forces between individual links, processing forces (e. g. cutting and pressing forces in forming machines and polygraphic machines, gas forces in internal combustion engines and compressors), have no influence on the foundation forces since they always occur in pairs and cancel each other out. 146 2 Dynamics of Rigid Machines In real machines in which the elasticity of the links plays a part, additional inertia forces (\u201cvibration forces\u201d) that have an effect on the foundation can occur due to deformation of the links in addition to the kinetostatic forces and moments. The resultant inertia forces and moments that act from the moving mechanism onto the machine frame are derived from the force and moment balances, see 2.3.2 and the forces and moments in Fig. 2.33. Since the motions are parallel to the x-y plane, Fz = 0, and the following forces result: Fx = \u2212 I\u2211 i=2 mix\u0308Si = \u2212mx\u0308S; Fy = \u2212 I\u2211 i=2 miy\u0308Si = \u2212my\u0308S. (2.303) The input moment already known from (2.209) can also be stated as follows, see also (2.199): Man = I\u2211 i=2 [mi(x\u0308Six \u2032 Si + y\u0308Siy \u2032 Si) + JSi\u03d5\u0308i\u03d5 \u2032 i] + W \u2032 pot \u2212Q\u2217. (2.304) The position of the overall center of gravity of all moving parts of a planar mechanism results from the individual positions of the centers of gravity from the conditions xS \u00b7 I\u2211 i=2 mi = I\u2211 i=2 mixSi; yS \u00b7 I\u2211 i=2 mi = I\u2211 i=2 miySi. (2.305) 2.5 Joint Forces and Foundation Loading 147 The resultant frame forces can thus be calculated from the acceleration of the overall center of gravity. It follows that these forces only depend on the motion of the overall center of gravity and the overall mass of the links. If the overall center of gravity remains at rest during the motion, the resultant of the frame forces is identical to zero. The individual frame forces have finite values, though, and usually a resulting moment Mz remains, see also Sect. 2.6.3. The kinetic moments are, see Figs. 2.35 and (2.90): MO kin x \u2261 I\u2211 i=2 [ mizSiy\u0308Si + (JS \u03b7\u03b6i\u03d5\u0308i + JS \u03be\u03b6i\u03d5\u0307 2 i ) sin \u03d5i \u2212 (JS \u03be\u03b6i\u03d5\u0308i \u2212 JS \u03b7\u03b6i\u03d5\u0307 2 i ) cos \u03d5i ] MO kin y \u2261 \u2212 I\u2211 i=2 [ mizSix\u0308Si + (JS \u03b7\u03b6i\u03d5\u0308i + JS \u03be\u03b6i\u03d5\u0307 2 i ) cos \u03d5i + (JS \u03be\u03b6i\u03d5\u0308i \u2212 JS \u03b7\u03b6i\u03d5\u0307 2 i ) sin \u03d5i ] MO kin z \u2261 I\u2211 i=2 [mi(ySix\u0308Si \u2212 xSiy\u0308Si)\u2212 JSi\u03d5\u0308i] (2.306) Note that they depend on the position of the coordinate system relative to the machine. It is recommended to select the center of gravity of the foundation block on which the mechanism is installed as the origin O of the coordinate system when addressing foundation issues, see Figs. 3.6 and 3.8. The forces that act on the frame can of course also be calculated from the superposition of all joint forces that act onto the frame. This method is laborious, however, since it requires the calculation of the internal joint forces. 148 2 Dynamics of Rigid Machines" + ] + }, + { + "image_filename": "designv10_3_0002897_j.engfailanal.2016.12.008-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002897_j.engfailanal.2016.12.008-Figure12-1.png", + "caption": "Fig. 12. The second order resonant mode of the gearbox housing.", + "texts": [], + "surrounding_texts": [ + "According to mechanical vibration theory, the differential equations representative of a mechanical system under general excitation [15,16] are given as follows. M\u20acX t\u00f0 \u00de \u00fe C _X t\u00f0 \u00de \u00fe KX t\u00f0 \u00de \u00bc F t\u00f0 \u00de \u00f02\u00de \u03b2 \u00bc 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u2010\u03c52 2 \u00fe 2\u03b4\u03c5\u00f0 \u00de2 q \u00f03\u00de Where, M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the system, respectively, X is the system response, F is the system suffered excitation, \u03b2 is the dynamic magnification factor, \u03bd the ratio of the external excitation frequency to the natural frequency of the system, and \u03b4 is the damping ratio. Eq. (3) indicates that, when the external excitation frequency approaches the natural frequency of the structure, i.e., as \u03bd approaches 1, \u03b2 attains a maximum value, and resonance ensues. The stress time history of Section A = {1025s,1890s} and the amplitude spectral density (ASD) are shown in Fig. 20. It is observed that the dominant frequency f of the stress signal is mainly distributed in the ranges 0\u2013150 Hz and 500\u2013650 Hz. The timefrequency joint analysis of point N02 in Section A is shown in Fig. 21. Some high-energy band frequencies fi related to speed v are observed. As derived elsewhere [17], the relation between v and fi can be given as f i \u00bc ki v; \u00f04\u00de where ki is the ith linear relationship between the ith band frequency fi and the speed v. Table 3 lists the primary frequency bandsfi when v = 306 km/h. In addition, Fig. 21 shows that the three frequency bands, i.e., 60 Hz, 573 Hz, and 608 Hz, remain unchanged during train deceleration. As fi pass through the unchanged frequency bands 573 Hz and 608 Hz, their root mean square (RMS) energies obviously increase. However, as fi pass through 60 Hz, their RMS energies remain constant. According to theory of random vibration [18] and the modal analysis simulation results discussed above, 573 Hz and 608 Hz should be the natural frequencies for this type of gearbox housing. However, 60 Hz is not a natural frequency of the gearbox. A frequency-domain structure damage assessment method [19], which compares the stress damage of the origin signal (Dn) and the damage of the origin signal of a band-stop filter at a particular frequency band (Db), was conducted to assess the damage effect of the 60 Hz, 573 Hz, and 608 Hz frequency bands. The damage effect factor \u03b1 is given as follows: \u03b1 \u00bc 1\u2212Db=Dn: \u00f05\u00de The \u00b15 Hz frequency band effect factors for 60 Hz, 573 Hz, and 608 Hz are listed in Table 4. It is concluded that the 573 Hz and 608 Hz frequency bands provide the greatest contribution to the stress signal and the 60 Hz frequency band contributes the least. When the train operates at a constant speed of 306 km/h, f5 = 571 Hz is very close to the first order natural frequency of the gearbox housing, whereas f6 = 602 Hz is also close, although less so, to the second order natural frequency. Therefore, the first mode at 573 Hz is excited easily and the second mode at 608 Hz is excited only occasionally. This result is demonstrated by test data analysis provided in Fig. 21. Meanwhile, it is also verified that a larger stress response occurs at N02 while the second mode (608 Hz) is excited." + ] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.13-1.png", + "caption": "Fig. 2.13 Nomenclature on the spur differential", + "texts": [ + " The distribution of the static and dynamic forces over several gears and the low bearing loads at coaxial positioning of the input and output shafts are advantages. This enables the superposition of the speeds and torques of multiple drives, and they are also used as differential gears, see VDI Guideline 2157 [36]. The equations of motion that describe the relationships between the input moments and angular accelerations shall now be established for a simple planetary gear mechanism as outlined in Fig. 2.13. This superposition gear mechanism (also called gear set, transfer, or differential gear) has two degrees of freedom (mobility n = 2). It consists of the sun gear 2, the ring gear 3, three planetary gears and the arm that carries the planetary gears 5, all of which pivot about the z axis. The radii r2 and r4, the moments of inertia J2, J3 and J5 with respect to the fixed axis of rotation, the mass m4 of each gear 4 and the moment of inertia J4 of one of the gears 4 about its bearing axis are given. The center of gravity S of each planet gear is in its bearing axis. The torques that act on the shafts of the members 2, 3, and 5 are to be taken into account. 2.4 Kinetics of Multibody Systems 107 The constraints form the starting point for the kinematic and dynamic analysis. They are established in general form based on Fig. 2.13 so that they also apply to special cases of spur differentials with one degree of freedom (e. g. \u03d5\u03073 = 0 or \u03d5\u03075 = 0). The constraints result from the fact that the relative velocities of the engaged gears are zero at their contact points (the pitch points). Therefore, the following applies: r2\u03d5\u03072 \u2212 [r2\u03d5\u03075 \u2212 r4(\u03d5\u03074 \u2212 \u03d5\u03075)] = 0 (2.161) (r2 + 2r4)\u03d5\u03073 \u2212 [(r2 + 2r4)\u03d5\u03075 + r4(\u03d5\u03074 \u2212 \u03d5\u03075)] = 0 (2.162) Four position coordinates were introduced here, but only two independent coordinates exist due to the two constraints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure12.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure12.5-1.png", + "caption": "FIGURE 12.5. Free body diagram of a 2R palanar manipulator.", + "texts": [ + "53) h a 2 m3a3x m3a3y - m 3g h a 3 Th e matrix [A] describes the geometry of the m echanism, the vector x is the unknown forces, and the vector b indicates the dynamic terms. To solve the dynamics of the four-bar m echanism, we must calculate the accelerations \"a, and \u00b0ni and then find the required driving moment \u00b0Mo and the joints ' forces. The force E, = F 3 - F o (12.54) is called the shaking f orce and shows the reaction of the m echani sm on the ground. Example 282 2R planar manipulator Newton -Euler dynamics. A 2R planar manipulator and its free body diagram are shown in Figure 12.5. Th e torques of actuators are parallel to the Z -axis and are shown by 12. Robot Dynamics 515 Qo and QI. The Newton-Euler equations of motion for the first link are o A Fo - F I +mlgJ Q o - Q I + \u00b0nl x Fo - \"m, x \u00b0F I and the equations of motion for the second link are (12.55) (12 .56) o A m2 0a2 (12 .57)F I + m 2g J Q I + \u00b0n2 x \u00b0F I 012 002. (12.58) There are four equations for four unknowns F o, F I , Q o, and QI . These equations can be set in a matrix form [A]x= b (12 .59) where 1 0 0 - 1 0 0 0 1 0 0 - 1 0 [A] = nly - n Ix 1 -mly mIx - 1 (12 ", + " Even order recursive translational acceleration. Find an equation to relate the acceleration of link (i) to the accelera tion of link (i - 2), and the acceleration of link (i) to the acceleration of link (i + 2). 5. Even order recursive angular acceleration. Find an equation to relate the angular acceleration of link (i) to the angular acceleration of link (i - 2), and the angular acceleration of link (i) to the angular acceleration of link (i + 2). 6. Acceleration in different frames. For the 2R planar manipulator shown in Figure 12.5, find ~az, &az, \u00b0 z z dOzaI, oal, oaz, an laI \u00b7 7. Slider-crank mechanism dynamics. A planar slider-crank mechanism is shown in Figure 12.11. 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 5.37. Eliminate the joints' constraint force and moment to derive the equations for the actuators' force or moment" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003467_j.jmatprotec.2018.01.029-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003467_j.jmatprotec.2018.01.029-Figure6-1.png", + "caption": "Fig. 6. (a) FESEM image of thin walls and powder particles entrapped in the channels. Schemes of theoretical hatching distance to ensure the fabrication of (b) dense parts and (c) well defined thin wall structures by LPBF.", + "texts": [ + " Keeping scan speed constant, and with an increase in the laser power, the wall shows an increase in width due to the higher intensity of the laser beam, which causes a higher volume of melting and results in a wider and deeper melt pool. In the case of thin walls built with a P of 120, 180, and 195W, the wall\u2019s width was observed to decrease with an increase in scan speed and balling phenomenon was not observed at these higher laser power settings. With the increasing of the hd from 0.20mm to 0.40mm, the gap grows by creating well-defined walls. As can be seen in Fig. 6a, the partially melted powder particles adhere to the borders of the track surface. If the gap has a size equal to or lower than the size of the biggest particles that adhere on the borders, it can be blocked by the same powders. In some cases, the biggest particles could be completely fused to the edge of the wall (Fig. 6a). Laser power and scanning speed have a significant influence on the stability of the scan tracks, and therefore on the construction of the thin walls and on their dimensions. But their ratio expressed as a linear energy (P/v), as well as a volumetric energy density (E), as confirmed by recent studies (Bertoli et al., 2017), is not able to provide information on the complexity that involves the melt pool formation and propagation, as well as the heat and mass transfer between the melt pool and the surrounding material, such as spattering of molten material (Matthews et al", + " the samples 1, 3 and 26 have the same E of 33.33 J/mm3 and hd of 0.20mm, but they have different track morphologies. The same can be stated for the samples 11 and 24 manufactured with an hd of 0.40mm and E of 50.000 J/mm3 (Fig. 7). In the same way, if only the linear energy is considered, the samples 6 and 11 have the same values due to the same P (60W) and v (100mm/s) but again the results obtained are different. Considering the effect of hd on the construction of the thin walls, when this increases from 0.20mm to 0.40mm (Fig. 6), the channels have enough space for the powders passing. A mathematical model of the relation between process parameters and thin walls was developed by regression analysis based on ANOVA results. Based on the previous analysis, the response equation was developed considering the process parameters significant for thin wall width. The following mathematical model (R2=75.4%) was developed (Eq. (2)): Wallwidth [mm]=\u22120.003+ (0.467\u00d7 hd)+ (0.963\u00d710\u22123\u00d7 P)+ (0.145\u00d7- 10\u22123\u00d7 v)\u2212 (0.1\u00d7 10\u22125\u00d7 P\u00d7 hd) \u2013 (0.542\u00d710\u22123\u00d7 v\u00d7 hd) (2) The very numerous fine particles in the AlSi10Mg powder, with a mean diameter less than 10 \u03bcm, tend to agglomerate on the surface of the bigger ones, creating some clusters of about 60 to 80 \u03bcm. Due to these agglomerations, to construct a thin-walled structure well-spaced from one another using only the building strategy (Fig. 6b and c), it is necessary to consider, during the choice of the hd, the gap produced by the process parameters values. Based on the ANOVA results, the following mathematical model (R2=93.5%) was developed for the gap (Eq. (3)): Gapwidth [mm]=\u22120.0202+ (0.469\u00d7 hd) \u2013 (0.405\u00d710\u22123\u00d7 P) \u2013 (0.62\u00d710\u22124- \u00d7 v)+ (0.525\u00d710\u22123\u00d7 v\u00d7 hd) (3) Then, from the following Eq. 4, it is possible to obtain the right value of the hatching distance for walls well-spaced: hd,thin wall=Wallwidth+Gapwidth (4) As a check of the above equations, samples have been made using different combinations of P, v and hd" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.36-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.36-1.png", + "caption": "Fig. 6.36 Milling machine frame; a) and b) Mode shapes v1 and v2, c) Locus for the coordinate q6", + "texts": [ + "326), the following is assumed with \u03c9\u22172 = 48EI/ml3: B = 0.008\u03c9\u2217M + 0.08C/\u03c9\u2217, i. e., a1 = 0.008\u03c9\u2217, a2 = 0.08/\u03c9\u2217. The eigenvalue problem of the undamped vibration system was solved in Sect. 6.3.4.2 so that the natural circular frequencies are known from (6.136). (6.144) specifies the vectors of the initial values in principal coordinates. Calculate the modal damping ratios Di and derive the equations for calculating the coordinates qk(t) and inertia forces Qk(t). Evaluate these as compared to the undamped vibrations (Fig. 6.9). Figure 6.36 shows the simplified calculation model of the frame of a milling machine and its two lowest mode shapes. The surface quality during milling depends on the relative motion between tool and workpiece at point A. The locus for the coordinate q6 was determined for an excitation F6 in the frequency interval of interest, see Fig. 6.36. Determine the natural frequencies from the locus and comment on the amplitude frequency response based on the mode shapes shown. Examine the calculation model shown in Fig. 4.40 for the harmonic excitation given there. \u03bc = J1/J2 = 0.2; \u03b3 = cT1/cT2 = 0.2; D = bT/(2J1\u03c9\u2217) = 0.1; \u03c9\u22172 = cT2/J2 Find:1.Matrices M, C, B and excitation vector f 2.Complex frequency response H22(j\u03a9) The measured (or calculated) amplitude frequency response of a periodically excited system typically includes several resonance peaks at the excitation frequencies f0i", + "14 The natural frequencies of the machine frame can be found in the locus since the amplitudes take relative extreme values there and the phases change relatively fast. This is how one finds the natural frequencies f2 = 140 Hz and f3 = 152 Hz. The residuum at f1 is small because the force application point vibrates in opposite phase to the upper frame portion during a fundamental oscillation and moves only slightly. The residuum at \u03a9 = \u03c92 is that large because the second natural vibration shows strong deflections at point A (Fig. 6.36b). If the cutter engagement frequency were in the vicinity of the first natural frequency, this would be much less hazardous than an excitation in the vicinity of the second natural frequency. S6.15 The amplitude frequency response D22(\u03a9) for this model has already been calculated in Sect. 4.4.3. (4.191) and Fig. 4.41 show it as a nondimensionalized amplitude function V = \u03d5\u03022/\u03d5st = \u03d5\u03022c2/M\u0302 . The matrices M, B, C and the excitation vector f are derived from a comparison of coefficients from the equations of motion (4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001133_systol.2010.5675968-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001133_systol.2010.5675968-Figure2-1.png", + "caption": "Fig. 2. Qball-X4 schematic diagram ( i\u03c4 : torque produced by motor i)", + "texts": [ + " The collective thrust is controlled by varying the speed of all the rotors simultaneously. 978-1-4244-8154-5/10/$26.00 \u00a92010 IEEE 371 The paper is undertaken in a nonlinear quadrotor model Qball-X4, developed by Quanser Inc. [5]. See Fig. 1. The following nonlinear models are described for using in baseline controller development and reconfigurable control allocation design. For the following discussion, let { }e e e eE O x y z= denote an earth-fixed inertial frame and { }B Oxyz= a body-fixed frame whose origin O is at the center of mass of the Qball-X4, as shown in Fig. 2. The absolute position of the Qball-X4 is defined by ( ), , Tx y z and roll, pitch, and yaw ( ), , T\u03c6 \u03b8 \u03c8 are defined as the angles of rotation about the x, y, and z axis, respectively. The behavior of the Qball-X4 model is governed by the following six equations. 1) Qball-X4 is a rigid body; 2) Air force can be ignored at low speed; 3) Qball-X4 is symmetric with respect to axis Ox, Oy and Oz. Using Euler angles parameterization, the airframe orientation in space is given by a rotation R from B to E, z y xR R R R= c c c s s c s c s c s s s c s s s c c s s c s c s s c c c \u03c8 \u03b8 \u03c8 \u03b8 \u03c6 \u03c6 \u03c8 \u03c8 \u03b8 \u03c6 \u03c6 \u03c8 \u03c8 \u03b8 \u03c8 \u03b8 \u03c6 \u03c6 \u03c8 \u03c8 \u03b8 \u03c6 \u03c6 \u03c8 \u03b8 \u03c6 \u03b8 \u03b8 \u03c6 \u2212 +\u23a1 \u23a4 \u23a2 \u23a5= + \u2212\u23a2 \u23a5 \u23a2 \u23a5\u2212\u23a3 \u23a6 The angular rates along body axes transform into Euler rates using the transformation matrix T given below, 1 tan s tan c 0 c s 0 sec s sec c T \u03b8 \u03c6 \u03b8 \u03c6 \u03c6 \u03c6 \u03b8 \u03c6 \u03b8 \u03c6 \u23a1 \u23a4 \u23a2 \u23a5= \u2212\u23a2 \u23a5 \u23a2 \u23a5\u23a3 \u23a6 According Newton\u2019s second law, Qball-X4 nonlinear dynamic equations are written as following, 1 (cos sin cos sin sin ) 1 (sin sin cos sin cos ) 1 (cos cos ) z z z x F m y F m z g F m \u03c8 \u03b8 \u03c6 \u03c6 \u03c8 \u03c8 \u03b8 \u03c6 \u03c6 \u03c8 \u03b8 \u03c6 = + = \u2212 = \u2212 + (1) ( ) ( ) ( ) y y z x x x y z z z x y I q M I I pr I p M I I qr I r M I I pq = + \u2212 = + \u2212 = + \u2212 (2) zF is the total lift produced by four rotors; , ,x y zI I I are the moments of inertia about x, y and z axes, respectively; g is the acceleration of gravity; ,x yM M and zM are the torque in the pitch, roll and yaw directions, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001669_115103-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001669_115103-Figure2-1.png", + "caption": "Figure 2. Schematic of vision sensor system design.", + "texts": [ + " Namely, it can move in the y-axis and z-axis, respectively, and can also rotate around the z-axis. During the deposition process, the welding gun was fixed on a thick plate, and it was stationary. Single-bead multi-layer walls were generated by moving the work flat along the y-axis. After depositing a layer, the work flat made a descent in the z-axis corresponding to a predefined layer height. It was then moved to the beginning of the thin wall, and a new layer was carried out. A vision sensor system is the premise of online measurement for bead geometry. As shown in figure 2, the vision sensor system consists of two passive vision sensors. The first vision sensor, used for bead width measurement, was fixed to the rear of the welding gun. It is composed of a CCD camera, a neural and a narrow-band filter. The included angle between the camera and welding gun was about 30\u25e6. The sensor for width measurement (SWM) was here utilized for detecting the tail of the pool, namely nearly solidified field. For better distinguishing the weld bead and the background, the center wavelength of the narrow-band filter was chosen as 650 nm. The reason is that deposited beads at high temperature mainly radiate infrared. As can be seen in figure 2, the second vision sensor, mounted on the side of the welding gun, was applied to measure the deposited bead height. The composition of the vision sensor is the same as the SWM\u2019s. The sensor for height measurement (SHM) was placed opposite the welding gun in order to monitor the nozzle to top surface distance (NTSD). The reason for this design is as follows. During the multi-layer deposition process, the welding gun was stationary. The work flat made a descent in the vertical direction with a predefined layer height after depositing a layer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.5-1.png", + "caption": "FIGURE 2.5. Corner P and the slab at fi rst , second, third, and final positions.", + "texts": [ + "4 aft er 30deg rotation about the Z-axis, follow ed by 30deg about the X axis, and then 90deg about the Y -axis can be found by first multiplying Q Z ,30 by [5,30, lO]T to get the new global position after first rotation [ X2] [COS30 -sin30 0] [ 5] [-10.68 ] Y2 = sin 30 cos30 0 30 = 28.48 , Z2 0 0 1 10 10.0 and then multiplying QX ,30 and [-10.68,28 .48, 10.0r to get the position of P aft er the second rotation [ X 3 ] [1 0Y3 0 cos3 0 Z3 0 sin 30 o ] [ -10.68 ] [-10.68 ] - sin 30 28.48 = 19.66 , cos 30 10.0 22.9 and finally multiplying QY,90 and [-10.68,19 .66, 22.9]T to get the final posi tion of P after the third rotation. Th e slab and the point P in first , second, third , and fourth positions are shown in Figure 2.5. [ X4 ] [ COS90 0 Sin 90 ] [ -10.68 ] Y4 = 0 1 0 19.66 Z4 - sin 90 0 cos 90 22.9 [ 22.90 ] 19.66 10.68 Example 4 Global rotation, local position . If a point P is moved to G r 2 = [4,3,2r after a 60deg rotation about the 38 2. Rotation Kinematics Z -axis, its position in the local coordinate is Q- l G Z ,60 r 2 [ COS 60 sin60 o -sin60 0 ]-1 [4] [4.60] cos 60 0 3 -1.95 . o 1 2 2.0 Th e local coordinate fram e was coincident with the global coordinate frame before rotation, thus the global coordinates of P before rotation was also G r 1 = [4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002201_tcyb.2016.2533393-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002201_tcyb.2016.2533393-Figure1-1.png", + "caption": "Fig. 1. Two inverted pendulums connected by a spring.", + "texts": [ + " However, an explicit estimation of the tracking errors Zi1 is impossible since the size of tracking errors depends on the unknown constants W\u2217 ij , \u03c90 ij, and \u03b50 i1. To illustrate the effectiveness of the proposed method, we present an example. Example 1: Let us illustrate the proposed decentralized adaptive neural output-feedback DSC technique by means of a mechanical system as that has been dealt with in [20] and [28]. That is, we consider the control of two inverted pendulums connected by a spring as depicted in Fig. 1. Each pendulum may be positioned by some switching torque inputs uik applied by a servomotor at its base. The equations of motion for the pendulums are described by x\u030711 = x12 (57a) x\u030712 = 1 J1 u1\u03c3 + f12 + d12 (57b) y1 = x11 (57c) x\u030721 = x22 (57d) x\u030722 = 1 J2 u2\u03c3 + f22 + d22 (57e) y2 = x21 (57f) where (x11, x21) T = (q1, q2) T and (x12, x22) T = (q\u03071, q\u03072) T are the angular displacements of the pendulums from vertical and angular rates, respectively. f12 = ((m1gr/J1) \u2212 (hr2/4J1)) sin y1 + (hr2/4J1) sin y2, d12 = (hr/2J1)(l \u2212 b), f22 = ((m2gr/J2) \u2212 (hr2/4J2)) sin y2 + (hr2/4J2) sin y1, and d22 = \u2212(hr/2J2)(l \u2212 b)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003192_j.snb.2016.02.109-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003192_j.snb.2016.02.109-Figure1-1.png", + "caption": "Fig. 1. Schematic of the proposed novel non-enzymatic biosensor. (A) Mask layo", + "texts": [ + " In the present study, a novel nonnzymatic glucose biosensor produced using a simple lithographic rocess is proposed. Specifically, photoresist AZ-1518 was spinoated onto a reclaimed silicon wafer. A mask with a hexagonal lose-packed circle array was then employed for exposure and evelopment to generate a hexagonal close-packed column array f the AZ-1518. A thermal melting process was than conducted to onvert each photoresist column into a photoresist hemisphere. inally, a gold thin film was sputtered onto the hemisphere array f AZ-1518 to form the sensing electrode. . Materials and methods Fig. 1 schematically illustrates the photolithographic process for he proposed non-enzymatic glucose biosensor. Fig. 1(A) shows the ask layout for 6 in. silicon wafer. This mask contains 40 cycles \u03d5 = 8 mm, the centre-to-centre distance between two neighboring iscs is 10 mm) with each cycle containing over 2 million hexagnal close-packed small circles (\u03d5 = 3 m, the centre-to-centre istance between two neighboring cycles is 6 m). Following the hotolithographic process, thermal melting process, and gold thin lm sputtering, the wafer was cut into forty 1 \u00d7 1 cm2 rectangles, ith each rectangle containing a cycle. Each rectangular sample as then packaged on a glass slide (as shown in Fig. 1(B)). GNPs ere deposited on the gold thin film electrode surface to complete he simple lithographic non-enzymatic glucose biosensor. Fig. 1(C) llustrates the schematic enlargement of sensing area. The senor electrode, which was composed of micro- and nano-structures, ould directly respond to glucose without any GOx and mediator. .1. Sensor fabrication Fig. 2 shows a schematic description of the sequential fabricaion procedures for the proposed simple non-enzymatic glucose iosensor, including silicon wafer cleaning and photoresist coatng, exposure and development, thermal melting, and gold thin film (A) After Au sputtering (inset: a cross sectional view)", + " To ensure the uniformity f the sputtered gold thin film, the samples were heated in an oven o 120 \u25e6C at a rate of 5 \u25e6C/min, with the temperature maintained for 0 min. Finally, the sample was cooled to room temperature. To assure the consistency of the sensing area, the gold thin lm sputtered electrode was packaged. First, a conductive silver ire was attached to a glass slide as the conducting wire. Then, a \u00d7 2 cm2 square of Parafilm with a hole (\u03d5 = 6 mm) was bonded to he sample to cover the non-sensing area (as shown in Fig. 1(B)). The GNPs were prepared using the well-known reduction ethod [20]. First, 100 mL of 0.01% HAuCl4 solution was stirred and eated to boiling point, and then 4 mL of 1% sodium citrate was dded and continuously stirred for 10 min. After 10 min, heating as stopped and the solution was allowed to cool to room temper- ture. The pH value of the solution was then adjusted to 11 using NaOH solution to increase the spacing between GNPs. Subseuently, 1.5 mL of 10 mM 11-mercaptoundecanoic acid 95% (MUA) ous scan rates (25, 50, 75, 100, 150, 200, 250, 300, 350, and 400 mV s ) in a 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.11-1.png", + "caption": "FIGURE 1.11. The RIIP.iP configuration of robotic manipulators.", + "texts": [ + " By replacing the third joint of an art iculate manipulator with a pris matic joint, we obtain the spherical manipulator. The term spherical manipulator derives from the fact that the spherical coordinates de fine the position of the end-effector with respect to its base frame . Figure 1.10 schematically illustrates the Stanford arm, one of the most well-known spherical robots. 1. Introduction 11 4. RIIPf--P The cylindrical configurat ion is a suitable configurat ion for medium load capacity robots. Almost 45% of industrial robots are made of this kind . The RIIPf--P configurati on is illustrat ed in Figure 1.11. The first joint of a cylindrical manipulator is revolute and produces a rot ation 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. 5. Pf--Pf--P The Cart esian configuration is a suitable configurat ion for heavy load capacity and large robots. Almost 15% of industrial robots are made of this configuration. The Pf--Pf--P configurat ion is illust rated in Fig ure 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002897_j.engfailanal.2016.12.008-Figure14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002897_j.engfailanal.2016.12.008-Figure14-1.png", + "caption": "Fig. 14. Arrangement of the field test.", + "texts": [ + " The first order resonant mode of the gearbox housing is the lateral bending mode with a natural frequency of 579 Hz, and the second order mode is the axial opening mode with a natural frequency of 618 Hz. Modal strain analysis was conducted, and the second order strain mode is shown in Fig. 13. The modal strain response distribution is similar to the simulated fatigue strength stress response distribution in the failure region of the gearbox housing. A three-dimensional coordinate system is employed in the present work. The vertical direction is perpendicular to the ground, and the longitudinal direction is in the direction of travel. Fig. 14 illustrates the arrangement of the test gearbox. Track testing was conducted on the Chibi-Wuhan dedicated passenger line, covering a distance of about 128 km. Three-component acceleration sensors were fixed on the gearbox housing and the axle box to obtain the vertical, lateral, and longitudinal accelerations in the worn wheelset (8th coach) and the new wheelset (1st coach). As shown in Fig. 15(a), an acceleration sensor was fixed on the wheel side of the gearbox housing to measure the maximum vibration induced by wheel-rail excitation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001337_s10846-013-9936-1-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001337_s10846-013-9936-1-Figure2-1.png", + "caption": "Fig. 2 Reference frames for manipulator arms. See Fig. 3 for detail on overall UAV-manipulator system", + "texts": [ + " Finally, nonlinear control techniques are tested and verified in simulations. These simulations and experiments serve to show the efficacy and performance of the proposed hybrid nonlinear control concept. The proposed mobile manipulating unmanned aerial system, featuring a quadrotor UAV and two multi DOF manipulators, is shown in Fig. 3, and a table of dynamic parameters is given in Table 1. Using the recursive Newton-Euler approach andDenavit-Hartenberg parameterization for forward kinematics, each arm is modeled as a serial chain RRRR manipulator (Fig. 2) [20]. The connection between the quadrotor body frame and the first joint of each arm is represented with static revolute joint with a constant angular offset for each MM-UAV arm (Link B-0). Applying the results from [21] quadrotor dynamics are introduced to the aerial platform of the robot. 2.1 Manipulator Model Denavit-Hartenberg (DH) parameters of the manipulator arms shown in Fig. 2 are given in Table 2, and Fig. 3 depicts the overall UAVmanipulator system. Parameters \u03b8 , d, a, and \u03b1 are in standard DH convention and q1 i , q 2 i , q 3 i , and q4 i are joint variables of each manipulator arm i = [A, B]. Since the whole aircraft is symmetrical, the general kinematic structure is identical for the right and left arms, the coordinate frames are the same for each arm, and only the link B-0 is different for the two arms. Reference frames are shown in Fig. 2 which relate the fist joint L1 to the end effector frame E. To make the DH parameters consistent, an additional, virtual frame LT is set in the origin of frame L4. With Denavit-Hartenberg parameterization, joint frames are set and direct kinematic equations for each serial chain are derived. This procedure is repeated for both manipulator arms. Individual links that form the arm are consistent in size, mass and shape (i.e. their mass mL, kinematic parameter a and tensor of inertia JL are identical)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001007_1.4025219-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001007_1.4025219-Figure3-1.png", + "caption": "Fig. 3 3-DOF single-loop planar kinematic chains: (a) 00 R 00 R 00 R R R(RRR)E, and (b) 00 R gRRR 00 R (RRR)E", + "texts": [ + " In summary, only the above four classes of CUs can be used to construct planar PMs composed of only R joints and the associated 3-DOF single-loop kinematic chains involving an (RRR)E virtual chain since all the other CUs include other types of joints. 2.3 Type Synthesis of Legs for Planar Parallel Kinematic Chains. Type synthesis of legs for planar parallel kinematic chains is to obtain the types of legs with a given wrench system, which is a subsystem of the wrench system of the E virtual chain. This can be carried out by first constructing 3-DOF single-loop kinematic chains using one or more CUs [10,14] and then obtain legs for planar PMs by removing the E virtual chain. For example, the 00 R 00 R 00 R R R(RRR)E (Fig. 3(a)) with a 1-f1-system is constructed using two planar CUs, 4-5 and 6-7-8-1-2-3. The axis of the basis f11 of the 1-f1-system is perpendicular to all the axes of the R joints within the same 3-DOF single-loop kinematic chain. It is noted that the two R joints in the 00 R 00 R 00 R R R(RRR)E (Fig. 3(a)) 3- DOF single-loop kinematic chain are generally inactive [10]. By removing the E virtual chain from the above 00 R 00 R 00 R R R(RRR)E 3- DOF single-loop kinematic chain, one obtains an 00 R 00 R 00 R R R leg (Fig. 4(a)) with a 1-f1-system. The axis of the basis f11 is perpendicular to all the axes of the R joints in the leg. For clarity and simplicity, slmn, which implies that R joints l, m, and n have parallel axes and denotes a unit vector parallel to the axes of these R joints, is represented by a solid round arrow. Ak denotes the axis of R joint k, which is not parallel to the axes of the other joints within the same leg. It is noted that in constructing 3-DOF single-loop kinematic chains with a 1-f0-system (such as the 00 R gRRR 00 R (RRR)E kinematic chain in Fig. 3(b)) by combining one planar 5R CU (5-6-7-8-1 in Fig. 3(b)) and one gRRR Bennett CU (2-3-4 in Fig. 3(b)), the axis of the supplement R joint of the gRRR CU (Fig. 2(d)) must be parallel to the axes of the 00 R joints. The axis of the basis f01 of the 1- f0-system is parallel to the axes of the 00 R joints and intersects the axes of the three R joints within the Bennett CU gRRR. For simplicity reason, this basis f01 is not shown in Fig. 3(b). The existence of the above f01 can be proved using the concept of reciprocal screws as in the case of a 3-DOF single-loop kinematic chain involving a Bennett CU and a spherical CU [14] or using the properties of a hyperboloid of one sheet. Journal of Mechanisms and Robotics NOVEMBER 2013, Vol. 5 / 041015-3 Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use All the legs for planar parallel kinematic chains obtained are listed in Table 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003637_j.mechmachtheory.2016.09.017-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003637_j.mechmachtheory.2016.09.017-Figure1-1.png", + "caption": "Fig. 1. The Timoshenko beam element.", + "texts": [ + " However, when they are in mesh, these rigid disks are connected by a spring-damper element representing the mesh stiffness and damping. In the literature, the finite element formulation is widely used to model shafts including either Euler beam models [10] or Timoshenko beam models [12,15]. Here, a Timoshenko beam formulation is employed as it can include the effects of the translational and rotary inertia, gyroscopic moments, and the shear deformation, which are expected to be significant especially in high-speed cases. There are 2 nodes for each Timoshenko beam element (as shown in Fig. 1), and six degrees of freedom at each node: u x y z \u03b8 \u03b8 \u03b8 x y z \u03b8 \u03b8 \u03b8={ , , , , , , , , , , , }e A A A xA yA zA B B B xB yB zB T (1) The mass Msi e , stiffness Ksi e and gyroscopic moment Gsi e matrices for the ith finite shaft element can be found in [12,15,16], and will not be detailed here. These matrices are assembled to form the mass Ms j, stiffness Ks j and gyroscopic moment Gs j matrices for the jth shaft (j=1 to N where N is the number of the shafts considered; i=1 tomj wheremj is the number of finite elements used to define the jth shaft)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000160_tie.2006.874261-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000160_tie.2006.874261-Figure1-1.png", + "caption": "Fig. 1. Two-link manipulator system.", + "texts": [ + " The dynamic equation of a robotic manipulator without any disturbance is M(q)q\u0308 + C(q, q\u0307)q\u0307 + G(q) = \u03c4 (2-1) where M is the n \u00d7 n inertia matrix, Cq\u0307 is the n \u00d7 1 centripetal and Coriolis torque vector, G is the n \u00d7 1 gravitational torque vector, and \u03c4 is the n \u00d7 1 motor torque vector, while q = [q1, . . . , qn]T is the n \u00d7 1 joint position vector. Especially, in the case of a two-link manipulator, the matrices of the dynamic equation can be expressed as (2-2), shown at the bottom of the next page [17], where l1 and l2 are the lengths, and m1 and m2 are the masses of the links, respectively. The geometric structure of a two-link manipulator is shown in Fig. 1. We have the following properties for the dynamics of a robotic manipulator [7]. Property 1: The inertia matrix M is characterized by the following properties. 1) Symmetric and positive definite MT = M . 2) Bounded below and above, i.e., \u00b51(q)I \u2264 M(q) \u2264 \u00b52(q)I , where \u00b51(q) and \u00b52(q) are scalars. For revolute links, they are constants. I is an identical matrix. Property 2: The Coriolis and centripetal term C has the following properties. 1) Matrix M\u0307 \u2212 2C is skew symmetric, i.e., for any vector X , XT(M\u0307 \u2212 2C)X = 0", + " In the real application, the fuzzy control output and the weight of the neural network are updated in each sampling time. \u03b1 is determined by the output of the fuzzy control of the last sampling time. Thus far, the architecture of the proposed FSSNC for robotic manipulators is presented. The stability of the control system is proved with Lyapunov\u2019s direct method. We also discussed its attractive merits theoretically. This section is to show the application of the proposed FSSNC to a two-link robotic manipulator and observe its performance. The structure of the manipulator is shown in Fig. 1. Equation (2-2) describes the dynamics model of a two-link robotic manipulator. Fig. 5 shows the structure of the control system. The control law is in (5-2), and the update law of the neural-network portion is presented in (5-13). The fuzzy control rule base is in Table I. The parameters are given as m1 =4 kg, m2 = 2 kg, l1 =2 m, l2 = 1 m, g = 9.8 m/s2 \u039b = [ 1 0 0 5 ] =diag[1, 5], K = [ 40 0 0 40 ] =diag[40, 40]. The initial position is q(0) = [0, 0]T rad and the desired end position is q = [1, 2]T rad" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002467_j.triboint.2017.01.035-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002467_j.triboint.2017.01.035-Figure1-1.png", + "caption": "Fig. 1. Contact angle and load of a ball.", + "texts": [ + " The thermal-induced preload is one of operationinduced additional forces, which is associated with uneven expansion of the bearing components. During the operation as the temperature of the bearing assembly increases, components of the bearing experience different expansion rates due to differences in their temperature and geometry. As a result, the initial interference at the bearing installation is affected, which leads to changes of the contact loads between parts, namely the real working loads are changed. Next in this section is the ball and force equilibrium of angular contact ball bearing with thermal expansion. As shown in Fig. 1, Fc is the centrifugal force, \u03b1i and \u03b1e are contact angles, and Qi and Qe are contact loads at the inner and outer ring respectively. Using the notation in Fig. 1, the local force vector can be obtained from the contact load and contact angle at inner ring of the bearing, and written as \u23a7 \u23a8\u23aa \u23a9\u23aa Q Q \u03b1 Q Q \u03b1 M = \u2212 cos = \u2212 sin = 0 . i i z i i r (1) The load equilibrium at the ball is determined by the following formula \u23a7\u23a8\u23a9 \u23ab\u23ac\u23ad \u23a7\u23a8\u23a9 \u23ab\u23ac\u23ad F F Q \u03b1 Q \u03b1 F Q \u03b1 Q \u03b1 = cos \u2212 cos + sin \u2212 sin = 0. z i i e c i i e r e e (2) Here, Fr and Fz are the radial and axial loads of bearing respectively, and the contact loads Qi and Qe are calculated by Hertzian theory for spherical contact, \u23aa \u23aa \u23a7 \u23a8 \u23a9 Q K \u03b4 Q K \u03b4 = = ,i i i e e e 3/2 3/2 (3) where Ki and Ke are the load-deflection parameters, \u03b4i is the contact deformation between ball and inner ring, and \u03b4e is the contact deformation between ball and outer ring" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001035_s0022112070000848-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001035_s0022112070000848-Figure1-1.png", + "caption": "FIGURE 1. The gcometry and co-ordinatc systems used in the analysis.", + "texts": [ + " Statement of the problem The problem considered herein is that of a single droplet or bubble moving in the z direction with constant velocity U parallel to the longitudinal axis of an infinitely long circular cylinder. In the cylinder there is a viscous fluid flowing in the x direction, with constant Poiseuillian velocity distribution and with a maximum velocity U,. The centre of the droplet is situated at a distance b from the cylinder axis. The co-ordinate systems employed here are cylindrical (R, a, 2) and spherical ( r , 8, $J). The origin of the spherical co-ordinate system coincides with the centre of the droplet. The co-ordinate systems are depicted in figure 1. The fluid around the droplet flows in creeping motion, i.e. with small Reynolds number (where Re = 2alU,(1 -b2/Ri ) - Ul/v , v is the kinematic viscosity). The inertial terms in the equations of motion may therefore be neglected. Thus, the equations of motion to be satisfied are and v2v = - 1 VP,, Pe 1 Pi v2u = -vpi, where v is the velocity vector of the continuous medium and u is the velocity vector inside the droplet, in terms of a co-ordinate system which moves with the droplet. The pressure p includes the potential gravity field" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.11-1.png", + "caption": "Fig. 6.11 Calculation model of a torsional oscillator with an elastic bearing", + "texts": [ + "6 Influence of an Elastic Bearing on the Natural Frequencies of a Torsional Oscillator The measured fundamental frequency of a drive deviated significantly from the one that was calculated using the calculation model according to Fig. 4.3a (torsionally elastic shaft and two rotating masses). The observed difference could not be explained by parametric uncertainties alone. The assumed cause of the deviations was the coupling of torsional and transverse vibrations due to bearing elasticity. Determine the natural frequencies for the calculation model shown in Fig. 6.11 of a torsionally elastic drive with a transmission step and horizontal bearing elasticity c of the gear 2 and compare them to the ones obtained for c \u2192\u221e (rigid bearing). 396 6 Linear Oscillators with Multiple Degrees of Freedom Pitch radii of the gears r1 = 0.175 m; r2 = 0.25 m Moments of inertia of the gears J1 = 0.5 kg \u00b7m2; J2 = 1, 6 kg \u00b7m2; J3 = 0.75 kg \u00b7m2 Gear mass 2 m = 52 kg Torsional stiffness of the drive cT = 5.6 \u00b7 104 N \u00b7m Bearing stiffness c = 4.48 \u00b7 106 N/m (4.27) as known equation for the fundamental frequency of a torsional oscillator 1", + " The following orthogonality relations of (6.102) to (6.105) are obtained: V TCV = diag(\u03b3i) = [ \u03b31 0 0 \u03b32 ] = [ 0.821 10 0, 0 0.0 8, 660 4 ] EI l3 , (6.162) V TMV = diag(\u03bci) = [ \u03bc1 0 0 \u03bc2 ] = [ 3.3642 0, 0 0.0 4.9321 ] m. (6.163) They are satisfied within the constraint of limited calculation accuracy. S6.6 For describing the individual bodies of the calculation model, the angles of rotation \u03d51, \u03d52 and \u03d53 of the three gears as well as the horizontal displacement x2 of gear 2 are introduced, see Fig. 6.11b. If one stipulates for the origins of the position coordinates that \u03d52(\u03d51 = 0, x2 = 0) = 0, the constraint for the condition |x2| r2 can be stated as r1\u03d51 \u2248 x2 + r2\u03d52. (6.164) 398 6 Linear Oscillators with Multiple Degrees of Freedom It can be \u201cread\u201d from Fig. 6.11b if one imagines an infinitely thin gear rack placed between gear 1 and gear 2. If the vector of the generalized coordinates is defined according to q = [\u03d51, \u03d52, \u03d53]T = [q1, q2, q3]T, (6.165) the kinetic and potential energy can be stated as follows: Wkin = 1 2 [ J1\u03d5\u03072 1 + mx\u03072 2 + J2\u03d5\u03072 2 + J3\u03d5\u03072 3 ] (6.166) = 1 2 [ J1q\u03072 1 + m (r1q\u03071 \u2212 r2q\u03072)2 + J2q\u03072 2 + J3q\u03072 3 ] (6.167) Wpot = 1 2 [ cT (\u03d53 \u2212 \u03d51)2 + c x2 2 ] = 1 2 [ cT (q3 \u2212 q1)2 + c (r1q1 \u2212 r2q2)2 ] .(6.168) The mass and stiffness matrices follow from the relations (6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003398_j.msea.2020.140002-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003398_j.msea.2020.140002-Figure1-1.png", + "caption": "Fig. 1. Camera integration into EOS M290 metal additive manufacturing machine: a) schematic of camera imaging and field of view and b) image of cameras installed overhead on machine for in-process monitoring.", + "texts": [ + " Lighting was provided by the machines internal overhead LED light with the lower side-mounted lighting deactivated to avoid surface shadows that could affect DIC correlation. Two images (one per camera) were taken for each powder layer during part production prior to laser melting of the layer. The field of view for the as-implemented DIC system was approximately 100 mm \ufffd 100 mm. Calibration of the DIC camera system was performed at the build level height immediately preceding the start of the build process. DIC parameters are provided in Table 1. Fig. 1 displays the camera integration and monitoring setup. The accuracy of the 3D-DIC system in this environment has been established in previous work, wherein the same experimental setup (camera positioning, lenses, machine and working distances, and lighting) was used [5]. The DIC system accuracy was established by imparting out of plane rigid body motion using the SLM machine J.L. Bartlett et al. Materials Science & Engineering A 794 (2020) 140002 platform controller, where DIC measured displacements were compared to the commanded displacement; for 10 \u03bcm displacements (1/3rd of the layer thickness), the mean DIC displacement was determined to be 10" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure11.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure11.4-1.png", + "caption": "Figure 11.4.1 Pure trailing arm: (a) side view, showing arm length LA, pitch arm radius RP; (b) wheel axis with static steer and camber angles; (c) rotation of point D about centre at B.", + "texts": [ + " 200 Suspension Geometry and Computation The pure trailing armhas its pivot axis exactly perpendicular to thevehicle centre plane. In general, there is wheel static camber and toe, but for simplicity initially consider these to be zero. The wheel axis is then parallel to the pivot axis. Bump then has zero effect on steer and camber angles (Table 11.4.1). The initial bump scrub and bump scrub variation coefficients are zero, and the geometric roll centre is at ground level. There is a variation of the pitch arm radius, Figure 11.4.1. The arm angle is given by sin uA \u00bc ZW HAx LA The initial, static, value of the arm angle is given by sin uA0 \u00bc ZW0 HAx0 LA and is generally non-zero. The simplest geometry occurs when the initial angle is zero, but in practice this may give excessive braking anti-rise (Chapter 10). Practical pure trailing arms often include some static toe and camber. These angles are always small, and can be expected to have only a limited effect on the bump coefficients. However, this really needs to be demonstrated rather than just claimed", + " Prospectively, then, d \u00bc d0 cos uA g \u00bc d0 sin uA For small angles, as before, this becomes d \u00bc d0 d0 2R2 P z2S g \u00bc d0 RP zS The result is therefore quadratic bump steer and linear bump camber coefficients \u00abBS2 \u00bc d0 2R2 P \u00abBC1 \u00bc d0 RP Because the static toe angles are likely to be small in all cases, and such angles are often introduced with the intention that the toe anglewill go even closer to zerowhen actually running, these effects are likely to be small. For example, with d0\u00bc 0.02 rad and RP\u00bc 0.45m we have \u00abBS2\u00bc 0.05 rad/m2\u00bc 0.028 deg/ dm2. By these simple expressions, summarised in Table 11.4.2, the effect of static wheel toe and camber angles are easily evaluated rather than just assumed to be insignificant. A more thorough analysis of the above geometry, now to be given, confirms that the expressions given are good approximations, and demonstrates a useful principle. Figure 11.4.1(b) shows the wheel axis geometry with the actual pivot axis GH. Nowas far as changes of steer and camber angles are concerned, rotations about alternative parallel axes are entirely equivalent, adding only a pure translation. Rotation about the real axis is of course necessary for evaluation of actual movement, such as bump displacements. In the case of the pure trailing arm, the real pivot axis is parallel to the Y axis, and parallel to the line AB. Therefore, for investigation of steer and Single-Arm Suspensions 203 camber angles only, simply consider the wheel and wheel axis to rotate about the line AB. Positive arm angle uA is a positive bump position, with a lowering of point C relative to B, and a lowering and forward movement of point D, the second point of the wheel axis AD. It is changes of the position of the line AD that are of interest, with point D rotating about B as seen in Figure 11.4.1(c). As established earlier, AD \u00bc L BC \u00bc L cos g0 sin d0 CD \u00bc L sin g0 After rotation, the value of XD, measured from the line AB, is The consequent steer angle is then given by sin d \u00bc XD L \u00bc cos g0 sin d0 cos uA \u00fe sin g0 sin uA Now introducing a small-angle approximation for the steer and camber (including cos g0\u00bc 1), and expanding the arm angle to the second term of its series, d \u00bc d0\u00f01 1 2 u2A\u00de \u00fe g0 uA Inserting the small-angle approximation uA \u00bc zS RP gives the toe-out steer angle as d \u00bc d0 \u00fe g0 RP zS d0 2R2 P z2S which is in agreement with the bump steer coefficients obtained earlier (Table 11.4.2). Similarly, for camber after rotation (see again Figure 11.4.2 (b)), relative to the line AB, the height of point D is and the sine of the camber angle is given correctly by sin g \u00bc ZD L \u00bc cos g0 sin d0 sin uA \u00fe sin g0 cos uA Using the small-angle approximations ford and g, and expanding the armangle to the quadratic term, gives g \u00bc d0 uA \u00fe g0\u00f01 1 2 u2A\u00de Now substituting the linear approximation for the arm angle in terms of the bump position gives g \u00bc g0 d0 RP zS g0 2R2 P z2S again in agreement with the semi-intuitive expressions of Table 11.4.2. 204 Suspension Geometry and Computation and camber angles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001894_icems.2011.6073360-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001894_icems.2011.6073360-Figure6-1.png", + "caption": "Fig. 6: Investigated PM machine.", + "texts": [ + " (7) in discrete form is ( )22 , , 1 , 1 StepN edd mag Step z k z k k P p f N V A A\u03c3 + = = \u22c5 \u22c5 \u22c5 \u22c5 \u22c5 \u2212\u2211 (8) According to the above relation (8), a 2D finite element (FE) model formulated by the magnetic vector potential Az is used to analyze the eddy current losses of a PM machine. A PM machine with surface mounted PMs in the rotor for the automotive steering application is considered during the following analysis. Using 2D FE methods the eddy current losses for the conventional and the new 12-teeth/10-poles winding are investigated. Figure 6 shows the geometry and the flux-lines distribution of the investigated PM machine. During the determination of the PM eddy current losses, the considered PM machine is investigated for the no-load and under load condition. Further, under load condition the PM machine is investigated for the conventional and also for the new 12-teeth/10-poles winding. It is important to underline here that the under-load simulations for the both winding types are performed for the same load (torque) condition, figure 7" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure5.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure5.9-1.png", + "caption": "Fig. 5.9 Planar timing mechanism", + "texts": [ + " Afterward, determine the angular acceleration of the driven link given the angular acceleration of the driver link. Hint: Write the equation of acceleration in screw form and apply the appropriate Klein form to both sides of such an equation. 3. Using a standard method, determine the symbolic equation of the angular acceleration of the driven wheel of the Geneva mechanism considering that the driver wheel rotates at a constant angular velocity !1 counterclockwise. 4. Carry out the singularity analysis of the 2RRR+PPR parallel manipulator based on the input\u2013output equation of velocity. 5. Figure 5.9 shows a planar timing mechanism. The motion of pin B is controlled by the linear slot A, which is being elevated at a constant velocity upward of 1:5 m=s as measured from the fixed reference frame. If r D 0:3 m and D 30\u0131, compute (a) the acceleration of pin B as measured from the Earth, (b) the relative acceleration of pin B as observed from the circular slot. Hint: Subdivide 130 5 Acceleration Analysis the timing mechanism into two different planar mechanisms and identify the corresponding j, k, and m bodies for each mechanism" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001368_978-3-642-41196-0-Figure3.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001368_978-3-642-41196-0-Figure3.11-1.png", + "caption": "Fig. 3.11 Coordinates of the pendulum model and decomposition of oscillation angle. (a) Coordinates of the pendulum model. (b) Decomposition of oscillation angle (Reprinted from Duan and Sun (2013), with kind permission from Springer ScienceCBusiness Media)", + "texts": [ + " In this section, a mathematical model representing the pendulum-like oscillation 86 3 UAV Modeling and Controller Design 3.3 PSO Optimized Controller for Unmanned Rotorcraft Pendulum 87 in the hover and stare state is obtained by using the Lagrangian method, and the corresponding linearized model is obtained in the neighborhood of the hover and stare equilibrium. The pendulum can be abstracted as a system consisting of the suspension point Oh, the pendulum rod OhOt, and the pendulum mass Ot (see Fig. 3.11). 88 3 UAV Modeling and Controller Design In Fig. 3.11, OXYZ is the ground-fixed coordinate system, Ohx1y1z1 represents a mobile ground coordinate system, with the point Oh as the origin and parallel to OXYZ, while Ohx2y2z2 is defined as the pendulum-body coordinate frame, which originates from Oh, and axis z2 points downward along the pendulum rod OhOt. Decompose the two-dimensional pendulum-like oscillation to one in the direction of axis X and Y, and the transition matrix R from Ohx2y2z2 to Ohx1y1z1 is obtained as follows: R D 2 4 cos y sin x sin y cos x sin y 0 cos x sin x sin y sin x cos y cos x cos y 3 5 (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000263_j.snb.2009.09.005-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000263_j.snb.2009.09.005-Figure2-1.png", + "caption": "Fig. 2. Enzymatic breakdown of glucose y", + "texts": [ + " The most commercially successful devices for glucose onitoring are the blood glucose biosensors, the initial concept of tors B 143 (2009) 430\u2013443 431 which was proposed by Clark and Lyons [17] which led to the first commercial glucose analyzer launched by Yellow Spring Instrument Co., Ohio. There are now over 40 blood glucose meters in the market, yet many challenges need attention [6,18]. Glucose oxidase (GOx/GOD) (EC 1.1.3.4) is a dimeric oxidoreductase enzyme with flavin adenine dinucleotide (FAD) as its cofactor, which is the redox centre involved in electron transfer. The enzymatic breakdown of glucose by GOx follows the sequence in Fig. 2. As is evident, glucose gets oxidized to gluconic acid with corresponding reduction of FAD to FADH2 which then transfers electrons to the natural acceptor O2 and regenerates itself, producing H2O2. After this biochemical phenomenon, H2O2 undergoes electrochemical oxidation at the anode at a defined potential, yielding current which forms the rationale of amperometric detection. The current is a measure of glucose conc. 1.2. Mechanism of polymerization of pyrrole monomer and immobilization of the enzyme Since the biological component, that is GOx, is to be immobilized for biosensor development it would be most appropriate to realize enzyme confinement in a manner that would allow direct electron transfer between the redox centre and the electrode", + " First-stage biosensors: a step ahead GOx was immobilized on poly methyl pyrrole (PMP) by elecrodeposition at +0.8 V vs. Ag/AgCl. The study presents observations f direct electron transfer between immobilized GOx and the gold lectrode during enzymatic breakdown of glucose. Unlike the comonly presented electrochemical oxidation of H2O2 as a marker or glucose conc., the authors have reported the activity in terms f enzyme redox GOxox GOxred, which is due to electron transfer etween FAD, the cofactor of GOx and the electrode and the reoxdation of the enzyme, from Fig. 2. To illustrate the findings FAD as immobilized onto PMP, electrodeposited on the gold workng electrode and cyclic voltammograms of FAD/PMP/Au electrodes ere recorded. The oxidation and reduction peaks were obtained at 0.43 and \u22120.48 V, respectively. Subsequently, FAD was replaced y GOx with its inherent FAD and the peaks were obtained at \u22120.54 nd \u22120.56 V, respectively under the same conditions. The proxmity of the values suggested that electron transfer indeed took lace between FAD of GOx and the electrode" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure3.21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure3.21-1.png", + "caption": "Fig. 3.21 Foundation of a piston compressor", + "texts": [ + "6 \u00b7 103 N \u00b7m Resilient intermediate layer between anvil bed and foundation: hammer felt d = 40 mm thick; dynamic modulus of elasticity of the hammer felt; E = 8 \u00b7 107 N/m2. Area between anvil bed and hammer: A = 0.5 m2 The foundation rests on 6 spring elements. Their total spring constant is c2 = 4 \u00b7 106 N/m. The assumed coefficient of restitution is k = 0.6. A horizontal piston compressor with a speed n = 258 rpm is to be installed onto the subsoil with high tuning. The size of the foundation block was determined from the guideline mF = (5 . . . 10)mM for n < 300 rpm. The system dimensions are shown in Fig. 3.21. The center of gravity of the entire system is above the area center of the base surface. The axes shown represent principal axes of inertia. 3.3 Foundations under Impact Loading 217 The following parameter values are given: Machine mass: mM = 1500 kg Foundation mass:mF = 12 000 kg Principal moments of inertia: Jx = 1.483 \u00b7 104 kg \u00b7m2; Jy = 0.725 \u00b7 104 kg \u00b7m2; Jz = 2.014 \u00b7 104 kg \u00b7m2 Distance of the center of gravity from the subsoil: sz = 0.47 m Outer foundation dimensions: Height: l1 = 0.8 m; Width: l2 = 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001308_tmag.2012.2203607-Figure18-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001308_tmag.2012.2203607-Figure18-1.png", + "caption": "Fig. 18. Eddy current distribution (axial -component) in magnet at 10 kHz. One magnet segment in axial direction (top) and five magnet segments in axial direction (bottom).", + "texts": [ + " The bore and magnet curvature and the eddy current reaction field are taken into account. The field waves are excited by current layers on the stator bore. The boundary conditions are shown in Fig. 15. Only half of the model in the axial direction is considered in 3-D FEM due to the symmetry. Space harmonic contents of the current layer in the threephase and single-phase configurations are shown in Figs. 16 and 17 according to the model in Fig. 15. The calculated eddy currents using 3-D FEM are shown in Fig. 18, top and bottom, for: 1) one magnet segment in the axial direction and 2) five magnet segments in the axial direction, respectively. The results are shown in Figs. 19 and 20. The simulations have been done for different axial numbers of magnet segments for travelling and pulsating wave conditions. Two phases are switched off in the pulsating wave condition. The third phase generates the standing pulsating field. The former condition is equivalent to single-phase PM machines. The inductance limited and resistance limited losses are visible in Figs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure5.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure5.1-1.png", + "caption": "Fig. 5.1 Spring-mass-damper system.", + "texts": [ + " Wo\u00b7 AWd =y'2Usin 1)0\u00b7 AI) WO\u00b7 AWq =y'2U cos 1)0\u00b7 At; y'2U = sinl)o\u00b7 Al) Xd(jm) y'2U = cosl)o\u00b7 Al) Xq(jm) Hence substituting Eqns. (7.25) and (7.26) in Eqn. (7.24): AM = UUo cos 1)0 + U 2 cos2 1)0 .[ __ 1__ ~] A6 Xd Xq (jm) Xd + U 2 sin2 I) 0 \u2022 [ 1 __ 1_] Xd(jm) Xq =K+jmC (7.26) (7.27) A.C. Operation of Synchronous Machines 149 The parameters K and C, obtained by calculating the real and imaginary parts of Eqn. (7.27), are analogous to the elastic and damping constants of the linear, two-dimensional, mechanical system of Fig. 5.1, for which the equation of motion would be -m2J. ~6 + jmC\u00b7 ~6 + K\u00b7 ~6 = ~Mt (7.28) The angular pulsation of the rotor due to a torque pulsation ~Mt is ~Mt ~6 = (7.29) (K - m 2J) + jmC However the parameters K and C of the electro-mechanical system are functions of m and are far from constant. The calculated values for a 2600 kVA, 28-pole, diesel-driven generator are given in Fig. 7.3. An earlier method of calculating the forced oscillations of a diesel-driven generator was based on the rather extreme assump tion that the relation between torque and rotor angle could be taken as the slope of the steady-state power-angle curve (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure6.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure6.5-1.png", + "caption": "FIGURE 6.5. A PRRR manipulator.", + "texts": [ + "\u00bb, + I,din ] S8l 23 C8123 0 u\u00bb. + hs812 0 0 1 d 0 0 0 1 81 + 82 + 83 81 + 82 5. m-RIIR articulated arm inverse kinematics. Figure 5.25 illust ra tes 3 DOF m-RIIR manipulator. Use the following transformation matrices and solve the inverse kinematics for 81 , 82 , 83 . [ 0000 1 0 - sin8 l ~I ] 0TI ~ SiYI 0 cos8 l - 1 0 0 0 [ cooO, - sin82 0 I, cos 0, ] IT, ~ Sir' cos 82 0 l 2 sin 82 0 1 d2 0 0 1 6. Inverse Kinematics 295 o o 1 o ~ ] 6. Kinematics of a PRRR manipulator. A PRRR manipulator is shown in Figure 6.5. Set up the links 's co ordinate frame according to standard DR rules . Determine the class of each link. Find the links ' transformation matrices. Calculate the forward kinematics of the manipulator. Solve the inverse kinematics problem for the manipulator. 7. * Space station remote manipulator system inverse kinematics . Shuttle remote manipulator system (SRMS) is shown in Figure 5.28 schematically. The forward kinematics of the robot provides the fol lowing transformation matrices. Solve the inverse kinematics for the SRMS", + " (a) velocity \"v, of the link at C, in terms of d, and di - l (b) angular velocity of the link \u00b0 Wi in terms of di and di - l (c) velocity \u00b0Vi of the link at C, in terms of proximal joint i velocity (d) velocity \"v, of the link at C, in terms of distal joint i +1 velocity (e) velocity of proximal joint i in terms of distal joint i + 1 velocity (f) velocity of distal joint i + 1 in terms of proximal joint i velocity 8. * Jacobian of a PRRR manipulator. Determine the Jacobian matrix for the manipulator shown in Figure 6.5. 374 8. Velocity Kinematics 9. * Spherical robot velocity kinematics. A spherical manipulator Rf-Rf-P, equipped with a spherical wrist , is shown in Figure 5.26. The t ransformation matrices of the robot are given in Example 149. Solve the robot's forward and inverse velocity kinemati cs. 10. * Space station remot e manipulator syst em velocity kinemat ics. The transform ation matrices for the shut t le remote manipulator sys tem (SRMS) , shown in Figure 5.28, are given in the Example 153. Solve the velocity kinematics of the SRMS by calculat ing the Jaco bian matrix" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.7-1.png", + "caption": "FIGURE 2.7. The arm of Example 6.", + "texts": [ + " When we get the coordinat es of points of the rigid body afte r the first rotation, our situation before the second rotation is similar to what we had before the first rot ation. Example 5 Successive global rotation matrix. The global rotation matrix after a rotation QZ,o: followed by QY,{3 and then Qx\" is Qx\"QY,{3Q z ,o: [ co:cj3 cvso: + co:s j3s\"'( so:s\"'( - co:qsj3 -cj3so: co:q - so:sj3s\"'( cosr; + q so:sj3 sj3 ]- cj3s\"'( cj3q . (2.27) Example 6 Successive global rotations, global position. The end point P of the arm shown in Figure 2.7 is located at [ ~ll ] = [ l c~se ] = [ 1 c~s 75 ] = [ 0~206 ] . z, l sin e 1sin 75 0.97 40 2. Rotation Kinematics -0.24 ] -0.93 - 0.27 (2.28) The rotation matrix to find the new position of the end point aft er - 29 deg rotation about the X -axis , follow ed by 30 deg about the Z -axis, and again 132 deg about the X -axis is [ 0.87 -0.44 GQB = QX,132QZ,30QX,-29 = - 0.33 - 0.15 0.37 0.89 and its new position is at [ X2 ] [ 0.87 - 0.44 - 0.24] [ 0.0 ] [-0.35] Y2 = - 0.33 -0.15 - 0.93 0.26 = - 0.94 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000218_j.mechmachtheory.2003.06.001-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000218_j.mechmachtheory.2003.06.001-Figure1-1.png", + "caption": "Fig. 1. Degrees of freedom of the elemental gear.", + "texts": [ + " Nomenclature b1, b2 pinion, gear face width d(g), dij continuous and discrete form of displacement at Mij, respectively D(g), Dij continuous and discrete form of bending stiffness coefficient at Mij, respectively G(g), Gij continuous and discrete form of shearing stiffness coefficient at Mij, respectively k(g), kij continuous and discrete form of direct stiffness coefficient at Mij, respectively Kc ij discrete contact stiffness at Mij L(t) instantaneous contact length Li(t) instantaneous length of the ith elastic foundation mn normal module Mij point at the jth cell of the ith elastic foundation ~nm unit normal vector to tooth flanks of solid m Ni(t) instantaneous number of discrete cells of the ith elastic foundation P(Mij) tooth load at the jth cell of the ith elastic foundation R ratio of the maximum dynamic tooth load to the maximum static tooth load Rbm base radius of solid m Tm mesh period T1, T2 limits of base plane (on pinion and gear base plane, respectively) (Fig. 2) T 0 1, T 0 2 limits of meshing area on base plane (Fig. 2) umj, vmj, wmj translational degrees of freedom of the jth section of solid m (Fig. 1) {V(Mij)} structure vector (Eq. (4)) X1j, X2j co-ordinates of Mij in the base plane (Fig. 2) Z number of teeth at apparent pressure angle bb base helix angle dm(Mij) displacement in the direction ~nm of Mij, a point of solid m de(Mij) equivalent normal deviation at Mij Dg width of a discrete cell (constant) D(Mij) mesh deflection at Mij /mj, wmj, hmj rotational degrees of freedom of the jth section of solid m (Fig. 1) g co-ordinate in contact line direction { }, { }T column vector, transpose of a vector Gears are known to be one of the major vibro-acoustic sources in rotating machinery and the prediction and control of gear vibrations have become important concerns particularly in automotive, aerospace and power generation industries. Over recent decades, numerous gear dynamic models have been proposed which range from single degree-of-freedom torsional [1\u20133], . . . to extended three-dimensional finite element models [4\u20136]", + " The modelling of the various displacement components associated with gear body, tooth and contact deflections is detailed below. One of the simplest approaches consists in modelling gear bodies by two node shaft finite elements in bending, torsion and traction [16] to be connected with the mesh interface model. Assuming that any transverse section of the pinion or gear body originally plane remains plane after deformation, the displacement field of the jth section can be characterised by a screw of co-ordinates (Fig. 1): fsmjg ~umj\u00f0Omj\u00de \u00bc vmj~Sj \u00fe wmj ~T j \u00fe umj~Z ~xmj \u00bc /mj ~Sj \u00fe wmj ~T j \u00fe hmj~Z ( \u00f03\u00de where m = 1 refers to the pinion, m = 2 to the gear and vmj, wmj, umj are the translational degrees of freedom of the jth section at its centre Omj; /mj, wmj, hmj are the rotational degrees of freedom of the jth section. The displacement at any point Mij of a section of the pinion or gear body in a direction~nm (~nm, unit vector) is deduced by dm\u00f0Mij\u00de \u00bc \u00f0~umj\u00f0Omj\u00de \u00fe ~xmj Omj ~Mij\u00de ~nm \u00bc fV m\u00f0Mij\u00degTfqmjg \u00f04\u00de where {qmj} = humj, vmj, wmj, /mj, wmj, hmji, degrees of freedom of the jth section {Vm (Mij)} T = hvm sinbb, vmcosbb sinat, vm ecosbbcosat, e sinbb (Rbmsinat Xmjcosat), sinbb (Rbmcosat+ Xmj sinat), eRbmcosbbi, vm = 1 on the pinion, vm = 1 on the gear, e = 1 for positive rotations of the pinion, e = 1 for negative rotations of the pinion Rbm, base radius of solid m, at, apparent pressure angle (other parameters are defined in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003401_j.tws.2020.106993-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003401_j.tws.2020.106993-Figure2-1.png", + "caption": "Fig. 2. Sketches of a two-layer graded model: (a) front view, and (b) side view.", + "texts": [ + "13 3 60-60-60-60 12.86 77.43 41.34 97.15 4 65-65-65-65 15.21 73.41 52.59 120.29 5 50-55-60-65 10.00 90.00 38.12 91.10 6 50-55-65-60 10.00 90.00 38.12 91.10 7 50-60-55-65 10.00 90.00 38.12 91.10 8 50-60-65-55 10.00 90.00 38.12 91.10 9 50-65-60-55 10.00 90.00 38.12 91.10 10 50-65-55-60 10.00 90.00 38.12 91.10 11 55-50-60-65 11.21 82.79 38.12 91.10 12 60-50-55-65 12.86 77.43 38.12 91.10 13 65-50-55-60 15.21 73.41 38.12 91.10 X. Xiang et al. Thin-Walled Structures 157 (2020) 106993 model are shown in Fig. 2. In Fig. 2, to make the two layers fit together well, the value of bi has to be equal to b1, where i refers to the arbitrary layer in the metamaterial; meanwhile, the bottom vertices, i.e., P11, have to line up with the top vertices, i.e., P21, and other layers should follow the same requirements. Thus, the multiple layer graded metamaterial has to follow the following constraints: bi = b1 (7) ai = a1cos\u03b11 cos\u03b1i (8) \u03b8i = cos\u2212 1 ( 1 \u2212 2sin2(\u03b81/2)sin2\u03b11 sin2\u03b1i ) (9) Based on equations (7) \u2013 (9), once the necessary parameters (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002647_s40964-018-0039-1-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002647_s40964-018-0039-1-Figure2-1.png", + "caption": "Fig. 2 a Full part geometry, b aluminum stand and substrate, and c fabrication of the first layer", + "texts": [ + " AM system The Inconel 718 powder used in the present study was supplied by EOS. The powder distribution and morphology are shown in Fig.\u00a01a, b. The average powder size was 32.2\u00a0\u00b5m. The sample was produced with an EOS M280 powder-bed fusion system, with settings as shown in Table\u00a01. Prior to part building, the building chamber was evacuated and subsequently back-filled with argon to ensure that the oxygen concentration was less than 1000\u00a0ppm. The initial base plate temperature was approximately 25\u00a0\u00b0C. 1 3 Figure\u00a02a shows the full part geometry. The part geometry was designed to highlight typical thermal, microstructural, and mechanical responses for powder-bed fusion. After part design in CAD software, the part file was transferred to the Materialise Magics software and placed in the center of the build area. The part was designed and placed to align with the laser vector patterns in a predictable fashion. Afterwards, the part file was sliced in EOS RP Tools and then imported into EOS PSW software to generate scanning vectors and assign processing parameters", + " The progression of the stripe during processing was perpendicular to the hatching pattern of that layer and adjacent stripes progressed in opposite directions. Within a stripe, adjacent hatches were also in opposite directions. The sample part contained 1750 layers, with an equivalent build time of approximately 35\u00a0h. A specialized aluminum vault was designed and used during the build to support the substrate and house the temperature data acquisition system. The vault and substrate used during the process are shown in Fig.\u00a02b, c illustrates fabrication of the first layer. 1 3 Tungsten\u2013rhenium, C-type thermocouples having a diameter of 270 \u00b5m were embedded in the build plate through holes 1.016\u00a0mm in diameter that were precision drilled from the bottom of the plate and extended to 0.25\u00a0mm below the top surface. Another hole 0.254\u00a0mm in diameter was precision drilled from the top surface to accommodate the thermocouple ball. A ceramic tube (1.0\u00a0mm diameter) with two internal channels was used to insulate the thermocouple leads" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003663_j.oceaneng.2018.02.007-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003663_j.oceaneng.2018.02.007-Figure3-1.png", + "caption": "Fig. 3. ODIN AUV and thruster configuration.", + "texts": [ + " (19), it shows that the variables \u03c62, \u03942 can enter the region in finite time. It also means that the estimated expression of the thruster fault effect fth can be presented as \u222b k3\u03942 \u00fe k4sign\u00f0\u03942\u00de \u00fe k5j\u03942j0:5sign\u00f0\u03942\u00de dt \u00fe L3P\u00fe 2 \u222b kc\u03941 \u00fe kdsign\u00f0\u03941\u00de \u00fe kej\u03941j0:5sign\u00f0\u03941\u00de dt In this section, an over-actuated AUV, e.g., ODIN AUV, is used to perform simulations to demonstrate the effectiveness of the new design. And the existing fault tolerant control law and fault reconstruction method are used to show the advantages of the developed method. ODIN AUV is shown in Fig. 3(a) and its dynamic model can be seen in (Podder and Sarkar, 2001). There are 8 identical thrusters to provide forces to control AUV, and its configuration figure is shown in Fig. 3(b). Also it is assumed that the magnitude of thrusters is 200N and ODIN AUV's initial position and velocity are \u03b7(0)\u00bc [1.0; 1.0; 1.0; \u03c0/18; \u03c0/18; \u03c0/9], _\u03b7(0)\u00bc [0.2; 0.2; 0.2; 0.2; 0.2; 0.2]. The ocean current is generated by using a first-order Gauss-Markov process (Fossen, 2011) _MVc \u00fe \u03bccMVc \u00bc \u03c9c (20) where MVc is the magnitude of ocean current velocity with respect to the inertial frame; \u03c9c is Gaussian white noise with mean value of 1.5 and variance value of 1 \u03bcc \u00bc 3. Also, the two angles about ocean current's direction, \u03b2c (sideslip angle) and \u03b1c (angle of attack), where \u03b2c is generated by the sum of Gussian noise with mean of 0 and variance of 50, and \u03b1c\u00bc \u03b2c/2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001078_j.ijheatmasstransfer.2013.04.050-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001078_j.ijheatmasstransfer.2013.04.050-Figure4-1.png", + "caption": "Fig. 4. Three-dimensional mesh of the FEM.", + "texts": [ + " Solid 70 [13], a thermal 3D brick element, which has a 3D thermal conduction capability, is utilized to mesh the entire FEM. Also, the element has eight nodes with a single degree of freedom, temperature, applicable to a 3D, steady-state or transient thermal analysis. In addition, For the sake of convection and radiation boundary conditions, it is extremely essential to generate the surface effect element in the exposed region of the geometric model just like skin wrapping the body and thus, surface effect element, surf152 is also employed for this thermal analysis. Fig. 4 illustrates the mesh of this FEM using two kinds of elements. In addition, in order to depict the process of mass transfer due to powder deposition on substrate, the element birth and death technique is applied to the 3D thermal analysis. Before applying any heat loads, for instance, heat flux or heat generation rate, the elements of cladding coatings must be killed and then the deactivated elements remain in the model but contribute a near-zero conductivity value to the overall matrix. While the heat loads are applied to the laser-scanned region, the dead elements would be activated with the moving heat source gradually" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002174_s00170-012-4560-y-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002174_s00170-012-4560-y-Figure5-1.png", + "caption": "Fig. 5 Planet gears with artificially created pitting damage of four levels", + "texts": [ + "2 Artificially created pitting damage Based on stress calculation [29], we found that pitting damages should first occur on the planet gears in the second-stage planetary gearbox. There are four planet gears in the second-stage planetary gearbox. We designed pitting damages on one of the planet gears with four pitting levels: baseline, slight, moderate, and severe. A pit was artificially created as a circular hole with a 3-mm diameter and 0.1-mm depth [30]. The number of pits varies with the pitting levels. The four planet gears associated with different fault levels of the pitting damages are shown in Fig. 5. Profiles of the four pitting levels created in the experiment are described as follows [31]: 1. The baseline level\u2014a brand new gear was considered the baseline level (see Fig. 5a); 2. The slight level\u2014three holes on a tooth and one hole on each of the two neighboring teeth (see Fig. 5b). The middle pitted tooth has a pitting area of 7.95 %. Each of the two neighboring teeth has a pitting area of 2.65 %. The most pitted tooth of the slight level meets the criterion of level two described in the ASM standard [32], that is, a pitting area within 3 to 10 % of the tooth surface area; 3. The moderate level\u2014ten holes on a tooth, three holes on each of the two neighboring teeth, and one hole on each of the next two neighbors (see Fig. 5c). The pitting areas on the five teeth are 2.65, 7.95, 26.5, 7.95, and 2.65 %, respectively. The most pitted tooth of the moderate level meets the criterion of level three described in the ASM standard [32], that is, a pitting area within 15 to 40 %; and 4. The severe level\u201424 holes on one tooth, 10 holes on each of the two neighbor teeth, and 3 holes on each of the next neighboring teeth (see Fig. 5d). The pitting areas of the five teeth are 7.95, 26.5, 63.6, 26.5, and 7.95 %, respectively. The most pitted tooth of the severe level meets the criterion of level four described in the ASM standard [32], that is, a pitting area within 50 to 100 %. 3.3 Data acquisition We conducted an experiment for each pitting level. The three no-fault planet gears and the one pitted planet gear were mounted in the second-stage planetary gearbox (see Fig. 4b) in one experiment. Four sensors were used to collect vibration signals with a sampling frequency of 10,000 Hz" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure7.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure7.6-1.png", + "caption": "Fig. 7.6 Example 7.2. Decomposition of the acceleration analysis", + "texts": [ + "66) Furthermore, the relative velocity vector kvm N is given by kvm N D Pl OuN=O; (7.67) where 7.3 Hyper-Jerk Equations in Screw Form 177 OuN=O D cos. /OiC sin. /Oj (7.68) is a unit vector along the arm of the robot. Meanwhile, Pl D d dt \u0152.1=4/ sin. t=2/ D . =8/ cos. t=2/: (7.69) Hence, jvm N D P Ok .1:5C l/ h cos. /OiC sin. /Oi i C Pl h cos OiC sin. /Oj i D h P .1:5C l/ sin. /C Pl cos. / i OiC h P .1:5C l/ cos. /C Pl sin. / i Oj; (7.70) or jvm N D 0:872Oi 0:956Oj! vN D 1:294 m=s. In order to approach the acceleration analysis, consider Fig. 7.6. The acceleration of the nozzle N as measured from point O, the vector aN D jam N , is computed as jam N D jak N C kam N C 2j!k kvm N ; (7.71) where, according to Fig. 7.6, jak N D aNt C aNt D R Ok rN=O C P Ok . P Ok rN=O/: (7.72) Meanwhile, kam N D Rl OuN=O; (7.73) where 178 7 Hyper-Jerk Analysis R D d dt . P / D . 3=24/ sin. t=2/ (7.74) and Rl D d dt .Pl/ D . 2=16/ sin. t=2/: (7.75) Furthermore, the Coriolis acceleration is computed as 2j!k kvm N D 2 P Ok Pl OuN=O: (7.76) Hence, jam N D h R .1:5C l/ sin. / P 2.1:5C l/ cos. /C Rl cos. / 2 P Pl sin. / i Oi C h R .1:5C l/ cos. / P 2.1:5C l/ sin. /C Rl sin. /C 2 P Pl cos. / i Oj; (7.77) or jam N D 1:0667Oi 0:5557Oj" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.1-1.png", + "caption": "FIGURE 5.1. Link (i) and its beginning joint i-I and its end joint i.", + "texts": [ + "1 Denavit-Hartenberg Notation A series robot with n joints will have n + 1 links. Numbering of links starts from (0) for the immobile grounded base link and increases sequentially up to (n) for the end-effector link. Numbering of joints starts from 1, for the joint connecting the first movable link to the base link, and increases sequentially up to n . Therefore, the link (i) is connected to its lower link (i - 1) at its proximal end by joint i and is connected to its upper link (i + 1) at its distal end by joint i + 1, as shown in Figure 5.1. All joints, without exception, are represented by a z-axis . We always start with identifying the zi-axes. The positive direction of the zi-axis is arbitrary. Identifying the joint axes for revolute joints is obvious , however, a prismatic joint may pick any axis parallel to the direction of translation. By assigning the Zi-axes, the pairs of links on either 200 5. Forward Kinematics side of each joint , and also two joints on either side of each link are also ident ified. 2. The xi-axis is defined along the common normal between the Zi- I and Zi axes, pointing from the Zi- I to the zi-axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003582_j.ijfatigue.2019.02.041-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003582_j.ijfatigue.2019.02.041-Figure5-1.png", + "caption": "Fig. 5. Case i), two cracks at each surface. Here c is referred to as the crack depth.", + "texts": [ + " Thus the specimen geometry analysed was an 80mm wide by 2.6mm thick AM Ti6Al-4V specimen containing a centrally located 6mm diameter hole. Since it is unclear what the effect of machining a hole in an AM Ti-6Al-4V structure will have on the fatigue critical location two cases, which both had A=62MPa \u221am, were analysed: (i) The hole was assumed to contain four cracks, with two diametrically opposed quadrant cracks (EIFS) at the intersection of the bore of the hole with each of the two free surfaces, see Fig. 5. (ii) The hole was assumed to contain two diametrically opposed semicircular cracks (EIFS) at the intersection of the bore of the hole with the free surface, see Fig. 6. In both analyses the EIFS assumed was a 1.27mm radius crack. The resultant computed lives are shown in Table 3 where we see that Case i), i.e. two diametrically opposed quadrant cracks (EIFS) at the intersection of the bore of the hole with each of the two free surfaces, was the most severe. The analysis was then repeated for values of A= 36" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000720_0278364910394392-Figure30-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000720_0278364910394392-Figure30-1.png", + "caption": "Fig. 30. Physical instantiation of the kinematic snake. Two optical mice on the middle link provide odometry data, including an estimation of constraint slip.", + "texts": [ + " The differential-drive car in its classical coordinate system has zero-valued height functions and thus represents one end of the spectrum of heightfunction analysis, with no translation information available from the functions, while the south-pointing chariot and rolling disk represent the other extreme, with the height functions providing an exact measure of the displacement over gaits. A key element of our future work will be an examination of this spectrum, with an eye towards incorporating it into a more fully differential geometric treatment of the coordinate change. We applied the gaits from the image-family in Figures 8 and 19 to a physical instantiation of the kinematic snake, shown in Figure 30, and plotted the resulting displacements in the original and optimized coordinates in Figure 31. During the experiments, we observed some backlash in the joints and slip in the constraints, to which we attribute the differences between the calculated and experimental loci in Figures 20 and 31. Even with this error, the BVI was a considerably more effective estimate of the displacement with the new coordinate choice than with the old choice. Under the old coordinate choice, the error in the the net direction of travel between the BVI estimate and the actual displacement ranged from 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000472_s00170-009-2265-7-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000472_s00170-009-2265-7-Figure3-1.png", + "caption": "Fig. 3 Top views of a three-way nozzles and b four-way nozzles", + "texts": [ + " The laser beam is focused by a lens with 127 mm focusing length through a central nozzle. Argon gas is supplied into the central nozzle to protect the focus lens from contamination and provide shielding to the melt pool. Powder feed nozzles with 0.97 mm inner diameter deliver fine powder streams to the melt pool. The powders used in this study are commercially available Inconel 718 powder (mesh size \u2212100/+325) manufactured by the plasma rotating electrode process method. In our DoE experiments, both three-way nozzles (Fig. 3a) and four-way nozzles (Fig. 3b) were tested for a comparison of the powder capture efficiencies (PCE) and the resultant deposition geometric features. All the deposition experiments were conducted inside a glove box where the concentration of oxygen was maintained below 20 ppm. 2.1 Screening design of experiments In the first step, a two-level fractional-factorial DoE was conducted to screen the various processing parameters of a single-track multilayer deposition process. With the screening DoE exercise, the feasibility domain can be quickly explored" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003207_s00170-016-9445-z-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003207_s00170-016-9445-z-Figure6-1.png", + "caption": "Fig. 6 Mesh model of the remanufactured impeller blade (a) Blade mesh (b) Laser cladding zone mesh (c) The third cladding layer mesh", + "texts": [ + "60 0.60/0.62 0.76/0.66 0.79/0.62 0.79/0.60 0.80/0.61 Poisson ratio \u03bc 0.32/0.31 0.34/0.37 0.36/0.42 0.38/0.39 0.42/0.48 0.45/0.52 0.47/0.46 linear expansive coefficient \u2202/10\u22126 \u00b0C 12.5/11.2 13.2/11.8 13.6/12.5 14.8/13.7 15.3/14.8 15.7/15.5 15.9/16.9 two main ways including thermal radiation and heat convection to exchange heat to the surroundings. Thus both convection and radiation should be taken into consideration. During stress analysis, nodes of A, B, C, and D at the end of the bottom showed in Fig. 6 were constrained. In this way, rigid body motion could be avoided. According to numerical procedure, 3D-remanufactured impeller model was built by software Pro/E (version 5.0) based on 3D surface reverse technology [19]. In order to reduce computing amount, a single remanufactured impeller blade, instead of the whole impeller, was applied to do the laser cladding simulation. The geometrical model is shown in Fig. 5. In meshing process, a non-uniform mesh was used to improve simulation accuracy and reduce computational cost. Figure 6 shows the FE model for laser cladding, and in total, there are 6622 nodes and 4896 elements meshed. As the blade thickness is 1.1\u223c1.5 mm, which is less than the laser diameter 3 mm, the blade can be directly deposited by a single layer as shown in Fig. 6. Six cladding layers were deposited in total, and the scan path was from left to right along the scaning direction. In transient thermal analysis, thermal conduction element solid70 was used. After completing the thermal analysis, the element type in mechanical analysis was solid187 with quadratic displacement behavior. The failure impeller was remanufactured successfully by laser cladding. Figure 7 shows the remanufactured impeller; the cladding is fine, uniform, and free of crack. In the next section, forming mechanism, microstructure, and remanufactured impeller quality will be discussed in detail" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure3.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure3.9-1.png", + "caption": "Fig. 3.9 Spring designs; a) Basic structure of a rubber spring; 1 Foundation or machine, 2 Rubber spring, 3 Mounting site; b) Steel spring arrangement", + "texts": [ + " Rubber springs or rubber-metal combinations are also used as discrete spring elements. Their ductility is lower due to their low maximum permissible load, and only natural frequencies of foundations over 5 Hz can be reached. The damping ratio of plants equipped like that is D = 0.01 to 0.1. 1.3.3 discusses the calculation of rubber springs. It should just be pointed out that, for large values of kdyn = cdyn/cstat, the static deflection is not suitable as a measure of the frequency to be isolated. Figure 3.9a shows a rubber spring that is commonly used for foundation designs. 3.2 Foundation Loading for Periodic Excitation 199 The dynamic stiffness of the subsoil or of isolating plates is approximated by foundation moduli. Calculation rules only account for the contact between foundation and subsoil at the base area of the foundation. The foundation moduli are spring constants per unit area and depend on the type of soil, density index, base area, and the static base pressure. The reference value is the foundation modulus Cz that acts in the vertical direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000882_j.rcim.2010.08.007-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000882_j.rcim.2010.08.007-Figure3-1.png", + "caption": "Fig. 3. Category 2.1.", + "texts": [ + " However, the f calculated by \u2018+\u2019 is not equal to zero. Therefore, the \u2018\u20187 \u2019\u2019 in Eq. (11) should be \u2018\u2018\u2013\u2019\u2019 in this matter. From Eq. (8)\u2013(11), we can find that the x, y parasitic motion is the function about c, y, r, while the f parasitic motion is the function only about c,y. To compare the parasitic motion of 3-PRS PM with different limb arrangements, we set the radius of the moving plane is 0.1 m, and the scope of c, y is \u00f0 60o,60o \u00de in the whole paper. Then, the parasitic motion of the 3-PRS PM in category 1 is depicted in Fig. 2. As shown in Fig. 3, three LPs intersect at a line with noncolinear spherical centers. We have au1 \u00bc r1ca r1sa 0 T , au2 \u00bc r2cb r2sb 0 h iT , au3 \u00bc 0 r3 0 T Because the attachment point Ci can only move in the limb plane, we have the following three constraint equations for each leg: l1y \u00bc l1xta, l2y \u00bc l2xtb, l3x \u00bc 0 \u00f012\u00de As shown in Fig. 3, we have li \u00bc ai\u00feP\u00bc Taui\u00feP and it can be rewritten as: l1x \u00bc x\u00feT11au1x\u00feT12au1y \u00bc x\u00fe\u00f0cycf\u00fescsysf\u00der1ca\u00fe \u00f0 cysf\u00fescsycf\u00der1sa l1y \u00bc y\u00feT21au1x\u00feT22au1y \u00bc y\u00feccsfr1ca\u00fecccfr1sa 8>>>< >>>: \u00f013:1\u00de l2x \u00bc x\u00feT11au2x\u00feT12au2y \u00bc x\u00fe\u00f0cycf\u00fescsysf\u00der2cb\u00fe \u00f0 cysf\u00fescsycf\u00der2sb l2y \u00bc y\u00feT21au2x\u00feT22au2y \u00bc y\u00feccsfr2cb\u00fecccfr2sb 8>>>< >>>: \u00f013:2\u00de l3x \u00bc x\u00feT12au3y \u00bc x\u00fe\u00f0 cysf\u00fescsycf\u00der3 l3y \u00bc y\u00feT22au3y \u00bc y\u00fecccfr3 8>< >: \u00f013:3\u00de Substituting l1x, l1y, l2x, l2y into the three constraint equations in Eq (12) yields y\u00feccsfr1ca\u00fecccfr1sa \u00bc \u00bdx\u00fe\u00f0cycf\u00fescsysf\u00der1ca\u00fe \u00f0 cysf\u00fescsycf\u00der1sa tan\u00f0a\u00de \u00f014\u00de y\u00feccsfr2cb\u00fecccfr2sb \u00bc \u00bdx\u00fe\u00f0cycf\u00fescsysf\u00der2cb\u00fe \u00f0 cysf\u00fescsycf\u00der2sb tan\u00f0b\u00de \u00f015\u00de x\u00bc \u00f0cysf scsycf\u00der3 \u00f016\u00de Using (14)\u2013(16), we can calculate the f parasitic motion as following: f\u00bc arctan scsy\u00f0lD F\u00de\u00feE\u00f0cc cy\u00de Ccc\u00felDcy\u00feEscsy Fcy \u00f017\u00de where l\u00bc r3=rp, C \u00bc cb ca, D\u00bc tanb tana, E\u00bc sb sa, F \u00bc sbtanb satana When the three LPs are arranged symmetrically, the angle between every two LPs is 1201, that is, a\u00bc 2101,b\u00bc 301. Without loss of generality, let r1\u00bcr2\u00bcr3\u00bcr, as shown in Fig. 3. Substituting these parameters into (14), (16), and (17), we have f\u00bc arctan sincsiny cosc\u00fecosy \u00f018\u00de x\u00bc \u00f0cysf scsycf\u00der \u00f019\u00de y\u00bc r 2 \u00f0 ffiffiffi 3 p ccsf\u00fecccf\u00fe ffiffiffi 3 p cysf ffiffiffi 3 p scsycf cycf scsysf\u00de \u00f020\u00de The parasitic motion of the 3-PRS PM in subcategory 2.1 is depicted in Fig. 4. Carretero presented the equations of the three parasitic motion of this kind of 3-PRS PM in [20], and the parasitic motion was drawn with the scope of c, y being ( 0.2,0.2), radian. As shown in Fig. 5, three LPs intersect at a line with noncolinear spherical centers, and two LPs are coincident and perpendicular to the other LP" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001600_c5cc04976h-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001600_c5cc04976h-Figure15-1.png", + "caption": "Fig. 15 Functionalization of electrode surfaces before application in microbial fuel cells (MFC). Adapted from Ref. 40 with the permission of Wiley.", + "texts": [ + " A microbial fuel cell (MFC) is a bio-electrochemical system that produces a current by using bacteria as electrocatalysts. In order to improve MFC performance, Barri\u00e8re and co-workers developed a method to improve the interface between electrodes and biofilms by grafting boronic acids on to the electrode surface for better adhesion towards electroactive bacteria.44 Graphite anodes were first modified with a phenylboronic acid pinacol ester by electrochemical reduction of aryl diazonium salts. After deprotection of the pinacol esters from the boronic acid groups, the modified electrodes were used as MFCs (Fig. 15). Compared to MFCs with unmodified electrodes, the boronic acid functionality resulted in a faster interaction with electroactive biofilms (reaching a stationary phase faster) and resulting in 1.6 fold higher power density and current density. This approach could be extended to biofilm development with pure electroactive cultures under controlled anode potential. Self-Assembled Monolayers and Structures formed with Boronic Acids. Over recent years, carbon nanotubes and graphene oxide have been the most common carbon materials used for electrode modification due to the high surface area available for boronic acid functionalisation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001874_tmech.2018.2818442-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001874_tmech.2018.2818442-Figure7-1.png", + "caption": "Fig. 7. Actuation cabling between joints", + "texts": [ + " 7 0 0 6 11 0 6 , /2 0 1, /2 N i i A A A A R P (3) By calculating the three independent actuator parameters of the manipulator 1 , , T d q , the inverse kinematics can be obtained. Payload and tensions will be analyzed in this section [31-32]. External forces and moments which are acting on the continuum module are presented, including friction, actuation and elasticity. Because of the axial force of each cable, actuation loading exerts the forces and moments on each joint. Besides, the contact forces between joints and cables lead to friction. Geometric analysis shown in Fig. 7 depicts the cabling between joints. These cables follow a straight path between the holes, so the cabling may be determined by calculating the coordinate of holes. Within each local joint frame and at the base of continuum module, the two position vectors of cable routing holes \u2013 1,lcl r and 2,lcl r are defined by Eq. (4), where 0 r is the radial dimension of the hole from the center of joint 1, 0 1 0 0 T lcl rr , 2, 0 1 0 0 T lcl r r (4) The position ,i j p of the th j cable in the th i joint may be obtained by using the i P , shown in Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001874_tmech.2018.2818442-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001874_tmech.2018.2818442-Figure8-1.png", + "caption": "Fig. 8. (a) Cross-section of vertebrae, (b) free-body diagram of vertebrae.", + "texts": [ + " These cables follow a straight path between the holes, so the cabling may be determined by calculating the coordinate of holes. Within each local joint frame and at the base of continuum module, the two position vectors of cable routing holes \u2013 1,lcl r and 2,lcl r are defined by Eq. (4), where 0 r is the radial dimension of the hole from the center of joint 1, 0 1 0 0 T lcl rr , 2, 0 1 0 0 T lcl r r (4) The position ,i j p of the th j cable in the th i joint may be obtained by using the i P , shown in Eq. (5). Furthermore, the cable force directions ,i j e may be written as the unit vector of ,i j p , shown in Fig. 8, and defined in Eq. (6). 1083-4435 (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. TMECH-07-2017-6836.R1 6 , , 1 ,i j i i j clc i j clc p P + R r R r (5) , , / i i j i j e p p (6) The cable tension along the continuum module and the friction on each joint make the loading analysis complicated. To calculate the friction on each joint, the cable\u2019s average tension before and after the joint is required", + " Therefore, an iterative approach is needed. The estimated contact friction for the cable will be needed to update the cable tensions of each joint along the continuum module. Then these updated tensions will be used to re-evaluate the friction. Continuous saturated viscous friction model will be used in this analysis, because when the cable sliding velocity is not close to zero, it can present the dynamic sliding friction accurately. In this analysis, a belt friction model is adopted as shown in Fig. 8 (a), because of the traverse of the cable routing holes. Figure 8 shows the key model parameters, Eq. (7) is the expression of the belt friction model, where ,i j is the contact angle of cable on th i joint defined in Eq. (8) and is the saturated viscous friction coefficient. According to Eq. (7) and (9), the force of friction , ,i j f F can be determined in the th j hole of the th i joint. And Eq. (9) will give the friction based on the difference of two tensions of th i joint. , , 1, i j i j i j T T e (7) , ( 1) ( 1) arccos i j i i i i ge e (8) , , , 1, 1 1 2 i j f i j i j i i T T F e e (9) Based on the formulations above, the contact angle ,i j will increase with deflection angle, meanwhile the tension force will also become larger according to the results of deflection force tests in Section V. As a result, the bottom tension is larger than the top tension. The contact force , ,i j con F that contains the friction effect might be determined by each cable and joint , as shown in Eq. (10), with the tensions and frictions shown in Fig. 8 (b). This magnitude of , ,i j con F is the difference of friction , ,i j f F , the bottom and the top tension 1, 1i j i T e , ,i j i T e . In the initial position, the friction is near zero and the bottom and top tensions of cable on each joint are considered to be equal, in other words, the difference of these forces is identically zero. , , 1, 1 , , ,i j con i j i i j i i j f T T F e e F (10) The distributed contact forces are decreasing along the NiTiNol tubes. The results for the separate segment can be transformed back into the global joint coordinate system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002048_j.ijheatmasstransfer.2017.01.093-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002048_j.ijheatmasstransfer.2017.01.093-Figure5-1.png", + "caption": "Fig. 5. Temperature profile in x-y plane at t = 0.56, 1.12, 1.68, 2.24 and 2.8 ms.", + "texts": [ + " The surface tension of the melting pool is a function of temperature. The top surface of the liquid melting pool is presented to be concave in Figs. 3 and 4(b) and also in the upcoming figures. The surface tension gradient and buoyancy force will drive the melting fluid flow to form flat or even sphere surface. Once the geometry of the melting pool is determined, whether balling phenomenon will occur can be predicted by the stability condition in reference [23]. To better understand the temperature distribution of the powder bed, Fig. 5 shows the temperature profile in the x-y plane at different moments. The black circle is the projection circumference of the laser beam. In Fig. 5(a), the temperature profiles are not exact circles due to the influence of the left boundary and transient temperature evolution. The unsmoothy in the isotherm of 3000 K is caused by the discontinuity of enthalpy and latent heat during boiling shown in Fig. 5(a)\u2013(e). The temperature profiles enlarge and change into ellipses with time increasing. The reason that the shape of the temperature contours are ellipses instead of circles is the heat accumulation in the movement of the laser beams as shown in the melting pool in Fig. 4. Once the shape of the temperature profile become stable and does not change with time, it is called steady state. In most literature, only the temperature field of the steady state is investigated. Experiments show that delamination and warping are most likely to occur at the edge of the SLM products, that is, at the beginning or ending of the tracks", + " [24]. The reason is that in the reference the vaporization of the melting pool is neglected. A large portion of the melting pool is removed by vaporization. In the following, the effect of vaporization will be addressed. Fig. 10 compares the results of interfaces with/ without considering vaporization. The case without considering vaporization overestimates the depth of the solidified track. Fig. 10 shows a flat platform at the top surface of the melting pool without vaporiza- tion. As shown in Fig. 5, the center of the melting pool has the highest temperature and the part over boiling temperature vaporizes. In experiment, the vaporization does occur and the fume can be observed even with optimal process parameters. In Fig. 11, one compares the results with temperature and phase dependence of the material properties and those with constant thermal conductivity k and specific heat c. The neglecting of temperature dependence of material properties results in an overprediction of the size and volume of the liquid pool" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001502_j.ymssp.2012.03.013-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001502_j.ymssp.2012.03.013-Figure2-1.png", + "caption": "Fig. 2. Illustration of kinematic quantities utilized in the analytical model. (a) Geometric parameters of a double row bearing shown for a back-to-back configuration; (b) Elastic deformation of a rolling element under load.", + "texts": [ + " To define the bearing stiffness matrix, the relationship between the mean bearing load vector fm \u00bc fFxm, Fym, Fzm, Mxm, Mymg T and mean displacement vector qm \u00bc fdxm, dym, dzm, bxm, bymg T (both vectors acting along the geometrical center of the bearing) has to be derived. Thus, the total elastic deformation of each rolling element (di j) is first determined utilizing the complex kinematics of the rolling elements of a double row angular contact bearing as outlined in Eqs. (2\u20137) and illustrated in Fig. 2 (i and j are the row and rolling element indices, respectively): \u00f0dr\u00de i j \u00bc \u00bddxm\u00femidi zbym cos\u00f0ci j\u00de\u00fe\u00bddym midi zbxm sin\u00f0ci j\u00de rL \u00f02\u00de \u00f0dz\u00de i j \u00bc dzm\u00feR\u00bdbxm sin\u00f0ci j\u00de bym cos\u00f0ci j\u00de \u00f03\u00de \u00f0dn r \u00de i j \u00bc \u00f0dr\u00de i j\u00feAo cos\u00f0ao\u00de \u00f04\u00de \u00f0dn z \u00de i j \u00bc \u00f0dz\u00de i j\u00fen i\u00f0Ao sin\u00f0ao\u00de\u00fe\u00f0dz0\u00de i \u00de \u00f05\u00de Ai j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0\u00f0dn r \u00de i j\u00de 2 \u00fe\u00f0\u00f0dn z \u00de i j\u00de 2 q \u00f06\u00de di j \u00bc Ai j Ao for di j40 0 for di jr0 8< : \u00f07\u00de here, ci j is the angular position of the rolling element (measured from \u00fex axis), rL is the radial clearance, R is the pitch radius, ao is the unloaded contact angle, and di z is the axial distance between the geometric center of the bearing and the ith bearing row. \u00f0dr\u00de i j and \u00f0dz\u00de i j are the radial and axial deflections, and \u00f0dn r \u00de i j and \u00f0dn z \u00de i j denote the radial and axial distances between the inner and outer raceway curvature centers of the loaded rolling element. Ai j and Ao are the loaded and unloaded distance between the inner and outer raceway curvature centers, respectively. Refer to Fig. 2(a), (b) for a schematic illustration of the geometric and kinematic parameters. Coefficient mi in Eq. (2) is a dimensionless constant and is \u2018 1\u2019 for i\u00bc1 (left row) and \u20181\u2019 for i\u00bc2 (right row). \u00f0dz0\u00de i in Eq. (5) defines an axial displacement preload on the ith row obtained by bringing the inner and outer raceways closer together by a distance \u00f0dz0\u00de i (for instance in the case of split inner rings [33]). \u00f0dz0\u00de i can have a positive value only if the radial clearance is eliminated (rL \u00bc 0). Note that \u00f0dz0\u00de i differs from \u00f0dz\u00de i j, which corresponds to an axial deflection caused by an external load; those two variables may add up or cancel each other out dependent on the value of ni, which is a dimensionless constant and dependent on the configuration of rolling elements as follows: Back-to-back configuration : ni \u00bc 1 for i \u00bc 1\u00f0Left row\u00de 1 for i \u00bc 2\u00f0Right row\u00de ( \u00f08a\u00de Face-to-face configuration : ni \u00bc 1 for i \u00bc 1 \u00f0Left row\u00de 1 for i \u00bc 2 \u00f0Right row\u00de ( \u00f08b\u00de Tandem configuration : ni \u00bc 1\u00f0n\u00de\u00f0Both rows\u00de \u00f08c\u00de The elastic deformation of the rolling element (di j) is then used in the Hertzian contact stress theory to obtain the resultant normal load (Qi j) on the element Qi j \u00bc Kn\u00f0d i j\u00de n \u00f09\u00de here, Kn is the rolling element load-deflection stiffness constant, which is a function of material properties and geometry [1]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure2.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure2.4-1.png", + "caption": "Figure 2.4.1 Vehicle on longitudinal gradient.", + "texts": [ + " For simulation purposes, it is necessary to know the road bank anglefR, and the curvature vector (i.e. k and fk, or other combination of data allowing k and fk to be evaluated). Methods of determining this information are considered later. The dynamic behaviour of the vehicle is normally analysed in road surface-aligned coordinates. These are distinct from the Frenet\u2013Serret coordinates generally used bymathematicians to analyse a curved line in space (see Appendix E). Consider a track with no bank angle, but with longitudinal gradient angle uR, as in Figure 2.4.1. The angle is considered constant, that is, the pitch curvature is temporarily zero. Analysis proceeds in road-aligned coordinates. The weight force W needs to be replaced by its components in those coordinates, as shown. The consequence of the normal component change is a reduction in the tyre vertical forces, although this is usually fairly small. The longitudinal component exerts an effective resistance on the vehicle for positive uR and, because it acts at the centre of mass, above ground level, in combinationwith the required opposing tractive force it gives a force couple in pitch and a resulting longitudinal load transfer. Figure 2.4.2 shows a vehicle in a trough of pitch radiusRN (and positive pitch curvaturekN), which,with zero road bank angle, is kV kN The normal curvature is kN \u00bc 1 RN The vehicle is shown in a position at which the road normal is vertical, in order to temporarily separate out the pitch curvature and pitch angle effects. The bank angle is still zero. A trough is considered to have positive curvature, whereas a crest has negative curvature. Also shown, incidentally, is the angle uLN subtended by thewheelbase" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001831_j.mechmachtheory.2011.08.009-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001831_j.mechmachtheory.2011.08.009-Figure2-1.png", + "caption": "Fig. 2. Contact line between the workpiece and the wheel during the form grinding process.", + "texts": [ + " Hence, assuming that the workpiece's surface position is represented in coordinate system S1 in two-parametric form r1(u,\u03b2), the transformation matrices S1 to St give the surface locus of the ground surface in coordinate system St: rt u;\u03b2;\u03d51\u00f0 \u00de \u00bc xt yt zt 1f gT \u00bc Mtc \u03b3m\u00f0 \u00deMca Et ; Lt\u00f0 \u00deMa1 \u03d51\u00f0 \u00der1 u;\u03b2\u00f0 \u00de \u00bc Mt1 \u03b3m; Et ; Lt ;\u03d51\u00f0 \u00der1 u;\u03b2\u00f0 \u00de \u00f01\u00de where Mtc \u03b3m\u00f0 \u00de \u00bc cos\u03b3m 0 sin\u03b3m 0 0 1 0 0 \u2212 sin\u03b3m 0 cos\u03b3m 0 0 0 0 1 2 664 3 775 Mca Et ; Lt\u00f0 \u00de \u00bc 1 0 0 \u2212Lt 0 1 0 \u2212Et 0 0 1 0 0 0 0 1 2 664 3 775 Ma1 \u03d51\u00f0 \u00de \u00bc 1 0 0 0 0 cos \u03d51 sin \u03d51 0 0 \u2212 sin \u03d51 cos \u03d51 0 0 0 0 1 2 664 3 775: Although the parameters Lt and the workpiece rotation angle \u03d51 are usually related as Lt=Pt\u03d51, here Pt is the screw parameter, which is determined based on the helical angle of the workpiece's pitch cylinder. During the grinding process, the universal machine settings are -art CNC technology allows the implementation of auxiliary flank modification (AFM) motions to achieve free-form flank modification based on nonlinear machine settings. According to differential geometry, consider that the workpiece rotation angle \u03d51 is the motion parameter, the locus normal is derived as follows: nt u;\u03b2;\u03d51\u00f0 \u00de \u00bc \u2202rt u;\u03b2;\u03d51\u00f0 \u00de \u2202u \u00d7 \u2202rt u;\u03b2;\u03d51\u00f0 \u00de \u2202\u03b2 \u2202rt u;\u03b2;\u03d51\u00f0 \u00de \u2202u \u00d7 \u2202rt u;\u03b2;\u03d51\u00f0 \u00de \u2202\u03b2 : \u00f02\u00de As illustrated in Fig. 2, when the wheel surface is conjugated to the workpiece surface, the normals on the contact line between the two surfacesmust pass through the axis of wheel zt. Because the three vectors nt, zt and rt are coplanar, the scalar triple product is equal to zero, as shown by the following equation: ft \u00bc nt u;\u03b2;\u03d51\u00f0 \u00de\u22c5 zt\u00d7rt u;\u03b2;\u03d51\u00f0 \u00de\u00bd \u00bc 0: \u00f03\u00de Solving the contact line in coordinate system St allows determination of the wheel profile. Because in the form grinding process the contact lines are identical at every instant \u2013 that is, the rotation angle of the workpiece is \u03d51=0 \u2013 the contact points can be solved using Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure8.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure8.2-1.png", + "caption": "Fig. 8.2 a Feasible activation set for 1 functional constraint. b The intersection of a 3D unit cube with a 2D plane is a 2D plane embedded in 3D", + "texts": [ + "3) Here, the constraint of setting \u03c4z to zero is expressed as \u03c4z = hT 4 \u00b7 \u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d a1 a2 a3 a4 a5 a6 a7 \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 = 0 (8.4) Therefore the feasible activation set is the portion of the 7DN-cube that intersects the plane defined by the linear equation hT 4 \u00b7 a = 0. All activation patterns contained in this 6D subset of the 7D space will meet the constraint of having no output \u03c4z . This will create the 3D feasible force set for the index finger while it produces no endpoint torques.2 As an explanation of this, consider Fig. 8.2 as a direct analogy. Here you have the intersection of a unit cube (3D object) with a 2D plane (i.e., one equation in 3 variables). Their intersection produces a feasible set that is a 2D plane embedded in 3D space because the dimensionality of the 3D object was reduced by 1 (i.e, the introduction of 1 constraint typically reduces the feasible space by 1 dimension). All points that are both on the plane and in the unit cube will satisfy all constraints. To make the force production task even more realistic and functional, consider that you are interested in all activation patterns that not only produce no output \u03c4z , but also produce no side-to-side fingertip forces", + " These are the kinds of forces you would use to roll a pencil with the index fingertip: any lateral forces would make the pencil twist and fall from your grasp. In this example, such side-to-side forces are in the z direction. Therefore, you would want to enforce 2 constraints ( fz \u03c4z ) = [ hT 3 hT 4 ] \u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d a1 a2 a3 a4 a5 a6 a7 \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 = ( 0 0 ) (8.5) 2If you are curious about what this looks like see Fig. 8.6. 8.2 Calculating Feasible Sets for Tasks with Functional Constraints 119 Using the analogy in Fig. 8.2 again, the intersection of the cube with 2 planes\u2014if it exists\u2014is a 1D line. That is, the activation patterns that meet all constraints lie on a 1D line embedded in 3D space. See Fig. 8.3. Turning back to our 7-muscle finger, the feasible activation set for all possible forces in the plane of finger flexion must meet both hT 4 \u00b7 a = 0 and hT 3 \u00b7 a = 0. That feasible activation set is a 5D convex set (7 \u2212 2 = 5) embedded in 7D. Figure8.4 shows the projection of the feasible activation set onto the feasible force set, which is naturally 2D because we are only plotting the 2 output dimensions fx and fy that are not constrained to be 0", + " 9Spatial in the sense of meeting the constraints in the space of neural activations, and temporal in the sense of implementing certain temporal dynamics. 150 9 The Nature and Structure of Feasible Sets We have recently developed a probabilistic method to characterize the internal structure of such high-dimensional convex sets embedded in evenhigher-dimensional spaces [78]. This method is best described by example. Consider a same representative 3 muscle limb as in Fig. 7.1, that leads to a 3D feasible activation set that is the intersection of a plane with a unit cube in the positive octant of activations as shown in Fig. 8.2. The question is, what are the probability density functions of muscle activations that satisfy the constraints? Applying the methodology in Fig. 9.1d would show us the bounds on the activation of each muscle as in [1] or [2], but we would not know which level of activity is most common for each muscle. Similarly, if we were to do PCA on data sampled from that feasible activation set, we would know the best-fit cross-correlations among the data points that give us the orientation of the plane as PCs, as in Fig", + " If the Hit-and-Run algorithm can properly sample from within the convex polytope, then the sampled points are representative of all points in the convex set, and the characteristics and probability distributions of those points describe well the details and statistics of the internal structure of the feasible activation set. The details and statistics are an informative characterization of the family of valid neural activation vectors, or muscle coordination patterns\u2014whose importance was described in Sects. 9.3 and 9.4 above. Consider the feasible activation set for the 3 muscle limb shown in Fig. 7.1, which is satisfying one constraint equation as in Fig. 8.2. The feasible activation set is the 2D convex polygon embedded in 3D, shown by the shaded plane. We see that the results of the Hit-and-Run algorithm are the probability density functions of the points that create the feasible activation set, Fig. 9.7e, f. Were we to use the bounding box approach, all we would know are the extremes of these distributions. We now see that those bounds apply, but that the distribution of neural activation within those bounds is far from uniform. That is, not all values of activation for each muscle are equally likely" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.2-1.png", + "caption": "Figure 11.2 depicts a moving body B in a global frame G. Assume that the body frame is at tac hed at the center of mass (C M) 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 infinit esimal force df and has a global velocity Gv p .", + "texts": [], + "surrounding_texts": [ + "452 11. Motion Dynamics\nR = 6356912 m at the pole to R = 6378388 m on the equator, then the vari ation of the acceleration of gravity becomes 0.53%. So, generally speaking, a sportsman such as a pole-vault er practi cing in the north pole can show a bett er record in a competition held on the equator.\nThe third term is called the Coriolis effect, Fc , which is perpendicular to both wand B vp. For a mass m moving on the north hemisphere at a latitude e towards the equator, we should provide a lateral eastward force equal to the Coriolis effec t to force the mass, keeping its direction relative to the ground.\nThe Coriolis effect is the reason of wearing the west side of railways , roads, and rivers. The lack of providing Coriolis force is the reason for turning the direction of winds, projectiles, and falling objects westward.\nExample 252 Work, force, and kinetic energy in a unidirectional motion. A mass m = 2 kg has an initial kin eti c energy K = 12 J . The mass is under a constant force F = F1 = 41 and moves from X (0) = 1 to X (t f) = 22 m at a terminal time t f . The work done by the force during this motion is t: J22W = F\u00b7 dr = 4dX = 21 N m = 21.J\nr (O) 1\nTh e kin etic energy at the terminal time is\nK(tf) = W - K(O) = 9J\nwhich shows that the terminal speed of the mass is\nV2 = J2K~f) = 3m/ s.\nExample 253 Time varying force. When the applied force is tim e varying,\nF(t) = mr (11.28)\nthen there is a general solution for the equation of motion because the char acteristi c and category of the motion differs for different F(t) .\nf(t)\nr(t)\n1 itf (to) + - F(t)dt m to .c:r(t o)+ f( to)(t - to) + - F(t)dt dt m to to\n(11.29 )\n(11.30)", + "11. Motion Dynamics 453\n11.2 Rigid Body Translational Kinetics\nIn these equations, GaB is the acceleration vector of the body CM in global frame, m is the total mass of the body, and F is the resultant of the external forces acted on the body at CM. Proof. A body coordinate frame at center of mass is called a central fram e. If the frame B is a central frame, then the center of mass, C M, is defined such that\n(11.34)", + "454 11. Motion Dynamics\nThe global position vector of dm is relat ed to its local position vector by\n(11.35)\nwhere G d B is the global position vector of the central body frame, and therefore,\nl GdB dm + GRB LBr dm dm\nl: GdB dm\nGd B l dm\nm GdB . (11.36)\nThe tim e derivative of both sides shows that\nand another derivative is\nG \u00b7 G r G \u00b7 d m v B =m e e > iB v\u00bb; m .\nHowever, we have df = G\" p dm and,\n(11.37)\n(11.38)\n(11.39)\nThe integral on the right-hand side accounts for all the forces acting on particles of mass in the body. The internal forces cancel one another out , so the net result is the vector sum of all t he externally applied forces, F , and therefore,\nIn th e body coordinate frame we have\nBRGGF\nm BRG GaB B m GaB B B Bm e\u00bb + m GWB x VB .\n\u2022\n(11.40)\n(11.41)" + ] + }, + { + "image_filename": "designv10_3_0002400_tvt.2018.2850923-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002400_tvt.2018.2850923-Figure1-1.png", + "caption": "Fig. 1. Schematic of an AET system.", + "texts": [ + " Such exploration will greatly help the automotive engineers and researchers to design UO-based robust SM controllers for other automotive systems. The remainder of this paper is organized as follows: Section II derives the AET dynamic model with the expressions of the bounded uncertainties. In Section III, an AITSM controller with stability proof is described, where the UO and the MRED are both discussed. Section IV provides with the experimental results for the verification of the developed control. Section V draws the conclusion. A schematic of a typical AET system is shown in Fig. 1, where a few components are included: a driver accelerator pedal, an electronic control unit (ECU), an AET mechanical body where a DC motor is connected to the output shaft of the throttle plate via a gear set, a double nonlinear return springs maintaining the stationary throttle plate at the default position and the working limp-home when giving zero control input, and two angle sensors to obtain the angular information of the driver pedal movement and the actual throttle opening. The major working principle of the AET system is illustrated as follows: The desired angle is first measured by the pedal angle sensor once the driver presses down the pedal and then delivered to the ECU in order to determine the appropriate air-fuel mixture for the engine, while the actual throttle angle is obtained from the throttle angle sensor at the same time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003857_j.engfailanal.2018.08.028-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003857_j.engfailanal.2018.08.028-Figure1-1.png", + "caption": "Fig. 1. Crack propagation paths of some helical gears: (a) gear crack in Ref. [49], (b) gear crack in Refs. [50, 51].", + "texts": [ + " Above-mentioned studies mainly focus on TVMS of spur gear pairs with crack, and the adapted methods mainly include analytical method [1], finite element (FE) method [16,33,34] and analytical-FE method [15,32]. The analytical method has a high efficiency and a good accuracy and it is mostly used to calculate the TVMS of spur gear pairs. For helical gear pairs, the analytical method is based on the slice method and the related studies mainly focus on the TVMS of healthy gear pairs. The studies on TVMS of helical gear pairs with crack are insufficient [24], especially under complicated spatial crack conditions [49\u201351] (see Fig. 1). Aiming at this deficiency, this paper mainly focuses on two aspects: (1) a new calculation method is proposed in order to improve the traditional slice method proposed in our previous study [26], and the efficiency and accuracy of the proposed method are verified by comparing with traditional method and FE method. (2) The TVMS calculation method of the helical gears with crack is presented, and the influences of the four different types of the spatial crack on the TVMS are discussed. The main structure of this paper is as follows: In Section 1, the research status is summarized" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003179_tie.2015.2442216-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003179_tie.2015.2442216-Figure4-1.png", + "caption": "Fig. 4. Seeded faults. (a) Sun gear fault. (b) Planet gear fault. (c) Ring gear fault.", + "texts": [ + " Their corresponding fault frequencies are represented as follows: ff,1 = s \u00b7 (f1 \u2212 fa) = f1z3s (z1 + z3) (7) ff,2 = 2(f2 + fa) = 4n1z1z3 (z23 \u2212 z21) (8) ff,3 = s \u00b7 fa = f1z1s (z1 + z3) (9) where ff,i represents the fault frequency at the ith gear component, and s represents the number of planet gears in the gearbox. For more details, see [44]. Tables II and III present the structural information and characteristic frequencies of the PGB used in this paper. Three types of PGB faults were created, namely, sun gear tooth fault, planet gear tooth fault, and ring gear tooth fault. Each type of gear faults was created by artificially damaging a tooth on a sun gear, a planetary gear, and a ring gear, respectively (see Fig. 4). During the seeded fault tests, PE strain signals were collected with a sampling rate of 100 kHz. The tachometer signals were simultaneously recorded along with the PE strain signals to get revolution stamps. Both the healthy gearbox and the gearboxes with seeded faults were tested at five different input shaft speeds, i.e., 10, 20, 30, 40, and 50 Hz. At each speed, five samples were collected. In addition to the shaft speed variation, varying loading conditions were applied at the output shaft of the gearbox, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure13.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure13.10-1.png", + "caption": "Figure 13.10.1 Example Axle 2, with Panhard rod lateral location: (a) side view; (b) front view; (c) plan view; (d) axometric three-quarter view.", + "texts": [ + " Then the interpolation values f2 and f3 followwith the normal displacements of points relative to the reference triangle, as specified earlier. Table 13.9.2 presents the successive iteration loop errors, where the quadratic convergence can be observed. Finally, the actual results for surge, sway, pitch angle and steer angle are given. The convergence error is sometimes exactly zero, but, for interest, 10 15 m is in any case only the diameter of the nucleus of an atom. 264 Suspension Geometry and Computation The second example axle has a Panhard rod for lateral location, with a single top longitudinal link, as shown in Figure 13.10.1. Table 13.10.1 shows the static point coordinates, the interpolation factors and the final results. Table 13.10.2 shows the sensitivity matrix values for three positions \u2013 static, initially displaced and final \u2013where significant differencesmay be seen. Also the distinctive values for the Panhard rod link are evident. Rigid Axles 265 By solving for a range of points through the suspension range and fitting a quadratic curve, the basic coefficients may be obtained. This has been done herewith 11 points for heave through a range 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003380_s40192-019-00164-1-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003380_s40192-019-00164-1-Figure1-1.png", + "caption": "Fig. 1 The AMB2018-01 bridge structure geometry", + "texts": [ + " The main focus was on part thickness, mass, tensile properties, void distribution, and cross section. AMB2018-04 included LPBF 3D builds of nylon 12 dog-bone specimens, built at different orientations with respect to the build axis. The primary focus was on tensile properties, void distribution, and local anisotropy of semicrystalline phase and morphology. AMB2018\u201101 AMB2018-01 consisted of LPBF 3D metal alloy builds of a bridge structure geometry that has 12 legs of varying size, as shown in Fig.\u00a01. A primary goal of AMB2018-01 was to provide a high fidelity set of coordinated measurements and process data, covering the full range from feedstock material to finished part. To our knowledge, no such detailed and multifaceted AM study had ever been attempted. AMB2018-01 included comprehensive characterization of the feedstock materials (https ://www.nist.gov/ amben ch/amb20 18-01-descr iptio n), detailed description of the laser scan pattern with sub-ms-level timing [12], in\u00a0situ thermocouple measurements within the build chamber [12], in\u00a0situ measurements of cooling rate and melt-pool length in every layer within the field of view (as illustrated in Fig.\u00a01) [12], ex situ characterization of the resulting residual strains and stresses [13], part distortion measurements after cutting part of the test piece off the build plate [13], multiple synchrotron X-ray and laboratory-based microstructure studies as a function of position and orientation within the build [14, 15], and measurements of 1 3 the phase evolution during residual stress annealing [15]. Correlations between the in\u00a0situ thermal measurements and the local residual stresses and microstructures should provide a rich proving ground for modelers and greatly enhance insight into how the microstructures, stresses, and properties evolve during LPBF builds", + "\u00a0 5, green indicates that at least one of the submissions for that challenge met the success criteria set by the AM-Bench Organizing Committee and the researchers who conducted the corresponding measurements. Red indicates that none of the submissions met those criteria. For all but two of the challenge problems with successful submissions, just one submitted simulation met the success criteria. The first exception is challenge AMB2018-01-RS, residual strains within the bridge structure shown in Fig.\u00a01. Two submissions to this challenge were deemed good and received first-place awards. The other exception is AMB2018-02-GS, the grain structure of single laser track cross sections. Here, one submission received a first-place award and another received a second-place award. The research teams that received awards for the AM-Bench challenge problems may be found on the AM-Bench web page at www.nist.gov/amben ch/award s. Ideally, it should be possible to correlate the quality of the model outputs with the methodology used for the simulations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001308_tmag.2012.2203607-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001308_tmag.2012.2203607-Figure1-1.png", + "caption": "Fig. 1. The 2-D model of surface mounted PM machine.", + "texts": [ + " An analytical equation was presented in [8] for eddy current losses of permanent magnets for higher time harmonics 20\u201330 kHz for NdFeB magnets, which is more accurate for interior permanent magnet synchronous machines. In this paper, analytical calculations of induced eddy currents with consideration of reaction field in SmCo magnets of a high speed surface mounted PM machine are presented [18]. Axial and circumferential magnet segmentation effects are considered in eddy current losses calculations. Fig. 1 shows the surface-mounted PM motor with parallel magnetization of magnet and single-layer three-phase winding. The speed of a four-pole PMmotor is 15 000 r/min with a fundamental frequency of 500 Hz. The used magnet is with magnetization 1.018 T and electrical conductivity 1.25e6 S/m. The applied current loading is 364.6 A/cmwith produced output torque 7.5 Nm. The inner diameter of the stator core, outer and inner diameters of magnet shell are 70, 65, and 53 mm, respectively. Axial length of the machine is 50 mm", + " The current layer distribution for only one phase excited versus three phase current layer is shown in the next section. Only a fundamental component of current layer is considered due to the main effect on the eddy current losses because of bigger wavelength and also for simplification of the analytical calculations. IV. 3-D TIME HARMONIC FINITE ELEMENT METHOD The equations used by the 3-D linear harmonic finite element analysis [8] and eddy current losses are given in (11). . In ANSYS, the real model of Fig. 1 with the winding distributed in slots was modified to an equivalent three-phase distributed current layer (Fig. 15) to reduce the calculation time. For example, the zone of 3 A slots is unified as one A current layer. As infinite iron permeability for stator and rotor is assumed, only air gap and the magnets must be modeled. The stator and rotor irons are replaced by normal flux boundary conditions (11) where , and are induced eddy current in permanent magnets, stator current density and electric scalar potential, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure5.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure5.5-1.png", + "caption": "Fig. 5.5 Rotor shapes a) Ja Jp (Roller shape), gyroscopic effect negligible b) Ja < Jp (Disk shape), gyroscopic effect substantial", + "texts": [ + "134) are (by comparing coefficients) JS \u03be\u03b6 = (Jp \u2212 Ja) sin \u03b3 cos \u03b3; JS \u03b7\u03b6 = 0; JS \u03b6\u03b6 = Ja sin2 \u03b3 + Jp cos2 \u03b3. (2.139) The kinetic moment that acts on the bearings would change its sign if \u03b3 became negative, i. e. the tilting were the other way. The product of inertia JS \u03be\u03b6 is \u201ctrying to tilt\u201d the rotor from its axis of rotation. The effect of the products of inertia can vividly be explained by the centrifugal forces that cause a moment about the negative \u03b7 axis in such a tilted rotor position. It is also relevant whether the rotor is a flat thin disk (Jp > Ja) or a long roller (Jp < Ja), see Fig. 5.5 and Table 5.2. For a circular cylinder, the difference of the principal moments of inertia is Jp \u2212 Ja = m(3R2 \u2212 L2)/12 in accordance with (2.96) and (2.120), that is, the sign of JS \u03be\u03b6 and the direction of the \u201ctilting moment\u201d depend on whether the rotor is thick (L < \u221a 3R) or thin (L > \u221a 3R). Rigid-body mechanisms are systems of rigid bodies that perform planar or spatial motions, depending on the motions of their input links. So-called generalized coordinates qk are used to describe the motion of such a system, each drive being assigned a coordinate and a generalized force Qk (k = 1, 2, ", + "24) The coupling that exists between the 4 equations is caused by the gyroscopic moment. One can see that decoupling occurs for \u03a9 = 0 (non-rotating shaft) so that only the displacement and tilt in one plane influence each other (y and \u03c8x or x and \u03c8y , respectively). The vibrations in the planes that are offset by 90\u25e6 can then be examined separately. The gyroscopic moments for rotors in which Jp Ja are relatively small as compared to other moments so that they can be neglected without any substantial loss in accuracy (e. g. textile mandrils), see Fig. 5.5a and Fig. 6.30. In the case of isotropic support, it is permissible and useful to use the rotating plane (r; z) formed by the z axis and the elastic line rather than the two fixed planes (x, z; y, z). The radial displacement r of the shaft center and the angle \u03c8 of the cone formed by the rotating tangent can be used as coordinates. The shaft shown in Fig. 5.4 corresponds to case 6 in Table 5.1, the influence coefficients being \u03b1 = d11, \u03b2 = d22, \u03b3 = \u03b4 = d12. The following equations apply likewise to cases 3 to 5", + " The principal excitation of a rotating shaft is represented by its unbalance excitation. As in this case, a natural frequency \u03c9i coincides with the angular velocity \u03a9 of the shaft, the resonance points are found as intersections of the straight line \u03c9 = \u03a9 and the curves according to (5.33). The critical speeds of rotation in the 324 5 Bending Oscillators same direction result from (5.31) where JR = Ja \u2212 Jp: 1 \u03c92 2,4 = 1 2 { \u03b1m+\u03b2(Ja\u2212Jp)\u00b1 \u221a [\u03b1m+\u03b2(Ja\u2212Jp)] 2\u22124(\u03b1\u03b2\u2212\u03b32)m(Ja\u2212Jp) } . (5.35) For all rotors where Jp/Ja > 1, see Fig. 5.5 and Table 5.2 where h d : Jp/Ja = 2, the root expression becomes larger than the preceding terms, and a negative \u03c92 emerges. In other words: There is only one resonance of rotation in the same direction for disk-shaped rotors (Fig. 5.6, point P1). Ja > Jp can apply to drum-shaped rotors. Then there are two resonance points also during rotation in the same direction because the curve of \u03c94(\u03a9) is flatter, see Fig. 5.6. The special case Ja \u2248 Jp is worth noting because for high speeds the frequency of unbalance excitation approaches asymptotically the second natural frequency for rotation in the same direction", + "55) The characteristic equation is derived from both equations by setting the expressions in parentheses to zero: 5.2 Fundamentals 331 \u03c92 \u2212 Jp\u03a9 JA \u03c9 \u2212 cl2 JA = 0. (5.56) From this follow the natural circular frequencies \u03c91,2 = Jp\u03a9 2JA \u2213 \u221a cl2 JA + ( Jp\u03a9 2JA )2 . (5.57) The influence of the gyroscopic effect can be evaluated using the characteristic parameter \u03b5 = Jp\u03a9 2JA\u03c90 = Jp\u03a9 2l \u221a cJA . (5.58) It is virtually negligible if \u03b5 < 0.05. The influence of the velocity of rotation \u03a9 on the natural frequencies is smaller for cylindrical rotors than for disk-shaped rotors, see Fig. 5.5. Note that according to (5.57) there are a \u201cpositive\u201d and a \u201cnegative natural circular frequency\u201d since the root expression is larger than the first summand. If one inserts the negative root in (5.54), one will see that it corresponds to another direction of rotation (\u201copposite direction of rotation\u201d: rotation of the rotor in opposite direction of 332 5 Bending Oscillators the vibration direction) than the positive root (\u201csame direction of rotation\u201d: rotation of the rotor in the same direction as the vibration direction)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000699_1.3085942-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000699_1.3085942-Figure2-1.png", + "caption": "Fig. 2 \u201ea\u2026 A view and \u201eb\u2026 the layout of the gear efficiency test machine", + "texts": [ + " he instantaneous power loss due to pocketing at the same control olume is found as 19 Pp,ij m = \u2212 vb,ij m Ab,ij m pb,ij m\u22121 + 1 2 vb,ij m\u22121 2 \u2212 vb,ij m 2 \u2212 ve,ij m Ae,ij m pe,ij m\u22121 + 1 2 ve,ij m\u22121 2 \u2212 ve,ij m 2 7a he average pocketing power loss of the entire gear mesh was ound by summing up losses from all J1 m control volumes of gear and J2 m control volumes of gear 2 and averaging over the num- er of the rotational increments m 1,M as ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms Pp = 1 M m=1 M j=1 J1 m Pp,1j m + j=1 J2 m Pp,2j m 7b It has to be noted here that the above formulations consider static oil levels. Any change in oil level as gears rotate was not included in this model 19 . 3.1 Test Machine and Test Procedure. A gear efficiency test machine used previously by Petry-Johnson et al. 41 to study losses of jet-lubricated gearboxes, as shown in Fig. 2 a , was used here with some modifications to perform gear pair oil churning experiments. Only the most relevant details of the test setup are provided here\u2014see Ref. 41 for a comprehensive description of the details of the machine, including its repeatability and accuracy. The test machine consists of two identical gearboxes, each containing one gear pair and four identical cylindrical roller bearings. In this power circulatory arrangement, one gear from each gearbox is connected to the corresponding gear of the other gearbox, as shown schematically in Fig. 2 b . The input shaft of the reaction gearbox is connected to a high-speed spindle through a flexible coupling and a precision noncontact type torque-meter. The high-speed spindle is driven by a belt with a 3:1 ratio speed increase from a variable speed ac motor. Figure 3 shows a picture of one of the gearboxes that is configured to perform dip-lubricated efficiency tests. The other gearbox has exactly the same arrangement. Valves of the oil return were closed in order to maintain an oil bath within each gearbox", + " Hence, the accuracy of the power easurements associated with the torque-meter accuracy was ather good. Meanwhile, actual repeatability of the test setup as a hole, including all mechanical and hydraulic aspects of the test achine as a gauge the same test performed in different days by ifferent operators, including reassembly of the gears was also cceptable. For instance, the repeatability of measured power vales at 6000 rpm was typically within 50 W. Oil temperature ithin each test gearbox shown in Fig. 2 b was measured by two hermocouples inserted from both sides of each gearbox near the ottom in a direction perpendicular to shaft axes. They were used o ensure that the bulk oil temperature levels within a gearbox are easonably uniform and also the temperatures of both gearboxes re equal. 3.2 Gear Specimens and Test Matrix. Two basic unity-ratio pur gear designs were implemented in this study. The design arameters of these test gears are provided in Table 1. Figure 4 hows a picture of some of these test gears" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.12-1.png", + "caption": "FIGURE 1.12. The PrPrP Cartesian configuration of robotic manipulators.", + "texts": [], + "surrounding_texts": [ + "1. Introduction 11\n4. RIIPf--P\nThe cylindrical configurat ion is a suitable configurat ion for medium load capacity robots. Almost 45% of industrial robots are made of this kind . The RIIPf--P configurati on is illustrat ed in Figure 1.11. The first joint of a cylindrical manipulator is revolute and produces a rot ation 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.\n5. Pf--Pf--P\nThe Cart esian configuration is a suitable configurat ion for heavy load capacity and large robots. Almost 15% of industrial robots are made of this configuration. The Pf--Pf--P configurat ion is illust rated in Fig ure 1.12.\nFor a Cartesian manipulator, the joint variables are the Cartesian co ordinates of the end-effector with respect to the base . As might be ex pected, the kinematic description of thi s manipulator is the simplest of all manipulators. Cartesian manipulators are useful for table-top assembly applications and, as gantry robots , for t ransfer of cargo.\n1.3.2 Workspace\nThe workspace of a manipulator is the total volume of space the end-effector can reach. The workspace is constrained by the geometry of the manipu lator as well as the mechanical const raints on the joints. The workspace is broken into a reachable workspace and a dext erous workspace. The reach able workspace is the volume of space within which every point is reachable", + "12 1. Introduction\nby the end-effector in at least one orientation. The dexterous workspace is the volume of space within which every point can be reached by the end effector in all possible orientations. The dexterous workspace is a subset of the reachable workspace .\nMost of the open-loop chain manipulators are designed with a wrist sub assembly attached to the main three links assembly. Therefore, the first three links are long and are utilized for positioning while the wrist is utilized for control and orientation of the end-effector. This is why the subassembly made by the first three links is called the arm, and the subassembly made by the other links is called the wrist.\n1.3.3 Actuation\nActuators translate power into motion. Robots are typically actuated elec trically, hydraulically, or pneumatically. Other types of actuation might be considered as piezoelectric, magnetostriction, shape memory alloy, and polymeric.\nElectrically actuated robots are powered by AC or DC motors and are considered the most acceptable robots. They are cleaner, quieter, and more precise compared to the hydraulic and pneumatic actuated. Electric motors are efficient at high speeds so a high ratio gearbox is needed to reduce the high RPM. Non-backdriveability and self-braking is an advantage of high ratio gearboxes in case of power loss. However, when high speed or high load-carrying capabilities are needed , electric drivers are unable to compete with hydraulic drivers .\nHydraulic actuators are satisfactory because of high speed and high torque/mass or power /mass ratios. Therefore, hydraulic driven robots are used primarily for lifting heavy loads . Negative aspects of hydraulics, be sides their noisiness and tendency to leak, include a necessary pump and other hardware.", + "1. Introduction 13\nPneumatic actuated robots are inexpensive and simple but cannot be controlled precisely. Besides the lower precise motion , they have almost the same advantages and disadvantages as hydraulic actuated robots.\n1.3.4 Control\nRobots can be classified by control method into servo (closed loop control) and non-servo (open loop control) robots. Servo robots use closed-loop computer control to determine their motion and are thus capable of being truly multifunctional reprogrammable devices. Servo controlled robots are further classified according to the method that the controller uses to guide the end-effector .\nThe simplest type of a servo robot is the point-to-point robot. A point to-point robot can be taught a discrete set of points, called control points, but there is no control on the path of the end-effector in between the points. On the other hand, in continuous path robots, the entire path of the end-effector can be controlled. For example , the robot end-effector can be taught to follow a straight line between two points or even to follow a contour such as a welding seam. In addition, the velocity and /or ac celeration of the end-effector can often be controlled. These are the most advanced robots and require the most sophisticated computer controllers and software development.\nNon-servo robots are essentially open-loop devices whose movement is limited to predetermined mechanical stops , and they are primarily used for materials transfer.\n1.3.5 Application\nRegardless of size, robots can mainly be classified according to their ap plication into assembly and non-assembly robots. However, in the industry they are classified by the category of application such as machine loading, pick and place, welding , painting, assembling, inspecting, sampling, manu facturing, biomedical , assisting, remote controlled mobile , and telerobot.\nAccording to design characteristics, most industrial robot arms are an thropomorphic, in the sense that they have a \"shoulder,\" (first two joints) an \"elbow,\" (third joint) and a \"wrist\" (last three joints) . Therefore , in total, they usually have six degrees of freedom needed to put an object in any position and orientation.\nMost commercial serial manipulators have only revolute joints. Com pared to prismatic joints, revolute joints cost less and provide a larger dex trous workspace for the same robot volume. Serial robots are very heavy, compared to the maximum load they can move without loosing their accu racy. Their usefulload-to-weight ratio is less than 1/10. The robots are so heavy because the links must be stiff in order to work rigidly. Simplicity of the forward and inverse position and velocity kinematics has always been" + ] + }, + { + "image_filename": "designv10_3_0000132_1.1691433-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000132_1.1691433-Figure5-1.png", + "caption": "Fig. 5 Illustration of the change of contact pressure \u201ePij k \u2026 p of a point ij as a function or r", + "texts": [ + " If point ap enters the contact zone at position r5m and remains within contact zone until position r5t , the sliding distance that occurs when gears rotate from any position r to r11 can be given in general terms as ~sap k !r\u2192r11 p 55 UI ~Xag!r11 g 2~Xap!r11 p I2 ( q5m r ~sap k !q21\u2192q p U , m50%). The bead width variation is then converted to laser parameter variation through transfer functions. Figure 14 shows the design of an adaptive interior toopath with variant bead width along the medial axis of an airfoil. As a result of the adaptive toolpath design, a G-codes program is generated with all the laser power/speed variations incorporated with the geometric toolpath information. High-pressure compressor airfoils were fabricated with the designed adaptive toolpath. During deposition, laser power is updated every 0.25 mm along the toolpath by calling to the bead width transfer function (Eq. 3) incorporated in the CNC program" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003392_j.addma.2020.101274-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003392_j.addma.2020.101274-Figure2-1.png", + "caption": "Figure 2 Schematic representation of L-DED a) block samples (the dashed lines indicate the areas in which the SEM images were taken) and b), c) bar samples from which tensile samples were obtained.", + "texts": [ + " When the BC was used, the oxygen content was evaluated using a MultiExact 5400 \u2013 SERVOPRO sensor. The oxygen content was kept lower than 0.1 % during the whole building process. The oxygen sensor was not used during the SG building process as, in this case, the oxygen content varied within the process because of the movement of the deposition head. The samples were built on austenitic stainless steel plates having the following dimensions: 150 \u00d7150 \u00d76 mm. Block (10 x10 x20 mm) and bar (93 x 12 x12 mm) samples (see Figure 2) were produced in both conditions: SG or BC. All samples were produced using the optimised parameters described in [21] that allow the obtainment of fully dense parts. The block samples were cut along the building direction, polished down to 1 \u03bcm and etched for 2 s in a solution containing 15 ml HCl + 10 ml HNO3 + 1 ml acetic acid. The microstructural analyses were carried out by a Leica DMI 5000 Optical Microscope (OM), a Phenom XL SEM and a Carl Zeiss MERLIN Field Emission Jo ur n l P re -p ro of Scanning Electron Microscope (FESEM) equipped with an Energy Dispersive X-ray Spectrometry (EDS) system. The inclusion content was investigated by means of the ImageJ software on the SEM images with a high magnification taken along the building direction (see locations indicated in Figure 2 a)). The area fraction at different distances from the substrate (at every 2.5 mm) was calculated on three images taken at the same height. The Primary Cellular Arm Spacing (PCAS) was evaluated by the triangle method on SEM images taken at 5000 X. In the triangle method, three central points of any three adjacent cellular dendrites form a triangle. The average PCAS of the three cells is the average of three lengths of three sides of cellular dendrites. Each mean PCAS value is achieved by averaging 40 measurements at different distance from the substrate", + " The contaminations content, in terms of oxygen, nitrogen and hydrogen, of the powder and the dense samples were analysed using the inert gas fusion method by means of a LECO ONH836 Oxygen/Nitrogen/Hydrogen elemental analyser on three specimens extracted at different height from each block L-DED sample. X-ray diffraction (XRD) analyses were carried out on the XZ cross-section of the block samples using an X-Pert Philips diffractometer (Cu K\u03b1) in a Bragg Brentano configuration with 2\u03b8 range= 20-110\u00b0 (operated at 40 kV and 40 mA with a step size 0.013 and 35 s per step). Two tensile samples were machined from each 12\u202f\u00d7\u202f12\u202f\u00d7\u202f93\u202fmm as-built bars (Figure 2 b) and c)). The tensile samples dimensions are based on the ASTM E-8 standard and had a 4 mm thickness (Figure 2 d)). The tensile samples were tested using a Zwick Z100 tensile machine using 8 \u00d7 10\u22123 s\u22121 as strain rate. 3. Results and discussion 3.1. Microstructure and composition In general, in L-DED materials grains and dendrites, morphology and size are defined by the thermal history of the component. Previous studies demonstrated that, due to the rapid cooling and to the directional heat Jo r al flow, L-DED 316L parts are characterised by large columnar grains containing \u03b3-dendrites and \u03b4-ferrite mainly located in the interdendritic zone [11]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.44-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.44-1.png", + "caption": "Fig. 2.44 Influence of mass parameters on the frame forces of a crank-rocker mechanism a) Kinematic schematic and center-of-mass trajectories, including the reduced masses m\u2217 i = mi/m; b) Polar diagrams of joint forces F12 and F14 Variant 1: \u2014\u2014\u2014-, Variant 2: \u2013 \u2013 \u2013 \u2013, Variant 3: \u2013 \u00b7 \u2013 \u00b7 \u2013 \u00b7", + "texts": [ + " The generalized mass m\u03d5(q) referred to the z axis has the dimension of a moment of inertia in the case of an input angle (q = \u03d5) and a similar form as the reduced moment of inertia known from (2.199), but must not be confused with that! 2.6 Methods of Mass Balancing 161 While the reduced moment of inertia Jred(\u03d5) is linked to the kinetic energy and the input torque, the m\u03d5(q) that results from the angular momentum is required for calculating the frame moment. The overall center of gravity of a mechanism normally moves along a trajectory as shown in Fig. 2.44; for an example, see (2.305). In addition to the center-of-mass trajectories, it shows the polar diagrams of the two frame forces of a crank-rocker mechanism for three variants of mass distribution. The masses m2 and m4 and their distances to the center of gravity \u03beS2 and \u03beS4 were varied. These curves are obtained at a constant angular velocity of the drive. The relationship of the center-of-mass trajectories to the polar diagrams is interesting. At a smaller extension of the center-of-mass trajectory, the joint forces for variant 2 also become smaller than for variant 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure7.16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure7.16-1.png", + "caption": "Fig. 7.16 Plate in a flow field; a) Parameters, b) Coordinates and forces", + "texts": [ + " One can reduce or prevent the stick-slip vibrations by \u2022 Reduction of the normal force FN acting onto the surfaces with friction \u2022 Increase of damping or friction \u2022 Interference with the time function of the normal force, e. g. additional vibrations \u2022 Lower slope of the descending friction characteristic, e. g. by another material \u2022 Increase of the natural frequency (smaller mass, stiffer spring). The critical speed for the severely simplified calculation model of an elastically supported plate that is exposed to an incident flow parallel to the plate plane is to be determined, see Fig. 7.16. In the horizontal position, static equilibrium exists and the hydro- or aerodynamic forces are zero. If the plate is deflected by an angle, a flow-dependent lifting force emerges, which, according to the laws of hydro- and aerodynamics, depends on a coefficient k, the density , the flow rate v, the length l, and the angle of the plate deflection \u03d5: F = k v2l\u03d5. (7.88) 496 7 Simple Nonlinear and Self-Excited Oscillators The force application point that is determined by the geometry of the component exposed to an incident flow is at a distance e from the center of gravity S. The force F is assumed to be acting perpendicularly to the plate, neglecting higher-order effects. Figure 7.16a shows the calculation model with two degrees of freedom for the plate exposed to an incident flow in its deflected state. The bearings are taken into account by the spring constants c1 and c2 and the inertia properties of the plate by the mass m and the moment of inertia J with respect to the axis through the center of gravity. The static forces (static weight, spring forces) are in equilibrium and are omitted here. The associated free-body diagram is shown in Fig. 7.16b. The restoring forces of the springs result from the product of the spring constants with the spring deflections, which depend on the deflection from the center of gravity y and the angle of rotation \u03d5 1 (sin \u03d5 \u2248 \u03d5, cos \u03d5 \u2248 1): F1 = c1 \u00b7 (y + l\u03d5) , F2 = c2 \u00b7 (y \u2212 l\u03d5) . (7.89) The equilibrium conditions are therefore \u2191: \u2212F1 \u2212 F2 + F \u2212my\u0308 = 0 (7.90) S : \u2212F1l + F2l + Fe\u2212 JS\u03d5\u0308 = 0. (7.91) If one inserts the forces captured by (7.89) into (7.92) and (7.93), one obtains the equations of motion of the system where q1 = y and q2 = l\u03d5 in the form m1q\u03081 + c11q1 + c12q2 = 0 (7" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000866_j.mechatronics.2012.01.005-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000866_j.mechatronics.2012.01.005-Figure1-1.png", + "caption": "Fig. 1. Smart Unmanned Aerial Vehicle (SUAV): tilt rotor aircraft developed by KARI, (a) airplane mode (fixed wing) and (b) helicopter mode (rotary wing).", + "texts": [ + " In addition, the command filter was applied to the TDC command to mitigate the effects of the phase delay that occurs when a sinusoidal command is applied. Furthermore, an actual flight test was performed, which clearly showed the effectiveness of the proposed control scheme. This promising control performance shows that TDC is an effective alternative for controlling the actuation system of the SUAV with substantial load variation. 2012 Elsevier Ltd. All rights reserved. The Smart Unmanned Aerial Vehicle (SUAV) is an aircraft with large-scale tilt rotor configuration being developed by the Korea Aerospace Research Institute (KARI), as shown in Fig. 1. The tilt rotor aircraft has both rotary-wing and fixed-wing modes, which enable it to execute both vertical takeoff like a helicopter and high-speed flight like an airplane [1\u20134]. A total of 12 Actuation Control Units (ACUs) are used to control the actuators of the flaperon, rotor, nacelle tilt, and elevator, for controlling the yaw, roll, and pitch angles of the SUAV and for changing its flight mode; each ACU receives the desired position commands from the Digital Flight Control Computer (DFCC), as illustrated in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000973_j.neucom.2012.11.027-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000973_j.neucom.2012.11.027-Figure1-1.png", + "caption": "Fig. 1. Definitions of the earth-fixed OXoYo coordinate frame and the body-fixed AXY coordinate frame.", + "texts": [ + " In the next section, the dynamic positioning mathematical model of ships with dynamics and disturbance uncertainties is discussed, and the control objective is then formulated. Section 3 details the design of the robust adaptive nonlinear control law for marine vessels based on vectorial backstepping and radial basis function neural networks. The simulation results are provided to validate the designed controller in Section 4, followed by the conclusions of the paper in Section 5. Definition of the reference coordinate fame of ship motion is illustrated in Fig. 1, where OXoYo is the earth-fixed frame and AXY is the body-fixed frame. The coordinate origin of the body-fixed frame is located at the gravity center of the ship. Assume that the ship has an XZ-plane of symmetry; surge is decoupled from sway and yaw; heave, pitch and roll modes are neglected. Then the nonlinear mathematical model of ships for the dynamic positioning can be described as follows in the presence of disturbances [2]: _Z \u00bc R\u00f0c\u00deu \u00f01:a\u00de Please cite this article as: J. Du, et al., A robust adaptive neural Neurocomputing (2013), http://dx" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure6.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure6.9-1.png", + "caption": "Fig. 6.9 Jerk: problem 5", + "texts": [ + " Considering that the cam does not rotate, determine the magnitude of the jerk of A in terms of if the slotted arm revolves with a constant counterclockwise angular rate P D !. 4. The disk shown in Fig. 6.8 rotates about a fixed axis passing through point O with angular velocity ! D 5 rad=s, angular acceleration \u02db D 2 rad=s2, and angular jerk D 3 rad=s3. The small sphere A moves in the circular slot in such a way that in the same instant we have \u02c7 D 30\u0131, P\u030c D 2 rad=s, R\u030c D 4 rad=s2, and \u00ab\u030c D 4 rad=s3. Determine the velocity, acceleration, and jerk of A. 5. Determine the input\u2013output equation of jerk of the 3-RPR parallel manipulator shown in Fig. 6.9 by resorting to reciprocal screw theory. Cheng, W.-T. (2002). Synthesis of universal motion curves in generalized model. ASME Journal of Mechanical Design, 124(2), 284\u2013293. Crossman, E. R. F. W., & Goodeve, P. J. (1983). Feedback control of hand movements and Fitts\u2019 law. Quarterly Journal of Experimental Psychology Section A\u2014Human Experimental Psychology, A35, 251\u2013278. References 157 Erkorkmaz, K., & Altintas, Y. (2001). High speed CNC system design, part I. Jerk limited trajectory generation and quintic spline interpolation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000879_1.2976454-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000879_1.2976454-Figure2-1.png", + "caption": "Fig. 2 Geometric arrangement of the cradle-style machine", + "texts": [ + " In he linear space R3, we introduce a single reference system S O ;x ,y ,z with unit vectors i , j ,k . The position vector pe Fig. represents the position of the points belonging to the generating ool surface e. In the frame S, it has components pe , , where he parameter is the arc length measured on the blade profile and is the revolution angle about the tool axis z and are the urface Gaussian parameters . 2.2 Machine Kinematics. A schematic representation of the ell known Gleason\u2019s cradle-style machine is shown in Fig. 2. ix-axis CNC \u201cfree-form\u201d machines are capable of emulating its otions. Moreover, their modern controllers are provided with the o-called universal motion concept UMC ; i.e., the basic machine ettings can vary during generation as polynomial functions of the radle rotation angle which acts as the motion parameter 15,16 . UMC increases the number of design variables that can e used to optimize the contact properties. For instance, the basic lank offset EM0 and sliding base XB0 are just the constant Xp p x=0 cutter axis R Zp fR1 x=L f P Q X f Zf x z Rp (II) (I) (III) f O pe ig", + " When it is applied, for example, to rotate vector pe around the unit vector jc by an angle 0, it performs the following operation on vectors not components : R pe,jc, 0 = pe \u00b7 jc jc + pe \u2212 pe \u00b7 jc jc cos 0 + jc pe sin 0 7 The tool surface pe , can change its orientation according to two subsequent rotations around the unit vectors jc and kc by the angles and : they are designated as tilt and swivel angles, respectively. Only the constant terms 0 and 0 of their polynomial expressions are retained in this work. By employing the rotation operator, the rotated tool surface is expressed by p\u0303e , = R R pe , ,jc, 0 ,kc, 0 8 with jc = cos q,sin q,0 , kc = 0,0,\u2212 1 9 where q is the basic cradle angle. The position vectors of the tool surface rotating with the cradle can be expressed with respect to point Oa Fig. 2 , p\u0302a , , = R p\u0303e , + e,a, 10 or to point Ob Fig. 2 , Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use w s a t t t p \u2212 p I m h p h g o e h g c r s o t F c J Downloaded Fr p\u0302b , , = p\u0302a , , \u2212 d 11 here d =Ob \u2212Oa and e=Sr jc. For simplicity, let us conider only the constant terms m0 , XD, and Sr0 machine root ngle, machine center to back, and radial setting, respectively of he polynomial functions m , XD , and Sr . Thus, vecors a, b, d , and e have the following components in frame S a = 0,0,1 12 b = cos m0 ,0,sin m0 13 d = XD cos m0 ,\u2212 EM , XB + XD sin m0 14 e = Sr0 cos q,Sr0 sin q,0 15 The enveloping family of surfaces , that is, the sequence of ool surfaces as seen from an observer rotating by with the inion/gear blank, can be obtained by imposing a counter-rotation to the vector p\u0302b , , according to p , , = R p\u0302b , , ,b,\u2212 16 Finally, the envelope surface , that is, the surface of the hyoid tooth, is given by p , , with f , , = me , \u00b7 he , , = 0 17 n the previous expression of the equation of meshing f =0, vector e , is the normal vector to the tool surface e, while vector e , , is parallel to the sliding velocity on surface e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure8.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure8.6-1.png", + "caption": "Fig. 8.6 3Dfeasible force set. This convexpolyhedron shows the 3D force capabilities ( fx , fy , fz) T of the human index finger as calculated from data collected in cadaver fingers [29, 30]. Here the constraint that is enforced is that the fingertip should produce 3D forces without any accompanying endpoint torque \u03c4z . The full output wrench is the 4D w = ( fx , fy , fz, \u03c4z) T , but enforcing the constraint on \u03c4z = 0 produces the 3D feasible force set shown. Figure adapted with permission from [30]", + "texts": [ + " To make the force production task even more realistic and functional, consider that you are interested in all activation patterns that not only produce no output \u03c4z , but also produce no side-to-side fingertip forces. These are the kinds of forces you would use to roll a pencil with the index fingertip: any lateral forces would make the pencil twist and fall from your grasp. In this example, such side-to-side forces are in the z direction. Therefore, you would want to enforce 2 constraints ( fz \u03c4z ) = [ hT 3 hT 4 ] \u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d a1 a2 a3 a4 a5 a6 a7 \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 = ( 0 0 ) (8.5) 2If you are curious about what this looks like see Fig. 8.6. 8.2 Calculating Feasible Sets for Tasks with Functional Constraints 119 Using the analogy in Fig. 8.2 again, the intersection of the cube with 2 planes\u2014if it exists\u2014is a 1D line. That is, the activation patterns that meet all constraints lie on a 1D line embedded in 3D space. See Fig. 8.3. Turning back to our 7-muscle finger, the feasible activation set for all possible forces in the plane of finger flexion must meet both hT 4 \u00b7 a = 0 and hT 3 \u00b7 a = 0. That feasible activation set is a 5D convex set (7 \u2212 2 = 5) embedded in 7D", + "3 shows that you can be doing your analysis in the feasible torque set, and call that the feasible input set, to produce the feasible endpoint wrench set, which would be your feasible output set. It all depends on the analysis you are doing. Having said this, mapping the feasible input set into the feasible output set translates into the computational geometry problem of finding the convex hull for a cloud of points in the space into which the mapping takes place. This is done as 8.3 Vertex Enumeration in Practice 123 per Algorithm 2. An example of a convex polyhedron representing a feasible output set is shown in Fig. 8.6\u2014the 3D feasible force set for the human index finger [20, 21]. Algorithm 2 Finding the feasible output set Require: Vertices of the feasible input set. These can be obtained as per Algorithm 1 from the matrices F0, R, J\u2212T or their combinations, depending on your definition of what is the input as per Fig. 7.3 \u2192 Project every vertex of the feasible input set by the matrices of interest that produce the desired output. For example, if you consider the feasible activation set as your input then \u2192 Multiply all vertices by F0 to find the feasible muscle force set \u2192 Multiply all vertices by [R F0] to find the feasible joint torque set \u2192 Multiply all vertices by [J\u2212T R F0] to find the feasible endpoint wrench set or feasible endpoint force set depending on the constraints you enforce end if return All pairs of vertices of the feasible activation space and the output they produce \u2192 Apply the convex hull operation to the projected vertices to find the convex polyhedron, polygon, or polytope (depending on the dimensionality of the output space)", + " In endpoint force space, versatility would be the ability to produce positive and negative forces in the x , y, and z directions, etc. Figure7.5 shows a case where having only muscles 1 through 3 does not suffice for the limb to be versatile because their feasible net joint torque set does not include positive torques at the second joint. It is only when muscle 5 is added that versatility is achieved. By contrast, Fig. 7.9 shows the case of 8 generators, where versatility was already achieved with generators 1 through 3\u2014independently of what \u2018space\u2019 we are in. Last, in the case of fingertip endpoint forces in Fig. 8.6, the origin of force production is at the fingertip, which is inside the feasible force set. There we see that the fingertip could feasibly produce or resist forces in every 3D direction: toward an object being grasped, or sideways to rotate the object, or away from the object. In [30] we show how the loss of some muscles can easily remove versatility. While 8.4 A Definition of Versatility 125 it is trivial to say that paralysis weakens, being able to show exactly how and in which directions the weakening occurs is critical to understand the disability\u2014and to design therapeutic or surgical strategies that restore as much versatility as possible [30]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002943_rpj-03-2019-0065-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002943_rpj-03-2019-0065-Figure5-1.png", + "caption": "Figure 5 CMMmeasurements highlighting EDM cut planes", + "texts": [ + " As presented in Table I, the three materials have different optimum process parameters and consequently different volumetric laser energy densities. Thus, the scanning speed, hatch spacing and layer thickness for each material were incorporated into the FEmodel. Ti-6Al-4V parts were produced on titanium build plate using a Renishaw a.m.400 machine equipped with argon gas. Invar 36 and SS 316L parts were produced on 18Ni-500 build plates using an EOSINT M280 machine equipped with nitrogen gas flow. Wire electrical discharge machining (EDM) was used to cut the part from the build plate whereby the middle web was left attached, as shown in Figure 5. Model development and boundary conditions The SLM process was modelled using an orthogonal Cartesian mesh consisting of superlayers, which are an average of multiple scan layers. Themodel does not explicitly consider the melt pool physics; moreover, each element was added at the melt temperature, (T|new element = Tm), with zero strain and the thermal stress accumulated as the part was cooled down and reheated again. If the effect of scanning strategy is to be determined, melt pool physics needs to be explicitly modelled", + " Nangle-Smith Rapid Prototyping Journal Volume 26 \u00b7 Number 1 \u00b7 2020 \u00b7 213\u2013222 As such, the thermal stresses predicted by the model accurately reflect parts made with optimal SLM process conditions that do not overheat or underheat the part. The FEmodel coupled a transient thermal analysis with static structural analysis in a multi-staged approach, as shown in Figure 1. The sequence includes a build step where elements are added, a dwell step between the end of one layer to the start of the subsequent layer and a cooldown step during which the laser was off where the part cooled down to ambient temperature. The final step of the static structural analysis was the removal of the build-plate according to Figure 5. The transient thermal model was governed by 3D Fourier heat conduction equations, as described in equation (2a). The model assumed homogenous and isotropic material properties that vary with temperature. The part size was 66mm 10mm 10mm, and the bottom of the build plate was set to have a constant temperature boundary condition of 40\u00b0C (T|z=0 = 40 \u00b0C). The sides of the part are given a Neumann zero heat flux boundary condition because heat loss to the loose powder bed on the sides of the part was assumed negligible", + " The analysis of the melt pool shape showed that the spatter formation was minimized and/or eliminated when the material was being processed using the optimum laser process parameters. This also showed that the size of the melt pool is within an effective range recommended by the machine manufacturer (200\u2013300 mm). The cantilever deflection that occurred after wire EDM was measured using a CMM, with a resolution of 0.1 mm. The measurements were obtained every 0.75mm, resulting in 40 measurement locations along the 50mm length (direction x), as shown in Figure 5. Three measurements were taken along the width of the cantilever (direction y) and averaged to minimize the effect of surface roughness. Figure 10a and 10b show the cantilever deflections measured experimentally and predicted by the model, respectively. The cantilevers were deflected downward in a convex shape as a result of stress relaxation after removing the build plate. More detail on the predicted deflection shapes can be seen in Figure 11b-d, and these shapes agree well with the experimental observations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000855_tie.2011.2159357-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000855_tie.2011.2159357-Figure2-1.png", + "caption": "Fig. 2. Typical SPM-type magnetic gear.", + "texts": [ + " Reference [1] proposes a surface-permanentmagnet-type (SPM-type) magnetic gear employing magnetic flux harmonics, [2], [5], and [11] propose a cycloid-type magnetic gear, [3] proposes an axial-gap-type magnetic gear, [4] proposes a variable-speed magnetic gear, [7] and [8] propose a magnetic harmonic gear, [6] proposes a magnetic gear with coils in the high-speed rotor, [9] proposes a linear-type magnetic gear, and [10] proposes a magnetic planetary gear. Among these new magnetic gears, an SPM-type magnetic gear employing magnetic flux harmonics, shown in Fig. 2, has gained attention because of its high transmission torque density. Unfortunately, it has a complex structure that has multipole magnets. Some studies on the SPM-type magnetic gear have been carried out [12]\u2013[20], but [12]\u2013[20] do not describe the cogging torque characteristics, except [12] and [18]. Reference [12] describes the influence of the gear ratio on the transmission torque characteristics, but the order of the cogging torque is not described. Reference [18] describes the order of the cogging torque, but the order due to the magnetic flux harmonics is not considered" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.36-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.36-1.png", + "caption": "FIGURE 5.36. A 2R planar manipulator.", + "texts": [ + "34, find the (a) DR table (b) link-type table (c) individual frame transfo rmation matrices i- 1Ti , i = 1,2 ,3 ,4 (d) global coordinates of the end-effector (e) orientation of the end-effector 'P . 3. A one-link RI-R( -90) arm. 256 5. Forward Kinematics For the one-link Rf-R( -90) manipulator shown in Figure 5.35 (a) and (b) , find the transformation matrices \u00b0T1 , ITz, and \u00b0Tz. Compare the transformation matrix ITz for both frame installations. 4. A 2R planar manipulator. Determine the link 's transformation matrices \u00b0T1, ITz, and \u00b0Tz for the 2R planar manipulator shown in Figure 5.36. 5. A polar manipulator. Determine the link 's transformation matrices ITz, zT3 , and IT3 for the polar manipulator shown in Figure 5.37. 6. A planar Cartesian manipulator. Determine the link 's transformation matrices ITz, zT3 , and IT3 for the planar Cartesian manipulator shown in Figure 5.38. 7. Modular articulated manipulators. Most of the industrial robots are modular. Some of them are manu factured by attaching a 2 DOF manipulator to a one-link Rf-R( -90) arm. Articulated manipulators are made by attaching a 2R planar manipulator, such as the one shown in Figure 5.36, to a one-link Rf-R( -90) manipulator shown in Figure 5.35 (a) . Attach the 2R ma nipulator to the one-link Rf-R( -90) arm and make an articulated manipulator. Make the required changes into the coordinate frames of Exercises 3 and 4 to find the link 's transformation matrices of the articulated manipulator. Examine the rest position of the manipula tor. 5. Forward Kinematics 257 258 5. Forward Kinematics 8. Modular spherical manipulators. Spherical manipulators are made by attaching a polar manipulator shown in Figure 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003485_j.jallcom.2019.03.082-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003485_j.jallcom.2019.03.082-Figure4-1.png", + "caption": "Fig. 4 Specimen for microhardness and printed density testing", + "texts": [ + " The results are presented in Fig. 2, which illustrates that the chemical compositions satisfy the standard values required for 316L stainless steel. M ANUSCRIP T ACCEPTE D Standard specimens were fabricated for testing the tensile strength. The overall size of each specimen was 60 \u00d7 12 \u00d7 0.6 mm (length \u00d7 width \u00d7 thickness), and the details are illustrated in Fig. 3. Fig. 3 Standard specimen for testing tensile strength (mm) The specimens for the printed density measurements are illustrated in Fig. 4. A total of 16 square samples were manufactured by the SLM process with the same parameters. (a) (b) M ANUSCRIP T ACCEPTE D The entire experiment was carried out according to the following steps: (1) Experiment : optimal placement orientation As illustrated in Fig. 5(a), the fabrication direction was always along the z-axis for the three different specimen groups. However, their placement orientations differed. The placement of group 1 was upright, while the placement of group 2 was edge-on, and the placement of group 3 was flat-on, as illustrated in Fig. 5(a). This designed experiment aimed to determine the optimal placement orientation to enhance the mechanical properties of parts manufactured by SLM. (2) Experiment : optimal hatch scanning angle Based on the optimal placement orientation, experiment was carried out to determine the optimal hatch scanning angle. As illustrated in Fig. 5(b), seven different specimen groups were fabricated, with seven different hatch scanning angles (0\u00b0, 15\u00b0, 30\u00b0, 45\u00b0, 60\u00b0, 75\u00b0, and 90\u00b0). As indicated in Fig. 4, seven cuboids (10 \u00d7 10 \u00d7 5 mm) corresponding to each specimen group were fabricated together to test the densities of the printed specimens. For each specimen group mentioned above, three specimens were fabricated to calculate the average value of the tested data and used in the entire experiment, as illustrated in Fig. 6. Fig. 5 Experimental scheme: (a) experiment : optimal placement orientation; (b) experiment : optimal scanning angle Microstructure: The Hitachi S4800 SEM was used to obtain the surface morphology and fracture morphology of the specimens", + "6661 The above experiment determined the optimal fabrication direction and placement orientation strategy. Thus, in experiment , the specimens were firstly placed referring to specimen 3, as indicated in Fig. 5(a), and the fabrication direction was the z-axis. Thereafter, seven specimen groups with scanning angles of 0\u00b0, 15\u00b0, 30\u00b0, 45\u00b0, 60\u00b0, 75\u00b0, and 90\u00b0 were fabricated once the optimal placement was established, in order to evaluate the optimal hatching scanning angle. The specimens (cuboids of 10 \u00d7 10 \u00d7 5 mm) for the printed density measurement are illustrated in Fig. 4(b, right). The parameters relevant to the printed density calculation for each experiment are listed in Table 3. Compared to the theoretical density of 316L stainless steel, the density ratio of specimens based on the SLM process was less than 1 and greater than 0.95, which demonstrates that the SLM process can be adapted to fabricate high-density parts in the engineering field. As indicated in Table 3, the highest density (7.655 g/cm3) and density ratio (95.9%) appeared at 30\u00b0 (printed angle), which demonstrates that specimen group 3, with a 30\u00b0 scanning angle, had the highest printed density and density ratio" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003423_j.renene.2014.12.062-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003423_j.renene.2014.12.062-Figure1-1.png", + "caption": "Fig. 1. Schematic diagrams of (a) torsional vibration model, (b) spring mass equivalent model.", + "texts": [ + " In this study, the uncertain analysis of the dynamics properties with the wind turbine geared transmission system is carried out utilizing the CIM. A gear torsional model with four degrees of freedom is established in Section 2.1 and the dynamic response of the uncertain geared system based on the CIM is given in the Section 2.2. Based upon those, numerical simulations are conducted to study the effects of interval parameters on dynamic responses of the geared system in Section 3. The conclusions are drawn in the last section. As shown in Fig. 1, the drive train of a wind turbine could be simplified as a one-stage gear pair system considering the blades and the generator as the motor and the load. In the model, the blades, the pinion, the gear and the generator are assumed as rigid disks. The gears are connected by a spring-damper on the line of action to represent the mesh stiffness and damping. Shafts are modeled as torsional spring-dampers and themoments of inertia of the driving and driven shafts are separately added to the moments of inertia of the pinion and the gear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003709_tie.2020.3001800-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003709_tie.2020.3001800-Figure1-1.png", + "caption": "Fig. 1. The configuration of the quadrotor.", + "texts": [ + " In Section III, the dual-loop practical fixedtime controller with disturbance rejection based on FxTDO is developed. Section IV provides simulation and experimental results to verify the efficiency and robustness. Finally, conclusions are drawn in Section V. Notations: In this paper, the following notations are adopted. For any non-negative \u03b1, \u2308x\u230b is defined as \u2308x\u230b\u03b1 = |x|\u03b1sign(x) for any x \u2208 R, and d\u2308x\u230b\u03b1 dx = \u03b1|x|\u03b1\u22121. For a vector x = [x1, \u00b7 \u00b7 \u00b7 , xn]T \u2208 Rn, \u2308x\u230b\u03b1 = [ \u2308x1\u230b\u03b1, \u00b7 \u00b7 \u00b7 , \u2308xn\u230b\u03b1 ]T . \u0393(a, b) = a 1+a (1 + b) for any non-negative a, b. The configuration of the quadrotor is shown in Fig. 1. We define a inertial reference frame I = {xI , yI , zI} and a bodyfixed frame B = {xB , yB , zB} whose origin is coincided with the center of gravity. The orientation of the bodyfixed frame with respect to the inertial frame is denoted by \u03b7 = [\u03d5, \u03b8, \u03c8]T \u2208 R3 composed of the three Euler angles. The attitude of a quadrotor is governed by a cascaded structure of kinetics and dynamics as follows [13]: \u03b7\u0307 = W\u22121 \u03b7 \u03c9 (1) J\u03c9\u0307 = \u2212\u03c9 \u00d7 J\u03c9 + \u03c4 + \u03c4d (2) where \u03c9 = [p, q, r]T \u2208 R3 is the angular velocity in the body-fixed frame, J = diag{Ixx, Iyy, Izz} \u2208 R3\u00d73 denotes the inertia matrix, and \u03c4 \u2208 R3 denotes the control torque" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003434_1.4033525-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003434_1.4033525-Figure8-1.png", + "caption": "Fig. 8 Temperature profile ( C) at the end of the final laser pass for 0 s dwell", + "texts": [ + " Finally, the average a lath width in the image w is obtained by inverting the line segment lengths k, calculating the mean inverse value, and using Tiley\u2019s relation w \u00bc 2 3 1=k\u00f0 \u00demean (15) Several micrographs are shown in Fig. 7, for a representative thin lath width and thick lath width. At each z height, three images are captured. These three measurements are used to calculate the average and standard deviations of lath width at each height. After performing a thermal analysis in CUBES VR (see Fig. 8), temperature results are input into the Kelly\u2013Charles model (future work will use measured temperature histories). Using the material properties suggested by Kelly and Charles, the results show poor agreement with experimental measurements of a lath width (106% error). The values of the material properties, before and after optimization, are shown in Table 1. Note that the properties that govern a growth and dissolution (a, b, and n) do not change significantly from the published values. On the other hand, kw and Tact, which govern equilibrium a lath widths, are both reduced by several orders of magnitude" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001380_tie.2014.2385034-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001380_tie.2014.2385034-Figure12-1.png", + "caption": "Fig. 12. Experimental setup.", + "texts": [ + " In the figure, the torque is normalized with respect to TN=2kIN and the speed with respect to the conventional nominal value of the mechanical speed, given by (33) As a comparison, the torque-speed characteristic of the PM BLDC drive with ideal square-wave phase currents is also traced in Fig.11 with dotted red line. Compared to the ideal square-wave current supply, the petal-wave one has a 5% greater value of nominal torque and a nearly equal increment in the base speed, partially due to the disregard of the phase resistance in (31). The experimental setup arranged to test the effectiveness of the petal-wave current supply is depicted Fig. 12. It is formed by two drives having the motors engaged each other through a gear. The in-wheel PM BLDC motor of the case study is on the right whilst the brake motor, which is of PM BLAC type, is on the left. The PM BLDC motor is equipped with three Hall sensors that output square-wave signals with the edges synchronized with the beginning of the positive and negative flat-top regions of the back-emfs. The motor of the brake drive is speed-controlled and exerts a torque that opposes that of the PM BLDC drive" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000410_10426914.2010.480999-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000410_10426914.2010.480999-Figure1-1.png", + "caption": "Figure 1.\u2014Schematic of the experimental setup.", + "texts": [ + " The whole process was captured at 10,000 frames per second (fps) as Audio Video Interleave (AVI) format data by a Photron Ultima APX high-speed camera. Illumination of the melt pool was provided by an Oxford Lasers copper vapor laser providing 511 and 578nm wavelength light. A narrow pass filter in front of the camera was used to block all other wavelengths, and the camera and the copper vapor laser were synchronized for maximum illumination during the process. A schematic of the experimental setup is shown in Fig. 1. The recorded AVI files were analyzed, and a novel technique was developed using MATLAB to extract quantitative data on the surface disturbance of the melt pool. Figure 2.\u2014(a)\u2013(e) Flow chart of image analysis done on the melt pool. (a) Original image of the melt pool. (b) Grey scale image with increased contrast using histogram equalization. (c) Melt pool extraction using thresholding. (d) Edge detection. (e) Disturbance calculation (Redline) with reference to the pool surface along with longest line segment (green line)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003544_tr.2016.2590997-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003544_tr.2016.2590997-Figure5-1.png", + "caption": "Fig. 5. Degrees of freedom for sun-planet and ring-planet gears.", + "texts": [ + " The magnitudes of GMS, ksp, and krp, in the stiffness matrix of the previous model, are modified using GMS obtained from the phased number of teeth in contact. Kim\u2019s model considered 12 degrees of freedom, including rotations and translations about x-, y-, z-axes for sun-planet and ring-planet relation. The model\u2019s equation of motion is [M ] {q\u0308} \u2212 [K] {q} = {F } (7) where [M] is the mass matrix; q is the displacement vector; q\u0308 is the acceleration vector; [K] is the stiffness matrix; and F is the external force vector. As shown in Fig. 5, the displacement vectors for sun-planet and planet-ring gears are (xs , ys, zs, \u03b1s, \u03b2s, \u03b3s, xp, yp, zp, \u03b1p, \u03b2p, \u03b3p) and (xp, yp, zp, \u03b1p, \u03b2p, \u03b3p, xr, yr, zr, \u03b1r, \u03b2r, \u03b3r), respectively. This model could consider the helix angle of gear teeth because it has 12 degrees of freedom and time-varying GMS can be included in stiffness components. The damping term can be ignored because the damping effect is not significant in characterizing the behavior of the planetary gear [33]. Among the aforesaid displacement vectors, this study focuses on the rotational displacements of the z-axis, \u03b3s, \u03b3p, and \u03b3r because we are focusing on the angular difference (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003053_978-0-8176-4962-3-Figure2.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003053_978-0-8176-4962-3-Figure2.1-1.png", + "caption": "Fig. 2.1. Inverted cart\u2013pendulum.", + "texts": [ + "8) where G \u2208 R m\u00d7n is a projection matrix satisfying the condition det [GB] = 0 Thus, the time derivative of s takes the form s\u0307 (x) = GB (u1 + \u03b3) 2.6 Example: LQ Optimal Control and ISM 15 The control u1 is designed as u1 = \u2212M (x, t) (GB)T s \u2225 \u2225 \u2225(GB) T s \u2225 \u2225 \u2225 M (x, t) > \u03b3+(x, t) (2.9) Therefore, taking V = 1 2s T s, and in view of (2.3), the following inequality is obtained: V\u0307 = ( (GB) T s, s\u0307 ) = (s, u1 + \u03b3) \u2264 \u2212 \u2225 \u2225 \u2225(GB)T s \u2225 \u2225 \u2225 ( M \u2212 \u03b3+ ) < 0 Hence, the integral sliding mode is guaranteed. Consider the following system: x\u0307 = Ax+B (u0 + u1) + \u03c6 representing a linearized model of an inverted cart\u2013pendulum of Fig. 2.1, where x1 and x2 are the car position and pendulum angle and x3 and x4 are their respective velocities. The matrices A and B take the following values: A = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 0 0 1 0 0 0 0 1 0 1.25 0 0 0 7.55 0 0 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 , B = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 0 0 0.19 0.14 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 The control u0 = u\u2217 is designed for the nominal system, where u\u2217 solves the following optimal problem subject to an LQ performance index: J (u0) = \u221e\u222b 0 xT0 (t)Qx0 (t) + u0 (t) T Ru0 (t) dt u\u22170 = argmin J (u0) It is known (see, e.g., [35]) that the solution of the previous optimal control is given in its state feedback representation by means of u\u22170 (x) = \u2212R\u22121BTPx where P is a symmetric positive definite matrix that is the solution of the algebraic Riccati equation ATP + PA\u2212 PBR\u22121BTP = \u2212Q For the considered matrices A and B, and taking Q = I and R = 1, we have that P and K := R\u22121BTP have the following values: P = \u23a1 \u23a2 \u23a2 \u23a3 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure15.30-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure15.30-1.png", + "caption": "Figure 15.30.1 Tangential velocity componentsVT1 andVT2 for the point P relative to F, derived from the out-of plane velocities VN1 etc. at each corner.", + "texts": [ + " The coordinates of P are solved by routine PointAT. Therefore all positions are known. The velocity of F is calculated by routine PointITV, using the factors f2 and f3. It remains to calculate the velocity of P relative to F. Length LPF is constant, so the relativevelocity is purely tangential. Drop a perpendicular from P1 onto line P2P3 with foot P4. The velocity VP/F of P relative to F is parallel to the plane, with the components shown,VT1 being parallel to line P1P4 and VT2 being parallel to line P2P3, Figure 15.30.1. The velocity of P4 can be found from the velocities of P2 and P3 by linear interpolation or extrapolation according to the position factor of P4 along P2P3 (P4 may be outside P1P3, with f4< 0 or f4> 1). Calculate the unit normal to the plane for F towards P. By dot products with this unit vector, the normal (out-of-plane) velocity components at each point, VN1,VN2,VN3 andVN4, can be determined, as seen in the figure. The angular velocity of the triangle may be considered in three components. The first is the inplane rotation, about an axis perpendicular to the plane, which has no effect on VP/F, so will not be 322 Suspension Geometry and Computation considered further" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002622_j.mechmachtheory.2016.06.002-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002622_j.mechmachtheory.2016.06.002-Figure2-1.png", + "caption": "Fig. 2. Geometrical representation of dual angles.", + "texts": [ + " The elements of the unit dual vector ua = u+eu0 describe a line parametrized by Plucker coordinates, while the dual number a = |a| =\u2016a\u2016 +e a0 \u2022 a \u2016a\u2016 represents the label. Regarding parametric representation, for Re(a) = 0 the equation is r = a\u00d7a0 \u2016a\u20162 + k a \u2016a\u2016 , \u2200k \u2208 R. The case Re(a) = 0 will prove itself very important for future results. For this case the geometrical representation is a set of parallel lines described by a0 \u2016a0\u2016 and labeled with a = |a| = e \u2016 a0 \u2016. Also, the parametric equation is r = v + k a0 \u2016a0\u2016 , \u2200v \u2208 V3, \u2200k \u2208 R. Remark 2. Any pair of dual vectors b, a \u2208 V3 {0} is characterized by a dual number a = a + ed (Fig. 2), which is refereed as their dual angle, computed using a = atan2(|ub \u00d7 ua|, ua \u2022 ub), (11) where ub and ua are the unit dual vectors of b and a recovered as in Theorem 1. If Re(a) = 0 and Re(b) = 0 then the dual angle can be directly computed using: a = atan2(|b \u00d7 a|, a \u2022 b). (12) 2.3. Dual tensors An R-linear application of V3 into V3 is called an Euclidean dual tensor: T(k1v1 + k2v2) = k1T(v1) + k2T(v2), \u2200k1,k2 \u2208 R, \u2200v1, v2 \u2208 V3. (13) From now on, any Euclidean dual tensor will be shortly called dual tensor and L(V3, V3) will denote the free R-module of dual tensors", + " (a) a0 \u00d7 b0 = 0 R# = ( I + eq\u0303 ) eau\u0303 (66) where a = atan2(|b0 \u00d7 a0|, b0 \u2022 a0), u = b0\u00d7a0 \u2016b0\u00d7a0\u2016 and q \u2208 V3 is arbitrarily chosen. (b) a0 \u00d7 b0 =0 R# = ( I + eq\u0303 ) eau\u0303 (67) where q \u2208 V3 is arbitrarily chosen, u is a unit vector perpendicular on a0 and b0, a = 0 if a0 \u2022 b0 > 0 or a = p if a0 \u2022 b0 < 0. Proof. If R \u2208 SO3 then |a|2 = a \u2022 a = (Rb) \u2022 (Rb) = b \u2022 b = |b|2, which implies that |a| = |b| equivalent with \u2016a \u2016=\u2016 b \u2016 and a \u2022 a0 = b \u2022 b0. Let R# be a particular solution for Eq. (59). Consider the dual vectors b = b + eb0 and a = a + ea0 to be geometrically represented as in Fig. 2. The mapping of the dual vector b over the dual vector a is done by the orthogonal dual tensor R#, which represents a screw displacement along the axis b \u00d7 a. Using Theorem 3 the dual tensor can be expressed as R# = eau\u0303, where a and u are given by Eqs. (62) and (63). \u2022 If Re(b \u00d7 a) = 0 and Re(b \u2022 a) > 0 the directed lines described by b and a have the same orientation one related to the other. Using Theorem 3 results that d = q \u2022 ub\u00d7a \u21d0\u21d2 q = b\u00d7a0+b0\u00d7a a \u2022 b . \u2022 If Re(b \u00d7 a) = 0 and Re(b \u2022 a) < 0 the dual tensor R# is built using a rotation of angle p around the axis with direction u = b\u00d7b0 ||b\u00d7b0|| and a translation q = b\u00d7a0+b0\u00d7a a \u2022 b " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.9-1.png", + "caption": "Fig. 1.9 Identification of the position of the kth axis of rotation in the body-fixed \u03be-\u03b7-\u03b6 system", + "texts": [ + "26) = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u222b (\u03b72 + \u03b62)dm symmetric \u2212 \u222b \u03b7\u03bedm \u222b (\u03be2 + \u03b62)dm \u2212 \u222b \u03be\u03b6dm \u2212 \u222b \u03b7\u03b6dm \u222b (\u03be2 + \u03b72)dm \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 . The moments of inertia, with regard to several (k = 1, 2, . . . , K) axes through the center of gravity, can be determined by the test described in 1.2.3, in which the period of a torsional vibration is measured. The moments of inertia JS kk are obtained for several suspension points. The position of the kth axis of rotation that passes through the center of gravity can be uniquely described in the body-fixed \u03be-\u03b7-\u03b6 system using the three angles \u03b1k, \u03b2k and \u03b3k, see Fig. 1.9. The moment of inertia with regard to the instantaneous axis of rotation that passes through the center of gravity when the body is suspended depends on the six elements of the inertial tensor as follows, see (2.61) in Sect. 2.3.1: JS kk = cos2 \u03b1k JS \u03be\u03be + cos2 \u03b2k JS \u03b7\u03b7 + cos2 \u03b3k JS \u03b6\u03b6 +2 cos \u03b1k cos \u03b2k JS \u03be\u03b7 + 2 cos \u03b1k cos \u03b3k JS \u03be\u03b6 + 2 cos \u03b2k cos \u03b3k JS \u03b7\u03b6 . (1.27) Measurement of the angles \u03b1k, \u03b2k, and \u03b3k that are enclosed by the axis of rotation k\u2013k and the directions of the body-fixed reference system is required", + "71): \u23a1\u23a3JS \u03be\u03be \u2212 J JS \u03be\u03b7 JS \u03be\u03b6 JS \u03be\u03b7 JS \u03b7\u03b7 \u2212 J JS \u03b7\u03b6 JS \u03be\u03b6 JS \u03b7\u03b6 JS \u03b6\u03b6 \u2212 J \u23a4\u23a6 \u00b7 \u23a1\u23a3 cos \u03b1 cos \u03b2 cos \u03b3 \u23a4\u23a6 = \u23a1\u23a30 0 0. \u23a4\u23a6 (1.34) The three eigenvalues are the principal moments of inertia: JI, JII, and JIII. The components of the three eigenvectors correspond to the three directional cosines that characterize the orthogonal system of the principal axes, which is rotated relative to the body-fixed \u03be-\u03b7-\u03b6 system. The principal moment of inertia JI relates to the principal axis I, which is rotated relative to the \u03be-\u03b7-\u03b6 system, analogously to Fig. 1.9, by angles \u03b1I, \u03b2I, and \u03b3I that can be calculated from the three directional cosines cos \u03b1I, cos \u03b2I, and cos \u03b3I. The orientations of the other two principal axes II and III can be determined analogously. The calculation becomes simpler when the real body has a plane of symmetry, which in the case on hand is assumed to be the \u03be-\u03b6 plane. Each axis that is perpendicular to the plane of symmetry is a principal axis of inertia, and determining the elements of the moment of inertia tensor becomes simpler, see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002936_j.jmapro.2019.03.006-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002936_j.jmapro.2019.03.006-Figure10-1.png", + "caption": "Fig. 10. Equivalent Von Mises stress evolutions in the first layer deposition.", + "texts": [ + " During the experimental measurements, the accuracy of the hole-drilling method is affected by many factors such as hole offset, hole diameter and hole depth errors, strain gage paste quality, and sensitivity differences. Especially, in the high residual stress areas, stress concentration will cause the hole yielding, resulting in greater measuring errors. In addition, the stress measured by the hole-drilling method is an average stress in 1\u20132mm depth. Overall, the established model is able to predict the residual stress distributions of a ten-layer single-pass component in GMA-based AM. Fig. 10 shows the Von Mises stress evolutions during the first layer deposition process. The liquid metal in the molten pool is free to deform, resulting in zero equivalent stress. While, the expansion of the heated metal adjacent to the molten pool is constrained by the surrounding substrate, and a large stress region appears on the substrate near the heat source. At the deposition starting point, the maximum equivalent stress is generated on the substrate in front of the deposition path. When the heat source acts on the midpoint, the deposited metal away from the heat source begins to cool down, leading to an increase of the equivalent stress" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003816_j.ymssp.2020.106903-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003816_j.ymssp.2020.106903-Figure10-1.png", + "caption": "Fig. 10. Bearing test rig.", + "texts": [ + " Multi-defects means that the number of defects is more than one and the type of defect is the same, such as all the defects are localized defects in inner raceway or outer race- way, not other kinds. Besides, compound faults means that the damages are of different types. The rotor unbalance and inner raceway defect are as an example to be discussed in Section 3.3 in this paper. In order to verify the correctness of the proposed model and the analysis for different defects, experiments are done on a bearing test rig as shown in Fig. 10. The defective bearing is set in bearing chock 1 and acceleration sensor is installed in the vertical direction. Both the width and depth of the penetrating defect are set to 0.5 mm. The sizes of defect are the same as in the literature [16]. The tested bearing is a cylindrical roller bearing with a penetration defect on the outer raceway. The location of defect can be seen in Fig. 11. Parameters of the bearing are listed in Table 1. Simulations and Experiments are carried out at different rotation speeds", + "4 Hz) than theoretical calculation (306.4 Hz). Take all the results from experiments and simulations together and show them in Table 2. It can be obtained from Table 2 that the differences in RPFO between the experimental/simulation and experimental/theoretical calculation increase with rotation frequency. The results from simulations is closer to experiments than theoretical formulas under different rotation frequencies. Experiments of bearing with a single defect on inner raceway are done on the rig as shown in Fig. 10. A number of experiments are carried out at different rotation speeds. Parameters of the bearing are shown in Table 3, and the sizes of defect are the same as outer raceway defect. Taking 3000 r/min as example, the acceleration responses and envelope spectra of bearing in vertical direction in experiment and simulation are shown in Figs. 14 and 15. As can be seen from Figs. 14 and 15, the experimental result is consistent with simulation. Both the acceleration responses have periodic impact components", + " The vibration responses of bearing with six-defects on inner raceway are analyzed here only. The schematic diagrams of bearings with six-defects on inner raceway are shown in Fig. 18. 1) Six defects of random distribution Parameters of bearing used in this part can be found in Table 3. Six defects are set on the inner raceway, and the angle between the defects and the Z-axis positive direction are 23 , 47 , 79 , 128 , 220 and 281 . The width and depth of the defects are 0.5 mm. The test rig is shown in Fig. 10 and the rotation speed is 600 r/min. The acceleration responses and envelope spectra of bearing in vertical direction are displayed in Fig. 19 and Fig. 20. From the acceleration responses of experiment and simulation, the time interval corresponding to the impacts caused by the same defect is the reciprocal of RPFI. Besides, the rotation frequency (fi), RPFI and harmonics are prominent in envelope spectra, and the 6RPFI also can be found. But the amplitude of 6RPFI is low because of the distribution of defects is random" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003099_tro.2016.2633562-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003099_tro.2016.2633562-Figure4-1.png", + "caption": "Fig. 4. Aerofoil section of a blade at a radial station r \u2208 [0, R] from the rotor hub. The figure shows the different elemental forces which include lift, drag, and the horizontal and vertical forces on the aerofoil in {C}. The flow angles and velocity components are also shown.", + "texts": [ + " Given that the rotor blades on quadrotors are usually stiff, as such do not flap as much as full-scale helicopter blades, we model \u03b2(\u03c8) using only the first two terms of a Fourier series harmonic model [12] with coefficients a0 , a1 , and b1 \u03b2(\u03c8) = a0 \u2212 a1 cos\u03c8 \u2212 b1 sin\u03c8. Let \u03b80 denote the physical pitch angle of the blade and \u03b3 denotes the Lock number, then the model for these coefficients are given by [12] a0 = \u03b3 8 [ \u03b80 ( 1 + \u03bc2) \u2212 4 3 \u03bb ] , a1 = 2\u03bc (4\u03b80/3 \u2212 \u03bb) 1 \u2212 \u03bc2/2 , b1 = 4 3\u03bca0 1 + \u03bc2/2 . Consider the rotor and a blade element shown in Fig. 4. The horizontal velocity component of the rotor blade at a radial distance r and azimuth angle \u03c8 is given by Uh(r, \u03c8) = r + (\u2212Vh +Wh + vi h) sin\u03c8. For the vertical velocity Uz(r, \u03c8) Uz(r, \u03c8) = vi z \u2212 Vz +Wz + r\u03b2\u0307(\u03c8) + (\u2212Vh +Wh + vih) \u00d7\u03b2(\u03c8) cos\u03c8. Normalizing or nondimensionalizing by dividing by the tip velocity of the rotor R, the following relationships are obtained: uz (r, \u03c8) = Uz (r, \u03c8) R , =\u03bb+ r R \u03b2\u0307(\u03c8)+ 1 R \u00d7(\u2212Vh+Wh+vih)\u03b2(\u03c8) cos\u03c8, = \u03bb + r R d\u03b2(\u03c8) d\u03c8 + \u03bc\u03b2(\u03c8) cos\u03c8 and uh(r, \u03c8) = Uh(r, \u03c8) R , = r R + \u03bc sin\u03c8", + " The elemental lift dL(r, \u03c8) and drag dD(r, \u03c8) forces expressed in {C} are defined by dL(r, \u03c8) = 1 2 \u03c1U 2(r, \u03c8)Cl(r, \u03c8)c(r) d r, dD(r, \u03c8) = 1 2 \u03c1U 2(r, \u03c8)Cd(r, \u03c8)c(r) d r where Cl and Cd are the element lift and drag coefficients, respectively, and are given by Cl(r, \u03c8) = Cl0 + Cl\u03b1\u03b1(r, \u03c8), Cd(r, \u03c8) = Cd0 +KC2 l (r, \u03c8), K > 0. c(r) and \u03b1(r, \u03c8) are the element chord and angle of attack, respectively. The constants Cl0 , Cd0 , Cl\u03b1 ,K are the zero-angle of attack lift coefficient, the zero-lift drag coefficient, the lift curve slope, andK a constant that depends on the blade planform geometry. From Fig. 4, the element angle of attack is defined by \u03b1(r, \u03c8) = \u03b8(r) \u2212 \u03c6(r, \u03c8) where \u03b8(r) is the blade section pitch and \u03c6(r, \u03c8) is the relative inflow angle at the blade section. For |\u03c6(r, \u03c8)| <10\u25e6 \u03c6(r, \u03c8) \u2248 tan\u22121 ( Uz (r, \u03c8) Uh(r, \u03c8) ) \u2248 Uz (r, \u03c8) Uh(r, \u03c8) . A consequence of Assumption 1, however, is that the angle of attack \u03b1(r, \u03c8) is approximately constant along the entire blade length of the \u201cnear ideal\u201d rotor [11]. The elemental forces in the e3 direction and in the horizontal plane span{e\u03031 , e\u03032} in {C} are given by [12] dFx(r, \u03c8) = dL(r, \u03c8) sin\u03c6(r, \u03c8) + dD(r, \u03c8) cos\u03c6(r, \u03c8), (11) dFz (r, \u03c8) = dL(r, \u03c8) cos\u03c6(r, \u03c8) \u2212 dD(r, \u03c8) sin\u03c6(r, \u03c8)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000770_j.jmps.2012.09.017-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000770_j.jmps.2012.09.017-Figure11-1.png", + "caption": "Fig. 11. Growing ring with foundation underneath.", + "texts": [ + " That is, as the foundation force strengthens, it becomes energetically favourable to buckle at higher mode, solutions which have higher bending energy but remain closer to the foundation. Next we consider the alternative configuration in which the foundation lies under the ring in its initial unstressed state. In this configuration, any growth of the ring induces not just a body force, but also a body couple (with the foundation attached to the bottom of the ring, as the ring expands the foundation induces a moment that serves to twist the ring and roll its centreline into the plane of the foundation, see Fig. 11). Thus, there is a non-zero register angle j, i.e. the angle of rotation of the cross section due to the applied couple. Writing the normal and binormal vectors m \u00bc cos\u00f0S=g\u00deex sin\u00f0S=g\u00deey, b\u00bc ez, \u00f080\u00de we have d\u00f00\u00de1 \u00bc cos jm\u00fesin jb, d\u00f00\u00de2 \u00bc sin jm\u00fe cos jb. Following Eq. (18), u\u00f00\u00de1 \u00bc g 1 sin j, u\u00f00\u00de2 \u00bc g 1 cos j, u\u00f00\u00de3 \u00bc 0. The foundation force is of the form (77), but now rA \u00bc r ad2, and the foundation is a circle of radius 1, located in the x\u2013y plane, i.e. q\u00bc m. The prebuckled solution has as centreline a circle radius g, located in the plane z\u00bch" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure6.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure6.2-1.png", + "caption": "Fig. 6.2 Diagram of a primitive synchronous machine with two field coils and two damper coils.", + "texts": [ + "2 ) - N '- l K m 1 /T m 1 + + G m 1 G 2 G m 1 G 1 G 2 Z l Tm 1 T m 1 K m 2 /T m 2 Z2 K x / T x - G m s K m 2 T m 2 -G x s K x T x For the purpose of numerical computations, the terminal voltage Urn t is obtained as follows from the axis components of voltage Urnt = V(Ud 2 + U q 2) (6.1) The elements of the regulator are assumed to be linear in deriving Eqn. (6.2). In practice, the voltage of any amplifier is limited between upper and lower boundaries. 6.3 Quadrature field winding. The divided-winding-rotor generator Instead of only the one field winding (Fig. 4.2), a synchronous machine may have two field windings represented by coils FD and FQ in Fig. 6.2. With an angle regulator feeding the quadrature-axis field and a voltage regulator feeding the direct-axis field, as illustrated in Fig. 6.3, the resultant field m.m.f. is positioned with respect to the rotor in such a way that the stability of the machine no longer depends on rotor acceleration or deceleration, [44]. The equations for the coils in Fig. 6.2 are similar to those in Section 4.6 except that the subscript f is replaced by fd. Equations (6.3) and (6.4) are needed to allow for the presence of the FQ coil. (6.3) l/Ifq = Lmq + Lfq Lmq Lmq Lmq Lmq + La Lmq (6.4) Lmq Lmq Lmq + Lkq Because of the symmetry of the new field winding, the equations for all the q-axis coils are similar to those for the corresponding d-axis coils and the q- and d-axis equivalent circuits are similar. Some new parameters such as Tq ', Tqo' and X q' are defined for the q-axis, in the same way as Td', TdO' and Xd' were defined in Section 4.6. In comparison with Eqns. (5.11) and (5.12) there now exists the additional state variable Wo l/Ifq and the additional input variable Ufq. The machine of Fig. 6.2 is therefore described by a set of non-linear differential equations which can be found by increasing by one the number of x and z variables in Eqn. (5.19). In practice it is difficult to construct a field winding on the quadrature axis of a large turbo-generator rotor. However, a practical solution is to divide the conventional slot arrangement of the rotor into two bands and replace the conventional concentric winding F by two separate lap windings Rand T as in Fig. 6.4, which shows the windings of a micro-machine used for experi mental investigations", + " Neither the R nor the T coil axis coincides with either the direct or quadrature axis and therefore, due to saliency, the axis of the flux wave produced by each coil does not coincide with the respective coil axis. The flux produced by a particular coil may be found by resolving the coil m.m.f. into two components along the direct and quadrature axes, then finding and adding vectorially the flux produced by each m.m.f. component. The relationship between the currents in the Rand T windings and those in the FD and FQ windings of Fig. 6.2 is given by the following transforma tion, based on the equivalence of the resultant m.m.f.s. g:fd = cos CPt N cos CPr 6:t Ifq -sin CPt N sin CPr Ir ~----~--------~ (6.5) where CPr and CPt are the angles defining the positions of coils Rand T and N is their turns ratio. The d. w.r. machine can be analysed by using the equations for the machine of Fig. 6.2, in conjunction with the transformation of Eqn. (6.5). The application of a synchronous machine with two field windings is discussed further in Section 7.6. If) x __ 0 ___ i-r .II --: I ~-I oL-. I ~ Earlier forms of governors for turbo-generators consisted of a hydraulic system operating on the main turbine valve and actuated by a speed signal produced by a centrifugal mechanism. The operation was relatively slow and there was a considerable dead-band effect in the jntermediate valves. It was generally assumed that the governor had no appreciable effect on the first swing of the machine after a transient disturbance, although the later swings were affected to some extent", + " Operation of Synchronous Machines ISS ventional machine extends the range of operation only when the generator is loaded. The quadrature-axis excitation regulation on the other hand allows generation at leading power factor at all loads, the current being limited only by heating. Different types of regulators have been described in Section 6.2 [33], but for the purpose of this illustration a proportionate regulator only is considered. The generator is connected to an infinite bus through a fixed-impedance as shown in Fig. 6.2 and the turbine torque is assumed to be constant. Equation (7.32) is used to represent the generator but !l.Mt and !l.ufq are equal to zero and the only control input is the field voltage !l.ufd. A test or calculation is made at a given operating point on the P-Q chart to determine whether the system is stable or unstable at that point. The theoretical stability limit is calculated by studying for example the loci of the three roots of the characteristic equation in the complex plane of Fig. 7.6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003207_s00170-016-9445-z-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003207_s00170-016-9445-z-Figure5-1.png", + "caption": "Fig. 5 Geometrical model of remanufactured impeller blade", + "texts": [ + " During stress analysis, nodes of A, B, C, and D at the end of the bottom showed in Fig. 6 were constrained. In this way, rigid body motion could be avoided. According to numerical procedure, 3D-remanufactured impeller model was built by software Pro/E (version 5.0) based on 3D surface reverse technology [19]. In order to reduce computing amount, a single remanufactured impeller blade, instead of the whole impeller, was applied to do the laser cladding simulation. The geometrical model is shown in Fig. 5. In meshing process, a non-uniform mesh was used to improve simulation accuracy and reduce computational cost. Figure 6 shows the FE model for laser cladding, and in total, there are 6622 nodes and 4896 elements meshed. As the blade thickness is 1.1\u223c1.5 mm, which is less than the laser diameter 3 mm, the blade can be directly deposited by a single layer as shown in Fig. 6. Six cladding layers were deposited in total, and the scan path was from left to right along the scaning direction. In transient thermal analysis, thermal conduction element solid70 was used" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000657_tmag.2009.2024159-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000657_tmag.2009.2024159-Figure1-1.png", + "caption": "Fig. 1. Types of analyzed motors. (a) IPM. (b) Inset. (c) SPM.", + "texts": [ + " The loss-reduction effect by the segmentation must vary with the location of the magnets in the rotor. From these viewpoints, we investigate the loss-reduction effects by the magnet segmentations in several types of synchronous motors. First, the difference in the loss-reduction effect due to the rotor types is estimated by the 3-D finite-element method (3-D FEM) that considers the carrier harmonics of the inverter. Next, a basic experiment with the magnet specimens is carried out in order to support the calculated results. II. INVESTIGATION BY 3-D FEM Table I and Fig. 1 show the specifications and types of the analyzed motors. Fig. 1(a)\u2013(c) shows the interior, inset, and surface permanent magnet types, respectively. The motors have one magnet per pole. An identical stator with distributed windings is employed for each motor. They are driven by a pulse-widthmodulated (PWM) inverter whose carrier frequency is 10 kHz. Manuscript received March 05, 2009. Current version published September 18, 2009. Corresponding author: K. Yamazaki (e-mail: yamazaki.katsumi@itchiba.ac.jp). Digital Object Identifier 10.1109/TMAG.2009.2024159 The formulations of the 3-D FEM that considers the carrier of the PWM inverter [3] are as follows: (1) (2) (3) where and are the magnetic vector and electric scalar potentials, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000699_1.3085942-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000699_1.3085942-Figure1-1.png", + "caption": "Fig. 1 Definition of oil churning parameters for a partially immersed gear pair", + "texts": [ + " The second category of churning power losses is formed by losses due to interactions of the gear pair at the gear mesh interface with surrounding medium oil , with squeezing/pocketing losses being the dominant mode of power loss. With the gear mesh pocketing power losses Pp and drag power losses predicted, the total oil churning spin power loss of a gear pair is given as PsT = Pd1 + Pd2 + Pp 2 Detailed formulations for each component of power loss are presented in Ref. 19 . Here, resultant formulas will be presented for the purpose of completeness before comparisons are made to the experimental data. Power loss due to drag on the periphery of a rotating gear, which is fully or partially immersed in oil, as shown in Fig. 1, is obtained as the product of the drag force and the tangential velocity along the periphery. The continuity equation and the Navier\u2013 Stokes equations of motion are used to determine the components of the oil velocity by assuming steady-flow conditions and then determining the components of shear stress and the drag friction coefficient that yields the drag force along the periphery. In its final form, the churning power loss of a gear i due to oil drag on its periphery is given as 19 Pdpi = 4 biroi 2 i 2 cos\u22121 1 \u2212 h\u0304i 3 Here, bi is the face width, h\u0304i=hi /roi is the dimensionless immersion parameter where hi is the static immersion depth, as shown in Fig. 1, roi is the outside radius of the gear, is the dynamic viscosity of the oil, and i is the rotational speed of gear in rad/s. Power loss due to drag on the faces sides of a gear is defined for laminar Re=2 iroi 2 / 10 5 and turbulent Re 10 6 flow regimes using boundary layer theory as 19 Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use P w o l o a t f t l a g w w c b t d c t t b w T v T f 1 b J Downloaded Fr Pdfi L = 0.41 k 0.5 i 2.5roi 4 2 \u2212 sin\u22121 1 \u2212 h\u0304i \u2212 1 \u2212 h\u0304i h\u0304i 2 \u2212 h\u0304i sin cos\u22121 1 \u2212 h\u0304i 4a dfi T = 0", + "32 mm and a 23-teeth gear pair having a module of m\u0303=3.95 mm, were included in the test matrix to collect data on the influence of gear module. Gear face width. Test with gears of module m\u0303=2.32 mm were performed with three different face width values to investigate the impact of the face width on spin power loss. The face width values used in Table 2 are b=14.2, 19.5, and 26.7 mm. Immersion depth. Figure 5 b shows various static oil levels considered for the actual test gearbox with the side cover removed. According to Fig. 1, these unity-ratio gear pairs with ro1 =ro2 have the same immersion depth h1=h2=h since gear centers Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use O r = d i o l o a r T = b o R 1 m = h\u0304 b m 6 c F r J Downloaded Fr 1 and O2 are on the same horizontal plane. Under this configu- ation, the dimensionless immersion parameter is given as h\u0304 h1 /ro1=h2 /ro2. The test matrix of Table 2 includes tests con- ucted at values of h\u0304=0.05, 0.5, 1.0, and 1.5. Here, h\u0304=0.05 is ntended to represent an oil level that is tangent to the pitch circle f the gears with only the addendum of the teeth immersed in the ubricant" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001502_j.ymssp.2012.03.013-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001502_j.ymssp.2012.03.013-Figure9-1.png", + "caption": "Fig. 9. Experiment with wheel-hub assembly and illustration of preloading mechanisms utilizing hydraulic jack (for radial direction) and shaft with threaded rod (for axial preloading).", + "texts": [ + "5 kN) are elevated, but they are considerably reduced for heavy axial preloads (such as 5 kN). Also, even though the undamped natural frequencies do not vary significantly, the shape of the resonant peaks are altered in comparison to the load-independent viscous damping model of Eq. (21). Since the damping characteristics of rolling element bearings are not very well understood, both damping models must be examined to assist us in interpreting vibration measurements as discussed in the next section. A new experiment composed of an automotive wheel-hub assembly, as shown in Fig. 9, is designed to assess the effects of bearing preloads on modal characteristics. A similar wheel-bearing unit has been investigated by Choi and Yoon [20] to optimize its design variables. In this system, the shaft is supported by a double row angular contact ball bearing in back-toback arrangement (with kinematic properties of Table 1) that has a split inner ring. The main reason a back-to-back arrangement is selected is its ease of preloading with a lock nut through a threaded rod [2], and this arrangement is found in many real-life applications (such as vehicle wheel bearings)", + " The bearing is initially unloaded in the axial direction. The initial radial preload for such bearings is given in terms of radial clearance that is between 0 and 30 mm (note that this negative clearance defines a displacement preload), which creates some uncertainty regarding the precise value of initial radial preload. Additional bearing preloads are applied via the following mechanisms. 1. Axial preload (Fz0): Applied through the shaft by tightening the nuts at both ends of threaded rod inside the shaft that can be seen in Fig. 9. The applied load is measured with a washer type load cell (Omega model LC901-5/8-50K, 28.6 mm outer diameter 16.4 mm inner diameter, 0 to 222.4 kN compression range, 9.39e-3 mV/V/kN) that is placed between one of the nuts and flange on the shaft. 2. Radial load (Fx0) with imposed moment: Applied as an external static shaft load \u00f0Fxm\u00de using a hydraulic jack that is placed on a stable base as shown in Fig. 9 while the bearing is axially preloaded at 2.67 kN. The applied radial load, which is carried by the wheel bearing, essentially imposes a moment load \u00f0Mym\u00de on the bearing as well. The amount of applied radial load is measured with a miniature compression load cell (Omega model LC307-3K, 12.7 mm diameter, 9.7 mm thick, 0 to 13.3 kN compression range, 0.109 mV/V/kN) which is attached at the top of the jack. An impulse hammer (PCB model 086C02, 0 to 445 N range, 11.2 mV/N) test is conducted at various axial and radial loads, and cross-point accelerance measurements are taken for numerous impact (f 1,f 2,. . .,f 5) and accelerometer locations (1, 2 and 3) as shown in Fig. 9. In these measurements the angular position of the shaft (and essentially the bearing) is kept the same for all preloads. In the following sub-sections, typical results are presented for various locations of a triaxial accelerometer (PCB model 356A15, 100 mV/g sensitivity in each direction, o5% transverse sensitivity) when the force (f1z) is applied on the left end of shaft (as shown in Fig. 9). Other force locations are incorporated to observe the mode shapes. The frequency range of interest of this study will be from 500 to 2500 Hz as the relevant vibration modes of the shaftbearing system occur within this region. The natural frequencies that occur below 500 Hz correspond to the lower order flexural modes of the casing itself, whereas the modes beyond 2500 Hz represent local motions. Thus, the modes of shaftbearing assembly are well separated from the rest of experimental system (or fixture) modes. Axial preloads ranging from 0.45 to 2.67 kN are applied with an increment of 0.22 kN; these are within 70.05 kN error margin as it is not possible to experimentally apply a precise amount of preload. Also, there is an uncertainty of 74 Hz in the frequency measurements based on the frequency resolution of acquired digital data. Accelerance results are presented for two accelerometer locations (1 and 2) in Fig. 9. Accelerance magnitude measurements at location 1 are first plotted in Fig. 10(a) up to 2500 Hz for all preloads. In this plot, the low-amplitude peak occurring around 65 Hz (though not very visible) corresponds to a casing mode and is thus beyond interest as mentioned earlier. The first preload-dependent mode occurs at 660 Hz when Fz0\u00bc0.45 kN, and its natural frequency increases to 810 Hz as the Fz0 is gradually increased to 2.67 kN. The peak amplitude at this mode significantly reduces with an increase in Fz0, resembling the load-dependent damping case described by Eq", + " 10(c) 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 0 2 4 6 8 10 12 14 Frequency (Hz) A cc el er an ce (1 /k g) Increasing axial preload Fig. 10(b) Fig. 10. Effect of axial preload on the measured axial accelerance magnitude spectra at location 1. (a) 1\u20132500 Hz, (b) 300\u20131000 Hz, (c) 2000\u20133800 Hz. Key: Fz0; ( ), 0.45 kN; ( ), 0.67 kN; ( ), 0.89 kN; ( ), 1.11 kN; ( ), 1.33 kN; ( ), 1.56 kN; ( ), 1.78 kN; ( ), 2.00 kN; ( ), 2.22 kN; ( ) 2.45 kN; ( ) 2.67 kN. The five degree-of-freedom analytical formulation of Fig. 3 is utilized once again (with damping coefficients based on measurements) to model the experiment of Fig. 9. Only the axial preload case is analyzed. This is because the radial preload case, as implemented with the hydraulic jack, affects the boundary conditions of the shaft-bearing system by creating an additional ground connection and thus imposes torsional stiffness which may not be included in the proposed stiffness model (i.e., the model is valid for shaft-bearing systems that are allowed to rotate freely about their rotational axis). Sample results for an intermediate axial preload (Fz0\u00bc1.56 kN) will be illustrated. Table 5 lists the measured (from experiment of Fig. 9) and predicted (using five degree-of-freedom model of Fig. 3) natural frequencies of the system. The predictions match well with the measurements with small errors. When there is no external radial or moment load applied in the model, natural frequencies at r\u00bc1 and r\u00bc2, as well as r\u00bc4 and r\u00bc5, are repeated (as mentioned earlier). With an application of a slight amount of load in the x-direction (Fxm\u00bc0.3 kN), these repeated roots separate as shown in the fourth column of Table 5. Now, the second, third, and fifth natural frequencies show a better match with measurements, but the estimation of the first natural frequency deviates further from experiments" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001619_tmag.2013.2285017-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001619_tmag.2013.2285017-Figure7-1.png", + "caption": "Fig. 7. Stator lamination of the original and modified HSPM.", + "texts": [ + " The thermal time constant of the rotor at standstill is about 55 min, which means the measurement errors are within 4% if the measurements are completed in 2 min. It can be seen from Section III that the rotor temperature rise is significantly high when compared with that of the stator, which decreases the motor output and increases the risk of demagnetization. The high temperature rise in rotor is mainly caused by two reasons: 1) high loss density and 2) insufficient cooling. In order to reduce the rotor temperature, several modifications are applied to the structure of the HSPM. First, to reduce the rotor loss density, as shown in Fig. 7, the stator tooth and tooth tips are enlarged slightly to filter asynchronous stator MMFs. Then the cooling air is forced into the rotor surface by closing the outer slots by increasing the stator yoke width and inserting slot fillets in the outer slots (see Fig. 7). Therefore, the axial air flow velocity at the rotor surface and corresponding convection heat transfer coefficients are improved. The iron loss density is decreased by increasing the tooth and yoke width after modification. However, the copper loss increases due to the thicker yoke and the cooling ability of the winding is decreased due to the removal of the outer air duct. To maintain the stator temperature level, the heat transfer surface of which is increased by planting fins on the motor frame and adding edges to the outer teeth" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000406_ma1003979-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000406_ma1003979-Figure10-1.png", + "caption": "Figure 10. Snapshots from the numerical simulations of thermal bending of a film whose thickness at 339K is 83.4 \u03bcm. Specimen dimensions areL=2000\u03bcm,W=500 \u03bcm, and t=108\u03bcm in the preparation state (wet, nematic,T=313K). From left to right: dry state atT=313, 338, and 361K.The bounding box corresponds to the preparation state. The vertical cross-section and the vertical line used for the evaluations of stress and strain are highlighted. A complete movie of the equilibrium deformations is available in the Supporting Information.", + "texts": [ + " To distinguish between the solutions and the data of the elastic equilibrium problem in eqs 18 and 19, in what follows, we will call F and C equilibrium deformation and equilibrium strain, whereas we will call F* and C* distortion and distortional strain. We solve eqs 18 and 19 numerically by implementing in the finite-element software COMSOL Multiphysics the nonlinear elastic problem based on the energy density given by eq 9, in which we use eq 14 and the values in Table 2 as the material parameters. Snapshots of the equilibrium deformations of a film (of thickness 83.4 \u03bcm at Tflat=339 K) resulting from drying and temperature changes are shown in Figure 10. The highly nonhomogeneous deformations in a boundary layer near the clamped end are due to the fact that in the simulations we assume that all components of the displacements vanish at the constrained end. A complete movie of the equilibrium deformations is available in the Supporting Information. The thickness of the film is relatively insensitive to thermal variations. The following estimates are obtained from the deformed shapes of Figure 10: t(Q0) = 84 \u03bcm, tflat = t(Qflat) = 83.4 \u03bcm, and t(1)=82.7 \u03bcm. This result supports the assumption of the T-independent t used in eq 4 and Figure 8 in the former section. The distribution of strains and stresses along a fiber parallel to z at the center (x=L/2, y=W/2) of the sample are plotted in Figures 11-13. As for strains, we consider those relative to the configuration of the system at Qflat, which is obtained from the reference one (preparation state) by the deformation Fflat: Fflat=F*(z,Qflat)= (vsw)1/3I" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001280_j.mechatronics.2013.04.002-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001280_j.mechatronics.2013.04.002-Figure13-1.png", + "caption": "Fig. 13. Schematic drawing of the pancake harmonic drive setup. The left panel shows the schematic drawing of the setup for identification of the torsional stiffness, while the right panel is the setup for validation purpose.", + "texts": [ + " The harmonic drive is driven by a DC motor type M2AA from ABB. This setup is equipped with two incremental encoders to measure the position on the input side and the output side after the reduction, while the current applied to the DC motor is measured in the servo amplifier. The encoder on the output side is connected to the shaft through timing belt transmission in order to increase the encoder sensitivity. These signals are processed and recorded by a dSPACE data acquisition board. The left panel of Fig. 13 shows the schematic of the setup. For the purpose of torsional stiffness identification the output shaft, which in this setup is connected to the circular spline, is locked and mounted to the ground, while the DC motor applies torque to the input shaft. The current applied to the motor is assumed to be proportional to the motor torque and will be used to construct the torsional stiffness. The input shaft connected to the wave-generator is driven by the motor, in which the torque balance can be written as: Tm \u00bc TI \u00fe Tf \u00fe T0 \u00f07\u00de 10 Real Torsional Stiffness where Tm is the motor torque generated by the amplifier current, TI is the inertia torque from motor armature and shaft, Tf is the friction torque in the motor and T0 is the load torque driving the input shaft to the harmonic drive", + " In order to verify the quality of the model structure and its parameters, another filtered random signal, with a different seed from the training set, has been applied to the system. The measured stiffness profile can be seen in Fig. 14, while Fig. 15 shows the modelled stiffness profile of the system. Both figures qualitatively show good fit, with performances of 1.59% for the MSE and normalized maximum error of 0.62. In order to validate the modelling scheme, simulations of the system under unconstrained motion (unlocked load) are developed (see right panel of Fig. 13). All of the individual models obtained from previous identifications are combined and merged into one integrated model for the assembled system. The integrated system model uses the measured angular displacements of a typical experiment as an input to the simulation. As a measure of the model performance, the applied motor torque of the simulation is compared to that of the experiment. A certain low inertial load J2 is attached to the output shaft, and, for verification purpose, a low frequency periodic signal is applied to the system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.24-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.24-1.png", + "caption": "FIGURE 11.24. A mass on a rotating ring.", + "texts": [ + " (a) the pivot 0 has a dictat ed motion in X direction X o = asin wt (b) t he pivot 0 has a dictat ed motion in Y direction Yo = bsin wt (c) the pivot 0 has a uniform motion on a circle ro = R coswt i + R sin wt J. 19. Equations of mot ion from Lagrangean. Consider a physical syst em with a Lagrangean as I:- = ~m (ax + biJ )2 - ~k (ax + by)2 . The coefficients m , k, a, and b are constant . 20. Lagrangean from equat ion of motion. Find the Lagrangean associa ted to the following equations of motions: (a) (b) .. e\u00b72r -r r 2 B+ 2r i: iJ o o 11. Motion Dynamics 503 E B 21. A mass on a rotating ring. A particle of mass m is free to slide on a rotating vertical ring as shown in Figure 11.24. The ring is turning with a constant angular velocity w = rp. Determine the equation of motion of the particle. The local coordinate frame is set up with the x-axis pointing the particle, and the y-axis in the plane of the ring and parallel with the tangent to the ring at the position of the mass. 22. * Particle in electromagnetic field. Show that equations of motion of a particle with mass m with a Lagrangian L ,.. 1 .2 ;f,. \u2022 J.- = -mr - e\"\"+ er . A 2 are 3 .. (8<1> 8Ai) \", . (8A j 8Ai) mqi = e - 8qi - at + e~ qj 8qi - 8qj where q~[~:] [~] Then convert the equations of motion to a vectorial form mr = eE (r , t) + ei x B (r , t) where E and B are electric and magnetic fields" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001007_1.4025219-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001007_1.4025219-Figure4-1.png", + "caption": "Fig. 4 Some legs for planar parallel mechanisms: (a) 00 R 00 R 00 R R R, (b) 00 R 00 R _R _R 00 R, (c) ~R 00 R 00 R 00 R~R, and (d) 00 R gRRR 00 R", + "texts": [ + " 3(a)) with a 1-f1-system is constructed using two planar CUs, 4-5 and 6-7-8-1-2-3. The axis of the basis f11 of the 1-f1-system is perpendicular to all the axes of the R joints within the same 3-DOF single-loop kinematic chain. It is noted that the two R joints in the 00 R 00 R 00 R R R(RRR)E (Fig. 3(a)) 3- DOF single-loop kinematic chain are generally inactive [10]. By removing the E virtual chain from the above 00 R 00 R 00 R R R(RRR)E 3- DOF single-loop kinematic chain, one obtains an 00 R 00 R 00 R R R leg (Fig. 4(a)) with a 1-f1-system. The axis of the basis f11 is perpendicular to all the axes of the R joints in the leg. For clarity and simplicity, slmn, which implies that R joints l, m, and n have parallel axes and denotes a unit vector parallel to the axes of these R joints, is represented by a solid round arrow. Ak denotes the axis of R joint k, which is not parallel to the axes of the other joints within the same leg. It is noted that in constructing 3-DOF single-loop kinematic chains with a 1-f0-system (such as the 00 R gRRR 00 R (RRR)E kinematic chain in Fig", + " 3, such information may help simplify the type synthesis of legs for E/PPP\u00bc PMs. As shown in the example at the beginning of this section, the wrench system of a leg for planar PMs is the same as the wrench system of its associated single-loop kinematic chain, which is obtained in constructing these kinematic chains using CUs. The leg-wrench system can also be easily obtained using the reciprocity conditions of screws based on the description of the legs in Table 1. For example, the ~R 00 R 00 R 00 R ~R leg (leg No. 29 in Table 1) for planar PMs shown in Fig. 4(c) has a 1-f0-system in a general configuration. The axes of the three 00 R joints are parallel. Therefore, the axis of the basis f01 of the 1-f0-system is parallel to the axes of the 00 R joints and intersects the axes, A1 and A5, of ~R joints 1 and 5. The axis of f01 can be constructed geometrically as follows. First, find the intersection of the projections of the axes of the two ~R joints on a plane perpendicular to the axes of the 00 R joints. Then, draw a line parallel to the axes of the 00 R joints through the above intersection", + " 13\u201319 legs in Table 1, which are associated with one planar CU and one spherical CU; Subclass 3: Nos. 20\u201329 legs in Table 1, which are associated with one planar CU and two co-axial CUs; Subclass 4: Nos. 30\u201332 legs in Table 1, which are associated with one planar CU and one Bennett CU. In the following, we will discuss how to generate legs for E/ PPP\u00bc PMs in a transition configuration from each subclass of legs for planar PMs. The legs for planar PMs of subclass 1 (Nos. 6\u201312 in Table 1) have a 1-f1-system. In each of these legs (see the No. 6 00 R 00 R 00 R R R leg in Fig. 4(a)), for example), the axes of two or three successive R joints are parallel, and the axes of the other R joints are also parallel. These legs all satisfy the conditions for translational PMs. Therefore, the Nos. 6\u201312 legs for planar PMs are legs for E/ PPP\u00bc PMs, as listed in Nos. 2\u20138 legs in Table 3. The No. 6 00 R 00 R 00 R R R leg for planar PMs (Fig. 4(a)) is the No. 2 00 R 00 R 00 R R R leg for E/PPP\u00bc PMs (Fig. 5(a)). The legs for planar PMs of subclasses 2\u20134 (Nos. 13\u201332 in Table 1) usually have a 1-f0-system. In each of these legs, all the axes of the 00 R joints remain parallel when the moving platform undergoes planar motion. However, they do not satisfy directly the conditions for legs for translational PMs. Following the above steps 2\u20135, we can obtain legs for E/PPP\u00bc PMs by rendering each leg so that all the R joints except the 00 R joints have parallel axes that are not parallel to the axes of the 00 R joints, if possible. A leg can be rendered by imposing additional constraints on all the R joints, except the 00 R joints, within the leg. The legs for planar PMs of subclass 2 (Nos. 13\u201319 in Table 1) are _R _R 00 R 00 R 00 R , 00 R 00 R 00 R _R _R, 00 R 00 R _R _R 00 R (Fig. 4(b)), 00 R _R _R 00 R 00 R , 00 R _R _R _R 00 R , _R _R _R 00 R 00 R , and 00 R 00 R _R _R _R. In each of these legs, the R joints except the 00 R joints are the successive _R joints. If we render all the axes of the _R joints to be parallel, all the successive _R joints are coaxial and degenerate to one R joint. Therefore, no leg for E/ PPP\u00bc PMs can be obtained from the above seven types of legs. The legs for planar PMs of subclass 3 (Nos. 20\u201329 in Table 1) are each composed of three 00 R joints and two inactive ~R joints. If we render each of these legs so that the axes of the two ~R joints are parallel, no two successive R joints become coaxial. From the ~R 00 R 00 R 00 R ~R leg (No. 29 in Table 1 as shown in Fig. 4(c)) for planar PMs, we can obtain a rendered ~R 00 R 00 R 00 R ~R (Fig. 5(b)) leg. In this rendered leg, all the 00 R joints are successive R joints with parallel axes, and the rendered ~R joints also have parallel axes. Therefore, the rendered ~R 00 R 00 R 00 R ~R leg for planar PMs is a leg for E/ Table 3 Legs for E/PPP 5 PMs in a transition configuration ci Class No. Type Description Leg-wrench system 1 5R 1 \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 The axes of two or three successive R (or ( 00 R )\u2018) joints within a leg are parallel, while the axes of the 00 R (or \u00f0~R\u00de0) joints within a PM are parallel", + " No leg for E/PPP\u00bc PMs can be obtained from the Nos. 22\u201323 and 26\u201328 legs in Table 1 for planar PMs, since in the associated rendered legs, there is no one group of R joints with parallel axes in which all the R joints are successive. Although legs for E/ PPP\u00bc PMs can be obtained from the Nos. 20, 21, 24, and 25 legs for planar PMs in Table 1, these legs have already been obtained from legs for PMs with a 1-f1-system. Finally, the legs for planar PMs of Subclass 4 (Nos. 30\u201332 in Table 1) are 00 R 00 R gRRR, 00 R gRRR 00 R (Fig. 4(d)), and gRRR 00 R 00 R . These legs are each composed of two 00 R joints and one Bennett CU gRRR. We cannot render any of these legs for planar PMs so that the axes of the three R joints within gRRR are parallel. Therefore, no leg for E/PPP\u00bc PMs can be obtained from these three types of legs. In summary, eight types of legs with a 1-f1-system have been obtained for E/PPP\u00bcPMs (Table 3) in a transition configuration. It is noted that each of the Nos. 2\u20138 legs in Table 3 has a 1-f1system in a regular configuration no matter whether the leg is in a transition configuration, the planar mode or spatial translational mode", + " In the \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 leg, the axes of the ( 00 R )\u2018 joints are now 00 R joints, while the two \u00f0~R\u00de0 joints become ~R joints whose axes are no longer parallel to each other. Therefore, this leg is now an 041015-6 / Vol. 5, NOVEMBER 2013 Transactions of the ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use ~R 00 R 00 R 00 R ~R leg. The wrench system of the ~R 00 R 00 R 00 R ~R leg is a 1- f0-system in which the axis of the basis wrench f1 01 is parallel to all the axes of the 00 R joints and intersects the axes of the two ~R joints (Fig. 4(c)). The sum of all its leg-wrench systems is a 2-f1-1-f0-system, and the moving platform can undergo 3-DOF planar motion. In the spatial translational mode (Fig. 6(c)), each 00 R 00 R 00 R R R leg has two groups of R joints with parallel axes: a group of three 00 R joints and a group of R joints. In the \u00f0~R\u00de0( 00R )\u2018( 00 R )\u2018( 00 R )\u2018\u00f0~R\u00de0 leg, the three ( 00 R )\u2018 joints become R joints whose axes are parallel but are not parallel to the axes of the 00 R joints in the 00 R 00 R 00 R R R legs, while the two \u00f0~R\u00de0 joints are now R joints with parallel axes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000339_s0022112005004829-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000339_s0022112005004829-Figure8-1.png", + "caption": "Figure 8. The induced velocity disturbance due to the dumbbell in simple shear flow. The two insets show the directions of the inertial lift forces acting on one of the point forces comprising the dumbbell on account of streamline curvature.", + "texts": [ + " This retardation is again in agreement with the analysis in the preceding paragraphs, and is responsible for the emergence of a stationary state for Re > Rec. To analyse the change in orbit constant due to migration across inertialess meridional trajectories, it is necessary to consider fluid motion induced orthogonal to the fibre-flow plane. For purposes of the following qualitative reasoning, that serves to determine the direction of the O(Re) drift, the fibre may be treated as a dumbbell comprising a pair of oppositely directed point forces, proportional to the local slip velocity, and displaced from one another by a distance of O(l) (see figure 8). The similarity of a fibre and a dumbbell at low Re can, in fact, be made quantitative. An analysis for a torque-free dumbbell in simple shear is virtually identical to the one carried out above, the only difference being that the spherical Bessel function corresponding to the fibre forcing in Fourier space is now replaced by an elementary sine function. It yields orbit equations of the same form, differing only in the values of the numerical constants. Thus the aforementioned conclusions with regard to change in both orbit constant and phase remain unchanged for a dumbbell in the limit Re 1", + " The near-field behaviour of the velocity fields, i.e. for distances r l from the point forces of the dumbbell or for r \u223c O(d) from the fibre axis, is very different; that for a fibre is logarithmic, characteristic of Stokes flow in two dimensions, while that close to the individual point forces in the dumbbell diverges as 1/r . In either case, however, the near-field contributions to the inertial torque are negligibly small, and are therefore not relevant to the argument that follows. Returning to figure 8, we first observe that owing to the antisymmetry of simple shear, the sense of the inertial couple can be deduced by considering the nature of the perturbed streamlines around only one of the two point forces. Further, as shown in figure 8, it suffices to consider the component of the point force in the flow direction, the effect of the gradient component being restricted to the fibre-flow plane. The flow component accelerates the ambient simple shear on one side relative to the other, leading to curved streamlines of the form shown in the inset. The nature of curvature clearly points to a resultant lift force in the positive gradient direction. The component of this lift force perpendicular to the fibre-flow plane, together with its antisymmetric counterpart, constitute the inertial couple" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001838_034002-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001838_034002-Figure1-1.png", + "caption": "Figure 1.Part design to evaluate CT scanning as a non-destructive testing technique showing various sized defects of different layer sizes.", + "texts": [ + " Notable errors in utilizing IR data have been identified in previous work, such as the mean radiant temperature and material emissivity, which can alter the data output of an IR camera. Compensation of IR variables identified in previous work (Rodriguez 2013) were utilized in this research for data capture and analysis. To test the IR camera\u2019s monitoring capabilities and evaluate its resolution, a part assembly was designed with intentionally seeded defects. Porosity sized from 100 to 2000 \u03bcm shaped as spheres, triangular prisms, cylinders and cubes were seeded within the part (figure 1(c)). Additionally, defects occupying three and four layers in thickness consisting of rectangular prisms, triangular prisms, and cylinders were placed to determine the effect frommelting of subsequent layers (figure 1(c)). The range in defect size was selected to provide a range of scales for pore sizes within the detection capability of the IR camera used in this research (640 \u00d7 480 pixels with a pixel length of \u223c260 \u03bcm) and within the EBM system\u2019s resolution where the smallest defects (100 \u03bcm) were below the reported resolution for the EBM manufacturing system (\u00b1200 \u03bcm). Furthermore, Schwerdtfeger et al (2012) has identified defects as large as \u223c2 mm wide while monitoring part fabrication in EBM using an IR camera. Figure 1(a) shows an assembly design that contained three different specimens fabricated with seeded defects and analyzed using CT scanning, including, (1) analyzed as-fabricated, (2) analyzed after post-processing, and (3) analyzed after exposure to an additional melt cycle over the porous area. The assembly was implemented to facilitate the comparison between the three different specimens. The wireframe view in figure 1(b) shows the defects that were seededwithin the part to be fabricated. The post-processing method that was evaluated in this study was HIP. A HIP cycle (900 \u00b0C\u00b1 4 \u00b0C and 102MPa\u00b1 1.4MPa for 135 min) was used on the specimen with seeded defects and was selected to achieve material densification at a temperature below Ti\u20136Al\u2013 4V\u2019s beta transus (Chanhok and Rizzo 1983) of 980 \u00b0C. The in situ defect correction method that was evaluated involved a re-melt of the affected area, or a procedure thatmimics the re-scan of a part", + " Figure 3(a) shows the build file created for the part with a re-melt where a second scan was implemented over the affected areas. Figure 3(b) shows the IR image prior to the re-melt and figure 3(c) shows the IR image after the re-melt cycle occurred. Figure 3(c) demonstrates that the seeded defects were no longer present and have been corrected by the second melt scan. CT scan data were reported in 60 \u03bcm slices. Figure 4 shows a selected slice from the CT scan data showing the assembly (assembly shown in figure 1(a)) of three parts (a defective part, a part subjected to HIPing, and a part subjected to re-melt of the defect areas) and includes the dimensions of the defects in the drawing above. The brightness and contrast of the original CT scanned image was adjusted to better differentiate pores from solid areas. After analysis, the defective part (top part with the seeded defects) showed the defects larger than 600 \u03bcm still present in the CT scan up. Upon further inspection, the defects spanning three and four layers in thickness were still present", + " Furthermore, smaller defects (<600 \u03bcm) were not detected by the IR camera used in this research, which can be improved by using a camera and optics system with improved resolution. In summary, this study demonstrated that IR imaging can be used in situ to positively identify porosity or defects during AM fabrication, and that this method can be used as a means for non-destructive evaluation of AM-fabricated parts. Furthermore, the developed in situ correction strategies can be used in conjunction Figure 6.Visualization comparison between IR layerwise data (a) andCT scanning data (b) for the part shown infigure 1(a) where the IR layerwise data only represents themiddle part of the assembly. with an automatic closed loop feedback control system as a means to correct defects if detected during part fabrication using powder bed fusion AM systems. As powder bed fusion AM technologies are increasingly desired to be used in end use part production, it is hoped that this study can be used to help ensure high quality, repeatable, and reproducible components are manufactured using these processes. The research presented here was performed at The University of Texas at El Paso (UTEP) within theWM KeckCenter for 3D Innovation (KeckCenter), providing access to state-of-the-art facilities and equipment as a result of funding, most recently, from the State of Texas Emerging Technology Fund" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001463_1.4029461-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001463_1.4029461-Figure5-1.png", + "caption": "Fig. 5 (a) Contact FE model of the ball and outer race; (b) the center cross section of the FE model in (a); (c) the FE model of the outer race in defect case 7; (d) the FE model of the outer race in defect case 2; and (e) the FE model of the outer race in defect case 15", + "texts": [ + "5 10 5 times the linearized stiffness of the bearing (2.9911 107 N/m for the ball bearing studied) [43,44]. The damping coefficient c in Eqs. (37) and (38) is within this range. In this study, the static FE analysis method is used to determine the factors in Eqs. (29) and (30). The defect sizes for different cases of interest are listed in Table 2. Only one ball and an outer race with a localized surface defect are modeled using the FE analysis method. The contact FE model of the ball and outer race is shown in Fig. 5(a), which is obtained using three-dimensional solid elements and three-dimensional node-to-surface contact elements that include the elastic Coulomb frictional effect. Since the lubrication film between the ball and races is under elastohydrodynamic conditions, the effect of the contact damping is insignificant, and the Hertzian or any dry contact analysis can be used [56\u201358]. The mesh size in the contact area is 0.05 mm. The bottom surface of the outer race is fixed and an external radial load is applied at the center of the top surface of the half ball (Fig. 5(b)). The displacements of nodes on the top surface of the half ball in the Y direction are coupled so that a uniformly distributed load is applied there. Furthermore, to avoid the singularity in the pressure and deformation at the edges of the defect, a small initial gap between the ball and contact point at an edge of the defect is defined and the contact nodes are aligned (Fig. 5(b)). The FE models of abnormal races for defect cases 7, 2, and 15 are shown in Figs. 5(c)\u20135(e), respectively. The results from the FE model can be used to obtain the contact stiffness between the ball and inner race because the size of the localized surface defect is so small that the difference between the radius of curvature of the inner race and that of the outer race can be neglected in the area of the localized surface defect. To verify the FE analysis method, the radial contact deformations from the FE model with a normal outer race for different radial loads are compared with those from Hertzian contact theory, as shown in Table 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.21-1.png", + "caption": "FIGURE 11.21. A rotating link.", + "texts": [ + " Show that the angular velocity of B and the velocity of the vehicle are gw B inB + (WE + 0 and f < 0 correspond to the driver and the follower, respectively. It is noticed from Figs. 14 and 15 that the maximum values of K,,, are almost the same for both the driver and the follower. This means that the crack propagation rates are almost the same for both the driver and the follower if the lubricant penetrates into the crack interior. However, we must consider whether the lubricant can penetrate into the crack interior or not. When the right end of the Hertzian contact pressure is to the left of the crack mouth, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001216_tro.2011.2168170-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001216_tro.2011.2168170-Figure9-1.png", + "caption": "Fig. 9. Cable routings configurations of the spatial S-R-U cable-driven open chain.", + "texts": [ + " Similar to the planar case, the force closure for the spatial case can be determined by the rearrangement of (49) as follows: T = A#W + N(A)\u03bb (50) where A#(=AT (AAT )\u22121) is the pseudoinverse of A, N(A) represents the null space of A, and \u03bb represents a 1-D vector. Because of the positive cable-tension constraint, (50) is now represented as seven linear inequalities: A#W + N(A)\u03bb \u2265 0. (51) The spatial S-R-U open chain achieves force closure at a particular pose, if there exists a common interval, bounded by these seven linear inequalities. Fig. 9 presents two cable routing configurations of the spatial S-R-U open chain, similar to those in the case study examples for the planar open chains. The force-closure analysis was carried out based on the same assumptions and conditions as in the planar case study examples. Randomly chosen poses (within the joint motion constraints) for Configuration C were able to achieve force closure. However, for Configuration D, it was unable to achieve force closure in its entire workspace. This is intuitively expected as n cables attached to the n-DOF segments are unable to provide the bilateral force/moment" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003489_j.ijfatigue.2019.06.008-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003489_j.ijfatigue.2019.06.008-Figure10-1.png", + "caption": "Fig. 10. Fatigue crack propagation diagrams of the 0\u00b0-oriented V2, V4, V5 and V6 IN625 LPBF specimens for a stress ratio of R= 0.5.", + "texts": [ + " For high SIF ranges (above 50MPam1/2), where the small-scale yielding criterion is not met, there is an abrupt increase in the crack growth rate for specimens V5 and V6. The estimated fracture toughness Kc is found lower for increasing porosity. This is in agreement with the tensile testing results showing a lower elongation for these specimens. Given the roughness of the fracture surface in the presence of porosity, additional tests were conducted at R=0.5 on 0\u00b0-oriented specimens to evaluate the crack growth rate with a minimum of roughnessinduced crack closure. The Paris diagrams for the 0\u00b0-oriented specimens are shown in Fig. 10 and depict a similar behavior: in the nearthreshold region, all specimens have an equivalent behavior as well as in the Paris regime, with the exception of specimen V6, for which the crack growth rate evolution is more erratic. Finally, using the Paris diagram obtained at R=0.1, the Paris Law\u2019s constants (C and m) were evaluated using the data points in the 15\u201350MPam1/2 SIF range. The threshold SIF range \u0394Kth was also measured according to the ASTM E647 method, using the value corresponding to a crack growth rate of 10-7 mm/cycle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000737_00368791111101830-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000737_00368791111101830-Figure5-1.png", + "caption": "Figure 5 Influence of design and operating temperature on bearing losses", + "texts": [ + " A comparison of the bearing losses for the sixth gear in a manual transmission of a middle class car for original design with preloaded cross-locating taper roller bearing arrangement and alternative design with locating four-point contact ball bearings and non-locating cylindrical roller bearings on the gearbox shafts and cross-locating angular contact ball bearings of the final drive wheel (Figure 4) was calculated according SKF-GRUPPE (Hrsg.) (2004). For medium load and medium speed conditions at low gear oil temperatures of 408C, relevant for the new European drive cycle (NEDC), a reduction of the bearing losses of more than 50 per cent was found for the alternative design, because of the preload on the cross-locating taper roller bearings. At high gear oil temperatures of 908C, where the preload is reduced to almost zero, the bearing loss reduction is still around 20per cent for the alternative design (Figure 5). Figure 2 Influence of bearing type on no-load losses 8 Radial bearings Axial bearings Maximum Minimum C = 20 kN Source: Wimmer et al. (2003) Ball be ari ng Self -al ign ing ba ll be ari ng Ang ula r b all be ari ng , s ing le- ro w Ang ula r b all be ari ng , tw oro w Fou r-p oin t c on tac t b all be ari ng Cyli nd ric al ro lle r b ea rin g Cyli nd ric al ro lle r b ea rin g, fu ll Nee dle be ari ng Self -al ign ing ro lle r b ea rin g Tap er ro lle r b ea rin g Axia l b all be ari ng Axia l b all -al ign ing ro lle r b ea rin g Axia l c yli nd ric al ro lle r b ea rin g Axia l n ee dle be ari ng f 0 * dm 3 ( 10 5 m m 3 ) 6 4 2 0 Figure 3 Influence of bearing type on load losses 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.23-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.23-1.png", + "caption": "Fig. 2.23 Press drive; a) schematic of mechanism, b) dependence of press force on angular velocity of rocker", + "texts": [ + " Since the number of steps is inversely proportional to the increment, this factor is not 32 but 16 for a given interval. High accuracy is often achieved by selecting small increments but there is a risk that round-off errors add up due to the large number of steps. It can be recommended 2.4 Kinetics of Multibody Systems 129 to select at least 20 steps per (estimated) period of a cycle of motion, that is roughly \u0394t = T0/20 for a period of T0. A baler consists of a crank-rocker mechanism, the geometrical parameters of which are characterized by r4/l5 1 and r4/l4 1, see Fig. 2.23a. The dynamic behavior is to be calculated taking into account the motor characteristic, the processing force at the output and the friction moment, focusing particularly on the analysis of the influence exerted by the flywheel. The mass of link 4 is assumed to be distributed across the adjacent links. r2 = 80 mm, r3 = 320 mm, r4 = 150 mm, l5 = 1, 0 m, x15 \u2248 l4, \u03beS5 = 1, 5 m. J2 = 0, 03 kg \u00b7m2, J3 = 10; 25; 100; 200 kg \u00b7m2, m5 = 40 kg, JS5 = 36 kg \u00b7m2. Press force F0 = 7, 6 kN, see curve in Fig. 2.23b, Friction moment MR = (7, 5 + 0, 022\u03d5\u03072 2) N \u00b7m referred to angle \u03d52 , determined experimentally, see also problem P1.6 (\u03d5\u03072 in rad/s) Motor torque Man = M0(1\u2212 \u03d5\u03072/\u03a9) with M0 = 10 200 N \u00b7m and \u03a9 = 2\u03c0n Synchronous motor speed: n = 750 min\u22121 Forces from static weights are deemed negligible as compared to inertia forces. 1. Function of reduced moment of inertia J(\u03d52) 2. Functions of angular velocity and input torque in steady-state operation 3. Influence of flywheel size on angular velocity and input torque by varying J3 4. Effective power, total power and efficiency of this press drive. The solution starts by establishing the constraints, see Fig. 2.23: r2\u03d52 = \u2212r3\u03d53, x45 \u2248 r4 cos \u03d53 + l4 x45 = x15 + l5 sin ( \u03c0 2 \u2212 \u03d55 ) \u2248 x15 + l5 \u00b7 ( \u03c0 2 \u2212 \u03d55 ) xS5 = x15 + \u03beS5 sin ( \u03c0 2 \u2212 \u03d55 ) \u2248 x15 + \u03beS5 \u00b7 ( \u03c0 2 \u2212 \u03d55 ) yS5 = \u03beS5 cos ( \u03c0 2 \u2212 \u03d55 ) \u2248 \u03beS5 (2.255) If the motor angle \u03d52 is defined as the generalized coordinate, the following applies: 130 2 Dynamics of Rigid Machines \u03d53 = \u2212r2 r3 \u03d52, \u03d5\u20323 = \u2212r2 r3 \u03d55 \u2248 \u03c0 2 \u2212 r4 l5 cos ( r2 r3 \u03d52 ) , \u03d5\u20325 \u2248 r4 l5 r2 r3 sin ( r2 r3 \u03d52 ) xS5 \u2248 \u03beS5 r4 l5 cos ( r2 r3 \u03d52 ) + x15, x\u2032S5 \u2248 \u2212\u03beS5 r4 l5 r2 r3 sin ( r2 r3 \u03d52 ) yS5 \u2248 \u03beS5, y\u2032S5 \u2248 0 (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003309_978-3-319-24729-8-Figure6.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003309_978-3-319-24729-8-Figure6.3-1.png", + "caption": "Fig. 6.3 Coaxial helicopter", + "texts": [ + " The main rotor is mounted on a swash plate that varies the pitch of the rotor blades to produce appropriate roll and pitch torques. \u00a9 The Author(s) 2016 B.A. Francis and M. Maggiore, Flocking and Rendezvous in Distributed Robotics, SpringerBriefs in Control, Automation and Robotics, DOI 10.1007/978-3-319-24729-8_6 69 Fig. 6.2 Ducted fan aircraft The configuration of a conventional helicopter is not ideal for a miniature flying robot, since the energy expended by the tail rotor is not used to generate lift. A more energy efficient configuration is that of a co-axial helicopter, displayed in Fig. 6.3. This helicopter has two rotors mounted on a common axis and rotating in opposite directions. In this configuration, both rotors contribute to producing a lift force. Moreover, if \u03c4r1 and \u03c4r2 denote the torques applied by motors to the two rotors\u2014see Fig. 6.3\u2014then the helicopter body is subjected to a differential torque, \u03c4r1 \u2212 \u03c4r2 , about the rotor axis, which can be used to prevent the helicopter from spinning. Like conventional helicopters, coaxial helicopters often use swash plates for steering. Quadrotor helicopters (also called quadrocopters) are the most common flying robots. The structure of a quadrotor helicopter is shown in Fig. 6.4. It has four coplanar rotors. Viewed from the top, the rotor shafts are placed on the vertices of a square. Two rotors on a diagonal of the square rotate clockwise; the other two rotate counterclockwise" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001330_j.engfailanal.2012.05.022-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001330_j.engfailanal.2012.05.022-Figure3-1.png", + "caption": "Fig. 3. Schematic graph of spall [5].", + "texts": [ + " The mesh stiffness must be affected by the presence of tooth crack or spalling failure. It is assumed in this investigation that the model is for a large gear defect with a unique tooth. The crack failure usually develops in the tooth root circle, so the crack failure is simulated as Fig. 2, where a = 45 , p = 5 mm. The spalling failure usually develops near the pitch line of the gears, and peels off in sheets. Therefore the spalling failure in this paper is modeled near the pitch line as a rectangular indentation having the dimensions A D P as shown in Fig. 3, where A = 2 mm, D = 40 mm and P = 2 mm. The mesh stiffness can be computed by the method given in [5,6]. The effects of the two failures on mesh stiffness are shown in Fig. 4. It has been found that the crack failure will affect the distortion of the whole gear until the crack tooth secedes, while the spall will affect the mesh stiffness merely when the defect part engages meshing. The two failures affect the mesh stiffness seriously, therefore we must consider the time-variant stiffness caused by the failures" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001330_j.engfailanal.2012.05.022-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001330_j.engfailanal.2012.05.022-Figure1-1.png", + "caption": "Fig. 1. Mechanical model of a gear-pair system on deformable bearings.", + "texts": [ + " The variant stiffness is only considered as the effect of crack, while the effect of spall is determined by both the variant stiffness and defect excitation function. The effects of the two failures on mesh stiffness and dynamic mechanism are analyzed by numerical simulation. Finally, theoretical results are qualitatively validated by the vibration characteristics of the fault signals measured on an experimental gearbox. The geared rotor-bearing model investigated in the present study is shown in Fig. 1. In this model, friction forces at the mesh point are assumed to be negligible. Because of this the transverse vibrations along the directions of the line of action and the vibrations along the direction perpendicular to the line of action are uncoupled. Bearings and shafts that support the gears are represented by equivalent damping and stiffness elements as shown in Fig. 1. The damping elements are characterized by linear viscous damp coefficients c1 and c2, and the stiffness elements are defined by k1 and k2. F1 and F2 are the excitation of bearings applied to the gears. The model takes into account the so-called static transmission error, and both the stiffness kg(t) and the static transmission error e(t) can approximately be considered as time\u2013periodic functions, and the fundamental frequency of both of the quantities equals the gear mesh frequency. e\u00f0t\u00de \u00bc fm \u00fe f1 cos\u00f0xet\u00de \u00f01\u00de where xe = z1x1 = z2x2 is the mesh frequency, the integers z1 and z2 stand for the tooth number of each gear, x1 and x2 are the constant angular velocity components of the gears, fm is the mean static transmission error, f1 is the harmonic coefficient" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure9-1.png", + "caption": "Fig. 9. Illustrations of: (a) the volume of designed body, (b) auxiliary intermediate surfaces, (c) determination of nodes for the whole volume, and (d) discretization of the volume by finite elements.", + "texts": [ + " (6) to (15) are then considered at each contact point to obtain Aci, poi, \u03b4i, pi(x), pi(y), \u03c3xi(z), \u03c3yi(z), \u03c3zi(z), \u03c3Ti(z), and \u03c3Toi, i=1,2. The approach for the development of finite element models is already known and has been proposed in [14]. Some features have been incorporated here to the finite elementmodels for a better control of themesh refinement around the contact point. The proposed approach is accomplished as follows: Step 1. Pinion and gear tooth surface equations and portions of the corresponding rims are considered for determination of the volumes of the designed bodies. Fig. 9(a) shows the volume for one tooth model of the pinion of a spur gear drive. Step 2. The volume of each tooth of the model is divided into six subvolumes using auxiliary intermediate surfaces 1\u20136 as shown in Fig. 9(b). Step 3. Node coordinates (Fig. 9(c)) are determined analytically considering tooth surface equations, portions of corresponding rims, and the set of variables for mesh refinement control that are described below. Step 4. Discretization of the model by finite elements using the nodes determined in the previous step is accomplished as shown in Fig. 9(d). Step 5. The set of variables for mesh refinement control affects to the number of finite elements around the contact point P (Fig. 10). A sensitive-contact region is defined around the contact point P as follows: (i) A group of elements of regular size with dimension l\u00d7 l\u00d7 l is created in the sensitive-contact region. (ii) The size l of the elements is controlled by dimension b and number Nb. Here, b is the length of the semi-minor axis of the contact ellipse that Hertz theory predicts; Nb is the number of elements that covers dimension b" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.8-1.png", + "caption": "Fig. 1.8 Torsional oscillator; a) Torsion rod suspension, b) Suspension from multiple filaments", + "texts": [ + "18) 20 1 Model Generation and Parameter Identification It follows from this that the sought after moment of inertia of the cylinder about axis S is: JS = T 2 4\u03c02 m2gl \u2212m1r 2 \u2212m2(l \u2212 r)2. (1.19) A torsional vibration system is frequently used to determine moments of inertia. The restoring moment is achieved by either a torsion rod or a suspension from multiple filaments. It is possible to calculate the spring constant itself (absolute method), however, the sought after moment of inertia is frequently compared to a known one by determining the period using a known extra mass (relative method). In this way, the spring constant is eliminated. When using a torsion rod suspension (Fig. 1.8a), the following applies to the centroidal axis (which is the axis of rotation): JS = T 2 4\u03c02 cT; cT = GIp l (1.20) Ip polar area moment of inertia of the circular cross-section of the rod, see (1.35) G shear modulus T period of the torsional vibration without extra mass. If a known moment of inertia JZ is attached to the unknown rotating mass JS, the following applies analogously to (1.20) (JS + JZ) = T 2 Z 4\u03c02 cT. (1.21) If one eliminates the torsional spring constant from (1.20) and (1.21), the result is: 1.2 Determination of Mass Parameters 21 JS = JZ T 2 T 2 Z \u2212 T 2 . (1.22) TZ is the period with extra mass. The torsional spring can be replaced by a suspension from multiple (two or three) filaments. Using the terms from Fig. 1.8b, the following results if the vibration amplitudes are small (rotation of the body to be studied about a centroidal axis): JS = mg 4\u03c02 T 2 ab h . (1.23) Small angles from the vertical axis of the filaments during the oscillations are desirable to stay in the linear range. This can be achieved by using long filaments so that h a and h b. The pendulum device is often suspended from the roof structure of the laboratory or from the overhead crane. An extra mass can also be used in this method. A second oscillation of the pendulum is performed for which a mass mZ, with a known moment of inertia JZ, is attached to the mass to be examined", + " In models, one takes this remarkable dynamic effect into account by introducing a dynamic spring constant as follows cdyn = kdyncst. (1.61) The following applies to the typical range of rubber hardness (35 to 95 Shore): kdyn = 1.1 to 3.0, see Fig. 1.16. For the operational safety of rubber springs, their strength and heating-up are critical. At frequencies greater than 20 Hz, kdyn \u2248 2.8 to 3.2. The moment of inertia of a crankshaft with respect to its axis of rotation is to be determined experimentally using a torsion rod suspension system (Fig. 1.8). The following applies to the torsion rod: length l = 380 mm; diameter d = 4 mm; shear modulus G = 7.93 \u00b7 104 N/mm2. A time of T = 41.5 s was measured for 50 full vibrations. The moment of inertia tensor of a symmetrical body is to be determined by experiment. Pendulum tests about the three axes shown in Fig. 1.18 (k = 1, 2 and 3), which are in the symmetry plane, were performed, from which the three moments of inertia about the axes 1, 2 and 3 could be determined. Given: Moments of inertia about these axes: JS 11, JS 22, and JS 33 Find: 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002987_s00170-016-8543-2-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002987_s00170-016-8543-2-Figure12-1.png", + "caption": "Fig. 12 Deposition directions of multi-layer single-bead. a In the alternating direction. b In the same direction", + "texts": [ + " To smooth the overlapping area, a method of keeping deposition current as constant and increasing deposit velocity in the arc striking area is attempted, namely, a reduction of the ratio of wire feed speed to deposit velocity. During the arc striking area, the deposit velocity decreases gradually from a high value of 7.5 mm/s to a normal value. The change step of deposit velocity was 0.26 in the sampling period of 0.25 s. The control effect is given in Fig. 11b, in which the metal knob on the overlapping surface cannot be observed clearly. The deposited closed-path wall presents an excellent surface quality. As shown in Fig. 12, there are two kinds of deposition methods for open-path parts, namely, deposition in the alternating and in the same direction. During deposition in the alternating direction, the deposition directions between adjacent layers are opposite. In the current layer, the arc is struck in the arc extinguishing area of the previous layer, and it is extinguished in the arc striking area of the previous layer. The geometry difference of arc striking and extinguishing area is effectively used for geometry compensation in adjacent layers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.16-1.png", + "caption": "FIGURE 5.16. Alte rnative method to derive the Denavit-Hartenberg coordinate transformation.", + "texts": [ + " Forward Kinematics transformation matrices are: 1 RII R(O) or RIIP(O) 2 RIIR(180) or RIIP(180) 3 K lR(90) or K lP(90) 4 Rl-R( -90) or Rl-P( -90) 5 Rf-R(90) or Rf-P(90) 6 Rf-R(-90) or Rf-P(- 90) 7 PIIR(O) or PIIP(O) 8 PIIR(180) or PIIP(180) 9 Pl-R(90) or Pl-P(90) 10 Pl-R(- 90) or Pl- P(-90) 11 Pf-R(90) or Pf-P(90) 12 Pf-R(- 90) or Pf-P(- 90) Example 140 DH coordinate transformation based on vector addition. The DH transformation from a coordinat e fram e to the other can also be described by a vector addition. The coordinates of a point P in frame B l , as shown in Figure 5.16, are given by the vector equation -----> -----> ----+ OlP = 02P + 0 102 (5.44) where BlM [ Sl S2 S3 r (5.45) Bla;? [ X l Yl Zl r (5.46) B 2 o;} [ X2 Y2 Z2 ] T . (5.47) 5. Forward Kinematics 221 However, they must be expressed in the same coordinate frame, using cosines of the angles between axes of the two coordinate frames . Xl X2 COS(X2, Xl) + Y2 COS(Y2, Xl) + Z2 COS(Z2, xd + Sl Yl X2 COS(X2 ' Yl) + Y2 COS(Y2, yr) + Z2 COS(Z2, Yl) + S2 Zl X2 COS(X2 , Zl) + Y2 COS(Y2 ' Zd + Z2 COS(Z2 , Zl) + S3 1 X2(0) + Y2(0) + Z2(0) + 1 (5.48) The transformation (5.48) can be rearranged to be described with the ho mogeneous matrix transformation COS(Y2 ,xr) COS(Y2 ' yd COS(Y2 ' zd o In Figure 5.16 the axis X2 has been selected such that it lies along the shortest common perpendicular between axes Zl and Z2 . The axis Y2 com pletes a right-handed set of coordinate axes. Other parameters are defined as follows: 1. a is the distance between axes Zl and Z2 . 2. a is the twist angle that screws the Zl -axis into the z2-axis along a. 3. d is the distance from the Xl -axis to the X2 -axis. 4. () is the angle that screws the X l -axis into the X2-axis along d. Using these definitions, the homogeneous transformation matrix becomes, lX' ] l'~' e - sinB COS a - sinBsin a \"'0,9 ] l~:]Yl _ smB cosB cos a cos Bsin a a'tZl - 0 - sin a cos a 1 0 0 0 or l rp = lT2 2rp (5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.20-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.20-1.png", + "caption": "FIGURE 11.20. The location on the Earth is defined by longitude 'P and latitude B.", + "texts": [ + " If the discriminant is zero, th en there are three real roots, of which at least two are equal. If the discriminant is negat ive, then there are three unequal real roots. Apply thi s theory for the characteristic equation of the matrix [1] and show that the principal moments of inerti a are real. 14. Kinematics of a moving car on the Earth. The location of a vehicle on the Earth is described by its longitude rp from a fixed merid ian , say, the Greenwich meridian , and its latitude f) from the equator, as shown in Figure 11.20. We at tach a coordinat e 500 11. Motion Dynamics frame B at the center of the Earth with z-axis on the equator's plane and y-axis pointing the vehicle. There are also two coordinate frames E and G where E is attached to the Earth and G is the global co ordinate frame. Show that the angular velocity of B and the velocity of the vehicle are gw B inB + (WE + P, , the opposite occurs (the notable exception is B 6 , , , see Figure 2a and Table 11) . merge continuously at the eigenlvalues P = P, for n odd. The branches B:l bifurcate down from the lowest eigenvalue P, = 0.0675 and merge, respectively, with BSfz at P f , = 0.0128. Similarly, BZ2 joins BC3 which joins BZ, which joins BL5 which joins BL6 which joins B17 which finally joins BL7 at P f 7 = 0.0124; see Figure 2b and Table IIB. The obvious mergers also occur for the B;, . Since BL7 and BL7 join at P f 7 i.e., The pairs of unsymmetric bifurcation branches B;, yf(e, \u2018 t 7 ) = y-(. - 8, \u2018 t 7 ) = y\u2019(. - e, \u2018 6 7 ) J B&(P) must be symmetric at P = P t 7 . Furthermore, the results show that The only symmetric bihrcation branches to merge directly with each other were B,,,, and B12,1 * 552 L. BAUER, E. L. REISS AND H. B. KELLER P near the critical loads PEl and Pg2. Graph Number P Branch l / 2 l 1 4 i 0.070 I 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000346_j.matdes.2010.08.052-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000346_j.matdes.2010.08.052-Figure4-1.png", + "caption": "Fig. 4. Observation plane after fatigue test.", + "texts": [ + " It is noted that the crack length that controls the RCF life depends not only on the inclusion size but also on its composition. This issue will be discussed further. Steel B1 specimen was RCF tested and observed in order to examine fatigue cracks around inclusions. The RCF tests were interrupted at the following number of cycles; N = 5 104, 1 105 and 1 106 until flaking failure occurred. The crack observation plane was parallel to the tangential line of the rolling track and adjusted to the center of the rolling track width, as shown in Fig. 4. After polishing the observation plane was etched by picral. The observation was performed by optical microscope (OM) and Field Emission Scanning Electron microscope (FE-SEM). Fig. 5 shows fatigue cracks initiated from inclusions observed by OM and FE-SEM. All the cracks present in Steel B1 at all interrupted number of cycles N = 5 104, 1 105 and 1 106 initiated from inclusions that were identified by XREDS as Al2O3. Cracks grew from any inclusions, regardless of their size. A fatigue crack initiated from a smaller inclusion is visible in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000339_s0022112005004829-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000339_s0022112005004829-Figure10-1.png", + "caption": "Figure 10. The sense of the inertial torques arising due to sedimentation and shear for tumbling motion in the plane of shear with 1g along the flow (a) and gradient (b) directions.", + "texts": [ + "3), leading to the following modified equation for the change in orbit constant: dC dt = [ 8\u03c0 15 Re ln \u03ba sin2 \u03b8 cos2 \u03c6 + 5 16 Re2 sed Re ln \u03ba ] C. (5.4) The time t above is scaled with the shear rate. The ratio of the respective time scales of migration across a Jeffery orbit is given by tsed tshear \u2248 128\u03c0 75 sin2 \u03b8 ( Re Resed )2 . (5.5) Fibres translating perpendicular to a planar shear flow therefore exhibit the same qualitative orientation distribution as neutrally buoyant fibres at comparable Re. The directions of the inertial torques due to sedimentation and shear are shown in figure 10 for 1g along the flow and gradient directions. The torques depicted therein are for a nearly circular Jeffery orbit close to the plane of shear, and for orientations approximately aligned with the flow direction, the latter because the dominant inertial changes occur in the nearly aligned phases of a Jeffery orbit when the angular velocity of the fibre becomes small. Clearly, for 1g in the flow direction, the sense of the inertial torques arising from the sedimentation and shear mechanisms is identical near the shearing plane" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003684_j.wear.2019.01.104-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003684_j.wear.2019.01.104-Figure2-1.png", + "caption": "Fig. 2. Sliding distance of the points on gear tooth surfaces.", + "texts": [ + " According to Hertz contact theory, the half-width of contact b(i, j) of any point (i, j) in the plane of action can be obtained by = + b i j E R i j R i j R i j R i j F t L t ( , ) 8 ( , ) ( , ) ( , ) ( , ) ( ) ( ) 1 2 1 2 (28) The contact pressure of the point ij on the tooth surface in the meshing process can be written as =p i j F t b i j L t ( , ) 4 ( ) 3 ( , ) ( )ij (29) The single point observation method was proposed by Andersson [8] to determine the sliding distance of the points on the gear tooth surfaces. As shown in Fig. 2, P1, P2 are the two contact points on the driving pinion and driven gear, vpi, vni, and v\u03c4i (i=1, 2) are the kinematic velocities, normal velocities and tangential velocities of the two contact points on the driving pinion and driven gear, respectively. According to the theory of gear engagement, the normal velocities of vn1 and vn2 are equal, while the sliding distance is generated in the tangential direction. Then, the general expression of the sliding distance of the point on driving pinion and driven gear can be given as =S b i j v v 2 ( , ) 11 2 1 (30) =S b i j v v 2 ( , ) 12 1 2 (31) According to the equations of contact pressure, fractional film defect, and sliding distance, the wear depths of the driving pinion and driven gear in one mesh cycle can be described as =h i j k L p i j S i j( , ) 100 ( , ) ( , )a 1,2 1,2 (32) After n0 mesh cycles, the wear depths can be expressed as = = h i j h i j( , ) ( , ) n 1,2 1 n 1,2 0 (33) The flow chart of wear depth computation on the gear tooth surfaces is illustrated in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001146_978-3-642-05022-0-Figure1-2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001146_978-3-642-05022-0-Figure1-2-1.png", + "caption": "Fig. 1-2. Experimental set-up. a) Outlook (left), b) Scheme (right)", + "texts": [], + "surrounding_texts": [ + "The main units of experimental set-up are presented in Fig.1. The laser (1) beam is transformed by optics (2) and directed to the object (3). The unit (2) contains beam forming optics (beam expander with spatial filter) and scan lens. The intensity distribution pattern is measured by detector unit (4) and detector signal is processed by computer (5). Computer controls the step motors (6) and (7) by means of interface in/out LC-012-1612. The motor (6) drives the laser unit and motor (7) connected to worm gear (8) drive the detector. Laser and detector are supplied by separate power sources (9) and (10). The experiment was limited to the edge effect \u2013 to the area located nearby the shadow border line (where the strong diffraction effect is expected). The scheme of the set-up is presented in Fig.1b. An object O, polished steel cylinder, is placed at the focal distance of scan lens SL. He-Ne laser with beam expander fixed to the X-stage XS, form the laser head LH. Scan lens, of the focal length c = 65mm, forms the beam waist 60\u03bcm along the Z axis. In order to avoid the inaccuracies caused by the instabilities of angular deflection, the entire laser head is scanned across the Z-axis (x1 movement, linear scanning). The detector unit (fixed to the rotary table RT, coaxially with object axis) is composed of photodiode D, aperture 0.3mm A and electronic circuit. It was calibrated with the power meter (LaserMate-Q, Coherent) and obtained signal (in V) is proportional to the measured light intensity. It is driven by step motor and its smallest linear displacement is 0.026\u03bcm. Fig.1 does not show many auxiliary components like: system assuring parallel laser travel, vibration protection set-up, dark chamber, detector electronics, etc." + ] + }, + { + "image_filename": "designv10_3_0000728_s0022-0728(83)80535-x-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000728_s0022-0728(83)80535-x-Figure1-1.png", + "caption": "Fig. 1. ( . . . . . . ) Cyclic vol tammogram of electrochemically pretreated glassy carbon electrode in the absence of NADH. (A) 0.4 m M N A D H , the first scan; (B) the second and successive scans; 0.1 M K-phosphate, pH 7.0, v ~ 10 mV s - t.", + "texts": [ + " This may be accounted for by the heterogeneous composition of functional groups and also by the difference in their microenvironment. The apparent rate constant of the process ks, calculated according to ref. 13 and considering the two-electron transfer, is equal to 0.4-0.8 s-~. Electrocata[ytic oxidation of NADH and ascorbic acid Introduction of NADH into the solution studied increases the anodic current in the Ep x region and decreases the cathodic current in the Ep ea region in a cyclic voltammogram of electrochemically pretreated glassy carbon electrodes (Fig. 1). The second sweep shows a slight decrease in the N A D H oxidation current, but during the following 5-10 cycles it remains constant. The current of N A D H oxidation in cyclic voltammetry corrected with the background current has a polarographic wave shape with E~/2 -~ 0.08 V (v = 10 mV s- l ) . An increase of the sweep rate to 100 mV s-1 does not influence the plateau current value, whereas E~/2 is shifted to 0.16 V. The current of N A D H oxidation determined at a fixed potential, as well as voltamperometric measurements using a rotating disc electrode, indicate that, contrary to untreated glassy carbon, the oxidation of N A D H on electrochemically pretreated glassy carbon starts from the surface groups oxidation potential, whereas the current plateau is observed at 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002081_j.actaastro.2013.01.010-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002081_j.actaastro.2013.01.010-Figure3-1.png", + "caption": "Fig. 3. Thruster misalignment.", + "texts": [ + " There are total 12 thrusters expressed in the body frame F p and arranged in six thruster pairs, fHi,Lig,i\u00bc 1,2, . . . ,6. The nominal thrust direction of each thruster is parallel to the corresponding body axis. Each thruster is fixed on the body and only provide limited unidirectional thrust, i.e., 0rHi,Lir f m, i\u00bc 1,2, . . . ,6, \u00f015\u00de while, with the notation f0 \u00bc \u00bdf 1,f 2, . . . f 6 T, each thruster pair fHi,Lig is able to provide bidirectional thrust fi along the corresponding dimension of the spacecraft, i.e., f i \u00bcHi Li: \u00f016\u00de To consider the thruster misalignment, as Fig. 3 depicts, each thruster Hi\u00f0Li\u00de is considered to be tilted over nominal thrust direction with small unknown constant angles, fahi,bhig\u00f0fali,blig\u00de,i\u00bc 1,2, . . .6, satisfying ahirahmi, bhirbhmi and aliralmi, blirblmi, \u00f017\u00de where fahmi,bhmig\u00f0falmi,blmig\u00de are estimated bounds of corresponding error angles fahi,bhig\u00f0fali,blig\u00de,i\u00bc 1,2, . . .6, respectively. Therefore, the control torque s and force f in (11)\u2013(14) are represented by thrust fHi,Lig in (A.1)\u2013(A.6). Since the error angles fahi,bhig (fali,blig), i\u00bc 1,2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003820_tits.2020.2987637-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003820_tits.2020.2987637-Figure5-1.png", + "caption": "Fig. 5. Magnetic field distribution at rated-load for (a) healthy condition (b) fault condition with R f = 100R1turn , (c) fault condition with R f = R1turn , (d) fault condition with R f = 0.01R1turn .", + "texts": [ + " In the figure, wt represents the average tooth width of the motor, wc represents the width of single-layer winding, and lg represents the distance between the end winding and the stator core. After the simulation model is built, the impacts of the ITSC on the machine characteristics will be investigated under different fault intensities and fault resistances in this section, which can provide the references of ITSC fault detecting signals. Magnetic field distribution will be affected in case of ITSC fault, as the amplitude of short circuit current is different from current flowing in healthy turns. Fig. 5 shows the magnetic field distribution inside the stator core before and after ITSC fault occurs, in which 5 turns of a phase are short circuit and fault resistance with R f = 100 R1turn, R f = R1turn, R f = 0.01 R1turn are considered, respectively. As can be seen from Fig. 5, when the fault resistance R f = 100R1turn, the magnetic density near the fault tooth is almost the same as that in the health condition, around 1.60T \u223c 1.73T. When the fault resistance R f \u2264 R1turn, the magnetic flux density around the fault tooth decreased significantly, to about 0.8T \u223c 1.0T. Besides, as shown in Fig. 5, points A, B and C locate on the central axis of stator teeth, points D and E are the locations where ITSC fault occurs, point C is the midpoint of points D and E, point A locates near the top of tooth, and point B is the midpoint of points A and C. In order to clarify the effects of ITSC faults and fault resistance on the flux density distribution, flux density at points A, B and C with different fault resistance (100R1turnc R1turn and 0.01R1turn) in one electrical period are shown in Fig. 6 as the rotor is rotating", + " In addition, after ITSC fault occurs, reduction of active number of turns in fault branch creates a circulating current Icl between two parallel branches, as shown in Fig. 10, which results in unequal voltage U between two branches. The circulating current Icl can be expressed by equation (1). Icl = ICb1 \u2212 ICb2 2 = U Zb1 + Zb2 (1) where, Zb1 and Zb2 represent the impedance of two branches respectively. The smaller the fault resistance is, the larger the Icl amplitude will be, which will increase the local armature reaction and influence the magnetic field density much as shown in Fig.5 and Fig.7. The circulation current Icl contains a large number of odd harmonics, such as 3rd, 5th, 7th and 9th, as shown in Fig. 10. It can be found that detecting the current difference and harmonic characteristics between two parallel branches is a good method to judge ITSC fault for windings with 2 branches. Fig. 11 gives the waveforms of line voltage with different fault resistance when short circuit turns n=5. As shown in Fig. 11(a), due to the reduced active number of turns, amplitude of line voltage decreases with the increase of fault resistance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003036_j.msea.2019.138052-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003036_j.msea.2019.138052-Figure1-1.png", + "caption": "Fig. 1. Comparison of model fidelities, including mesh (left), phase field (left side color), and thermal field (right side color scale), at 20\u03bcs. The high fidelity model in a) used an adaptive meshing technique to refine phase boundaries, allowing for a sharper interface and higher solid viscosities. In b), the medium fidelity model used a coarser mesh to permit more parameter combinations, but some resolution of the interface was lost, which required lower solid viscosity for convergence, which allowed some deformation of the particle. In c), the low fidelity model only calculates thermal conduction for particles assumed to be stationary at the equilibrium wetting position (neglecting meniscus deformation for low mass particles). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)", + "texts": [ + " It was found that temperature dependent material properties introduced significant instabilities for lower fidelity models, so two sets of properties were used for different model fidelities as specified in Tables 2\u20135. Stainless steel 316 L and other parameters were chosen to most closely correspond to conditions used in previous high speed imaging experiments [3]. Initial particle velocity was set to 4m/s. For the high and medium fidelity models, boundary conditions were slip, closed, and thermally insulating on the outer perimeter boundary (as diagrammed in Fig. 1b). On the top and bottom boundaries temperature was fixed to ambient and the melt pool temperature respectively. Heat flux into the particle from the incident laser can be estimated from the laser intensity, the particles surface emissivity, and the particles cross section, so instead of including this directly in the numeric model the heat transport from the two mechanisms of conduction from the melt pool and radiation can instead be directly compared to each other to find the dominant mode, as discussed in following sections", + " Mobility (\u03b3) is set to approximately 1e-10 m\u02c63/s along the phase boundaries for the baseline simulation, and is scaled for different simulations according to the proportions proposed in Ref. [28]: \u03b3 r\u03b5 \u03c3t ~ sim 2 (4) Where tsim is the total time the simulation is run, r is particle radius, \u03c3 is surface tension, and \u03b5 is the interface thickness parameter, which is tuned to =\u03b5 25 l 2 , where l is the refined element size, which was found to provide at least eight elements across each phase interface after adaptive refinement. A timeline of the thermal and phase field evolution of the \u2018baseline\u2019 case for each fidelity of model is shown in Fig. 1. Parameters used for the baseline case can be found in Table 1. As can be seen, the model successfully predicts particle capture by surface tension and melting through conduction. As shown in Fig. 2, the initial kinetic energy of the particle is imparted to the molten steel, creating a ripple which travels to the outer edge of the modelled domain. After the particle has been heated by thermal conduction with the melt pool to the solidus temperature, it begins to melt, using the thermal field to adjust the phase composition along the interface, as enforced by the weak form Equation (2)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.10-1.png", + "caption": "FIGURE 1.10. Illustration of Stanford arm; an RI-R.lP spherical manipulator.", + "texts": [ + "lP The spherical configuration is a suitable configuration for small ro bots. Almost 15% of industrial robots, Stanford arm for instance, are made of this configuration. The Rf-R..lP configurat ion is illustrat ed in Figure 1.9. By replacing the third joint of an art iculate manipulator with a pris matic joint, we obtain the spherical manipulator. The term spherical manipulator derives from the fact that the spherical coordinates de fine the position of the end-effector with respect to its base frame . Figure 1.10 schematically illustrates the Stanford arm, one of the most well-known spherical robots. 1. Introduction 11 4. RIIPf--P The cylindrical configurat ion is a suitable configurat ion for medium load capacity robots. Almost 45% of industrial robots are made of this kind . The RIIPf--P configurati on is illustrat ed in Figure 1.11. The first joint of a cylindrical manipulator is revolute and produces a rot ation 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_3_0002746_j.applthermaleng.2017.12.019-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002746_j.applthermaleng.2017.12.019-Figure11-1.png", + "caption": "Fig. 11. Experimenta", + "texts": [ + " 7\u201310 are calculated when the axial load is 600 N. Considering the bearing configuration, we can think the load, including the thermal-induced loads is distributed equally to each bearing set. 5. Experiment and discussion In order to verify the thermal networks model established, the experiments were also implemented to measure the temperature variation of node To1 and To2, namely the temperature rise of outer rings, by the resistance temperature sensors. The experimental rig and testers are presented in Fig. 11. The front bearings 7014C of high-speed spindle were selected as test objects. The lock-ring pre-tightening was chose to preload the bearings and obtain a proper axial load. And more details on the test rig are as follows in Table 6. In experimenting the oil was first mixed with air at the oil-air lubrication rig, and next the oil-air mixture was simultaneously delivered to two bearings by outer rings. We changed the oil/air flow rate through AMO-IIID, and the spindle speed was regulated via the universal variable speed AC driver" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure6.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure6.3-1.png", + "caption": "Fig. 6.3 Kinematics of the 5 DOF arm model shown in Fig. 6.1 during an experimentally measured disc throw as reported by [4]. Figure adapted with permission from [5]", + "texts": [ + " Last, you can extract the joint angles from experimental measurements. Video, motion capture, inertial measurement units, etc. are used routinely to measure limb movements by locating fiducial markers on the body\u2014and then either human operators or algorithms are used to extract the joint angles. These classical methods commonly use regression models, model-based estimation, Kalman filters, etc., and are described in, say, [6, 7]. More recently consumer products have been developed for \u2018markerless\u2019 motion capture [8]. As an example, Fig. 6.3 takes the joint angles extracted from motion capture recordings on an arm during a disc throw from [4], and plots them using the 5 DOF arm model in Fig. 6.1 and Eq. 6.7. Now that we have the basic kinematic concepts in place, we can define the problem of overdetermined tendon excursions. First, we need some definitions that go beyond those presented in Chap. 4. Tendon excursion is a clinical term that relates the distance a tendon traverses as the limbs move and muscles contract. Mechanically speaking, we need to be more precise to understand the overall changes in the length of the musculotendon", + " A relatively realistic model of a human arm could include 17 independent muscles. As in [5], these muscles can be those listed in Table 6.1. From such a table of anatomical data one can assemble a moment arm matrix that, as per the convention in Eq. 4.21, has as many rows as there are degrees of freedom (i.e., 5), and as many columns as there are muscles (i.e., 17). Such a moment arm matrix can be transposed to calculate tendon excursions as per Eq. 4.26. Consider the disc throw motion shown in Fig. 6.3 using the moment arm matrix for the arm as per the data in Table. 6.1, the kinematic model in Fig. 6.1, and the timehistories of joint angles from [4]. From this we can calculate the muscle velocities for all 17 muscles in the model. We assumed, conservatively, that the initiation of forward motion, release, and follow-through portions of the throw lasted 450 ms; and approximated it as 45 unique postures at 10 ms time steps, as illustrated in Fig. 6.3. Figure 6.6 shows that the muscle fiber velocities in many muscles are either very fast concentrically (<\u22125 muscle fiber lengths per second), or eccentrically (<5 muscle fiber lengths per second) throughout the motion. So these muscles are either close to losing their ability to produce concentric force, or are at risk of rupturing eccentrically, respectively. For an extended discussion of these results, see [5]. This overdetermined problem raises several important questions and suggests several lines of research" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000855_tie.2011.2159357-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000855_tie.2011.2159357-Figure4-1.png", + "caption": "Fig. 4. Imaginary magnet.", + "texts": [ + " (2) Moreover, the magnetic flux distribution \u03c6(\u03b8) can be obtained as follows: \u03c6(\u03b8)= \u221e\u2211 m=1 amR0 sin{(2m\u22121)Nh\u03b8} + \u221e\u2211 l=1 \u221e\u2211 m=1 alam 2 [cos{(2l\u22121)Ns\u2212(2m\u22121)Nh}\u03b8 \u2212 cos{(2l\u22121)Ns+(2m\u22121)Nh}\u03b8] . (3) The magnetic flux distribution contains the H1(m), H2(l,m), and H3(l,m) order components, which are shown in\u23a7\u23a8 \u23a9 H1(m) = (2m \u2212 1)Nh H2(l,m) = (2l \u2212 1)Ns \u2212 (2m \u2212 1)Nh H3(l,m) = (2l \u2212 1)Ns + (2m \u2212 1)Nh. (4) The stationary part modulates the magnetic flux density distribution from the high-speed rotor magnets to produce a new imaginary magnet, shown in Fig. 4, which has Nh and Ns \u00b1 Nh pole pairs. When the high-speed rotor is rotated \u0394\u03b8, the magnetic flux \u03c6(\u03b8) is expressed as \u03c6(\u03b8)= \u221e\u2211 m=1 amR0 sin{H1(m)(\u03b8+\u0394\u03b8)} + \u221e\u2211 l=1 \u221e\u2211 m=1 alam 2 [ cos { H2(l,m) ( \u03b8\u2212H1(m)\u0394\u03b8 H2(l,m) )} \u2212 cos { H3(l,m) ( \u03b8+ H1(m)\u0394\u03b8 H3(l,m) )}] . (5) From (5), the magnetic flux components H1(m), H2(l,m), and H3(l,m) each rotate \u0394\u03b8, \u2212H1(m)\u0394\u03b8/H2(l,m), and H1(m)\u0394\u03b8/H3(l,m), respectively. To operate as a reduction gear, the number of pole pairs in the low-speed rotor should be equal to H2(l,m) or H3(l,m)", + " Therefore, the relationship among Nh, Ns, and Nl can be obtained as follows: (2l \u2212 1)Ns = Nl \u00b1 (2m \u2212 1)Nh. (6) The gear ratio is then obtained as follows: Gr = \u2213 (2m \u2212 1)Nh Nl (7) where the minus sign indicates that the low-speed rotor rotates in the opposite direction of the high-speed rotor. The cogging torque of the high-speed rotor Th(\u03b8) when both rotors rotate in accordance with the gear ratio is mathematically formulated. The total cogging torque consists of the cogging torque from the stationary part T1(\u03b8) and the cogging torque from the imaginary magnet shown in Fig. 4 [T2(\u03b8)]. We will first formulate T1(\u03b8). From the transformation law of magnetic energy to kinetic energy, the following equation is derived T (\u03b8) = \u2212\u2202W (\u03b8) \u2202\u03b8 (8) where W (\u03b8) is the magnetic energy. If we assume that the magnetic energy is only stored in the air gap where the magnetic resistance is high, then we can express W (\u03b8) as W (\u03b8) = 1 2\u03bc0 \u222b V B2dV. (9) The initial position of the high-speed rotor and stationary part is set as \u03b8 = 0, and the rotation angle of the high-speed rotor is expressed using \u03b4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003954_coase.2019.8843291-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003954_coase.2019.8843291-Figure1-1.png", + "caption": "Figure 1. Schematic of AMMT system", + "texts": [ + " Section II introduces the experimental build setup. The details of the data collected during the build and analysis of the image data is presented in Section III. Section IV and Section V present model validation results and discussions. An experimental L-PBF build was conducted on the Additive Manufacturing Metrology Testbed (AMMT) at National Institute of Standards and Technology (NIST) [32]. The AMMT is a fully customized metrology instrument that enables flexible control and measurement of the L-PBF process. Figure 1 shows the schematic of the AMMT system. Two cameras were installed for process monitoring, including a high resolution camera that captures the layerwise images of the entire part, and a high-speed camera used to capture melt pool images. The Galvo mirror system and the beam splitter allow the high-speed camera to focus on current laser melting spot. Emitted light from the melt pool, through a 850 nm bandpass filter (40 nm bandwidth), is imaged on the camera sensor. On AMMT both Galvo and laser command are updated on field programmable gate array (FPGA) at 100 KHz" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002728_chicc.2016.7555074-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002728_chicc.2016.7555074-Figure4-1.png", + "caption": "Fig. 4: Roll/Pitch axis model [10].", + "texts": [], + "surrounding_texts": [ + "In this section, we only consider the movement in the X and Y directions ( \u22114 i=1 Fi \u2248 Mg) , and with the as- sumption that roll, pitch and yaw angles are close to zero (\u03c6, \u03b8, \u03c8 \u2248 0) [15]. Therefore the X and Y position model can be simplified as follow MX\u0308 = Mg\u03b8, (11) MY\u0308 = \u2212Mg\u03c6. (12) We select X , X\u0307 , vx, sx as the state variables. X is the displacement in the X direction. X\u0307 denotes the linear velocity along X axis. A variable sx is introduced here to use an integrator in the feedback structure which is defined as s\u0307x = X . So the state space equations can be written as \u23a1 \u23a2\u23a2\u23a3 X\u0307 X\u0308 v\u0307x s\u0307x \u23a4 \u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a3 0 1 0 0 0 0 g 0 0 0 \u2212\u03c9 0 1 0 0 0 \u23a4 \u23a5\u23a5\u23a6 \u23a1 \u23a2\u23a2\u23a3 X X\u0307 vx sx \u23a4 \u23a5\u23a5\u23a6+ \u23a1 \u23a2\u23a2\u23a3 0 0 \u2212\u03c9 0 \u23a4 \u23a5\u23a5\u23a6 \u03b8, (13) where vx is defined as vx = \u03c9 s+ \u03c9 \u03b8. (14) The Y position model is similar to the X position model, so the state space equations can be written as\u23a1 \u23a2\u23a2\u23a3 Y\u0307 Y\u0308 v\u0307y s\u0307y \u23a4 \u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a3 0 1 0 0 0 0 g 0 0 0 \u2212\u03c9 0 1 0 0 0 \u23a4 \u23a5\u23a5\u23a6 \u23a1 \u23a2\u23a2\u23a3 Y Y\u0307 vy sy \u23a4 \u23a5\u23a5\u23a6+ \u23a1 \u23a2\u23a2\u23a3 0 0 \u2212\u03c9 0 \u23a4 \u23a5\u23a5\u23a6\u03c6, (15) where s\u0307y = Y and vy = \u03c9 s+ \u03c9 \u03c6. (16)" + ] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure6.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure6.1-1.png", + "caption": "Fig. 6.1 Example 6.1. Rocket fired vertically", + "texts": [ + "4), we write j m P D jd dt jam P D jd dt jam Q C jd dt j\u02dbm rP=Q C jd dt j!m j!m rP=Q : (6.5) The time derivatives given in Eq. (6.5) are displayed below: jd dt jam Q D j m Q; jd dt j\u02dbm rP=Q D j\u02dbm .j!m rP=Q/C j m rP=Q; jd dt j!m j!m rP=Q D j\u02dbm .j!m rP=Q/C j!m j\u02dbm rP=Q C j!m .j!m rP=Q/ : 9>>>>>>>= >>>>>>>; (6.6) Therefore, substituting Eqs. (6.6) into Eq. (6.5) and reducing terms yields j m P D j m Q C j m rP=Q C 2j\u02dbm j!m rP=Q C j!m j\u02dbm rP=Q C j!m j!m j!m rP=Q : (6.7) 136 6 Jerk Analysis Example 6.1. The rocket is fired vertically and tracked by radar as shown in Fig. 6.1. Determine general expressions to compute the velocity, acceleration, and jerk of rocket m as measured from the radar j. Solution. According to the fixed reference frame XY , which has associated unit vectors Oi and Oj, the position vector of point P of the rocket may be established as follows: 6.2 Fundamental Jerk Equations 137 Hence, the velocity vector v of the rocket is obtained as v D d dt r D h Pr cos. / r P sin. / i OiC h Pr sin. /C r P cos. / i Oj: (6.9) However, since the rocket moves vertically, then evidently the component along the X-axis of v vanishes, yielding Pr cos" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.21-1.png", + "caption": "Fig. 1.21 Test stand for determining the characteristic parameters of a rubber spring; 1 Loading and guidance, 2 Rubber spring", + "texts": [ + " The following estimation provides a mean value if the time until the vibrations have practically decayed is used for counting. The very small amplitudes should be ignored since \u201cyet another theory\u201d applies to those. If the decay can be tracked to about 4 % of the initial value, a calculation similar to (1.106) results in the approximation formula D \u2248 0.5 n\u2217 , (1.109) where n\u2217 is the number of vibrations until complete decay. It is desirable to determine the spring and damping characteristics at the same frequencies and amplitudes that occur under real operating conditions. Figure 1.21 shows the schematic of a test station for determining the parameters of a rubber spring and the calculation model. The energy losses due to internal damping occur because the force/deflection diagram under load does not match the one after load removal. Instead, the two curves form a hysteresis curve for steady-state motion whose area provides a measure of the energy lost during a full vibration cycle since the area in a force/deflection dia- 50 1 Model Generation and Parameter Identification gram is proportional to a work" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000993_j.jsv.2011.12.010-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000993_j.jsv.2011.12.010-Figure1-1.png", + "caption": "Fig. 1. Mechanical model of spur gear pair.", + "texts": [ + " The spur gear dynamic model with local tooth spall and time-variant mesh stiffness is established based on the model set up by El Badaoui et al., and analytical solutions of the model are obtained. The effect of spall on mesh stiffness and dynamic response is analyzed, and the vibration characteristic caused by spall is evaluated by statistical indicators. Finally, theoretical results are qualitatively validated by the vibration characteristics of spalling fault signals measured on experimental gearbox. The mechanical model of the gear-pair system investigated in the present study is shown in Fig. 1. According to this two-degree-of-freedom torsional model, the centers of both gears are not allowed to move laterally. The model takes into account the so-called static transmission error, which represents geometrical errors of the teeth profile and spacing. Moreover, both the stiffness K(t) and the static transmission error e(t) can approximately be considered as time-periodic functions, and the fundamental frequency of both of the quantities equals the gear meshing frequency. e\u00f0t\u00de \u00bc f m f 1cos\u00f0oet\u00de (1) where oe \u00bc z1o1 \u00bc z2o2 is the meshing frequency, the integers z1 and z2 stand for the teeth number of each gear, o1 and o2 are the constant angular velocity components of the gears, fm is the mean static transmission error, f1 is the harmonic coefficient" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003590_s11071-019-05073-8-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003590_s11071-019-05073-8-Figure1-1.png", + "caption": "Fig. 1 Schematic of flexible-joint manipulator model", + "texts": [ + " The problems formulation is presented in Sect. 2. Section 3 describes the IT2FNN approximator. In Sect. 4, we derive the proposed controller and verify stability of the closed loop using Lyapunov approach. Section 5 presents the feasibility and the effectiveness of proposed controller for flexible-joint manipulator by comparing with the others control methods. Finally, conclusions are drawn in Sect. 6. 2 Problem formulation This section is referenced from [17]. A schematic model of a single-link flexible-joint manipulator is shown in Fig. 1. We assume that its joint can only be deformed when rotating in a vertical plane in the direction of joint rotation. The operating mechanism of the flexible-joint manipulator is that the motor shaft and the rigid link are, respectively, driven by the motor and spring to rate. Assuming that the viscous damping is ignored and the states are measurable, its dynamic equation is given by { I q\u03081 + MgL sin q1 + K (q1 \u2212 q2) = 0 J q\u03082 + K (q2 \u2212 q1) = u (1) where q1 \u2208 Rn and q2 \u2208 Rn are the angular displacements of flexible-joint link and motor, K is the spring stiffness of joints, u \u2208 Rn is the external input, which is the torque delivered by the motor, I and J are, respectively, the moment of inertia of flexible-joint link and the motors, M is the mass of flexible-joint link, and L is the length between the center of gravity of the manipulator and flexible-joints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002307_j.jmapro.2017.05.004-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002307_j.jmapro.2017.05.004-Figure2-1.png", + "caption": "Fig. 2. Schematic of the wall width, TWW is the total wall width, and EWW is the effective wall width.", + "texts": [ + " Then stable molten pool is ormed with the sustaining heat input and solidifies rapidly after he current transforms into base current. A pure titanium substrate with the size of 150mm \u00d7 150mm \u00d7 5 mm was treated by mechanical polishing and fixed on the workbench firstly, then a deposition wall (100 mm long, about 15 cm high) was fabricated under each group of deposition parameters. The widths of the walls were quantified in the cross sections using ImageJ software. In consideration of the poor surface finish, the cross sections are divided into three areas (see Fig. 2). Area A is the effectively usable region, Area B and C need to be removed after additive manufacturing. TWW refers to the total wall width, and EWW refers to the effective wall width. The surface quality is evaluated by the surface waviness (SW), which is calculated as (TWW \u2013 EWW)/2. The first five layers are not taken into account because the condition is not steady due to the cooling effect of the base plate [17]. Five different positions on each deposition wall were selected to measure the values of EWW and SW" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure26-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure26-1.png", + "caption": "Fig. 26. Schematic illustration of: (a) boundary conditions for the pinion and the face-gear and (b) rigid surfaces applied for boundary conditions of the pinion.", + "texts": [ + " The models are determined analytically by application of the tooth surface equations. The desired number of elements are taken on longitudinal and profile directions. Fig. 25(a) and (b) show the finite element models for one tooth of the pinion and the face-gear. The development of the finite element model of the face-gear is complicated due to the specific structure of the face-gear tooth (see Fig. 11). The setting of boundary conditions on pinion and face-gear models is accomplished considering the fol- lowing ideas (see Fig. 26 for the case of a three-tooth model): (i) Nodes on two tooth sides and bottom part of the portion of the face-gear rim are considered as fixed (Fig. 26(a)). (ii) Nodes on two tooth sides and the bottom part of the pinion rim form a rigid surface (Fig. 26(a) and (b)). (iii) A reference node N (Fig. 26(b)) located on the axis of the pinion is used as the reference point of the previously defined rigid surface. Reference point N and the rigid surface constitute a rigid body. (iv) At the reference point N only one degree of freedom is defined as free, that is rotation about the pinion axis, while all other degrees of freedom are fixed. Application of a torque T in rotational motion at the reference point N allows to apply such a torque to the pinion model. The contact algorithm of the finite element analysis computer program requires definition of contacting surfaces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure12.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure12.1-1.png", + "caption": "Fig. 12.1 is a diagram of a repulsion motor in which the stator winding is on the direct axis, while the armature has a single pair of brushes displaced by Q from the direct axis. The corresponding primitive machine is Fig. 1.5 with winding G omitted. The transformation from the (a,f) frame of reference to the (d,q,f) frame is based on the fact that the resultant m.m.f. produced by the two fictitious windings D and Q is equal to that produced by the actual armature winding A. Hence the current transformation is given by", + "texts": [], + "surrounding_texts": [ + "below by the single-phase repulsion motor. Interconnected systems are illustrated by a pair of induction motors used as power selsyns. Reluctance motors and change-pole induction motors can be analyzed by the two-axis method, except where the winding arrangement is irregular enough to invalidate the assumption about the winding harmonics. Analysis of change-pole motors under transient conditions has received little attention and it is not possible to say at what point the two-axis theory would become too inaccurate. In the following section the bracket notation is used for matrices in order to avoid confusion with the bold letters indicating phasors. t 2.2.1 Repulsion motor or (i] = [C] [i'l The primitive impedance matrix [Z] is found by omitting G from Eqn. 0.5) and putting Ld = Lq = La. Hence [Z] = Rf + LfrP LmdP LmdP Ra + LaP LaW 02.2) -Lmd w -LaP Ra + LaP The power is invariant (see Section 13.2). Hence [Z'] = [CT ] [Z] [C] and the voltage equations are found to be ~ = ~R_f_+_L_f_f_P ______ ~_L_m_d_p_cO_s_a-1~ ~ Lmd(P cos a - w sin a) Ra + LaP lj" + ] + }, + { + "image_filename": "designv10_3_0002742_s00170-017-0932-7-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002742_s00170-017-0932-7-Figure3-1.png", + "caption": "Fig. 3 Quasi-static analytical model of a BCC lattice structure and its boundary conditions", + "texts": [ + " The sizes of the unit cells were determined by considering themanufacturing accuracy of the used SLM system. In this paper, the edge size of the unit cell was 5mm, and theminimum diameter of the struts in the structure with AR = 10 was ~ 0.43 mm. As Figs. 1g and 2b show, there were six unit cells along the directions of length and width, while there were three unit cells in the height direction, which was parallel to the build orientation in the SLM system. Due to the symmetry of the CADmodels, one-quarter symmetric analytical models were established, as shown in Fig. 3. To obtain internal stress distribution of a lattice structure when sustaining compressive load, its dynamic balance equation was established as M\u00bd \u20acuf g \u00fe C\u00bd u\u02d9 \u00fe K\u00bd uf g \u00bc Pf g \u00f03\u00de where [M], [C] and [K] are mass matrix, damping matrix and stiffness matrix, respectively. \u20acuf g, u\u02d9f g, and {u} are acceleration matrix, velocity matrix and displacement matrix, respectively. {P} is the force matrix sustained by the structure. {u}, u\u02d9f g and \u20acuf g were calculated analytically at any given time t through the above equation using central difference method, where \u20acuf g and u\u02d9f g at time t are \u20acuf gt \u00bc 1 \u0394t2 uf gt\u2212\u0394t \u22122 uf gt \u00fe uf gt\u00fe\u0394t \u00f04\u00de u\u02d9 t \u00bc 1 2\u0394t uf gt\u00fe\u0394t \u2212 uf gt\u2212\u0394t \u00f05\u00de When t = 0, u\u02d9 0\u2212\u0394t \u00bc uf g0\u2212\u0394t u\u02d9 0 \u00fe \u0394t2 2 \u20acuf g0 \u00f06\u00de The above-mentioned analytical method requires a definite total analysing time period, which was determined by conducting frequency analysis on the corresponding structure", + " (9), the second-order natural frequency of the structure was obtained, and the second-order frequency was then used to calculate the minimum time period (MTP). The actual time period of each model was set to be two or three times that of the MTP, thus ensuring the success of the quasi-static analysis and avoiding a time-consuming analytical process due to arbitrary and unreasonable time periods. The analytical models for prediction of lattice structures were established using ABAQUS. As shown in Fig. 3, two symmetric boundary conditions were established. The compression load was applied using the displacement technique. Two rigid surfaces with two reference points (RPs) were built to simulate the compression head and the bottom surface of the testing machine. During the simulation process, RP1 moved downward by 5 mm, while RP2 remained in place. The displacement load was applied gradually in order to guarantee the accuracy of the quasi-static analysis, which complied with a smooth-step curve related to the above-mentioned time period" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure13.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure13.7-1.png", + "caption": "Figure 13.7.1 Steer rotation of a point.", + "texts": [ + " (2) Rotate the triangle by the steer angle correction (Z axis). (3) Rotate the triangle in pitch about the axle wheel-to-wheel centreline. Note that the axle iterative solution does not actually imply any particular sequence of angles defining the axle position (e.g. roll before steer before pitch). The final result of this process is simply the axle point position coordinates. The angle sequence arises subsequently when the coordinate position is interpreted as a combination of angular displacements. Rotation of the triangle in steer is easy, Figure 13.7.1, with the Z coordinate playing no part. Given the initial (X1, Y1), R \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X2 1 \u00fe Y2 1 q d1 \u00bc atan Y1 X1 where the initial angle evaluation must obtain the correct quadrant (e.g. in Fortran use atan2). Then X \u00bc R cos \u00f0d1 \u00fe d\u00de Y \u00bc R sin \u00f0d1 \u00fe d\u00de 262 Suspension Geometry and Computation Pitching of the axle is conveniently achieved by usingXT3 as the variable, that is, theX coordinate of the upper point of the triangle, solving for a new triangle point having a knownX coordinate (XT3 \u00fe DXT3) and known distanceLT fromPT1 andH2LT fromPT2", + " Hence the first four sensitivities to X are easily determined. Similarly, for axle lateral (sway) displacement Y, the link sensitivities are qLK qY \u00bc mK where m is the Y-direction cosine. For the sensitivity to the steer angle, a numerical approach is convenient. A small temporary axle test steer displacement dT is made to the triangle, the four link connection points are calculated, and the link space length changes evaluated. Alternatively, themovement of each link point could be calculated as was shown in Figure 13.7.1, but in terms of coordinate changes, the dot product of this taken with the link direction. For the pitch sensitivity, again a numerical solution is required, using a small test increment DXT3 on triangle point 3, evaluating the link connection point positions and changes of space length. In the case of the numerical evaluation of sensitivities, the question arises as to the size of increment to use. This is not highly critical, but in practice a linear displacement in metres or angular displacement in radians of 10 4 to 10 11 works well, using 8-byte variables, with 10 7 being near the centre of the range" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003881_s00170-019-03996-5-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003881_s00170-019-03996-5-Figure1-1.png", + "caption": "Fig. 1 Sample design for chemical etching", + "texts": [ + " Also, a difference of 5 min is considerable for the electropolishing process so the time influence on the results can be evident. In this research, the sample was designed to be smaller than the scanning envelope of the micro-CT equipment. The thickness of the struts was also selected as a function of some experimental results from the literature [25, 26, 40]. It was found in some studies that the material loss after etching and electrochemical polishing (EP) was important [25, 26, 40]. Taking that information into consideration, a dimension of 2.5 mm was chosen for the internal struts shown in Fig. 1. The length of the struts was determined from the equipment used to characterize the surface finish. Twelve struts were chosen because it is a compromise between the roughness measurement time and the quantity of data gathered. Furthermore, the distance between the struts rows was large enough so that roughness measurement of the top and bottom internal flat planes can be done. Because internal roughness measurement was needed, the sample needed to be cut, and therefore, the distance between the strut rows needed to be big enough, in order to be cut with a hacksaw" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001264_j.jmatprotec.2011.09.012-Figure14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001264_j.jmatprotec.2011.09.012-Figure14-1.png", + "caption": "Fig. 14. Same depositing direction of single-pass multi-layer component.", + "texts": [], + "surrounding_texts": [ + "Different deposition directions will result in the different thermal stress evolution and distribution. To investigate the effect of depositing directions on the residual stress and residual strain of the single-pass multi-layer weld-based rapid prototyping, the single-pass ten-layer depositing process in the same depositing H. Zhao et al. / Journal of Materials Processing Technology 212 (2012) 276\u2013 285 283 d F s t t d l d F irection is also simulated. The depositing direction is illustrated in ig. 14. The material properties, the finite element mesh, the heat ource model, the initial condition, the boundary conditions, and he other depositing parameters except for the depositing direcion are the same as that of the depositing process in the reverse irection. Similarly, the stress of fore layer is partially released by the rear ayer, whereas the stress releasing direction in the same direction eposition is contrary from that in the reverse direction deposition. ig. 15. Residual stresses along central lines on substrate after depositing processes of di The comparison of residual stress distributions along the central lines of the substrate in the two depositing processes of different directions is shown in Fig. 15. The difference between residual stresses along the central line EF of components deposited in different directions is small. Along the central line GH, the residual stress of component deposited in the same direction is larger than that of component deposited in the reverse direction. The comparison of residual stresses along the central line of top surface in two depositing processes of different directions is shown in Fig. 16. The longitudinal and transversal residual stresses are both in the compressive state. The longitudinal and transversal residual stresses on the top surface in the same direction depositing are larger compressive stress than that in the reverse direction depositing. After the deposition in different directions and cooling down to the room temperature, the residual equivalent plastic strain comparison of single-pass multi-layer components deposited in different directions is shown in Fig. 17. After the two different depositing processes, the maximum residual equivalent plastic strains both appear at the connection areas between the components and the substrates, and the plastic strain at the starting arc side is larger than that at the ending arc side. The residual equivalent plastic strain distribution of the component deposited in the same direction is asymmetric and the maximum residual fferent directions. (a) Residual stresses on EF and (b) residual stresses on GH. 284 H. Zhao et al. / Journal of Materials Processing Technology 212 (2012) 276\u2013 285 ted in e u i c m m i i a a t d d 5 o n r c ( ( ( ( quivalent plastic strain is 0.0938. On the other hand, the residal equivalent plastic strain distribution of component deposited n the reverse direction is almost symmetric except for that in the onnection area between the component and the substrate and the aximum residual equivalent plastic strain is 0.0925. The maxium residual equivalent plastic strain of the component deposited n the same direction is larger than that of the component deposited n the reverse direction. Therefore, the reverse depositing direction is more approprite than the same depositing direction in terms of residual stress nd residual strain distributions. The probability of the large plasic deformation and cracks happening at the local areas in the same irection depositing process will be larger than that in the reverse irection depositing process. . Conclusions The thermal stress evolution and the residual stress distribution f single-pass multi-layer weld-based rapid prototyping compoent are researched and the effect of depositing directions on the esidual stress and the residual strain is analyzed. Following conlusions can be drawn from the study: 1) The variation trends of simulated residual stresses are in agreement with experimental results. In the weld-based rapid prototyping, there exist stress release effects of rear layers on fore layers. The effect of the heat source on the underside layers decreases with the increase of the depositing height. 2) Equivalent stress cycles at different layers of the component have similar variation trends and stress peaks descend with the increase of depositing height. Points in deposition layers undergo the stress cycle with decreasing stress peaks and the equivalent stress reaches the maximum at the end of the cooling stage. 3) The stress distributions in different areas of component have apparently different characters. The residual stress in the middle part of component keeps stable relatively, whereas relatively larger fluctuations of stresses exist in the starting and ending arc areas. The deposition of the last layer dominates the residual stress of component with the current process param- eters. 4) The residual stress and the maximum residual equivalent plastic strain of component deposited in the reverse direction are smaller than that of component deposited in the same direction. different directions. (a) Same direction and (b) reverse direction. With other parameters being constant, the residual stress and residual strain distribution can be improved by optimizing depositing directions." + ] + }, + { + "image_filename": "designv10_3_0001280_j.mechatronics.2013.04.002-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001280_j.mechatronics.2013.04.002-Figure1-1.png", + "caption": "Fig. 1. Harmonic drive components (reproduced from [1]).", + "texts": [ + " Each setup comprises a different type of harmonic drive, namely the high load torque and the low load torque harmonic drive. The results show an accurate match between the simulation torque obtained from the identified model and the measured torque from the experiment, which indicates the reliability of the proposed model. 2013 Elsevier Ltd. All rights reserved. Invented by Walton Musser in 1955, primarily for aerospace applications, harmonic drives are high-ratio, compact torque transmission systems. As shown in Fig. 1, this nascent mechanical transmission, occasionally labelled \u2018strain-wave gearing\u2019, employs a continuous deflection wave along a non-rigid gear, the so-called \u2018flexspline\u2019, to allow gradual engagement of gear teeth. Besides a thin-walled flexible cap with small external gear of the flexspline, a harmonic drive also contains two other important components, namely a wave-generator, which is a ball-bearing assembly with a rigid elliptical inner-race, and a circular-spline, a rigid ring with internal teeth machined along a slightly larger pitch diameter than that of the flexspline" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.9-1.png", + "caption": "FIGURE 4.9. An RPR manipulator robot .", + "texts": [ + "88) [ ui vers q; + cq; Ru,q, = UlUz vers q; + u3sq; UlU3vers q; - uzsq; and Ul Uz vers q; - u3sq; u~ vcrs q; + cq; UZU3vcrs q;+ UlSq; U l U3vers q; + uzsq; ] UZU3 vcrs q; - ulsq; u5 vcrs q; + cq; (4.89) d - Ru,q, d = (4.90) [ dl (1 - ui) vers q; - Ul vers q; (dzuz + d3U3) + sq; (dZU3 - d3Uz) ] dz(1 - u~) vers q; - Uz vers q; (d3U3 + d1ud + sq; (d3Ul - d1U3) . d3(1 - u5) vers q; - U3vers q; (d1Ul + dzuz) + sq; (d1Uz - dzud Example 89 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 4.9. Position vector of P in frame B2 (XZyz zz) is zrp. Frame Bz (XZyz zz) can rotate about zz and slide along Yl . Frame B 1 (XIYl Zd can rotate about the Z -axis of the global frame G(OXYZ) while its origin is at c d l . The position of P in G(OXYZ ) would then be at CR1l Rzzr p + CR11 dz+ c d l bi 0, \u2212bi < yi < bi yi + bi , yi < \u2212bi (7) and fm(ym) = \u23a7 \u23aa\u23a8 \u23aa\u23a9 ym \u2212 bm, ym > bm 0, \u2212bm < ym < bm ym + bm, ym < \u2212bm (8) where fi (i = 1, 2) are the bearing clearance functions for the support bearings; bi (i = 1, 2) are the clearances; denotes the gear backlash function; ym = \u03b7 + y1 \u2212 y2 \u2212 e(t); bm is the backlash. Substitute Eqs. (4), (5) and (7) into Eq. (3) to derive the modified gear system mathematical model \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 m1 y\u03081 + C1(t)y\u03071 \u2212 Cm(t)y\u0307m + K1(t) f1(y1) \u2212 Km(t) fm(ym) = \u2212(Cm(t)e\u0307(t) + Km(t)e(t)) = F1 m2 y\u03082 + C2(t)y\u03072 + Cm(t)y\u0307m + K2(t) f2(y2) + Km(t) fm(ym) = (Cm(t)e\u0307(t) + Km(t)e(t)) = F2 me y\u0308m + Cm(t)y\u0307m + Km(t) fm(ym) = Fm + F2 + Ft (9) where Ft = (me y\u03081 \u2212 me y\u03082) is the dynamic load. Let \u03c9n = \u221a Kam/me, \u03c9bi = \u221a Kai/mi (i = 1, 2) and introduce the nominal dimension b into Eq. (9), the nondimensionalized gear system mathematical model can be derived in the following matrix form: \u23a1 \u23a3 1 0 0 0 1 0 \u22121 1 1 \u23a4 \u23a6 \u23a1 \u23a3 \u00a8\u0303y1\u00a8\u0303y2\u00a8\u0303ym \u23a4 \u23a6 + 2 \u23a1 \u23a3 \u03be11 0 \u2212\u03be13 0 \u03be22 \u03be23 0 0 \u03be33 \u23a4 \u23a6 \u23a1 \u23a3 \u02d9\u0303y1\u02d9\u0303y2\u02d9\u0303ym \u23a4 \u23a6 + \u23a1 \u23a3 K11 0 \u2212K13 0 K22 K23 0 0 K33 \u23a4 \u23a6 \u23a1 \u23a3 f\u03031(y\u03031) f\u03032(y\u03032) f\u0303m(y\u0303m) \u23a4 \u23a6 = \u23a1 \u23a3 F\u03031 F\u03032 F\u0303m \u23a4 \u23a6 (10) where y\u03031 = y1 b , y\u03032 = y2 b , y\u0303m = ym b , \u03bei i = Ci (t\u0303) 2mi\u03c9n (i = 1, 2), \u03bei3 = Cm (t\u0303) 2mi\u03c9n , \u03be33 = Cm (t\u0303) 2me\u03c9n , t\u0303 = \u03c9nt , Kii = Ki (t\u0303) mi\u03c9 2 n , Ki3 = Km (t\u0303) mi\u03c9 2 n , K33 = Km (t\u0303) me\u03c92 n , F\u0303i = Fi mi b\u03c92 n , F\u0303m = Fm+F2 meb\u03c92 n ; the bearing clearance and backlash are f\u0303i (y\u0303i ) = \u23a7 \u23aa\u23a8 \u23aa\u23a9 y\u0303i \u2212 b\u0303i , y\u0303i > b\u0303i 0, \u2212b\u0303i < y\u0303i < b\u0303i y\u0303i + b\u0303i , y\u0303i < \u2212b\u0303i (11) and f\u0303m(y\u0303m) = \u23a7 \u23aa\u23a8 \u23aa\u23a9 y\u0303m \u2212 b\u0303m, y\u0303m > b\u0303m 0, \u2212b\u0303m < y\u0303m < b\u0303m y\u0303m + b\u0303m, y\u0303m < \u2212b\u0303m (12) where b\u0303i = bi/b and b\u0303m = bm/b. 2.2 The gear backlash estimation The backlash is the gap along the circumference direction of a gear pair [22]. In the gear meshing movement, although the gear pair is initially designed as nonbacklash meshing, there actually present backlash due to manufacture error and gear tooth wear and so forth. The gear tooth wear plays an important role in generating nonlinear dynamic backlash [20]. Traditional backlash estimationmethods include fixed value and normal distribution (N(\u03bc, \u03c3 ), where \u03bc denotes the mean value and \u03c3 denotes the standard deviation). However, previous researches [21] suggested that due to complex wear process the distribution of the gear tooth characters would not strictly meet a random distribution but follow a kind of chaotic motion. The fractal expression can be then well described the gear tooth characters. Hence, in this work the fractal theory is employed to estimate the gear backlash. The Weierstrass-Mandelbort (WM) function curve [31,32] is a standard fractal function curve to simulate/estimate the gear tooth profile character. The WM function for gear backlash estimation can be described as bm(t) = \u221e\u2211 k=\u2212\u221e \u03bb(D\u22122)k sin(\u03bbk t); \u03bb > 1, 1 < D < 2 (13) where D is the fractal dimension; \u03bb is the scale coefficient and was found to be a suitable value around 1.5 for precise analysis on gear tooth profile [31,32]. Fig- ures 2, 3 and 4 compare the fractal estimated backlash curves at \u03bb = 1.5 with the normal distribution curves. The fractal backlashwere estimatedwith different fractal dimensions D = 1.1, 1.5, and 1.7, respectively. The mean value and standard deviation of each fractal backlash curve were calculated to obtain the corresponding normal distribution curve. It can be seen in Figs. 2a, 3a and 4a that with the increase in fractal dimension D the severity of the backlash fluctuation increased although the general changing rhythm of the fractal curves was similar to each other. However, in Figs. 2b, 3b and 4b it can be noticed that there was little change in the normal distribution curves. The gear backlash was described as a random process by the normal distribution method while in theory the backlash would not strictly meet a random distribution. Because the evolution of the gear tooth profile is very slow, the backlash in continuous gear meshing movement may present quasi-periodic characteristics. Hence, by observing the quasi-periodic characteristics from the fractal curves in Figs. 2a, 3a and 4a it can infer that the fractal backlash expression approach is more suitable than the normal distribution method [22]. This viewpoint was discussed in the following section. Similar to gear backlash, the bearing clearance was also estimated by the fractal theory. 3 Validation and results 3.1 Numerical simulations Numerical method was used to calculate the dynamic response of the proposed gear nonlinear model. The simulation parameters were: K1(t) = K2(t) = 0.5 + 0.01 cos(0.1t), Km(t) = 1.0 + 0.2 cos t , \u03b31 = \u03b31 = 1.5, \u03b3m = 1.7, e(t) = 0.2 cos 4t , Fm = 0.25, me = 1.0. The dynamic response of the gear system in Eq. (10) was calculated using Runge\u2013Kutta method. Figure 5 gives the calculation results of the gear dynamics using fixed values of the backlash (bm = 0.25) and bearing clearance (b1 = b2 = 0.01). It can be seen in Fig. 5a that the dynamic response presented quasi-periodic because the chaotic attractor appeared with irregular circles and the Poincar\u00e9 map distributed into fractal points in Fig. 5b. The gear system operated in stable state with one dominated quasi-periodic cycle. Figures 6, 7 and 8 show the gear dynamics using normal distribution of the backlash and bearing clearance (b1 = b2 = 0.1bm). It can be seen in Fig. 6a that the gear system operated in stable state with two dominated quasi-periodic cycles and the fractal points appeared in the Poincar\u00e9 map in Fig. 6b. Comparing with Fig. 5a, it observed more intensive vibration around the quasi-periodic cycles in Fig. 6a when the time varying backlash and bearing clearance were considered. Moreover, when increasing the parameters of the normal distribution functions in Figs. 7 and 8, it can be seen that the gear system was no longer in stable quasi-periodic movement but followed into chaotic motions. In practice, time varying backlash and bearing clearance always appear in the gear system. The dynamic response of real-world gear system often presents strong nonlinear and non-stationary characteristics [4]. In many practical gearboxes chaotic motions are found in the vibration analysis. Hence, the calcu- lation results in Figs. 6, 7 and 8 reflected closer gear dynamics to practical results than the fixed values of the backlash and bearing clearance. Figures 9, 10 and11provide the gear dynamics using fractal estimation of the backlash and bearing clearance (b1 = b2 = 0.1bm). It can be noticed in the figures that all of the gear dynamic responses under different fractal dimensions (D = 1.1, 1.5, and 1.9) showed obvious chaotic motions. With the increase of fractal dimen- sions, the chaotic attractor become stranger, indicating stronger chaos of the gear dynamics. The chaotic motions in Figs. 9, 10 and 11 were more intensive than that in Figs. 6, 7 and 8. In order to assess the performance of the fractalmethod and the normal distribution method, the experimental data was used to compare the simulation results. 3.2 Experimental validation The experiment data were recorded from the coal cutter gear transmission system shown in Fig. 12. The experimental system consists of a data acquisition module, a 3HP driving motor, a two-stage planetary gearbox, a two-stage spur gearbox, and a controllable magnetic brake. Table 1 lists the configuration of the planetary and spur gearboxes. The vibration response of the gearboxwas collectedby thevibration sensors. Four sensors were installed on the spur gearbox (see Fig. 12). Sensors 1 and2weremountedon the left side of thegearbox in vertical and horizontal directions, respectively, and sensors 3 and 4 were mounted on the right side of the gearbox in vertical and horizontal directions, respectively. The sample frequency was 512,000Hz. During the test, in order to simulate the mining environment, x 10\u22125 (a) 6 x 10\u22126 (b) a hammer was used to knock the gearbox. Figures 13, 14, 15 and 16 show the gearbox dynamics of the experimental data from the four sensors. In Fig. 13a it can be seen that a strange attractor was observed and due to interference the phase diagramdistorted. In Fig. 13b, the Poincar\u00e9 map presented clear fractal points. These observations indicated the chaotic motion of the gear dynamic response from sensor 1. Similar results can be observed in Figs. 14, 15 and 16 when the signals from sensors 2 to 4 were investigated. Comparing the phase diagrams of different sensors in Figs. 13a, 14a, 15a and 16a it can be seen that the shapes and scales of the phase diagrams variedwith each other. This is probably a consequence of the influence of the planetary gearbox, the other shafts of the spur gearbox, and the locations of the sensors. The shapes of the phase diagrams between sensors 1 and 2 in Figs. 13a and 14a were slightly different and so were Figs. 15a and 16a between sensors 3 and 4,which implied that the installation direction of the sensor was another influence factor. It can also be seen that the scale fluctuation of the sensor signals at the left side of the gearbox in Figs. 13a and 14a was much greater than that at the right side of the gearbox in Figs. 15a and 16a. This is because the sensors at the left side were close to the planetary gearbox and thus the recorded signals of sensors 1 and 2 were directly influenced by the dynamics of planetary gears. In order to validate the simulation results using experimental data, the phase diagram and Poincar\u00e9 map in Figs. 5, 6, 7, 8, 9, 10 and 11 were compared with Figs. 13, 14, 15 and 16. It can be noticed in Figs. 13a, 14a, 15a and 16a that the main trend of the waveforms in the experiment was determined by two irregular circle patterns and their transitional process though strong noisewas observed. However, in Figs. 5a and 6a the waveforms presented only one irregular circle pattern and in Figs. 7a and 8a although two irregular circle patterns were observed the irregular circles presented a decentralized trend.Hence, the phase diagrams obtained by the fix value and normal distribution methods did not match well to the main trend of the phase diagrams in the experiment. In contrast, in Figs. 9a, 10a and 11a provided the phase diagramswith two irregular circle patterns and the transitional process between the patterns was clearly observed. It is encouraged to discover that the shape of the chaotic attractor in Fig. 11a matched to that in the experiment in Figs. 13a, 14a, 15a and 16a. Moreover, by comparing the Poincar\u00e9 maps between Figs. 11b and 15b, the Poincar\u00e9 map calculated using fractal backlash at D = 1.9 was similar to that of sensor 3 in terms of both shape and scale. These results inferred that the dynamic response obtained by the fractal backlash at D = 1.9 provided the closest result to the experimental result among the simulations. In order to quantitatively measure the similarity between the simulation results to the experiment, the two-dimension (2D) correlation analysis was applied to the simulation and experimental results. The correlation coefficients of each phase diagram in the simula- tion in Figs. 5a, 6a, 7a, 8a, 9a, 10a and 11a to the experimental phase diagrams in Figs. 13a, 14a, 15a and 16a were calculated. In order to eliminate the scale effect of the phase diagrams, the normalization processing was employed to each phase diagram in Figs. 5a, 6a, 7a, 8a, 9a, 10a, 11a, 12a, 13a, 14a, 15a and 16a. The 2D correlative coefficient was calculated by rd = \u2211 m \u2211 n ( PSmn \u2212 PSmn ) ( PEmn \u2212 PEmn ) \u221a \u2211 m \u2211 n ( PSmn \u2212 PSmn )2 \u2211 m \u2211 n ( PEmn \u2212 PEmn )2 (14) where rd is the correlative coefficient, PSmn denotes the simulationmatrix of the phase diagram,PSmn is the mean matrix of PSmn , PEmn denotes the experimental matrix of the phase diagram, and PSmn is the mean matrix of PEmn . In this work the matrix dimensions were m = 2 and n = 1,500,000. Table 2 shows the correlation degrees between the simulation and experimental results. It can be seen in the table that the phase diagram calculated by fixed backlash value (Fig. 5) failed to match any phase diagrams of the four sensors. The correlation degree was below 0.23. This means that the fixed backlash value method was not reasonable to estimate the gear tooth characters and hence was not able to establish a reliable link between the simulation and experimental results. As for the normal distribution method, the correlation degree was very low and the best correlation degree was 0.55 between Fig. 8a and the sensor 2. However, by checking Figs. 8a and 14a, the shape and scale of the chaotic attractors did not look similar. Unlike the fixed value and normal distribution methods, it can be seen that the phase diagram obtained by the fractal backlash at D = 1.9 provided the highest correlation degree of 0.76 to that of the sensor 3. By checking Figs. 11 and 15, it suggested that the scale of the chaotic attractors between the simulation and experiment is very close and although strong noise appeared in the experiment in Fig. 15a the main trends matched between the simulation and experiment results, which can be convinced by comparing the Poincar\u00e9 maps between Figs. 11b and 15b. On the other hand, if the fractal dimension D was not proper, the correlation degree become low. It can be seen in Table 1 that whenD = 1.1, the best correlation of the simulation result to the four sensors was 0.42 and whenD = 1.5 the best correlation was 0.66. These results demonstrated that the fractal expression method estimated more precise results of the backlash and bearing clearance than the fixed values and the normal distribution method. Consequently, more reliable simulation results were obtained. 3.3 Discussions In this work amulti-degree of freedomnonlinearmodel was established for coal cutter gear system taking the gear tooth characters into account. The nonlinear factors, including the time varying stiffness and damping, backlash and bearing clearance, weremodeled into the gear system. The numerical simulations were conducted to calculate the dynamic response of the gear system. The calculation results showed significant differences between different estimation methods for the backlash and bearing clearance. It is clear in Figs. 2, 3 and 4 that the fractal expression method can provide details about the fluctuation of the backlash, while the normal distribution simply described the backlash dynamics as a complete random process. Hence, the fractal expressionmethodmay bemore effective for the estimation. Compared the simulation results with the experimental validation in Sect. 3.2, it can be noticed that the fractal expression method provided more precise gear dynamics than the other two methods. The reason was that the fractal expression method provided better and reasonable estimation results for the backlash and bearing clearance. The comparison result is consistent with the conclusion in [22]. In [22] the classical single degree of freedom gear dynamicmodel with fractal expression estimated backlash was investigated; however, only numerical simulation was carried out to compare the gear dynamics between fractal expression, fixed value and normal distribution method. The experiment data were not provided to compare the simulation results and hence there was not a straightforward conclusion about the performance of the three methods. In this work, the experiment was implemented to provide strong support to the simulation results, and it is encouraged to discover that the dynamic response using fractal backlash at D = 1.9 presented reliable simulation result when compared with the experimental data. A straightforward conclusion can be drawn about the advantage of fractal expression method over the other two ways. Moreover, since the classical single degree of freedom (SDOF) model was adopted in [22], the effect of the support bearings was not considered in the dynamic response. Compared with the dynamics of the SDOF model in [22], the dynamic response of the MDOF model in this work was more complicated and presented more intensive chaotic motions. According to the experimental results, the practical gear vibration presented complex chaotic characteristics. Hence, the establishedMDOFmodel describedmore accurate gear nonlinear dynamics than the SDOF model. It is more reliable to use the presented MDOF model to investigate the gear fault mechanism." + ] + }, + { + "image_filename": "designv10_3_0001957_j.finel.2017.07.002-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001957_j.finel.2017.07.002-Figure2-1.png", + "caption": "Fig. 2. Model one set up. Dimensions in mm.", + "texts": [ + " It is two-dimensional and uses the level set method to simulate the formation of the final bead shape under surface tension and gravity forces. The geometry of the molten bead and the solidification time are imported from the first model. Model number two starts as the melt pool approaches melting temperature and ends when it drops below melting temperature. By using temperature dependent dynamic viscosity the solidification is modeled. All equations were taken directly from the COMSOL Multiphysics user's manual [21]. Model one consists of three rectangular boxes which make up a powder, solid, and build plate domain. Fig. 2 depicts the model setup with the powder domain stacked on top of the solid domain which is stacked on top of the build plate. The dimensions of each domain are specified in Table 1, where the Y-dimension is halved in the model's geometry due to planar symmetry. The powder domain, solid domain, and build plate domain represent the fresh powder layer, previously built layers, and the build plate, respectively. The laser is represented by moving Gaussian distrusted volumetric heat source that decays linearly with depth [22]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001506_s00170-012-4721-z-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001506_s00170-012-4721-z-Figure1-1.png", + "caption": "Fig. 1 Setup for laser arc hybrid welding", + "texts": [ + " A fiber laser was coupled with a tungsten inert gas (TIG) electric arc in order both to overcome the precise fit-up requirement for the joint geometry, which depends on the small beam focus diameter, and to exploit the beam deep penetration. Several experiments were made on dissimilar AISI 316 L butt welds. Two configurations of the welding source were studied; they were the laser-leading (LaTIG) and the TIG-leading (TIG-La). In the former, the laser preceded and in the latter followed the arc with respect to the welding direction (Fig. 1). The effects of the laser power, travel speed, arc current, and arc voltage were tested. The base plates were welded without any surface preparation. The joints were characterized in terms of the transverse cross-section defectiveness, the microstructure, the microhardness, and the tensile test. The efficiency of the welding process was evaluated by the ratio between the area of the fused zone and line energy. LAHW is a versatile welding technique. In fact, it tends to maximize benefits and minimize the drawbacks that characterize each combined welding process", + " It was characterized by three-axis controlled robotic units (xy-z), focus head with dual-axis control (\u03b1\u2013\u03b2) and a fixed work plan. The maximum linear speed along x-y-z axis was 20 m/min and the maximum rotational speed along the axis \u03b1 and \u03b2 66 rpm. The welding machine was equipped with an ytterbium laser source with a maximum power of 4 kW and a wavelength of 1,070 nm. The TIG source was characterized by a maximum current of 500 A in continuous mode. The combined welding source consisted of a laser source and a TIG torch, which was tilted by a \u03b8 angle respect to the workpiece surface (Fig. 1). The distance between the tungsten electrode tip and the laser beam axis was indicated with laser arc distance (DLA). The position of the two sources respect to the welding direction determined two different welding setups: laser leading (La-TIG) in which the laser is located before the TIG and TIG leading (TIG-La) where the TIG is the first acting source. Table 3 shows the process parameters at-a-glance for both configurations La-TIG (samples 1, 2, and 3) and TIG-La (samples 4, 5, and 6). The tests were conducted on 3 mm dissimilar thick butt weld" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002296_115601-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002296_115601-Figure2-1.png", + "caption": "Figure 2. Design of PBD specimen (dimensions in millimeter except volume in cubic centimeter (ccm)).", + "texts": [ + " A further advantage of this design choice is that no special or automated machining technology is needed. The user can open the specimen in the laboratory manually next to the measurement equipment. Exposure to environmental conditions such as air or moisture is reduced to a minimum while the in situ powder condition remains intact. The PBD specimen was designed following the morphological analysis as shown in tables\u00a01 and 2. This PBD specimen is 34 mm tall and has a combined nominal inner volume of 6 cm3. As shown in figure\u00a02, the diameter and the height of the inner cylindrical cavity are equal. This requirement is based on the dimensional relationship of the density cup for the apparent density measurement of metal powders according to the ASTM B212 (2009) standard. As previously described, the upper end of the cone was designed in a way that the user would be able to punch a hole through the ceiling by using a 3 mm round chisel (see figure\u00a02, Detail B). Hence, no material was removed from the specimen that could affect the metal powder or the following measurements. The specimens were built and used to collect stainless steel (S17-4 PH) metal powder in situ during a test build inside a PBF machine at the national institute of standards and technology (NIST). Nine of these specimens (labeled 1.1 through 3.3) were arranged three-by-three on a steel build platform with a size of 250 mm by 250 mm (see figure\u00a03). Note that a lattice support structure (figure 4) is needed to support each Meas" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003865_acs.2955-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003865_acs.2955-Figure1-1.png", + "caption": "FIGURE 1 The hexacopter used for the controller validation and the coordinate systems, where < w > and < b > are the global and the body coordinate systems, respectively [Colour figure can be viewed at wileyonlinelibrary.com]", + "texts": [ + " However, according to Liu et al,20 there are some challenges for the designers of control systems: the vehicle dynamics is MIMO, highly nonlinear and highly coupled, and involves various uncertainty sources, including parametric uncertainties. As a matter of fact, the parameters modeling the dynamics of such vehicles are difficult to measure and can even vary with the environmental conditions or the task itself. In the literature, several approaches can be found to model a multirotor helicopter. Most of them are based on the dynamic equation using Euler-Lagrange or Newton-Euler equations, respectively. Figure 1 displays the hexacopter and references frames defined. Kim et al21 used Euler-Lagrange equations to describe the dynamic model of a quadrotor that can be extended to any multirotor. This model has six outputs with four independent inputs, therefore, the hexacopter is an underactuated system. Accordingly, it is impossible to control all the states at the same time.22 Thus, a practical solution is controlling the multirotor position (x, y, z) and the yaw angle (\ud835\udf13), which introduces stable zero dynamics into the system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002522_j.ymssp.2016.03.014-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002522_j.ymssp.2016.03.014-Figure9-1.png", + "caption": "Fig. 9. Multi-body dynamic model.", + "texts": [ + ", Vibration mechanisms of spur gear pair in healthy and fault states, Mech. Syst. Signal Process. (2016), http://dx.doi.org/10.1016/j.ymssp.2016.03.014i Fig. 19. Deflection curves of the input shaft shaft. Fig. 20. Misalignment between the output and magnetic powder brake. caused by the convolution algorithm and the nonlinear feedback, such as high-order mesh frequencies, spurious resonant frequencies and their modulation sidebands. A rigid-flexible coupling simulation model of a single stage gearbox shown in Fig. 9 is built in LMS virtual lab. The parameters of the gear pair are listed in Table 1. The material of the gearbox is set as gray iron TH250, with density 7150 kg/m3, elasticity modulus 9000 GPa and Poisson's ratio 0.3. The mesh force between the gear pair is simulated by \u201cGear Contact\u201d, the stiffness and damping property between shafts and gearbox are simulated by \u201cBushing\u201d. The bolted connection between gearbox and base is simulated by four fixed joints. After the grid division on the gearbox housing by the tetrahedral mesh, the flexible housing has 278,333 units and 62,319 nodes in total", + " Define the exciting point as one of the finite element nodes on the bearing bore of the output shaft, Please cite this article as: Y. Li, et al., Vibration mechanisms of spur gear pair in healthy and fault states, Mech. Syst. Signal Process. (2016), http://dx.doi.org/10.1016/j.ymssp.2016.03.014i Fig. 22. The artificial broken teeth on the input gear. Fig. 23. Frequency response function from output shaft's bearing pedestal to measuring point 1. the response point as one of the finite element nodes on the top of the gearbox housing which is right above the exciting position, as shown in Fig. 9. The time-varying mesh stiffness ( )k t in the simulation model is given according to Eq. (2). Let the dynamic mesh stiffness ( )k t1 be the two order harmonics expansion, as shown in Fig. 10. Although the vibration responses analyzed in Section 2 are displacement signals, for the widely use of acceleration signal in engineering, both the vertical displacement signal and acceleration signal of the response point are collected for comparison. The sampling frequency is set as 8192 Hz, and the sampling time is 5 s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001619_tmag.2013.2285017-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001619_tmag.2013.2285017-Figure9-1.png", + "caption": "Fig. 9. CFD calculation results of the modified HSPM under the rated condition. (a) Velocity vector distribution. (b) Temperature distribution (half model).", + "texts": [ + " However, the copper loss increases due to the thicker yoke and the cooling ability of the winding is decreased due to the removal of the outer air duct. To maintain the stator temperature level, the heat transfer surface of which is increased by planting fins on the motor frame and adding edges to the outer teeth. Losses and the temperature distribution of the modified HSPM are calculated by using the same method presented above. The air flow rate, and phase current are kept the same with the original one. CFD calculated results are shown in Fig. 9. It can be seen from Fig. 9(a) that the air flow is now forced into the inner slot. More cooling air flows axially through the air gap due to the limited flow passage, which increases the convection heat transfer coefficients. Calculated hottest spot in the winding is 97.0 \u00b0C, which is only 1.0 \u00b0C higher than that of the original structure. The highest rotor temperature is 118.9 \u00b0C. The motor temperature is measured by using the same method with that of the original one under the same condition. Measured values of the highest temperature in the winding and the rotor are 98" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003197_s11661-016-3478-7-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003197_s11661-016-3478-7-Figure2-1.png", + "caption": "Fig. 2\u2014Teardrop shapes for building on 0 angle, as drawn (top) and fabricated (bottom): (a) tube, (b) horizontal t-shape, (c) vertical t-shape, and (d) reduction.", + "texts": [ + "[4] Considering these limitations, it could be stated that SLM is an asymmetric fabrication method depending on the building direction. The critical angle for overhang lies between 35 and 40 deg, and it is a material-dependent parameter.[4,5] With a larger angle than the critical angle, the build will be successful without support structures. Building without support structures is beneficial, especially in internal channels where manual removal is challenging or nearly impossible. Therefore, an internal channel cross-sectional shape of a round with a self-supporting cone with a 45-deg angle (Figure 2) described by Thomas[3] was chosen to be the best shape investigated as an internal channel possibility for building on the xy-plane at the 0 deg. During slicing of a round cross section into 2D sections, a SLM machine appoints different build parameters to different areas of the slices. These are core, up-skin, down-skin and contour.[21] Changing parameters helps to control the build more efficiently. These build parameters affect the piece roughness. Four different tubing shapes (Figure 1) with round cross sections of 10 mm were designed according to shapes commonly used in the hydraulic manifold", + " These pieces were produced by tilting the parts 5-deg in comparison to the recoating direction from EOS AlSi10Mg and EOS Ti64 powders with EOS\u2019s EOSINT M270 DUAL Mode machine. Parameters used for AlSi10Mg and Ti6Al4V are compiled in Table I. The layer thickness is 0.03 mm for both materials, and the building platform temperature for aluminum is 373 K (100 C) and for titanium is 353 K (80 C). Pieces were manufactured from AlSi10Mg with different building angles of 0, 35, 40, 45, 60, 80, and 90 deg with respect to the building platform (Figure 3). In order to build the pieces in horizontal 0-deg angles, a round cross section was modified to teardrop shape (Figure 2) consisting of a round bottom and triangle with 45-deg decline in the top, so being self-supporting. Teardrop is a geometric figure that resembles most the round cross section without modifying too much. However, a sharp edge can be disadvantageous in thin wall structures. Ti6Al4V pieces were manufactured only with 45-deg build angle. Fabricated pieces were first analyzed optically with macrophotography and a stereomicroscope for any abnormalities before cutting. The internal diameter and roundness were checked optically by fitting an ellipse on the top and bottom surfaces of the pieces in ImageJ" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-FigureA.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-FigureA.9-1.png", + "caption": "Fig. A.9 Coordinate frames assigned to planar 2 link arm with the Denavit\u2013Hartenberg convention and corresponding Denavit\u2013Hartenberg parameters. This example also serves to show that one can label the basis vectors of 3D frames of reference by other names, such as x, y, and z, which are then assigned to a specific frame of reference by their subscripts as in x2, y2, and z2", + "texts": [ + "35 is called the homogeneous transformation matrix defined as [2, 3] T n+1 n = \u23a1 \u23a3 Rn+1 n pn,n+1 0 0 0 1 \u23a4 \u23a6 (A.36) v0 = T 1 0 T 2 1 T 3 2 T 4 3 T 5 4 v5 (A.37) T 5 0 = T 1 0 T 2 1 T 3 2 T 4 3 T 5 4 (A.38) v0 = T 5 0 v5 (A.39) where T 5 0 = \u23a1 \u23a3 R5 0 p0,5 0 0 0 1 \u23a4 \u23a6 (A.40) A.8 Standard Denavit\u2013Hartenberg Convention As a brief aside I introduce the Denavit\u2013Hartenberg convention [11]. It is a useful and popular convention to place and describe frames of reference conveniently and concisely. You will surely encounter it in the robotics literature. It is shown for the arm example in Fig. A.9. For an in-depth discussion see [2, 11\u201313]. Each frame of reference (after the global frame of reference 0) is placed in a systematic manner to obey the convention and accurately define each of the 4 parameters. This convention is most often discussed as articulating frame n \u2212 1 to frame n (and not from frame n to n +1 as is the case for rotation and homogeneous transformation matrices). According to the convention, we defined each axis of rotation as a z-axis about which the next distal link rotates (i", + " To transform from 1 DOF zn\u22121 to the next distal DOF zn via their common normal xn (which points toward zn), one needs 4 Denavit\u2013Hartenberg parameters (\u03b8 , d, a, \u03b1). The 4 \u2018standard\u2019 Denavit\u2013Hartenberg parameters (as opposed a variant, the \u2018modified\u2019 Denavit\u2013Hartenberg parameters) are specified as follows [12]: \u2022 Rotation of xn\u22121 about zn\u22121 by an angle \u03b8n \u2022 Translation along zn\u22121 by dn \u2022 Translation along xn\u22121 by an , and \u2022 Rotation of zn\u22121 about xn by \u03b1n By convention, the DOF joint variable is \u03b8n for revolute joints (my qn DOF in this book where the link length is an), and dn for prismatic joints. The parameters for the arm example are shown in Fig. A.9. Once the Denavit\u2013Hartenberg parameters are determined, the procedure for finding the endpoint is standardized (in fact, it was developed to be implemented computationally for arbitrary systems) by means of homogeneous transformations expressed in terms of these parameters. The 4 \u00d7 4 homogeneous transformation matrix is shown in Eq. A.41. The nth parameter set can be used to transform points from frame n back to frame n \u2212 1. T n n\u22121 = \u23a1 \u23a2\u23a2\u23a3 cos(\u03b8n) \u2212 sin(\u03b8n) cos(\u03b1n) sin(\u03b8n) sin(\u03b1n) an cos(\u03b8n) sin(\u03b8n) cos(\u03b8n) cos(\u03b1n) \u2212 cos(\u03b8n) sin(\u03b1n) an sin(\u03b8n) 0 sin(\u03b1n) cos(\u03b1n) dn 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (A.41) Let us take the arm shown in Fig. A.9 as a brief example. The transformation matrix T 2 1 uses the Denavit\u2013Hartenberg parameters from frame 2 and the transformation matrix T 1 0 uses the Denavit\u2013Hartenberg parameters from frame 1 to produce the following transformation T 2 0 matrix, from which we can directly get the coordinates of the endpoint as the last column of the homogeneous transformation matrix shown in Eq. A.42. T 2 0 = T 1 0 T 2 1 = \u23a1 \u23a2\u23a2\u23a3 0.966 \u22120.259 0 11.5 0.259 0.966 0 25.9 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (A.42) While this is not an exhaustive treatment of the kinematics of serial manipulators, homogeneous transformations, or the Denavit\u2013Hartenberg convention, it suffices for the purposes of this book to know that there are several ways to find the location and orientation of the endpoint of a limb in analytical form" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.3-1.png", + "caption": "Fig. 2.3 Description of a spatial rotation", + "texts": [ + "6) These two times three equations each correspond to a matrix equation if one introduces the vector l\u2217 = (x\u2217, y\u2217, z\u2217)T and the rotational transformation matrix A1: A1 = \u23a1\u23a31 0 0 0 cos q1 \u2212 sin q1 0 sin q1 cos q1 \u23a4\u23a6 ; AT 1 = \u23a1\u23a31 0 0 0 cos q1 sin q1 0 \u2212 sin q1 cos q1 \u23a4\u23a6 . (2.7) The rotational transformation matrix is orthonormal, resulting in the following relationship with the unit matrix E A1(A1) T = E; (A1) T = (A1) \u22121. (2.8) Thus the relationships (2.6) are as follows: l = A1l \u2217; l\u2217 = (A1) Tl. (2.9) In a spatial rotation, the elements of the rotational transformation matrix A depend on three angles to be defined specifically. The cardan angles that are designated q1, q2 and q3 here are used to describe the position of the body, see Fig. 2.3. The fixed x-y-z system and the body-fixed \u03be-\u03b7-\u03b6 system coincide in the initial position. When rotating the outer frame about the angle of rotation q1, the x axis is retained (x = x\u2217), and the plane of the inner frame becomes the new y\u2217-z\u2217 plane. The angle of rotation q2 describes the rotation of the inner frame about the positive y\u2217 axis that coincides with the y\u2217\u2217 axis, so that the x\u2217\u2217-z\u2217\u2217 plane, which is perpendicular to that, takes a new position. The angle of rotation q3 finally relates to the z\u2217\u2217 axis that coincides with the \u03b6 axis of the body-fixed coordinate system. The \u03be-\u03b7 plane is perpendicular to z\u2217\u2217 = \u03b6. The body-fixed \u03be-\u03b7-\u03b6 system takes an arbitrary rotated position relative to the fixed x-y-z system upon these three rotations. Each of the three rotations in itself represents a planar rotation about another axis. According to Fig. 2.3, the following three elementary rotations apply: l = A1l \u2217; l\u2217 = A2l \u2217\u2217; l\u2217\u2217 = A3l. (2.10) The rotational transformation matrices for rotations about the y\u2217 and z\u2217\u2217 axes can be obtained starting from the projections onto the other planes in analogy to Fig. 2.2. The following matrices implement the rotations about the angles q2 and q3 of the respective axes: 72 2 Dynamics of Rigid Machines A2 = \u23a1\u23a3 cos q2 0 sin q2 0 1 0 \u2212 sin q2 0 cos q2 \u23a4\u23a6 ; A3 = \u23a1\u23a3 cos q3 \u2212 sin q3 0 sin q3 cos q3 0 0 0 1 \u23a4\u23a6 . (2", + "20) but also by projecting the angular velocity vector onto the directions of the respective system of reference. Differentiation of the velocity in (2.25) and (2.27) finally provides the absolute acceleration of a point in the following form: r\u0308 = v\u0307 = d(r\u0307O + \u03c9\u0303l) dt = r\u0308O + \u02d9\u0303\u03c9l + \u03c9\u0303l\u0307 r\u0308 = v\u0307 = r\u0308O + A( \u02d9\u0303\u03c9 + \u03c9\u0303 \u03c9\u0303)l = r\u0308O + ( \u02d9\u0303\u03c9 + \u03c9\u0303\u03c9\u0303 ) l, (2.28) 2.2 Kinematics of a Rigid Body 75 where the first line uses coordinates in the fixed system and the second line references the rotational transformation matrix and the coordinates in the body-fixed coordinate system. Figure 2.3 shows a rigid body that can freely rotate (in the sketched massless apparatus) about three axes in space. A rigid body that can only perform three rotations is called a gyroscope. The position of the gyroscope can be uniquely described using cardan angles q = (q1, q2, q3) T, see. (2.14). If one uses the matrix A and its time derivative A\u0307 to determine the product according to (2.20), one obtains the matrix of the tensor of angular velocity \u03c9\u0303, which contains the following components as matrix elements: \u03c9x = q\u03071 +q\u03073 sin q2 \u03c9y = q\u03072 cos q1 \u2212q\u03073 sin q1 cos q2 \u03c9z = q\u03072 sin q1 +q\u03073 cos q1 cos q2", + "29) For the body-fixed reference system, the components of the angular velocity are derived according to (2.21) using the \u03c9 = AT\u03c9 transformation after performing matrix multiplication and some manipulations of the trigonometric functions: \u03c9\u03be = q\u03071 cos q2 cos q3 +q\u03072 sin q3 \u03c9\u03b7 = \u2212q\u03071 cos q2 sin q3 +q\u03072 cos q3 \u03c9\u03b6 = q\u03071 sin q2 +q\u03073. (2.30) The magnitude \u03c9 of the angular velocity \u03c9 results from (2.24): \u03c9 = \u221a q\u03072 1 + q\u03072 2 + q\u03072 3 + 2q\u03071q\u03073 sin q2. (2.31) It follows from here that the magnitude of the angular velocity for gimbal-mounting according to Fig. 2.3, at constant angular velocities is not constant in general, but only if either (q\u03071 or q\u03072 or q\u03073) is zero. If the condition is met that the fixed x-y-z-system and the body-fixed \u03be-\u03b7-\u03b6system coincide in their initial positions, the angle coordinates \u03d5x \u2248 q1; \u03d5y \u2248 q2; \u03d5z \u2248 q3, (2.32) can be introduced for small angles of rotation |q1| 1; |q2| 1; |q3| 1 (2.33) that describe \u201csmall motions\u201d. Since sin qk \u2248 qk and cos qk \u2248 1, it follows from (2.14) and (2.20): 76 2 Dynamics of Rigid Machines A \u2248 \u23a1\u23a3 1 \u2212\u03d5z \u03d5y \u03d5z 1 \u2212\u03d5x \u2212\u03d5y \u03d5x 1 \u23a4\u23a6 (2", + " Pure rolling of the center plane of the roller at the grinding level is assumed. Roller radius R Distance to the center of gravity \u03beS Angular velocity of the axle \u03d5\u0307(t) Find: 1.Rotational transformation matrix A 2.Angular velocity vector both in fixed (\u03c9) and in body-fixed (\u03c9) coordinate directions 3.Velocity and acceleration distribution along AB 78 2 Dynamics of Rigid Machines S2.1 The system in Fig. 2.4 is a special case of the gimbal-mounted gyroscope with regard to the rotational motion, see Fig. 2.3. The body-fixed components of the angular velocity of the body result from (2.30) with \u03b1 = q1, \u03b2 = q2 = 0 and \u03b3 = q3 as follows: \u03c9 = [ \u03c9\u03be, \u03c9\u03b7 , \u03c9\u03b6 ]T = [\u03b1\u0307 cos \u03b3, \u2212\u03b1\u0307 sin \u03b3, \u03b3\u0307]T. (2.36) The components of the angular acceleration \u03c9\u0307 are the derivatives with respect to time: \u03c9\u0307\u03be = \u03b1\u0308 cos \u03b3 \u2212\u03b1\u0307\u03b3\u0307 sin \u03b3 \u03c9\u0307\u03b7 = \u2212\u03b1\u0308 sin \u03b3 \u2212\u03b1\u0307\u03b3\u0307 cos \u03b3 \u03c9\u0307\u03b6 = \u03b3\u0308 . (2.37) The position of point P is described, according to (2.17), using the body-fixed reference point O, the rotational transformation matrix A, and the coordinate in the body-fixed system: rP = rO + lP = rO + AlP " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.26-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.26-1.png", + "caption": "Fig. 2.26 Slider-crank mechanism; a) nomenclature, b) curve of the reduced moment of inertia", + "texts": [ + " Given: moments of inertia of the motor: J2 = 2, 14 kg \u00b7m2; coupling: J3 = 1, 12 kg \u00b7m2; gear mechanism 1: J4 = 22, 6 kg \u00b7m2; referred to gear mechanism 2: J5 = 4540 kg \u00b7m2; transmission output engine room: J6 = 1, 185 \u00b7 108 kg \u00b7m2; Top section masses: m7 = 2, 05 \u00b7 104 kg; m8 = 1, 85 \u00b7 105 kg; Top section lengths: l7 = 110 m; l8 = 61 m; Gear ratios: u42 = u43 = 627; u54 = u64 = 36, 2 Note that the sequence of indices is relevant for the gear ratio (\u03d5\u2032 k = u2k = 1/uk2) and that it is defined as the ratio of input to output angular velocities, see (2.212). 1.Input torque of the motor required to move the top section at an angular acceleration of \u03d5\u03086 = 0.0007 rad/s2. 2.Input torque M6 referred to the swivel axis. 134 2 Dynamics of Rigid Machines Slider-crank mechanisms are used for transforming rotational into translational motions (and vice versa). The moment of inertia referred to the crank angle is required for dynamic calculations. Given: Dimensions and parameters according to Fig. 2.26a. 1.Reduced moment of inertia Jred using 2 equivalent masses for the connecting rod 2.Mean value Jm for the reduced moment of inertia 3.Input torque at \u03d5\u03072 = \u03a9. \u03bb = l2/l3 1 applies to the crank ratio. This fact can be utilized by expanding the appearing root expressions into series and neglecting \u03bb2 with respect to 1. Two possible placements of the flywheel can be used in a design. Either JS1 or JS2 are to be used to maintain a specific coefficient of speed fluctuation, see Fig. 2.27. Moments of inertia JM; JG; J0; J1; J1 J0; coefficient of speed fluctuation \u03b4zul; Gear ratio u21 = n1/n2 > 1", + " Slider-crank mechanisms are used in many machines for converting rotating into reciprocating motions (and vice versa) so that mass balancing has met with special interest for quite some time. Let us first derive the conditions for the complete inertia force balancing in a slider-crank mechanism without offset. Complete balancing of the resultant frame 164 2 Dynamics of Rigid Machines moment can be achieved using additional rotational inertia, see VDI Guideline 2149 Part 1 [35]. The position of the center of gravity of the slider-crank mechanism follows from the link positions according to Fig. 2.26: (m2 + m3 + m4) rS = m2rS2 + m3rS3 + m4rS4 (2.336) If the motion plane is identified with the plane of complex numbers for the purpose of compact mathematical treatment, then r = x+jy = r \u00b7ej\u03d5 = r \u00b7(cos \u03d5 + j sin \u03d5) (j = \u221a\u22121) applies and the position of the centers of gravity of the links can be stated as follows in accordance with Fig. 2.26: rS2 = \u03beS2e j\u03d52 ; rS3 = l2e j\u03d52 + \u03beS3e j\u03d53 ; rS4 = l2e j\u03d52 + l3e j\u03d53 (2.337) Insertion into (2.336) provides the center-of-mass trajectory: (m2 + m3 + m4)rS = m2\u03beS2e j\u03d52 + m3(l2e j\u03d52 + \u03beS3e j\u03d53) +m4(l2e j\u03d52 + l3e j\u03d53) = ej\u03d52(m2\u03beS2 + m3l2 + m4l2) + ej\u03d53(m3\u03beS3 + m4l3) (2.338) The center of gravity remains at rest (r\u0308S = o), and there are no resultant inertia forces that act onto the frame if the following balancing conditions are satisfied (setting the expressions in parentheses to zero): m2\u03beS2 + (m3 + m4)l2 = 0 (2", + " Perform mass balancing on the crank shears as shown in Fig. 2.49 in such a way that complete balancing of the forces is achieved by adding balancing masses to the crank and to the rocker. roll 170 2 Dynamics of Rigid Machines S2.11 According to (2.303), and taking into account the functions xSi = xSi (\u03d52(t)) and ySi = ySi (\u03d52(t)), one can write: Fx = \u2212\u03d5\u03082 I\u2211 i=2 mix \u2032 Si \u2212 \u03d5\u03072 2 I\u2211 i=2 mix \u2032\u2032 Si; Fy = \u2212\u03d5\u03082 I\u2211 i=2 miy \u2032 Si \u2212 \u03d5\u03072 2 I\u2211 i=2 miy \u2032\u2032 Si (2.348) Since the nomenclature used here mostly coincides with that in Fig. 2.26a, the first-order position functions can be taken directly from Table 2.1; the prerequisite stated there regarding the crank ratio \u03bb is satisfied. \u03bb = l2/l3 = 0, 04 m/0, 75 m = 0, 0533\u0304 1 is obtained for the given parameter values. Using the functions from Table 2.1, and after another differentiation with respect to \u03d52, one obtains: x\u2032\u2032 S2 = \u2212\u03beS2 \u00b7 cos \u03d52; y\u2032\u2032 S2 = \u2212\u03beS2 \u00b7 sin \u03d52 x\u2032\u2032 S4 = \u2212l2 \u00b7 (cos \u03d52 + \u03bb cos 2\u03d52) (2.349) The balancing mass has the following center-of-gravity coordinates in the fixed system, see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002645_j.addma.2017.11.005-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002645_j.addma.2017.11.005-Figure1-1.png", + "caption": "Figure 1: DED cylinders were deposited onto Ti6Al4V substrates in order to facilitate turning experiments. Cylinder dimensionsinternal diameter-62 mm, outer diameter- 72 mm, height- 50 mm, wall thickness-5mm", + "texts": [ + " However, there is a shortage in contributions to understanding the machining issues associated with the post processing of DED Ti6Al4V. ACCEPTED M ANUSCRIP T In this study, the effect of heat treatment, tooling and processing routes on the machinability of DED components are investigated. This study aims to also further investigate the role of microstructural variation on machinability and the resulting surface properties. 2.0 Experimental Methods The DED apparatus used here is as described in a previous study [5]. An array of cylinders were produced using this technique. A CAD model of the cylinders is shown in Figure 1. The substrate used was a titanium alloy plate of 12 mm thickness. The DED process was repeatable with the components built to dimensions without obvious distortion. The deposition parameters used for the creation of the cylinders is detailed in Table 1. Optimum parameters used in deposition of the components was taken from the previous study where similar sized cylinders were deposited [5]. Post deposition heat treatment was carried out on a selection of the deposited cylinders in a vacuum furnace operating at a vacuum pressure of less than 10-3 mbar for all processes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002809_tmag.2015.2493150-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002809_tmag.2015.2493150-Figure1-1.png", + "caption": "Fig. 1. The motor geometry in the s-plane", + "texts": [], + "surrounding_texts": [ + "The CM method is an analytical and numerical tool for solving all kinds of 2D fields (magnetostatic, electrostatic, etc.). This combined analytical and numerical method offers far more facilities than other analytical and semi-analytical methods. In this paper, three CMs are used to reach the main canonical domain (annular domain) [27-29]." + ] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure8.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure8.8-1.png", + "caption": "Fig. 8.8 Simplified phasor diagram for the initial current and", + "texts": [ + " Hence the use of the phasor diagram to detennine the initial currents after a sudden change follows the same lines as the steady-state two-axis method. Simplified phasor diagrams for transient changes When the generator is connected to a power system the calcula tions required by the two-axis theory become rather complicated. The method is greatly simplified if the assumption is made that each quadrature-axis reactance is equal to the corresponding direct-axis reactance, that is: Xq = Xd' (zero 'transient saliency'), Fig. 8.8 is a phasor diagram showing the result of these assumptions. The points N, N' and N\" on the two-axis diagram (shown dotted) move to M, M' and M\", which all lie ~n a straight line through P perpendicular to the current phasor l PM is the synchronous reactance drop (-jXdl), PM' is the transient reac tance drop (-jX d '1), and PM\" is the sub transient reactance drop (-jX d\"l). The assumption that Xq = Xd for steady operation means that the generator is treated as a unifonn air-gap machine. Us. the voltage behind synchronous reactance, is then equal to OM, and the generator can be represented by a source of constant voltage Us with the synchronous reactance Xd in series", + " With this assumption U', the voltage behind transient reactance, is equal to OM', and the generator can be represented by a source of constant voltage U' with the transient reactance X d' in series. For the calculation of 'rapid' transients, where the initial values of voltage and current immediately after a sudden change are required, the approximate method assumes that the machine has 'zero subtransient saliency', or that Xq \" = Xd\". For most modern machines the assumption is a reasonable one, particularly as the sub transient reactance is small compared with the reactances in the external power system. U\", the voltage behind sub transient reactance, is equal to OM\" in Fig. 8.8, and the generator can be represented by a source of constant voltage U\" with the subtransien t reactance X d\" in series. Synchronous Generator Short-Circuit and System Faults 191 The approximate methods discussed above provide the basis for simple means of detennining the currents in a power system under certain conditions, since the generator can be replaced by its driving voltage and reactance appropriate to the particular condition. The system then becomes an ordinary network of lumped elements and any of the well-known methods of network analysis can be used", + "44), is neglected the voltage drops suddenly from the original voltage U to the initial voltage Xe U/(X d' + Xe), which would be calculated by considering the generator to have a voltage U behind its transient reactance. Finally the steady voltage XeU/(Xd + Xe) could be calculated in accordance with ordinary steady-state theory by considering the generator to have a voltage U behind its synchronous reactance. Thus the curve showing the variation of the terminal voltage could be calculated by using the phasor diagram of Fig. 8.7 or Fig. 8.8 to determine the initial transient values and the steady value, and then fitting in appropriate time constants for the components of the change. The transient time constant Td t' depends on the external reactance. It is equal to Td' when Xe = 0 (short-circuit), and is equal to TdO ' when Xe = 00 (open circuit). For any given load impedance, Td t' is intermediate between these two extremes. Similarly the subtransient time constant Td t\" is intermediate between Td \" and TdO \". A calculation of this kind is valuable in studying the action of a voltage regulator used to maintain a constant voltage" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001188_cca.2010.5611206-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001188_cca.2010.5611206-Figure1-1.png", + "caption": "Fig. 1. Configuration, inertial and body fixed frame of the quadrotor.", + "texts": [ + " Indoor flight requires a suitable type of vehicle as well as suitable control, navigation and collision avoidance algorithms. Concerning the vehicle type, helicopter-like vehicles are among the most promising candidates with respect to size, weight, maneuverability and the ability for slow and even hovering flight. One special helicopter-like vehicle with the additional advantage of a simple construction and rotor mechanics is the quadrotor. The quadrotor is a system with four propellers in a cross configuration, see Fig. 1 for a sketch of a quadrotor UAV. While the front and the rear motor rotate clockwise, the left and the right motor rotate counter-clockwise which nearly cancels gyroscopic effects and aerodynamic torques in trimmed flight. One additional advantage of the quadrotor compared to a conventional helicopter is the simplified rotor mechanics. By varying the speed of the single motors, the lift force can be changed and vertical and/or lateral motion can be generated. However, in spite of the four actuators, the quadrotor is a dynamically unstable nonlinear system that has to be stabilized by a suitable control system", + " The nonlinear controller as derived in [6] is first shortly introduced, followed by a short introduction in the reinforcement learning algorithm applied in this work. Finally, some first experimental as well as simulation results are presented in order to compare the two approaches. The general dynamic model of a quadrotor UAV has been presented in a number of papers, see e.g. [1], [3], [4], [5] or [6], and therefore will not be discussed here in all details again. We consider an inertial frame and a body fixed frame whose origin is in the center of mass of the quadrotor, see Fig. 1. The attitude of the quadrotor is given by the roll, pitch and yaw angle, forming the vector \u2126T = (\u03c6, \u03b8, \u03c8), while the position of the vehicle in the inertial frame is given by the position vector rT = (x, y, z). The dynamic model of the quadrotor can be derived by applying the laws of conservation of momentum and angular momentum, taking the applied forces and torques into account (see [6]). The thrust force generated by rotor i, i = 1, 2, 3, 4 is Fi = b \u00b7 \u03c92 i whith the thrust factor b and the rotor speed \u03c9i, and the law 978-1-4244-5363-4/10/$26", + "00 \u00a92010 IEEE 2130 of conservation of momentum yields r\u0308 = g \u00b7 0 0 1 \u2212R(\u2126) \u00b7 b/m 4\u2211 i=1 \u03c92 i \u00b7 0 0 1 (1) Herein, R(\u2126) is a suitable rotation matrix. With the inertia matrix I (a pure diagonal matrix with the inertias Ix, Iy and Iz on the main diagonal), the rotor inertia JR, the vector M of the torque applied to the vehicle\u2019s body and the vector M G of the gyroscopic torques of the rotors, the law of conservation of angular momentum yields: I\u2126\u0308 = \u2212 ( \u2126\u0307 \u00d7 I\u2126\u0307 ) \u2212M G + M (2) The vector M is defined as (see Fig. 1) M = Lb(\u03c92 2 \u2212 \u03c92 4) Lb(\u03c92 1 \u2212 \u03c92 3) d(\u03c92 1 + \u03c92 3 \u2212 \u03c92 2 \u2212 \u03c92 4) (3) with the drag factor d and the length L of the lever. The gyroscopic torques caused by rotations of the vehicle with rotating rotors are M G = IR(\u2126\u0307 \u00d7 0 0 1 ) \u00b7 (\u03c91 \u2212 \u03c92 + \u03c93 \u2212 \u03c94) (4) The four rotational velocities \u03c9i of the rotors are the real input variables of the vehicle, but for a simplification of the model, the following substitute input variables are defined: u1 = b(\u03c92 1 + \u03c92 2 + \u03c92 3 + \u03c92 4) u2 = b(\u03c92 2 \u2212 \u03c92 4) u3 = b(\u03c92 1 \u2212 \u03c92 3) u4 = d(\u03c92 1 + \u03c92 3 \u2212 \u03c92 2 \u2212 \u03c92 4) (5) Defining uT = (u1, u2, u3, u4) and (\u03c91 \u2212 \u03c92 + \u03c93 \u2212 \u03c94) = g(u) and introducing the vector of state variables xT = (x\u0307, y\u0307, z\u0307, \u03c6, \u03b8, \u03c8, \u03c6\u0307, \u03b8\u0307, \u03c8\u0307), evaluation of (1) until (5) yields the following state variable model: x\u0307 = \u2212(cosx4 sin x5 cos x6 + sin x4 sin x6) \u00b7 u1/m \u2212(cosx4 sin x5 sin x6 \u2212 sinx4 cos x6) \u00b7 u1/m g \u2212 (cos x4 cosx5) \u00b7 u1/m x7 x8 x9 x8x9I1 \u2212 IR Ix x8g(u) + L Ix u2 x7x9I2 + IR Iy x7g(u) + L Iy u3 x7x8I3 + 1 Iz u4 (6) Herein, we use the abbreviations I1 = (Iy \u2212 Iz)/Ix, I2 = (Iz\u2212Ix)/Iy and I3 = (Ix\u2212Iy)/Iz " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001941_tnnls.2015.2506267-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001941_tnnls.2015.2506267-Figure5-1.png", + "caption": "Fig. 5. Networked-control-based robotic mechanism with a backlash gearing connection.", + "texts": [ + " Moreover, these control algorithms also have obtained a widespread of applications, such as those in bilateral teleoperation robots and synchronization of time-delayed Lur\u2019e chaotic systems. Taking this pioneering research as basis, we will further consider the coexistence problem of transmission time delays, quantization, and asymmetric actuator backlash in our future research. In the first example, let us consider a networked-controlbased robotic manipulator with asymmetric backlash nonlinearity, as visualized in Fig. 5. Its dynamics has the following Lagrangian equation form [55]: Jq\u0308(t)+ Dq\u0307(t)+ MgL sin(q(t)) = u(t) u = B(vq), vq = q(v) (58) where q and q\u0307 denote the angle and angular velocity of the rigid link, respectively. J represents the rotation inertia of the servo motor. D is the damping coefficient, while L is the length from the axis of joint to the mass center. The mass of the link is notated as M. g is the gravitational acceleration. The specific system parameters are summarized in Table I. In this simulation, the objective is to control the system output q(t) to track the desired trajectory qr = sin(4t)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000952_cpa.3160230402-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000952_cpa.3160230402-Figure12-1.png", + "caption": "Figure 12. Graphs of W ( 0 ) for P = 6 x decreasing from k = lop5 (the thin sphere) to k = 2 x low6. For k = the solution corresponds to a point on and a sequence of values of k The values of k x lo5 are 1, 0.8, 0.6, 0.4, and 0.2 for the graphs numbered 1 through 5 in that order.", + "texts": [], + "surrounding_texts": [ + "We shall discuss the relevance of the results previously described to the axisymmetric buckling of perfect spherical shells under idealized experimental conditions; that is \u201cGedanken buckling\u201d. We discuss primarily the thick sphere since the results are most comprehensive in this case. But our remarks are equally applicable to the thin sphere and no doubt to a wide range of k values. The basic premise is that we have determined all of the relevant axially symmetric equilibrium states of the shell for all loads in some large range: 0 P 5 P,,, . Constant reference to Figures l a and 2 and Table I1 is required for this discussion. We imagine the pressure increasing continuously from P = 0 and allow only axisymmetric deformations. The sphere contracts radially (corresponding 560 L. BAUER, E. L. REISS AND H. B. KELLER to the trivial solution w 0) for small P since this is the only existing equilibrium state. However, as soon as P exceeds Pkl = P& = 0.01045, two additional equilibrium states exist corresponding to the branches B6,1 and B 6 , 0 . Suppose for the present that the shell does not jump or is somehow constrained from jumping to another equilibrium state. Then as the load continues to increase the sphere uniformly contracts, regardless of the numerous states which AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 56 1 become possible, until P finally reaches the lowest eigenvalue. In the thick sphere case this is P, . At this pressure it may be possible for the sphere to deviate from perfect sphericity without jumping by merely deforming continuously into the bifurcated mode of solution. In general, if the bifurcation branch branches up (down) this smooth transition can occur only for P increasing (decreasing). Thus since B5,1 branches down from P5 such a smooth transition cannot occur at P5 as P increases.8 For other values of k , e.g., k = 1.2 x the lowest eigenvalue is symmetric (see Figure 13). Therefore, a smooth transition into the bifurcation branch as P increases is possible. 562 L. BAUER, E. L. REISS AND H. B. KELLER We recall that for the bifurcation branches B2m,l passing through each symmetric eigenvalue P,, , the energy e2m. l ( P ) is monotone decreasing. Thus as P increases beyond some P,, the unbuckled state has more energy than the state on B2m,l . If we make the reasonable assumption that at a bifurcation point states with least energy are preferred, then the thick sphere smoothly deforms into the state on B,,l as P goes from P, past P, . However, suppose k=.ooi , P=.oi996 Figure 14a. Graphs of W(f3) for two of the 16 solutions at P = 0.01996 for the thick sphere. Two other solutions are shown in Figure 14b. The remaining solutions are not shown since they differ little from the first solution shown in Figure 14b. Figure 14h. Graphs of W(0) for two of the 16 solutions at P = 0.01996. AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 563 the shell remains spherical as P increases beyond P, and P,. Then at the unsymmetric eigenvalue P, , whose branches B7fl bifurcate up, the smooth transition can occur onto one of the unsymmetric branches. Thus in summary, if jump-buckling is somehow prevented or just does not occur, the uniformly contracted sphere smoothly deforms into a nonspherical shape as P increases past a symmetric eigenvalue or an unsymmetric eigenvalue which branches up. We call smooth transitions to nonspherical states, as P increases, \"bifurcation buckling\". Then all the symmetric eigenvalues, P,, , are bifurcation buckling loads and so are those unsymmetric eigenvalues, P, ,+ l , with upward branching solutions. Let us now consider that bifurcation buckling has occurred at P = P, and P continues to increase. The states of deformation correspond to solutions on some upward bifurcating branch B n , l . However, as P increases beyond the upper critical point P x l , the deformation cannot vary continuously with P since the branch Bn,l ceases to exist. Thus the shell must jump to some other non-adjacent equilibrium state. Therefore, we call P g l a jump buckling load. Clearly, Pz\",,l are all jump buckling loads and so are those Pz\",+l,l which are endpoints of upward bifurcating branches. For example, PFl = 0.0858 for the thick sphere is a jump buckling load while P z l = P, + 0.0675 is not. Let us return to the unconstrained thick sphere experiments in which bifurcation buckling need not precede jump buckling. As has been observed, only uniform contraction can occur for P < P t l which we therefore term the lower buckling load PL. Since P, is not a bifurcation buckling load, we conclude that as P increases over the interval PL = 0.01045 < P < P, = 0.07062 the thick sphere can become nonspherical only by jumping into a buckled state. The multiplicity of solutions varies over this interval. For example, at P = 0.01 5 there are eight such solutions corresponding to the branches 9: B,*o, B6,1 , BZ1 , B& , 32,. Of these solutions only those on B6,1 and B& have more energy than the unbuckled state at P = 0.015. The states with negative energy are in some sense preferred to the unbuckled state. Jumping to a state of negative energy cannot occur for P < P f o . We must invoke some mechanism for the shell to jump into one of these states of negative energy. The usual such mechanism is attributed to imperfections and/or disturbances of the original spherical shell, of the loading procedure, of the shell support, etc. The transition is actually dynamic and since there are many buckled states present with energy less than the unbuckled state we do not know which state is the one finally preferred. The number and character of the buckled states which coexist at a given pressure may influence the possibility of jump buckling. Thus the triggering mechanism which causes the shell to jump, no doubt, depends on the interaction of the As another example, consider P = 0.01996 where there are 16 solutions on the branches: B6,0 , B,,l, B& , j = 1, 2, . . . , 7 . All but the three solutions on B,,l and B z l have less energy than the uniformly contracted sphere with P = 0.01996. In Figures 14a, b we show 4 of these s o h tions. 564 L. BAUER, E. L. REISS AND H. B. KELLER imperfections, disturbances and the kind of buckled states that exist a t a given pressure. The possible buckling mechanism just described is such that precise jump buekling loads cannot be defined. However, we note that, for P just below a symmetric eigenvalue or an unsymmetric eigenvalue whose bifurcated solutions branch down, there must always be buckled states very close to the unbuckled state but with slightly more energy. An example is P, for the thick sphere. These states could also supply the triggering mechanism for jump buckling in experiments with very small imperfections or disturbances. In such a case the observed jump buckling load should be less than the lowest eigenvalue, that is, P, for the thick sphere. Of course, if the imperfections are so small that they do not cause jump buckling, then as P increases bifurcation buckling must occur a t P, and finally jump buckling must occur at P x l . If we allow axially unsymmetric states there may be additional bifurcation branches and other buckled states. A numerical study of these additional bifurcation branches has not yet been initiated. However an analysis of the axially unsymmetric bifurcation branches near the eigenvalues and the effects of imperfections is given in [8] using a different shell theory. We have only considered axisymmetric deformations in this study. Appendix I" + ] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.20-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.20-1.png", + "caption": "FIGURE 2.20. A position vector r, in a local and a global frame.", + "texts": [ + " Alternatively, rotation of a local frame when the position vector B r 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 (Oxy z) with respect to a fixed global frame G(OXYZ) , as shown in Figure 2.20. 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 B r and Gr respectively. The transformation from G r to B r is equivalent to the required rotation of the body frame B(Oxyz) to be coincided with the global frame G(OXYZ). 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: (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002912_1.4039092-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002912_1.4039092-Figure4-1.png", + "caption": "Fig. 4 FE meshes of (a) thin-walled rectangular part without selective mesh coarsening, (b) thin-walled cylindrical part without selective mesh coarsening, (c) thin-walled rectangular part with selective mesh coarsening, and (d) thin-walled cylindrical part with selective mesh coarsening", + "texts": [ + " Similar to the conventional method, the new framework was implemented using the hybrid method for the thermal simulation and the inactive method for the structural analysis. Thermal and structural analyses of each layer were performed sequentially as per the schematic in Fig. 2. Selective mesh coarsening was implemented in four stages as illustrated in Fig. 3 for both the parts. Grayscale represents the relative mesh density of each mesh region. Implementation of each mesh region of the part is shown in Table 5. The discretized geometries used for the smaller parts for both the new and conventional FE frameworks are shown in Fig. 4 (at the last discretization step). Figures 4(a) and 4(b) are the FE meshes used for the conventional analysis without any selective mesh coarsening. Figures 4(c) and 4(d) are the FE meshes used in the new framework. Eight-node hexagonal elements, DCC3D8 for thermal analysis and C3D8 for structural analysis, were used for both the frameworks [21]. Laser heat source was modeled using universal cylindricalinvolution-normal [22] model Q r; z\u00f0 \u00de \u00bc kKzgLP p 1 exp Kzs\u00f0 \u00de\u00f0 \u00de exp kr2 \u00fe Kzz r \u00bc x2 \u00fe y2 (9) where gL is the laser efficiency, x, y, and z are the local coordinates, KZ\u00bc 3/s represents heat source power exponent, s is the laser beam penetration depth, k \u00bc 3=r2 0 is the beam focus coefficient, and r0 is the radius of the laser beam" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001657_icra.2015.7139508-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001657_icra.2015.7139508-Figure2-1.png", + "caption": "Fig. 2. The quad tilt rotor UAV developed.", + "texts": [ + " Section III explains dynamics modeling for the quad tilt rotor UAV. 978-1-4799-6923-4/15/$31.00 \u00a92015 IEEE 2326 Section IV proposes control system with low calculation cost for on-board calculation on the basis of PID control. Section V shows simulation and experimental verification. Finally Section VI summarizes the conclusions. The developed UAV has 8 control inputs, four of which are used for the rotation of the propeller and four of which are used for the tilting motion for each propeller. Fig. 2 shows the quad tilt rotor UAV developed. It weigh 1.4 [kg], has a diameter of 0.45 [m] (without propellers), and a height of 0.25 [m]. The body frame of the UAV is constructed from a medium density fiberboard and each rotor rod is made of carbon fiber. The tilt rotor mechanism is unique development. The rotor is tilted using of a radio-controlled servo (MD260, Hnege Co). The rotor rods radiate from the center of the body. Their root is mounted on the rotation axis of the tilt servo. Furthermore, each rotor rod is supported by a bearing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001858_s00170-017-0066-y-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001858_s00170-017-0066-y-Figure9-1.png", + "caption": "Fig. 9 The comparison result between the TM and SM by using the 3D optical scanner", + "texts": [ + "9 ) Bd(oita r N/ S Scan speed(mm/min) (a) (b) (c) In order to evaluate the geometric accuracy of the sprocket tooth after laser cladding, a 3D optical scanner (3DSS-STD-II) with a resolution of 0.03 mm was used to measure the surface of the sprocket tooth which has just been repaired. The point cloud of the repaired zone was imported to the Geomagic Studio software, and the repaired zone was compared with the standard model of the sprocket tooth. The comparison result between the test model (TM) and standard model (SM) is shown in Fig. 9. The maximum positive deviation (+2.974 mm) is found in the A and C zones, which can be attributed to the accumulation of the powder in laser cladding. The positive deviation in the C zone also offers the machining al lowance for machining of the sprocket . Meanwhile, the negative deviation is also found in the B and D zones. The deviation in B zone is related to the fillet between the SM and TM or the wear of the sprocket in the course of service. However, the deviation of the D zone can be attributed to the powder loss in laser cladding" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001337_s10846-013-9936-1-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001337_s10846-013-9936-1-Figure3-1.png", + "caption": "Fig. 3 Complete model of the mobile manipulating unmanned aerial system", + "texts": [ + " First, and extensive mathematical model of the aerial robot system is presented, followed by a stability analysis of low level attitude controllers. Next, the two nonlinear adaptive control techniques are presented (i.e. gain scheduling and model reference adaptive control). Finally, nonlinear control techniques are tested and verified in simulations. These simulations and experiments serve to show the efficacy and performance of the proposed hybrid nonlinear control concept. The proposed mobile manipulating unmanned aerial system, featuring a quadrotor UAV and two multi DOF manipulators, is shown in Fig. 3, and a table of dynamic parameters is given in Table 1. Using the recursive Newton-Euler approach andDenavit-Hartenberg parameterization for forward kinematics, each arm is modeled as a serial chain RRRR manipulator (Fig. 2) [20]. The connection between the quadrotor body frame and the first joint of each arm is represented with static revolute joint with a constant angular offset for each MM-UAV arm (Link B-0). Applying the results from [21] quadrotor dynamics are introduced to the aerial platform of the robot. 2.1 Manipulator Model Denavit-Hartenberg (DH) parameters of the manipulator arms shown in Fig. 2 are given in Table 2, and Fig. 3 depicts the overall UAVmanipulator system. Parameters \u03b8 , d, a, and \u03b1 are in standard DH convention and q1 i , q 2 i , q 3 i , and q4 i are joint variables of each manipulator arm i = [A, B]. Since the whole aircraft is symmetrical, the general kinematic structure is identical for the right and left arms, the coordinate frames are the same for each arm, and only the link B-0 is different for the two arms. Reference frames are shown in Fig. 2 which relate the fist joint L1 to the end effector frame E" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003035_j.ast.2019.06.017-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003035_j.ast.2019.06.017-Figure3-1.png", + "caption": "Fig. 3. Four-wheel pyramid configuration.", + "texts": [ + ", see [24] and [29]), the derived controller not only makes the settling time and residual sets of the attitude and angular velocity errors independent on system initial conditions as well as design parameters, but also can specify the maximum overshoots of the attitude errors less than preset constants. In this section, simulation experiments are carried out on a small satellite to testify the efficacy of the proposed algorithm. The satellite carries a charge-coupled device (CCD) camera to take high-resolution images of some hot areas, and is equipped with four reaction wheels (abbreviated as RW1-RW4) mounted in a typical pyramid configuration for attitude motion [16], as shown in Fig. 3. The maximum output torque of each reaction wheel is set to 0.5 Nm. The nominal inertia of the satellite is given as J = [55, 0.3, 0.5; 0.3, 65, 0.2; 0.5, 0.2, 58] kg\u00b7m2. The disturbance torque takes the same form as that given in [15]. In the simulations, the initial conditions of the satellite are set as \u03c3 (0) = [0.5, 0.2, 0.6]T and \u03c9(0) = [\u22120.01, 0.01, 0.01]T rad/s. The desired attitude trajectory is specified by the initial attitude \u03c3 d(0) = [0, 0, 0]T and the angular velocity \u03c9d = 0.573 \u00d7 [cos(t/40), sin(t/30), \u2212 cos(t/50)]T deg/s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure3.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure3.9-1.png", + "caption": "Fig. 3.9 Phasor diagram of a salient pole synchron ous generator.", + "texts": [ + " For a machine with salient poles (indicated by dots in Fig. 3.5), the m.m.f. diagram in Fig. 3.6 remains unchanged. However, the flux density no longer bears the same ratio to the m.m.f. at every point, and therefore must be determined by resolving the armature m.m.f. into components Fd andFq along the two axes. It is assumed that each component of m.m-:f. produces a proportional flux along the same axis, but that the factor of proportionality is different for the two axes. The figure OSLT of Fig. 3.9 is the modified voltage phasor diagram based on this assumption. The component phasors Fd and Fq in the space phasor diagram of m.m.f.s (Fig. 3.6) correspond to component phasors Id and Iq in the time phasor diagram of currents (Fig. 3.9). The voltage induced by the direct-axis component of flux is represented by LT in Fig. 3.9, and is equal to jXm dId , where X md is the direct-axis magnetising reactance. Similarly the voltage induced by the quadrature-axis component of flux, represented by SL, is equal to jXmqIq , where X mq is the quadrature-axis magnetizing reactance. The open-circuit voltage Uo, the internal voltage Uj, the resistance and leakage reactance drops, and the terminal voltage U remain as before. The voltage phasor equation of Fig. 3.9 is where Xq = Xm q + Xa (quadrature-axis synchronous reactance). (3.5) Thus the two-axis phasor diagram of the salient-pole machine is in itself little more complicated than the diagram of the unifonn air-gap machine. It is, however, more difficult to apply, because The Steady-State Phasor Diagrams of A.C. Machines S3 the resolution of the current phasor introduces the unknown angle (J. It is not possible to derive a simple single equivalent circuit for determining the current corresponding to a given supply voltage", + " The angle 0 is also called the load angle, because its value varies progressively with the load. If the rotor lags behind the reference axis, 0 is positive, and the machine acts as a motor, developing motoring torque which tends to accelerate the rotor. When the rotor leads the reference axis, the machine is a generator and causes the opposite effect. The curve relating the input power P and the load angle li is called the power-angle characteristic. The value of li is given by the angle between Uo and U in the phasor diagram of Fig. 3.9, which has been drawn particularly for generator action when the value of li is negative. Hence the angle between U and Uo is the positive angle lig = -li. Moreover the electrical input power P is negative for generator operation, and the generator output is Pg = -P. The relation between Pg and lig can be deduced from Fig. 3.9 as a simple expression if the armature resistance Ra is neglected. The Steady-State Phasor Diagrams of A.C. Machines 55 are used for the magnitudes of the phasors representing the currents, the magnitudes of the direct and quadrature-axis components of synchronous reactance drop are Xd1d and Xqlq. Thus Fig. 3.10 agrees with Eqn. (3.5) if the resistance drop is omitted. In order to determine 1) g' a line RQ is drawn perpendicular to the current phasor, meeting OS at Q, and a perpendicular QN is dropped on OR produced", + " The safe operating region on the P-Q chart is limited by the following consideration: curve AB is part of a circle with centre M and is determined by the maximum safe field current; curve BC is part of a circle around 0 and is determined by the maximum safe armature current; the horizontal line CD is determined by the maximum safe prime mover output while the vertical line MD is the theoretical steady-state stability boundary occurring, in a uniform air-gap machine, when l) = 90 degrees. In practice, Z is not permitted to move as far left as line MD, because the latter represents a condition of instability where the smallest increment in load causes the machine to fall out of step. Hence a safety margin between MD and curve EF is allowed. The area enclosed by points ABCFE is called the safe operating area. A similar chart based on Fig. 3.9 can be drawn for the salient pole machine [18]. Chapter Four The General Equations of A.C. Machines Any machine, other than those with commutators, consists of a set of coils for which voltage equations can be written in terms of self and mutual inductances and resistances. The machine however differs from a static circuit in that the coils are in relative motion and consequently that some of the inductances are functions of the relative position. The idealized synchronous machine of Fig. The self-inductances Lff, Lkk d, Lkk q of the field and damper coils and the mutual inductance Lfkd, between F and KD, are all constants", + " operation, the speed of the machine is the constant synchronous speed wo. The field voltage and current are constant, the damper currents are zero, and the armature phase voltages and currents are balanced three-phase quantities. Hence, if zero time is taken as the instant when phase e = wof, U z = i z = O. From the transformation equations (4.5) and (4.7), the voltage and current in phase A are: ~a = ~d cos wof + U q si.n wof, } la =ld cos w of+iq smwof. 133 (7.1 ) Now if the voltage and current in phase A are represented by phasors U and I, as in Fig. 3.9, the components of the phasors are related to the axis quantities as shown below. The component phasors of current are indicated in Fig. 3.9 by the symbols Id and Iq in heavy type. Let the magnitudes of the components be denoted by I d and I q in ordinary type. Then Hence Id = Id + j \u2022 0, Iq=O+jlq Similarly let the magnitudes of the components of voltage be Ud and Uq . ia = Re[y'2(ld +jlq)eiwot] } = y'2(ld cos wot - Iq sin wot), U a =y'2(Ud cos wot - Uq sin wot) (7.2) Since both pairs of relations stated by Eqns. (7.1) and (7.2) hold for all values of t, it follows, by equating coefficients, that id = y'2Id, Ud =y'2Ud, iq = - y'2Iq , u q =-y'2Uq \u2022 Hence for steady operation at synchronous speed the axis voltages and currents are all constant quantities independent of time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002203_j.msea.2016.04.042-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002203_j.msea.2016.04.042-Figure1-1.png", + "caption": "Fig. 1. Configuration of fatigue specimen.", + "texts": [ + " The chemical composition (wt%) of the conventional type 630 was as follows; Cr: 15.58, Ni: 4.22, Cu: 3.31, Mn: 0.81, P: 0.35, Nb: 0.28, Si: 0.26, C: 0.04, S: 0.01, Fe: bal. This material had been solution treated at 1050 \u00b0C for 1 h, followed by water quenching in the as-received condition. Hereafter, this material was referred as \u201cconventionally melted (CM) specimen\u201d. The smooth round-bar fatigue specimens with a diameter of 8 mm and a gauge length of 10 mm were fabricated by the SLM method as shown in Fig. 1. Prior to fatigue tests, the gauge section of specimen was mechanically polished using progressively finer grades of emery paper followed by buff-finish. Table 1 shows the mechanical properties of CM type 630 after solution treatment. In the SLM and SLM-quenched specimens, tensile test was not performed due to the limitation of sample number. Fatigue tests in laboratory air at an ambient temperature were performed using an Ono-type four-point rotating bending fatigue testing machine with a capacity of 98 Nm operating at a frequency of 57 Hz", + " In the data plotted on da/dN-\u0394K/E relationship, where E\u00bc174 GPa in Table 1 was used, the results of SLM and SLM-quenched specimens are within the 1 2 band. On the other hand, the data of CM specimen are on the upper boundary of the band. Therefore, it is concluded that the fatigue crack growth resistances of SLM and SLM-quenched specimens are similar to the other metallic materials, while the CM specimen has slightly lower growth resistance. In the present study, the SLM and SLM-quenched specimens had lower fatigue strengths than the CM one in spite of higher growth resistances. That is because specimen size is relatively small as shown in Fig. 1, and consequently fatigue lives are mainly dominated by fatigue crack initiation resistances. 5. Conclusion Fatigue tests of type 630 stainless steel fabricated by selective laser melting (SLM) method were conducted. Post-heat-treated (SLM-quenched) and conventionally-melted (CM) type 630 were also used for comparison. The fatigue strengths and crack growth behavior were discussed on the basis of the results of fatigue tests and fractographic observations. The results obtained are as follows. ) In the CM specimen, the microstructure consisted of uniformlydistributed fine acicular martensite" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000339_s0022112005004829-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000339_s0022112005004829-Figure1-1.png", + "caption": "Figure 1. Coordinate system used for calculation of fibre drift in simple shear flow.", + "texts": [ + " The general form for such a term, excluding contributions arising from solid-body rotation, is given as (pcorr)i = \u03b11 Eij\u2126jkpk + \u03b12 \u2126ijEjkpk + \u03b13 EijEjkpk +\u03b14 (Eklpkpl)\u2126ijpj + \u03b15 (Eklpkpl)Eijpj , (3.13) where the \u03b1i are proportionality constants. Purely axial contributions of the form c p, c being a scalar, must be added in order for the fibre to be inextensible, i.e. for ( p\u0307jeff + Re p\u0307corr) \u00b7 p =0 to be satisfied; they do not lead to a change in orientation, however, and are therefore not included in (3.13). For a general linear flow, one can always choose a fibre-aligned orthogonal coordinate system (see figure 1) with the 1-direction along the fibre axis p, and the 3-direction perpendicular to the vorticity vector (\u03c9). Thus, 13 is directed along \u03c9 \u2227 p; for simple shear, this constrains it to lie in the flow\u2013gradient (XY ) plane. With this system of axes, elements such as \u212623, E23 etc. are seen to drive fluid motion in a plane transverse to the fibre axis, leading to velocity disturbance fields that scale with the fibre diameter rather than its length, and are therefore not relevant in the slender-body approximation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure14.20-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure14.20-1.png", + "caption": "Figure 14.20 illustrates a polar manipulator that is controlled by a torque Q and a force P . The base actuator rotates the manipulator and a force P slides the second link on the first link. Find the optimal controls to move the endpoint from PI (1.5 m, 1 m) to Pz(-1, 0.5 m) for the following data:", + "texts": [], + "surrounding_texts": [ + "14. * Tim e Optimal Control 639\n9. * Motion of a mass under friction and spring forces.\nFind the optimal control command If(t)1 ~ lOON to move the mass m = 1kg rest-to-rest from x(O) = 0 to x(tf) = 10m. The mass is moving on a rough surface with coefficient J.L and is attached to a wall by a linear spring with stiffness k, as shown in Figure 14.18. The value of J.L and k are\n(a)\n(b)\nJ.L = 0.1\nJ.L =0.5\nk = 2N/m\nk = 5N/m.\n10. * Convergence conditions.\nVerify Equations (14.92) to (14.97) for the convergence condition of the floating-time algorithm.\n11. * 2R manipulator moving on a line and a circle.\nCalculate the actuators' torque for the 2R manipulator, shown in Figure 14.19, such that the end-point moves time optimally from P1(1.5m, 0.5m) to P2(0 , 0.5m) . The manipulator has the following characteristics:\nThe path of motion is\nml\nh IP(t)1\nIQ(t)1\nm2 = 1kg\nl2 = 1m\n< 100Nm\n< 80Nm", + "640 14. *Time Optimal Control\nml = 5kg IQ(t)1 :::; 100Nm\nmz = 3kg IP(t)1 :::; 80Nm\n13. * Control of an articulated manipulator.\nFind the time optimal control of an articulated manipulator, shown in Figure 5.25, to move from H = (1.1,0.8,0.5) to Pz = (-1,1,0.35) on a straight line. The geometric parameters of the manipulator are given below. Assume the links are made of uniform bars .\nd l = 1m lz = 1m ml = 25kg IQI(t)l:::; 180Nm mz = 12kg IQz(t)1 < 100Nm h = 1m m3 = 8kg IQ3(t)1 :::; 50Nm", + "15\nControl Techniques\n15.1 Open and Closed-Loop Control\nA robot is a mechanism with an actuator at each joint i to apply a force or torque to derive the link (i). The robot is instrumented with position , velocity, and possibly accelerat ion sensors to measure the joint variables' kinemati cs. The measur ed values are usually relative. They are kinematics information of the frame Bi, attached to the link (i) , relative to the frame B i - 1 or Bo.\nTo cause each joint of the robot to follow a desired motion , we must pro vide the required torque command. Assume that the path of joint variables qd = q(t) are given as functions of time. Then, the required torques th at cause the robot to followthe desired motion are calculated by the equat ions of motion and are equal to\n(15.1)\nwhere the subscripts d and c stand for desired and controlled respectively. In an ideal world, the variables can be measur ed exactly and the robot can perfectly work based on the equations of motion (15.1). Then, the actu ators' control command Qc can cause the desired path qd to happen. This is an open-loop control algorithm, that the control commands are calculated based on the equat ions of motion and a known desired path of motion . Then, the control commands are fed to the system to generate the desired path. Therefore, in an open-loop control algorithm, we expect the robot to follow the designed path, however, there is no mechanism to compensate any possible error.\nNow assume that we are watching the robot during its motion by measur ing the joints' kinematics. At any instant there can be a difference between the actual joint variables and the desired values. The difference is called error and is measured by\ne e (15.2) (15.3)\nLet 's define a cont rol law and calculate a new control command vector by\n(15.4)\nwhere k p and k D are constant control gains. The control law compares the actual joint variables (q , q) with the desired values (qd' qd), and generat es" + ] + }, + { + "image_filename": "designv10_3_0000332_physrevlett.99.174302-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000332_physrevlett.99.174302-Figure1-1.png", + "caption": "FIG. 1. (a) A cantilever bending towards its side illuminated by a spot (P. Palffy-Muhoray). (b) Radiation penetration with linear absorption length d giving light-induced bend.", + "texts": [ + " They have large moduli and are perhaps better called nematic glasses [5]. Unlike elastomers, their directors, the ordering direction on average of rods, seem to be immobile under elongations imposed at an angle and also probably do not rotate during photo processes [6]. Since photons are absorbed by the dye components in the nematic, then light penetrating the face of a nematic photo cantilever will be attenuated, and hence the contractions generated will diminish with depth. Curvature of the cantilever results, Fig. 1(a). It is important in micro-optomechanical systems (MOMS) where elements can be optically induced to bend as glassy cantilevers [7] and, e.g., as elastomeric photo-swimmers [8]. Sheets of polydomain nematic photo glass can be induced to bend by absorption, the bend direction being that of the light polarization [9]. Simple absorption gives (Beer\u2019s law) an exponential decay of intensity with depth and hence also an exponentially decaying conversion of straight to bent (trans!cis) forms of the dye molecules", + " The light intensity (Poynting flux) is I, and our constant subsumes an absorption cross section per chromophore (assumed independent of nematic order\u2014itself another source of nonlinearity that is discussed in the polydomain case [12]), and a quantum efficiency [14]. is the cis state lifetime. The characteristic intensity, Ic 1= is a material constant. If we reduce I by its value at the surface, I0, then with I x I x =I0 and I0=Ic, a measure of the incident intensity, one has at depth x nc x I= 1 I ; nt x 1= 1 I : (1) The reduced intensity is I 1 at the entry surface x 0, see Fig. 1(b). Ignoring for the moment attenuation (I I0), gives us a measure of how much a beam of intensity I0 leads to conversion to cis, Eqn. (1), by the comparison of I0 to Ic, that is the balance of the forward to the thermal backward rates I0 = 1= . In the Eisenbach experiments [15], the average conversion was nc 0:84 and thus 5. Note that is independent of chromophore concentration, but it does depend on the choice of the light polarization [14]. Experimentally, it is easiest to determine for a system dilute in chromophores, where one can ignore the complications arising when attenuation is significant", + " With photo-bleached surface layers, radiation penetrates well beyond x d, and equally, contraction extends deep into the bulk, certainly beyond the Beer penetration depth d. For 0:5, a point of inflection first appears at the surface and moves inwards with increasing intensity. The cis fraction at the inflection is always nc 1=3 in this model. The surface cis concentration is nc 0 = 1 and rises to saturation, nc 1, as intensity increases. The precise form of the cantilever bend depends critically on the shape of these nc x curves. Since nc x changes shape with increasing intensity, we will find an elastic response highly nonlinear with intensity. Figure 1(b) shows a cantilever with radius of curvature R. The geometric strain from bending is x=R K, where R and K are constants to be determined for a given thickness w and illumination . The actual strain relative to the new natural length created by illumination is x=R K p which, if we further reduce throughout by the dimensionless constant connecting photo-strain and cis concentration, that is A, we obtain x=R K nc x for the effective reduced strain. When we take Young\u2019s modulus, E, not to vary with illumination, strain directly gives the stress" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001241_978-3-319-02636-7-Figure3.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001241_978-3-319-02636-7-Figure3.4-1.png", + "caption": "Fig. 3.4 Tora system", + "texts": [ + " Note that the segway is an extended version of the cartinverted-pendulum technology. The sliding mass on cart [29] is illustrated in Fig. 3.3. Assume that there is a friction coefficient B between the mass m and the cart of mass M . Denoting by x1 the position of the mass m with respect to the cart and by x2 the position of the cart, the equations of motion of this system are given by mx\u03081 \u2212 B(x\u03071 \u2212 x\u03072) = 0 Mx\u03082 + B(x\u03071 \u2212 x\u03072) = \u03c4 3.9 Examples of Underactuated Mechanical Systems 29 The Tora system2 depicted in Fig. 3.4, is composed of an oscillatory platform which is controlled via a central mass [35]. The inertia matrix M(q) and the potential energy V (q) are given by M(q) = [ m1 + m2 m2r cosq2 m2r cosq2 m2r 2 + I2 ] and V (q) = 1 2 k1q 2 1 + m2gr cosq2 where q1 is the platform displacement, q2 is the pendulum angular, m1 is the mass of the cart, m2 the mass of the eccentric mass, r the radius of the rotation, k the spring constant, I2 the inertia of the arm, g the gravity acceleration, and \u03c4 is the torque input" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001578_tmag.2010.2093509-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001578_tmag.2010.2093509-Figure3-1.png", + "caption": "Fig. 3. Two typical positions of an FSPMLG. (a) Flux distributions in position 1. (b) Flux distributions in position 2.", + "texts": [ + " In order to investigate FSPMLGs, a single-side FSPMLG ideal model is built in Fig. 2. The linear generator is made up of a stator and translator. The translator comprises a plurality of teeth and slots. The stator has six U-shaped stacks, each of which is constructed with one slot and two tooth bodies. Each phase has two U-shaped stacks. The phase coil is wound in the slots of the corresponding stacks with a PM positioned between adjacent U-shaped stacks. Displacers are positioned between the phases. Two typical positions of an FSPMLG are shown in Fig. 3. When the translator moves from position 1 to position 2, the main PM flux linked in this coil changes from negative maximum to positive maximum. The change of flux linked in the armature windings induces emf. In order to obtain three-phase sinusoidal emf, the physical distance between the central axis of the phase coils is 0018-9464/$26.00 \u00a9 2011 IEEE TABLE I DATA OF THE SINGLE-SIDE FSPMLG , and the electrical angle is , where and are the integers, and , which is the distance between two teeth, is the pole pitch of the translator", + " According to FEA, the model surface is subdivided into many triangles. The energy formula is changed into (6) where is the total number of triangular elements, is the magnetic field intensity, and is the magnetic flux density at element . The equation of force is rewritten after (6) is discretized by linear interpolation (7) where is the magnetic permeability at element . The no-load performance of the FSPMLG is investigated by using FEM. The magnetic-field distributions at two typical positions are shown in Fig. 3. It can be seen that the main PM flux changes with the position of translator. In order to investigate the nature of emf, the flux-linkage produced by the PM is analyzed. The waveforms of one-phase flux-linkage, the three-phase voltage, and the cogging force at a speed of 0.5 m/s, respectively, are shown in Fig. 5. As shown in Fig. 5, it can be found that the FSPMLG has less harmonic components of emf and less cogging force than those of the conventional PM linear synchronous generators. Due to the extra end effects, the cogging force is not as regular as that of rotational FSPM machines" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003475_j.optlastec.2018.10.019-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003475_j.optlastec.2018.10.019-Figure5-1.png", + "caption": "Fig. 5. Properties of the plume-spatter signature, (a) schematic segmentation for the captured image and (b) detail characteristics for the target region.", + "texts": [ + " The part placement, laser scanning direction, and gas flow velocity had an effect on the part quality. The gas flow against the scanning direction led to better part quality [31]. In this work, the laser beam always moved against the gas flow direction in the chamber. 6000 frame images were obtained for each state. Melted tracks from various process parameters and with different widths are shown in Table 1. In the processing image, there existed properties among the plume and spatter, which determined the states of the melting results as shown in Fig. 5. They are properties from the plume (T1), the spatter (T 2), and the whole target region of the plume and spatter (T3). Binary images were required in addition to the raw image to measure the properties. The raw intensity image was converted to a binary image using a threshold from the Otsu's method [32]. When the spatters were closer to the camera lens, they not only became larger but also faded, since the spatter temperature was falling and the spatter was out of the focus. In order to eliminate the noise from light reflected by the metal powder bed and the flying spatter closer to the camera, the components that had fewer than eight pixels from the binary image were removed from the plume and spatter image", + " Intensity profiles of pixels in each image (T2 3) had different behavior with other portions of the same layer, which were related to the defects [20]. The max and mean intensities (T5 3andT6 3) were calculated from the raw image. For the whole target region of the plume and spatter, the smallest convex polygon that contained both spatter and plume determined the convex hull. Areas of the plume, the spatter, and the whole target region (T1 1, T1 2, and T1 3) were calculated from the binary image. As demonstrated in Fig. 5, lengths of the plume and the spatter (T2 1 and T2 2) were defined as the rectangle size along the y-direction. The rectangle was the smallest one that covered the target plume or spatters region. The rectangle size along the x -direction was taken as the width of the plume and the spatter (T3 1 and T3 2). The angle between the target region major axis and x -axis indicated the orientations of the plume and the spatter (T4 1and T4 2). The boundaries of target regions were the perimeter of the plume or the spatter (T5 1 or T5 2). The sum (T6 2) was counted and the situations (right T3 3 or left T4 3 of the plume axis) were found about the spatter. The detailed segmentation and property discrimination of the image was calculated as the illustration in Fig. 5 and Table 2. Based on the experimental observations, there were three typically features about the tracks from the experimental design as shown in Fig. 6. When the energy input was lack, melted beads could not connect to each other. Therefore, balls took shape because of weak wettability as illustrated in Fig. 6(a). It was defined as the underheating melted states. These balls would lead to porous and high surface roughness part. Satellites on the tracks in Fig. 6(b and c) came from the powder and liquid spatter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002897_j.engfailanal.2016.12.008-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002897_j.engfailanal.2016.12.008-Figure11-1.png", + "caption": "Fig. 11. The first order resonant mode of the gearbox housing.", + "texts": [], + "surrounding_texts": [ + "According to mechanical vibration theory, the differential equations representative of a mechanical system under general excitation [15,16] are given as follows. M\u20acX t\u00f0 \u00de \u00fe C _X t\u00f0 \u00de \u00fe KX t\u00f0 \u00de \u00bc F t\u00f0 \u00de \u00f02\u00de \u03b2 \u00bc 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u2010\u03c52 2 \u00fe 2\u03b4\u03c5\u00f0 \u00de2 q \u00f03\u00de Where, M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the system, respectively, X is the system response, F is the system suffered excitation, \u03b2 is the dynamic magnification factor, \u03bd the ratio of the external excitation frequency to the natural frequency of the system, and \u03b4 is the damping ratio. Eq. (3) indicates that, when the external excitation frequency approaches the natural frequency of the structure, i.e., as \u03bd approaches 1, \u03b2 attains a maximum value, and resonance ensues. The stress time history of Section A = {1025s,1890s} and the amplitude spectral density (ASD) are shown in Fig. 20. It is observed that the dominant frequency f of the stress signal is mainly distributed in the ranges 0\u2013150 Hz and 500\u2013650 Hz. The timefrequency joint analysis of point N02 in Section A is shown in Fig. 21. Some high-energy band frequencies fi related to speed v are observed. As derived elsewhere [17], the relation between v and fi can be given as f i \u00bc ki v; \u00f04\u00de where ki is the ith linear relationship between the ith band frequency fi and the speed v. Table 3 lists the primary frequency bandsfi when v = 306 km/h. In addition, Fig. 21 shows that the three frequency bands, i.e., 60 Hz, 573 Hz, and 608 Hz, remain unchanged during train deceleration. As fi pass through the unchanged frequency bands 573 Hz and 608 Hz, their root mean square (RMS) energies obviously increase. However, as fi pass through 60 Hz, their RMS energies remain constant. According to theory of random vibration [18] and the modal analysis simulation results discussed above, 573 Hz and 608 Hz should be the natural frequencies for this type of gearbox housing. However, 60 Hz is not a natural frequency of the gearbox. A frequency-domain structure damage assessment method [19], which compares the stress damage of the origin signal (Dn) and the damage of the origin signal of a band-stop filter at a particular frequency band (Db), was conducted to assess the damage effect of the 60 Hz, 573 Hz, and 608 Hz frequency bands. The damage effect factor \u03b1 is given as follows: \u03b1 \u00bc 1\u2212Db=Dn: \u00f05\u00de The \u00b15 Hz frequency band effect factors for 60 Hz, 573 Hz, and 608 Hz are listed in Table 4. It is concluded that the 573 Hz and 608 Hz frequency bands provide the greatest contribution to the stress signal and the 60 Hz frequency band contributes the least. When the train operates at a constant speed of 306 km/h, f5 = 571 Hz is very close to the first order natural frequency of the gearbox housing, whereas f6 = 602 Hz is also close, although less so, to the second order natural frequency. Therefore, the first mode at 573 Hz is excited easily and the second mode at 608 Hz is excited only occasionally. This result is demonstrated by test data analysis provided in Fig. 21. Meanwhile, it is also verified that a larger stress response occurs at N02 while the second mode (608 Hz) is excited." + ] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure7.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure7.3-1.png", + "caption": "Figure 7.3.2 Axle mean inclination GA and axle camber gA together give the individual wheel inclinations.", + "texts": [ + " More elaborately, including a second-order term, g \u00bc g0 \u00fe \u00abBC1zS \u00fe \u00abBC2z 2 S \u00fe \u00f07:2:4\u00de where \u00abBC2 is the quadratic bump camber coefficient. The axle line is the line joining the centres of the twowheels at the opposite ends of the axle. Here, the term \u2018axle\u2019 is applied broadly to include the two wheels of an independent suspension. The wheel inclination angle and camber angle aremeasured from the perpendicular to the axle line.Axle roll angle (the roll angle of the axle line) and road surface transverse-section angles also affect the camber of the wheel relative to the road, but are accounted for separately, Figure 7.3.1. When there is suspension roll, the individual wheels are in suspension bump and have camber changes relative to the body. For an independent suspension, thesewheel cambers can be accounted for separately, but it is also possible towork in terms of the symmetrical and antisymmetrical axle values, the axle mean inclination and the axle mean camber, respectively. In Figure 7.3.1(d) note that, with clockwise rotation positive, a negative path inclination gives a positive wheel inclination relative to the road. The axle mean inclination angle (nothing to do with the axle roll angle) is the mean of the inclination angles of the two wheels of the axle: GA \u00bc 1 2 \u00f0GR \u00feGL\u00de \u00f07:3:1\u00de For an ideally symmetrical vehicle, this is zero. By substitution, it is equal to the semi-difference of the wheel camber angles, arising from constructional imperfections or compliance camber: GA \u00bc 1 2 \u00f0gR gL\u00de \u00bc gd \u00f07:3:2\u00de The antisymmetrical component, called the axle camber angle, is the semi-difference of the inclination angles, gA \u00bc 1 2 \u00f0GR GL\u00de \u00f07:3:3\u00de This is also equal to the mean of the camber angles: gA \u00bc 1 2 \u00f0gR \u00fe gL\u00de \u00bc gm \u00f07:3:4\u00de Then the individual right and left wheel inclination angles are GR \u00bc GA \u00fe gA GL \u00bc GA gA \u00f07:3:5\u00de The static camber angles are: gR0 \u00bc \u00fe GA0 \u00fe gA0 gL0 \u00bc GA0 \u00fe gA0 \u00f07:3:6\u00de The axle camber angle (Figure 7.3.2, the mean camber angle) is the intended design value, once being normally positive but nowadays often negative, and usually negative on racing cars to give the best cornering grip and to equalise the temperature distribution across the tread. The antisymmetrical component, the difference of (static) camber angle values, arises on a passenger car only because of production tolerances, although it is used deliberately on some racing cars, essentially those that operate on circuits with turns in one direction only, for example US left-turn \u2018oval\u2019 tracks" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001076_j.wear.2013.11.016-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001076_j.wear.2013.11.016-Figure3-1.png", + "caption": "Fig. 3. Loading conditions on line of action [21,22], (a) meshing points of internal gear (b) load distribution along meshing line.", + "texts": [ + " This surface pressure occurs along whole sliding distance and has a value of; P \u00bc 2Ft \u03c0aH2\u00f0aH2 yi 2\u00de1=2 \u00f010\u00de where yi is the distance from the center of the Hertz contact, \u03c1 is the equivalent curvature radius of the contacting surfaces, E is the equivalent elasticity modulus of materials and aH is calculated as follows; aH \u00bc ffiffiffiffiffiffiffiffiffiffi 4Ft\u03c1 \u03c0E r \u00f011\u00de 1 \u03c1 \u00bc 1 \u03c11 1 \u03c12 \u00f012\u00de and 1 E \u00bc 1 \u03bd12 E1 \u00fe1 \u03bd22 E2 \u00f013\u00de Tangential force Ft which causes the pressure on the surface is calculated as follows: Ft \u00bc 2Mb d0b \u00f014\u00de Because more than one tooth couples are in contact during meshing in gear mechanisms, the load affects in the form of partial load in the beginning and end of meshing. The point A is the start point of meshing, B and D are the beginning and ending points for the single meshing points, C is the pitch point and E is the end of the meshing point. In that case, load affects as overall load between points B and D. In the AB and DE regions the theoretical tooth load is half of the total tooth load. Accordingly, distribution of the tooth load that is formed by tooth force on the surface along line of action is as shown in Fig. 3(a). This distribution is valid if gears are totally rigid. In practice, distribution of the load is as shown in Fig. 3(b) since gear are not totally rigid and thus deform under load [21,22]. The pinion and internal gear which were used in experimental studies were St50 steel with a surface hardness of 160\u2013170 HB (Fig. 4). The geometrical properties of gears are given in Table 1. In Table 1 subscript 1 and 2 shows the pinion and the internal gear respectively. For experimental studies, a pinion-internal gear fatigue and wear test apparatus which has the same working principle with FZG closed circuit power circulation system [23,24] is manufactured and wear experiments are performed (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001141_s10846-014-0072-3-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001141_s10846-014-0072-3-Figure1-1.png", + "caption": "Fig. 1 Quadrotor UAV configuration", + "texts": [ + " To objectively evaluate the performance of PSO method, the optimization technique of backstepping control parameters by using genetic algorithm (GA) such as the works published in [27, 28] is employed. The main advantage of the proposed method is that the structure of the control system is simple but very effective. Furthermore, the nonlinear property of the dynamic system is well preserved, since the controller design does not require any linearization. The effectiveness of the proposed robust control scheme is verified by simulation results. 2 Quadrotor Systems Modeling 2.1 Quadrotor Description The quadrotor UAV, shown in Fig. 1, has four rotors to generate the propeller forces Fi=1,2,3,4. The four rotors can be thought of as two pairs, (1,3)@(front, back) and (2,4)@(left, right). Fig. 2 shows the various movements of a quadrotor due to rotor speeds changes. In order to develop the model of the quadrotor, reasonable assumptions are established in order to accommodate the controller design. The assumptions are as follows: Assumption 1: Quadrotor is a rigid body and has symmetric structure. Assumption 2: Aerodynamic effects can be ignored at low speed. Assumption 3: The rotor dynamics are relatively fast and thus can be neglected. Assumption 4: The quadrotor\u2019s center of mass and body-fixed frame origin coincides. 2.2 Quadrotor Dynamic Model Let consider earth fixed frame E = {xe, ye, ze} and body fixed frame B = {xb, yb, zb}, as seen in Fig. 1. Let q = (x, y, z, \u03c6, \u03b8, \u03c8) \u2208 R6 be the generalized coordinates for the quadrotor, where (x, y, z) denote the absolute position of the rotorcraft and (\u03c6, \u03b8, \u03c8) are the three Euler angles (roll, pitch and yaw) that describe the orientation of the aerial vehicle. Therefore, the model could be separated in two coordinate subsystems: translational and rotational. They are defined respectively by: \u03be = (x, y, z) \u2208 R3 (1) \u03b7 = (\u03c6, \u03b8, \u03c8) \u2208 R3 (2) The dynamic model of quadrotor is derived from Newton-Euler approach" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002156_978-3-642-27482-4_8-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002156_978-3-642-27482-4_8-Figure9-1.png", + "caption": "Fig. 9 Unitrack (left) and F-track (right) robots", + "texts": [ + "com/thing:7209 design was not only its functionality but its property of being parametric. Just changing some parameters, different tracks can be obtained, as well as the necessary pinions. In addition, 3mm plastic spool was used as pins for the links. Therefore no special screws and nuts were necessary. The latest version is shown in figure 8. It is also available in thingiverse16, along with some videos showing how it moves. A different approach was taken by Jon Goitia. He focused on designing robots with articulated tracks. The first design was Unitrack17, shown in figure 9 (on the left and in the middle). It is an autonomous track driven by a hacked Futaba 3003 servo (the same servo used for the Miniskybot). It consist of two wheels attached to the servo and five standard o-rings used as tracks. Another o-ring is used as the transmission system between the servo and one wheel. Unitrack is also parametric, therefore the wheel\u2019s diameter and number of o-rings can be easily changed. This innovative design was for one month the first most popular thing on thingiverse, which is not easy to achieve (currently there are more than ten thousand things!). 16 http://www.thingiverse.com/thing:8559 17 http://www.thingiverse.com/thing:7640 Once Unitrack was fully functional, the F-track robot was created, shown in figure 9 (on the right). It consist of four articulated independent Unitracks joined to a body. This design is an example on how the creativity emerges from some students when they are stimulated. Our new robotic platform combines two important features. On one hand it is open hardware, so that anyone can study, modify and distribute the robot. On the other hand the robot is printable making it very easy for the people to materialize it. The result is that anyone in the wold with access to Internet and to an open-source 3D printer can copy the robot, improve it or create derived design" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002484_j.jsv.2018.06.011-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002484_j.jsv.2018.06.011-Figure3-1.png", + "caption": "Fig. 3. Test rig of our planetary gearbox.", + "texts": [ + " In such a scenario, a modified SER, namely Modified Sideband Energy ratio (MSER) is proposed. With a bandwidth empirically selected, the energy of the characteristic frequencies among the bandwidth is calculated rather than single peaks. Comparison results of both SER and MSER will be provided. The experimental data are acquired from a planetary gearbox test rig at the University of Electronic Science and Technology of China (UESTC) Equipment Reliability and Prognostic and Health Management Laboratory (ERPHM). The configuration of the test rig is shown in Fig. 3. Fig. 3 shows that the experimental set-up consists of a spur gearbox and a one-stage planetary gearbox driven by a 2.24 kW three-phase electrical motor controlled by a motor speed controller. A vibration accelerometer (with sensitivity of 100 mV/g and frequency range 0\u201310 kHz) was used for capturing vibration data. The experiments operated on the planetary gearbox and the rotational speeds were set at 1800 and 3000 rpm with 2.4 s data. The sampling frequency was set to 10240 Hz. For each sun gear fault scenario, 10 groups of data were measured under above mentioned rotational speeds" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002270_1464419314546539-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002270_1464419314546539-Figure1-1.png", + "caption": "Figure 1. Geometry of a cylindrical roller with full crown profile.", + "texts": [ + " These elements are elastic and can be subjected to deformation actually, which would affect the results of analysis. Such solutions were provided by Gao et al.57 Clearly, there are many aspects to take into consideration in bearing dynamic analysis. The emphasis of the current work is on the effect of bearing defects on its vibration response. Therefore, for time efficient analysis, it is important to make certain simplifying assumptions, such as those made above. The geometry of a roller is shown in Figure 1. For avoiding the stress on the surface, the roller has fully crowned geometry. Lb, Le and Lp are total length, effective length and central flat land length, respectively. Crown radii, corner radii and diameter are represented by Rc, Rrc and db, respectively. In order to calculate non-Hertzian contact forces, the roller should be divided into slices. The radius reduction cb of each slice is expressed as48,50 cb\u00bc 0 Lp 2 4xk4 Lp 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 c L2 p 4 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 c x 2 k q Le 2 4xk4 Lp 2 , Lp 2 4xk4Le 2 8< : \u00f01\u00de where xk is the axial coordinate value of the slice element k relative to the roller centre, which is described as xk \u00bc 0:5\u00fe k 0:5 n Le \u00f02\u00de where n is the slice number, and Le\u00bcLb 2Rrc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002474_s00170-017-0922-9-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002474_s00170-017-0922-9-Figure3-1.png", + "caption": "Fig. 3 Schematic of the face milling test setup", + "texts": [ + " The roughness was measured in an Olympus LEXT OLS 4000 Confocal Laser Microscope. For each sample, 20 measurements were made on the top surface located between the clearance holes (16) and after the holes (4), see Fig. 2. The hardness of each sample was measured at 40 locations using a Rockwell C test, as shown in Fig. 2. In order to minimize the influence of the as-built surface irregularity, the SLM surfaces were ground very lightly prior to the hardness measurements. Face milling experiments were performed on the 16 SLM samples. The test setup is shown schematically in Fig. 3. Note that the cutting forces were measured using a three-component Kistler 9257B dynamometer. A 50.88-mm-diameter face milling cutter (Kennametal KSSR25ORP430C3) with four round ceramic inserts (Kennametal RPG43E) were used. The samples were clamped using four screws to the mounting plate, which was fixed to the dynamometer. Cutting was performed in one pass with the tool moving in the y direction (feed direction). All milling tests were carried out at a constant axial depth of cut of 500 \u03bcm and a constant feed of 0", + " Phase homogenization remains after aging but the hardness is greatly increased and it becomes similar to the hardness obtained in the conventional process. The typical solidification \u201cdrops\u201d of components obtained with SLM are clearly evident in Fig. 5a\u2013c. Cutting forces were acquired during milling of the NT, PT, and the TT samples at low and high cutting speeds. The NT sample was also investigated to understand the effect of SLM build direction (0\u00b0 and 90\u00b0) on the milling performance. The milling forces were acquired according to Fig. 3, which explains the direction of tool movement relative to the workpiece. For force analysis, the data collected during the second step (see Fig. 6) were used in order to avoid the effect of the geometrical discontinuity due to the mounting holes. An example of the measured force is presented in Fig. 6. If we consider step 2, according to Fig. 7, for a cutting speed of 190 m/min, and the 4 cutting tool inserts with an angular spacing \u03b2 = 90\u00b0 and the sample length, we have a working angle 2\u03c6 = 103" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002453_1.4032079-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002453_1.4032079-Figure2-1.png", + "caption": "Fig. 2 Mechanical principle diagrams of (a) source-metamorphic mechanism, (b) roller\u2019s DOFs and workspace, and (c) metamorphic process", + "texts": [ + " Considering that the motor drives screw to provide power source, substitute P for the source kinematic pair bi and substitute the two degrees-of-freedom (DOF) (R and P) of the source-MRM for the executive kinematic pair bj in Eq. (1), the working-phase mechanisms 1M and 2M can be expressed as follows: P [ XR \u00bc PPR R R \u00bc a6A1 \u00bc \u00bda6; A1; af \u00bc 1M (2) P [ XP \u00bc PPR RPP \u00bc a6A2 \u00bc \u00bda6; A2; af \u00bc 2M (3) R and P represent for the revolute and prismatic joint. \u201c Q \u201d and \u201c\u2014\u201d represent for slider and connecting rod. One metamorphic gene is a combination of two joint (e.g., a6 \u00bc PPR as shown in Fig. 2(a)). One metamorphic cell is a combination of two genes (e.g., A1 \u00bc a1a1 \u00bc R R R). The generation of the source-MRM SM from the genetic evolution synthesis can be expressed as follows: SM \u00bc 1M [ 2M \u00bc \u00bda6; A1; af [ \u00bda6; A2; af \u00bc \u00bd\u00f0a6 a1\u00de; \u00f0A1 [ a6 [ A2 a1\u00de; \u00f0af [ af \u00de \u00bc \u00bda6; a1; \u00f0A1 [ a6 [ a5\u00de; af \u00bc \u00bda6; a1;A1a5; af \u00bc PPR R R RPP (4) From the biological topologies expressed in Eq. (4), mechanical principle diagrams of the source-metamorphic mechanism can be established, as shown in Fig. 2(a). The DOF of the vertical roll is two, as shown in Fig. 2(b). The P DOF is used to control the distance of the vertical rolls, and the R DOF is used to avoid space interference. Constraints are added to reduce the redundant local DOF of the mechanism and ensure the metamorphic process. Reducing redundant DOF makes the transmission part of MRM a local four-bar linkage mechanism. In addition, the rigidity of the metamorphic mechanism is improved by taking advantage of the locking-position characteristic of four-bar linkage mechanism. In the source mechanism state, the spring constraint limits the horizontal movement of the vertical roll, as shown in Fig. 2(c). The source mechanism turned into the first working-phase mechanism. As the motor drives the lead screw, the sliding block moves downward, as shown by the dotted arrow. When it reaches the locking position of the four-bar linkage mechanism, the rigid constraint limits the rotation of the bars. The whole mechanism changes into a 0DOF mechanism in an instant. When the sliding block continues moving, the spring constraint gets released by the driven force from the sliding block. The four-bar linkage mechanism in the dashed frame is equivalent to one link rod" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003700_j.mechmachtheory.2020.103832-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003700_j.mechmachtheory.2020.103832-Figure7-1.png", + "caption": "Fig. 7. Interaction between outer ring and bearing house.", + "texts": [ + " There is slight deviation between the results at low applied axial loads, one reason is that the experimental results themselves fluctuate at low applied axial load; another reason may be that the accurate lubricant parameters should be determined, it can be found that when the lubricant parameters is reasonably determined, the simulation results well match the experimental results. Moreover, there are also some work to estimate the bearing dynamic characteristics through monitoring vibration of the bearing house. The results from the proposed model are compared with the experimental results in reference [27] . To this end, another degree of freedom of bearing is introduced into the present bearing model as shown in Fig. 7 , the vibration of bearing house can be expressed as follows: m h \u0308z h + c h \u0307 zh + k h z h = F h (35) where stiffness coefficient k h is set as 1.5 \u00d7 10 7 N \u00b7m \u22121 and damping coefficient c h is set as 1.8 \u00d7 10 3 N s m \u22121 according to reference [28] . The frequency spectrum of the radial displacement of the bearing house obtained by present dynamic model and the experimental results from Babu et al. [27] are listed in Table 2 . It can be found that the simulation results of proposed model agree well with published experimental results" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.16-1.png", + "caption": "Fig. 4.16 Nonredundant planar parallel manipulators", + "texts": [ + " Hint: Obtain two closure equations from the triangle O1O2P indicated in Fig. 4.13. Finding the corresponding time derivatives of such equations allows us to solve the velocity analysis. 10. In Example 4.7 we considered that v4 D !2. Give a justification, if any, for this assumption. 11. The Geneva wheel of Example 4.7 is a little case that illustrates how easy it is to formulate the velocity analysis of parallel manipulators when reciprocal screw theory is used. Determine the input\u2013output equation of velocity of the planar parallel manipulators shown in Fig. 4.16 by resorting to reciprocal screw theory. 4.4 Exercises 95 12. The link c of the six-bar dwell mechanism in Fig. 4.17 rotates with a generalized velocity Pq. The topology of the mechanism is such that the angular velocity Pq produces an oscillatory linear velocity Px. Determine the input\u2013output equation of velocity of the planar mechanism. 13. The mechanism shown in Fig. 4.18 is used to produce high torque in the shaft at B and is a good example to which to apply screw theory. The gear unit is pivoted at A and produces a constant angular velocity of 5 rad/s counterclockwise as observed from A to C over the right-hand screw", + " Give a justification, if any, for this assumption. Solution. The joint rate v4 denotes the angular velocity of Earth as observed from body D while !2 denotes the angular velocity of body D as observed from Earth. Hence, v4 D !2. 11. The Geneva wheel of Example 4.7 is a little case that illustrates how easy it is to formulate the velocity analysis of parallel manipulators when reciprocal screw theory is used. Determine the input\u2013output equation of velocity of the planar parallel manipulators shown in Fig. 4.16 by resorting to reciprocal screw theory. Solution. 3-RPR parallel manipulator. The velocity state of the moving platform m, body labeled 3, as observed from the fixed platform f , body labeled 0, may be written in screw form through any of the connector limbs as follows: 0! i 1 0$1 i C 1! i 2 1$2 i C 2! i 3 2$3 i D 0V3; i D 1; 2; 3; where 1! i 2 D Pqi is the active joint rate of the robot manipulator. Furthermore, consider that $i is a line in Pl\u00fccker coordinates pointed from point Ai to 15.2 Chapter 4: Velocity Analysis 329 point Bi" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003870_j.msea.2019.02.015-Figure17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003870_j.msea.2019.02.015-Figure17-1.png", + "caption": "Fig. 17. Schematic illustration of a bead generated by laser irradiation: forming mechanism for the solidified metal structure.", + "texts": [ + " Accordingly, the randomly shaped pores observed in the Al\u20134Si\u20132.5Mg SLM specimen were shrinkage cavities. In this section, we discuss the formation mechanism of metal structures in the Al\u20134Si\u2013Mg SLM specimens based on the results presented in Section 3.2. For the macrostructures in Fig. 5(-2), note that the half-cylindrical beads with a 0.1 mm depth were formed by laser irradiation. This means that three or four layers containing the already solidified lower layers were melted beyond the recoated powder layer. Fig. 17 depicts a schematic illustration of a half-cylindrical bead formed by laser irradiation on a cross-section perpendicular to the laser scan direction. The outer peripheral parts of the melted beads were in contact with the already solidified lower layer. The heat supplied by the laser irradiation dissipated through the solid layers because the solid naturally had a much higher thermal conductivity than either the powder layer or surrounding argon atmosphere [47,48]. Simultaneously, the interfaces on the solid parts could act as heterogeneous nucleation sites [49]", + " Subsequently, a heat effect was induced by laser irradiation of the next layer. Since the heat effect was induced repeatedly during the layer-by-layer process, Si and Mg diffused and condensed at the cell boundaries. As a consequence, the fine Mg2Si phase was probably annihilated even if it had formed during this process. Fig. 7 presents that the crystal grains of the Al\u20134Si\u2013Mg SLM specimens became refined with increasing Mg content. The crystal growth proceeded radially backward from the periphery to the center of a bead, as shown in Fig. 17. During the process, the solidification proceeded with excreting the solute elements to form a diffused field condensed with the solute elements at the liquid side in front of the solidification interface [53,54]. Accordingly, compositional supercooling should occur at the liquid of the solidification front because of the solidifying point being depressed by the condensation of the solute elements. Here, the conditions for compositional supercooling to occur are generally expressed as follows [54]: P ) = 0 2 %(bG E,(P), E,(% PI = 0 . (4.3\u2019) AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 539 In rewriting (4.3) we have indicated the dependence of u on P which was previously ignored to simplify the notation. Differentiating each of these identities with respect to P, we obtain, recalling (4.4a), U P \u2019 ( $ T ) i l ( P ) + U 3 4 T ) i 2 ( P ) = - U y ( $ T ) , u:\u2019(:n) t l (P) + U P \u2019 ( b ) i B ( P ) = - Uk\u201c\u2019($n) , (4.8) where we have introduced (4.9a) i = 1 , 2 . By differentiating in (4.2) we find with the aid of (2.9b) and (4.4d) that 1- u 4 ( q (4.9b) U(5)(0) = 0 . The coefficients in (4.8) are already computed for use in the final Newton iterate (4.5b). Thus only the additional system (4.9b) is solved to evaluate kl and i2 from (4.8). Then for initial estimates we use the first two terms in the Taylor expansion : (4.10) t y \u2019 ( P f A P ) = E j ( P ) & t j ( P ) A P , j = 1 , 2 . The derivatives l j ( P ) are of physical interest, especially when P is near a bifurcation point or near a local maximum or minimum point of P(5;). The corresponding continuation analysis and computation for variation of the geometric parameter k follow in an obvious manner. In fact, to replace P by k only the right-hand side in (4.8) need be changed by using the components of (4.11a) Proceeding the same way as in the derivation of (4.9b) we find that (4.llb) , U(S\u2019(0) = 0 . 540 L. BAUER, E. L. REISS AND H. B. KELLER 4.3. Parallel shooting for the full sphere. We treat the full sphere by employing the previous procedure for two hemisphere^.^ We integrate from each pole to the equator and adjust four parameters in order to satisfy four continuity conditions at the equator. Consider the two initial value problems, (4.12a) (4.12b) o S e j g T , Here the ti are the four initial parameters, two for each of the two initial value problems. The solutions of these problems are denoted by u(0; t1 , Ez) and v(0; E 3 , la). If we can find ti such that (4.13) U j ( h E l , t 2 ) = % ( B G 5 s , E , ) Y j = 1,2,3,4, then a solution of the full sphere problem is given by (4.14) For fixed P and k, the number of distinct solutions of Problem S is equal to the number of distinct real roots (tl , l2 , 5 , E4) of (4.13). The equations (4.13) are also solved by Newton's method. Now however there are two nonlinear systems (4.12) and four linear variational systems to be solved for each Newton iteration step. The numerical integration of the initial value problems is done in the same way as for the hemisphere. All convergence criteria are the same as in the hemisphere calculations. Corresponding continuity methods in both k and P are also used for obtaining initial iterates. It is inconvenient to treat the full sphere by integrating from 0 = 0 and adjusting El and t2 to satisfy the two boundary conditions at 8 = v. Some of the derivatives are indeterminate a t 0 = v, and the derivatives of some of the auxiliary variables U(') and U(2) are infinite there. Numerically, these singularities are handled more readily by the special starting procedure, (4.6) and (4.7), than by integrating up to v - E, and then using special formulas. AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 541 4.4. Parallel shooting for hemispheres. For some of the solution branches for the hemisphere problem boundary layers occur at 8 = 0 or 8 = BT; see the discussion in Section 5. When a boundary layer occurs at 8 = in, the solution varies rapidly in a small neighborhood of 8 = BT. Thus small variations in the parameters El and t2 produce large variations in the solution of (4.2) a t 0 = $T. When a boundary layer occurs at 8 = 0, u, and up essentially vanish in an interval a < 8 2 +T. Then relatively large changes in El and E2 produce small changes in the solution at 8 = QT. In both cases the simple shooting method of subsection 4.1 is unsatisfactory for an accurate determination of the roots of (4.3) and parallel shooting is employed. Thus we select a point 8 , in the interval 0 < 0, < $7 and integrate from 8 = 0 to 8 , and from 8 = $7 to 8,, . The corresponding four initial parameters are determined from continuity requirements anaIogous to (4.13). The procedure is completely analogous to the parallel shooting for the full sphere described in subsection 4.3. Appropriate values of 0 , are determined from numerical experiments. 5. Presentation of Results Extensive numerical solutions of Problem S have been obtained for shells with k = (the thin sphere) over a wide range of P values. For k = 1.2 x a less extensive P range has been covered. At the fixed pressure P = 6 x solutions have been obtained for various k in the range low5 k 2 2 x We shall describe the thick sphere results that seem most relevant to buckling and briefly mention significant differences for the thin sphere case. The implications of these results for axisymmetric buckling are discussed in Section 6. The thick sphere computations are summarized in Figures 1 and 2 where we plot P vs. A(P) and e ( P ) . The quantity (the thick sphere) and k = is a measure of the amplitude of the deviation of the deformation at load P from the uniformly compressed state, w = 0. Similarly e (P) , defined in (2.19), is proportional to the difference between the potential energies of the buckled and unbuckled states at the same load, P. The circles and crosses on the P-axis denote, respectively, the symmetric and unsymmetric eigenvalues of the linear theory (see Table IA in Section 3). Each point ( A ( P ) , P) with A(P) > 0 on the graphs in Figure 1 represents buckled states, i.e., nontrivial solutions of Problem S. If the point corresponds to a symmetric state, then it represents a single solution. If it corresponds to an unsymmetric state, then it represents a pair of solutions. The graphs show that for fixed values of P, Problem S may have many solutions. To describe and 542 L. BAUER, E. L. REISS AND H. B. KELLER Figure la. Graphs of P vs. the amplitude A , which is defined in equation (5.1), corresponding to the 7 lowest symmetric eigenvalues and the 4 lowest unsymmetric eigenvalues for the thick sphere k = 0.001. The circles on the P-axis indicate the symmetric eigenvalues and the crosses the unsymmetric eigenvalues. Several of the lower symmetric branches BaSj and the lower unsymmetric branches B , 2 j are explicitly labeled in the graph. Several of the upper P X j and lower P$,J critical loads are also shown. The branches B& , j = 1, 2, * . . , 7, and and B6,0 are not completely shown in the figure since the corresponding values of A are too large. They are shown in Figure 1 b. The circles on the graphs indicate the pressures a t which unsymmetric branches merge with symmetric branches. dicates the pressure at which Bsf, merge with BSel. 544 L. BAUER, E. L. REISS AND H. B. KELLER values of - (&e)lI3 are too large. They are shown in Figure 2b. discuss this multiplicity, we decompose the graphs of A(P) into single-valued segments of maximal extent and denote each such segment by Bn,, with integers n and j . The procedure for choosing appropriate values of n and j is described in subsection 5.1. This is equivalent to decomposing the graph of e(P) in Figure 2 into monotone segments of maximal extent. The P coordinates of the end points of the segments are denoted by Pt,, and PEj . We call them, respectively, the lower and upper critical points of the segment. If each point on Bn,i corresponds to a symmetric (unsymmetric) solution, then we denote the branch of solutions corresponding to Bn,j as Bn,j(P) (B;,j(P)). The P-axis corresponds to the unbuckled states. We shall not include this branch in our discussion of the multiplicity. Buckled solutions of Problem S are said to bifurcate from the unbuckled solution at or from a pressure Po if there is a solution branch, y(0 , P), depending AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 545 546 L. BAUER, E. L. REISS AND H. B. KELLER continuously on P such that y(0, Po) = 0 and y(0, P ) $ 0 for P # Po but IP - POI sufficiently small. This solution branch is called a bifurcation branch. The bifurcation branch need not exist for P in a full neighborhood of Po . If it exists, locally, for P > Po ( 0.05; compare Figures 3a and 4a with Figures 3c and 4c. However, for P near PL 6.1 = P t o = 0.0105 the shapes on both branches are quite similar. Thus there 548 L. BAUER, E. L. REISS AND H. B. KELLER ----- Graph 9 Number 1 2 3 4 5 6 7 8 Branch B, , l + * %.l B6v0 550 L. BAUER, E. L. REISS AND H. B. KELLER 4 AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 55 1 is no abrupt change in mode (see Figures 3b and 4b). As P increases the states on B,,, develop a boundary layer near 8 = $7~. For example, at P = 0.10, t ( 8 ) is almost constant over 0 s 0 s and then changes rapidly over in < 8 < $7 to satisfy the boundary conditions. The graph of w(0) is approximately a parabola with maximum at 8 = 0 so that the deformed sphere is essentially two pushed-in hemispheres joined at the equator. The development of the boundary layer and the simple pushed-in shape of the sphere on B6,, suggests that this mode and branch of solutions continue to exist as P + + 00. The rapid decay of energy e,,,(P) would seem to be consistent with this assumption. The results shown in Figures 3 and 4 and elsewhere indicate that the amplitudes of the solutions on B,,, and on parts of other branches may be so large that the shell theory is not applicable. Therefore, these results do not have significance for real shells. A real shell would deform plastically at these large stresses. These remarks also apply to corresponding branches for the thin sphere. I n Figures 5 and 6 we show four solutions on the branches B6,1, Be,, and B6,3 E B4,1 . One of these solutions is for P = 0.0712594, near the critical pressure PZl = P z 2 , and another is for P = 0.0678672 near the critical pressure P t 2 = P t l . The other solutions are for P near the bifurcation loads P, and P, . These solutions have distinct mode shapes and relatively small amplitudes since P is close to P, or P, . This behavior is typical for all even n since the solutions on different symmetric bifurcation branches Bn,l have distinctly different deformation and stress modes for P near P,, and as P varies the solutions continuously change on each branch and merge with the solutions on some other branch which is usually not a bifurcation branch.6 Thus all symmetric solutions are connected as P varies up and down on the appropriate symmetric branches. The energy variation on all branches is, as previously noted, monotone decreasing. However, for P < P, , the energy on most symmetric branches is mainly positive but, for P > P, , the opposite occurs (the notable exception is B 6 , , , see Figure 2a and Table 11) . merge continuously at the eigenlvalues P = P, for n odd. The branches B:l bifurcate down from the lowest eigenvalue P, = 0.0675 and merge, respectively, with BSfz at P f , = 0.0128. Similarly, BZ2 joins BC3 which joins BZ, which joins BL5 which joins BL6 which joins B17 which finally joins BL7 at P f 7 = 0.0124; see Figure 2b and Table IIB. The obvious mergers also occur for the B;, . Since BL7 and BL7 join at P f 7 i.e., The pairs of unsymmetric bifurcation branches B;, yf(e, \u2018 t 7 ) = y-(. - 8, \u2018 t 7 ) = y\u2019(. - e, \u2018 6 7 ) J B&(P) must be symmetric at P = P t 7 . Furthermore, the results show that The only symmetric bihrcation branches to merge directly with each other were B,,,, and B12,1 * 552 L. BAUER, E. L. REISS AND H. B. KELLER P near the critical loads PEl and Pg2. Graph Number P Branch l / 2 l 1 4 i 0.070 I 0.0712594 I 0.678672 1 0.074 I this symmetric state lies on the branch . The value Pk, is not a critical pressure for B6,1. see Table 11. Equal energy loads are found on the branches B t 2 and B& . Graphs of typical solutions on branch B21 are shown in Figures 7a and 8a. Solutions a t some of the upper and lower critical loads P z j and P k j are shown in Figures 7b and 8b. The transition from one branch to another is indicated by these graphs. We note that on BZ1 the \u201csouthern\u201d hemisphere is less distorted than the \u201cnorthern\u201d hemisphere which suffers a relatively large indentation, or dimple, around the pole. Similar features occur in all the B& branches. In fact, we find that P& < P t , < PCl ; AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 553 At each of the unsymmetric eigenvalues P, , for n = 7 , 3 and 9, the solutions B$,l bifurcate up and go through a series of mergers with intermediate branches. Finally, B:, joins BGi for some j at P = P x j or P = Again the symmetric state into which the unsymmetric pairs of solutions finally merge is found to lie on some symmetric branch of solutions. For example, B t 3 join B4,4 at PF3 = 0.0646. Thus we find the amazing result that all bifurcation branches, for both symmetric and unsymmetric modes, are connected to each other by means of intermediate branches. The energies on the bifurcation branches B2#l for n = 7, 3, 9 are negative for P > P , . They are also negative on BnS2 for a limited range of P values. 554 L. BAUER, E. L. REISS AND H. B. KELLER AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 555 is close to P t , & 0.0123971, this solution is nearly symmetric. 5.2. The thin spheres. The results for the thin sphere, k = 10-5, are summarized in Figures 9 and 10. For this value of k the lowest eigenvalue is also unsymmetric. The eigenvalues for k = low5 (see Table IB of Section 3) , are closely spaced. For example a 10% change in P from P = P,, spans seven additional eigenvalues. A 1 yo change includes two additional eigenvalues. The solutions for the thin sphere are qualitatively similar, in many respects, 556 L. BAUER, E. L. REISS AND H. B. KELLER to those previously discussed for the thick sphere.? All the branches bifurcating from symmetric eigenvalues are continuously connected in the same way as for the thick sphere. The solution branch bifurcates down from the lowest eigenvalue P I , . The solution branches bifurcate up from the next two unsymmetric eigenvalues P,, and P I , and have negative energy for P near the eigenvalues. We have not completely investigated the unsymmetric branches of the solution for the thin spheres. However, numerical results that are not shown in the graphs indicate that the unsymmetric solutions connect with the symmetric ones in the same way as for the thick sphere. The formation of boundary layers as P varies on B16,j is more pronounced for the thin sphere than for the corresponding branch of the thick sphere. A feature of the thin sphere that has not been observed for the thick sphere is the existence of isolated solution branches. They are branches that are not connected to any of the solutions which bifurcate from the eigenvalues. For example, one of these occurs for P in the interval 0.006005 < P < 0.010338. 7 Perhaps the most significant difference is the increase in the multiplicity of the solutions as k decreases. For example, for the thick sphere, 7 different symmetric solutions were determined at P = 0.07. For the thin sphere, 46 different symmetric solutions were determined at P = 0.007. AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 557 There are critical loads at P = 0.007760, 0.006095, 0.010338 and 0.006005. The energies on this branch are in the interval 0.119 < (se)ll3 < 0.232. Since the energy is large and positive this branch is not shown in Figure 9. We have not found any isolated branches with negative energy. 558 I (e l27 ( -.I( - .2 - .3' - .4 L. BAUER, E. L. REISS AND H. B. KELLER k = 10-5 Figure lob. Graphs of ( 4 ~ ) ~ ' ~ vs. P for the lower part of El,,, and for the branches B,,,, , BI6,- , and a part of E16 , -2 . 5.3. Boundary layers. We have observed in subsection 5.1 (see Figures 3 and 4) that for the bifurcation branch from the lowest symmetric eigenvalue, a boundary layer forms at 8 = &r. A second boundary layer was observed to develop at 8 = 0 as k -+ 0 ; the solution is small everywhere except at 8 = 0. In Figures 1 2 and 13 we show the formation of this boundary layer by presenting graphs of solutions for a sequence of decreasing values of k (compare with AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 559 P,, &0.0073640, P I , t 0.007392. Figures 3 and 4). These results partially substantiate Friedrichs\u2019 conjectures in [4] about the formation of \u201cdimples\u201d as k -+ 0." + ] + }, + { + "image_filename": "designv10_3_0001725_17452759.2015.1008643-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001725_17452759.2015.1008643-Figure2-1.png", + "caption": "Figure 2. Work flow of file preparation for the impeller job. (a) STL file exported from Magics. (b) ABF file showing the sliced structures after using the EBM Build Assembler. (c) Simulation results from EBM Build Control 3.2.", + "texts": [ + "5 V. The compositions of \u03b1 and \u03b2 phases were measured by energy-dispersive X-ray spectroscopy (EDX) equipped in the TEM. Vickers microhardness tests were carried out on the metallography samples using a Future Tech FM-300e micro hardness tester. A load of 1 kg and a 15-second dwell time were adopted. The hardness test is a suitable mechanical test for our experiment since it is a non-destructive test and it allows a quick estimation of mechanical properties for samples with varying dimensions. Figure 2 illustrates the work flow for the preparation of the impeller build file. Magics software was mainly used for fixing the part and creating supports if they are necessary. Figure 2(a) shows the STL file of impeller exported from Magics. The STL file was sliced into a 2D compressed layer file (ABF file) with a thickness of 0.05 mm by using the EBM Build Assembler software, as shown in Figure 2(b). Only the ABF file can be imported into the embedded EBM Control software for additive manufacturing in the Arcam A2XX machine. It is noted that each prepared build file should be simulated by using EBM Control before starting a job. EBM Control simulation could indicate the approximate build time. During the EBM build process, various problems arose. Some of them resulted in failures of the build. Figure 3(a) shows the appearance of numerous metallisation on the inner surface of the heat shield after some builds" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001069_j.mechmachtheory.2009.09.001-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001069_j.mechmachtheory.2009.09.001-Figure1-1.png", + "caption": "Fig. 1. The example system. All gear meshes are represented by the springs in red color. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)", + "texts": [ + " For example, the gear mesh deflection expressions are different in compound [15] and simple, singlestage planetary gear rotational models [11,14,16]. Some of these models are incorrect in handling gear mesh deflections. Others are correct but do not provide enough detail to expose the source of differences with other models. This study clarifies the confusion. 2. Purely rotational model of compound planetary gears The purely rotational model of an example two-stage compound planetary gear is shown in Fig. 1 (no bearing/shaft stiffnesses are shown). Each carrier, central gear (i.e., sun gear or ring gear), and planet has a single rotational degree of freedom. All external supports and shaft connections are modeled as linear torsional stiffnesses. The gear meshes are represented by stiffness elements, which could be time-varying or nonlinear depending on the research needs. . All rights reserved. x: +1 614 292 3163. ). Fig. 1 also illustrates the concepts of planet train and planet set. A planet set is all the planets associated with a particular carrier. Each planet set is divided into several planet trains. Two planets are considered to be in the same planet train if they are in mesh with each other (meshed-planets) or connected to each other by a shaft (stepped-planets) [3]. 2.1. Choice of coordinates The absolute rotations of central gear j and carrier i are h\u0302j g and h\u0302i c. hj g and hi c are the rotations incurred by the nominal constant rotation speeds of central gear j and carrier i, respectively", + " ; a \u00f028\u00de where ki c;ps; kji g;ps; Ii c;ps, and hi ps are all cidi 1 column vectors given in Appendix A. 3. Characteristics of natural frequencies and vibration modes Numerical results from (18) show that the natural frequencies and vibration modes have distinctive properties when all planet trains within the same planet set are identical and equally spaced. All vibration modes can be classified into two types: overall modes and planet modes. Stage 1 Stage 2 . 6. The overall mode (associated with x5 \u00bc 902 Hz) of the example system in Fig. 1 and Table 1. The deflections of carriers are not shown. In an overall mode, all planet trains in the same planet set have identical motions. There are exactly a\u00fe b\u00fe Pa i\u00bc1di overall modes. Each mode is associated with a distinct natural frequency. Fig. 6 shows a typical overall mode for the compound planetary gear in Fig. 1 with the system parameters in Table 1. Planet modes exist when the system has a stage with two or more planet trains. In planet modes, only the planets in one stage have motion, and all other components have no motion. Stage i has di sets of degenerate (for ci P 3\u00de planet modes, with each having natural frequency multiplicity ci 1. The total number of planet modes of stage i is \u00f0ci 1\u00dedi. In addition, any planet train\u2019s motion in this stage is a scalar multiple of an arbitrarily chosen planet train\u2019s motion. Fig. 7 shows a set of planet modes of stage 1 for the system in Fig. 1 and Table 1. The complete list of natural frequencies is collected in Table 2. The above properties differ from the summary of vibration properties in [15] in two ways. Firstly, [15] separates a \u201drigid body\u201d mode from the above two types. Secondly, the number of overall modes is a\u00fe b\u00fe Pa i\u00bc1di 2 in [15], instead of a\u00fe b\u00fe Pa i\u00bc1di. The rigid body mode that [15] separates from all other modes is actually an overall mode. In the rigid body mode all planet trains in the same planet set have identical motions, which is the characteristic of an overall mode" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002335_tfuzz.2014.2382132-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002335_tfuzz.2014.2382132-Figure1-1.png", + "caption": "Fig. 1. Two inverted pendulums connected by a spring.", + "texts": [ + " \u03bbmax(\u2217) (\u03bbmin(\u2217)) denotes the largest (smallest) eigenvalue of the matrix \u2217. A function \u03b1 :R+ \u2192R+ is of class K if \u03b1 is continuous, strictly increasing, and \u03b1(0) = 0. If \u03b1 is also unbounded, it is of class K\u221e (see [16]). In this section, we illustrate the research motivation about decentralized adaptive output-feedback control of switched large-scale nonlinear systems by means of a practical example of two inverted pendulums [4], [11]. That is, we consider the control of two inverted pendulums connected by a spring as depicted in Fig. 1, which can be considered as a benchmark example of the large-scale system [23], [24], [29]. Each pendulum may be positioned by a torque input ui applied by a servomotor at its base. The equations which describe the motion of the pendulums are defined by x\u030711 =x12, (1a) x\u030712 = (m1gr J1 \u2212 hr2 4J1 ) sinx11 + hr 2J1 (l \u2212b)+ u1 J1 + hr2 4J1 sinx21, (1b) y1 =x11, (1c) x\u030721 =x22, (1d) x\u030722 = (m2gr J2 \u2212 hr2 4J2 ) sinx21 \u2212 hr 2J2 (l \u2212b)+ u2 J2 + hr2 4J2 sinx11, (1e) y2 =x21, (1f) where (x11,x21) T = (q1,q2) T and (x12,x22) T = (q\u03071, q\u03072) T are the angular displacements of the pendulums from vertical and angular rates, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003309_978-3-319-24729-8-Figure1.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003309_978-3-319-24729-8-Figure1.4-1.png", + "caption": "Fig. 1.4 Twelve problems: the goal can be flocking or rendezvous; the robots can be integrator points, unicycles, or flying vehicles; the neighbour sets can be fixed or proximity dependent", + "texts": [ + ", the unicycle model); the sensing constraint (what sensors are available, and who can see whom at any given time); and the control specification (e.g., rendezvous). In this book we focus on three model classes: integrator points, kinematic unicycles, and flying vehicles. We present two types of sensing constraints: fixed neighbour structure and proximity-based neighbour structure. Finally, we investigate two control specifications: flocking and rendezvous. In this way we have 2 \u00d7 2 \u00d7 3 = 12 problems (Fig. 1.4). It will turn out that not all twelve problems make sense, since flocking is a degenerate problem for integrator points. Moreover, many of these problems are as yet open. In the case of a proximity-based neighbour structure, flocking is an open problem for all model classes, and rendezvous has been solved only for integrator points. In the case of a fixed neighbour structure, the flocking problem has been solved for both unicycles and flying vehicles, while the rendezvous problem has been solved only for integrator points and unicycles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003449_tmag.2017.2696559-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003449_tmag.2017.2696559-Figure8-1.png", + "caption": "Fig. 8. Back-EMF versus width and thickness of PM on stator.", + "texts": [ + " The air-gap flux density will also be first increase and then decrease with the increase of the stator PM thickness because the stator PM thickness will influence both flux linkage and equivalent air-gap length. Finally, the stator PM width and thickness are chosen to be 18mm and 8.25mm, respectively. It\u2019s worth noting that the dimensions of the vertically magnetized mover PM not only affect the no-load back-EMF but also have influence on the current density. So the mover PM thickness cannot be too large in order to ensure the heat loading within a reasonable value. The no-load back-EMF versus stator and mover PM width and thickness are shown in Fig. 8 and Fig. 9. All those optimized values of the key geometry parameters of the proposed machine are listed in Table I. The three LPMVMs used in comparison share the same geometry size, turns per phase and phase current. The input electric parameters are listed in Table II. The comparison of back-EMF, average thrust and power factor of three LPMVMs are shown in Fig. 10 to Fig. 12. The no-load back-EMF e can be obtained by: \ud835\udc52 = \u2212 \ud835\udc51\ud835\udf13\ud835\udc5a \ud835\udc51\ud835\udc61 (3) where \u03c8m is the flux linkage introduced by PMs. Since the noload back-EMF is introduced by the PM flux linkage, the proposed LPMVM with a higher air-gap flux density can offer a larger no-load back-EMF, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure6.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure6.7-1.png", + "caption": "Fig. 6.7 Jerk: problem 3", + "texts": [ + " The orientation of the bar is given according to the expression D 0:25 C 0:1t C 0:05t2 C 0:075t3, where the angle is given in radians and the time t is in seconds. The position of the slider is commanded to follow the expression r D 0:6 0:25t 0:025t2 C 0:001t3, where r is given in meters and t in seconds. Determine the velocity, acceleration, and jerk of the slider at time t D 3 s. 3. In the development of cam profiles due to tribological implications and the ability of the actuated body to follow the cam profile without chatter, the jerk must be taken into proper account. The cam shown in Fig. 6.7 is designed in such a way that the position of the center of the roller A must follow the function r D b c cos. /, where b > c. Considering that the cam does not rotate, determine the magnitude of the jerk of A in terms of if the slotted arm revolves with a constant counterclockwise angular rate P D !. 4. The disk shown in Fig. 6.8 rotates about a fixed axis passing through point O with angular velocity ! D 5 rad=s, angular acceleration \u02db D 2 rad=s2, and angular jerk D 3 rad=s3. The small sphere A moves in the circular slot in such a way that in the same instant we have \u02c7 D 30\u0131, P\u030c D 2 rad=s, R\u030c D 4 rad=s2, and \u00ab\u030c D 4 rad=s3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000941_j.mechmachtheory.2011.12.005-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000941_j.mechmachtheory.2011.12.005-Figure1-1.png", + "caption": "Fig. 1. Dynamic model of the spur gear pair.", + "texts": [ + " Frequency\u2013response equation, jump phenomenon and stability analysis are investigated in various cases of primary, super-harmonic and sub-harmonic resonances. Moreover, a comprehensive physical parametric study is accomplished to evaluate the effect of various dynamic and manufacturing parameters such as stiffness and damping values, detuning parameter and excitation amplitude on the DTE amplitude. Attractive nonlinear behavior of the DTE amplitude is observed under super/sub harmonic resonances in comparison with the primary resonance case (for various case studies while the mentioned dynamic parameters are varied). As shown in Fig. 1, a gear system is composed of two perfect involutes spur gears mounted on input and output axles. Neglecting the backlash initially, the equations of motion for two gears are described as [1\u201311,17,21]: I1\u20ac\u03b81 \u00fe c r1 _\u03b81\u2212r2 _\u03b82 h i r1 \u00fe k r1\u03b81\u2212r2\u03b82\u00bd r1 \u00bc Ti I2\u20ac\u03b82\u2212c r1 _\u03b81\u2212r2 _\u03b82 h i r2\u2212k r1\u03b81\u2212r2\u03b82\u00bd r2 \u00bc \u2212To \u00f01\u00de where the inertias of the input and output axle/driver elements are denoted by I1 and I2; k and c are the linear stiffness and structural damping of the gear pair; \u03b81, \u03b82 and r1, r2are the angular displacements and radius of the gear wheels; Ti and To are the input and output torques, respectively (for discussion on the restoring force, see Appendix A)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002005_j.ijfatigue.2014.01.029-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002005_j.ijfatigue.2014.01.029-Figure3-1.png", + "caption": "Fig. 3. (a) Global finite element model of the RCF ball-on-rod test consisting of three S contact region. The white square is the domain of interest in the global model, chosen for the center. The stress fields obtained from the global model are used as boundary cond", + "texts": [ + " The stress distributions obtained from global model are transferred to the submodel in the form of stress boundary conditions (BCs). With these BCs, submodel is run which then provides local elastic\u2013plastic stress/strain fields in the steel matrix surrounding carbide particles. This twostep global\u2013local modeling approach takes into account the effect of both RCF loading and heterogeneous inclusions to correctly investigate the ratcheting phenomenon. Further discussion about these two models is presented in Sections 3.3 and 4.2. The global FE model shown in Fig. 3a, consists of M50-NiL rod (with graded hardness/yield strength/microstructure) at the center, which is radially loaded by three lubricated silicon nitride (Si3N4) balls, resulting in three elliptical Hertzian contacts. As a result, the contact region near ball-rod interface is subjected to a maximum Hertzian stress of 5.5 GPa which was used in experiments [30\u201332]. This value of peak Hertzian stress induced at the ball-rod interface in experiment is matched in the 2D FE simulation of Hertzian contact", + " Linear CPE4T (4 node plane strain quadrilateral) coupled temperature-displacement elements are used as they allow specification of temperature dependent material properties required to model the graded material properties of M50-NiL. It is shown in past [17,34,41,42] that such modeling approach results in accurate specification of the graded material properties. On the other hand, each Si3N4 ball is modeled as a homogeneous material with elastic material response using E = 310 GPa [43]. Each Si3N4 ball is meshed with approximately 12000 CPE4 elements. Global FE model shown in Fig. 3a simulates the RCF test without taking into consideration the influence of microstructural heterogeneities i.e. carbide particles. The NIKH model used for FE simulations is based on J2 plasticity. Therefore, the von-Mises stress governs yielding of a material and therefore, its stress distribution in the vicinity of contact region is shown in Fig. 3b. It can be observed that the maximum stress in M50-NiL rod occurs in the subsurface at a depth of about 150 lm. As a result of such high Hertzian stresses, the subsurface material deforms plastically and develops a plastic zone in the form of a circumferential ring, shown in Fig. 4. The plastic zone is developed slightly beneath the surface at a depth of about 60 lm and it extends up to 270 lm as shown in Fig. 4. As the case region of M50-NiL rod is approximately 2.5 mm thick [44], the entire plastic zone is well contained inside the case layer", + " To achieve this, a small area, representative of the carbide microstructure scale, is chosen within the global model for submodeling with a carbide particle embedded in it. The smaller area of the submodel and refined mesh facilitate the study of physics associated with the effect of carbide particles under RCF. Such \u2018submodeling\u2019 approach allows incorporation of complex material and geometric details, which in general cannot be incorporated in the global model due to large differences in length scales. As shown in Fig. 3b, a small domain of interest in the subsurface of the rod (indicated by white square) is chosen for the submodel. The size of this domain is roughly 20 20 lm, which is approximately equal to the projected area of Vickers indent (at 100 g load) measured in the experiments [31]. Such small scale of submodel permits sufficiently accurate study of stress\u2013strain fields in the vicinity of a carbide particle with a well-refined mesh. The domain is located at a depth of about 150 lm from the surface where the von-Mises stress reaches its peak value (Fig. 3b), a potential site for subsurface fatigue crack nucleation [5]. In general, the location of this domain can be arbitrarily chosen to study the influence of carbide particles at various depths. A circular carbide particle with properties of the vanadium carbide is included at the center of domain (Fig. 3b and c). The submodel can be considered a unit cell with a circular carbide at the center. The ratio of carbide area to unit cell will determine the carbide volume fraction. Since carbide particles in M50-NiL are circular and are uniformly distributed [35] with minimal interaction, modeling a single carbide within a unit cell is appropriate. For this submodel, the time varying stress fields obtained from the global model are applied as boundary conditions on its edges (see Fig. 3c). The incorporation of carbide particles in the submodel thus introduces heterogeneity into the domain. Fig. 6 shows the equivalent plastic strain field in the vicinity of carbide particle inside the submodeling domain. The maximum strain accumulation in the steel matrix surrounding the carbide particle ( 1.6%) is an order of magnitude greater than the nominal strain away from particle ( 0.24%), thus clearly manifesting the effect of strain amplification. It should be noted that such strain amplification is significantly higher in high strength bearing steels because of their low strain hardening exponents and higher percentage of carbide particles", + " The presence of such non-zero mean stress is the primary requirement for a material to accumulate continuous plastic strain via ratcheting in each RCF cycle as discussed in the following sections. Fig. 7 shows the variation of shear stress for a single RCF cycle, but in order to investigate the ratcheting phenomenon, it is necessary to simulate multiple RCF loading cycles which will allow continuous accumulation of ratcheting strain in the vicinity of the carbide particle. This is achieved by analyzing two revolutions of the test rod (see Fig. 3a), which corresponds to six RCF cycles of each material point. Fig. 8 shows the variation of orthogonal shear stress (blue curve) and accumulation of equivalent plastic strain (black dotted line) for six RCF cycles experienced by a single material point located at 150 lm below the surface in global model (without carbides) and in submodel (with carbide) respectively. Such analysis can be repeated at different depths to get the spatial variation in cyclic hardening of a material via ratcheting. It is observed from Fig", + " The material points which are on the diametrically opposite sides of carbide particle show nearly identical behavior. The points at 45 , 135 , 225 and 315 orientations undergo a shear stress cycle with similar stress amplitudes. Despite similar stress amplitudes ( 1100 MPa), the mean stress values at these orientations differ significantly i.e. 175 MPa at 45 and 225 , and 55 MPa at 135 and 315 . This difference in the mean stress values at these orientations can be attributed to the rolling direction of rod with respect to the balls (see Fig. 3a). If the rolling direction was reversed, then mean stress values at these locations would switch. Compared to these oblique orientations, the points at 0 , 90 , 180 and 270 orientations experience shear stress cycles with high stress amplitude ( 1700 MPa) and higher mean stress (>110 MPa). The ratcheting behaviors at these orientations are summarized in Fig. 11a. Eight different curves representing ratcheting strain accumulation at various orientations around a carbide particle are shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure7.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure7.8-1.png", + "caption": "Figure 7.8 illustrates a slider link on a rotating arm . Calculate", + "texts": [], + "surrounding_texts": [ + "7. Angular Velocity 339\nExercises\n1. Notation and symbols.\nDescribe the meaning of\na- GWB b- B WG G d- g WB B f- ~WGc- GWB e- B WG\ng- gWl h- ~Wl . 3 G ' k- gWl 1- JWi '1- 2Wl j- RB\nm- G rp(t) G 0- b.R p- b.p Gd Bd\nn- 2 Vp q- - r- - dt dt\nGd Gd Bd v- G r p\nG \" x- GVBs- _ G r p t- _ B r p u- - B r p w- d p dt dt dt\n2. Local position, global velocity.\nA body is turning abo ut the Z-axis at a constant ang ular rate a = 2 rad/ sec. Find the global velocity of a point at\n3. Global position, constant angular velocity.\nA body is turning abo ut the Z-axis at a constant angular rate a = 2 rad/ s. Find the global position of a point at\nafter t = 3 sec if the body and global coordinate frames were coinci dent at t = 0 sec.\n4. Turning about x-axis .\nFind the angular velocity matrix when the body coordinate frame is turning 35 deg / sec at 45 deg about the x-axis.\n5. Combined rotation and angular velocity.\nFind the rotation matrix for a body frame after 30 deg rotation about the Z-axis, followed by 30 deg about the X -ax is, and then 90 deg about the Y-axis . Then calculate the angular velocity of the body if it is t urn ing with a = 20 deg / sec, /3 = - 40 deg / sec, and /y = 55 deg / sec about the Z, Y, and X axes respect ively.", + "340 7. Angular Velocity\n6. Angular velocity, expressed in body frame.\nThe point P is at rp = (1,2,1) in a body coordinate B(Oxyz) . Find gwB when the body frame is turned 30 deg about the X -axis at a rate '1 = 75deg / sec, followed by 45 deg about the Z-axis at a rate a = 25 deg / sec.\n7. Global roll-pitch-yaw angular velocity.\nCalculate the angular velocity for a global roll-pitch-yaw rotation of 0: = 30 deg, f3 = 30 deg , and 'Y = 30 deg with a = 20 deg / sec, ~ = -20 deg / sec, and '1 = 20 deg / sec.\n8. Roll-pitch-yaw angul ar velocity.\nFind gwB and GW B for the role, pit ch, and yaw rates equal to a = 20 deg / sec, ~ = -20 deg / sec, and '1 = 20 deg / sec respect ively, and having the following rotation matrix:", + "7. Angular Velocity 341\nand find B v and B a of m at eM of the slider by using the rule of mixed derivative\n12. * Differentiating in local and global frames.\nConsider a local point at B r p = ti + j. The local frame B is rotating . G b . b h Z . C I I \"\u00ab B Cd G Bd G dIII y o a out t e -axis. a cu ate dt rp, dt rp, dt rp, an Cd B dt rp.\n13. * Skew symmetric identity for angular velocity.\nShow that\n14. * Transformation of angular velocity exponents.\nShow that\n15. * An angular velocity matrix identity.\nShow that\nand C}k = (_I)k w2(k - l ) (w2 1 _ ww T ) .\n16. * Angular velocity and global triple rotation frequencies.\nFind the angular velocity in terms of the 12 cases of triple global rotations in Appendix A.\n17. * Angular velocity and local triple rotation frequencies.\nFind the angular velocity in terms of the 12 cases of triple local ro tations in Appendix B." + ] + }, + { + "image_filename": "designv10_3_0000566_tro.2006.889485-Figure17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000566_tro.2006.889485-Figure17-1.png", + "caption": "Fig. 17. Body free diagram of the experimental system.", + "texts": [ + " 16(d)], and finally, the power was turned off [Fig. 16(e)]. The pictures in Fig. 16 show that propulsion occurs when a traveling wave is created, as is expected for low Reynolds number. No propulsion was observed when the beam was actuated by a standing wave, Fig. 16(c). The experimental results were reproducible, and no aging was observed due to heating of the piezo tail. The magnitude of the propulsion force was calculated by considering the torque force equilibrium at the fixed hanging point, shown in Fig. 17. There are four dominant forces in the system: the propulsive force ; the weight of the swimming tail ; the weight of the input wire ; and the floating force . The propulsive force attained in the experiment was as follows: N (28) where kg is the mass of the tail, kg/m is the density of the fluid, kg is the mass of the tail, m/s is gravity, m is the maximal distance the tail traveled, and 2 m is the height of the hanging point. The amplifier used is able to supply only square waves to the actuator, thus the input voltage is defined as follows: (29) where 60 V -60 V The influence of the square wave on the swimming tail can only be estimated because the analytical model was developed for sinusoidal input voltages" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000108_i2008-10388-1-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000108_i2008-10388-1-Figure4-1.png", + "caption": "Fig. 4. Geometry of the idealized stroke of a rigid rod consisting of N particles of radius a with distance l0 between the centers of adjacent beads. The length parameter L is defined as L = (N \u2212 1)l0.", + "texts": [ + " As expected, F(z) only depends on z roughly over the length L of the filament and then becomes constant. Now, we consider the time average of F(z > L) over one beating cycle as a suitable measure for fluid transport, which we call pumping performance F\u0304\u221e = 1 T \u222b t+T t dt\u2032 F(z > L, t\u2032) , (28) where T is the period of one actuation cycle. To understand how well the magnetically actuated filament transports fluid, we compare it to an idealized stroke of a rigid rod with the same length parameter L = (N \u2212 1)l0 and the same thickness as the filament (see Fig. 4): 1) In the transport stroke the rod is oriented perpendicular to the bounding surface and it is dragged parallel to the surface along a distance L keeping its center a distance L/2 + 3a above the surface. 2) The rod is then rotated by 90\u25e6 to be parallel to the surface and then in the recovery stroke it is dragged along its long axis to its original position with a separation of d + 3a above the surface. In unbounded Stokes flow, the first and second part of the stroke use the respective maximal and minimal hydrody- namic resistance to produce a net fluid transport over one cycle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003099_tro.2016.2633562-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003099_tro.2016.2633562-Figure3-1.png", + "caption": "Fig. 3. Different frames of reference of a quadrotor and its rotors. The inertial frame fixed on the earth {A} and body-fixed frame attached to the vehicle {B} along with rotor reference frame {C} and tip-path-plane {D}.", + "texts": [ + " The TPP rotates with the rotor and is also aligned with the tilt of the rotor due to blade flapping and, to first order, the rotor is stationary in this frame. Throughout the paper, e1 , e2 , e3 are used to denote unit vectors in the x, y, z directions, respectively. Consider the control volume shown in Fig. 2 associated with a slightly tilted actuator disc, a result of the rotor experiencing both translational and axial air motion with velocity V \u2208 R3 . This is the relative velocity between the vehicle\u2019s body-fixed frame {B} and inertial frame {A} expressed in {B} as shown in Fig. 3. The stream velocity is equal in magnitude but opposite in direction to the vehicle velocity V when there is no wind but is the sum when the wind velocity W \u2208 R3 expressed in {B} is present, i.e., vs = \u2212 V + W \u2208 R3 . The spinning rotor induces additional air velocity vi \u2208 R3 through the rotor so that the total air velocity through the rotor va is va = vi + vs . We denote the velocity of the wake far downstream by v\u221e. All these velocities are expressed in {B}. Remark 1: The induced velocity on a rotor is a nonuniform distribution and its effect can be modeled by Mangler and Squire method [11], [12], [18]", + " 1 CT where we do not provide symbols for the positive constants for the moment. Fig. 5 graphs \u03ba versus CT for low disc loading (helicopters) and high disc loading (quadrotor) rotors, the rotor system used for the experimental work in this paper and based on values obtained in Section IV. For the rotors on our quadrotor vehicle where CT << 10\u22124 , the dominant part of the model is the hyperbolic term 1/CT . This is supported by experimental results shown in Fig. 7 of Section IV. Note that the model plotted in Fig. 5 is supported by [18, Figure 3.18, pg. 105], although the nature of the high disc loading model is not considered by Leishman as it is not relevant to the helicopter rotors discussed [18]. In practice, the rotor for our vehicle will never function outside of the dominant region where 0 < CT << 10\u22123 . In this region, the linear term const.CT is negligible, while the hyperbolic term can be approximated by a linear function 1 CT \u2248 const. C\u0304T \u2212 const. C\u03042 T (CT \u2212 C\u0304T ) where C\u0304T is an operating point. Thus, it is sufficient to approximate the \u03ba model by a linear model in the region of operation of such rotors by \u03ba = d0 + d1CT (17) where d0 > 0 is a positive constant and d1 < 0 is a large and negative constant" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure8-1.png", + "caption": "Fig. 8. Contacting model used for finite element analysis.", + "texts": [ + " Avoidance of worm singularities requires the limitation of worm threads. The contents of the paper cover the computerized approach for avoidance of singularities and undercut- ting of the tools that generate the face-gears. The contents of the paper also describes a stress analysis based on finite elements. The advantage of the approach developed in this paper is that the contacting models are developed automatically using analytical determination of the surfaces of the gear teeth and the rim (Fig. 8). Localization of bearing contact in a face-gear drive requires application of a shaper with tooth number Ns N1 = 2 or 3, where Ns and N1 are the tooth numbers of the helical shaper and the pinion of the gear drive, respectively. The face-gear tooth surface is generated as the envelope to the family of shaper tooth surfaces. Previously the design of face gear drives was based on application of a spur involute shaper and pinion [13,14,16,17]. In the case of application of a face-gear drive with a helical pinion, it becomes necessary to determine the most favorable type of geometry to be applied", + " (ii) Improvements of contact mentioned above may be accompanied by slight deviation of the path of contact from initially assigned longitudinal orientation. (iii) The iterative optimization process can exclude areas of severe contact (see below). The two examples, 2 and 3, shown in Table 2 correspond to two sets of design parameters obtained by optimization. Fig. 27 shows that the paths of contact are oriented: (i) across the surface for an involute pinion (Fig. 27(a)) and (ii) in longitudinal direction for a pinion determined by a parabolic rack-cutter (Fig. 27(b) and (c)). Fig. 8 shows the applied contact model of three pairs of teeth. Figs. 28\u201331 show the results of stress analysis and formation of the bearing contact. Details of elements of the three tooth model (Fig. 8) area as follows: First order elements (enhanced by incompatible modes to improve their bending behavior [3]) have been used to form the finite element mesh. The total number of elements is 71,460 with 87,360 nodes. The material is steel with the properties of Young s modulus E = 2.068 \u00b7 105MPa and Poisson s ratio 0.29. A torque of 4000Nm has been applied to the pinion in the three cases. Fig. 28(a) and (b) show the formation of the bearing contact on the face-gear tooth surface in examples 2 and 3, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001680_j.triboint.2011.11.025-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001680_j.triboint.2011.11.025-Figure4-1.png", + "caption": "Fig. 4. Coordinate transformation of the involute function.", + "texts": [ + " An involute curve changes its curvature constantly as the distance to the base circle increases. In the calculation model, the real involute curves map the tooth flank profiles for any position of the contact point on the length of action. Therefore, the involute curves must be described in the x\u2013z plane of the local Cartesian coordinate system. Because it moves along the involute during meshing, the curve of the involute is initially described in a fixed plane coordinate system (x0, z0) with its origin at the center of the gear wheel (see Fig. 4). The location of any point Yinv on the involute is defined in the fixed coordinate system (x0, z0) as a function of the roll angle cyinv: x0inv\u00f0cyinv\u00de \u00bc rb\u00f0sin\u00f0cyinv\u00de _ cyinvcos\u00f0cyinv\u00de\u00de \u00f02\u00de z0inv\u00f0cyinv\u00de \u00bc rb\u00f0cos\u00f0cyinv\u00de\u00fe _ cyinvsin\u00f0cyinv\u00de\u00de \u00f03\u00de Transferring the point Yinv to the x\u2013z plane of the local Cartesian coordinate system necessitates first calculating the location of the contact point Y0, relative to the center of the gear wheel as the profile angle ay0 and the radius ry0: ay0 \u00bc arctan T1A\u00fesy0 rb " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002261_1.4007348-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002261_1.4007348-Figure2-1.png", + "caption": "Fig. 2 Soft DEM contacts (superscript I 5 inertia fram; r 5 rotating body frame; a 5 azimuthal frame). (a) Ball-ball conformal contact. (b) Inner race reference frames. (c) Ball-race non-conformal contact.", + "texts": [ + " The degree of overlap is then used to determine the contact forces acting on the bearing components. To simplify the overlap calculations, bearing components are assumed to be made of simplified geometry consisting of sections of sphere and cylinders. The overlap d between the elements is given by d \u00bc R1 \u00fe R2 r1 r2 D E - for conformal contacts (1) or d \u00bc R1 R2 \u00fe r1 r2 D E - for nonconformal contacts (2) where R1 and R2 are the radii of the bodies, and r1 and r2 are the position vectors of the bodies. Figure 2(a) depicts a conformal contact between two balls while Figs. 2(b) and 2(c) depict a nonconformal contact between ball and inner race. Please note that Eq. (1) and Eq. (2) should be used in the appropriate frame of references. The normal contact force can be determined using the overlap (Eqs. (1) and (2)) and Hertzian force-deflection relationship FN \u00bc Kd3=2 (3) where K is the Hertzian stiffness coefficient. This approach of calculating normal contact force is much simpler and less computationally intensive than the method described by Gupta [17]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001180_tim.2011.2159322-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001180_tim.2011.2159322-Figure6-1.png", + "caption": "Fig. 6. Hardware structure of the system simulator.", + "texts": [ + " The data collection part consists of the high-pass filter and amplifier to filter out the offset in the signal to the microphone, the bandpass filter to remove the aliasing and the dc components, and the 16-b 100 ksps A/D converter circuits. The process arithmetic part processes the algorithms previously mentioned using a TMS320F28335 DSP bus-type module. The data from the data collection part are manipulated in the process arithmetic part to obtain the arrival time of the sound signal from the faulty insulators, the arrival time difference between microphones, the distance and orientation from the sound source to the microphones, and, finally, the coordinates of the sound source. Fig. 6 illustrates the data collection and the process arithmetic parts functionally. While the DSP module is calculating the distances and angles from the sound source to the microphones and coordinates of the sound source, the obtained data are continuously sent to the PC through the universal asynchronous receiver/transmitter communication channel. Fig. 7 shows the sound signals received at the three microphones. After the cross-correlation algorithm on the DSP, the arrival time differences between the microphones, for example, \u0394n12, are calculated" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001050_0191-8141(80)90019-x-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001050_0191-8141(80)90019-x-Figure1-1.png", + "caption": "Fig. 1. Axes used to describe the relative orientations of the first folds and the second folding movements. The wave train drawn in solid lines at the left represents real folds in layering after the first movements. The wave train drawn at the right represents imaginary folds formed by the second movements alone (i.e. in a dyke injected normal to a 2 between the two episodes of folding). Below are shown both sets of axes and the angles ct, fl, ~ and 6.", + "texts": [ + " The resulting patterns are thought to sufficiently represent the range of patterns to be encountered in nature, even though natural superposed folding, or synchronous cross-folding, must rarely occur by such simple deformations. The interference patterns figured here were calculated by a computer program described elsewhere (Thiessen, in press). This program permits any number of folding movements to be superposed in any desired relative orientations and the calculation and display of serial, two-dimensional crosssections in any desired orientation. Following Ramsay (1967, p. 521) we designate the shear direction in the second axial planes az and the direction normal to this in the axial planes b2 (Fig. 1). Poles to the first and second axial planes are designated ct and c2 respectively. The direction of the first fold axis is termed f l (Ramsay 1967, fig. 10-2) and the normal t o f t in the first axial planes is dr. Where the first folds are assumed to have formed by heterogeneous simple shear on the first axial planes, at and bt are respectively the slip direction in the first axial planes and the normal to the slip direction. Notice that a t and bt describe the movements that produced the first folds, while dt and f t describe the orientation of the resulting first fold forms" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.3-1.png", + "caption": "FIGURE 1.3. 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 4 1. Introduction 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 1.3 (a)-(c) , and 1.4 (a)-(c) respectively. The coordinate of an active joint is controlled by an actuator. A passive joint does not have any actuators and its coordinate is a function of the coordinates of active joints and the geometry of the robot arms . Passive joints are also called ina ctive 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_3_0002571_j.ymssp.2019.106275-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002571_j.ymssp.2019.106275-Figure5-1.png", + "caption": "Fig. 5. The relationship between the bearing outer ring and pedestal with clearance fit.", + "texts": [ + " The rotational motion of the RBE coupled with the bearing inner ring is described with Euler\u2019s rotation equations: Ij _xj \u00fexj Ij xj \u00fe cbr xj \u00bc Mr j \u00feMr b1 \u00f08\u00de where Ij is the inertia matrix of the jth RBE; cbr is the damping matrix of the bearing in three rotational directions. The interactions between bearing outer ring and pedestal are calculated by the model as follows. 2.4. The interactions of the bearing outer ring and pedestal Clearance fit is employed between bearing outer rings and pedestal. In our model, rigid preload type is taken, the axial DOF and all the rotational DOFs of the outer ring are restricted. So the interactions between bearing outer ring and pedestal are mainly in radial direction. Fig. 5 shows the relationship between the bearing outer ring and pedestal with fit clearance d0. The bearing pedestal is in the Cartesian inertial coordinate system-yoz. O is the coordinate system center which coincides with the inner hole geometric center of the bearing pedestal. Fig. 5(a) shows the initial state, Ro is the outer radius of the bearing outer ring, Rp is the inner hole radius of the bearing pedestal. At this time, the center of the bearing outer ring coincides with the coordinate system center. When the bearing is loaded, relative movement occurs between bearing outer ring and pedestal as shown in Fig. 5(b). O1 y; z\u00f0 \u00de is the geometric center of the bearing outer ring in the Cartesian inertial coordinate system-yoz. OO1 ! is the relative displacement between bearing outer ring and pedestal, cAB is the contact area. The contact deformation d hpi at the angular position hpi can be expressed as: d hpi \u00bc ycoshpi \u00fe zsinhpi do hpi 2 cAB 0 hpi R cAB ( \u00f09\u00de A spring-damper model shown in Fig. 6 is proposed to calculate the interaction force between the bearing outer ring and pedestal. As shown in Fig. 6, a serial of spring-damper elements distribute equably in radial direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure11.15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure11.15-1.png", + "caption": "Figure 11.15.2 Bump scrub geometry for a rigid arm with pivot axis slope.", + "texts": [ + " The leading arm, with extreme anti-dive, is less of a problem in this respect. 222 Suspension Geometry and Computation The steered transverse arm was more successful, and was used for many years on small rear-engined family saloons. To minimise the kingpin inclination variation and the camber change, the arm was made long, with the pivot axis close to the vehicle centreline, Figure 1.6.3. In the case of a rigid arm with zero slope of the pivot axis, and no wheel angles, the bump scrub is particularly simple to analyse. In Figure 11.15.1(a), which is the view along the pivot axis, the distance from that axis to the central contact point is LC (not LA to the wheel centre), and the angle of this radius from the horizontal is uC. The radiusRC is slightly different fromRA because of thewheel camber, but this small difference is neglected here. In the plan view of Figure 11.15.1(b), for a locked-wheel vehicle, the resulting total scrub will be perpendicular to the pivot axis, along direction AC. For a (small) suspension bump zS, the total scrub is s \u00bc LC du sin uC \u00bc zS tan uC The total locked-wheel scrub rate coefficient is therefore \u00abBScd0;T \u00bc tan uC \u00bc HAx RC HAx RA This total locked scrub resolves into directions along the prospectively rolling wheel and perpendicular to it. Normally the small wheel steer angle is neglected, so that the scrub can be resolved more simply into vehicle X (longitudinal) and Y (lateral) components. The longitudinal scrub coefficient, relevant to braking, is \u00abBScd0;X \u00bc \u00abBScd0;T sin uAx \u00bc HAx sin uAx RA but RP sin uAx \u00bc RA so \u00abBScd0;X \u00bc HAx RP Similarly, the Y component of the scrub gives a lateral scrub rate coefficient \u00abBScd0;Y \u00bc \u00abBSc0;T cos uAx giving \u00abBScd0;Y \u00bc HAx RS This lateral component is the one relevant to handling and the roll centre height, and the result here agrees with the simple calculation normally used. The case of a pivot axis with slope ismore complex, Figure 11.15.2.With an arm angularmotion du, the tangential displacement of the contact point of the locked wheel is t \u00bc LC du which occurs in the sloping plane perpendicular to the axis. This resolves into s1 \u00bc t sin uC in the horizontal plane and s2 \u00bc t cos uC in the sloping plane. This latter part further resolves into s3 \u00bc t cos uC sinfAx in the horizontal plane and zS \u00bc t cos uC cosfAx vertically. The Y component of the scrub is sY \u00bc s1 cos uAx \u00fe s3 sin uAx \u00bc t sin uC cos uAx \u00fe t cos uC sinfAx sin uAx The lateral scrub rate is therefore \u00abBScd0;Y \u00bc sY zS \u00bc tan uC cos uAx cosfAx \u00fe sinfAx sin uAx cos fAx Now HAx RS \u00bc HAx RA RA RS \u00bc tan uC cos fAx cos uAx and sin uAx \u00bc LCD RS so \u00abBScd0;Y \u00bc HAx RS \u00fe LCD tan fAx RS \u00bc HAx RS \u00fe HS HAx RS \u00bc HS RS whereHS is the height of the swing centre, so the conventional simple expression is applicable even when the axis is sloped" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002767_j.ijheatmasstransfer.2019.07.053-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002767_j.ijheatmasstransfer.2019.07.053-Figure6-1.png", + "caption": "Fig. 6. Adopted computing domain.", + "texts": [ + " It then compared the results from three aspects: particle size distribution, powder bed tightness, and lamination thickness. In addition, the computing resources are configured as Intel Xeon Gold 5120 CPU (32 GB RAM). The material used in this paper is the 316L stainless steel, and its alloy composition (mass percentage) is Fe 65.395, C 0.03, Si 1.0, Mn 2.0, P 0.045, S 0.03, Ni 12.0, Cr 17.0, and Mo 2.5. Table 1 shows the required physical properties of 316L stainless steel [25]. Table 2 shows the heat source parameters used herein, and the absorption coefficient was considered to be a constant. Fig. 6 is the adopted computing domain with an overall size of 1000 lm 150 lm 130 lm with a substrate thickness of 50 lm and a mesh size of 2.5 lm. During the calculation, the initial temperature was 300 K, the total formation was set to 600 ls, and the laser started to move from the horizontal coordinate (100 lm, 75 lm) with stops after 500 ls. In terms of computational efficiency, the average calculation time required for the SLM singlepass formation was 8 h. To analyze the influence of particle size distribution, powder bed tightness, and lamination thickness on the SLM single-pass formation, the single-layer powder beds under different conditions were obtained by Yade (Table 3)", + " The powder bed distributions in the case where the average values are inconsistent and half widths are uniform are shown in Fig. 7. The number of particles in the singlelayer powder bed is significantly reduced as the average particle size increases. The tightness of the large-sized particle powder bed is significantly lower. Fig. 8 is the simulation results of the temperature field and the solid-phase fraction during the formation at different times in calculation scheme A1. The cross-sectional view is the Y-direction middle section of the calculation domain shown in Fig. 6. The metal particles were melted by heat to form the molten pool once the laser began to act on the powder bed; as the laser moved forward, new particles were continuously filled in the front of the molten pool, and the tail of the molten pool gradually cooled down to form n flowchart. the solidified track. Some of the substrate was also melted by heat and solidified. Finally, the area in which the laser acted in the powder bed formed the continuous solidified track. Fig. 9 shows the local temperature field and velocity field distributions of the middle section at a certain moment in the calculation scheme A1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002860_tie.2019.2941132-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002860_tie.2019.2941132-Figure5-1.png", + "caption": "Fig. 5. Coordinate transformation for the ocean current", + "texts": [ + " The reference speed here is the tracking speed that HOV expected to achieve. If the current is taken into account, the expected reference speed needs to be changed. For the ocean current [ 0 0 0]T E x y zu u w in the inertial coordinate system, it can be time-varying or constant. In the later simulation study, for the sake of simplification, the ocean current in the inertial coordinate system is assumed to be constant. The ocean current in the body-fixed coordinate system can be obtained by the following transformation (Fig. 5): cos sin sin cos u x y v x y w z u u u v u u w w (5) where , ,u v wu v w are the currents at surge direction, sway direction, heave directions. The expected relative speed with the ocean current is: ' ' ' ', , ,d d u d d v d d w d du u u v v v w w w r r (6) 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. The whole kinematic control system is taking the HOV system as a control system with state = T x y z \u03b7 and input T u v w rv " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003688_s11837-019-03773-5-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003688_s11837-019-03773-5-Figure1-1.png", + "caption": "Fig. 1. WAAM process setup and fabricated ER70S-6 wall.", + "texts": [ + " The microstructures of the as-printed and heat-treated samples were characterized using optical and scanning electron microscopy (OM and SEM) and electron backscatter diffraction (EBSD) analysis. In addition, Vickers microhardness measurements and uniaxial tensile testing along both deposition and building directions were carried out to evaluate the mechanical properties of the component. In this study, a low-carbon low-alloy steel ER70S6 wire with diameter of 0.9 mm was used to build up a wall-shape component on a ASTM A36 mild steel base plate using the wire arc additive manufacturing method. Figure 1 shows the setup of the WAAM process, the fabricated ER70S-6 wall, and the orientation of tensile testing samples along the deposition (horizontal) and building (vertical) directions. The nominal chemical composition of the feedstock wire (in wt.%) was 0.06% to 0.15% C, 1.40% to 1.85% Mn, 0.80% to 1.15% Si, \u00a3 0.04% S, \u00a3 0.03% P, \u00a3 0.15% Cr, \u00a3 0.15% Mo, \u00a3 0.03% V, \u00a3 0.5% Cu, and balance Fe. The surface of the base plate with dimensions of 250 mm 9 150 mm 9 12 mm was wire brushed, then cleaned in acetone ultrasonically to remove oxide layers and degrease the surface prior to deposition of the first layer of the part", + " Note also that the samples were polished and etched before applying the indentations to evaluate the effect of different microstructures on the microhardness of the sample. To investigate the effect of solidification defects on the anisotropic mechanical behavior of the 3D-printed component, an Instron load frame was used to perform uniaxial tensile testing at crosshead speed of 8 mm/min on samples prepared from the deposition (horizontal) and building (vertical) directions based on the ASTM E8m-04 standard subsize specimen with dimensions of 100 mm 9 25 mm 9 5 mm.17 As shown in Fig. 1, tensile samples were prepared from different locations along both the deposition and building directions. Open-to-the-surface solidification defects on the horizontal and vertical tensile samples before and after tensile testing were detected using a Leica A60 F stereomicroscope. Figure 2a schematically illustrates two successive beads in the as-printed WAAM ER70S-6 sample, indicating four distinguishable zones with distinct microstructure, i.e., melt pool center, melt pool boundary, and the HAZ covering two different regions in the previously solidified bead" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.18-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.18-1.png", + "caption": "FIGURE 2.18. Local roll-pitch-yaw angles.", + "texts": [ + "94) therefore, [~:] [ cos () cos 'l/J sin 'l/J ~ ][!]- cos (} sin 'l/J cos'l/J sin o \u00b0 [!] [ cos ,p _ sin,p n[ ~:] cos e cos e sin 'l/J cos'l/J - tan() cos 'l/J t an () sin 'l/J 2. Rotation Kinematics 59 In case of small Cardan angles, we have and 2.7 Local Roll-Pitch-Yaw Angles Rotation about the x-axis of the local frame is called roll or bank, rot ation 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 2.18. The local roll-pitch-yaw rotation matrix is Az,,pAy,oAx,cp [ cec\"IjJ c<.ps\"IjJ + sec\"IjJs<.p - ces\"IjJ c<.pc\"IjJ - ses<.ps \"IjJ se -ces<.p s<.ps\"IjJ - c<.psec\"IjJ ] c\"IjJs <.p + c<.pses\"IjJ . (2.95) cec<.p Note the difference between roll-pitch-yaw and Euler angles, although we show both utilizing .p, e, and \"IjJ . 60 2. Rotation Kinematics Example 26 * 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 fram e is e WB Wx t + W y ) + w),,, rpe

0 \u22122\u03b1u/(My) if u \u2264 0 with the fact y, \u03b1 \u2208 R+, one gets \u2202f(\u00b7)/\u2202u > 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002156_978-3-642-27482-4_8-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002156_978-3-642-27482-4_8-Figure4-1.png", + "caption": "Fig. 4 Miniskybot. Minimal version", + "texts": [ + " This is important because in doing so it is guaranteed that anyone will be able to read, understand and modify the design files without license issues and using their preferred computer platform (Linux, Mac, BSD, Windows...). The Miniskybot is a differential drive robot composed of printable parts and two modified (hacked) hobby servos. It has been designed so that it can be printed on open source reprap-like 3D-printer. Two mechanical designs have been developed: the minimal version and the 1.0. The first prototype developed was a minimal robot chassis. The idea was to design a printable robot with the minimal parts, a kind of \u201chello world\u201d robot. It is shown in figure 4. It consist of only four printable parts: the front, the rear and two wheels. They are all attached to the servos by means of M3 bolts and nuts. Standard O-rings are used as wheel tires. For making the robot stable, the rear part has two support legs that slide across the floor. Therefore this prototype is only valid for moving on smooth flat surfaces. The goal of this first design was to show the students a minimal fully working mobile robot for stimulating their minds. They were encouraged to improve this initial design" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure15.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure15.4-1.png", + "caption": "FIGURE 15.4. A controlled inverted pendulum.", + "texts": [ + "43) f e m (Xd - kDe - kpe) + ex + kx X -Xd (15.44) (15.45) reduces the error differential equation to e+ kDe + kpe = O. Th e solution of the error equation is (15.46) e AeA1t + BeA2t -kD \u00b1 Jk'b - 4k p (15.47) (15.48) where A and B are fun ctions of initial conditions, and ), 1,2 are solutions of the characteri stic equation (15.49) Th e solution (15.41) is stable and e --+ 0 exponentially as t --+ 00 if ko > O. 650 15. Control Techniques Example 331 Inverted pendulum. Cons ider an inverted pendulum shown in Figure 15.4. Its equation of motion is ml20- mgl sine = Q. (15.50) To control the pendulum and bring it from an initial angle e = eo to the vertical-up posit ion, we may employ a feedback control law as Q = -kDO - kpe - mgl sin e. (15.51 ) The parameters ko and k p are positive gains and are assumed constants. The control law (15.51) transforms the dynamics of the system to 2 \" . ml e + kDe + kpe = 0 (15.52) showing that the system behaves as a stable mass-spring-damper. In case the desired position of the pendulum is at a nonzero angle, e = ed, we may employ a feedback control law based on the error e = e - ed as below, 2 \"Q = ml ed - kDe - kpe - mglsine" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002173_j.jfranklin.2012.01.003-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002173_j.jfranklin.2012.01.003-Figure1-1.png", + "caption": "Fig. 1. An underwater vehicle-manipulator system.", + "texts": [ + " Further, the magnitude of the gains, and hence the energy expenditure, is reduced by neural network-based identification of the system dynamics as well as hydrodynamic disturbances. The effectiveness of the new approach is illustrated with simulation studies of a six degrees of freedom (DOF) AUV with a three DOF on-board manipulator. Several researchers have addressed the modeling of underwater vehicle-manipulator systems, e.g., [3,15\u201317]. In this paper, based on one of the models [17], the dynamics of an underwater vehicle-manipulator system as shown in Fig. 1 is expressed as H\u00f0q\u00f0t\u00de\u00de \u20acq\u00f0t\u00de \u00feHA\u00f0q\u00f0t\u00de\u00de_v\u00f0t\u00de \u00fe S\u00f0q\u00f0t\u00de, _q\u00f0t\u00de\u00de _q\u00f0t\u00de \u00feD\u00f0q\u00f0t\u00de,v\u00f0t\u00de\u00dev\u00f0t\u00de \u00fe B _q\u00f0t\u00de \u00fe Csgn\u00f0 _q\u00f0t\u00de\u00de \u00fe g\u00f0q\u00f0t\u00de\u00de \u00fe b\u00f0q\u00f0t\u00de\u00de \u00bc u\u00f0t\u00de \u00f01\u00de The matrices and vectors in Eq. (1) are as follows: q\u00f0t\u00de \u00bc qT v \u00f0t\u00de,q T m\u00f0t\u00de T is the (6\u00fen)x1 vector, where qv\u00f0t\u00de 2 R6 1 is the vector of vehicle positions and orientations, qm\u00f0t\u00de 2 Rn 1 is the vector of manipulator joint angles in the bodyfixed reference frame, and v\u00f0t\u00de 2 R\u00f06\u00fen\u00dem is the flow velocity on a segment of the UVMS. A strip theory [16] is applied to the above modeling using the flow velocity v\u00f0t\u00de" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000784_ac50039a007-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000784_ac50039a007-Figure3-1.png", + "caption": "Figure 3. Effect of time on voltammetric curves at v = 2 mV s-' for NADH at the rotating GCE (10 rps), corrected for background current. Solution composition: 0.85 mM NADH: 2 mM NAD': 0.5 M KCI; 0.05 M Tris buffer; pH 7.1. Number indicates the chronological order of the cycle; a indicates a scan with increasingly positive potential and b with decreasing potential; S identifies the steady-state pattern obtained after ca. 2 h (with forward and back scans)", + "texts": [ + " The behavior observed in sulfate background with a clean electrode is probably due to surface phenomena, e.g., specific adsorption of sulfate on graphite electrodes with resultant swelling of the graphite (7-9). This sulfate effect indicates the sensitivity of the electrochemical behavior of NADH to phenomena which may affect the electrode surface. 2. Time Ef fec t . On continuously repeated cyclic scanning (0 to 0.8 V) a t the RDE, El, slowly shifts positively while the limiting current (iJ remains practically constant (Figure 3). The magnitude of the E , J 2 shift decreases with each new cycle; after ca. 2 h , the curve reaches a steady-state shape (S in Figure 3; the difference in il between curves 1 and S corresponds to NADH electrolyzed during the 2 h. Curve S can also be obtained by holding the RDE a t 0.75 V for 30 min. Such an El,* shift, which can be observed with any solution containing 1 mM NADH, 2 mM NAD+, 0.5 M KC1, and 0.05 M phosphate or Tris buffer, occurs a t the same slow rate between pH 5 and 9.5, as well as when Na2S04 replaces KC1 and the pH exceeds 7. With Na2S04 at pH less than 7, a curve similar to B of Figure 2 is initially recorded; El,2 shifts positively with time (repeated cycles or RDE held at 0", + "0), the electrode was removed, rinsed with distilled water, and immersed ill a new deoxygenated background solution; the voltammogram then recorded at the stationary electrode (Figure 5; curve I) shows a peak a t a potential corresponding to the reduction of NAD+ (6); in a cyclic experiment, only background current is recorded during the second scan (curve 11), i.e., the curve I peak can only be due to reduction of NAD+ adsorbed a t the electrode surface. The peak height increases linearly with v as expected for reduction of an adsorbed species. The adsorbed NAD\u2019 is reduced and desorbed a t potential more negative than -1.3 V since curves similar to l a in Figure 3 and 1\u2019 in Figure 4 are recorded if the initial potential is more negative than -1.3 V. Thus, it is possible to clean the electrode surface of adsorbed NAD+ by the Blaedel and Jenkins (4 ,10) pretreatment of alternatingly applying potentials of -1.5 and +1.5 V. I t is also safe to assume that , when steady state voltammetry was used to study the oxidation of NADH at the rotated GCE (4. IO), the procedure actually allowed for slow coverage of the electrode surface with adsorbed NAD+. Oxidation at a Covered GCE", + "496 x l o 3 x r~(Bn,)\u201d~ D\u201c2 (ref. 11) with Dn, = 0.43 and D = 2 x 10.\u2018 cm2 s - \u2019 , is 560. not to expose it to potentials more negative than -0.5 V. A covered electrode should not be held in the range of -0.5 to 0.3 V for longer than a few minutes in order to minimize the slow desorption of NAD\u2019. Exposure of the electrode to an NADH solution a t potentials, at which the latter is oxidized, reforms the adsorbed NAD+ layer. O p t i m u m Procedures and Their Analytical Applicabili ty. With a covered electrode, curve S of Figure 3 is obtained on the first scan a t the RDE for a background of 0.3 M KC1 or 0.25 M Na2S04, 0.05 M Tris or phosphate buffer a t pH between 5 and 9.5, and NAD+ initially added or not. Characteristics of the wave are given in Table I. The i and E reproducibilities over a micromolar NADH concentration range a t two different GCE are summarized in electrode E,, mV Electrode covered Data given are the mean and standard deviation for Data given are the mean and e Independent of GC-2 Electrodeb 4.9 0.33 z 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002183_j.ijfatigue.2013.08.015-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002183_j.ijfatigue.2013.08.015-Figure2-1.png", + "caption": "Fig. 2. Schematic of a gear tooth contact.", + "texts": [ + " In addition, the stress fields are considered to be elastic within the applied loading range. In view of Fig. 1, next three sections describe the three main steps used in prediction of micro-pitting, namely the gear EHL model, surface/near surface stress formulation and the multi-axial fatigue model. As a gear pair rotates in mesh with the angular velocities of X1 for gear 1 (driving gear) and and X2 for gear 2 (driven gear), the contact point C moves along the line of action B1B2 as shown in Fig. 2. In the process, the contact radii r1 \u00bc B1C and r2 \u00bc B2C vary with the contact position, resulting in the time-varying surface velocities of v1 = X1r1 and v2 = X2r2 in the direction of rolling and sliding x. In addition, the tooth force is time dependent in accordance to the tooth-to-tooth load sharing of the gear pair. With all these transient parameters, the lubricated contact behavior at one mesh position is no longer an isolated event. Instead, it is dependent on those of the previous mesh positions, largely impacting the lubrication film thickness and hydrodynamic pressure [1]. As such, the gear transient EHL formulation [1] is used to determine the surface traction distributions, capturing these transient characteristics of lubricated gear contacts. Representing the contact of a spur gear pair as a line contact, the hydrodynamic fluid flow between the surfaces is governed by the one-dimensional transient Reynolds equation of [1,23\u201326] @ @x f \u00f0x; #\u00de @p\u00f0x; #\u00de @x \u00bc @\u00bdv r\u00f0#\u00deq\u00f0x; #\u00deh\u00f0x; #\u00de @x \u00fe @\u00bdq\u00f0x; #\u00deh\u00f0x; #\u00de @# \u00f01a\u00de where x points into the direction of rolling (Fig. 2) and # is the time. The pressure p, film thickness h and lubricant density q are all dependent on both x and #. The rolling velocity vr is defined as the average of the surface velocities, i.e. v r \u00bc \u00f0v1 \u00fe v2\u00de=2. The lubricant non-Newtonian behavior (shear dependence of viscosity) is modeled assuming an Eyring fluid such that the flow coefficient f is given as [1,23\u201326] f \u00f0x; #\u00de \u00bc q\u00f0x; #\u00deh3\u00f0x; #\u00de 12x\u00f0x; #\u00de cosh sm s0 \u00f01b\u00de where x is the lubricant low shear viscosity and sm=s0 is the ratio of mean viscous shear stress to lubricant reference stress, taking the form of sm=s0 \u00bc sinh 1\u00bdxvs=\u00f0s0h\u00de with v s \u00bc v1 v2 being the sliding velocity that is also variable along the line of action", + " The micro-pitting fatigue behavior of a spur gear pair whose design parameters are specified in Table 1 is simulated using the model proposed above. In the analysis, perfect involute profiles are assumed and no lead crowns are applied. Under the input torque of 430 N m, the resultant tooth force density W 0 and Hertzian pressure ph distributions predicted by the load distribution model are shown in Fig. 5, where evident edge loading condition is observed owing to the lack of lead crown. Here / is the gear 1 roll angle as defined in Fig. 2. Because of the non-uniform pressure distribution along the face width direction, the face width of the gear tooth is discretized into M segments (M \u00bc 13 in this study) as shown in Fig. 6, each of which is considered to conform the line contact condition. The line contact fatigue analysis is performed for these tooth segments (m 2 \u00bd1;M ) individually. The reference frame of \u00f0/;Y ; Z\u00de in Fig. 6 is attached to the tooth surface and does not move with the contact. With the rotational speed of gear 1 set at 2200 rpm, the resulted time-varying vr , vs and slide-to-roll ratio SR \u00bc vs=v r as the contact moves continuously from the start-of-active-profile (SAP) to the tip of gear 1 are plotted in Fig", + " An example pair of roughness profiles is shown in Fig. 8. It is assumed that these profiles vary negligibly during contact. A typical turbine oil Mil-PRF-23699 is used as the lubricant with its temperature controlled at 90 C. The relevant properties of this lubricant can be found in [22,24,26]. The finite field and the shaded loading zone of the computational domain defined in Fig. 3 have the dimensions of LF \u00bc 12amax and LC \u00bc 6amax, respectively, where amax is the maximum half Hertzian width as the contact moves along the line of action B1B2 in Fig. 2. The mesh size (quadratic boundary element size) within the loading region is set as Dx \u00bc 2 lm, and three boundary elements are used in the transition region on each side of the loading region. A total of 500 time instances are used to define the travel of the contact point C along the line of action, during which, the computational domain of Fig. 3 moves with C while its dimension and mesh do not vary. Fig. 9 shows the instantaneous surface normal and tangential traction distributions obtained from the gear lubrication model and the stress components of rx, ry and rxy of gear 1 under the plane strain condition at the lowest-point-of-single-tooth-contact (LPSTC)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003473_acs.accounts.8b00243-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003473_acs.accounts.8b00243-Figure1-1.png", + "caption": "Figure 1. (a) Schematic of a phoretic catalytic Janus colloid producing motion by asymmetrically decomposing hydrogen peroxide at the hemispherical platinum coated surface (shaded dark). (b) Experimental trajectory (2 \u03bcm diameter) for a phoretic catalytic Janus colloid (white line) determined from video microscopy observation. Reproduced with permission from ref 26. Copyright 2011 American Chemical Society. The orientation of the fluorescent colloid can be determined as the platinum coating masks fluorescent emission and appears dark. The effect of Brownian translations and rotations are visible as discussed in the text. Quantitative analysis shows that the angles \u03b81 (instantaneous orientation) and \u03b82 (subsequent propulsive step direction) are well correlated throughout the trajectory, proving that the direction of thrust corotates with the Janus colloids orientation. (c) Janus colloid propulsion velocity as a function of particle diameter at constant hydrogen peroxide concentration. Reproduced with permission from ref 27. Copyright 2012 APS. (d) Mean displacements predicted for Janus colloids as a function of time and colloid diameter, based on the variations in velocity shown in (c). The ridge feature in the 3D surface indicates there is a specific Janus colloid size that is predicted to have moved furthest from the origin after a given time period. The size of the expected \u201cwinner\u201d of this virtual race between differently sized colloids increases as a function of time. This is because the smaller colloids rapid Brownian rotation produces a tortuous trajectory, despite their intrinsically higher propulsion velocities.", + "texts": [ + " Catalytic active colloids consequently provide a viable route to reduce the technological complexity of current systems. For balance, it should be noted that drawbacks for catalytic propulsion include fuel depletion. Historically, the current experimental and theoretical interest in motile catalytic colloids stems from initial observations of motility for bimetallic nanorods,11 and the hypothesized and soon experimentally verified enhanced motion observed in catalytic Janus colloids12 (Janus refers to the hemispherical distribution of catalyst: the colloids are \u201ctwo faced\u201d, like the Roman god, Figure 1a. This asymmetry is often produced by line of sight metal evaporation). Since these findings in the mid-2000s, a large number of additional catalytic swimming \u201cdevices\u201d have been studied.13 These examples can be categorized into two main groups: bubble swimmers, where motion is clearly linked to the momentum generated when catalytically formed gas bubbles detach from a catalytically active region14 (e.g., tubular swimmers15,16), and phoretic swimmers, where no bubble detachment is observed. Phoretic swimmers instead produce motion by self-generating local gradients,17 such as concentration or electric field", + " The prevalent use of this reaction reflects the rapid room temperature decomposition kinetics that produces rapid propulsion velocities. Finally, the focus here is on the micrometer size range: it may be more challenging to control motion at smaller scales. \u25a0 CATALYTIC JANUS COLLOID TRAJECTORIES Before discussing ways to increase control of Janus colloids, it is first instructive to describe their individual unconstrained trajectories. A key feature of phoretic Janus colloid propulsion is that the propulsive velocity vector corotates with the orientation of the asymmetrical colloid, Figure 1a. This was first predicted theoretically, and then confirmed by establishing a quantitative correlation between the orientation of the Janus colloid cap and the subsequent direction of motion, Figure 1b.26 From this finding, it is straightforward to predict trajectories, assuming propulsion does not modify the colloids\u2019 Brownian translations and rotations. Intuitively, it is apparent that the Brownian diffusion will introduce translational \u201cnoise\u201d to the trajectory, so a criteria for useful propulsion is that the magnitude of the catalytic velocity, v dominates Brownian translations. Simultaneously, Brownian rotation randomly reorientates the Janus colloid, and the propulsion vector. Consequently, while catalytic propulsion initially produces \u201cballistic\u201d motion (i", + " Systematic statistical analysis of trajectories for differently sized Janus colloids confirms that experimental systems display these expected features.27 As a result, unconstrained Janus colloid trajectories can be simulated by simple stochastic equations,28 and provide a system that mimics the much-simulated active Brownian particle scenario.29 Experimental data also shows propulsion velocity significantly reduces at larger Janus colloid sizes (v scales as 1/r) due to intrinsic features of the propulsion mechanism, Figure 1c.27 This limits the utility of unconstrained Janus colloids for directed transport because a tradeoff between rapid motion and directional transport occurs as a function of particle size, Figure 1d. Practically, these factors cap the distance over which useful autonomous point A to point B transport using unconstrained Janus colloids is possible. In fact, some differences between this simple model of catalytic Janus colloids motion and experimental data exist. For example, the apparent Brownian rotation rate of Janus colloids has been found to increase with propulsion velocity, reducing the range of ballistic motion.12,30 The origin of this phenomenon has not yet been determined. In addition, it is practically difficult to produce a perfect hemispherical catalyst coating on a Janus swimmer, and deviations in cap symmetry in real systems introduce additional rotational propulsion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure12-1.png", + "caption": "Fig. 12. Finite element model: (a) pinion and gear tooth models, (b) slice of the pinion tooth model, and (c) detail A of the pinion tooth model.", + "texts": [ + " Application of a torque T1 in rotational motion at the reference pointN allows to apply such a torque to the pinion model while the gear model is held at rest. Step 7 Elements of first order have been considered in the finite elementmesh. This type of elements is recommended for contact simulations [15]. Step 8 Contact formulation is based on a surface-to-surface discretization, a finite-sliding tracking approach, and a slave\u2013master contact algorithm [15]. Elements of the model required for the formation of pinion-slave tooth surface and gear-master tooth surface are automatically identified. Fig. 12 shows an example of a finite element model of a spur gear drive with one pair of teeth. 5. Numerical examples This section covers stress analyses based on the Hertz theory and the finite element method for several cases of design. A general-purpose computer program [15] has been applied for the stress analyses based on the finite element method. The approach for the development of the numerical examples is as follows: (1) Gear data for three designs of a spur gear drive are considered. Each design of the gear drive is based on a different amount of crowning in longitudinal direction of their pinion tooth surfaces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003886_j.mechmachtheory.2019.103693-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003886_j.mechmachtheory.2019.103693-Figure5-1.png", + "caption": "Fig. 5. Force and torque parallelepiped of T-Bot at position p .", + "texts": [ + " The force and torque balance equations of the T-Bot can be deduced as T 1 + T 2 + T 3 + F S + F E = 0 , (15) M 1 + M 2 + M 3 + M 4 + M 5 + M 6 + M E = 0 . (16) The cable tensions are determined by F S and F E . The condition that T 1 , T 2 , and T 3 have positive solutions in Eq. (15) is equivalent to the condition that vector \u2212F S \u2212 F E falls in the triangular pyramid composed of u 1 , u 2 , and u 3 . If the maximum cable tension is limited to f max , then the corresponding condition turns into the vector \u2212F S \u2212 F E falls within the parallelepiped composed of f max u 1 , f max u 2 , and f max u 3 , as indicated in Fig. 5 (a). The process of solving the external force that the CDPR can withstand in the direction of n (or acceleration that can be achieved in this direction) is as follows: (1) Given the terminal position p . (2) Calculating the vectors u 1 , u 2 , and u 3 , and the spring force F S . (3) Drawing the force parallelepiped with f max u 1 , f max u 2 , and f max u 3 as the edges and point P as the apex. (4) Drawing the vector \u2212F with point P as its origin and Q as its end. Q locates inside the force parallelepiped", + " Take M I as an example, the magnitude and direction of M 1 = T 1 ( r 2 \u00d7 u 1 ) are uniquely determined, whereas the direction of M 2 = \u03b11 T 1 ( r 1 \u2212 r 2 ) \u00d7 u 1 is determined, however, its magnitude is variable. Let M T = M 1 + M 3 + M 5 , both the direction and magnitude of M T are known given the p and F E regardless of the torque. Eq. (16) can be transformed into M 2 + M 4 + M 6 = \u2212 ( M 1 + M 3 + M 5 ) \u2212 M E = \u2212M T \u2212 M E , (17) where M 2 + M 4 + M 6 forms a torque parallelepiped with T 1 ( r 1 \u2212 r 2 ) \u00d7 u 1 , T 2 ( r 2 \u2212 r 3 ) \u00d7 u 2 , and T 3 ( r 3 \u2212 r 1 ) \u00d7 u 3 as the edges and P as the apex, as indicated in Fig. 5 (b). If the vector \u2212M T \u2212 M E locates inside the torque parallelepiped, then the torque balance state of the end effector can be realized and the orientation can be maintained, otherwise, the end effector will rotate. Similarly, the volume of the parallelepiped determines the external torque set that the robot can withstand at position p in all directions if the external force is given, which is the torque capacity of the robot at position p . From the torque analysis, the directions of the three torque vectors of the T-Bot are determined by ( r 1 \u2212 r 2 ) \u00d7 u 1 , ( r 2 \u2212 r 3 ) \u00d7 u 2 , and ( r 3 \u2212 r 1 ) \u00d7 u 3 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000056_s0263574707003530-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000056_s0263574707003530-Figure8-1.png", + "caption": "Fig. 8. Cutting of the 6R into two 3R serial chains.", + "texts": [ + " Moreover, one has to attach two copies of a coordinate frame L = R , called the \u201cleft\u201d and the \u201cright\u201d frame, to the resulting mechanisms in the following way: \u2022 The origin is the foot of the common normal of the third and fourth axis on the fourth axis. \u2022 The x-axis is aligned with the common normal of the third and fourth axes. \u2022 The z-axis coincides with the fourth axis. The resulting mechanisms are two open 3R chains, called the \u201cleft\u201d and the \u201cright\u201d 3R chain. The base frame of the left one is 0 and the end effector frame is L, the base of the right one is 6 with the end effector R (see Fig. 8). The pose of L with respect to 0 is given by T1 = M1 \u00b7 G1 \u00b7 M2 \u00b7 G2 \u00b7 M3 \u00b7 G3. (25) This is exactly the canonical 3R chain for which the canonical constraint manifold was developed. This manifold was the intersection of one of the Segre manifolds SM1c, SM2c, or SM3c resp. the intersection of one of the 3-spaces Tcp or Tcw with the Study quadric. Which one of the constraint manifolds has to be taken depends on the Denavit\u2013 Hartenberg parameters of the 6R manipulator, because in http://journals.cambridge" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001578_tmag.2010.2093509-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001578_tmag.2010.2093509-Figure2-1.png", + "caption": "Fig. 2. Configuration of a single-side FSPMLG.", + "texts": [ + " The translator of the generator is connected Manuscript received May 25, 2010; revised August 15, 2010 and October 10, 2010; accepted November 07, 2010. Date of current version April 22, 2011. Corresponding author: H. Yu (e-mail: htyu@seu.edu.cn). 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.2010.2093509 to the buoy, through which the translator is moved with the motion of a sea wave. In order to investigate FSPMLGs, a single-side FSPMLG ideal model is built in Fig. 2. The linear generator is made up of a stator and translator. The translator comprises a plurality of teeth and slots. The stator has six U-shaped stacks, each of which is constructed with one slot and two tooth bodies. Each phase has two U-shaped stacks. The phase coil is wound in the slots of the corresponding stacks with a PM positioned between adjacent U-shaped stacks. Displacers are positioned between the phases. Two typical positions of an FSPMLG are shown in Fig. 3. When the translator moves from position 1 to position 2, the main PM flux linked in this coil changes from negative maximum to positive maximum" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003532_j.conengprac.2015.05.008-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003532_j.conengprac.2015.05.008-Figure3-1.png", + "caption": "Fig. 3. Dynamic model.", + "texts": [ + " Thus, main contributions of this work are the adaptation and improvement of the dynamic sideslip observer and the double steering controller (Section 2), the enhancement of the stabilization controller based on the derivation of the non-linear controller dynamic coefficient and its extension to a system with four steered wheels (Section 3), and the experimental validation of combination of both controllers with a dynamic sideslip observer (Section 4). Two levels of modeling are used to control the bi-steerable mobile robot considered in this paper. They are depicted below. The first one in Fig. 2 is based on kinematics; it is dedicated to the formal control laws computation and a first step of observation. The second one in Fig. 3 is based on dynamic equations; it allows deriving an observer for grip condition, enhancing the reactivity of estimation to feed the control according to encountered conditions. The model (hereafter called \u201cextended kinematic model\u201d) developed by Cariou et al. (2009) is depicted in Fig. 2. As classically done for mobile robot purpose (Scheding, Dissanayake, Nebot, & Durrant-Whyte, 1997), the vehicle is viewed as a bicycle in a top view, and it is located with respect to the path to be followed (Fr\u00e9net frame)", + " This condition is satisfied in practice if the path tracking is properly initialized and if the robot remains close enough to the path. The model (1) is suitable for control law design and sideslip angles estimation at low speed. But high dynamics encountered at higher speed, with the experimental off-road robot, lead to an inaccurate estimation of sideslip angles. Indeed, the settling timeFig. 2. Extended kinematic model (path tracking framework). together with neglected dynamical phenomena do not permit a sufficiently reactive observation. In order to catch dynamic phenomena, the dynamic model depicted in Fig. 3 is considered in a yaw frame representation. Many approaches for vehicle dynamics have been proposed in the literature (Gillespie, 1992), but require the knowledge of numerous parameters, difficult to be known accurately in off-road motion (Innocenti et al., 2004). In order to preserve compatibility with the extended kinematic model and a simple perception system, a bicycle representation is still used (as a top view of the 2D representation depicted in Fig. 2). This model introduces the following notations: LR and LF are the half wheelbase that define the longitudinal position of the center of gravity G" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.33-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.33-1.png", + "caption": "Fig. 2.33 Forces and moments at a dyad", + "texts": [ + " Noise caused by vibrations of the mechanism links and the housing, and the risk of interference with the technological flow are the reason why designers have to deal with the occurring dynamic joint forces in greater detail. Below, a handy method for calculating the joint forces for planar mechanisms that are composed of simple groups of links with revolute joints will be described. The algorithm is based on formulae that apply to a respective dyad, see also VDI Guideline 2729 [36]. The definition of the forces that act onto a mechanism link can be seen from Fig. 2.33. Note that the components of the forces and moments are defined uni- 2.5 Joint Forces and Foundation Loading 143 formly in the directions specified for reasons of systematics, which in turn helps meet the requirements of computational processing. The force that is exerted onto link j by link k is designated F jk and its components are defined positive in accordance with the coordinate directions. The equal and opposite counterforce is designated as F kj and is defined in the same way. Therefore, Fxjk + Fxkj = 0, Fyjk + Fykj = 0 (2", + "297) Efficient algorithms for calculating the joint forces are based on the decomposition of multilink mechanisms into simple (statically determinate) groups of links. In mechanisms with varying transmission ratio , the kinetic energy of all moving transmission links varies with the position of the mechanism. There is a permanent exchange of kinetic energy among the mechanism links via the joint forces. The work that is performed at the joint (j, k) by the joint force F jk on link j has the same magnitude as the joint force F kj on joint k, see Fig. 2.33. The two forces that are applied at the \u201cjoint point\u201d in the free-body diagram have the opposite sign (F kj = \u2212F jk). In sum, the work of the joint force that acts onto the adjacent links (action = reaction) equals zero. Reaction forces thus do not perform any work in the overall system. Now this view is generalized for an arbitrary link i (i = 2, 3, . . . , I). The mechanical work that the joint force Fik on a link i (that is viewed independently and cut free) depends on the path along which this joint travels during the motion", + " cutting and pressing forces in forming machines and polygraphic machines, gas forces in internal combustion engines and compressors), have no influence on the foundation forces since they always occur in pairs and cancel each other out. 146 2 Dynamics of Rigid Machines In real machines in which the elasticity of the links plays a part, additional inertia forces (\u201cvibration forces\u201d) that have an effect on the foundation can occur due to deformation of the links in addition to the kinetostatic forces and moments. The resultant inertia forces and moments that act from the moving mechanism onto the machine frame are derived from the force and moment balances, see 2.3.2 and the forces and moments in Fig. 2.33. Since the motions are parallel to the x-y plane, Fz = 0, and the following forces result: Fx = \u2212 I\u2211 i=2 mix\u0308Si = \u2212mx\u0308S; Fy = \u2212 I\u2211 i=2 miy\u0308Si = \u2212my\u0308S. (2.303) The input moment already known from (2.209) can also be stated as follows, see also (2.199): Man = I\u2211 i=2 [mi(x\u0308Six \u2032 Si + y\u0308Siy \u2032 Si) + JSi\u03d5\u0308i\u03d5 \u2032 i] + W \u2032 pot \u2212Q\u2217. (2.304) The position of the overall center of gravity of all moving parts of a planar mechanism results from the individual positions of the centers of gravity from the conditions xS \u00b7 I\u2211 i=2 mi = I\u2211 i=2 mixSi; yS \u00b7 I\u2211 i=2 mi = I\u2211 i=2 miySi" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002517_1.4033662-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002517_1.4033662-Figure10-1.png", + "caption": "Fig. 10 Illustration of the point and lines at which the following results are shown", + "texts": [ + " 138, NOVEMBER 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935392/ on 02/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use this section compares Goldak\u2019s model to the two new models. The temperature results are compared along a line in the middle of the substrate. The displacement results are compared along a free edge of the substrate and are compared at node 1 on the free corner. These verification locations are illustrated in Fig. 10. Temperature versus x location is compared with the Goldak\u2019s model in Fig. 2(a) for LI and Fig. 2(b) for EE. The Ds\u00bc 0.5 curves in Figs. 2 and 11 are the results of the Goldak\u2019s model (Eq. (12)), while the other curves are the results of the new heat source models. As expected, the results for both models converge monotonically toward that of the Goldak\u2019s model as the time increment decreases. To facilitate comparison of different models, a dimensionless time increment size Ds is introduced Ds \u00bc vsDt c (19) Because Goldak\u2019s model requires Ds 1, this parameter provides a measure of how large the time increments used for the new models are relative to those used for the Goldak\u2019s model" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000445_bf00365591-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000445_bf00365591-Figure1-1.png", + "caption": "Fig. 1. Schematic presentation of the measured values; (e) height of the prothoracic coxae, (4-) height of the mesothoracic coxae, (A) height of the metathoracic coxae, a angle between the meso- and metathorax, fl angle between the metathorax and the horizontal baseline", + "texts": [ + " Concerning the latte~ one must discriminate between \"up the step\" and \"down the step '~ walks. To measure the height of the body of the insect when walking over the plane and the different irregularities, the films were evaluated frame by frame with the aid of a single frame projecto i and a digitizer combined with a programmable calculator (Hew i lett-Packard 9810). In each frame the three distances from the fore- I middle-, and hind coxae to the baseline, given by the level of the styrofoam plane, were computed. Figure 1 shows these distance~ as well as the two angles ~ and fi, which additionally were computed by the calculator. Angle c~ is a measure of the angle between the mesothorax and the metathorax, while fl describes the angle between the metathorax and the horizontal baseline. The height of the coxae of the three thoracic segments computed with respect to the baseline are symbolized in Figure 1 as well as in the figures to come in the following way: the height of the coxae of the prothorax by a circle, that of the mesothorax by a cross and that of the metathorax by a triangle. In the case of the step-shaped irregularities one can think of two different baselines, an upper and a lower one. To make the measurements comparable in these cases the lower baseline was always used as a reference line. The total number of animals used in these experiments was 18, the total number of runs analysed was 60", + " As the third configuration also occurs when walking down a step, this effect is probably produced by the increased depth of this \"step\". Thus the angle/~ in these two configurations becomes negative, while angle e still has a positive value. This can be estimated from the fact, that the distances between the heights of the coxae of pro- and mesothorax as well as of meso- and metathorax are nearly equal (Fig. 3a, configuration 3, 4), while the distance between the coxae of the meso- and metathorax is smaller than that between the coxae of the pro- and the mesothorax (Fig. 1). The last two experiments have been done with steps up and down as above but with a much greater height (14 mm). This is a considerable irregularity for the stick insects used here as one can see, when comparing the height of the step with that of the body in normal horizontal walking (Fig. 3b, c). As in Figure 3b (step up) no qualitative difference relative to Figure 2a can be seen, but Figure 3c shows a significant difference compared to Figure 2b. Here, as in Figure 3a, in some configurations the order of the height of the coxae is the inverse of the normal order", + " This model might describe the behaviour of quadrupedal mammals as it seems to you to be for example with dogs walking free over an uneven surface. In sixlegged insects this is only possible, if the thoracic joints can be moved in the walking animal within their morphologically given limits. A change of the angle between pro- and mesothorax in the stick insect does not essentially change the differences in the heights between the coxae of the prothorax and the mesothorax, because the distance between the promesothoracic joint and the coxae of the prothorax is very small (Fig. 1). Therefore in this sense only the meso-metathoracic joint seems to be important. This means, that for this model the value of the angle (Fig. 1) should depend very much on the shape of the walking surface. Since in the model discussed first the angle ~ always has to be constant, the measurement of this angle offers a possibility to discriminate between these two models. Therefore for the different configurations shown in Figures 2 and 3 the expected values of c~ were computed assuming the second model to be true. These values ~mod are compared with-the values ~exp, which had experimentally been measured in the corresponding step arrangements by plotting eexp against C~mod(Fig", + " Except of these extreme situations just discussed one can say as a first approximation, that when walking over irregularities as investigated here, the body of the insect can be regarded as rigid, and therefore t h e second model described in Section D can be excluded. Although the rigidity of the body agrees with the first model described in Section D, you must also exclude the first model because of other properties of the experimental results. So the position of the body described by the angle between the metathorax and the horizontal baseline (Fig. 1, angle/~) is not always constant as required by the first model. As a rough approximation this angle/~ corresponds to the mean slope of that part of the walking surface, which is situated within the range of the animal's body. This means, that if the animal climbs up, as in the step up or the first part of the obstacle or the second part of the ditch, the angle /~ is greater, and when climbing down, 13 is smaller compared withe the value of/~ when the animal walks on the horizontal surface. While, when walking over the horizontal plane, the mean value of the angle/~ is 7", + " As the posture of the body should be the result of an equilibrium state, that posture with the smallest sum of deviations has been computed. This sum of deviations is calculated by summing up the absolute values of the three deviations Ah, weighted by the corresponding characteristic. These weighted deviations can be regarded as described above as a measure for the additional torque, which each segment produces to reach its normal height. They can be given in relative units. Since not every position of the body is possible because of the rather long abdomen (Fig. 1), additionally some mechanical limitations had to be respected in the calculation. The height of the coxae of the mesothorax was not allowed to be smaller than half height of the coxae of the prothorax, as the coxae of the metathorax lie almost exactly in the middle of the body. When walking over the ditch, the height of the coxae of the metathorax were not allowed to be smaller than the height of the walking surface. This model can then be formulated as a computer programm. A limitation 31 caused by the programm was that in this calculation the values of the height of the prothorax as well as of the mesothorax could only assume discrete values in increments of 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure12.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure12.6-1.png", + "caption": "Fig. 12.6 Example 12.2. Parallel manipulator provided with a triangular-prism moving platform", + "texts": [ + "16) Finally, the closure equations associated to the forward displacement analysis are obtained based on expressions (12.11) and (12.12). The system of equations may be solved by using special software like Maple\u00a9through the library Homotopy. 266 12 Gough\u2019s Tyre Testing Machine However, it is unfortunately a very time-consuming task. Furthermore, not all the solutions may be obtained with such software. Thus, the efficacy of the Algorithm 795: PHCpack is noticeable. Example 12.2. With reference to Fig. 12.6, the exercise is devoted to computing the forward displacement analysis of a six-legged parallel manipulator provided with a regular triangular-prism moving platform whose dimensions, using SI units through the numerical example, are given by e D 1=4 and f D p3. Furthermore, the fixed platform is also a regular triangular prism, where the side of the equilateral triangle is g D 2 p 3 while the height of the prism is given by h D 3. On the other hand, the instantaneous generalized coordinates, or limb lengths, are given by q1 D 2, q2 D 5=2, q3 D 9=4, q4 D 39=20, q5 D 43=20, and q6 D 7=4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003296_1.4935711-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003296_1.4935711-Figure3-1.png", + "caption": "FIG. 3. Simulation results showing melt pool at the midpoint of five deposition layers: (a) first layer, (b) second layer, (c) third layer, (d) fourth layer, and (e) fifth layer.", + "texts": [ + " By conservation of mass between the powder jet mass flow rate and measurements of the dimensions of a singlelayer LAM deposit, the catchment efficiency can be calculated as28 gc \u00bc qpbVlhw _m ; (3) where Vl is the laser scanning speed, b is the shape factor, h is the deposit height, and w the is deposit width. b is approximately 2/3 since the deposit layer does not fully occupy the full rectangular box volume. In this simulation, an initial value of catchment efficiency estimated from experimental measurement of height and width of a single-layer LAM deposit made with the same process parameters as used for the simulation. Based on measurements, the catchment efficiency is 0.47. The 3D illustrations displayed in Fig. 3 depict the numerically computed deposit geometry and melt pool for five successive layers in three dimensions. The beam travels from left to right for odd numbered deposit layers, and it returns immediately in the opposite direction for the evennumbered layers. The red colored region represents temperatures above the liquidus temperature of IN718. Figure 4 shows the calculated time variation of temperature with at the midlength, midcenter surface point on each of five successive deposit layers. The first peak occurs when the laser beam passes over the midlength, midcenter point on the surface of the first layer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000824_iros.2007.4399407-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000824_iros.2007.4399407-Figure2-1.png", + "caption": "Fig. 2. A double inverted pendulum with foot can apply torques at the ankle and hip joints. The location of the center of pressure must be underneath the foot", + "texts": [ + " For this reason, we derive a controller that takes into account these constraints, ensuring that the robot remains balanced and upright with its feet flat on the ground. The balance controller is derived below for fully-actuated, unconstrained planar dynamic systems with equations of motion of the form, M(\u03b8)\u03b8\u0308 = \u03c4 \u2212N(\u03b8, \u03b8\u0307) (1) where \u03b8 is a vector of joint angles, M is the inertia matrix, \u03c4 are the joint torques, and N is a vector containing the gravitational, centripetal and coriolis forces. We use planar inverted pendulum models, like the one in Fig. 2, to present the controller. Even though there is no explicit foot in our model, it is assumed to be flat on the ground at all times, contributing no kinetic or potential energy. The definition of the center of pressure still applies as long as it remains within the area the foot would cover. We initially ignore the presence of the foot, which imposes limits on the location of the CoP, and hence limits on the ankle torques. We use a two-part balance controller inspired by the hip and ankle strategies" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.7-1.png", + "caption": "FIGURE 4.7. Point P in a local frame B2 (X2Y2Z2) .", + "texts": [ + " Motion Kinematics Hence, the transformation matrix from C to A is ATC ATBBTC [ ARB Ad l ][ B~C B~z ]a I [ ARBa BRc ARB Bdz + Ad l ]I [ A ~C A~Z ] (4.82) and therefore, the inverse transformation is CTA = [ BR'Sa A R~ - BR'S AR~ [AIRB Bdz + Ad l ] ] [ BR'S aAR~ - BR'S Bd z l - AR~ Ad l ] [ AR'S - AR'S Adz]a I ' (4.83) The value of homogeneous coordinates are better appreciated when sev eral displacements occur in succession which, for instance, can be written as (4.84) rather than GR4 4rp +Gd 4 = Gu, eRz eR3 eR4 4r p + 3d 4 ) + Zd 3) + ld z) + Gd l. (4.85) Example 87 Homogeneous transformation for multiple frames. Figure 4.7 depicts a point P in a local frame Bz (XZyzzz) . The coordinates of P in the global frame G(0 XYZ) can be found by using the homogeneous transformation matrices. The position of P in frame Bz (xzyzzz) is indicated by zrp. Therefore, its position in frame B, (XlYlZl) is (4.86) 4. Motion Kinematics 147 and therefore, its position in the global frame G(OXYZ) would be [t] [ C~l c d l ][~j]1 [ C~2 c d l ][ 1 R 2 ' ~'][~n1 0 [ CR 20 CR 2 cR2 l d2 + c d l ][ ~n (4.87) 1 Example 88 Rotation about an axis not going through origin" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002938_j.engfracmech.2019.03.040-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002938_j.engfracmech.2019.03.040-Figure3-1.png", + "caption": "Fig. 3. In-situ high temperature SEM fatigue experiment system.", + "texts": [ + " In order to achieve a mirror-like surface, these specimens were mechanical polished using SiC paper with grit scales of 400, 800, 1500, 2000, 5000 and 7000, respectively, and finally with 0.5 \u03bcm liquid pastes using ultrasonic vibration polishing technique. The final harvested specimens had a thickness of 0.5mm. In-situ high temperature tensile fatigue tests were conducted in the chamber of the SEM (SS-550, Shimadzu, Japan), in which the loading system was controlled using an electro hydraulic servo system and the maximum loading capacity of the in-situ tensile fatigue machine was 1.0 kN, with maximum frequency of 10 Hz, as shown in Fig. 3. The specimen was heated by means of thermal radiation inside a vacuum chamber. The heating system could heat the specimen up to 800 \u00b0C with temperature control accuracy of\u00b1 2 \u00b0C [16]. In the following, fatigue experiments of Al-Si10-Mg samples were performed at 25 \u00b0C, 100 \u00b0C, 200 \u00b0C, 300 \u00b0C, 400 \u00b0C, 500 \u00b0C and 600 \u00b0C, respectively. All fatigue experiments were carried out with sinusoidal waveform loading mode at frequency 5.0 Hz. The peak stress was 160MPa at the stress ratio R=0.2 by using load controlled mode, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure4-1.png", + "caption": "Figure 4. Modelling of the flexible gearbox housing.", + "texts": [ + " Dynamic excitations of the gearbox housing in service can be divided into internal excitation and external excitation. Internal excitation is generated by gear meshing and transmitted through the bearings to the gearbox housing. External excitation includes the drive torque from the motor and the impacts from the wheel\u2013rail system. In the model, a fixed reference coordinate, located at the centre of the gearwheel bearing hole of the gear box housing, is used to describe the flexible deformation, as shown in Figure 4. The inertia system is used to describe the location and orientation of the selected body reference frame. The position vector at any point Pi on the gearbox housing due to the internal and external excitations is defined with respect to the inertia system, such as15 ri \u00bc Ri \u00fe Ai \u00bdui0 \u00fe u0\u00f0u, t\u00de \u00f01\u00de where Ri is the position vector of the body reference frame, Ai is the transformation matrix from the body reference frame to the inertia frame, ui0 is the undeformed local position of point Pi, and u0 u, t\u00f0 \u00de is the deformation vector at this point" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000759_s1560354708050079-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000759_s1560354708050079-Figure2-1.png", + "caption": "Fig. 2. Body on a sphere.", + "texts": [ + " 5 2008 Veselova\u2019s system [16] describes the motion of a rigid body with a fixed point under constraint (1.15). Setting r = 0 and \u03bb = 0 in (1.17), we have I\u03c9\u0307 = I\u03c9 \u00d7 \u03c9 + \u03b3 \u00d7 \u2202U \u2202\u03b3 + \u03bb0\u03b3, \u03b3\u0307 = \u03b3 \u00d7 \u03c9, (1.21) where \u03bb0 = \u2212 ( I\u22121\u03b3, I\u03c9 \u00d7 \u03c9 + \u03b3 \u00d7 \u2202U \u2202\u03b3 ) (I\u22121\u03b3,\u03b3) . (1.22) Rubber body on a sphere [14]. If a rubber body moves on the sphere of radius a, then the equations presented in the previous section must be modified. However, it can be shown that if we denote by \u03b3 the normal of the sphere at the contact point (projected on the movable axes, see Fig. 2), then the equations describing the evolution of the vector \u03c9 remain the same as in system (1.18). In this case, the equations describing the motion of the vector \u03b3 can be obtained from the condition that the velocities of the contact point on the sphere and on the body coincide. Finally, we obtain I\u0303\u03c9\u0307 = I\u0303\u03c9 \u00d7 \u03c9 \u2212 mr \u00d7 (\u03c9 \u00d7 r\u0307) + \u03b3 \u00d7 \u2202U \u2202\u03b3 + \u03bb0\u03b3, \u03b3\u0307 + \u03c9 \u00d7 \u03b3 = 1 a r\u0307. (1.23) The tensor I\u0303, the vector (\u03b3), and the undetermined multiplier \u03bb0 are defined by the same relations as on the plane. As a \u2192 \u221e, system (1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002212_s00170-016-9510-7-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002212_s00170-016-9510-7-Figure6-1.png", + "caption": "Fig. 6 Twin-wire a heat density and b temperature distribution at a given point", + "texts": [ + " The primary aim of the present work is to simulate the metal deposition using finite element method with specific application to AM using twin-wire GMAW. The validity of the model depends on accurate prediction of temperature in the combined fusion zone from the twin arcs. Amongst the superposition and the equivalent heat source models discussed earlier, the superposition approach is implemented in the current study, with the distance between the heat sources taken as 6 mm. The heat distribution obtained from the superposition of two double ellipsoidal heat sources is illustrated in Fig. 6a. Figure 6b represents the temperature profile over the substrate and deposit from the heat distribution that is shown in Fig. 6a. The material of the filler wire and substrate plate used in experiments was ER70S-6 and C45, respectively, both belonging to the low-carbon steel family. The temperaturedependent material properties for comparable class of material have been presented in Karlsson and Josefson [30\u201332]. These set of material properties have been used in literature, like Abid et al. for instance, to predict residual stresses with ER70S-6 as the filler wire [33]. Hence, the same material properties have been adopted in the present study (see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure2-1.png", + "caption": "Fig. 2. Results of simulation of meshing and contact of a gear drive wherein the pinion tooth surface are provided with whole crowning: (a) path of contact, and (b) function of transmission errors.", + "texts": [ + " The amount of longitudinal crowning is established by parabola coefficients alf and alb, respectively. More details about these parameters can be found in [1,12]. The surface topology shown in Fig. 1(b) is a particular case of the one shown in Fig. 1(a) wherein parameters uot=uob and lof= lob. 2) Simulation of meshing and contact of pinion and gear tooth surfaces is performed assuming that point contact exists. The algorithm of tooth contact analysis [5] is applied for determination of contact points and the function of transmission errors. Fig. 2 shows the results of application of TCA to a spur gear drive with a pinionwith whole crowning as the one shown in Fig. 1(b). 3) An algorithm for application of the Hertz theory in gear drives with localized bearing contact has been developed and applied for stress analysis of a spur gear drive with localized bearing contact wherein the pinion tooth surface is provided with whole crowning (see Fig. 1(b)). Two cases are considered: (i) contact at a single point when just one pair of teeth is in contact, and (ii) contact at two points corresponding to the contact points of two consecutive pairs of contacting teeth" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002740_rnc.3812-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002740_rnc.3812-Figure1-1.png", + "caption": "Figure 1. Inertial wheel pendulum.", + "texts": [ + " Remark 5 Notice that, from Theorem 1, it can be seen that w0 is the main tuning parameter, as long as both matrix A and Hn are Hurwitz. That is, regardless how these matrices are proposed, we can always find a w0 > 1, such that the conditions in Theorem 1 hold. However, to find suitable or admissible values for control parameters \u00b9w0; A;Hn\u00ba, it would be very useful to implement a program to numerically check the corresponding inequalities. That is because if the value of w0 increases, the peaking phenomena will appear. Let us consider the underactuacted inertial wheel pendulum showed in Figure 1. This system is described by the following set of normalized differential equations ([37]): :: 1 D 1 1 .sin 1 u/ ; :: 2 D 1 1 . sin 1 C u/ ; (32) Copyright \u00a9 2017 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control (2017) DOI: 10.1002/rnc where 1 and 2 are the angles, < 1 is a dimensionless parameter, and \u2018.\u2019 stands for the time derivative with respect to the normalized time. It is well known that the normalized inertial wheel pendulum has a relative degree equal to four with respect to the output: F D 1 C 2; (33) because : F D : 1 C : 2; :: F D sin 1; F " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001110_iet-epa.2010.0159-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001110_iet-epa.2010.0159-Figure8-1.png", + "caption": "Fig. 8 Geometric configurations of the modelled motor using 3D TSFEM", + "texts": [ + " These vibration frequencies can be monitored using accelerometers fixed to the outer casing of the PMSM. Tables 4 and 5 summarise the amplitude of the side-band components at frequencies (A\u2032 + B\u2032/P)fs for different degrees of static and dynamic eccentricities, respectively. 41 & The Institution of Engineering and Technology 2012 Magnetic field distribution within the motor can be obtained by FEM. The stator currents, torque and speed of the motor can be then determined using other specifications of the motor. The 3D scheme of the simulated PMSM has been displayed in Fig. 8. The stator consists of laminated M-19 sheets and has 36 slots and each slot has been filled by 44 turns. The simulated motor has a fractional slot winding and the windings are two layers in which all coils of the same phase have been put in series. The motor has radially magnetised NdFeB PMs mounted on the surface of a solid mild-steel rotor core. In this simulation, windings are star connected and included no circulating currents. It is noticeable that harmonic components have not been used as an index and only the amplitude of the side-band components has been employed as an index for fault identification", + " Since harmonic components have not been utilised for fault recognition, the variation of the harmonic components does not have noticeable effects on our fault detection procedure. It is obvious that mentioned difference in windings should be taken into account for loss 42 & The Institution of Engineering and Technology 2012 calculation in the simulation procedure in comparison with the experimental results. The model includes 563 980 nodes and 210 848 second-order elements. However, in order to illustrate 3D configuration of the rotor elements clearly, the symbolic meshed rotor is shown in Fig. 8. Since in this approach, spatial distribution of the stator windings, skin effects, non-linear characteristics of the ferromagnetic and PM materials, geometrical and physical characteristics of the stator slots and PMs have been taken into account, it has been used to model and analyse the healthy and faulty PMSM under different types of eccentricity. In this modelling, non-uniformity of the air gap because of static, dynamic and mixed eccentricities in different degrees is modelled. Transient analysis of rotating machines (RM) is employed for modelling and analysing the PMSM with mechanical coupling [20]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002621_s00170-015-8216-6-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002621_s00170-015-8216-6-Figure8-1.png", + "caption": "Fig. 8 Partition of the surface in the curved overhanging structure and its relation with energy input", + "texts": [ + " The overhanging plane is totally covered by the overhanging structure when the angle is less than 47\u00b0 (Fig. 5a), and the surface becomes rough abruptly. After the energy input is decreased to 0.15 J/mm, the angle that led to the formation of the overhanging structure decreases to 40\u00b0. The large area of the overhanging structure does not form until the obliquity angle is 30\u00b0 (Fig. 5c, d). For the overhanging structure fabricated by laser penetration, it is found that the four fabricated parts under different energy inputs have the following four regions (Fig. 8a): no dross surface, dense-sinking transition surface, totally sinking surface, and forming failure surface. In the overhanging structure fabricated with varying laser energy parameters, the angle corresponding to each region is different. The junction angles between different regions in the four curved overhanging structure were labeled, to determine the angle range of each region. Then, the impact of different energy input parameters was analyzed on the angle that led to the formation of the overhanging part. Figure 8b shows the curve after analysis of the measurements. These three curves describe the obliquity angles of the overhanging plane corresponding to the following three cases; i.e., when the overhanging structure begins to form, the overhanging part gets fully covered, and the parts cannot be fabricated effectively under energy input parameters. A small obliquity angle \u03b8 or a thick layer implies that the overhanging portion a between the adjacent layers is large. While fabricating the curved overhanging structure, it would form the overhanging part without a support below, during the slicing of layers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003881_s00170-019-03996-5-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003881_s00170-019-03996-5-Figure2-1.png", + "caption": "Fig. 2 Complete post-processing setup", + "texts": [ + " Also, two other samples were selected for the validation process. One of them has the roughness that is less than the average Ra of the DOE samples and the other one has a higher roughness. Those samples were selected so the impact of the starting roughness on the results can be observed. The other two samples were used as dummy samples for electrochemical polishing and chemical etching to define the process parameters before starting the Taguchi experiment. The complete experimental setup assembly is shown in Fig. 2. The chemicals used in this research are aggressive and strong. For this reason, the material selected for this setup (beaker, sample holder, and cathode holder) is polytetrafluoroethylene (PTFE), also known as Teflon. The same setup can be used for both, with some additional parts in the electrochemical polishing process. A 400-ml beaker was used to contain the different chemicals. Before the post-processing, the samples are cleaned for 10 min in an ultrasonic bath in acetone to remove any organic matter on the part" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002484_j.jsv.2018.06.011-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002484_j.jsv.2018.06.011-Figure1-1.png", + "caption": "Fig. 1. Schematic of a planetary gear system.", + "texts": [ + " Different kinds of gear health scenarios will be used for testing. The rest of this paper is organized as follows: In Section 2, the amplitudes of the characteristic frequencies are mathematically discussed in terms of the reported model in Ref. [17]. In Section 3, theoretical explanations of SER are provided for different gear types. Finally, a modified SER method is proposed. Experimental studies will be given to validate the diagnostic effects in Section 4. Finally, Section 5 concludes the whole paper. As given in Fig. 1, a typical configuration of a planetary gearbox is considered in this paper. The ring gear is fixed, the sun gear rotates as the power input and the planet carrier rotates as the power output. The sensor is fixed on the housing to collect the vibration data. Phenomenological models reported in Ref. [17] have provided explicit mathematical expressions to describe the vibration behaviors of different types of gear faults. However, amplitudes of the key sideband components were not explicitly discussed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000918_12.2018412-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000918_12.2018412-Figure4-1.png", + "caption": "Figure 4. Drawing of the mirror based window protection housing. A mirror located above the vacuum chamber opening directs the image through a Sapphire window located out of the line-of-sight of metallization atoms and X-Rays.", + "texts": [ + "org/ on 09/23/2013 Terms of Use: http://spiedl.org/terms Kapton film, back-to-back, results in a window system with a transmission less than 0.0028%. In order to increase the infrared transmission of the window system the Quartz window was replaced with a 2 mm thick Sapphire window with an IR transmission of 86.3%. This window system now has a transmission of 0.73%, resulting in a much larger dynamic range in the thermal images. An alternate approach currently under development at ORNL is a single mirror periscope as shown in Figure 4. The periscope sets over a second view port on the top surface of the ARCAM vacuum chamber. The interior of the periscope is open to the build chamber and forms a vacuum seal with the top of the chamber. A mirror directs the Field-of-view of the IR camera down into the build chamber and eliminating the limited depth of field issue from the first port. The only other optical element between the IR camera and the powder bed is a sapphire window to allow imaging into the vacuum system. This system eliminates the need for the Kapton film since the window is no longer in the line-of-sight of the powder bed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure2.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure2.2-1.png", + "caption": "Fig. 2.2 In this book, limbs are modeled as serial linkage mechanisms (also called open kinematic chains). When defining the kinematics of such arrangements of rigid bodies, it is typical to attach a unique frame of reference to each rigid body, and thereafter perform the analysis on those frames of reference. However, this example has N frames of reference but only N \u2212 1 rigid bodies and DOFs. The last frame of reference is used to describe the location and orientation of the endpoint with respect to frame N \u2212 1", + "texts": [ + " The mathematical expression for calculating the thumb endpoint coordinates for any set of joint angles is quite complicated, and even difficult to calculate by inspection. However, we are able to calculate the endpoint position in relation to a base frame in a systematic way if we use homogeneous transformations. Appendix A provides a brief introduction to these tools. It is imperative that you read it before continuing if you have not worked with the fundamentals of linear algebra or robot kinematics recently. A limb is an open kinematic chain because it is a serial arrangement of articulated rigid bodies, Fig. 2.2. The posture of the limb is determined by its kinematic DOFs of the system, defined in this book by variables q1, q2, q3, . . . , qN , that are also called generalized coordinates in mechanical analysis. In the case where anatomical joints are assumed to be rotational joints, the generalized coordinates are angles; but they can also be linear displacements for prismatic joints in robotic systems or in anatomical joints that can slide. As mentioned above, using pure rotational joints (pin, universal, or ball-and-socket joints) is common in musculoskeletal models [5], but it is a critical assumption that can have important consequences to the validity and utility of the model [2\u20134, 11]. Based on the techniques presented in Appendix A, a forward kinematic model of a limb is created using the following steps: Take Fig. 2.2 as an example. Recall that we describe rigid bodies by attaching a frame of reference to each body, and homogeneous transformations are used to relate adjacent frames of reference. From now on, we do not speak of the rigid links any more, but only treat the frames of reference. This allows you to find5 T endpoint base = T N 0 (2.3) N or A \u2208 R M\u00d7N , respectively. Indices that are lowercase italicized letters like n, i , or j signify a number within a range. The letter M need not stand for muscles, or n for an intermediate frame of reference", + "4 discuss the importance of defining and allocating the DOFs of a limb in a specific order. See, for example, the kinematic models of the thumb in [10, 11]. 2. Extract the position of the endpoint from the homogeneous transformation T N 0 . Note that in Eq. 2.5 the vector pN 0 is the location of the endpoint with respect to the base. 3. Extract the orientation of the endpoint from the homogeneous transformation T N 0 . The orientation of the last link is given by the matrix RN 0 . But notice that the limb in Fig. 2.2 is generic enough that, by having many DOFs, it raises the issue of kinematic redundancy. More on this in Sect. 7.1. Consider the planar, 2 DOF, limb shown in Fig. 2.3. This limb is anchored to ground, where ground is the base frame, or frame 0. The first DOF (i.e., q1) rotates the first link in a positive (as per the right-hand-rule) direction. The second DOF (i.e., q2) rotates the second link with respect to the first link as shown in Fig. 2.2. This is an important convention in kinematic analysis in robotics: the generalized rotational coordinates qi are relative to the prior body. Other branches of engineering and physics prefer all angles to be measured with respect to the base frame. But it will become apparent why this simplifies the arithmetic of this kinematic analysis. Importantly, this also means that we need to define a reference posture of the limb for which all angles are 0, as all adjacent frames of reference are aligned with each other" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003703_j.mechmachtheory.2020.103889-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003703_j.mechmachtheory.2020.103889-Figure3-1.png", + "caption": "Fig. 3. The vector diagram of the forces acts on the local ball.", + "texts": [ + " 5 D + \u03b4ok (5) where the elastic deformations in the ball-raceway contacts can be calculated by: { \u03b4ik = ( P ik / K ik ) 2 / 3 \u03b4ok = ( P ok / K ok ) 2 / 3 (6) where K ik and K ok are the load-deformation coefficients in the inner and outer raceway contacts, and P ik and P ok the elastic contact forces of the inner and outer raceways. According to the above equations, in order to obtain the elastic deformation in the ball-raceway contacts, the elastic contact forces P ik and P ok should be determined first. In order to obtain the explicit expressions of the elastic contact forces P ik and P ok , the vector diagram method is applied in the force analysis of the local ball instead of the orthogonal decomposition method. As shown in Fig. 3 , the mechanical equilibrium equation of the local ball in vector form is given as: \u2212\u2192 F ck + \u2212\u2192 P ik + \u2212\u2192 f ik + \u2212\u2192 P ok + \u2212\u2192 f ok = 0 (7) where \u2212\u2192 F ck is the vector of ball centrifugal force, and \u2212\u2192 f ik , \u2212\u2192 f ok are the vectors of the ball-raceway friction forces. Instead of the Raceway Control Theory in Jones-Harris model [2\u20134] the relations between the elastic contact forces and friction forces in the ball-raceway contacts are determined by the equal friction coefficient assumption [28] . [ T ik T ok ] = \u03bc [ P ik P ok ] (8) where the friction coefficient \u03bc can be written as: \u03bc = 2 M gk ( P ik + P ok ) D (9) where M gk is the gyroscopic moment of ball. In addition, as shown in Fig. 3 , the action force in the ball-inner raceway and ball-outer raceway contacts can be further simplified as: { \u2212\u2192 F ik = \u2212\u2192 P ik + \u2212\u2192 f ik \u2212\u2192 F ok = \u2212\u2192 P ok + \u2212\u2192 f ok (10) According to the sine theorem of the plane triangle, the relations of the sizes among the load vectors \u2212\u2192 F ck , \u2212\u2192 F ik and \u2212\u2192 F ok are given as: F ik sin \u03b8ok = F ok sin \u03b8ik = F ck sin ( \u03b8ik \u2212 \u03b8ok ) (11) where the included angles \u03b8 ik and \u03b8 ok can be obtained according to Fig. 3: { \u03b8ik = \u03b1ik \u2212 \u03b1k \u03b8ok = \u03b1ok \u2212 \u03b1k (12) Based on the Eqs. (9) and (10) , one can obtain: { \u03b1 = arctan ( 1 P ik + P ok 2 M gk D ) \u03b8ik \u2212 \u03b8ok = \u03b1ik \u2212 \u03b1ok (13) So the explicit expressions of the elastic contact forces P ik and P ok are given as: \u23a7 \u23aa \u23a8 \u23aa \u23a9 P ik = F ik cos \u03b1 = F ck sin ( \u03b1ok \u2212 \u03b1k ) sin ( \u03b1ik \u2212 \u03b1ok ) cos \u03b1 P ok = F ok cos \u03b1 = F ck sin ( \u03b1ik \u2212 \u03b1k ) sin ( \u03b1 \u2212 \u03b1 ) cos \u03b1 (14) ik ok Besides, the inertia forces of ball can be expressed as: { F ck = 0 . 5 m d m \u03c9 2 mk M gk = J \u03c9 mk \u03c9 bk sin \u03b2k (15) where m is ball mass and J is ball mass moment, and \u03c9 i is the revolution angular speeds of the inner ring, and the ball spinning and revolution angular speeds \u03c9 bk and \u03c9 mk can be determined by the assumption of no macro sliding in ballraceway contacts [29] " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure16-1.png", + "caption": "Figure 16. Test bench. (a) Schematic of rig and (b) test rig indoor.", + "texts": [ + " To validate the accuracy of the dynamics model and the simulation results, rig tests in the laboratory and field experiments on the Beijing\u2013Shanghai high-speed rail line, respectively, were carried out. Acceleration was measured on the gearbox housing and axle box. Figure 15 shows the locations of the accelerometers. The acceleration data were collected both in the lateral and the vertical directions with a sampling frequency of 5000Hz. The rig consisted of one full-scale bogie with a scaled roller (Figure 16), and the roller was designed to be replaceable to simulate all types of wheel defects, such as wheel flat, wheel tread peeling, and polygonal wheel wear. During the rig tests, the motor of the rig drove the roller via the transmission system, and the wheelset was driven by the roller. To imitate the operating situation closely, a weight equivalent to the weight of the car body was applied to the body bolster, and the roller sets were inclined correspondingly to simulate the rail cant. The radius and the order of polygonal wear of the wheelset and roller are related as follows Rw Nw \u00bc Rr Nr \u00f08\u00de where Rw and Rr are, respectively, the radii of the wheelset and roller and Nw and Nr are the orders of polygonal wear of the wheelset and roller" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003215_s00170-017-0410-2-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003215_s00170-017-0410-2-Figure1-1.png", + "caption": "Fig. 1 Rectangular parts produced in horizontal and vertical directions", + "texts": [ + " It is found that previous research works has not focused much on the effect of built direction in direct metal laser sintered (DMLS) Ti\u20136Al\u20134V alloy with respect to wear and corrosion. Hence, this research work is dedicated to report the findings of dry rotary wear and corrosion behaviour of horizontal built and vertical built DMLS Ti\u20136Al\u20134V specimens. Gas atomized Ti\u20136Al\u20134V alloy spherical powder (TLS Technik GmbH& Co. Germany) with an average particle size of 45 \u03bcm was used to produce rectangular parts of size 100 \u00d7 30 \u00d7 15 mm in vertical and horizontal directions as shown in Fig. 1 at Centre for Rapid Prototyping and Manufacturing, Bloemfontein using DMLS technology in EOSINT M270 machine. The set process parameters are 170 W laser power, scanning speed 1400 mm/s, layer thickness 30 \u03bcm, laser spot size 140 \u03bcm and high purity argon build atmosphere acting as a shield to avoid oxidation of Ti. Using horizontal carbolite tube furnace, heat treatments were done by purging argon gas with the following procedures. 1. Heating to 1100 \u00b0C (HT-1) at the rate of 5 \u00b0C/min, 1 h holding and the cooling rate was 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000320_ip-b.1988.0042-Figure69-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000320_ip-b.1988.0042-Figure69-1.png", + "caption": "Fig. 69 Mathematical model: transverse view", + "texts": [ + " The small width of the motor being analysed might be responsible for this low accuracy as there will be an uncertainty in transverse effect correction factors. A paper by Freeman [4] illustrates the use of the layer method to calculate both the levitation and propulsion forces on a single-sided LIM. 3-dimensional layer methods [87-89] have also been developed. The longitudinal and transverse effects are modelled by a double Fourier series approach. Not only is the linear motor replaced by an infinite array of motors along the longitudinal axis (as in Fig. 67) it also has an infinite array of motors positioned along the transverse axis, as shown in Fig. 69. The MMF produced by the primary windings can then be replaced by a double Fourier series. Iteration of the calculation allows the permeability of each layer to be adjusted to allow for saturation. Results from Boldea and Babescu in Reference 87 where Hy, n Pn 1/2 where k = 2^/wavelength, //x \u201e, and /zyi \u201e = permeability in the x and ^-directions, respectively, and con = Sn co, and Sn = slip of nth layer. In eqn. 5, By is the complex phasor magnitude of flux density, by = Re {By exp \\_j\\(ont \u2014 kx)]}, and the solution is B = A cosh yn y + C sinh yn y (6) where A and C depend on the boundary conditions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003544_tr.2016.2590997-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003544_tr.2016.2590997-Figure1-1.png", + "caption": "Fig. 1. Circumferential angles between the planet gears when the gears are distributed with the same contact conditions (i.e., in-phase state with dotted lines and arrows) and uniformly along the ring gear (i.e., out-of-phase with a solid line and arrow).", + "texts": [ + " In this condition, the meshes in contact between sun-planet meshes and ring-planet meshes are described as being \u201cin-phase.\u201d Theoretically, the same amount of load will be equally distributed among the ring-planet and sun-planet meshes. On the other hand, an \u201cout-of-phase\u201d condition can oc- cur when the number of teeth in contact varies. From the design point of view, the out-of-phase condition is desirable, because vibration and noise in gears can be efficiently suppressed in this condition [23]. Fig. 1 shows the in-phase and out-of-phase states of the planetary gear. In the in-phase state, the planet gears have the same contact condition as indicated with dotted lines and arrows. When the planet gears are distributed uniformly along the ring gear, however, the planetary gear has an out-of-phase state, as indicated with the solid line and arrow. These phased contact conditions of gear teeth arising from the planet phasing effect lead to phased GMS behaviors in the planetary gear. This phased GMS results in different dynamic behaviors of a planetary gear from spur and helical gears" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.11-1.png", + "caption": "Fig. 2.11 Free-body diagram", + "texts": [ + "124) 98 2 Dynamics of Rigid Machines so that one obtains three equations for the unknown components of the bearing forces and the input torque from (2.119) to (2.124): \u2212FA\u03b7a + FB\u03b7b = JS \u03be\u03b6 \u03d5\u0308\u2212 JS \u03b7\u03b6 \u03d5\u03072 (2.125) FA\u03bea\u2212 FB\u03beb = JS \u03b7\u03b6 \u03d5\u0308 + JS \u03be\u03b6 \u03d5\u03072 (2.126) Man + (FA\u03be + FB\u03be)\u03b7S \u2212 (FA\u03b7 + FB\u03b7)\u03beS = JS \u03b6\u03b6 \u03d5\u0308 (2.127) Three other equations for the unknown quantities follow from the center-of-gravity theorem. (2.79) applies in the space-fixed reference system. However, it is useful to express it in bodyfixed components in accordance with (2.82). The following applies because of r\u0308O \u2261 o, see Fig. 2.11: m( \u02d9\u0303 \u03c9 + \u03c9\u0303 \u03c9\u0303)lS = F . (2.128) Since the external forces are the unknown bearing forces in A and B, one can also write: FA + FB = m( \u02d9\u0303 \u03c9 + \u03c9\u0303 \u03c9\u0303)lS. (2.129) In detail, this equation with the vector lS = (\u03beS, \u03b7S, \u03b6S)T and the tensor matrices is as follows: \u02d9\u0303 \u03c9 = \u23a1\u23a3 0 \u2212\u03d5\u0308 0 \u03d5\u0308 0 0 0 0 0 \u23a4\u23a6 ; \u03c9\u0303 = \u23a1\u23a3 0 \u2212\u03d5\u0307 0 \u03d5\u0307 0 0 0 0 0 \u23a4\u23a6 (2.130) and after multiplication of the three matrices, respectively 2.3 Kinetics of the Rigid Body 99 FA\u03be + FB\u03be = m(\u2212\u03d5\u0308\u03b7S \u2212 \u03d5\u03072\u03beS) (2.131) FA\u03b7 + FB\u03b7 = m(\u03d5\u0308\u03beS \u2212 \u03d5\u03072\u03b7S). (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000491_978-3-540-79029-7-Figure2.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000491_978-3-540-79029-7-Figure2.8-1.png", + "caption": "Fig. 2.8 Forbidden zones in the vector space", + "texts": [ + " The values either of Tr or of Tl become very small in the boundary zone between the sectors or near one of the standard vectors u1 ... u6. For some commonly used digital signal processing structures (refer to the application example with TMS 320C20/C25 in section 2.4) the PWM synchronization is directly coupled to the interrupt evaluation of the timer counters for Tr and Tl. For these structures the values of Tr and Tl must never fall below the interrupt reaction times causing another limitation of the utilizable area. The arising forbidden zones are shown in figure 2.8. According to theory (refer to fig. 2.3) the modulated voltage in the context of control or digital signal processing looks like in figure 2.9 for the samplings periods (k-1), (k) and (k+1). The voltage output sequence in period (k) ( ) ( ) ( ) ( ) ( ) ( )7 7 0 0/r r l l l l r rT T T T T Tu u u u u u leads to the following time relation: ( ) ( )0 0k k 1 2 2synch p T T T T= + 28 Inverter control with space vector modulation Restrictions of the procedure 29 For a dynamic process with us(k-1) \u2260 us(k) is also T0(k-1)/2 \u2260 T0(k)/2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002780_icra.2015.7139416-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002780_icra.2015.7139416-Figure2-1.png", + "caption": "Fig. 2: The model of the aerial robot. Red frame is the inertial frame and blue frame is the body frame. Both frames ought to coincide with the origin O. They are separated here only to illustrate axis directions.", + "texts": [ + " A different approach is used to derive the control law, which is similar to ours. However, they did not implement the controller on a real UAV. Only simulation results are presented. Their work is adopted in [13] for trajectory control of small UAVs. Compared with our work, the focus of [13] is micro UAV control. Their work deals with UAVs that are small and light weight. In this section we define our notation for rotation parametrization and review some basic knowledge of Lie Group and Lie Algebra. As shown in Figure 2, if we denote the inertial frame as A and B the body frame. We can represent the bases of frame B using the axes of frame A, with coordinates xab, yab, zab \u2208 R3. Then we define matrix Rab = [xab yab zab] as the rotation matrix from frame B to frame A. For any points qb in frame B, its coordinates in frame A is qa = Rabqb All possible rotations form the rotation group of R3, namely SO(3). The group structure of SO(3) leads to composition rule for rotations. If we have three frames A, B and C. Then we have Rac = RabRbc Therefore, given frame A and frame C, it is always possible to choose an intermediate frame B such that Rac can be decomposed into Rab and Rbc", + " Each propeller generates torque \u2206Fi perpendicular to the plane on which the robot base resides. We choose the local northeast-down (NED) coordinate frame as the inertial frame, and the roll-pitch-yaw coordinate frame as the body frame. Since we do not consider translation in this case, both the inertial frame and the body frame have their origins located at the center of mass of the robot. Our aerial robot has X shape so roll axis equally divide the angle between the arm of motor 1 and the arm of motor 4. Directions of frame axes are shown in Figure 2. Based on this model, we define: R \u2208 SO(3), the rotation of the aerial robot expressed as frame transform from the body frame to the inertial frame; J \u2208 R3\u00d73, the inertia matrix expressed in the body frame; \u03c9b \u2208 R3, the angular velocity in the body frame; \u03c4 \u2208 R3, the control torque generated by the actuators of the robot, expressed in body frame as well. With above definition, we present robot kinematic as a first order system R\u0307 = R\u03c9\u0302b (2) which is rewritten from (1). Then by Euler equation we can write the robot dynamics as J\u03c9\u0307b + \u03c9b \u00d7 J\u03c9b = \u03c4 (3) The control goal of our algorithm is to move from the current rotation Rc to a target rotation Rt" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure9.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure9.2-1.png", + "caption": "Fig. 9.2 Geometric scheme of the RR + RRR parallel wrist", + "texts": [ + "2 Infinitesimal screws of the 3R2T parallel manipulator . . . . . . . . . . . . 194 Fig. 8.3 Example 8.1. Time history of the angular and linear velocities of the center of the moving platform . . . . . . . . . . . . . . . . . . . . 201 List of Figures xxi Fig. 8.4 Example 8.1. Time history of the angular and linear accelerations of the center of the moving platform . . . . . . . . . . . . . . . . 201 Fig. 9.1 The RR + RRR spherical parallel manipulator . . . . . . . . . . . . . . . . . . . . 206 Fig. 9.2 Geometric scheme of the RR + RRR parallel wrist. . . . . . . . . . . . . . . . 207 Fig. 9.3 Infinitesimal screws of the RR + RRR parallel wrist . . . . . . . . . . . . . . 211 Fig. 9.4 Example 9.3. Time history of the angular quantities of the knob as measured from the base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Fig. 10.1 The 3-RRPS parallel manipulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Fig. 10.2 3-RRPS parallel manipulator. Active revolute joint ", + " The mobility of the mechanism can be easily explained if we take into account that because of the chosen architecture, while the RRR-type limb is a 3-DOF spherical serial manipulator, the connection of the knob though the RR-type limb is such that the knob cannot rotate along an axis perpendicular to the axes of the revolute joints of this leg. Therefore, the wrist at hand is limited to 2 DOF. 9.3 Finite Kinematics of the Parallel Wrist 207 In this section the displacement analysis of the limited-DOF spherical parallel manipulator is presented. Because of the robot\u2019s simple architecture, closed-form solutions are easily derived. The parameters and generalized coordinates of the mechanism are outlined in Fig. 9.2. The forward position analysis of the parallel wrist is formulated as follows. Given the generalized coordinates q1 and q2, we must compute the rotation matrix R of the knob with respect to the base. To accomplish this, consider that XYZ is a reference frame attached to the base whose origin O is instantaneously coincident with the point of zero linear kinematic properties of the moving knob. Next, it immediately emerges that the coordinates of points P1 and P3 are obtained as P1 D .0; r sin q1; r cos q1/ P3 D ", + " (2003), the inverse position analysis is immediately solved, taking advantage of the decoupled motions of the knob. In fact, let C D .CX; CY ; CZ/ be the coordinates of point C where C2 XCC2 YCC2 Z D r2. The generalized coordinates q1 and q2 are immediately obtained as q1 D arctan CY CZ (9.7) and q2 D arctan CX CZ ; (9.8) respectively. In this section the velocity, acceleration, and jerk analyses of the parallel wrist are addressed by screw theory. To reach this goal, the infinitesimal screws representing the kinematic pairs of the mechanism are depicted in Fig. 9.2. 210 9 Two-Degree-of-Freedom Parallel Wrist Let ! be the angular velocity of the knob. Furthermore, let VO D ! vO be the velocity state of the knob as measured from the base where, to simplify the analysis of the robot, point O is chosen as the reference pole; that is, the velocity vO of point O vanishes (vO D 0). The six-dimensional vector VO may be expressed in screw form through any of the two limbs of the manipulator as follows: Pqi 0$1 i C 1! i 2 1$2 i C 2! i 3 2$3 i D VO; i D 1; 2; (9.9) where 2$3 1 is an auxiliary screw representing a fictitious revolute joint introduced to satisfy an algebraic requirement, that is, 2", + " On the other hand, the forward velocity analysis consists of computing the velocity state VO given the generalized speeds Pq1 and Pq2. Example 9.2. The input\u2013output equation of velocity of parallel manipulators may be obtained using different sets of reciprocal screws. This example shows how the input\u2013output equation of velocity of the parallel wrist at hand may be obtained by using a different strategy than that used at the beginning of this subsection. For clarity, most of the notations used in Fig. 9.2 are repeated here (see Fig. 9.3). Solution. The procedure avoids the inclusion of virtual screws. The velocity state of the knob as measured from the base may be written in screw form through the 2-DOF kinematic chain as follows: Pq1 0$1 1 C 1!1 2 1$2 1 D VO: (9.15) Let L1 be a line of Pl\u00fccker coordinates passing through point P1 parallel to the OC line. Applying the Klein form of this line to both sides of Eq. (9.15) and canceling terms leads to Pq1 \u02da 0$1 1IL1 D fVOIL1g : (9.16) 212 9 Two-Degree-of-Freedom Parallel Wrist On the other hand, based on the 3-DOF kinematic chain, the velocity state VO may be written in screw form as follows: Pq2 0$1 2 C 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure2-1.png", + "caption": "Fig. 2. Example of applications of face-gears.", + "texts": [ + " (2) The generation of the face-gear of the drive may be accomplished: (i) by a shaper and (ii) a grinding or cutting worm provided by a special thread surface (see Section 8). The contents of this paper cover: (i) Avoidance of singularities, undercutting, and pointing of generated surfaces. (ii) Simulation of meshing and contact for determination of transmission errors and shift of bearing contact. (iii) Enhanced stress analysis. Application of face-gear drives with helical pinions is illustrated with examples of gear drives (see Section 2). The developed theory is illustrated with numerical examples. The train is formed (Fig. 2(a)): (i) by co-axial face-gears 1 and 4 and (ii) carrier c at which are mounted helical pinions 2 and 3. Pinions 2 and 3 are rigidly connected and perform: (a) transfer motion with carrier c and (b) relative motion about carrier. The helix angles of pinions 2 and 3 are of the same directions in order to reduce the axial load on carrier c transformed from the pinions. Assume that face-gear 4 is fixed and the train is used as a planetary one. It follows from the kinematics of the train that x1 xc xc \u00bc m\u00f0c\u00de 12 m\u00f0c\u00de 34 \u00bc \u00f0 1\u00deN 2 N 1 \u00f0 1\u00deN 4 N 3 : \u00f01\u00de Then, we obtain m\u00f04\u00de c1 \u00bc xc x1 \u00bc 1 1 N 2N 4 N 1N 3 \u00bc N 1N 3 N 1N 3 N 2N 4 : \u00f02\u00de Here, xc and x1 are the angular velocities of rotation of carrier c and face-gear 1; m\u00f04\u00de c1 is the gear ratio of the train where carrier c and face-gear 1 are the driving and the driven members of the gear train and gear 4 is held at rest; Ni (i = 1,2,3,4) is the tooth number", + " In the case where N2 = N3, we obtain that m\u00f04\u00de c1 \u00bc N 1 N 1 N 4 : \u00f03\u00de A substantial reduction of angular velocity xc may be obtained. However, the efficiency of the train depends substantially on the applied gear ratio m\u00f04\u00de c1 . Note: The gear train may be applied as well as a differential considering that the driving link is the carrier and the two driven members are 1 and 4. The advantage of such a differential is that zones of meshing (between 2 and 1, between 3 and 4) are separated and this enables increasing the precision and conditions of contact. Numerical example 1: The train of Fig. 2(a) is formed as follows: output gear N1 = 100, planet gears N2 = N3 = 17, fixed gear N4 = 88, crossing angle c = 75 , helix angle b = 10 . From Eq. (3) it follows that m\u00f04\u00de c1 \u00bc xc x1 \u00bc 100 100 88 \u00bc 8:333: \u00f04\u00de For such a gear train we might expect an efficiency of about 77.5%, computed considering a power lost of 2% at each meshing. The train is formed (Fig. 2(b)): (i) by co-axial face-gears 1 and 3 and (ii) carrier c at which are mounted Np planets 2 (i), i = 1, . . . ,Np. Spur or helical gears may be applied. Extended axial dimensions of planets 2(i) are required for simultaneous mesh of face-gears 1 and 3. Each planet is rotated independently with respect to the carrier. It follows from the kinematics of the train that x1 xc xc \u00bc m\u00f0c\u00de 12 m\u00f0c\u00de 23 \u00bc \u00f0 1\u00deN 3 N 1 : \u00f05\u00de Thus, we obtain m\u00f03\u00de 1c \u00bc x1 xc \u00bc N 1 \u00fe N 3 N 1 : \u00f06\u00de Here, m\u00f03\u00de 1c is the gear ratio of the train where face-gear 1 and carrier c are the driving and the driven members of the gear train. Gear 3 is held at rest. The advantages of such a train are the compact dimensions, and the disadvantage is that possibilities of optimization of meshing between gears 1\u20132 and 2\u20133 are reduced, since gear 2 is in mesh simultaneously with gears 1 and 3 (see below). This train can be applied as well as a differential. Numerical example 2: The train of Fig. 2(b) is formed as follows: output gear N1 = 88, planet gears N2 = 17, fixed gear N3 = 100. From Eq. (6) it follows that m\u00f04\u00de 1c \u00bc x1 xc \u00bc 88\u00fe 100 88 \u00bc 2:136: \u00f07\u00de The advantage of the discussed planetary train is the possibility to provide a small gear ratio, that cannot be obtained from a conventional face-gear drive. The gear ratio provided by this mechanism is much lower than the one obtained, with the same gears, in example 1. However, the efficiency would be much better, around 98%, if the same efficiency of the gears is assumed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003608_tcst.2020.3006184-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003608_tcst.2020.3006184-Figure6-1.png", + "caption": "Fig. 6. Quadrotor UAV developed in the flight dynamics and control laboratory. (a) Quadrotor UAV. (b) Attitude control test.", + "texts": [ + " In this section, the proposed geometric adaptive controller is validated by the flight experiments. Its hardware and software are custom-designed and developed in-house. To demonstrate the capability of rejecting the disturbances, flight experiments are performed under wind disturbances generated by an industrial fan. First, we describe the hardware and software configurations. Then, we present the experimental results in two sections, including attitude and flight trajectory trackings. Additional experimental results are available in [21]. The quadrotor platform is shown in Fig. 6. It has four brushless DC electrical motors (700-kV T-Motor) paired with 11 \u00d7 3.7 carbon fiber propellers. To control the rotational speed of the motors, each one is connected to an electronic speed control (MikroKopter BL-Ctrl v2), which receives the commands through the Inter-integrated Circuit (I2C) protocols from an onboard computer. All computations are performed on an embedded system-onmodule (NVIDIA Jetson TX2) running a Linux operating system (Ubuntu 16.04 with JetPack 3.3). The onboard computer is attached to an expansion board (Connect Tech\u2019s Orbitty Carrier), which is connected to a custom-designed printed circuit board", + " Additional software is developed for the ground server that transmits commands to the quadrotor and receives the flight data from the onboard computer to monitor the quadrotor responses. We used the Glade library to design a graphical user interface. It is used to monitor the flight data and to enhance user interactions. The flight data are saved in the host computer for postprocessing. We first perform experiments for the attitude control. Here, the quadrotor is attached to a spherical joint to prevent any translation. In particular, the spherical rolling joint (SRJ012CP from Myostat Motion Control) is affixed to an aluminum bar, as illustrated in Fig. 6(b). It allows up to 30\u00b0 in roll and pitch, and unlimited yaw. As the spherical joint is below the mass center, this setup resembles the dynamics of an inverted rigid pendulum, and there is an additional gravitational torque to be considered in (4). As such, the control moment in (18) is augmented by a canceling term. Moreover, the moment of inertia is translated to the center of rotation [21]. The wind speed generated with the fan is measured using a TriSonica-Mini 3-D sonic anemometer as follows" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003498_j.jmatprotec.2019.116398-Figure14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003498_j.jmatprotec.2019.116398-Figure14-1.png", + "caption": "Fig. 14. Demonstrative part showing the advantages of SLM technique in fabricating the complex-shape parts.", + "texts": [ + " Those defects deteriorate the metallurgical bonding between adjacent melts, resulting in easier cracking during tensile tests. As a result, the tensile properties are much worsened for the samples fabricated at a hatch distance of 0.20mm. Based on the optimized processing parameters in particular the hatch distance (P= 140 W, v =600mm/s, h =0.16mm), demonstrative parts, including parts of turbine, combustion chamber and compressor for a microturbine engine, have been fabricated by SLM and are presented in Fig. 14. The as-fabricated parts show excellent geometry precision and surface finishing, demonstrating that the SLM technique has the capability to process the materials with poor formability like IMCs into complex-shape parts. The light-weight Ti\u201322Al\u201325Nb has a similar working temperature upper limit as some of the Ni-based superalloys such as IN718. It is hoped that one day such SLM-prepared Ti\u201322Al\u201325Nb parts can be commercialized in products, such as microturbine engines for e.g. drones, by making good use of its low density and high mechanical performance at both room temperature and elevated temperatures" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003700_j.mechmachtheory.2020.103832-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003700_j.mechmachtheory.2020.103832-Figure1-1.png", + "caption": "Fig. 1. Coordinate system of ball bearing.", + "texts": [ + " The traction coefficients under different temperatures are calculated based on the five-parameter rheological model, and then integrated with the developed dynamic model (in section 2); the dynamic behavior of bearings with consideration of lubricant temperature is investigated. The strategy for optimally determining the type of lubricants under extreme operating temperatures is further proposed. Five rectangular coordinate systems are defined to describe the motions of different bearing components as shown in Fig. 1 . The descriptions of each coordination system are given as following: (1) Inertial coordinate system [O; X,Y,Z ]: the origin O coincides with the outer ring, X axis is coincident with the center line of bearing and the YZ plane is parallel to the radial plane. (2) Coordinate system of the j th ball [O bj ; x bj ,y bj ,z bj ]: the origin O bj is located at the center of j th ball, x bj is parallel to the X axis, y bj z bj plane is parallel to YZ plane and the y bj axis is along the radial direction of bearing", + " The interaction forces between ball and cage pocket are shown as Fig. 4 . The cage pocket is subjected to the normal contact force F j bcn and frictional force F j bc f from ball, and these forces can be expressed as the function of relative motion between ball and cage. Assuming that the cage coordinate system coincides with the inertial coordinate system at the initial state, when the bearing operates under loading, the motion of cage center in inertial coordinate system is: r i c = [ 0 , y c , z c ] (11) As shown in Fig. 1 , the position of the j th pocket in cage coordinate system is: r c p j = [ 0 , d m 2 sin \u03d5 j , d m 2 cos \u03d5 j ] (12) Defining r p bpj is the vector of the j th ball\u2019s center relative to the j th pocket\u2019s center in pocket coordinate system, and it can be expressed as: r p bp j = T pi [ r i b j \u2212 r i c \u2212 T ic r c p j ] (13) where the transform matrix T pi and T ic are formulated as follows: T pi = [ T pc ] [ T ic ] \u22121 (14) T ic = \u23a1 \u23a2 \u23a3 1 0 0 0 cos \u03b8cage \u2212 sin \u03b8cage 0 sin \u03b8cage cos \u03b8cage \u23a4 \u23a5 \u23a6 (15) T pc = \u23a1 \u23a2 \u23a3 1 0 0 0 cos \u03d5 j sin \u03d5 j 0 \u2212 sin \u03d5 j cos \u03d5 j \u23a4 \u23a5 \u23a6 (16) Assuming that the clearance between ball and pocket is C p , then the deformations \u03b4bpj between the j th ball and cage pocket can be calculated using the following formulations: \u03b4bp j = C p \u2212 \u221a \u2223\u2223r p bp jx \u2223\u22232 + \u2223\u2223r p bp jy \u2223\u22232 (17) Therefore, according to the Hertz theory, the contact force between the j th ball and pocket can be expressed as follows: F j bcn = \u23a7 \u23a8 \u23a9 K l \u221a \u2223\u2223r p bp jx \u2223\u22232 + \u2223\u2223r p bp jy \u2223\u22232 \u03b4bp j \u2265 0 K c \u2223\u2223\u03b4bp j \u2223\u2223 + K l C p \u03b4bp j < 0 (18) In Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002302_j.ymssp.2017.01.032-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002302_j.ymssp.2017.01.032-Figure11-1.png", + "caption": "Fig. 11. Local faults (artificially seeded). On (a) planet gear, (b) sun gear, (c) ring gear.", + "texts": [ + " For the local fault on the ring gear, we can see in the results from both models multiple sidebands spaced at nNfc , but only in lumped-parameter model results, multiple sidebands spaced at nfc are observed. The experimental measurements are taken on two test rigs, TR 1 and TR 2. Both test rigs include the same single-stage spur-gear planetary gearbox, an asynchronous motor and data acquisition system. The only difference is the loading unit: TR 1 uses a DC generator, whereas TR 2, a magnetic particle brake controlled by a current signal. The TR1 is showed in Fig. 10. The parameters of the planetary gearbox were presented in Table 2. Fig. 11a\u2013c show the faulty planet, faulty sun and faulty ring, respectively (artificially seeded). The case of faulty planet is carried out on TR 1 and the faulty sun and faulty ring are carried out on TR 2. Waveform and frequency spectra of measured vibration of measured vibrations of planetary gear with a local fault on planet gear, sun gear and ring gear are presented in Figs. 12\u201314, respectively. In Fig. 12a, we can see impacts related to the fault, as both models predicted (Fig. 7). In Fig. 12b, which shows the spectrum of the measured vibration, the higher amplitude sidebands are spaced at n\u00f0f p \u00fe f c\u00de from other sidebands at nfc measured from f g , n 2 Z" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.33-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.33-1.png", + "caption": "FIGURE 5.33. Illustration of a gear joint to define Sheth coordinate tr ansforma tion.", + "texts": [ + "181) The transformation for a screw joint may be expressed in terms of the relative rotation e [ cosO - sin e 0 ~ jiTj = sine cos e 0 0 0 1 0 0 0 or displacement h rcoo' . h 0 ~ ] - SlIli _sin K p cos !l 0 T j - P P 0 0 1 0 0 0 (5.182) (5.183) The coordinate frames are installed on the two connected links at the screw joint such that the axes Wj and z; are aligned along the screw axis, and the axes Uj and Xi coincide at rest position. 5. Forward Kinematics 253 Example 162 * Sh eth transformation matrix at a gear joint. Th e Sheth method can also be utilized to describe the relative motion of two links connected by a gear joint. A gear joint, as shown in Figure 5.33, provides a proportional rotation, which has 1 DOF. The axes of rotat ions indicate the axes W j and Zi , and their common perpendi cular shows the ii vector. Th en, the Sheth parameters are defined as a = R ; + R j , b = 0, c = 0, a = 0, (3 = (}j , 'Y = (}i , to have [ cos (1+ c)(}i -r, ~ sine! ~\u00a3)Bi where 5.6 Summary - sin (1+ c) () i cos (1 + c) (}i o o o Rj (1+ c) COS (}i ] o R j (1 + c) sin () i 1 0 o 1 (5.184) (5.185) Forward kinematics describ es the end-effecto r coord inate fram e in the base coordinate frame of a robot when the joint variables are given" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure1.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure1.12-1.png", + "caption": "Figure 1.12.2 A compound crank axle with coil springs (Opel).", + "texts": [], + "surrounding_texts": [ + "The \u2018trailing-twist\u2019 axle, now often known as the \u2018compound-crank\u2019 axle, is illustrated in Figures 1.12.1\u20131.12.3. The axle concept is good, but the new name is not an obvious improvement over the old one. This design is a logical development of the fully-independent trailing-arm system. Beginningwith a simple pair of trailing arms, it is often desired to add an anti-roll bar. Originally, this was done by a standard U-shaped bar with twomountings on the body locating the bar, but allowing it to twist. Drop links connected the bar to the trailing arms. A disadvantage of this basic systemwas that the anti-roll bar transmitted extra noise into the passenger compartment, despite being fitted with rubber bushes. This problem was reduced by deleting the connections to the body, instead using two rubber-bushed connections on each trailing arm, so that the bar was still constrained in torsion. This was then simplified mechanically by making the two arms and the bar in one piece, requiring the now only semi-independent axle to flex in bending and torsion. This complicated the geometry, but allowed a compact system that was easy to install as a prepared unit at the final assembly stage. As seen in the figures, to facilitate the necessary bending and torsion the cross member of the axle is an open section pressing. The compound crank axle is now almost a standard for small passenger cars." + ] + }, + { + "image_filename": "designv10_3_0001339_j.commatsci.2011.02.018-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001339_j.commatsci.2011.02.018-Figure3-1.png", + "caption": "Fig. 3. Schematic representation of material addition procedure during the deposition process; (a) melt-pool boundary determined based on the nodal temperature at t = t1, (b) activated elements at room temperature (in blue) for solution at t = t1 + Dt, (c) activated elements associated with the nodes within the melt-pool in a symmetric half-view with respect to Y\u2013Z plane.", + "texts": [ + " In Time step: 2, within the intersectional area of the melt pool and powder stream, Smelt powder, the inactive elements attached to the substrate surface are activated. With the newly developed geometry, the model is solved for the updated location of the laser beam which is calculated from the laser scan velocity and scanning direction. By repeating this procedure for successive time steps, the accumulation of added elements will form the geometry of the deposited material, as illustrated in Fig. 3a. The number of layers of elements, nl, to be activated in each time step can be determined from the deposition height, Dh, and the element side length, lel: g1 \u00bc Dh lel \u00f09\u00de Assuming a uniform and steady flow of powder particles into the deposition zone, the deposition height Dh in each time step can be calculated as follows: Dh \u00bc _mCDt qp\u00f0pr2 L \u00fe 2rLVDt\u00de \u00f010\u00de where Dt (s) is the solution time step, _m (kg/s) the powder feed rate, qp (kg/m3) the powder density and V (m/s) the laser scan velocity. Based on the criteria used for approximation of the powder catchment efficiency C, the term _mCDt equals to the amount of powder in each time step entering the intersectional area of the laser beam circular column and the substrate surface. The term \u00f0pr2 L \u00fe 2rLVDt\u00de represents the area swept by the laser beam on the substrate surface in one time step. Fig. 3 shows schematically the activation procedure of the newly added elements in one time step. As can be seen in Fig. 3a, the selected elements in grey have temperatures higher than a pre-defined melting temperature. The resultant curved interface repre- a The melting temperature, Tm. b The modified value of the specific heat capacity calculated from the actual value, i.e., 800, to account for the release of the latent heat of fusion at the melting point. c The modified value of heat conductivity for temperatures higher than the melting point to consider the effect of Marangoni flow. The original value is multiplied by a factor of 2.5. d The emissivity values are considered for polished surfaces. sents the estimated 3D projection of the melt-pool boundary on the surface. Based on the calculated number of the layers of elements nl, the inactive elements associated with the outer surface of the melt-pool area are activated, as shown in Fig. 3b. The new model is then solved considering the ambient temperature for the newly activated elements, depicted in the darkest colour in Fig. 3c. Heat flux boundary condition from the laser beam irradiation is applied only on upper face of the surface elements located within the intersectional area of the laser beam column and the built model. The deposition process of AISI 304L is modelled and the simulation outputs are experimentally verified for the temperature history of the substrate and the clad geometrical development. To validate the simulation results, the single-track deposition of AISI 304L steel on a 25 20 5 mm3 substrate of the same material is numerically and experimentally performed using the operating parameters given in Table 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002897_j.engfailanal.2016.12.008-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002897_j.engfailanal.2016.12.008-Figure13-1.png", + "caption": "Fig. 13. The second order strain mode of the gearbox housing.", + "texts": [ + " A fairly large structural stress concentration is observed at the inner surface of the inspection window corner, which is consistent with observed gearbox-housing failures. Partial constraints (UX = UZ = 0) were applied on the center point of the wheel-axis rings. The results are shown in Figs. 11 and 12, and are listed in Table 1. The first order resonant mode of the gearbox housing is the lateral bending mode with a natural frequency of 579 Hz, and the second order mode is the axial opening mode with a natural frequency of 618 Hz. Modal strain analysis was conducted, and the second order strain mode is shown in Fig. 13. The modal strain response distribution is similar to the simulated fatigue strength stress response distribution in the failure region of the gearbox housing. A three-dimensional coordinate system is employed in the present work. The vertical direction is perpendicular to the ground, and the longitudinal direction is in the direction of travel. Fig. 14 illustrates the arrangement of the test gearbox. Track testing was conducted on the Chibi-Wuhan dedicated passenger line, covering a distance of about 128 km" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002780_icra.2015.7139416-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002780_icra.2015.7139416-Figure1-1.png", + "caption": "Fig. 1: Comparsion of trajectory of rotation using two different control methods.", + "texts": [ + " Most existing methods use Euler Angles to parametrize the rotation of a UAV, and yaw-roll-pitch angles are separately controlled with separated target angles [7], which linearize the rotation of UAV. This approach inherently neglects the manifold structure of rotation. When the UAV is rotating, it is actually moving from one point to another on SO(3). All movements on SO(3) must take the manifold structure into account as velocity constraints. A smooth movement trajectory is prefered. However, separate control of yaw-roll-pitch angles results in a non-smooth trajectory, because it is only the local approximation of SO(3). As illustrated in Figure 1. Moreover, if point A and B are far from each other, separate control may not be able to decide target yaw-pitch-roll angles because of gimbal lock problem of euler angles. As a consequence, separate control limits the maneuverability of UAVs. Complex UAV maneuver controls such 1Yun Yu, Shuo Yang, Mingxi Wang are with DJI Innovations and the Department of Electronic & Computer Engineering, Hong Kong University of Science & Technology {yyuao, syangag, mwang}@ust.hk 2Cheng Li, Zexiang Li are with the Department of Electronic & Computer Engineering, Hong Kong University of Science & Technology {cliac, eezxli}@ust" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003173_j.jmst.2020.10.001-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003173_j.jmst.2020.10.001-Figure2-1.png", + "caption": "Fig. 2. (a) Schematic of the tool-path of deposition, (b) the fabricated BAMS of SS316", + "texts": [ + " 1. The bead height and idth are measured to be 3 mm and 7 mm, respectively, for both aterials. Based on these measurements, a 3.5 mm offset is used etween the beads in the same layers. To maintain a constant conact tip-to-work distance (CTWD), a 3 mm offset in the z-direction s used between layers. For the multi-bead and multi-layer deposition, the individual eads were deposited on the xy-plane, and the subsequent layers ere offset in the z-direction. The tool path is presented schematially in Fig. 2(a). During the deposition of odd layers on the xy-plane, he beads were deposited in the y-direction. For the even layers, the eposition pattern was rotated 90\u25e6 counterclockwise. The offset alue between beads on the xy-plane was set at 3.5 mm to mainain a 50 % overlap between two adjacent beads (bead width of \u223c mm). The offset value after each layer in the z-direction was set t 3 mm. The deposition parameters are presented in Table 2. The ire-feed speed and welding speed were maintained constant to implify the process. The current and voltage values were set by he synergic program of the respective material. A total of 19 layers were deposited, including 11 with SS316 L nd 8 with In625. As shown in Fig. 2(d), the tensile specimens were 7 mm in length and cut from the top. Hence, depositing 8 layrs of In625 ensures that the interface is located in the middle. n previous research [27\u201329], a significantly high residual stress is eported in the layer near the substrate. Depositing 11 layers of Table 1 Chemical composition [weight percent (wt.%)] of SS316 L and In625 consumable wires. %C %Mn %Si %S %P %Fe %Cr %Ni %Mo %Nb + Ta %Cu SS316 L 0.02 2.1 0.81 0.01 0.02 63.7 18.9 11.8 2.2 \u2013 0.23 In625 0.02 0.1 0", + " Espeially in later layers, a slow cooling rate supplemented by the eat build-up may cause the newly deposited molten metal to rip off. Besides, continuous deposition can result in a heterogeeous thermal history among layers and can result in inconsistency n microstructures and mechanical properties. To maintain conistency, the part was allowed to cool down to an intermediate L and s F m A [ 3 3 3 H t p a r ( f C N temperature of 200 \u25e6C, after depositing each layer. Following the mentioned procedures, the solid bimetallic cube shown in Fig. 2(b) was fabricated. The deposited block was later detached from the substrate. As the present work focuses on the BAMS and the bimetallic interface, the substrate-to-deposit interface is not further investigated. To study the microstructural features and microhardness of the BAMS, specimens were prepared from the SS316 L and In625 sides as well as from the interface on the yz-plane. The specimens were then grinded and polished, following the general metallography procedure [30]. For etching of the SS316 L and In625 sides, glyceregia and aqua regia were used, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003236_j.jmapro.2018.06.033-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003236_j.jmapro.2018.06.033-Figure7-1.png", + "caption": "Fig. 7. Geometric assumptions for the bead and molten zone geometries as circularly shaped with defined parameters, according to [33] in LMD used as a coating process.", + "texts": [ + "5) as a ratio between the Rayleigh length zr and the defocusing distance in the z-direction, which is abbreviated by z relative to the equipment-specific smallest focal spot diameter df taken from [32] as = + \u23a1 \u23a3\u23a2 \u23a4 \u23a6\u23a5 d z d z z ( ) 1f r 2 (4.5) As previously mentioned, the LMD process parameters have to be adjusted to achieve optimized bead geometries in terms of the desired application. In order to improve the surface quality in the coating processes, it is assumed in [33] that the geometry of the resulting beads can be considered as circularly shaped, which is visualized in Fig. 7(a). In contrast to the structure-building application, in case of a multi-layer LMD process depositing beads next to each other (e.g., coating application), a certain bead spacing >d 0c and x 0, the two areas are determined by = \u2219 \u2212 \u2212 \u2212 \u23a1\u23a3 \u23a4\u23a6 = \u23a1 \u23a3\u23a2 + \u2212 \u23a1\u23a3 \u23a4\u23a6 \u23a4 \u23a6\u23a5 \u2212 \u23a1 \u23a3\u23a2 + \u2212 \u23a1\u23a3 \u23a4\u23a6 \u23a4 \u23a6\u23a5 + \u2212 \u2212 \u2212 \u2212 \u2212 ( ) A R d R R A R R R R H R \u03c9 d sin ( ) sin ( ) sin [ ][ ]. c d R d d \u03c9 R \u03c9 \u03c9 d R d d c 1 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 c c c c c c (4.7) In addition [33], described the overlapping ratio \u03bcc of the beads as follows: = \u2212\u03bc \u03c9 d \u03c9 ( ) .c c (4.8) As formerly stated, the beads were welded into the substrate, which results in high bonding", + " These results illustrate that it is possible to process specific bead shapes and dilution ratios by using different parameter sets, thereby allowing the tailoring of the desired geometric features. During the deposition of a given componential geometry, the position of one layer next to a subsequent layer has to be precisely prearranged in order to achieve high surface quality. Therefore, the overlapping ratio \u03bcc and the optimum bead spacing dc, as shown in Fig. 4(b), needs to be precisely determined. In the following section, the optimum bead spacing based on the geometrical assumptions from Fig. 7 are analysed by using the process parameters of Wg =16.4 kJ/g and a kfactor of 1.4 on the pre-heated substrates of TS =150 \u00b0C and 300 \u00b0C. Through geometric examinations of the beads, the values of H and \u03c9 for the specific process parameters were determined. By using Eq. (4.7), an optimum bead spacing of dc =2.45mm in the case of a pre- heated substrate of TS =150 \u00b0C has been calculated. According to Eq. (4.8), this leads to an overlapping of =\u03bcc 18 percent. The surface shapes of the conducted experiments for different bead spacing are shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.1-1.png", + "caption": "FIGURE 11.1. Principa l coordinate frame for a symmetric L-section.", + "texts": [ + " (11.14) However, (11.15) that shows 1W2 is equal to the difference of the kinetic energy between terminal and initial points. (11.16) Example 247 Position of center of mass. Th e posit ion of the mass center of a rigid body in a coordinate frame is indicated by re and is usually m easured in the body coordinate fram e. B re ~ r rdm (11 .17) mJB [ ~zc~ ] [ ~ f: ~~: ] (11.18)\u00a3J~ z dm 450 11. Motion Dynamics Applying the mass center integral on the symmetric L-section rigid body with p = 1 shown in Figure 11.1 provides the CM of th e section. The x position of C is Xc ~ r xdmmiB ~l x dA b2 + ab - a2 4ab + 2a2 (11.19) and becaus e of symmetry, we have b2 + ab - a2 uc = - Xc = 4ab+ 2a2 . (11.20) Example 24 8 Every force syst em is equiv alent to a wrench. Th e Poinsot theorem says: Every fo rce system is equivalent to a single force, plus a moment parallel to the forc e. Let F and M be the resultant force and moment of the fo rce system. We decompose the moment in to parallel and perpendicular components, M il and M j , to the fo rce axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.5-1.png", + "caption": "FIGURE 1.5. Illust ation of a 3R manipulator.", + "texts": [ + " Typically the manipulator should possess at least six DOF: three for positioning and three for orientation. A manipula- 1. Introduction 5 tor having more than six DOF is referred to as a kinematically redundant manipulator. 1.2.3 Manipulator The main body of a robot consist ing of the links, joints, and other st ructural 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 1.5 schematically illustrat es a 3R manipulator. 1.2.4 Wrist The joints in the kinematic chain of a robot between the forebeam and end effector 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 1.6 shows a schematic illustration of a spherical wrist, which is a Rf--Rf--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 ort hogonal if the length of their common normal tends to zero. Out of the 72 possible manipulators, the important ones are : R IIRIIP (SCARA) , Rf-R1.R (articulated) , Rf-R1.P (spherical) , RIIPf-P (cylindri cal), and Pf-Pf-P (Cartesian). 1. RIIRIIP The SCARA arm (Selective Compliant Arti culated Robot for Assem bly) shown in Figure 1.7 is a popular manipul ator, which, as its name suggests, is made for assembly operations. 2. Rf-R.lR The Rf-R1.R configuration, illustrated in Figure 1.5, is called elbow, revolut e, art iculat ed, or anthropomorphic. It is a suit able configurat ion 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 art iculated robot is shown in Figure 1.8 to indicate the name of different components. 1. Introduction 9 10 1. Introduction 3. RI-R..lP The spherical configuration is a suitable configuration for small ro bots. Almost 15% of industrial robots, Stanford arm for instance, are made of this configuration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003816_j.ymssp.2020.106903-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003816_j.ymssp.2020.106903-Figure11-1.png", + "caption": "Fig. 11. The location of defect.", + "texts": [ + " In order to verify the correctness of the proposed model and the analysis for different defects, experiments are done on a bearing test rig as shown in Fig. 10. The defective bearing is set in bearing chock 1 and acceleration sensor is installed in the vertical direction. Both the width and depth of the penetrating defect are set to 0.5 mm. The sizes of defect are the same as in the literature [16]. The tested bearing is a cylindrical roller bearing with a penetration defect on the outer raceway. The location of defect can be seen in Fig. 11. Parameters of the bearing are listed in Table 1. Simulations and Experiments are carried out at different rotation speeds. The vibration responses obtained from 4200 r/ min are detailed analyzed here. Figs. 12 and 13 are the vibration responses and the envelope spectra of tested bearing in vertical direction. According to the acceleration response, the periodic impact with the same amplitude can be found and interval between adjacent impacts corresponds to roller passing frequency of outer raceway (RPFO)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure5-1.png", + "caption": "Fig. 5. Illustration of principal directions corresponding to principal curvatures on plane \u03a0.", + "texts": [ + " Scalar coefficients \u03bb1 and \u03bb2 are determined wherein Ar is a new point that belongs to the new surface \u03a3r. Function (|\u03bb1(x,y)|+|\u03bb2(x,y)|) is designated as h(x,y) for the purpose of simplicity and represents the gap between pinion and gear tooth surfaces when these surfaces are in contact at point P. (iv) Principal directions and curvatures of surface \u03a3r are obtained by determination of maximum and minimum values of its normal curvature at point P [5]. Principal directions are given by angles \u03bcI and \u03bcII respect to axis xP (see Fig. 5) and principal curvatures are designated as \u03baI and \u03baII, respectively. The principal curvature radii are given by RI=1/\u03baI and RII=1/\u03baII. In a spur gear drive, since \u03bcI=0 rad and \u03bcII=\u03c0/2 rad, axes xp and yp coincide with the principal directions. (v) Ratio a/b of the lengths of major and minor semi-axis of the contact ellipse given by the Hertz theory is related with principal curvature radii RI and RII as [10]: RI RII = a b 2 E e\u00f0 \u00de\u2212K e\u00f0 \u00de K e\u00f0 \u00de\u2212E e\u00f0 \u00de : \u00f04\u00de Here, e = ffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u2212 b2 a2 r is the eccentricity of the ellipse; K e\u00f0 \u00de = \u222b\u03c0 = 2 0 1\u2212e sin2\u03b8 \u22121=2 d\u03b8 is the complete elliptic integral of the first kind [13]; E e\u00f0 \u00de = \u222b\u03c0 = 2 0 1\u2212e sin2\u03b8 1=2 d\u03b8 is the complete elliptic integral of the second kind [13]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003605_j.jmatprotec.2020.116723-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003605_j.jmatprotec.2020.116723-Figure1-1.png", + "caption": "Fig. 1. Deposition model for a single-pass multi-layer wall. (a) Low deposition efficiency and (b) High deposition efficiency.", + "texts": [ + " E-mail addresses: bw677@uowmail.edu.au (B. Wu), zengxi@uow.edu.au (Z. Pan). Journal of Materials Processing Tech. 283 (2020) 116723 0924-0136/ \u00a9 2020 Elsevier B.V. All rights reserved. T problem. Finally, as mentioned by Bai et al. (2018), only the first weld bead is deposited on a flat surface and the following layers are deposited on a convex surface. Because of the lack of side support, it is easy for the molten metal to flow down. As a result of the overflow of the weld pool, the wall width increases with wall growth (Fig. 1a). The solution to this problem increases the deposition efficiency, making possible the production of higher walls with fewer layers (Fig. 1b). Solutions for the overflow problem have been suggested in the literature. Some researchers propose methods to facilitate heat dissipation. Lu et al. (2017) observed that the steel wall becomes higher when constructed on a water-cooled copper base in GMAW-WAAM. Li et al. (2018) produced thinner and higher aluminum walls using thermoelectric coolers based on the Peltier effect in GMAW-WAAM. Ogino et al. (2018) verified that the steel wall becomes higher and thinner in GMAW-WAAM when the inter-pass time is correctly adjusted" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003808_j.msea.2019.138815-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003808_j.msea.2019.138815-Figure2-1.png", + "caption": "Fig. 2. (a) Laser-cladded AM sample, (b) Schematic view of the micro-tensile test specimen with dimensional specifications in mm.", + "texts": [ + "5 kW high power laser beam was focused (using a 400 mm focal length) on the substrate steel plate in order to generate a molten pool with the 420-stainless steel metallic powders injected simultaneously at the rate of 20 g/min with coaxially flowing argon gas as a shield to protect the molten pool from oxidation. The LC process was performed when the substrate plate was positioned at both a horizontal orientation (\u03b1 = 0\u00b0) and an angular orientation (\u03b1 = 30\u00b0) while the deposition head was normal to the base. Table 2. Process parameters Process Parameters Data Laser power 2.5 kW Laser scanning speed 10 mm/s Powder feed rate 20 g/min Focal length of lens 400 mm Contact tip to workpiece distance 21 mm Laser spot diameter 4.3 mm A miniature type tensile test specimen (as shown in Fig. 2b) was designed to study the Three samples from the transverse direction were selected for heat treatment. The samples were kept inside the furnace for an hour at (565\u00b110)\u00b0C. The aim of this heat treatment was to compare the microstructure and tensile properties of the as-cladded transverse sample with the heat-treated sample from the same direction. The metallographic samples were cut transversely (TD) and longitudinally along the The electron microscopy observations were done with an FEI Quanta 200 FEG scanning electron microscope (SEM) equipped with energy dispersive X-ray spectroscopy (EDS)", + " [30] S. Kou, Welding Metallurgy, Second Edition, Second Edi, A John Wiley & Sons, Inc., New Jersey, 2003. doi:10.1016/j.theochem.2007.07.017. [31] K. Zhang, S. Wang, W. Liu, X. Shang, Characterization of stainless steel parts by Laser Metal Deposition Shaping, J. Mater. 55 (2014) 104\u2013119. doi:10.1016/j.matdes.2013.09.006. Fig. 1. Schematic view of powder deposition for the fabrication of the 3D AM parts using the laser cladding process, (a) base orientation, and (b) angular deposition, \u03b1 = 30\u00b0. Fig. 2. (a) Laser-cladded AM sample, (b) Schematic view of the micro-tensile test specimen with dimensional specifications in mm. Fig. 3. Schematic location of the sample for microstructural and EBSD analysis; BD-laser cladding build direction, TD-Transverse Direction, ND- Normal Direction. Fig. 4. Comparison of engineering stress and strain between the as-cladded (AC-L) and prehardened (PH-L) samples in the longitudinal direction. Fig. 5. SEM image of cross-sectional microstructure (a) Pre-hardened rolled sample, (b) ascladded AM sample of AISI 420 MSS (etched with Ralph reagent); PAGB \u2013 Prior austenite grain boundary" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.8-1.png", + "caption": "FIGURE 1.8. Structure and terminology of a Rf-K1R elbow manipulator equipped with a spherical wrist .", + "texts": [ + " RIIRIIP The SCARA arm (Selective Compliant Arti culated Robot for Assem bly) shown in Figure 1.7 is a popular manipul ator, which, as its name suggests, is made for assembly operations. 2. Rf-R.lR The Rf-R1.R configuration, illustrated in Figure 1.5, is called elbow, revolut e, art iculat ed, or anthropomorphic. It is a suit able configurat ion 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 art iculated robot is shown in Figure 1.8 to indicate the name of different components. 1. Introduction 9 10 1. Introduction 3. RI-R..lP The spherical configuration is a suitable configuration for small ro bots. Almost 15% of industrial robots, Stanford arm for instance, are made of this configuration. The Rf-R..lP configurat ion is illustrat ed in Figure 1.9. By replacing the third joint of an art iculate manipulator with a pris matic joint, we obtain the spherical manipulator. The term spherical manipulator derives from the fact that the spherical coordinates de fine the position of the end-effector with respect to its base frame " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000491_978-3-540-79029-7-Figure5.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000491_978-3-540-79029-7-Figure5.10-1.png", + "caption": "Fig. 5.10c Possible current trajectories at instant t0", + "texts": [ + " Therefore, it also shows two-point behaviour. The method can be used in field synchronous as well as in stator-fixed coordinates. The principle block structure is shown in the figure 5.9. Fig. 5.8 Tolerance-circle of the predictive current controller Fig. 5.9 Block structure of the predictive current control If the actual vector is overlaps the tolerance-circle at the time t0, the predictive controller must, using the information provided by the observer, \u2022 calculate all possible trajectories of the current vector (figure 5.10a) for each of the seven possible standard voltage vectors, and \u2022 following a certain criterion determine the optimal voltage vector for the chosen current trajectory. 150 Dynamic current feedback control in drive systems The trajectories can be calculated as follows: ( ) ( ) ( ) ( ) ( ) ( ) 0 0 0 0 0 0 s s s t t s s s t t dt t t t dt dt t t t dt = = = + = + * * * ii i ii i (5.1) In the equation (5.1) the currents ( ) ( )0 0 and s st t*i i are known. The numerical derivation of produces s sd dt* *i i , and for calculation of sd dti the following equation is used: ( ) ( ) ( )0s gs s k t td k dt L =u ui (5.2) with: The formula (5.2) follows from the figure 5.10b in which the stator resistance is neglected. The induced e.m.f. is calculated by a machine model in the observer. Depending on the chosen trajectory (k = 0, 1, ... , 7) the following error vector: ( ) ( ) ( ), ,s s st k t t k= *i i i (5.3) can be calculated. For a detailed derivation the interested reader is referred to the mentioned literature. Here only the final equation (5.4), which shows the different error trajectories (figure 5.10c) in dependency on the chosen voltage vectors, is given. 0 0 = 0, 1, ... , 7 = one of the seven possible standard voltage vectors = the induced e.m.f. at instant = leakage inductance on the stator side s g s k k t t t L u u Survey about existing current control methods 151 ( ) ( ) ( ) ( )22 2 0 1 0 2 0,s st k t t a t t a t t= = + +i i (5.4) The error trajectories have the form of a parabola. From the figures 5.10a and 5.10c it can be seen, that the firing pulses corresponding to the voltage vectors 4 5 and u u would increase the error, while all others would decrease it", + " In addition, the number of necessary switchovers of the semiconductor switches should be as small as possible. Therefore the following criterion is appropriate: ( ) ( ) max t k n k = (5.5) 2. For fast change of current (dynamic operation): This case produces very fast changes of the set point vector s *i , and it requires that the actual vector is follows the set point vector exactly and as fast as possible. us(k) will then be chosen according to the following criterion: ( ) mint k = (5.6) For the example in figure 5.10c, using the first criterion would result in choosing vectors u1 or u3, whereas the second criterion yields vector u6. 152 Dynamic current feedback control in drive systems The predictive control is predominantly used in high power drives, where the assumption of a negligible stator resistance is fulfilled widely and where a very large rotor time constant allows the choice of a relatively large sampling period, what is necessary because of the extensive required calculations. The disadvantage of all nonlinear current control methods consists in the bad current impression in the area of inverter over-modulation, resulting in a certain orientation error and corresponding torque deviation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003497_j.triboint.2019.105960-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003497_j.triboint.2019.105960-Figure3-1.png", + "caption": "Fig. 3. Coordinate systems of a double-row TRB: (a) global system, (b) coordinate system determining roller location, (c) local cylindrical systems, and (d) local inclined systems.", + "texts": [ + " The rolling elements are distributed uniformly in space and the effects of forces from cages and roller skewing are neglected. The inner ring rotates freely about its own axis and therefore the associated loads in the rotating direction of roller are not considered, and the outer ring is fixed. A quasi-static double-row TRB model with five DOFs is presented by considering the frictional force, as partially discussed in a conference paper [23]. A global coordinate system, \u00f0x; y; z\u00de, for the double-row TRB is established, where the origin is selected at the bearing center as demonstrated in Fig. 3(a). The cylindrical coordinate systems, \u00f0rM;\u03c8 ;zM\u00de, are established in Fig. 3(b\u2013c), where the subscripts M \u00bc 1, 2 indicate the right and left rows of the double-row TRB, respectively. \u00f0rM;\u03c8; zM\u00de coordinate system also has the origin point at the bearing center O, and angle \u03c8 is defined by the location angle of the roller. The origin PM (M \u00bc 1, 2) is the intersection point between the roller axis and the normal line on the raceway in the middle of the roller contact length as illustrated in Fig. 3(c). Moreover, with the inclined angles of \ufffd\u03b1m, two inclined coordinate systems \u00f0\u03beM;\u03b6M; \u03b7M\u00de are introduced as shown in Fig. 3(d). An external load vector is applied on the double-row TRB [24], as shown in Fig. 3(a) fFgT \u00bc \ufffd Fx;Fy;Fz;Mx;My \ufffd (1) Under the load {F}, the displacement vector of the inner ring can be written as f\u03b4gT \u00bc \ufffd \u03b4x; \u03b4y; \u03b4z; \u03b3x; \u03b3y \ufffd (2) The relationship of displacement vectors of inner ring cross-section, J. Zheng et al. Tribology International 141 (2020) 105960 fuMg T \u00bc fuM;r; uM;z; \u03b8Mg and fuM;\u03b1mg T \u00bc fuM;\u03be; uM;\u03b6; \u03b8Mg; in local cylin- drical and inclined coordinate systems can be calculated by using transformation matrices as fuMg \u00bc \u00bdRM \ufffdf\u03b4Mg (3) \ufffd uM;\u03b1m \ufffd \u00bc \u00bdKM \ufffdfuMg (4) Meanwhile, the relationship of roller displacement vectors, fvMg T \u00bc fvM;r; vM;z; \u03c6Mg and fvM;\u03b1mg T \u00bc fvM;\u03be; vM;\u03b6; \u03c6Mg; in local cylindrical and inclined coordinate systems can be described by \ufffd vM;\u03b1m \ufffd \u00bc \u00bdKM \ufffdfvMg (5) Here, the transformation matrices, [KM] and [RM] are given by \u00bdKM \ufffd \u00bc 2 4 cos\u03b1m sin\u03b1m 0 sin\u03b1m cos\u03b1m 0 0 0 1 3 5 (6) \u00bdRM \ufffd \u00bc 2 4 cos \u03c8 sin \u03c8 0 \ufffdzp sin \u03c8 \ufffdzp cos \u03c8 0 0 \ufffd1 \ufffdrp sin \u03c8 \ufffdrp cos \u03c8 0 0 0 \ufffdsin \u03c8 \ufffdcos \u03c8 3 5 (7) where the signs \u201c\u00fe\u201d and \u201c-\u201ccorrespond to different rows" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.8-1.png", + "caption": "Fig. 2.8 Free-body diagram with forces and moments acting on the roller", + "texts": [ + "95) (MO \u03be , MO \u03b7 and MO \u03b6 ) of the resultant external moment MO result from the external forces that act on the body, i.e. the input torque Man, the static weight mg and the reaction forces (FN and FH) at the contact point. It 92 2 Dynamics of Rigid Machines is more favorable to write the moment equilibrium about the y\u2217 axis and about the z axis, rather than the moment equilibrium about the \u03b7 and \u03b6 axes. The following can be derived for the \u03be axis both formally from (2.97) to (2.99) and by inspection (Fig. 2.8b and c): MO kin \u03be \u2261 \u2212Jp\u03c8\u0308 = \u2212FHR (2.100) about the z axis (see Fig. 2.8a and b): MO kin \u03b6 cos \u03c8 \u2212MO kin \u03b7 sin \u03c8 \u2261 Ja\u03d5\u0308 = Man \u2212 FH\u03beS (2.101) and about the y\u2217 axis, see Fig. 2.8a and c: MO kin \u03b6 sin \u03c8 + MO kin \u03b7 cos \u03c8 \u2261 Jp\u03d5\u0307\u03c8\u0307 = (FN \u2212mg)\u03beS. (2.102) These are the equations for calculating the input torque as well as the reaction forces FN and FH. One can express the results using the parameters given in the problem statement \u2013 the above form, however, is better suited to recognize the \u201corigin\u201d of each term, such as the gyroscopic effect of the rotor. The horizontal force that ensures adhesion is FH = Jp\u03c8\u0308 R = Jp R2 \u03beS\u03d5\u0308 = 1 2 m\u03beS\u03d5\u0308. (2.103) 2.3 Kinetics of the Rigid Body 93 The input torque, that causes the given function \u03d5(t) is Man = ( Ja + Jp \u03be2 S R2 ) \u03d5\u0308 = m\u03d5\u0308(3R2 + L2 + 18\u03be2 S) 12 (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001329_taes.2015.140339-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001329_taes.2015.140339-Figure1-1.png", + "caption": "Fig. 1. Definitions of vectors and frames.", + "texts": [ + " The expressions In and On are n \u00d7 n unit and zero matrices, respectively. For any a = [a1, . . . , an]T \u2208 R n, tanh(a) = [tanh(a1), . . . , tanh(an)]T, where the hyperbolic tangent function is tanh(ai) = (eai \u2212 e\u2212ai )/(eai + e\u2212ai ) and satisfies |tanh(ai)| < 1, tanh(ai) = 0, if and only if ai = 0(i = 1, . . . , n). A. Chaser and Target Dynamics The control problem in which an uncertain chaser spacecraft tracks a tumbling space target is considered in this paper. Frames and vectors are depicted in Fig. 1, where Fi = {Oxiyizi} is the Earth-centered inertial frame and Fc = {Cxyz} and Ft = {Txtytzt} are the body-fixed frames of chaser and target spacecraft, respectively; the origins C and T are the centers of mass for chaser and target spacecraft, respectively. The fixed point P with respect to the target is the chaser\u2019s desired proximity 2434 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 51, NO. 3 JULY 2015 position along the direction of the target docking port, and the solid arrows {r, re} and dashed arrows {r t, rpt, pt} are the related position vectors represented in frame Fc and frame Ft, respectively", + " By defining the kinetic energy function E(t) = (1/2)(\u03bctmtrT t r t + mtv T t vt + \u03c9T t Jt\u03c9t) \u2265 0 and calculating its time derivative E\u0307(t) = \u2212\u03bctmtrT t S(\u03c9t)r t \u2212 mtv T t S(\u03c9t)vt \u2212 \u03c9T t S(\u03c9t)Jt\u03c9t \u2261 0, we know E(t) \u2261 E(0) = (1/2)[\u03bctmtrT t (0)r t(0) + mtv T t (0)vt(0) + \u03c9T t (0)Jt\u03c9t(0)] < \u221e. Thus, the tumbling target\u2019s position rt, linear velocity vt, and angular velocity \u03c9t are always bounded. B. 6-DOF Integrated Relative Motion Dynamics The rotation matrix from Ft to Fc is [16] R = I3 \u2212 4 ( 1 \u2212 \u03c3 T e \u03c3 e ) ( 1 + \u03c3 T e \u03c3 e )2 S (\u03c3 e) + 8( 1 + \u03c3 T e \u03c3 e )2 S2 (\u03c3 e) , (3) and the relative attitude in terms of MRP is \u03c3 e = \u03c3 t ( \u03c3 T\u03c3 \u2212 1 )+ \u03c3 ( 1 \u2212 \u03c3 T t \u03c3 t )\u2212 2S (\u03c3 t) \u03c3 1 + \u03c3 T t \u03c3 t\u03c3 T\u03c3 + 2\u03c3 T t \u03c3 . (4) According to Fig. 1, the position and velocity of point P represented in frame Ft can be obtained by rpt = r t + pt, vpt = vt + S (\u03c9t) pt, (5) where pt \u2208 R 3 is a constant vector in frame Ft. The relative position, relative velocity, and relative angular velocity represented in frame Fc can be derived by re = r \u2212 Rrpt, ve = v \u2212 Rvpt, \u03c9e = \u03c9 \u2212 R\u03c9t. (6) By substituting (6) into (1) and using the identities R\u0307 = \u2212S(\u03c9e)R, r\u0307pt = vpt \u2212 S(\u03c9t)rpt , and R\u22121 = RT, we can obtain the relative motion equations in frame Fc [12]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.32-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.32-1.png", + "caption": "Fig. 6.32 Calculation model of a textile mandril; a) Drawing, b) Calculation model, c) Sleeve spring damper element of the mandril bearing", + "texts": [ + "201): S = C\u22121 22 C21 = l 14EI [ 4 \u22121 \u22121 2 ] 2EI l3 [ 3l 0 3l 3l ] = 3 7l [ 3 \u22121 1 2 ] . (6.224) The reduced stiffness matrix is obtained from (6.223) and (6.224) using (6.204): Cred = C11 \u2212 STC21 Cred = 2EI l3 [ 6 0 0 6 ] \u2212 3 7l [ 3 1 \u22121 2 ] 2EI l3 [ 3l 0 3l 3l ] (6.225) Cred = 6EI 7l3 [ 2 \u22123 \u22123 8 ] This is the stiffness matrix of the model with two degrees of freedom known from 6.2.2.1 and determined there in a different way (by forming the inverse matrix of D), see (6.32). Figure 6.16a shows the calculation model of a textile mandril, see also Fig. 6.32. The package (mass parameter: m2, J2) sits on the stepped shaft. The shaft is supported by a housing, which corresponds to an elastically supported rigid body characterized by the mass parameters m1 and J1. Of interest is the influence of the mass parameters on the natural frequencies and mode shapes. It is to be calculated in particular how an increase in the mass m2 by 20 % affects the first two natural frequencies and the four mode shapes. 6.4 Structure and Parameter Changes 413 The mass matrix of this system can be represented according to (6", + " Damping forces are assumed to be proportional to the velocity to simplify the mathematical treatment, even though they are practically never exactly proportional to the velocity. This is also called viscous damping. The great benefits of this approach are 1. that one obtains linear differential equations that can be treated easily, 2. that this approach expresses a loss of mechanical energy during the vibrations (warming), and 3. that one can make do with a few parameter values only, see Sect. 1.4. Components with defined damping properties are intentionally used in various branches of mechanical engineering, e. g. sleeve springs for textile mandrils (Fig. 6.32c), hydraulic torsional vibration dampers in marine diesel engines (Fig. 4.45), frictional dampers on crankshafts (Fig. 4.42), e. t. c. Rubber springs, rubber couplings, rubber tires, cables, V belts, leaf and disk springs are often used because they have good damping properties. Concrete has in some cases taken the place of cast metal structures for machine tool frames due to its high damping characteristics. If one starts from discrete damping elements, the damping forces referred to the coordinates q are obtained in general form as fd = Bq\u0307 (6", + " The resonance curve differs only slightly from that of the undamped system in areas outside resonance, if the damping ratios Di are small. Damping frequently becomes supercrit- 6.6 Damped Vibrations 455 ical at higher natural frequencies (Di > 1) so that no resonance peaks form, see e. g. Figure 6.30. Amplitude frequency responses can be calculated for each harmonic of qk(t) and recorded as functions of \u03a9 as so-called cascade diagram. Textile mandrils work at high speeds and belong to the machine sub-assemblies that cannot be designed or improved without an exact dynamic analysis. Figure 6.32 shows the design drawing of a textile mandril and the corresponding calculation model. Note that hydraulic dampers with a damping spiral (sleeve spring) as shown in Fig. 6.32c are used at both bearings. Figure 6.33a shows the calculated amplitude frequency response of the footstep bearing force, Fig. 6.33b that of the displacement of the mandril tip as a result of the unbalance-excited vibrations. The damping constant bF of the footstep bearing was varied to find out at which values the amplitude 456 6 Linear Oscillators with Multiple Degrees of Freedom maxima to be passed through during start-up and coast-down remain as small as possible. Figure 6.33 shows how much the resonance amplitudes are determined by the damping of the footstep bearing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001860_s10853-017-1169-4-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001860_s10853-017-1169-4-Figure1-1.png", + "caption": "Figure 1 Schematic demonstrating build orientation of tensile component cuboids (a) and thermal expansion cubes (b), as well as test orientations for thermal expansion analysis (c).", + "texts": [ + " Samples were mounted in conducting resin, ground and polished using SiC pads in grades from P800-P2500 and diamond suspension polish from 3 to 1 lm, to reveal polished vertical and horizontal sections. Two sections were prepared of each sample, with three micrographs taken for each section\u2014allowing for calculation of mean values with standard error. This method is preferred over displacement techniques as it reveals the quantity and morphology of porosity that may exist within a sample. Samples for microstructural analysis were etched using a 2% Nital solution (98 ml of IMS with 2 ml of nitric acid). Tensile rounds were machined from cuboids fabricated in the x\u2013y orientation, see Fig. 1, to ASTM A370 standard sizing. Tensile components built in x\u2013y (built with the gauge length in the x\u2013y plane, rather than z plane) have been found to display slightly higher tensile strength than those built in z [8]. Therefore, the x\u2013y orientation represents a maximum tensile strength for the as-deposited state. It is noted that the same investigation [8] found that elongation was greater in tensile components built in the z plane; therefore, x\u2013y plane components represent a minimum for elongation", + "105 g/cm3 as measured by helium gas pycnometry on a Micromeritics AccuPyc 1340 Pycnometer) and Poisson\u2019s ratio (0.3) [2]. The samples were fabricated as 8 mm cubes, with the parallel surfaces ground to ensure sufficient contact, and measurements were taken four times per sample for two samples. Thermal expansion analysis was conducted on a PerkinElmer Diamond TMA; the CTE measurements were taken on the same 8 mm cubes from the ultrasonic measurements. Testing was conducted for both x\u2013y and z orientations, see Fig. 1, as per ASTM standard E831 using a heating rate of 5 K per min, with three cycles per sample. The sensitivity of the device is 0.02 lm. Power, exposure time and point distance are all controlling variables of laser energy, either per unit time or unit length. Plotting density against one of the three is nonsensical as it neglects the influence of the other two. As such, LP, ET and PD have been dimensionally reduced into a single parameter of 1D line energy density. This is an appropriate use of energy density since layer thickness and hatch spacing are fixed; thus, any variation in density is purely a consequence of the absorbed energy" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002587_9783527684984-Figure7.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002587_9783527684984-Figure7.7-1.png", + "caption": "Figure 7.7 shows three commonly used types of impellers or stirrers.The six-flat blade turbine, often called the Rushton turbine (Figure 7.7a), is widely used. The standard dimensions of this type of stirrer relative to the tank size are as follows:", + "texts": [ + " When liquid mixing with this type of impeller is accompanied by aeration (gassing), the gas is supplied at the tank bottom through a single nozzle or via a circular sparging ring (which is a perforated circular tube). Gas from the sparger should rise within the radius of the impeller, so that it can be dispersed by the rotating impeller into bubbles that are usually several millimeters in diameter. The dispersion of gas into bubbles is in fact due to the high liquid shear rates produced by the rotating impeller. Naturally, the patterns of liquid movements will vary with the type of impeller used. When marine propeller-type impellers (which often have two or three blades; see Figure 7.7c) are used, the liquid in the central part moves upwards along the tank axis and then downwards along the tank wall. Hence, this type of 7.4 Mechanically Stirred Tanks 113 impeller is categorized as an axial flow impeller. This type of stirrer is suitable for suspending particles in a liquid, or for mixing highly viscous liquids. The power required to operate a stirred tank is mostly the mechanical power required to rotate the stirrer. Naturally, the stirring power varies with the stirrer type. In general, the power requirement will increase in line with the size and/or rotating speed, and will also vary according to the properties of the liquid", + " Live steam is often used to sterilize the inside surfaces of the fermentor, pipings, fittings, and valves. Instrumentation for measuring and controlling the temperature, pressure, flow rates, and fluid compositions, including oxygen partial pressure, is necessary for fermentor operation. (Details of instrumentation and control for fermentation are provided in Chapter 13.) 12.2 Some fermentation broths are highly viscous, and many are non-Newtonian liquids that follow Equation 2.6. For liquids with viscosities up to approximately 50 Pa s, impellers (Figure 7.7a\u2013c) can be used, but for more viscous liquids special types of impeller, such as the helical ribbon-type and anchor-type, are often used. When estimating the stirrer power requirements for non-Newtonian liquids, correlations of the power number versus the Reynolds number (Re; see Figure 7.8) for Newtonian liquids are very useful. In fact, Figure 7.8 for Newtonian liquids can be used at least for the laminar range, if appropriate values of the apparent viscosity \ud835\udf07a are used in calculating the Reynolds number" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002850_j.matdes.2019.107630-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002850_j.matdes.2019.107630-Figure1-1.png", + "caption": "Fig. 1. (a) Schematic of WAAM utilizing gas metal arc welding. (b) An example of WAAM produced turbine blades and resulting build times.", + "texts": [ + " A second goal of the study was to ascertain if as-built DED 304L overall fatigue behavior could replicate that of conventional 304L. Such findings could greatly motivate the use of these processes and materials in engineering applications without the need for costly and time-consuming post processing treatments. Metastable 304L single bead walls were prepared using gas metal arc welding (GMAW) on an AISI 304L baseplate. A non-proprietary open source WAAM machine with in-process monitoring was utilized (Fig. 1a) [20]. The processing steps involved arc melting of metal wire in a linear fashion to form a single layer, followed by a short pause until the part cooled down to 200 \u00b0C. The process was repeated again until wall geometries approximately 10 cm wide were completed. A shielding gas of 90%He, 7.5%Ar, and 2.5% CO2was utilized. Optical Emission Spectroscopy (OES) composition analysis indicated the following for the as-built walls: 0.02% C, 19.74% Cr, 1.68% Mn, 9.36% Ni, 0.029% P, 0.018% S, 0.76% Si, 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure14.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure14.4-1.png", + "caption": "Fig. 14.4 Infinitesimal screws of a kinematically equivalent Delta robot", + "texts": [ + " None of the contributions cited in this paragraph considers combining Eqs. (14.2) and (14.5) as an approach to the displacement analysis of the Delta robot. Of course, such a combination can be implemented in the robot developed by Pierrot et al. (2009). In this section the velocity and acceleration analyses of the robot at hand are addressed by screw theory. It is important to note here that the Delta robot is kinematically equivalent to the 3-RUU translational parallel manipulator if the orientations of the universal joints (\"U\") are properly established (see Fig. 14.4). To avoid handling Jacobian matrices with deficient ranks, pseudo-kinematic pairs are introduced in the analysis of the mechanism; for instance, the Delta robot is modeled as a 3-R*RUU translational parallel manipulator, where R* denotes an imaginary revolute joint. With these assumptions in mind, the model of the screws is depicted in Fig. 14.4. The Pl\u00fccker coordinates of the screws contained in the ith complex limb are computed under the following considerations: (1) 0$1 i denotes the screw associated to the virtual revolute joint R*; (2) 1$2 i is the screw associated to the active revolute joint; (3) 2$3 i and 3$4 i are the screws representing the universal joint connecting the arm to the forearm whose primal parts intersect at point Bi. Meanwhile, the universal joint connecting the forearm to the moving platform is simulated by the screws 4$5 i and 5$6 i , whose primal parts intersect at point Ci" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001448_j.cja.2013.06.004-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001448_j.cja.2013.06.004-Figure2-1.png", + "caption": "Fig. 2 Folding-wing morphing aircraft.", + "texts": [ + ", hr}, that is, h 2 H :\u00bc Xr i\u00bc1 aihi : ai P 0; Xr i\u00bc1 ai \u00bc 1 ( ) \u00f09\u00de Then the LPV controller\u2019s state-space matrices are given by AK\u00f0h\u00f0t\u00de\u00de BK\u00f0h\u00f0t\u00de\u00de CK\u00f0h\u00f0t\u00de\u00de DK\u00f0h\u00f0t\u00de\u00de :\u00bc Xr i\u00bc1 ai\u00f0t\u00de AKi BKi CKi DKi \u00f010\u00de where AKi, BKi, CKi, DKi can be obtained off-line, and AK(h(t)), BK(h(t)), CK(h(t)), DK(h(t)) will update dependently on the parameter h(t) in real time. 3. Longitudinal LPV model in wing shape varying for foldingwing morphing aircraft In this article a folding-wing morphing aircraft which has a tailless flying wing configuration is studied (shown in Fig. 2). The wings include inner wings and outer wings, which can be folded by smart actuators to change their shape. In the wing transition process, the inner wings rotate and the outer wings keep level. When the wing shape is changing, the dynamic response of the morphing aircraft will be dependent on time-varying aerodynamic forces and moments, which are both functions of the wing shape. In Ref. 16 the folding-wing morphing aircraft is regarded as a variable geometry rigid body, and a six-DOF nonlinear dynamic model in the wing folding process is founded" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure12.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure12.9-1.png", + "caption": "FIGURE 12.9. Illustration of position vectors and force system on link (i).", + "texts": [ + " Calculating the required actuators' force to hold a robot in a specific configuration is called robot statics. In a static condition, the globally expressed Newton-Euler equations for the link (i) can be written in a recursive form where \u00b0F i - L \u00b0Fe i \u00b0Mi - L \u00b0Me i + i_Pdi X \u00b0Fi (12.266) (12.267) (12.268) Therefore, we are able to calculate the action force system (F i - 1 , Mi-d when the reaction force system (-Fi , -Mi ) is given. The position vectors and force systems on link (i) are shown in Figure 12.9. Proof. In a static condition, the Newton-Euler equations of motion (12.26) and (12.27) for the link (i) reduce to force and moment balance equations = 0 (12.269) O. (12.270) 12. Robot Dynamics 545 These equations can be rearranged into a backward recursive form \u00b0F i - I: \u00b0F e i \u00b0Mi - I: \u00b0Me i - \u00b0ni x \u00b0F i _ 1 + \"m, x \u00b0Fi. (12.271) (12.272) However, we may transform the Euler equation from C, to Oi-1 and find the Equation (12.267) . Practically, we measure the position of mass center r, and the relative position of B, and B i - 1 in the coordinate frame B, attached to the link (i)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000737_00368791111101830-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000737_00368791111101830-Figure15-1.png", + "caption": "Figure 15 Geometry of standard C-type gears and low-loss gears", + "texts": [ + " For same nominal load capacity calculated according to DIN 3990, a wider face width is required for low-loss gears compared to the standard gear design. It has to be mentioned that load capacity calculation according to DIN 3990 is no longer valid due to values of pressure angle and profile contact ratio out of the defined parameter field of validity. In an ongoing project, the load-carrying capacity of low-loss gears is investigated and calculation methods will be adjusted. C-typegearsand low-lossgearsweremanufactured(Figure15) and tested with respect to total gearbox power loss savings at different operating conditions. Wimmer et al. (2005) found for low-loss gears with minimum sliding speeds compared to standard gears, a reduction of total gearbox power loss between some 75 per cent at low speed of v \u00bc 0.5m/s and some 35 per cent at high speed of v \u00bc 20m/s (Figure 16) with a mean potential of some 50 per cent power loss savings. Besides the required wider gear face width for adequate load capacity, it has also to be considered that higher bearing forces may occur depending on the designed helix angle and the larger pressure angle compared to standard gears" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003881_s00170-019-03996-5-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003881_s00170-019-03996-5-Figure4-1.png", + "caption": "Fig. 4 As-built characterization internal average roughness. a\u2013d The diagram of the internal surface. e The result of the measurement", + "texts": [ + " In fact, because those surfaces were altered, they were not included in the DOE results, but their values have been recorded after each post-processing procedure to provide additional information on the different processes. Figure 3b also shows that the roughness standard variation between the two samples under investigation was small. Only the right surface had a 2-\u03bcm difference in this case. For the internal AB characterization, the two samples were cut open using a hacksaw to be able to reach the investigated features. The position of the measurement of the internal surfaces is shown in Fig. 4a\u2013d. The result of the measurement is shown in Fig. 4e. It is found that the internal surfaces possess a significantly higher roughness compared with the external surfaces. The reason was that most of the internal features were not supported during the printing process which results in a higher roughness. An interesting fact in this characterization is that when each surface is compared one by one, the deviation between the results is quite high. Furthermore, if the grand average of both samples is compared, the deviation is low. Therefore, a high number of measurements are done in this work to minimize the impact of each surface on the final Ra improvement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000665_800905-FigureA-3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000665_800905-FigureA-3-1.png", + "caption": "Fig. A-3 - One spring from a four-spring suspension with torque rods (see Fig. 5)", + "texts": [], + "surrounding_texts": [ + "8 0 0 9 0 5 9\nand (b) the effective spring rate decreases if either the amplitude of stroking is increased or the nominal static load is descreased. Since truck leaf springs are complicated nonlinear devices, involving hysteretic damp ing, their representation in detailed analyses of vehicle dynamics studies of ride, braking, or handling is not easily accomplished using linear approximations or simplified models. Accordingly, a mathematical method for repre senting the force-deflection properties of truck leaf springs has been presented and discussed herein.\nREFERENCES 1. R.W. Murphy, J.E. Bernard, and C.B. Winkler, \"A Computer-Based Mathematical Method for Predicting the Braking Performance of Trucks and Tractor-Trailers.\" Phase I Report:\nMotor Truck Braking and Handling Performance Study, Highway Safety Research Institute, University of Michigan, Ann Arbor, September 15, 1972. 2. P.S. Fancher, Jr., \"Pitching and Bouncing Dynamics Excited During Antilock Braking of a Heavy Truck.\" Proceedings, 5th VSD-2nd IUTAM Symposium, Vienna, Austria, September 19-23, 1977, pp. 203-221.\n3. C.C. MacAdam, \"Computer Simulation and Parameter Sensitivity Study of a Commercial Vehicle During Antiskid Braking.\" 6th VSD3rd IUTAM Symposium, Berlin, Germany, September 1979. APPENDIX A\nFigures A-l through A-4 plus Figure 8 illustrate the overall force versus deflection characteristics of the leaf springs examined in this research investigation.\n1000 lbs\nDEFLECTION-\nFig. A-l - Tapered-leaf front spring", + "10 800905", + "8 0 0 9 0 5\nAPPENDIX B The figures in this appendix ( B - l through B-5) provide comparisons between test results obtained at 0.5 and 6.0 Hz. Four sets of data (at two amplitudes of deflection and two nominal loads) are presented for each of the springs\ntested. Although the data measured at 6.0 Hz contain high frequency fluctuations, examina tion of the data presented in this appendix indicates that the force-deflection charac teristics measured at 6.0 Hz are practically the same as the results obtained at 0.5 Hz." + ] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure9-1.png", + "caption": "Fig. 9. Flux density distributions. (a) SPM. (b) CPM1-1. (c) CPM1-2. (d) CPM2. (e) CPM3. (f) HPM1. (g) HPM2.", + "texts": [ + " This is due to that the tangential PMs can improve the working airgap flux density. From the above, the rotor parameters of all these machines can be determined and listed in TABLE II. IV. ANALYSIS AND COMPARISON OF PERFORMANCES In the previous section, the rotor parameters of conventional and proposed machines are optimized by FE analysis when the stator parameters and copper loss are constant. In this section, the electromagnetic performances of the proposed machines (CPM2, CPM3, HPM1 and HPM2) are investigated and compared to the SPM and CPM1 machine. Fig. 9 shows the 2D FE predicted open-circuit flux density distributions in the 9-slot/10-pole machines with the conventional and proposed rotors, whilst Figs. 10 (a) and (b) show their open-circuit airgap flux density and corresponding harmonic contents. It can be seen that the working airgap flux density (5th) is the main harmonic content for all these machines. For the conventional SPM machine, there are only 5ith (i=odd) harmonics when the slot effects is neglected. 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission", + " However, the SPM machine has the largest output torque (power) in these machines, and therefore has the largest efficiency. Distinctly, the CPM2 and CPM3 have the largest stator core loss in all the machines due to the saturation of the stator core, which results from the subharmonic of the airgap flux density, as shown in Figs. 9 (d) and (e). The rotor core loss is much lower than the stator core loss for all the machines, and this is due to that the flux density of rotor changes little over time. From Fig. 9 (f), it can be seen that the saturation in the stator yoke of the HPM1 still occurs. Therefore, the stator core loss of the HPM1 is larger than that of the CPM1-1, CPM1-2 and HPM2. In addition, the HPM2 has the slightly larger total iron loss than the CPM1-1 and CPM1-2 machine. However, the iron loss of the conventional CPM and proposed HPM machines are much smaller than the copper loss due to the low speed, i.e., 1500 rpm. Therefore, the proposed HPM machines (HPM1 and HPM2) can exhibit similar efficiency to the conventional CPM machines (CPM1-1 and CPM1-2)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure2.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure2.10-1.png", + "caption": "Figure 2.10.2 Use of four ride-height sensors for logger evaluation of road camber angles (rear view).", + "texts": [ + " Possibly also useful, the spatial rate of change of path radius is dR ds \u00bc d ds 1 kP 0 @ 1 A \u00bc dkP ds d dkP 1 kP 0 @ 1 A Hence dR ds \u00bc tP k2P \u00bc tPR2 \u00f02:9:7\u00de Also dR dt \u00bc dR ds ds dt \u00bc tPR2V \u00f02:9:8\u00de 58 Suspension Geometry and Computation and d dt 1 R \u00bc dkP dt \u00bc tPV \u00bc _R R2 \u00f02:9:9\u00de d ds 1 R \u00bc dkP ds \u00bc tP \u00f02:9:10\u00de Associated with the path turn-in tP (units m 2), tP \u00bc dkP ds we may define a car turn-in tC for a given velocity V: tC \u00bc dkP dt \u00bc dkP ds ds dt \u00bc tPV \u00f02:9:11\u00de This has units m 1 s 1. The subscript C for car rather than V for vehicle is used because V is used elsewhere as a subscript for vertical. Figure 2.10.1 shows the general casewhere the effective road bank angle isfR,measured between the tyre contact points. Note that for a road with non-straight (curved or piecewise linear) cross-section, the road bank angle must be defined by the line joining the centres of the contact patches. Because the road crosssection is not straight, the road anglesmeasured from thefR position \u2013 the road camber angles, at the tyres, left and right \u2013 are gRL and gRR, defined positive as illustrated. These angles give corresponding changes of the tyre camber angles, influencing the tyre camber forces. The road bank angles at the tyre positions are then fRL \u00bc fR gRL fRR \u00bc fR \u00fe gRR Figure 2.10.1 Road bank and camber geometry (track cross-sectional shape). Road Geometry 59 To analyse this in a simulation, the data set for the road needs, in principle, four extra data items for each point of the path, these being the road camber angles, one for each of the four tyres. It would normally be acceptable to use only two road camber angles on the basis that the front and rear tracks are nearly the same. The road camber angles, as defined in Figure 2.10.1, cannot be deduced directly from normal logger data, but are easily obtained with a special set-up. The equipment required is a set of four body ride-height meters, for example lasers, placed along a transverse line (perpendicular to the centreline), as in Figure 2.10.2. For best results, the spacing of the tyre-area sectional mid-points should equal the track (tread). This is assumed in the following analysis, but is not absolutely essential. The spacing width between sensors across the tyre area isw. The road bank anglefR is not known, and cannot be deduced here, but is not required. The fourmeasured ride-height values are z1, . . ., z4. Thevalues at the centre of the left and right tyres (at track spacing) are therefore zL \u00bc 1 2 \u00f0z1 \u00fe z2\u00de zR \u00bc 1 2 \u00f0z3 \u00fe z4\u00de The sensor reference line is rolled from the road mean bank line by fSen \u00bc arcsin zL zR T \u00bc arcsin z1 \u00fe z2 z3 z4 2T Relative to the sensor reference line, the two road angles are fRL \u00bc arcsin z2 z1 w fRR \u00bc arcsin z3 z4 w The actual road camber angles are therefore gRL \u00bc fRL \u00fe fSen gRR \u00bc fRR fSen Explicitly, gRL \u00bc arcsin z2 z1 w \u00fe arcsin zL zR T gRR \u00bc arcsin z3 z4 w arcsin zL zR T The road bank angle varies with longitudinal path position s, and hence the bank angles are different at the two axles, according to the local road torsion kfRS (rad/m), defined as kfRS \u00bc dfR ds The difference of road bank angles between the two axles depends on the road torsion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001238_ja1095254-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001238_ja1095254-Figure6-1.png", + "caption": "Figure 6. Schematic drawing of the director field orientation in diskand fiber-like LCE particles. In the disks (a), the mesogens are aligned in concentric rings around the particle. These rings become smaller and smaller inside the particle, ending in a defect axis in the middle. The fibers (b) have a bipolar orientation with all mesogens aligned parallel to the fiber\u2019s long axis. This defect-free configuration leads to the drastic shape changes observed in these samples.", + "texts": [ + " From the maxima in the diffuse wide angle reflection, we concluded that both the disks and the fibers possess a regular orientation. However, the patterns also prove that the director field orientation of the two samples is completely different. For disk-like particles, the director is oriented in the plane of the disk, which is perpendicular to the symmetry axis (short axis of the 5309 dx.doi.org/10.1021/ja1095254 |J. Am. Chem. Soc. 2011, 133, 5305\u20135311 disk). For the fibers, the director is oriented parallel to the symmetry axis (=fiber axis). In more detail, for disks, the mesogens are aligned in concentric rings (Figure 6a). These rings become smaller inside the particle and end in a disclination axis. When scattering is performed on such a particle from the side (Figure 5a), regions with the director perpendicular to the X-ray beam (central regions) and parallel to it (side regions of the oblate object) are seen simultaneously. This leads to the superposition of an X-ray pattern with clear maxima (X-rays perpendicular to the director) and a pattern with a uniform scattering intensity (X-rays parallel to the director), and such a pattern is shown in Figure 5a. If the X-rays hit the particle from the top, the director is perpendicular to the beam, but it takes all possible orientations in the plane of the disk. This results in an equal intensity distribution over all angles \u03c7 (see Figure 5b). For the fibers, the situation is less complex. The director is aligned parallel to the fiber\u2019s axis in a bipolar arrangement (sketched in Figure 6b). This orientation leads to a selective scattering at the meridian as it was previously reported in the literature for oriented films and thicker fibers.18,38 As the LC-polymer used for this investigation is known to shrink parallel to the director during isotropization10,19 (and Figure 1ii), this difference in orientation perfectly explains the difference in shape change. The fibers contract along the fiber axis, which is parallel to the director, and the disks expand parallel to their short axis, because they shrink in the plane of the disk (along the director), and so they have to expand perpendicularly to keep a constant density" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000068_s0898-8838(08)60043-4-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000068_s0898-8838(08)60043-4-Figure9-1.png", + "caption": "FIG. 9. Direct electrochemistry of p-cresol methylhydroxylase. (a) Response at an edge-plane graphite electrode in 10 mM KCl/10 mM HEPES (pH 7.4) buffer containing 10 mM spermine. Scan rate: 5 mV sec-l. (b) Response upon addition of enzyme to -30 FM. (c) A repeat of (b) a t reduced sensitivity. (d) Catalytic response upon addition of p-cresol (3 mM) to solution.", + "texts": [ + " It is an a2p2 tetramer, with one subunit containing a covalently bound FAD and the other containing a c-type heme group. It has been shown (57) recently that direct electron transfer between PCMH and an edge-plane graphite electrode is achieved in the presence of a range of electroinactive cationic species (promoters). The results are listed in Table I, with the structures of the promoters depicted in Fig. 8. In the absence of the substrate, p-cresol, a quasireversible cyclic voltammogram ascribed to the electrode reaction of the heme group in the intact enzyme is observed (Fig. 9a and b). In the presence of the substrate, the electrochemical response is greatly enhanced by the catalytic reaction between the enzyme and the substrate (Fig. 9c and d). The electrocatalytic currents arise not from mediated reaction via the cleaved cytochrome subunit, but from direct electron exchange between the electrode and the enzyme. One envisages interactions leading to the formation of an enzyme-promoter-electrode assembly. The adsorption of PCMH onto an edge-plane graphite electrode in the presence of a promoter obeys (58) the Langmuir isotherm. The nature of this interaction is more likely to be physical, as the estimated standard free energy of adsorption is relatively small" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.5-1.png", + "caption": "Fig. 6.5 Model of an overhead crane for calculating the dynamic loads when lifting and lowering the load; 1 Motor, 2 Cable drum, 3 Trolley, 4 Crane girder", + "texts": [ + " There are algorithms for auto- 372 6 Linear Oscillators with Multiple Degrees of Freedom matic bandwidth minimization of matrices that one can use in the case of arbitrary initial coordinate numbering (and the resulting high bandwidth). For the example in Table 6.2, Case 1, calculate the elements m23 and m24 of M. Establish the system matrices of the vehicle model that is given in Table 6.2, Case 1, using the substructure matrices specified in Table 6.3. Calculate the elements of the mass matrix M and the stiffness matrix C for the coordinate vector qT = [x1, x2, r\u03d5M/i] for the calculation model of an overhead crane (Fig. 6.5). Check if the stiffness matrix is singular and give a physical interpretation. Reduced moment of inertia of the hoist JM Reduced mass of the crane m1 (referred to the position of the trolley) Mass of the hoisted load m2, gear ratio i, spring constant of the crane girder c1 (referred to the position of the trolley), axial spring constant of the cable c2, cable drum radius r Note: Introducing the parameter r\u03d5M/i as a generalized coordinate q3 has the advantage that all components of the vector q (and thus the elements of C and M) are equal in dimension", + "149) yields the frequencies fH = 20.51 Hz and fN = 36.26 Hz, a good approximation of f3 and f4. The first two mode shapes are mainly determined by the frame deformations. The vertical oscillation approximately corresponds to the 3rd mode shape. Since the support structure became stiffer and lost mass due to the simplification, the estimated frequency is fH > f3. 6.3 Free Undamped Vibrations 395 State the equations of motion and initial conditions for the following loading cases of the overhead crane shown in Fig. 6.5: a)Load m2 falls with the initial velocity u into the cable of the resting crane (gripper drops into the holding cables) b)Load drops suddenly (breakage of the load handling device) c)Sudden motor shutdown during lifting (uh = const., crane at rest) d)Load m2 is suddenly caught by a rigid obstacle during lifting. What are the equations for calculating the cable force and the bending moment in the center of the crane girder? Note: The coordinate origin of x1 is the static equilibrium position of the unloaded crane, that of x2 is the end of the unloaded cable" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure7-1.png", + "caption": "Figure 7. FE model of the gear pair. (a) FE model and boundary conditions and (b) position of engagement.", + "texts": [ + "2 Assuming that the deformations of the pinion and gear teeth are pi and gi, respectively, the mesh stiffness can be given as follows km \u00bc Xn i\u00bc1 Fij= pi \u00fe gi \u00f06\u00de where n is the number of teeth and Fij is the meshing contact force. In order to determine the mesh stiffness, the FE method is adopted in this study and the geometric parameters of the helical gear drive employed in Huang et al.3 are adopted. Furthermore, the FE model of the gear pair is established in the ANSYS software environment, as shown in Figure 7. It comprises 65,758 nodes and 54,660 elements. The DOFs of nodes on the inner diameter of the gearwheel are coupled to the node located at the centre of it, so does the pinion. A fixed displacement constraint was applied to the node located at the centre of the gearwheel. A torque was applied to the node located at the centre of the pinion, and all DOFs other than rotation around the axis of symmetry were fixed. Then, the distributed forces applied to the pinion, and the deformation of the pinion and gearwheel were obtained" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure5-1.png", + "caption": "Fig. 5. Simplified main PM magnetic circuit of HPM1 and HPM2. (a) Equivalent magnetic circuit. (b) Flux lines in slotless model.", + "texts": [ + " 3. It can be seen that the main PM flux does not pass the airgap above the iron-poles, and it is closed through the PMs with different polarity. These are confirmed by the FE predicted flux distributions of their slotless models in Fig.4 (b). Consequently, the airgap flux density of CPM2 and CPM3 have undesirable subharmonics, especially 1st, which will result in the saturation of the stator yoke in practical models, and the reduction of the working airgap flux density (5th) and output torque. Fig.5 (a) shows the main PM magnetic circuits of CPM2 and CPM3 with tangential PMs (i.e. HPM2 and HPM3). The tangential PMs represent large reluctances for the SPMs, and they can provide additional flux. Therefore, the main PM flux goes through the airgap above the iron-poles of HPM1 and HPM2, which are confirmed by FE analysis, as shown in Fig.5 (b). Consequently, the saturation of the stator back-iron in practical models can be reduced, and the working airgap flux density (5th) and output torque can be enhanced. Moreover, due to the reduction of the subharmonics, the torque ripples in HPM1 and HPM2 can be reduced. III. OPTIMIZATION OF ROTORS The Jmag software package is adopted to perform the transient analysis. The same sinusoidal current under id=0 control is supplied for the optimization of these rotors. The variations of average torque and torque ripple with PM- arc ratio p in the CPM1 are shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003605_j.jmatprotec.2020.116723-Figure21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003605_j.jmatprotec.2020.116723-Figure21-1.png", + "caption": "Fig. 21. The forces on the weld pool and the overflow phenomenon.", + "texts": [ + " Thus, the fluid flow was minimized in the borders and, consequently, the overflow was minimized since part of the molten pool flowed inward. The main forces that act on the molten metal during layer deposition are from gravity (G), welding arc (Fa), droplet impact (Fd), surface tension (\u03c3), buoyancy (Fb), viscous friction between the molten pool and the solid material (f) and normal reaction (N). By considering these as concentrated forces, a simplified force model is obtained and presented in Fig. 21. The resultant force (Fr), as demonstrated by Eq. 5, makes the molten pool flow to the sides. = + + \u2212 + + +Fr G Fa Fd \u03c3 Fb N f( ) (5) From this analysis, the overflow problem can be minimized by increasing the holding forces (\u03c3, Fb, N and f) and decreasing the forces which contribute to the weld pool collapse (G, Fa and Fd) during the layer deposition. Eqs. 6 (Meng et al., 2017), 7 (Han et al., 2013), 8 (Lin and Eagar, 1986) and 9 (Sahoo et al., 1988) can be used to calculate G, Fb, Fa and \u03c3, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003820_tits.2020.2987637-Figure23-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003820_tits.2020.2987637-Figure23-1.png", + "caption": "Fig. 23. Motor temperature distribution under rated conditions: (a) main view, (b) sectional view.", + "texts": [ + " The insulation grade of the motor design is class H, and the maximum allowable temperature is 180\u25e6, so that the motor is still within the safe operating range even if it works under 6 times overload in 10s. The temperature rise curves of each part in 10s are shown in Fig. 22. It can be seen that the temperature on the winding is much larger than that on other parts followed by the stator core and the rotor with the lowest temperature. Under the rated state, the simulation result of the steadystate temperature rise of the motor is shown in Fig. 23. Under the steady state condition, the highest temperature point is at the bottom of the slot, which is near the rotation axis. Because it is far from the outer surface of the rotor and difficult to dissipate heat, the temperature at the bottom of the stator slot is the highest, reaching a maximum of 119.1\u25e6, but this is still within the safe operating range of the motor. The transient thermal analysis of the fault winding is performed by FEM, and the temperature rise of the motor fault winding in 30 seconds under different fault resistances is observed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000311_tro.2008.2006870-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000311_tro.2008.2006870-Figure1-1.png", + "caption": "Fig. 1. Three kinds of rough terrain. (a) Uneven. (b) Even but inclined. (c) Uneven and inclined.", + "texts": [ + " To solve problems 1\u20133) for legged robots with redundant joints, we developed a practical contact force control framework based on passivity [7] that can effectively handle simultaneous multiple contact forces and unknown external forces. This paper presents our recent results utilizing a contact force control framework that focuses on adaptation to unknown rough terrain. In this paper, adaptation to rough terrain means adaptation to 1) local; 2) global changing of the ground surface; or 3) their combination (Fig. 1). This paper also discusses balancing on a low-friction surface with an unknown friction profile. For position-controlled legged robots, adaptation to 1) has been successfully achieved by mechanical (passive) compliance of the foot (e.g., [8]) and/or (active) compliance of the ankle joints (e.g., [9]). On the other hand, adaptation to 2) was achieved by a stabilizing controller with measured zero moment point (ZMP) [9], [10]. The method in this paper differs from past approaches because we simultaneously achieve both adaptations by full-body joint torque control without directly measuring the external forces (including ZMP) and the terrain information", + " The figure shows that the actual contact forces are tracking the desired ones. On the other hand, in this figure we can see larger tracking error in CoP compared to normal GRFs because in our current experiments, the actual CoP is roughly estimated only by the normal GRFs. This section explains the controller\u2019s adaptability to rough terrain including inclined surfaces or steps without measuring the contact forces or terrain shape. Recall again the rough terrain addressed in this paper: 1) local or 2) global changing of the ground surface, or 3) their combination (Fig. 1). In general, these cases occur in a time-varying manner. In this paper, since we do not use visual information or contact force measurement, we assume that the foot is always located above or on the ground before adaptation. 1) Local Terrain Adaptation: Let us start with a simple example: a rigid block laid on a step, as shown in Fig. 6, where x is the CoM position of the block measured from the right edge of the step. There are three equilibrium states in this system. If x < 0, the block can stay on the step [Fig", + " 6(d) is that \u2016rS 1 \u2212 rS 2\u2016 is allowed to change because there are no constraints between the feet. Assume active balancer (10) is applied to achieve x = 0. If the inclination is fixed, then the robot may achieve asymptotical stabilization: x \u2192 0. If the incline is dynamically changing, the robot compliantly changes its posture to adapt to the ground. However, in this case, it may be difficult to maintain x = 0 without a dynamic model of inclination. 3) Combination: Finally, let us discuss the combined case in Fig. 1(c). For example, we consider Fig. 8, where a robot model with flat feet is standing on ground, which is suddenly inclined. We suppose the active balancer (10) is always applied so that CoM is the origin (ORG), defined as the center of the feet. It immediately computes recovery GAF to pull the CoM back to its origin. At the same time, the orientation of each foot is automatically adapted to the inclination by the distributed contact forces, as shown in Fig. 6(d). Therefore, ground adaptation in this case is achieved by a combination of active (feedback) balancing control and our contact force distribution scheme" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.7-1.png", + "caption": "Fig. 2.7 Directional angles within the rigid body; a) Identification of a direction k (such as k = I, II, III); b) Identification of the position of a \u03bek-\u03b7k-\u03b6k system in the \u03be-\u03b7-\u03b6 system", + "texts": [ + "57) can be expressed using the moment of inertia JS kk with respect to the instantaneous axis of rotation labeled with index k. The following applies: JS kk\u03c92 = JS \u03be\u03be\u03c9 2 \u03be +JS \u03b7\u03b7\u03c92 \u03b7+JS \u03b6\u03b6\u03c9 2 \u03b6 +2(JS \u03be\u03b7\u03c9\u03be\u03c9\u03b7+JS \u03b7\u03b6\u03c9\u03b7\u03c9\u03b6 +JS \u03b6\u03be\u03c9\u03be\u03c9\u03b6). (2.58) Thus the kinetic energy is simply Wkin = 1 2 mv2 S + 1 2 JS kk\u03c92. (2.59) The moment of inertia JS kk refers to the direction of the instantaneous axis of rotation, see the application in Sect. 1.2.4. The direction of the instantaneous axis of rotation k can be described with respect to the directions of the body-fixed reference system using the angles \u03b1k, \u03b2k, and \u03b3k, see Fig. 2.7a. The components of angular velocity with respect to this direction are 2.3 Kinetics of the Rigid Body 83 \u03c9\u03be = \u03c9 cos \u03b1k; \u03c9\u03b7 = \u03c9 cos \u03b2k; \u03c9\u03b6 = \u03c9 cos \u03b3k. (2.60) The dependence of the moment of inertia JS kk on these angles can be determined from (2.58) and (2.60): JS kk = JS \u03be\u03be cos2 \u03b1k + JS \u03b7\u03b7 cos2 \u03b2k + JS \u03b6\u03b6 cos2 \u03b3k +2(JS \u03be\u03b7 cos \u03b1k cos \u03b2k + JS \u03b7\u03b6 cos \u03b2k cos \u03b3k + JS \u03b6\u03be cos \u03b3k cos \u03b1k). (2.61) The matrix of the moment of inertia tensor with respect to the center of gravity is defined in the body-fixed system by: J S = \u222b (\u0303l\u2212 l\u0303S)T(\u0303l\u2212 l\u0303S)dm", + "68) Thus the moments of inertia always have their smallest values with respect to axes of gravity because \u201cSteiner terms\u201d are added for other axes. The components of the moment of inertia tensor also change when switching to rotated body-fixed axes \u03be1-\u03b71-\u03b61. In analogy to (2.22), when it comes to the transformation between fixed and body-fixed directions, a transformation matrix can be used that is designated as A\u2217. The directional cosines in A\u2217 then refer to the nine angles, \u03b1\u03bek to \u03b3\u03b6k, that are defined as in Fig. 2.7b between the \u03be-\u03b7-\u03b6 system and the \u03bek-\u03b7k-\u03b6k system that has the same point O as its body-fixed origin. The moment of inertia tensor (here, exemplarily with respect to the center of gravity S \u2013 it applies in analogy to each body-fixed point) is transformed when rotating in the body-fixed reference system with the matrix A\u2217 = \u23a1\u23a3 cos \u03b1\u03bek cos \u03b2\u03bek cos \u03b3\u03bek cos \u03b1\u03b7k cos \u03b2\u03b7k cos \u03b3\u03b7k cos \u03b1\u03b6k cos \u03b2\u03b6k cos \u03b3\u03b6k \u23a4\u23a6 (2.69) by the following matrix multiplications: J S = A\u2217J\u2217SA\u2217T; J\u2217S = A\u2217TJ S A\u2217. (2.70) The matrix J S contains the components known from (2", + " The principal moments of inertia JS I , JS II and JS III are the three eigenvalues of the eigenvalue problem (J S \u2212 JSE)a = o, (2.71) which can be solved numerically using known software if parameter values are given. The three eigenvectors associated with the eigenvalues ak = [cos \u03b1k, cos \u03b2k, cos \u03b3k]T; k = I, II, III (2.72) 86 2 Dynamics of Rigid Machines contain, as elements, the directional cosines, which define the orientation of the principal axes with spatial angles \u03b1k, \u03b2k and \u03b3k relative to the original \u03be-\u03b7-\u03b6 system, see also Fig. 2.7a. They are normalized in such a way that (aI) TaI = (aII) TaII = (aIII) TaIII = 1; (aI) TaII = (aII) TaIII = (aIII) TaI = 0 (2.73) and det(aI, aII, aIII) = 1. The transformation matrix A\u2217 H = [aI, aII, aIII] (2.74) is formed from these three eigenvectors, so that the moment of inertia tensor for the central principal axes can be expressed as follows: J\u0302 S = A\u2217T H J S A\u2217 H = \u23a1\u23a3JS I 0 0 0 JS II 0 0 0 JS III \u23a4\u23a6 . (2.75) The deviation moments with respect to the principal axes are zero. Symmetry axes of a homogeneous rigid body are principal axes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002914_rnc.4038-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002914_rnc.4038-Figure1-1.png", + "caption": "FIGURE 1 Reference coordinate frames", + "texts": [ + " The superscripts T and \u22121 represent the matrix transposition and matrix inverse, respectively. | \u00b7 | denotes the absolute value, and || \u00b7 || represents the Euclidean norm of a vector or a matrix. For any constant \ud835\udefe , the function x \u2192 \u2308x\u230b\ud835\udefe is defined as \u2308x\u230b\ud835\udefe = |x|\ud835\udefesign(x) for any x \u2208 R, where sign(\u00b7) is the standard signum function. Based on the definition, we have d\u2308x\u230b\ud835\udefe dx = \ud835\udefe|x|\ud835\udefe\u22121, \u2308x\u230b = x, and x\u2308x\u230b = |x|2. To formulate the relative motion model between the chaser and the target spacecraft clearly, the drawing of the relative motion and several frames are presented in Figure 1. Let Fi be the the Earth center internal frame. The body-fixed frame of the chaser is denoted by Fb, whose origin is located in the center mass with 3 basic axes pointing along the principal axes of inertia. Assume that only the gravity is effected on the noncooperative target, the relative translational motion model of 2 spacecraft described in frame Fi is presented as31 d2re dt2 = \u2212\ud835\udf07 ( rt||rt||3 \u2212 r\ud835\udc5d||r\ud835\udc5d||3 ) \u2212 F m \u2212 \ud835\udc53d m , (1) where re = rt \u2212 rp is the relative position vector from the chaser spacecraft to the target spacecraft, where rp and rt are the position vectors of the chaser and the target spacecraft, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001076_j.wear.2013.11.016-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001076_j.wear.2013.11.016-Figure1-1.png", + "caption": "Fig. 1. Mechanics of gear tooth contact [20], (a) beginning of contact, (b) contact on pitch point and (c) end of contact.", + "texts": [ + " Archard's wear equation; V s \u00bc K W H \u00f01\u00de where V is the volume of worn material, s is the sliding distance between contacting surfaces, K is the dimensionless wear coefficient, W is the applied load and H is the surface hardness of worn material. It is necessary to take into account the differential sliding and rolling motions from the beginning to the end of meshing tooth contact to use this equation in gears. At the beginning of tooth contact, tooth root of driven gear (pinion) contacts with the tooth tip of the driving (internal gear) gear Fig. 1(a). During contact, this region is under the effect of sliding and rolling action. Sliding velocity changes continuously to the pitch of the circle. Sliding velocity is zero on the pitch circle because it is equal with opposite direction for the pinion and internal gear Fig. 1(b). In this region, tooth couples make only rolling motion. At the end of contact, sliding is between the tooth tip of pinion and tooth root of internal gear Fig. 1(c). It is more appropriate to investigate wear on local points rather than during contact because the effect of sliding and rolling are different on interacting surfaces. If wear is described to any point \u2018p\u2019 from meshing surfaces, Archard's wear equation can be written as follows; hp \u00bc Z s 0 kPds \u00f02\u00de where h is the wear depth of point \u2018p\u2019, k is the dimensional wear coefficient and P is the local contact pressure. According to Andersson, if single point observation method [16] is applied to meshing gears, in other words, if it is required to express wear of any point where the tooth profiles of pinion-internal gear couple are meshing with each other during meshing depending on running interval, the wear model can be written as follows; hp;\u00f0n\u00de \u00bc hp;\u00f0n 1\u00de \u00fekPp;\u00f0n 1\u00desp \u00f03\u00de where hp, (n) is the wear depth at point \u2018p\u2019 on the flank after n running interval, hp, (n 1) is the wear depth at the same point but one running interval before, Pp, (n 1) is the pressure on point \u2018p\u2019 and sp is the sliding distance of point \u2018p\u2019" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure3.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure3.2-1.png", + "caption": "Fig. 3.2 Diagram of an induction motor.", + "texts": [ + " wave rotates at the same speed as the poles, it can be resolved into two components, one along each axis. The corresponding components of the flux wave can then be found as explained on p. 15. Hence the salient-pole synchronous machine requires a two-axis theory. The usual theory of the uniform air-gap synchronous machine and of the induction motor does not depend on resolving the flux into the axis components and is thus a true rotating field theory. However, they can also be studied as a special case of the two-axis theory. Fig. 3.2 is a diagram of an idealized two-pole induction motor having phase coils AI, Bl ,Cion the stator and A2, B2 , C2 on the rotor (for clearness only coil A2 is shown in the diagram). The induction motor has no obvious axis of symmetry since both members are cylindrical. In Fig. 3.2 the position of the quadrature axis has been chosen arbitrarily to coincide with the axis of the stationary coil AI. The phase sequence is Al -CI -BI. The Steady-State Phasor Diagrams of A.C. Machines 45 Coil A2 rotates with the rotor at the constant speed woO - s), where Wo is the synchronous speed and s is the slip. During steady operation the m.m.f. and flux waves due to the balanced polyphase currents in each winding rotate relative to the stator at synchronous speed w 0 and combine to form the resultant air-gap m.m.f. and flux waves. The instant at which the resultant m.m.f. wave, represented by the space phasor F, is on the direct axis (drawn horizontally), is indicated on Fig. 3.2. At the same instant, the component m.m.f.s due to the primary and secondary currents respectively are represented by the space phasors Fl and F2 at angles (- 1) and (1800 - 2) to the vertical. Since the three phasors move round together at speed w 0, they can be related by a stationary phasor diagram (Fig. 3.3a). If core losses are neglected, the resultant flux wave due to F also has its axis on the direct axis, and consequently the internal voltage, opposing that induced in the primary phase AI, has its maximum value at the instant considered", + "3c the phasor sUj, like Uj in Fig. 3.3b, represents the voltage opposing the induced voltage. If the secondary winding carried polyphase currents such that the current in phase A2 was in phase with the secondary induced voltage, the secondary currents would set up an m.m.f. on the quadrature axis at the instant when the flux is along the direct axis. This relation holds whatever the actual position of the secondary winding may be at that instant. Since, for the operating condition indicated in Fig. 3.2, F2 is displaced from the quadrature axis by the angle (1T - cJ>2), it follows that the secondary current phasor h is displaced by (1T - cJ>2) from sUj , as shown in the time phasor diagram of Fig. 3.3c. In the secondary voltage phasor diagram (Fig. 3.3c), the sum of sUi> the resistance drop R2h, and the leakage reactance drop jsX 21 2, is zero, since the secondary winding is short-circuited. The theory of the induction motor is thus based on three separate phasor diagrams. When a per-unit system is used, the primary and secondary m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure7.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure7.2-1.png", + "caption": "Figure 7.2.2 Suspension bump causes wheel camber angle change (rear view).", + "texts": [ + " There can be camber angles relative to the vehicle body, corresponding to d, and camber angles relative to the road surface, corresponding to a. The body roll angle f then corresponds to the attitude angle b. A distinctionmust also bemade between the inclination angle and the camber angle. For a givenwheel, these have the same magnitude but with a different sign convention. Inclination is positive for right-hand rotation about the forward longitudinal axis, which is clockwise in rear view. Camber is positive with the top of the wheel outward from the vehicle centreline, Figure 7.2.1. Here, the wheel inclination angle will be represented by G (Greek capital gamma), whereas the wheel camber angle will be denoted by g (Greek lower case gamma). The basic relationship between the inclination and camber angles for the two sides of the vehicle is therefore simply that on the right-hand side they are the same, but on the left-hand side there is a change Suspension Geometry and Computation J. C. Dixon \u00a9 2009 John Wiley & Sons, Ltd. ISBN: 978-0-470-51021-6 of sign: There is a small static camber setting on a wheel, denoted g0. On a passenger car this is chosen to minimise wear. On a racing car it is almost invariably negative. The wheel camber relative to the body changes as the suspension moves in bump, Figure 7.2.2. The bump camber angle of a single wheel, gBC, is the increase of camber angle, compared with the static value, due to suspension bump deflection zS. For a linear model, the total camber angle at a given suspension bump is g \u00bc g0 \u00fe gBC \u00f07:2:2\u00de Linearly, the bump camber angle is gBC \u00bc \u00abBC1zS \u00f07:2:3\u00de 144 Suspension Geometry and Computation where the linear bump camber coefficient \u00abBC1 depends on the suspension geometry, and would be positive for positive-going camber on a rising wheel. The basic units of the bump camber coefficient are rad/m, although commonly expressed as deg/dm (deg/inch in the USA)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002504_s00170-014-6057-3-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002504_s00170-014-6057-3-Figure3-1.png", + "caption": "Fig. 3 Spiral strategy. a Representation of the strategy over the real blade. b Representation of the strategy over the tested part. c Representation of the spiral strategy pattern. d Complete test part", + "texts": [ + " However, as discussed below, the results of these preliminary tests have not been satisfactory, since the behavior of the machine axes presents nonuniform feed rates resulting in nonhomogeneous material deposition and defects on the final part. Thus, the following section describes the steps of path generation and parameter optimization performance. 3.1 Laser path generation and optimum trajectory considerations The designed test part is a blade section of a blisk which is a typical aerospace part where laser cladding can be applied. Each blade is built by several layers, whose geometry is based on the previously deposited layers. As seen in Fig. 3, in relation to the laser path pattern, a spiral strategy has been selected for each layer. The performance of this strategy does not require the laser to switch on and off during the deposition process except for the initial and final steps. Besides, the strategy presents high continuity, and no intermediate spaces between paths are left so that the laser does not need to go twice trough the same point. Finally, the distance between tracks is programmed as a function of the laser spot diameter to be able to fill in the whole blade thickness" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002809_tmag.2015.2493150-Figure14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002809_tmag.2015.2493150-Figure14-1.png", + "caption": "Fig. 14. The FPM model", + "texts": [ + " In this paper, the balanced sinusoidal three phase currents with RMS value 4 (A) are injected into the stator windings of the analyzed PMSM. Under this condition, the influence of magnetic saturation and electric loading is investigated on the on-load PM and armature field components, the on-load PM Back-EMF, and the on-load torque components. Fig. 13 shows a simulation flowchart. The Frozen Permeability Method (FPM) acts based on FEM. The FPM algorithm used in this paper is as follows: The magnetic saturation is ignored in the rotor yoke (for SPM motor). The stator core is divided into 72 elements, as shown in Fig. 14. The PM and armature excitations are applied simultaneously. The average value of the magnetic flux density is calculated for all elements of the stator core in one complete time cycle (20 ms). 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. > FOR CONFERENCE-RELATED PAPERS, REPLACE THIS LINE WITH YOUR SESSION NUMBER, E.G., AB-02 (DOUBLE-CLICK HERE) < 7 The average value of the magnetic field intensity is calculated for all elements of the stator core in one complete time cycle (20 ms) by using the BH curve" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000769_physrevlett.109.138102-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000769_physrevlett.109.138102-Figure1-1.png", + "caption": "FIG. 1 (color online). (a) Simplified flagellar beat of Chlamydomonas showing flagellar shapes at equidistant times representing a full beat cycle (T 15 ms), adapted from [34]. The flagellar bending waves are approximately planar and mirror-symmetric. Each point on a flagellum moves on a periodic orbit with respect to a material frame of the cell body. (b) The idealized model swimmer consists of three equal spheres connected by a frictionless scaffold. The first and second sphere (located at r1 and r2) can move along a circular trajectory as indicated, being driven by internally generated active torques. (The arrows correspond to the case !0 > 0).", + "texts": [ + " Mechanical interactions are thought to underlie the coordinated beating of several flagella as observed in pairs of sperm cells [3] or in ciliary arrays, where hundreds of short flagella beat in synchrony as metachronal waves [4]. Recently, the biflagellate green alga Chlamydomonas has emerged as an experimental model system for flagellar synchronization [5\u20137]. A Chlamydomonas cell swims forward by the approximately planar and mirror-symmetric bending waves of its two flagella, thus resembling a breast swimmer [8]; see Fig. 1(a). The synchronous beating of the two flagella is important for swimming along a straight path [9]. Free swimming cells often exhibit synchronized flagellar beating [8,9], raising the question of the underlying synchronization mechanism. For flagella attached to a solid substrate, long-range hydrodynamic interactions can induce flagellar synchronization [10\u201316]. Synchronization of the flagella of a moving swimmer, however, shows different features: Here, we show that flagellar synchronization can occur as a result of local hydrodynamic friction forces, even in the absence of hydrodynamic interactions. A model swimmer for biflagellar synchronization.\u2014 Inspired by Chlamydomonas swimming, we propose a model swimmer of maximal simplicity that retains its basic symmetries. The swimmer consists of three spheres of equal radius a and respective positions rj \u00bc \u00f0xj; yj; 0\u00de attached to a planar and mirror-symmetric scaffold; see Fig. 1(b). The swimmer is immersed in a viscous fluid of viscosity and the swimmer\u2019s scaffold is frictionless. The sphere located at r3 mimics a cell body and defines a material frame of the swimmer with orthonormal vectors e1 \u00bc \u00f0cos 3; sin 3; 0\u00de, e3 \u00bc \u00f00; 0; 1\u00de, and e2 \u00bc e3 e1, where the angular variable 3 characterizes rotations of the swimmer (around the z axis) with respect to the (x, y, z) laboratory frame; see Fig. 1(b). The first and the second sphere move along circular orbits of radius R, ri \u00bc si \u00fe R\u00f0 sin\u2019ie1 \u00fe cos\u2019ie2\u00de, i \u00bc 1; 2, being connected by frictionless lever arms to joints located at the corners si \u00bc r3 \u00fe l\u00bd\u00f0 1\u00deie1 \u00fe e2 of an isosceles triangle; see Fig. 1(b). Thus, l sets the size of the swimmer. The orbits are parametrized by respective phase angles \u2019i, i \u00bc 1; 2 such that b\u00f0\u2019i\u00f0t\u00de \u2019i\u00f00\u00de\u00de=\u00f02 \u00dec denotes the number of full rotations of the ith sphere since time t \u00bc 0 with respect to the material frame of the swimmer. Similarly, b\u00f0 i\u00f0t\u00de i\u00f00\u00de\u00de=\u00f02 \u00dec with i \u00bc 3 \u00fe \u2019i denotes the number of rotations with respect to the laboratory frame. Below, the dynamics of the phase angles\u2019i is given in terms of active driving torques; the cases _\u2019i < 0 and _\u2019i > 0 correspond to either a clockwise or counterclockwise revolution of the driven spheres (viewed along e3), respectively. The revolving motion of these driven spheres provides a simplified representation of the periodic bending waves of the two slender flagella of Chlamydomonas [10,11], for which each point on a flagellum follows a PRL 109, 138102 (2012) Selected for a Viewpoint in Physics PHY S I CA L R EV I EW LE T T E R S week ending 28 SEPTEMBER 2012 0031-9007=12=109(13)=138102(5) 138102-1 2012 American Physical Society periodic orbit in a material frame of the cell body; see Fig. 1(a). We neglect inertial effects, which implies that fluid flow is governed by the Stokes equation of zero Reynolds number hydrodynamics [1,17]. We consider the hydrodynamic friction force Fj and torque Tj (defined with respect to r3) exerted by the jth sphere on the viscous fluid during motion of the swimmer; T0 j \u00bc Tj Fj \u00f0rj r3\u00de denote torques with respect to rj. For free swimming, force and torque balance holds, Fext \u00bc 0 and Text \u00bc 0 with Fext \u00bc F1 \u00fe F2 \u00fe F3, Text \u00bc T1 \u00fe T2 \u00fe T3. The linearity of the Stokes equation implies a linear relationship between the generalized velocity vector for planar motion of the three spheres, _q0 with q0 \u00bc \u00f0x1; y1; 1; ", + " For example, the equation for j\u00bc4, corresponding to q4 \u00bc \u20191, represents a torque balance between a hydrodynamic friction torque, \u00f01=2\u00de@Rh=@ _\u20191 \u00bc F1 \u00f0@r1=@\u20191\u00de \u00fe T0 1z, and a net motor torque m1 _\u20191 provided by active driving. This motor torque obeys a linear torque-velocity relation with stall torque m1, similar to the net driving force used in [10]. An analogous statement holds for the second sphere. We finally obtain an equation of motion of the swimmer [20], _q \u00bc 1\u00f00; 0; 0; m1; m2\u00deT: (2) We first discuss the case of exactly opposite driving torques m1 \u00bc m2, which results in a counterrotation of sphere 1 and sphere 2 [Fig. 1(b)], similar to the mirror-symmetric beat patterns of the two flagella of Chlamydomonas [Fig. 1(a)]. The angular frequency !0 \u00bc m1= sets an (inverse) time scale of motion. If !0 > 0, the revolution of the first sphere is counterclockwise and clockwise for the second. The two cases !0 > 0 and !0<0 are mapped onto each other by time reversal. Net propulsion due to hydrodynamic interactions.\u2014For m1 \u00bc m2, there exists an orbit with perfect in-phase dynamics characterized by \u00bc 0, where \u00bc \u20191 \u00fe \u20192. Below, we show that this orbit is stable for !0 < 0, but unstable for !0 > 0. If initially 3\u00f0t \u00bc 0\u00de \u00bc 0, the swimmer will move parallel to the y axis in an oscillatory manner: In the limit of small spheres and small circular orbits, a l, R l, we find to leading order _y \u00bc \u00f02=3\u00deR", + " Previous research demonstrated that elasticity of the rotating objects introduces additional degrees of freedom that can break symmetries and thus stabilize synchronization [11,12]. However, reversibility may also be broken without evoking elasticity as in the case of our three-sphere swimmer. A realistic flagellar beat.\u2014The conceptual framework of our model swimmer can be extended in a straightforward manner to any mirror-symmetric microswimmer whose swimming stroke is characterized by two phase angles \u20191 and \u20192. As an example, consider the idealized flagellar beat in Fig. 1(a): During a beat cycle, the centerline ri of each of the two flagella can be expressed as a function of arclength s, 0 s L, and phase angles \u2019i, i \u00bc 1; 2, with _\u20191 > 0 and _\u20192 < 0 that characterize the phase of the beat cycle: With respect to a material frame (r3; e1, e2, e3) of the cell body, ri\u00f0s; \u2019i\u00de \u00bc r3 \u00fe ci1\u00f0s; \u2019i\u00dee1 \u00fe ci2\u00f0s; \u2019i\u00dee2, i \u00bc 1; 2. By mirror symmetry of the two flagella, c1j\u00f0s; \u2019\u00de \u00bc \u00f0 1\u00dejc2j\u00f0s; \u2019\u00de. We make the simplifying assumption that hydrodynamic forces do not alter the sequence of flagellar shapes (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003931_j.electacta.2018.08.140-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003931_j.electacta.2018.08.140-Figure1-1.png", + "caption": "Figure 1", + "texts": [ + " CySH (97%), cupric sulfate (98%), potassium 136 M ANUSCRIP T ACCEPTE D 7 ferricyanide (98%), ethylenediaminetetraacetic acid (EDTA, 99%), citric acid (99%), uric 137 acid (99%), oxalic acid (98%), catechol (99%), sucrose (99.5%), and D-glucose (99.5%) 138 were obtained from Sigma-Aldrich. Sodium hydroxide (99%) and sodium sulfate (99%) 139 were purchased from J. T. Baker Chemical Co. Ultrapure water (resistivity 18.2 M\u2126 cm) 140 was obtained from a Barnstead NANOpure water purification system and used to 141 prepare all the solutions. 142 143 Preparation of disposable Cu/SPAuE strips 144 The SPAuEs used in this work were a kind gift from TaiDoc Technology Corp., as shown 145 schematically in Fig. 1 (left). The disposable electrode strips were manufactured based on 146 the combination of screen printing and sputter coating methods, comprising two electrode 147 patterns laid on a PET substrate. The details of the electrode manufacturing process can 148 be found elsewhere [29]. The bare SPAuE comprises a screen-printed Ag pseudo-149 reference electrode and gold working electrode on the same strip. The geometric surface 150 area of the bare SPAuE was determined by CV measurement of the ferri/ferrocyanide 151 redox couple in 0", + " Kim, Analytical detection of 678 biological thiols in a microchip capillary channel, Biosens. Bioelectron. 40 (2013) 679 362. 680 [56] A.K. Elshorbagy, A.D. Smith, V. Kozich, H. Refsum, Cysteine and obesity, Obesity 681 20 (2012) 473. 682 M ANUSCRIP T ACCEPTE D 31 [57] A. Safavi, N. Maleki, E. Farjami, F.A. Mahyari, Simultaneous electrochemical 683 determination of glutathione and glutathione disulfide at a nanoscale copper 684 hydroxide composite carbon ionic liquid electrode, Anal. Chem. 81 (2009) 7538. 685 M ANUSCRIP T ACCEPTE D 32 686 Figure 1. Schematic diagram of the preparation of disposable Cu/SPAuE sensing 687 platform. Prior to deposition, central part of the electrode was covered with duct tape to 688 define the deposition area of copper as indicated by the red dashed line. 689 690 M ANUSCRIP T ACCEPTE D 33 691 Figure 2. SEM images of (a) SPAuE, (b) SPCuE, and (c) SPCE before and (d-f) after 692 copper electrodeposition at -0.4 V (versus an Ag pseudo-reference electrode) for 480 s in 693 the electrolyte solution of 10 mM CuSO4 + 100 mM Na2SO4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure7.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure7.3-1.png", + "caption": "Fig. 7.3 Example 7.1. Decomposition of the acceleration analysis", + "texts": [ + "2, evidently the velocity of A fixed in body k as observed from j is obtained as jvk A D ! rA=O, where rA=O D xOi C yOj is the position vector of A with respect to O. Furthermore, the velocity of A fixed in body m as observed from k is given by kvm A D PuOj. Hence, we have jvm A D ! .xOiC yOj/C PuOj D !yOiC .!xC Pu/Oj; (7.17) or jvm A D 2:5OiC 5:75Oj! vA D 6:27 m=s. On the other hand, the total acceleration of sphere A as measured from body j, the vector aA D jam A , can be computed as aA D jam A D jak A C kam A C 2j!k kvm A : (7.18) With reference to Fig. 7.3, it follows that jak A D aAt C aAn D \u02db rA=O C! .! rA=O/; (7.19) while kam A D RuOj: (7.20) Furthermore, the Coriolis acceleration is computed as 166 7 Hyper-Jerk Analysis 2j!k kvm A D 2! PuOj: (7.21) Therefore, one obtains aA D \u02db rA=O C! .! rA=O/C RuOjC 2! Pu Oj D .\u02dbyC !2xC 2! Pu/OiC .\u02dbx !2yC Ru/ Oj; (7.22) or aA D 39:75Oi 9:50 Oj! aA D 40:869 m=s2. On the other hand, the jerk of the sphere A, the vector A D j m A , is computed as j m A D j k A C k m A C 3j\u02dbk jvm A C 3j!k kam A C 3j!k .j!k kvm A /; (7" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000604_biorob.2008.4762872-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000604_biorob.2008.4762872-Figure1-1.png", + "caption": "Fig. 1. Schematic of a bevel-tip needle interacting with a soft elastic medium.", + "texts": [ + " The FE model includes contact between the needle tip and tissue, and also incorporates a cohesive zone model to simulate the tissue cleavage process. This paper is organized as follows: Section II presents the mathematical preliminaries required to obtain the tissue elasticity and toughness values. Section III describes the experiments to measure tissue elasticity and toughness. Section IV provides details on the FE simulations and sensitivity studies. Finally, Section V summarizes the work done and provides possible directions for future work. The deflection of a bevel-tip needle is a function of several parameters (Figure 1): the needle\u2019s Young\u2019s modulus( E, units: N m2 ) , second moment of inertia ( I, units: m4 ) , 978-1-4244-2883-0/08/$25.00 \u00a92008 IEEE 224 and tip bevel angle (\u03b1); the tissue\u2019s nonlinear (hyperelastic) material property ( C10, units: N m2 ) , rupture toughness( Gc, units: N m ) , and coefficient of friction (\u00b5); and input displacement from the robot controller (u, units: m). Dimensional analysis provides an organized method to group dimensionally similar variables [5]. Thus, the radius of curvature of the needle (\u03c1 , units: m) can be written as a function, f , of these parameters \u03c1 = f E, I,\u03b1\ufe38 \ufe37\ufe37 \ufe38 needle ,C10,Gc,\u00b5\ufe38 \ufe37\ufe37 \ufe38 tissue , u\ufe38\ufe37\ufe37\ufe38 input " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001330_j.engfailanal.2012.05.022-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001330_j.engfailanal.2012.05.022-Figure2-1.png", + "caption": "Fig. 2. Schematic graph of tooth crack [6].", + "texts": [ + " (2) can be simplified as M\u20acu\u00fe C _u\u00fe Ku \u00bc fb \u00fe f \u00f0t\u00de \u00f03\u00de where u\u00f0t\u00de \u00bc \u00f0y1 y2 y\u00deT, M\u00bc m1 0 0 0 m2 0 mg mg mg 2 64 3 75;C\u00bc c1 0 cg 0 c2 cg 0 0 cg 2 64 3 75;K\u00bc k1 0 kg\u00f0t\u00de 0 k2 kg\u00f0t\u00de 0 0 kg\u00f0t\u00de 2 64 3 75;fb\u00bc F1 F2 F3 0 B@ 1 CA;f \u00f0t\u00de\u00bc 0 0 mg\u20ace\u00f0t\u00de 0 B@ 1 CA;mg \u00bc I1I2 I1r2 2\u00fe I2r2 1 ;F3\u00bc I2r1M1\u00fe I1r2M2 I1r2 2\u00fe I2r2 2 The numerical parameters of the gear system are given in Table 1. The mesh stiffness must be affected by the presence of tooth crack or spalling failure. It is assumed in this investigation that the model is for a large gear defect with a unique tooth. The crack failure usually develops in the tooth root circle, so the crack failure is simulated as Fig. 2, where a = 45 , p = 5 mm. The spalling failure usually develops near the pitch line of the gears, and peels off in sheets. Therefore the spalling failure in this paper is modeled near the pitch line as a rectangular indentation having the dimensions A D P as shown in Fig. 3, where A = 2 mm, D = 40 mm and P = 2 mm. The mesh stiffness can be computed by the method given in [5,6]. The effects of the two failures on mesh stiffness are shown in Fig. 4. It has been found that the crack failure will affect the distortion of the whole gear until the crack tooth secedes, while the spall will affect the mesh stiffness merely when the defect part engages meshing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001657_icra.2015.7139508-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001657_icra.2015.7139508-Figure3-1.png", + "caption": "Fig. 3. Coordinate systems.", + "texts": [ + " The maximum control outputs are 12 channels. The control frequency is 200 [Hz]. The developed board is equipped with a 9 DOF inertial measurement unit in a single chip (MPU 9150, InvenSense). Flight logs are recorded on a micro-SD card. The position is obtained from a GPS receiver module (LEA-6H module, uBlox) in outside flight and is obtained from a motion capture system in indoor flight. This section explains the dynamics model of the quad tilt rotor UAV. The symbols used in this paper are listed in Table. I. Fig. 3 shows the coordinate systems defined in this paper. The term \u03a3W defines the earth-fixed coordinate system (inertial coordinates), \u03a3B defines the body-fixed coordinate system, and \u03a3Pi (i= 1\u22124) defines each rotor-fixed coordinate system. The earth-fixed coordinate system defines the XW axis as true north, the YW axis as east, and the ZW axis as perpendicular downward. The rotation motion about the XB, YB, and ZB axes are defined as roll, pitch, and yaw and the rotation angle around each axis is denoted as \u03c6 , \u03b8 , and \u03c8 , respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002321_j.optlastec.2018.10.025-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002321_j.optlastec.2018.10.025-Figure1-1.png", + "caption": "Fig. 1. Schematic of experiment system.", + "texts": [ + " Q235 steel plate, which size was 200mm\u00d7100mm\u00d710mm, was taken as substrate in the experiment. Taking mechanical processing to remove the oxide skin on the surface, and rub down the base plate, then using ethyl alcohol to rinse surface and drying plate. Using 24CrNiMo alloy steel powder as raw material, which chemical compositions are shown in Table 1. Experiment equipment is FL-Dlight02-3000w semiconductor laser device with the control system and powder feeder system. DLD technology is adopted to prepare different height samples under different EAD. Experiment system is shown in Fig. 1 and the technological parameter is shown in Table 2. The different layer samples were successfully prepared under different laser powder with the interval of 200W. The prepared different deposition samples were processed into cubes. Each of them had certain height of substrate, then cut off the substrate after metallographic observation to measure the samples\u2019 relative density through Archimedes drainage method. Taking abrasive papers of 240#, 400#, 800#, 1000#, 1200#, 1500#, 2000# respectively to polish samples with water, then putting them on the polishing machine with 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002484_j.jsv.2018.06.011-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002484_j.jsv.2018.06.011-Figure9-1.png", + "caption": "Fig. 9. Physical scenarios of one planet gear.", + "texts": [ + " 8 (c), (d), with the selection of shaft rotation-induced sidebands \u22116 m=1 fmesh \u00b1 mfshaft , the SER calculated with neither peak point nor the bandwidth can detect the sun gear fault scenarios. The results also show that for a fault detection of a specific component of a planetary gearbox, the corresponding fault-induced sidebands embrace the most fault information compared to other sideband components. Three different types of a planet gear health scenarios are also considered to demonstrate the diagnostic effect. Real physical scenarios including healthy, root crack, and tooth breakage scenarios are shown in Fig. 9. Similarly, the comparison results for modified MSER and SER under rotation speeds of 1800 rpm (30 Hz) and 3000 rpm (50 Hz) are shown in Figs. 10 and 11, respectively. From Figs. 10 (a) and 11 (a), with the selection of planet gear fault-induced sidebands \u22116 p=1 fmesh \u00b1 mfplanet, for different rota- tion speed conditions, the MSER with an empirical bandwidth setting of 2 Hz could clearly separate the three health scenarios. On the other hand, for Figs. 10 (b) and 11 (b) it can be seen that the three health scenarios are mixed together based on the traditional SER calculated with the peak point" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure13-1.png", + "caption": "Fig. 13 (c) coo", + "texts": [ + " (iii) Using coordinate transformation from S1 and S2 to Sf, we represent the conditions of continuous tan- gency of R1 and R2 in a fixed coordinate system Sf as r \u00f01\u00de f \u00f0u1; l1;/1\u00de r \u00f02\u00de f \u00f0us; ls;ws;/2\u00de \u00bc 0; \u00f031\u00de n \u00f01\u00de f \u00f0u1; l1;/1\u00de n \u00f02\u00de f \u00f0us; ls;ws;/2\u00de \u00bc 0; \u00f032\u00de fs2\u00f0us; ls;ws\u00de \u00bc 0: \u00f033\u00de (iv) The system of nonlinear equations (31)\u2013(33) contains six independent nonlinear scalar equations and seven unknowns since jn\u00f01\u00def j \u00bc jn\u00f02\u00def j \u00bc 1. The solution of this system is based on an iterative process. The Jacobian of the system of equations differs from zero since surfaces R1 and R2 are in point tangency. Using the theorem of implicit function system existence [4], we may represent the solution of the system of equations (31)\u2013(33) by functions of input parameter /1. The iterative process of solution is based on the Newton\u2013Raphson method. Fig. 13(a) and (d) illustrate the applied coordinate systems S1, S2, and Sf. Auxiliary fixed coordinate systems Sa, Sb, and Sc (Fig. 13(b)\u2013(d)) are applied for simulation of errors of installment Dcm, DE, and Dq. Here, magnitude B represents the center distance between the shaper and the pinion and is given by B \u00bc mn 2 Ns N 1 cos b : \u00f034\u00de The results of TCA for face-gear drives with two types of geometry are as follows: (i) The bearing contact is oriented across the surface wherein helical pinion and shaper have been applied. (ii) Similar results have been obtained for a face-gear drive with a spur involute pinion and shaper. (iii) Errors of alignment Dc of the shaft angle, Dq of the axial displacement of the face-gear or DE of the offset of the pinion do not cause transmission errors", + " The two types of geometry have been analyzed through three examples using the design parameters shown in Table 2. Example 1: A conventional face-gear drive with an involute helical pinion has been considered. Correc- tion DE for the drive has not been applied. Examples 2 and 3: A face-gear drive with modified tooth surfaces of the pinion and the shaper is considered. The modification is based on application of parabolic cutters for determination of tooth surfaces. Correction of meshing is provided by application of offset parameter DE (see Fig. 13), variation of relations between parabola coefficients of parabolic rack-cutters, location of the apex of the parabolic profiles (see Fig. 4), and plunging of the disk that generates the helical pinion [14]. Optimization of design parameters in the second type of geometry is an iterative process that enables to obtain: (i) Larger dimensions of the instantaneous contact ellipse and more favorable orientation of the contact ellipse (we remind that the point contact of the pinion and the face-gear tooth surfaces is spread under the load over an elliptical area)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure11.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure11.9-1.png", + "caption": "Figure 11.9.1 The transverse arm with sloped axis: (a) side view, (b) plan view.", + "texts": [ + " Within the practical range, The transverse-arm pivot axis may be sloped out of the horizontal plane, at angle fAx whilst remaining parallel to the centreline in plan view, giving the sloped-axis transverse arm. Typically this is done to obtain anti-squat and anti-rise characteristics, or bump steer, to be analysed here. For consistency with trailing and semi-trailing arms, positive slope angle fAx will be considered to be when the axis rises towards the rear of the vehicle. Practical swing axle design may use positive or negative values of pivot axis inclination. Figure 11.9.1 illustrates this case. For practical values of axis inclination, the effect on camber is small, but the effect on steer is significant. In Figure 11.9.1(a), when thewheel bump is zW zS, the centre of the wheel will move forwards by zS tan fAx with a resulting bump toe angle (toe-out as positive) of d \u00bc zS tan fAx RS with, therefore, a first bump steer coefficient 212 Suspension Geometry and Computation As a matter of interest, in 1940 Henry Ford was granted a patent for a swing axle explicitly featuring a slope angle to give bump toe-out, Figure 11.9.2. With a large load on the vehicle, or in riding bumps, the large first bump camber coefficient of the swing axle causes rather a large camber angle with associated side forces, which cause excessive tyre wear. This can be offset by introducing bump toeout (negative \u00abBS1) to reduce the net side force to zero. The relevant tyre characteristics are the cornering stiffness Ca relating the cornering force to the slip angle, and the camber stiffnessCg relating the side force to the camber angle. For a suspension bump zS, the first-order bump steer and camber angles are d \u00bc \u00abBS1zS g \u00bc \u00abBC1zS The consequent tyre side force is FY \u00bc Cad \u00fe Cgg \u00bc Ca\u00abBS1zS \u00fe Cg\u00abBC1zS To eliminate the bump side force requires \u00abBS1 \u00abBC1 \u00bc Cg Ca Now the ratio of the tyre coefficients is mainly a characteristic of the tyre carcase construction", + " Nowadays, radial-ply tyres are normal for passenger cars, with a ratio of about 0.05. A swing axle has a first bump camber coefficient of about 1.7 rad/m ( 10 deg/dm), so for bias-ply tyres the required bump steer coefficient is about plus 1.5 deg/dm, and for radial ply tyres about 0.5 deg/dm. Using, from Table 11.9.1, fAx \u00bc \u00abBS1RS with a swing arm radius of about 0.6m, the required axis slope is 9 for bias ply tyres and 3 for radial ply tyres. The negative slope means that the axis should be down towards the rear, in agreement with Figure 11.9.2. Single-Arm Suspensions 213 Analogous to the semi-trailing arm, the semi-transverse arm has a pivot axis in the horizontal plane, but angled in planview, the pivot axis being fairly closely but not exactly parallel to theX axis. For consistency with semi-trailing arms, the angle of the axis can be measured alternatively from the negative Y-axis direction (left wheel), giving the sweep angle cAx. However, as in Figures 11.0.1 and 11.10.1, the actual deviation from a simple transverse arm is the complementary angle, the axis yaw angle, which will be denoted by uAx: uAx \u00bc p 2 cAx This angling of the axis has several effects" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002702_1.4029988-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002702_1.4029988-Figure3-1.png", + "caption": "Fig. 3 Bearing geometry with defect on outer race and radial load distribution", + "texts": [ + " This effect has been demonstrated by Singh et al. [29] in the results of finite element formulation but the authors verified the source of impulsiveness in the output of the numerical simulation as well as experiments to be the destressing, impact, and restressing phases. Therefore, the effect of total picture of all the balls is not considered in this work and the emphasis is laid on the impact caused by the ball strike against the trailing edge of the defect, either with some load or only due to its inertia. 2.1 Mathematical Formulation. Figure 3 describes the bearing geometry along with the defect on the outer race and the distribution of radial load. It is assumed that the outer race is stationary, inner race rotates with angular velocity xs of the shaft, and the balls rolls with an angular velocity xb. The symbols \u201cL\u201d and \u201cT\u201d in the figure denote the leading and trailing edges of the defect. The following assumptions are incorporated to arrive at the mathematical form of the forcing function: (a) the ball undergoes pure rolling motion, (b) bearing components are as rigid bodies except for contact zones, (c) deformation at the edge occurs according to the Hertzian theory of elasticity; small elastic motions are considered and plastic deformation is neglected, (d) the effect of lubricating film is neglected" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003707_j.addma.2020.101265-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003707_j.addma.2020.101265-Figure4-1.png", + "caption": "Fig. 4. Single wall at the travel speed of 40 cm/min.", + "texts": [ + " Single weld beads of 100.0 mm length with 20 layers were deposited layer-by-layer. After each layer, the deposition direction was changed and the process paused for 5 s before resuming the deposition process. The waviness (Wt) was computed according to DIN EN ISO 4287 standard as the greatest difference of amplitudes. The waviness was evaluated using macrographs. Specimens were extracted from the center of the wall from the 4th layer upwards due to thermal instabilities in the first few layers [24], as shown in Fig. 4. A band saw was used to cut the walls with the thickness of 10.0 mm. The specimens then were ground and polished with grade P4000 sandpaper and 3.0 \u03bcm polishing paste, respectively. Macrographs were captured by means of the Leica DFC290 stereomicroscope and the DFC209 HD camera with magnification \u00d70.65. Single weld beads have a certain thickness [14]. For thicker walls, a multi-bead strategy appears to be appropriate. Fig. 5 shows a schematic of a multi-bead overlapping model, the overlapping length between adjacent beads (l) is equal to two-thirds of the bead width (w) [20]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure7.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure7.4-1.png", + "caption": "Fig. 7.4 Zonotopes representing the feasible torque set (left) and the feasible wrench set (right). They are obtained from the column vectors defined in Eqs. 7.13 and 7.16. Given that endpoint wrench in this example is planar force, the feasible wrench set is actually a feasible force set as it only contains the output force components fx and fy (i.e., no torque components, see Sect. 2.6). Note these unconstrained feasible sets are both zonotopes because they are created purely by the Minkowski sum of the generator vectors as in Fig. 7.2. Adapted with permission from [2]", + "texts": [ + "3 starts with the cube that is the most general feasible activation set, which first creates the parallelepiped of the feasible muscle force set, and then the zonotopes of the feasible joint torque, and feasible output wrench sets. Note that the column vectors \u03c4 i and wi are in the units of joint torques and end- point wrenches, respectively. Their positive linear combinations specify the set of all possible outputs in those spaces. If we consider them as the vi vectors of Fig. 7.2, we can build the zonotopes that correspond to the feasible joint torque set and the feasible output wrench set as shown in Fig. 7.3. In the specific simple case shown in Fig. 7.4, the endpoint wrench is a planar force vector\u2014consisting of fx and fy components only. This zonotope is called the feasible force set, and not the feasible wrench set because the endpoint output contains no torques (see Sect. 2.6). Note that we are studying the general case of the unconstrained feasible torque, wrench, and force sets, as shown in Fig. 7.3. I call these \u2018unconstrained\u2019 feasible sets because they describe what the system can do when you simply combine all possible actions without regard to functional constraints or goals, such as canceling out some elements of the output wrench w while keeping others" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002270_1464419314546539-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002270_1464419314546539-Figure3-1.png", + "caption": "Figure 3. Angular position of different defects in the bearing: (a) defective outer raceway and (b) defective inner raceway.", + "texts": [ + "50 The general force vector acting on the roller in the roller azimuthal frame is Fa b \u00bc Xn k\u00bc1 TiaT 1 ir T 1rraT 1 rac Fc c \u00fe Fc t \u00f020\u00de Then, the force vector acting on the raceway in the inertial frame will be given by the equation Fi r \u00bc Xn k\u00bc1 T 1ir T 1rraT 1 rac F c c Fc t \u00f021\u00de at University of Sydney on September 6, 2014pik.sagepub.comDownloaded from The moment vector acting on the roller in the rollerfixed frame is defined as Mb b \u00bc Xn k\u00bc1 rbkc TibT 1 ir T 1rraT 1 rac Fc c \u00fe Fc t \u00f022\u00de And, the moment vector acting on the raceway in the race-fixed frame is computed as Mr r \u00bc Xn k\u00bc1 Tir rirc T 1ir T 1rraT 1 rac F c c Fc t \u00f023\u00de Localized surface defects modelling As shown in Figure 3, when the roller passes through a defect on the raceway, the contact deflection suddenly changes due to the absence of material. As a result, the variations of forces and moments acting on the bearing components are produced. For the changed forces and moments, the alterative deflection should be described as \u00bc d 04mod f 0 4 d other \u00f024\u00de where d is the defect deflection excitation, 0 is the initial angular position of the defect zone and d is the desired length of the defect in the tangential direction and expressed as d \u00bc Wd= dri=2\u00f0 \u00de for inner race Wd= dro=2\u00f0 \u00de for outer race \u00f025\u00de The angular position f can be determined as f \u00bc j for outer race r j for inner race \u00f026\u00de where r is the rotation angle of the shaft along the axis Xi" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000088_tia.2006.870044-Figure16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000088_tia.2006.870044-Figure16-1.png", + "caption": "Fig. 16. Motor #3.", + "texts": [ + " These findings, although demonstrated on relatively small motors, are explained in the paper in such a way that they are anticipated to be valid, regardless of the motor rating. APPENDIX MOTORS FOR TESTS AND ANALYSIS Three motors were used for the analysis and the tests (Figs. 15\u201317). 1) Motor #1: Four phase; 8/6; rated torque: 2.0 N \u00b7 m; base speed: 2500 r/min; 42 V. 2) Motor #2: Three phase; 12/8; rated torque: 1.0 N \u00b7 m; base speed: 3000 r/min; 42 V (Fig. 15). 3) Motor #3: Four phase; 8/6; rated torque: 0.8 N \u00b7 m; base speed: 2500 r/min; 12 V; 8 turns per pole (Fig. 16). The authors would like to thank L. Frost, E. Nedelcu, and S. Rawski of Delphi Research Labs for their support during experimentation and their colleagues at Delphi-Saginaw Steering Systems, Delphi-E&C Dayton TC, and Delco-Electronics for the hardware and general project support. [1] C. M. Stephens, \u201cFault detection and management system for fault tolerant SR motor drives,\u201d IEEE Trans. Ind. Appl., vol. 27, no. 6, pp. 1098\u20131102, Nov./Dec. 1991. [2] T. J. E. Miller, Switched Reluctance Motors and Their Control" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003660_tpel.2017.2782562-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003660_tpel.2017.2782562-Figure4-1.png", + "caption": "Fig. 4. Operating modes of the AHB converter (a) Magnetization (b) Freewheeling (c) Demagnetization.", + "texts": [ + " For a 3-phase SRM, if only discrete components are considered, the AHB converter requires 6 switches and 6 diodes, while the adopted modular converter needs 8 switches and 8 diodes, which means that the AHB converter is cheaper in terms of power devices. However, it should be noted that the main purposes of converter construction with switch modules are to reduce system complexity, increase the integration and reliability and enhance the flexibility of component selection and converter construction. Magnetization, freewheeling, and demagnetization are three operating modes of the conventional AHB converter as shown in Fig. 4. According to the analysis of the modular converter in [15], there are two forms for each operating mode, namely single phase and two phases in series, and the current directions of two neighboring phases are reverse when energized simultaneously, as shown in Fig. 5. Fig. 6 shows the phase currents and switching logic of a 3-phase SRM with AHB and modular converter under hysteresis current control method, where \u03b8 is the rotor position and i is the phase current. It can be seen that the phase currents for the AHB converter are unidirectional, while bidirectional for the modular converter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure15.22-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure15.22-1.png", + "caption": "Figure 15.22.1 Factors f2 and f3, and out-of-plane displacement s for PointATinit and PointAT.", + "texts": [ + " Purpose: \u2018Point \u201cAbove\u201d a Triangle initialisation\u2019 \u2013 to obtain factors for use by routine PointAT to determine the position of a point relative to a triangle, the point being in any relative location (above, below or in the plane of the triangle). The triangle may subsequently move in anyway, taking the point with it, but the triangle must retain its shape. Inputs: The coordinates of the defining points of the triangle in a knownposition, and the coordinates of the point to be analysed Outputs: Factors f2 and f3 (for the foot of the perpendicular; see Figure 15.22.1), and the directed out-of plane distance s Notes: A vectorised version of this routine solving many points is useful. Solution:Drop theperpendicular fromP into the planeof the triangle, using routinePointFPT, giving the foot pointF and the signedout-of plane distance s. Dependingonhow routinePointFPTiswritten, the signof s may need to be changed here. The foot F may then be analysed by routine PointITinit to give f2 and f3. Taking the cross product ofP2 P1 andP3 P1 in that order gives a vector perpendicular to the plane of the triangle", + " relative to) a triangle (above, below or exactly in the plane), using the factors obtained in an initial position by PointATinit Inputs: The triangle point coordinates and the factors from PointATinit analysing the initial position Outputs: The coordinates of P Notes: This problem/routine is also sometimes known as \u2018Pole-on-a triangle\u2019, \u2018Rod-on-a-triangle\u2019 or, consequently, just \u2018Perch\u2019. A vectorised version of this routine solving many points is useful. Solution: Use the provided factors f2 and f3, Figure 15.22.1, to obtain a point in the plane of the triangle, using routine PointIT. This is the foot F of the perpendicular from the point, so calculate the normal to the plane by N \u00bc \u00f0P2 P1\u00de \u00f0P3 P1\u00de Move from F along this normal by a distance s (possibly negative), reaching P. Comments: The order of vectors in the calculation ofNmust be the same as in PointATinit, or the out-of- plane displacement will be reversed. There are no particular problems provided that the defining triangle is good (points not in line)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001463_1.4029461-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001463_1.4029461-Figure1-1.png", + "caption": "Fig. 1 Schematic diagrams of localized surface defects on races and their effects on the deflections of a ball: (a) a defect on the inner race and (b) a defect on the outer race", + "texts": [ + " A two degree-of-freedom (2DOF) dynamic model of a deep groove ball bearing that incorporates a localized surface defect with different sizes is used to investigate the vibrations of the ball bearing. The simulation results are compared with those from the previous defect models. An experimental investigation is also presented to validate the proposed model. The relationship between the time-varying contact stiffness and defect sizes is studied here. Localized surface defects on inner and outer races are schematically shown in Fig. 1. It is well known that the contact between a ball and an inner or outer race can be considered as a point contact between two spheres at the beginning when the race is normal, as shown in Fig. 2(a). However, when a defect occurs on the surface of a race, the contact between the ball and race becomes that between the ball and a line when the ball reaches an edge of the defect, as shown in Fig. 2(b). For a normal bearing, the contact stiffness between the ball and race can be calculated using Hertzian contact deformation theory, and the nonlinear load\u2013deformation relationship can be written as [54] F \u00bc Kd1:5 (1) where F is the externally applied force, K is the contact stiffness between the ball and race, and d is the radial deformation of contact surfaces between the ball and race" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001230_tcst.2011.2158213-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001230_tcst.2011.2158213-Figure1-1.png", + "caption": "Fig. 1. Helicopter\u2019s body-fixed frame, the TPP angles, and linear/angular velocity components.", + "texts": [ + " The linearized dynamic model proposed in [9] has been successfully adopted for control applications in a large number of small-scale helicopters of different sizes and specifications [4], [10]\u2013[13]. These experimental applications indicate that the modeling approach proposed in [9] provides a generalized and physically sound solution for developing practical linear models for small-scale helicopters. The helicopter motion variables are expressed with respect to a body-fixed reference frame defined as , where the center is located at the center of gravity (CG) of the helicopter. The directions of the body-fixed frame orthonormal vectors are shown in Fig. 1. The helicopter\u2019s linear and angular velocity vectors, with respect to the body-fixed frame, are denoted by and , respectively. The helicopter attitude is expressed by the roll ( ), pitch ( ) and yaw ( ) angles. The helicopter motion variables are shown in Fig. 1. There are four control commands associated with helicopter piloting. The control input is defined as , where and are the collective controls of the main and tail rotor, respectively. The collective commands control the magnitude of the main and tail rotor thrust. The other two control commands , are the cyclic controls of the helicopter, which control the inclination of the tip-path-plane (TPP) on the longitudinal and lateral direction. The TPP is the plane in which the tips of the blades lie and it is used to provide a simplified representation of all the rotor blades. The TPP is characterized by two angles, and , which represent the tilt of the TPP at the longitudinal and lateral axis, respectively. The inclination of the TPP can be seen in Fig. 1. By controlling the inclination of the TPP the pilot indirectly controls the helicopter moments. The TPP is itself a dynamic system, which is coupled with the fuselage dynamics. The adopted linear model represents the dynamic response of the helicopter perturbed state vector from the reference flight condition. In this case, the reference operating condition is hover. The linear state space model is described by (1) where the state vector is given by (2) The entries of the matrices and , based on [9], are given in Table I" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure13-1.png", + "caption": "Fig. 13. Distribution of stator and rotor core loss density. (a) SPM. (b) CPM1-1. (c) CPM1-2. (d) CPM2. (e) CPM3. (f) HPM1. (g) HPM2. (1500 rpm, 4 Arms)", + "texts": [], + "surrounding_texts": [ + "The copper losses only consider the DC losses, i.e., the AC losses resulting from the skin and proximity effects are neglected. The end coils are assumed to be semicircular shape for simplification [27], and the copper losses is calculated to be 18.81W at the rated current. Figs. 13 and 14 show the distributions of core and PM loss density in the seven typical machines at rated current and speed, respectively. TABLE III lists the iron loss Piron (including eddy loss of stator core Pe_s, hysteresis loss of stator core Ph_s, eddy loss of rotor core Pe_r, hysteresis loss of rotor core Ph_r, PM eddy loss Pm) and the efficiencyof these machines. It can be seen that the SPM machine has larger iron loss than the conventional CPM machines (CPM1-1 and CPM1-2) and proposed HPM machines (HPM1 and HPM2) due to the larger flux density. However, the SPM machine has the largest output torque (power) in these machines, and therefore has the largest efficiency. Distinctly, the CPM2 and CPM3 have the largest stator core loss in all the machines due to the saturation of the stator core, which results from the subharmonic of the airgap flux density, as shown in Figs. 9 (d) and (e). The rotor core loss is much lower than the stator core loss for all the machines, and this is due to that the flux density of rotor changes little over time. From Fig. 9 (f), it can be seen that the saturation in the stator yoke of the HPM1 still occurs. Therefore, the stator core loss of the HPM1 is larger than that of the CPM1-1, CPM1-2 and HPM2. In addition, the HPM2 has the slightly larger total iron loss than the CPM1-1 and CPM1-2 machine. However, the iron loss of the conventional CPM and proposed HPM machines are much smaller than the copper loss due to the low speed, i.e., 1500 rpm. Therefore, the proposed HPM machines (HPM1 and HPM2) can exhibit similar efficiency to the conventional CPM machines (CPM1-1 and CPM1-2)." + ] + }, + { + "image_filename": "designv10_3_0003223_j.matpr.2017.07.258-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003223_j.matpr.2017.07.258-Figure9-1.png", + "caption": "Fig. 9. GTAW-AM process and experimental equipment: (a) schematic drawing shown the GTAW-AM process; (b) the experimental setup and electric resistance heating element", + "texts": [ + " The focus of this research study is to determine the effect of interpass temperature on the microstructure and micro hardness of the in-situ alloyed and additively manufactured titanium aluminide components, and thereby decides upon a suitable interpass temperature for future application of this process. [4] 3.3.1Materials and method Five straight walls with 20 layers each were produced by GTAWAM using a water cooled CK machine mount torched to a Kemppi MasterTIG MLS 2000 inverter power supply at a 120 A current, 3.5 mm arc length, 100 mm/min welding speed, 850 mm/min Ti wire-feeding rate and 775 mm/min Al wire-feeding rate. The manufacturing process and the equipment used in the current work are shown in Fig. 9. The first layer was joined to the substrate on which the torch created a melt pool. A twin wire feeder arrangement was used to individually deliver the feed Ti and Al wires into the melt pool to form a layer when the molten metal solidified.A new layer was subsequently deposited onto the previous layer after the torch and the twin wire feedstock nozzles were raised by a vertical distance equal to the layer thickness. The process was repeated to deposit consecutive layers until the walllike part was fully constructed in a layer-by-layer manner" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.14-1.png", + "caption": "Fig. 4.14 Screws associated to the kinematic pairs of the Geneva wheel", + "texts": [ + "107) leads to a linear system of two equations in the unknowns w2 and v00 P . Solving such a system, one obtains the general expressions !2 D !1r1 cos. C \u02c7/=r2; v00 P D !1r1 sin. C \u02c7/; (4.108) where r2 and \u02c7 are computed according to the geometry of the triangle O1CP; that is, r2 D 0:1854 m and \u02c7 D 42:3789\u0131. Hence with the substitution of numerical data, one finally obtains !2 D 0:8161 rad/s and v00 P D 0:4765 m/s. In what follows the velocity analysis of the Geneva wheel is approached using screw theory. To this end, the modeling of the screws is depicted in Fig. 4.14. While $1, $2, and $4 are infinitesimal screws associated to revolute joints, the screw $3 is associated to the prismatic joint simulating the adjustable distance 92 4 Velocity Analysis between points P and O2. According to the closed kinematic chain O1PO2, it is evident that the equation of velocity in screw form of the Geneva wheel may be written as follows: v1$1 C v2$2 C v3$3 C v4$4 D 0; (4.109) where the involved infinitesimal screws, taking point O1 as the reference pole, are computed as $1 D 2 66666664 0 0 1 0 0 0 3 77777775 ; $2 D 2 66666664 0 0 1 r1 sin" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001110_iet-epa.2010.0159-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001110_iet-epa.2010.0159-Figure2-1.png", + "caption": "Fig. 2 Geometric and windings configurations of the modelled motor", + "texts": [ + " Saturation is considered by an air gap length with twice the number of poles and twice the frequency of the fundamental wave [19]. Therefore the radial air gap length is effectively larger at the regions of maximum flux density. Thus, air gap length can be defined as follows g(w, t) = Rav \u2212 rssCos(Sw) \u2212 rsaCos(2vst \u2212 2Pw) (3) In the SE fault, the rotational axis of the rotor coincides with the rotor symmetrical axis and they displace from the stator symmetrical axis. In the SE fault depicted in Fig. 2a, the air gap distribution is non-uniform and time independent. 37 & The Institution of Engineering and Technology 2012 a SE case b DE case c Motor windings (black: phase A; grey: phase B; white: phase C) According to Fig. 2a, the air gap length upon the SE for the rotor offset by a distance rSE can be expressed as follows g(w, t)=Rav \u2212rssCos(Sw)\u2212rsaCos(2vst\u22122Pw)\u2212rseCos(w) (4) In the DE fault, the minimum air gap length depends on the rotor angular position and it rotates around the rotor. In this eccentricity, the symmetry axis of the stator and rotation axis of the rotor is identical, but the rotor symmetry axis has been displayed. In such a case, which has been exposed in Fig. 2b, the air gap around the rotor is non-uniform and the minimum air gap depends on the time and rotor angular position. Thus, the air gap length because of DE can be determined as follows g(w, t) = Rav \u2212 rssCos(Sw) \u2212 rsaCos(2vst \u2212 2Pw) \u2212 rdeCos(vrt \u2212 w) (5) In the ME fault, both SE and DE exist and centres of rotor rotation, stator and rotor are displaced. The air gap length in the faulty motor under ME can be derived as follows g(w, t) = Rav \u2212 rssCos(Sw) \u2212 rsaCos(2vst \u2212 2Pw) \u2212 rseCos(w) \u2212 rdeCos(vrt \u2212 w) (6) Since vr \u00bc (1/P)vs, (6) is expressed as follows g(w, t) = Rav \u2212 rssCos(Sw) \u2212 rsaCos(2vst \u2212 2Pw) \u2212 rseCos(w) \u2212 rdeCos vs P t \u2212 w ( ) (7) The air gap length is rewritten as follows g(w, t) = Rav 1 \u2212 rss Rav Cos(Sw) \u2212 rsa Rav Cos(2vst \u2212 2Pw) ( \u2212 rse Rav Cos(w) \u2212 rde Rav Cos vs P t \u2212 w ( )) (8) Equation (8) can be simplified as follows g(w, t) = Rav 1 \u2212 dssCos(Sw) \u2212 dsaCos(2vst \u2212 2Pw) ( \u2212 dseCos(w) \u2212 ddeCos vs P t \u2212 w ( )) (9) 38 & The Institution of Engineering and Technology 2012 where dss \u00bc rss/Rav, dsa \u00bc rsa/Rav, dse \u00bc rse/Rav and dde \u00bc rde/Rav" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001138_c3sm51654g-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001138_c3sm51654g-Figure1-1.png", + "caption": "Fig. 1 Schematic for wrinkling and folding in LCE\u2013PS bilayer.", + "texts": [ + "33 Here we show that this relatively simple system enables a rich response beyond reversible folding through variation of several system parameters: the thickness ratio of PS to LCE, the overall aspect ratio of the bilayer, the relative stiffness of the top lm and LCE, bilayer preparation temperature, and patterning of the top passive lm. Finite element method (FEM) simulations can predict the self-folding behaviour of LCE bilayers and are in quantitative agreement with experimental observations (Fig. 1). Soft Matter, 2014, 10, 1411\u20131415 | 1411 Pu bl is he d on 2 6 N ov em be r 20 13 . D ow nl oa de d by U ni ve rs ity o f W in ds or o n 30 /1 0/ 20 14 0 1: 26 :5 4. Monodomain LCEs are prepared using the two-step crosslinking method34 (see ESI for more details, Fig. S1\u2020). The resulting monodomain LCEs spontaneously change shape as a function of temperature,35,36 and the shape change is fully reversible on both heating and cooling over several cycles, as shown in Fig. 2. LCE bilayers are prepared by a lm-transfer technique (see ESI, Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002936_j.jmapro.2019.03.006-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002936_j.jmapro.2019.03.006-Figure6-1.png", + "caption": "Fig. 6. Mechanical boundary conditions of the substrate.", + "texts": [ + " The temperature-dependent mechanical properties are presented in Fig. 5. During the deposition process, the heat conduction equation by Fourier for transient non-linear heat transfer analysis is given as follows: \u2202 \u2202 \u2202 \u2202 + \u2202 \u2202 \u2202 \u2202 + \u2202 \u2202 \u2202 \u2202 + = \u2202 \u2202x k T x y k T y z k T z Q \u03c1C T t ( ) ( ) ( ) ( )p (1) where x, y, z are the coordinates in the reference system; k is the thermal conductivity; T is the current temperature; Q is the energy generated per unit volume within the workpiece; \u03c1 is the density; Cp is the specific heat capacity; t is the time. As shown in Fig. 6, mechanical boundary conditions are used to prevent rigid displacement of the substrate along the X, Y and Z directions. The thermal boundary conditions consisting of surface convection heat loss and radiation heat loss are considered according to the relation proposed in Abid and Siddique [14]: = \u2212 \u2212 +h \u03b5 \u03c3 T T T T h ( ) ( ) em bol amb amb con 4 4 (2) where h is the combined heat transfer coefficient; hcon is the convection coefficient; \u03b5em is the emissivity; \u03c3bol is the Stefan-Boltzmann constant; T is the surface temperature of the part; Tamb is the ambient temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.17-1.png", + "caption": "Fig. 2.17 Geometrical and mechanical parameters in a four-bar linkage with a translational spring", + "texts": [ + "202). The equation of motion thus results from (2.209) with W \u2032 pot = m5gy\u2032S5 and Q\u2217 \u2261 Q to become[ J2 + J3u 2 23 + J4u 2 24 + m5 ( r2r34 r32 )2 ] \u03d5\u03082 + m5g(r2r34/r32) = Man (2.214) 118 2 Dynamics of Rigid Machines Four-bar linkages with a rotating input link are used in many machines in the form of crank-rocker mechanisms (output link 4 rocks back and forth) or double-crank mechanisms (output link 4 rotates fully) to generate non-uniform motions. The given quantities are the lengths li shown in Fig. 2.17, the center-of-gravity coordinates \u03beSi in the body-fixed reference system, the masses mi and moments of inertia JSi, which are causing inertia forces and moments. A spring force, the magnitude of which can be calculated from the spring constant c and the spring deflection, which in turn results from the unstretched spring length l0 and the instantaneous spring length l, acts in addition to the input torque M2 and the static weight of the links. The spring length depends on the fixed coordinates x15, y15 and the body-fixed coordinates of the pivot point (\u03be35, \u03b735). Sought-after quantities are general formulae for calculating the reduced moment of inertia and the other terms that enter into the equation of motion of the rigid machine for q = \u03d52. The equations for calculating the angles \u03d53 and \u03d54 are derived from the constraints. These express the fact that the projections of the coordinates of the joint points onto the two coordinate directions form a solid straight line (loop), see Fig. 2.17: l3 cos \u03d53 = l4 cos \u03d54 + l1 \u2212 l2 cos \u03d52 (2.215) l3 sin \u03d53 = l4 sin \u03d54 \u2212 l2 sin \u03d52 (2.216) Squaring and adding yields l23 = l24+l21+l22\u22122l1l2 cos \u03d52+2l4(l1\u2212l2 cos \u03d52) cos \u03d54\u22122l4l2 sin \u03d52 sin \u03d54. (2.217) 2.4 Kinetics of Multibody Systems 119 If one solves this equation, the result obtained after some intermediate calculations with the abbreviations a34 = 2(l2 cos \u03d52 \u2212 l1)l4 N , b34 = 2l2l4 sin \u03d52 N , w34 = a2 34+b2 34 (2.218) and the denominator N = (l2 cos \u03d52 \u2212 l1) 2 + l22 sin2 \u03d52 + l24 \u2212 l23 (2.219) is the sine and cosine of \u03d54: sin \u03d54 = b34 \u2212 a34 \u221a w34 \u2212 1 w34 , cos \u03d54 = a34 + b34 \u221a w34 \u2212 1 w34 . (2.220) The other unknown trigonometric functions are most easily derived from (2.215) and (2.216) using (2.220): cos \u03d53 = l4 cos \u03d54 \u2212 l2 cos \u03d52 + l1 l3 , sin \u03d53 = l4 sin \u03d54 \u2212 l2 sin \u03d52 l3 . (2.221) This allows the calculation of all (zeroth-order) position functions of the centers of gravity, see Fig. 2.17: xS2 = \u03beS2 cos \u03d52, yS2 = \u03beS2 sin \u03d52 xS3 = l2 cos \u03d52 + \u03beS3 cos \u03d53, yS3 = l2 sin \u03d52 + \u03beS3 sin \u03d53 xS4 = l1 + \u03beS4 cos \u03d54, yS4 = \u03beS4 sin \u03d54. (2.222) The first-order position functions are then derived by differentiation with respect to the input coordinate q = \u03d52: x\u2032S2 = \u2212\u03beS2 sin \u03d52, y\u2032S2 = \u03beS2 cos \u03d52 x\u2032S3 = \u2212l2 sin \u03d52 \u2212 \u03beS3\u03d5 \u2032 3 sin \u03d53, y\u2032S3 = l2 cos \u03d52 + \u03beS3\u03d5 \u2032 3 cos \u03d53 x\u2032S4 = \u2212\u03beS4\u03d5 \u2032 4 sin \u03d54, y\u2032S4 = \u03beS4\u03d5 \u2032 4 cos \u03d54. (2.223) Here, the as yet undetermined first-order position functions of the angles \u03d53 and \u03d54 appear", + " The spring moment is derived from the potential spring energy Wpot F = c(l \u2212 l0) 2/2: W \u2032 pot F = Mc = c(l \u2212 l0)l \u2032 = cll\u2032 ( 1\u2212 l0\u221a l2 ) . (2.230) The spring length in the loaded condition is calculated from the coordinates of both spring pivot points using the Pythagorean theorem: l2 = (x35 \u2212 x15) 2 + (y35 \u2212 y15) 2. (2.231) Implicit differentiation results in: 2ll\u2032 = 2(x35 \u2212 x15)x \u2032 35 + 2(y35 \u2212 y15)y \u2032 35 (2.232) and provides the expression required for (2.230). The position functions of the spring pivot point are required for this. One can gather from Fig. 2.17 that the following geometrical relationships apply: x35 = l2 cos \u03d52 + \u03be35 cos \u03d53 \u2212 \u03b735 sin \u03d53 y35 = l2 sin \u03d52 + \u03be35 sin \u03d53 + \u03b735 cos \u03d53. (2.233) Their partial derivatives are 2.4 Kinetics of Multibody Systems 121 x\u203235 = \u2212l2 sin \u03d52 \u2212 (\u03be35 sin \u03d53 + \u03b735 cos \u03d53)\u03d5 \u2032 3 y\u203235 = l2 cos \u03d52 + (\u03be35 cos \u03d53 \u2212 \u03b735 sin \u03d53)\u03d5 \u2032 3. (2.234) The spring moment according to (2.230) thus becomes: Mc = c [(x35\u2212x15) x\u203235+(y35\u2212y15) y\u203235] [ 1\u2212 l0\u221a (x35\u2212x15)2 + (y35\u2212y15)2 ] . (2.235) Now all portions of the moment that are included in the equation of motion (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003309_978-3-319-24729-8-Figure2.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003309_978-3-319-24729-8-Figure2.4-1.png", + "caption": "Fig. 2.4 The unicycle", + "texts": [ + "3, we turn to unicycles and bicycles.1 These are kinematic models. Of course, a real robot has dynamics too, but this can frequently be removed by a high-gain inner loop as we just did in Fig. 2.2. Sometimes, it is convenient to make the complex plane the workspace where the robots live. Recall that every complex number w can be written uniquely in polar form as w = vej\u03b8, where v = |w| and \u03b8 is a real number in the interval [0, 2\u03c0). A kinematic unicycle is a robot with one steerable drive wheel (see Fig. 2.4). If we assume that the wheel is always perpendicular to the ground, we may represent the unicycle on the complex plane as in Fig. 2.5, where z := x + jy is the position vector and ej\u03b8 the normalized velocity vector. Convention. In Fig. 2.5 we represent a complex number in two different ways. First, z is shown as a dot, obviously at the correct location in the complex plane. On the other hand, ej\u03b8, which is a complex number too, is shown as an arrow. The convention is likely familiar. An element ofC (orR2) can be regarded geometrically as a geometric vector or a point" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.39-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.39-1.png", + "caption": "Fig. 2.39 Effects of balancing masses on a rotor", + "texts": [ + " For practical purposes, a rotor can often be considered to be rigid as long as its speed is about half of its smallest critical speed, which also de- 154 2 Dynamics of Rigid Machines pends on the support conditions of the rotor. In an elastic rotor, the balancing state changes with its speed due to deformation. Unbalances often arise as a result of manufacturing inaccuracies and material inhomogeneities. An axisymmetrically designed component does not really have an ideal axisymmetric mass distribution. An unbalance is defined as the product of a point mass mi and its distance ri from the axis of rotation, see Fig. 2.39: Ui = miri (2.321) For a single rotating point mass, a centrifugal force Fi = miri\u03a9 2 = Ui\u03a9 2 (2.322) occurs at the angular velocity \u03a9. The unbalances in a rotor are typically distributed unevenly and randomly in space. Since there are always unbalances, dynamic forces develop when rotors rotate. These forces can have an adverse effect on 1. the bearing forces (surface pressure, wear, service life . . . ) 2. the loads on frame and foundation (excitation of vibrations) 3. loads inside of the rotor", + " A static unbalance occurs if the center of gravity is not located on the axis of rotation. A dynamic unbalance of the rotor occurs when the central principal axis of inertia (that passes through the center of gravity) does not coincide with the axis of rotation. Both phenomena are always superposed in practice. During balancing, the mass distribution of the rigid rotor is adjusted by balancing in two planes so that the static and dynamic unbalances are compensated. m1, m2, \u03be1, \u03be2, \u03b71 and \u03b72 are determined from the measured bearing forces or displacements, see Fig. 2.39. The following analysis is to show that two balancing masses in two different balancing planes are generally sufficient to completely balance an arbitrary rigid rotor. According to (2.325), the bearing forces that vary harmonically with the angular frequency \u03a9 depend on four components FA\u03be, FA\u03b7, FB\u03be, and FB\u03b7. Balancing is based on the idea that these four components (that have to be determined by experiment for a given real rotor) must be produced in the opposite direction by additional balancing masses and thus to compensate their sum on each bearing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001053_tmag.2011.2104969-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001053_tmag.2011.2104969-Figure1-1.png", + "caption": "Fig. 1. Symbols and types of sub-regions. (a) Subdomain model without toothtips. (b) Subdomain model with tooth-tips.", + "texts": [ + " Compared with the conventional subdomain model, the subdomain model considering the tooth-tips predicts similar flux density in the air gap and magnets, but shows significantly higher accuracy for the flux density in the slot openings and slots. The finite-element (FE) results validate the analytical predictions. The analytical modeling is based on the following assumptions: 1) infinite permeable iron materials; 2) negligible end effect; 3) unity relative permeability of magnet; 4) simplified slot but with tooth-tips as shown in Fig. 1(b), rather than the ideal slot adopted in the conventional model as shown in Fig. 1(a); 5) non-conductive stator/rotor laminations; and 6) uniform distributed current density in coil\u2019s conductor area. The coils can be accommodated in the slot in two ways as shown in Fig. 2, viz. non-overlapping and overlapping windings. The single layer winding, viz. one coil side per slot, can be considered as a special case of either Fig. 2(a) or (b), having current densities . In the overlapping winding machine, to make the two parts of each slot have the same area. 0018-9464/$26.00 \u00a9 2011 IEEE Non-Overlapping Winding Machine: The vector potential is used to illustrate the magnetic field due to armature reaction, which satisfies [23], [24]: (1) where is the current density", + " The governing function for the region of magnets and air gap can be given by [8]: (2) where and are the radial and circumferential positions. By the variable separation method, the general solution of vector field in the magnets and air gap can be obtained as (3) where and are the radii of the stator bore and rotor yoke surface, respectively, and , , , and are coefficients to be determined. The governing function for the regions of the slots excluding slot opening is [8]: (4) The general solution of the vector field in the th slot can be expressed by (5) where is the slot position, is the slot width angle as shown in Fig. 1(b), and are the radii of the bottom and top of the slot, respectively, and are coefficients to be determined, is constant, is a particular solution due to current density, and (6) The current density in the th slot shown in Fig. 3 for the non-overlapping winding can be expressed by (7) for , where (8) (9) A particular solution can be found as (10) Thus, the vector potential distribution in the slot can be given by (11) According to boundary condition along the slot bottom adjacent to infinite permeable lamination, the circumferential component of the flux density should be zero. Thus (12) (13) where (14) Therefore, the vector potential distribution in the slot can be derived as (15) The governing function for the regions of slot openings is (16) The general solution of vector field in the th slot opening can be given by (17) where is the slot opening width angle as shown in Fig. 1(b), and are the coefficients to be determined, is constant, and (18) The radial and circumferential components of flux density can be obtained from the vector potential distribution by (19) Therefore, the flux density in the air gap and magnets can be obtained as (20) for the radial component and (21) for the circumferential component. The flux density in the th slot can be expressed as (22) for the radial component and (23) for the circumferential component. The flux density in the th slot opening can be expressed as (24) for the radial component and (25) for the circumferential component" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure4.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure4.2-1.png", + "caption": "Fig. 4.2 Anatomical cases for posture of the limb-dependent moment arms", + "texts": [ + " \u2022 Constant moment arms Whenever an articulation can be modeled as a circular pulley, the scalar equation 4.3 can be used to calculate joint torque. There are precious few anatomical joints with such geometry, but this is an assumption that is often used as a first approximation in musculoskeletal models [1]. Such joints can be represented as shown in Fig. 4.1. \u2022 Posture-dependent moment arms Consider the more common case where the bone contours cannot be considered a circular pulley, the moment arm is created by a system of ligamentous pulleys (Fig. 4.2), or the tendons bow-string away from the joint (Fig. 4.3). In these cases it is clear that r(q) needs to be calculated for each joint angle. In the case of the non-circular pulley (Fig. 4.2a), the shape of the cam defines r(q). In the case of Fig. 4.3 Anatomy of posture-dependent moment arms where the tendon can bowstring away from the bones r q r q a b c A B C tendon pulleys (Fig. 4.2b) or bowstringing (Fig. 4.3), it is necessary to consider the detailed geometry. As an example, Fig. 4.3 represents an idealized biceps muscle that bowstrings as the elbow flexes. In this case, using a classical geometric analysis of triangles where the sides are lower case letters a, b, and c, and angles are upper case letters A, B, and C we have r b = sin(A) \u21d2 r = b sin(A) (4.4) Given that the DOF of the joint is the angle q defined from the vertical, we obtain C = 180 \u2212 q c = \u221a (a + b cos(q))2 + (b sin(q))2 Law of sines: sin(C) c = sin(A) a (4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure7.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure7.2-1.png", + "caption": "Fig. 7.2 Example 7.1. Decomposition of the velocity analysis", + "texts": [ + " We must compute the total instantaneous velocity, acceleration, jerk, and hyper-jerk of sphere A considering that the instantaneous coordinates of A are given by x D 0:75 m and y D 0:5 m. Solution. Let XYZ be a fixed reference frame with associated unit vectors OiOjOk whose origin is located at point O. The total velocity of the sphere A, the vector vA D jvm A , can be obtained as vA D jvm A D jvk A C kvm A ; (7.16) where j denotes the fixed reference frame. Meanwhile, k denotes the disk, whereas body m is the proper sphere A. 7.2 Fundamental Hyper-Jerk Equations 165 With reference to Fig. 7.2, evidently the velocity of A fixed in body k as observed from j is obtained as jvk A D ! rA=O, where rA=O D xOi C yOj is the position vector of A with respect to O. Furthermore, the velocity of A fixed in body m as observed from k is given by kvm A D PuOj. Hence, we have jvm A D ! .xOiC yOj/C PuOj D !yOiC .!xC Pu/Oj; (7.17) or jvm A D 2:5OiC 5:75Oj! vA D 6:27 m=s. On the other hand, the total acceleration of sphere A as measured from body j, the vector aA D jam A , can be computed as aA D jam A D jak A C kam A C 2j" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001308_tmag.2012.2203607-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001308_tmag.2012.2203607-Figure15-1.png", + "caption": "Fig. 15. FEM Model for eddy current calculations (ANSYS 3-D).", + "texts": [ + " Only a fundamental component of current layer is considered due to the main effect on the eddy current losses because of bigger wavelength and also for simplification of the analytical calculations. IV. 3-D TIME HARMONIC FINITE ELEMENT METHOD The equations used by the 3-D linear harmonic finite element analysis [8] and eddy current losses are given in (11). . In ANSYS, the real model of Fig. 1 with the winding distributed in slots was modified to an equivalent three-phase distributed current layer (Fig. 15) to reduce the calculation time. For example, the zone of 3 A slots is unified as one A current layer. As infinite iron permeability for stator and rotor is assumed, only air gap and the magnets must be modeled. The stator and rotor irons are replaced by normal flux boundary conditions (11) where , and are induced eddy current in permanent magnets, stator current density and electric scalar potential, respectively. The bore and magnet curvature and the eddy current reaction field are taken into account. The field waves are excited by current layers on the stator bore. The boundary conditions are shown in Fig. 15. Only half of the model in the axial direction is considered in 3-D FEM due to the symmetry. Space harmonic contents of the current layer in the threephase and single-phase configurations are shown in Figs. 16 and 17 according to the model in Fig. 15. The calculated eddy currents using 3-D FEM are shown in Fig. 18, top and bottom, for: 1) one magnet segment in the axial direction and 2) five magnet segments in the axial direction, respectively. The results are shown in Figs. 19 and 20. The simulations have been done for different axial numbers of magnet segments for travelling and pulsating wave conditions. Two phases are switched off in the pulsating wave condition. The third phase generates the standing pulsating field. The former condition is equivalent to single-phase PM machines" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003845_j.matchar.2018.01.035-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003845_j.matchar.2018.01.035-Figure1-1.png", + "caption": "Fig. 1. Geometry of the tensile specimens with dimensions given in mm and designed so as to be representative of a single strut of a lattice structure.", + "texts": [ + " Xray microtomography was used to identify the critical defects and to try to quantify the effect of post-treatments on the static mechanical behaviour. Several simple approaches are finally proposed to take into account the presence of the identified defects and thus rationalize the results. Cylindrical tensile specimens with a gauge length of 10mm and a nominal diameter of 2mm were produced vertically, i.e. with their tensile axis aligned with the building direction, using an ARCAM A1 EBM machine and Ti-6Al-4 V ELI powder, see Fig. 1. The unusual geometry of the tensile specimens, i.e. with a relatively small nominal diameter (2 mm) was deliberately chosen so as to be representative of a single strut of a lattice structure (large surface to volume ratio). The chemical composition of the initial powder batch is given in Table 1. The standard \u201cMelt\u201d build theme recommended by ARCAM for a layer thickness of 50 \u03bcm was chosen to define the set of melting parameters and scanning strategy used during the EBM process. Several types of post-treatment were applied to the as-built tensile specimens: Hot Isostatic Pressing (HIP) and chemical etching as well as a combination of both in order to investigate their effect on the tensile mechanical properties" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002587_9783527684984-Figure7.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002587_9783527684984-Figure7.12-1.png", + "caption": "Figure 7.12 Conceptual sketches of two types of microreactor-heat exchanger (a) parallel flow and (b) cross flow.", + "texts": [ + "26b, respectively. \u2022 As a result of the first two points, microreactor systems aremuchmore compact than conventional systems of equal production capacity. \u2022 There are no scaling-up problems with microreactor systems. The production capacity can be increased simply by increasing the number of microreactor units used in parallel. Microreactor systems usually consist of a fluid mixer, a reactor, and a heat exchanger, which is often combined with the reactor. Several types of system are available. Figure 7.12, for example, shows (in schematic form) two types of combined microreactor-heat exchanger. The cross-section of a parallel flow-type microreactor-heat exchanger is shown in Figure 7.12a. For this, microchannels (0.06mm wide and 0.9mm deep) are fabricated on both sides of a thin (1.2mm) metal plate. The channels on one side are for the reaction fluid, while those on the other side are for the heat-transfer fluid, which flows countercurrently to the reaction fluid. The sketch in Figure 7.12b shows a crossflow-type microreactorheat exchanger with microchannels that are 0.1\u00d7 0.08mm in cross section and 10mm long, fabricated on a metal plate. The material thickness between the two fluids is 0.02\u20130.025mm. The reaction plates and heat-transfer plates are stacked alternately, such that both fluids flow crosscurrently to each other. These 7.9 Microreactors 129 microreactor systems are normally fabricated from silicon, glass, metals, and other materials, using mechanical, chemical, or physical (e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.2-1.png", + "caption": "FIGURE 2.2. Position vector of point P when local frames are rotated about the Z-axis.", + "texts": [ + " The position vector rl of PI can be expressed in body and global coordinate fram es by XIZ+ YI.J +zlk x.i + ylJ + ZIK X l = Xl YI = YI zl = Zl (2.9) (2.10) (2.11) where B r l refers to the position vector rl expressed in the body coordinate frame B , and Gr l refers to the position vector rl expressed in the global coordinate frame G. If th e rigid body undergoes a rotat ion c\u00a5 about th e Z-axis, t hen th e local frame Oxyz , point P , and th e position vector r will be seen in a second position, as shown in Figure 2.2. Now the position vector r 2 of P2 is expressed in both coordinate frames by X2Z + Y2) + Z2 k x2i + Y2J + Z2K. (2.12) (2.13) Using th e definition of the inner product and Equ ation (2.12) we may 2. Rotation Kinematics 35 write or equivalently j . r2 = j . X2 2+ j . Y2) + j . Z2 k j . r2 = j . X2 2+ j . Y2) + j . Z2 k k . r2 = k . X22 + k . Y2)+ k . Z2k (2.14) (2.15) (2.16) [ Z. 2 J . 2 k '2 j .) j. ) k .) i. ~ ] J\u00b7k k .t. (2.17) The elements of the Z -rotation matrix, Qz.\u00ab, are called the direction cosines of B r 2 with respect to OXYZ" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002723_j.ijleo.2016.06.115-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002723_j.ijleo.2016.06.115-Figure1-1.png", + "caption": "Fig. 1. A schematic representation of solution domain.", + "texts": [ + " The governing equation for heat transfer of 3D heat conduction is given as follows: k ( \u22022 T \u2202x2 + \u2202 2 T \u2202y2 + \u2202 2 T \u2202z2 ) + Q = cp \u2202T \u2202t (1) where T and t is temperature and time respectively, , k, cp is density, thermal conductivity and specific heat, respectively to metal powder and substrate material. Q is heat generated per volume within the media. The initial temperature T0 is set as 300 K. The boundary condition, for inside conduction and surface convection and radiation, can be expressed as [18]: k \u2202T \u2202n \u2212 q + h (T \u2212 T0) + \u03b5 ( T4 \u2212 T4 0 ) = 0 (2) where n is vector of powder surface, q is input heat flux, h is coefficient of heat convection, is Stefan-Boltzmann constant, and \u03b5 is emissivity. A schematic representation of solution domain is shown in Fig. 1. The model includes an underneath metal substrate and upside AlSi10Mg powder bed with respective dimension of 2.4 mm \u00d7 0.5 mm \u00d7 0.4 mm and 2 mm \u00d7 0.1 mm \u00d7 0.25 mm. The layer thickness is 50 m and five layers are built-up. The laser scanning direction is along X-axis. For exact calculation, powder part is meshed by minor Solid70 element with dimension of 0.02 mm \u00d7 0.01 mm \u00d7 0.01 mm. The substrate is meshed as a larger non-uniform grid. The model is meshed into 49,000 elements and 55,726 nodes. Also, the model is symmetric with respect to X-Z plane so that only half needs to be modeled to decrease computational time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001325_tia.2014.2321029-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001325_tia.2014.2321029-Figure5-1.png", + "caption": "Fig. 5. (a) Parallel gear stage, (b) dynamic model representation, and (c) model representation in Simscape/SimDriveline.", + "texts": [ + " These studies, however, focus on the internal dynamics of the gearbox, and the developed model packages are not readily compatible with available wind turbine aeroelastic CAE tools. In this paper, a purely torsional model of the gearbox with constant meshing stiffness is built in the Simscape/ SimDriveline environment. The model development and analysis on both planetary and parallel gear stages will be discussed in this subsection, followed by some remarks on the integration and simulation of this model with the aeroelastic CAE tool of interest (i.e., FAST) in Section VI. 1) Parallel Gear Stage: Fig. 5a shows a parallel gear set, which is a torque reducer, commonly employed in wind turbine drivetrains. Fig. 5b represents its flexible equivalent, in which the meshing stiffness acts along the line of action of the meshing gears. This meshing stiffness kmesh, with respect to the input gear, can be represented as [15]: 2 1 )cos( bgearmesh rkk where the gear tooth stiffness kgear can be determined according to standards [26]\u2013[27]. 2) Planetary Gear Stage: Fig. 6 shows a planetary gear set with three planet gears, which is a similar configuration to the one installed in the GRC turbine. The rotational input is from the carrier of the planetary gear stage, which provides rotational motion through the planet gears, and finally to the sun gear. The ring gear is modeled to have flexible coupling with the fixed gear housing. Flexibility between the meshing planet and ring gears and between the meshing planet and sun gears can be modeled similar to that of a parallel gear set using (4), as shown in Fig. 5b. Fig. 7 shows a purely torsional model of a planetary gear set built in the Simscape/SimDriveline (4) 0093-9994 (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. environment. This model can be adapted for any M equispaced-planet gear set. Eigenfrequencies of a system can be found either analytically or numerically. Equations of motion of a wind turbine drivetrain are used to compute the eigenfrequencies in [18], [24]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003605_j.jmatprotec.2020.116723-Figure23-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003605_j.jmatprotec.2020.116723-Figure23-1.png", + "caption": "Fig. 23. R directions for T2. (a) Forward deflection. (b) Without deflection. (c) Backward deflection.", + "texts": [ + " Besides, since the arc pressure decreases when the arc length increases, as shown by Fan and Shi (1996), Fa decreases when the welding arc is deflected. Furthermore, as described by Li et al. (2016), an additional electromagnetic force (Fm) is introduced to the weld pool when MAO is applied. As shown in Fig. 22, the direction of Fm is the same as the arc deflection. The influence of Fm on the movement of the molten metal was evident for T2 because the frequency of oscillation was low. As demonstrated in Fig. 23, Fr changes its direction when Fm is acting. For T3 and T4, which were at high frequencies of oscillation, the weld pool did not change its movement because of its inertia. Eq. 13 presents the formula to calculate Fm. = \u00d7Fm J B (13) where J is the current density. In this work, the influence of Magnetic Arc Oscillation on the geometry of steel and titanium walls produced by GTAW-WAAM and the process stability was investigated. Based on the results, the main conclusions are: (1) Magnetic Arc Oscillation can minimize the overflow of the weld pool, make walls thinner, improve the distribution and homogeneity of material along the wall length and increase the deposition efficiency" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure15.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure15.6-1.png", + "caption": "FIGURE 15.6. An inverted pendulum.", + "texts": [ + " In case of a path given by q = qd(t) , we define a modified PD controller in the form Q = D(q)qd + C(q, q)qd + G(q) - kDe - kj-e and reduce the closed-loop equation to D(q)e + (C(q, q) + kD ) e + kj-e = O. (15.97) (15.98) The linearization of this equation about a control point q = qd = cte pro vides a stable dynamics for the error signal (15.99) 15.4 Sensing and Control Position, velocity, acceleration, and force sensors are the most common sensors used in robotics. Consider the inverted pendulum shown in Figure 15.6 as a one DOF manipulator with the following equat ion of motion : ml2(j - cO - mgl sin () = Q. (15.100) From an open-loop control viewpoint , we need to provide a moment Qc(t) to force the manipulator to follow a desired path of motion (}d(t) where (15.101) In robotics, we usually calculate Qc from the dynamics equation and dictate it to the actuator. 656 15. Control Techniques The manipulator will respond to the applied moment and will move. The equation of motion (15.100) is a model of the actual manipulator", + " Control Techniques and reduce the system to a third-order equation in an error signal. Then, find the PID gains such that the characteristic equation of the system simplifies to 4. Linearization. Linearize the given equations and determine the stability of the lin earized set of equations. 2= X2 + Xl COSX2 X2 + (1+ Xl + X2)Xl + Xl sin z-, 5. Expand the control equations for a 2R planar manipulator using the following control law: 6. One-link manipulator control. A one-link manipulator is shown in Figure 15.6. (a) Derive the equation of motion. (b) Determine a rest-to-rest joint path between 8(0) = 45 deg and 8(0) = -45 deg. (c) Solve the time optimal control of the manipulator and determine the torque Qc(t) for m = 1kg l 1m IQI < 120Nm. (d) Now assume the mass is m = 1.01kg and solve the equation of motion numerically by feeding the calculated torques Qc(t). Determine the position and velocity errors at the end of the motion. (e) Design a computed torque control law to compensate the error during the motion " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure6.14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure6.14-1.png", + "caption": "Figure 6.14.1 Rigid axle with leaf-spring location and steering.", + "texts": [ + " Before the introduction of independent front suspension, all cars had a rigid front axlewith steering. They suffered from a variety of rather severe steering problems. When the rigid axle with longitudinal leaf springs is used at the front, as on some trucks and off-road vehicles even today, it is subject to all the effects described earlier, plus additional effects because of the steering linkage. The critical steering link is always the one that connects the sprung and unsprung parts of the steering. Figure 6.14.1 shows a typical arrangement with front steering and a rear spring shackle. Here CD is the drag link, D is the connection to thewheel hub, and C is the connection to the Pitman arm on the steering box, fixed to the sprung mass. When the axle moves, D has an ideal no-steer arc centred on the ideal centre E. If E and C do not coincide, there will be steering errors. As early as the 1920s, it was attempted tomatch the E andCpositions for rollmotions, butwith disappointing results. The reason is that the arc of D is different for each of roll, single-wheel bump, and heave, and different again with braking 140 Suspension Geometry and Computation because of axle wind-up" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003462_j.prostr.2017.11.061-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003462_j.prostr.2017.11.061-Figure1-1.png", + "caption": "Fig. 1. Specimens 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 (2015).", + "texts": [ + " As a complementary assessment, the defect population of the samples was studied through micro X-ray Computed Tomography (\u00b5CT). The authors expect with this work to encourage further studies on the effect of the process parameters on the fatigue behaviour, envisioning the adjustment and improvement of the Processing-Structure-Properties-Performance relationships of AlSi10Mg produced via Additive Manufacturing. 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. 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 J.mm3, used to produce high quality parts, and a set with 90 \u00b5m layer thickness at about 22 J.mm-3 for a drastically increased build up rate. The energy input (E) is described in Eq.1 where P is the laser power (in J.s-1), v is the scan velocity (in mm.s-1), dh is the hatch distance (in mm) and hth is the layer thickness (in mm) (Thijs et al", + " Both inner hatch parameter sets used a scan regime which rotates the hatch orientation about 67\u00b0 from layer to layer to reduce the texture in the grain structure. Furthermore the majority of the samples were produced on a pre heated build plate at 165 \u00b0C except condition ID 1 where the base plate heating was set to 35 \u00b0C. \ud835\udc38\ud835\udc38\ud835\udc38\ud835\udc38 = \ud835\udc43\ud835\udc43\ud835\udc43\ud835\udc43/(\ud835\udc63\ud835\udc63\ud835\udc63\ud835\udc63 \u00d7 \ud835\udc51\ud835\udc51\ud835\udc51\ud835\udc51\u210e \u00d7 \u210e\ud835\udc61\ud835\udc61\ud835\udc61\ud835\udc61\u210e ) (1) Author name / Structural Integrity Procedia 00 (2017) 000\u2013000 3 The milled specimens (ID 1 to 6) were printed as bars and then machined to the geometry shown in Fig. 1c. For the net shaped specimens, the surface was either jet blasted (ID 9 to11) with \u201cIEPCONORM_C\u201d (iepco ag), or treated through vibratory polishing (ID 7 and 8), or left in its \u201cas built\u201d condition without surface treatment (ID 12). The heat treatment used in conditions ID 1, 3 and 5 was applied to reduce the residual stresses present in the specimens, which are characteristic of the additive manufacturing process (Tang and Pistorius (2017)). Ana D. Brand\u00e3o et al. / Procedia Structural Integrity 7 (2017) 58\u201366 61 4 Author name / Structural Integrity Procedia 00 (2017) 000\u2013000 The characterization of the specimens comprised an analysis of the defect population present in a selected number of samples", + " (2012); Aboulkhair et al. (2016); Mower and Long (2016); Greitemeier et al. (2016)). The higher roughness is often described as the root cause for this trend, as it might allow earlier crack initiation from the free surface, working as a stress concentration region. This work shows that different post-process treatments, such as jet blasting (ID 9 to 11) or vibratory polishing (ID 8) result into very similar fatigue performances for the same process parameters. However, when the contour parameter (illustrated in Fig. 1b) was excluded the fatigue behaviour is significantly improved to levels similar to the ones exhibited by the milled specimens. To the best of our knowledge the influence of this parameter in mechanical properties has never been studied. As such, further investigation is needed in order to understand the impact of this change in the scan strategy during the AM process, in the fatigue properties as well as in the microstructure of the AM samples. In addition, it is observed that the selected heat treatment (applied only to the samples produced with a layer thickness of 90 \u00b5m, ID 1 and ID 5) has a detrimental effect on the fatigue properties on the AlSi10Mg specimens, at the stress level tested" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001039_tfuzz.2013.2279543-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001039_tfuzz.2013.2279543-Figure2-1.png", + "caption": "Fig. 2. Two inverted pendulums connected by a spring and a damper.", + "texts": [ + " In particular, in (97), if the values of the constraint parameter, \u03c1i,jl (t) and \u03b4i,jl , are selected as ei,jl (t)/\u03c1i,jl (t) \u2192 \u00b11 or ei,jl (t)/\u03c1i,jl (t) \u2192 \u00b1\u03b4i,jl , then \u2202Ri,jl \u2192 \u00b1\u221e, and the resulting error increases, which can give rise to the closed-loop system stability problem and to a violation of the prescribed constraint conditions. V. APPLICATION EXAMPLE In this section, we present a simulation conducted using a nonlinear MIMO system to evaluate the performance of our prescribed partial error constraints against uncertainties. Two inverted pendulums composed of spring and damper connections, and nonlinear friction, as shown in Fig. 2, were used as a control system for the constraint problem of the full-state tracking errors [17]. The pendulum angle and angular velocity were controlled using the torque inputs generated by a servomotor at each base. The dynamic equation of the inverted pendulum can be described as J1 \u03b8\u03081 = m1gr sin \u03b81 \u2212 0.5Fr cos(\u03b81 \u2212 \u03b8) \u2212 Tf1 + u1 (98) J2 \u03b8\u03082 = m2gr sin \u03b82 + 0.5Fr cos(\u03b82 \u2212 \u03b8) \u2212 Tf2 + u2 (99) where \u03b81 and \u03b82 are angular positions, J1 = 0.5 kgm2 and J2 = 0.625 kgm2 are the moments of inertia, m1 = 2 kg and m2 = 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002651_17452759.2018.1442229-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002651_17452759.2018.1442229-Figure6-1.png", + "caption": "Figure 6. Additional features designed for reference and clamping purposes during 5-axis CNC machining: (a) fixtures supporting the bracket during machining operations and (b) fixture for boring operation and cutting of additional features.", + "texts": [ + " A 5-axis CNCmachine is considered for the finishing process, with two different bracket positionings. Two additional features were designed for the first positioning, and these were used as the main reference. These features are two arms with a final cylindrical perforated part that allows the passage of a screw and coupling with a threated hole that is located in a square block. The arms are linked directly to the bracket and will subsequently be removed: these features are highlighted in green in Figure 6. Another element is the base on which the upper part of the bracket will be placed: this element is the red\u2013purple component in Figure 6(a) and includes a sliding cylinder to hold the component. This fixture has not been integrated in the part design, but it may be fabricated by means of AM. In this way, all the PART REQUIREMENTS OPTIMAL DESIGN FINAL DESIGN Adding allowances and features for finishing TO D4L-PBF FEA (a) (c) (d) (e) (b) Figure 5. Application of the integrated L-PBF methodology to a case study. degrees of freedom of the part are constrained. After finishing the rear area of the structure and the hole coupled with the bearing, the part is rotated by 180 degrees, and the same auxiliary arms are used to hold the bracket during the boring operation (Figure 6(b)). The last operation involves cutting off the auxiliary arms. The weight of the final part is 0.115 kg, which, compared to the initial mass of the bracket corresponding to the maximum envelope, means a reduction in weight of 63% (Figure 5(e)). The final model (Figure 7) is produced using an EOSINT M 270 Dual Mode machine. This type of machine uses a 200 W fiber laser, with a wavelength of 1060\u20131100 nm, focused on a 0.1 mm diameter to melt the metallic powder. The layer was 30 \u03bcm thick and the building platform was kept at 100\u00b0C" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002922_j.ymssp.2018.05.028-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002922_j.ymssp.2018.05.028-Figure5-1.png", + "caption": "Fig. 5. Geometry of contacting bodies. (a) Ball-outer-raceway contact, and (b) ball-inner-raceway contact.", + "texts": [ + " The normal contact force calculation between the ball-outer raceway is similar to that of the ACBB, which is also based on their geometrical relationship and Hertz contact theory. Detailed modeling process can refer to [16,18] and won\u2019t be repeated in this section. However, some attention should be made when calculating the Hertz contact stiffness coefficient Kbir between the ball and inner raceway due to their special contact form. The detail is explained as follows. The contact form between the ball-inner raceway and ball-outer raceway is different, and the geometry of ball-outerraceway contact and ball-inner-raceway contact are shown in Fig. 5(a) and (b), respectively. In Fig. 5 (a), \u2018\u2018Body I\u201d and \u2018\u2018Body II\u201d represent the outer raceway and the ball, respectively. The \u2018\u2018Plane 1\u201d represents the plane along the axial direction, i.e., \u2018\u2018Plane 1\u201d always passes through the X axial and is perpendicular to the Y-Z plane. \u2018\u2018Plane 2\u201d represents the plane orthogonal to the \u2018\u2018Plane 1\u201d, and \u2018\u2018Plane 2\u201d is always parallel to the Y-Z plane. The radii of curvatures of the outer raceway and ball in two main planes can be given by rI1 \u00bc f od; rI2 \u00bc d\u00f01\u00fe c\u00de 2c ; rII1 \u00bc d=2; rII2 \u00bc d=2; \u00f05\u00de where c \u00bc d cosao dm , where ao denotes the contact angle between the ball and outer raceway and dm denotes the bearing pitch diameter. In Fig. 5 (b), \u2018\u2018Body I\u201d and \u2018\u2018Body II\u201d represent the ball and inner raceway, respectively. The radii of curvatures of the ball and inner raceway in two main planes can be expressed by rI1 \u00bc d=2; rI2 \u00bc d=2; rII1 \u00bc 1; rII2 \u00bc rIRo; \u00f06\u00de As the Hertz contact coefficient is related to curvature and curvature sum of the two contacting bodies, the differences of the curvature between the ball-inner-raceway contact and the ball-outer-raceway contact should be considered when calculating the Hertz contact coefficients" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003820_tits.2020.2987637-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003820_tits.2020.2987637-Figure2-1.png", + "caption": "Fig. 2. ITSC motor model.", + "texts": [ + " As to this machine, the windings are concentrated around the stator teeth, and the number of parallel branches of each phase winding is 2. Fig. 1 is a schematic diagram of ITSC fault, assuming one branch of phase C has ITSC faults and the fault winding in series. Table I shows the main parameters of the PMSM. A 2D FEM of the PMSM without considering control method is carried out and simulated, which focuses on the intrinsic characteristics of ITSC fault. ITSC fault occurs in the bottom of the slot, shown as Fig. 2. The external circuit model of the inter-turn short circuit is shown in Fig. 3. A contact resistance R f is adopted in this model to represent the fault path, whose value R f depends on many factors, such as heating caused by fault current, duration of the short circuit and property of insulation material. Generally, ITSC fault starts from a small winding insulation breakdown, causing a certain amount of fault current I f to further damaging the insulation. Under this effect, R f quickly decreases and I f increases" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.17-1.png", + "caption": "Fig. 4.17 Six-bar dwell linkage", + "texts": [ + " Finding the corresponding time derivatives of such equations allows us to solve the velocity analysis. 10. In Example 4.7 we considered that v4 D !2. Give a justification, if any, for this assumption. 11. The Geneva wheel of Example 4.7 is a little case that illustrates how easy it is to formulate the velocity analysis of parallel manipulators when reciprocal screw theory is used. Determine the input\u2013output equation of velocity of the planar parallel manipulators shown in Fig. 4.16 by resorting to reciprocal screw theory. 4.4 Exercises 95 12. The link c of the six-bar dwell mechanism in Fig. 4.17 rotates with a generalized velocity Pq. The topology of the mechanism is such that the angular velocity Pq produces an oscillatory linear velocity Px. Determine the input\u2013output equation of velocity of the planar mechanism. 13. The mechanism shown in Fig. 4.18 is used to produce high torque in the shaft at B and is a good example to which to apply screw theory. The gear unit is pivoted at A and produces a constant angular velocity of 5 rad/s counterclockwise as observed from A to C over the right-hand screw", + " The input\u2013output equation of velocity of the robot at hand results in JT 0V3 D Pq; where J D $1 $2 $3 is the screw-coordinate Jacobian matrix of the robot where $1 and $2 are lines in Pl\u00fccker coordinates pointed from their respective points Bi to points Ci, while $3 is a line in Pl\u00fccker coordinates pointed from point A3 to point C3. Furthermore, is an operator of polarity, while Pq D Pq1 \u02da 0$1 1I $1 Pq2 \u02da 0$1 2I $2 Pq3 T is the first-order driver matrix of the parallel manipulator under consideration. 12. The link c of the six-bar dwell mechanism (see Fig. 4.17) rotates with a generalized velocity Pq. The topology of the mechanism is such that the angular velocity Pq produces an oscillatory linear velocity Px. Determine the input\u2013output equation of velocity of the planar mechanism. Six-bar dwell mechanism. Infinitesimal screws Solution. Referring to the above figure, we can obtain the velocity state of the moving platform m as observed from the fixed platform 0 by solving the kinematics of the four-bar linkage indicated by the loop L1. Then the velocity state may be written in screw form through the third limb as follows: Px0$1 3 C 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002761_j.ijplas.2019.06.002-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002761_j.ijplas.2019.06.002-Figure1-1.png", + "caption": "Fig. 1. Tensile specimens on their respective build plates (a) and laser path (b) with respect to processing frame where BD is build direction, RD is recoat direction, and GF is gas flow direction. Vertical and diagonal samples were fabricated together in one build session, and horizontal in a separate session.", + "texts": [ + " Elemental composition of the powder is provided in Table 1 and was determined by Praxair Surface Technologies via inductively coupled plasma mass spectrometry (ICP-MS) and a LECO combustion infrared detection technique. Tension and compression samples were built on top of a steel plate while being supported by an additively manufactured scaffolding structure, which was built simultaneously with the samples (also made of MM509). A schematic of the tensile specimens on the build plate is shown with respect to the processing frame in Fig. 1a. Processing parameters for the MM509 samples were based on the EOS LPBF IN718_Performance 1.0 parameter set (2014) that uses a scan speed of 960.0mm/s and laser power of 285.0W. The same set was used in a number of other studies (Gribbin et al., 2019; Kelley et al., 2015). The optimal parameters for MM509 were a slightly elevated laser power and a slightly slower rastering speed relative to the parameters for Inconel. Laser spot diameter at the melt pool was approximately 100 \u03bcm. When rastering, the laser performed a series of linear passes across the powder surface until a single layer was completed. The recoater then removed any debris that resulted from the sintering and re-applied a new 40 \u03bcm thick layer of powder to the surface. The direction of the laser path was then rotated 67\u00b0 counterclockwise, as shown in Fig. 1b, and the process was repeated. The motivation for this rotation parameter is explained in Gribben et al. (Gribbin et al., 2016) and aims to eliminate material anisotropy. During manufacturing, the build chamber was sealed to prevent contamination and had a constant flow of ultra-high purity (UHP) Ar with O2 content< 0.1%. Moreover, the build plate was kept at 80 \u00b0C to reduce loading by thermal cycles. The laser power was high enough to melt two or three previously sintered layers in addition to the newly coated powder layer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.40-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.40-1.png", + "caption": "FIGURE 5.40. Assembled spherical wrist .", + "texts": [], + "surrounding_texts": [ + "5. Forward Kinematics 259\nLab el the coordinat e frames attached to the spherical wrist in Fig ure 5.40 according to the frames that you inst alled in Exercise 10. Determine the transformation matrices 3T6 and 3T7 for the wrist.\n12. Articulat ed robots .\nAttach the spherical wrist of Exercise 11 to the articulated manip ulator of Exercise 7 and make a 6 DOF art iculated robot . Change your DR coordinate frames in the exercises accordingly and solve th e forward kinematics problem of the robot .\n13. Spherical robots.\nAttach the spherical wrist of Exercise 11 to the spherical manipulator of Exercise 8 and make a 6 DOF spherical robot . Change your DR coordinate frames in the exercises accordingly and solve the forward kinematic s problem of the robot.", + "260 5. Forward Kinematics\n14. Cylindrical robots.\nAttach the spherical wrist of Exercise 11 to the cylindrical manip ulator of Exercise 9 and make a 6 DOF cylindrical robot. Change your DR coordinate frames in the exercises accordingly and solve the forward kinematics problem of the robot.\n15. An RIIP manipulator.\nFigure 5.41 shows a 2 DOF RIIP 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 261\n17. SCARA manipulator.\nA SCARA robot can be made by attaching a 2 DOF RIIP manipulator to a 2R planar manipulator. Attach the 2 DOF RIIP manipulator of Exercise 15 to the 2R horizontal manipulator of Exercise 16 and make a SCARA manipulator. Solve the forward kinematics problem for the manipulator.\n18. * SCARA robot with a spherical wrist.\nAttach the spherical wrist of Exercise 11 to the SCARA manipulator of Exercise 17 and make a 7 DOF robot. Change your DH coordinate frames in the exercises accordingly and solve the forward kinematics problem of the robot .\n19. * Modular articulated manipulators by screws.\nSolve Exercise 7 by screws.\n20. * Modular spherical manipulators by screws.\nSolve Exercise 8 by screws.\n21. * Modular cylindrical manipulators by screws.\nSolve Exercise 9 by screws.\n22. * Spherical wrist kinematics by screws.\nSolve Exercise 11 by screws." + ] + }, + { + "image_filename": "designv10_3_0003846_j.renene.2018.01.072-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003846_j.renene.2018.01.072-Figure2-1.png", + "caption": "Fig. 2. Finite element models of sun-planet and ring-planet pairs. (a) sun-planet pair and (b) ring-planet pair.", + "texts": [ + " A more comprehensive description for mesh phase relations in planetary gears can be found in Ref. [38]. The above parameters of time-varying mesh stiffness and transmission error can be pre-determined through loaded tooth contact analysis (LTCA). To formulate the time-varying mesh stiffness accurately, a three-dimensional finite element model for the sun-planet (as well as the ring-planet) gear pair with/without incipient fault is developed in ABAQUS/Standard. The related parameters of the planetary gear train can refer to Table 2. As shown in Fig. 2, a tooth crack with a depth of 0.25mm is set on the sun gear, which is quite small compared to the tooth thickness. This crack level is assumed to be an incipient fault. The reducedintegration element C3D8R is adopted to mesh the whole bodies of the engaged gears, which can avoid locking phenomena in the finite element analysis to guarantee the accuracy of the solution [39e41]. The material of gears is linearly elastic with Young's modulus E\u00bc 2.06 105MPa and Poisson's ratio n\u00bc 0.3. The tooth conjunction is modeled as general contact which includes elastic Coulomb frictional effects", + " In these finite element models, Newton-Raphson algorithm is used to solve the contact problem of gear pairs including the geometric nonlinearity and contact interface nonlinearity. Taking the sun-planet pair as an example, the tooth with root crack is discretized with refined grids while the rest part has relatively coarse grids. The total element number is 196,700, the total node number is 225,401 and the total DOF number of the model is 676,203. The number of gauss integration points is 196,700. The complete finite element model is shown in Fig. 2(a). Two reference points are created at the centers of input gear and output gear, which are connected to the gear hubs with coupling constraints. The output gear is fixed and the input gear is set to rotate only about its rotational axis. A torque is applied at the rotational axis of the input gear to make the input and output gear tooth surfaces contact with each other. The torsional mesh stiffness of the meshing gears Kmt can be calculated as Kmt \u00bc TFI qRF (12) where TFI is the input torque applied on the input gear, qRF is the resulting rotation angle of the input gear hub" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.35-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.35-1.png", + "caption": "Fig. 6.35 Free-body diagram for \u03d5\u0307M \u2261 \u03a9", + "texts": [ + "377) is the mass matrix, C = [ cV + (cL + cZ) cos2 \u03b1 \u2212 (cL \u2212 cZ) cos \u03b1 \u2212 (cL \u2212 cZ) cos \u03b1 cL + cZ ] (6.378) 6.6 Damped Vibrations 459 is the stiffness matrix, B = [ bV + 2b cos2 \u03b1 0 0 2b ] (6.379) is the damping matrix, and f = [ U\u03a92 sin \u03a9t; 0 ]T . (6.380) is the right-hand side vector (U = me). One would also have obtained the system of the equations of motion (6.376) if the equilibrium conditions had been established at both wheels in the free-body diagram, taking into account d\u2019Alembert\u2019s principle, see Fig. 6.35. The reader is encouraged to verify this way of establishing the equations of motion for himself/herself. The forces in the slack and driving strands result both from the pretensioning and from the deformations caused by the vibrations (see (6.365)) and their variations over time: FL = Fv 2 cos \u03b1 + cL(R\u03d5\u2212 r\u03a9t\ufe38 \ufe37\ufe37 \ufe38 =q2 \u2212q1 cos \u03b1) + b(R\u03d5\u0307\u2212 r\u03a9\ufe38 \ufe37\ufe37 \ufe38 =q\u03072 \u2212q\u03071 cos \u03b1) (6.381) FZ = Fv 2 cos \u03b1 + cZ(r\u03a9t\u2212R\u03d5\ufe38 \ufe37\ufe37 \ufe38 =\u2212q2 \u2212q1 cos \u03b1) + b(r\u03a9 \u2212R\u03d5\u0307\ufe38 \ufe37\ufe37 \ufe38 =\u2212q\u03072 \u2212q\u03071 cos \u03b1). (6.382) The motor torque required for generating the predefined motion \u03d5M(t) = \u03a9t is derived from the equilibrium of moments at the motor armature: MM = (FZ \u2212 FL)r + U cos \u03a9t \u00b7 q\u03081" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure28-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure28-1.png", + "caption": "Fig. 28. Contact and bending stresses at a contact point of the face-gear in examples: (a) 2 and (b) 3.", + "texts": [ + " 28\u201331 show the results of stress analysis and formation of the bearing contact. Details of elements of the three tooth model (Fig. 8) area as follows: First order elements (enhanced by incompatible modes to improve their bending behavior [3]) have been used to form the finite element mesh. The total number of elements is 71,460 with 87,360 nodes. The material is steel with the properties of Young s modulus E = 2.068 \u00b7 105MPa and Poisson s ratio 0.29. A torque of 4000Nm has been applied to the pinion in the three cases. Fig. 28(a) and (b) show the formation of the bearing contact on the face-gear tooth surface in examples 2 and 3, respectively. The path of contact is orientated longitudinally and edge contact is avoided. The dimensions of the contact ellipse are increased in example 3. Fig. 29(a) and (b) show the formation of the bearing contact on the pinion surface for examples 2 and 3, respectively. Fig. 29(b) shows that a severe contact area appears in the pinion surface in example 3, but the stresses are still allowable" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure4.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure4.1-1.png", + "caption": "Figure 4.1.1 Some example tyre types and tread forms (Goodyear).", + "texts": [ + " Bump and body heave influence the wheel camber and steer angles relative to the body and road, and also influence the spring and damper forces and hence the tyre vertical force. These all influence the tyre lateral force. The terms \u2018bump\u2019 and \u2018droop\u2019 may also be applied to velocities to show the direction of motion; in that case it should be borne inmind that a bump velocitymay occur in a droop position, and vice versa. Bump velocities also affect the slip angle because of the scrub velocity component. Body roll in cornering gives a combination of bump and droop on opposite wheels, relative to the body. Figure 4.1.1 shows an assortment of tyres with widely varying tread patterns for various applications. For a given vehicle, the best wheel/tyre width and tread form depend on the road material (tarmac, mud, snow, surface water, etc.) and surface shape (roughness, etc.). Tyre geometry can be an extremely complex subject, particularly for the analysis of carcase reinforcement, which will not be discussed here; this section covers only basic wheel and tyre deflection geometry and terminology. Figure 4.2.1 gives the basic dimensional definitions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001831_j.mechmachtheory.2011.08.009-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001831_j.mechmachtheory.2011.08.009-Figure1-1.png", + "caption": "Fig. 1. Coordinate systems of a universal form grinding machine.", + "texts": [ + " However, in this proposed correction method, the machine settings of the CNC machine are still translated from the universal machine. In order to explain clearly, the previous mathematical models are rewritten in this section. According to the theory of conjugate surfaces, the contact lines on the work gear and the wheel construct their respective surfaces; hence, using a work gear as a virtual tool for inversely grinding the wheel allows derivation of the wheel axial profile. This spatial relationship between the wheel and the ground work gear in the universal form grinding machine is shown in Fig. 1. Such a virtual machine has three universal machine settings, Et, \u03b3m, and Lt, the center distance between the wheel and work gear centers, the setting angle of the wheel, and the axial movement along the workpiece axis, respectively. In standard operation, the first two terms are constant and the last is a linear function of the work gear's rotation angle \u03d51. Although in general, the setting angle of the wheel \u03b3m is equal to the helical angle of the work gear, occasionally that angle is adjusted slightly to control the shape of the contact line, thereby improving the grinding condition [3]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003209_j.mechmachtheory.2016.11.015-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003209_j.mechmachtheory.2016.11.015-Figure4-1.png", + "caption": "Fig. 4. The analyzed FE model of the meshing spur gears.", + "texts": [ + " This technique was utilized in order to maintain the quality of FE elements. In order to assess the proposed strategy for multi-objective optimization of gear micro-geometry, a pair of identical spur gears was analyzed, for which Table 1 summarizes the geometric parameters. Below, we provide a short presentation of the utilized FE model, description of each of the output quantities and their meaning to gear design. The procedure of tooth profile modification was carried out on the FE model shown in Fig. 4. The gear bodies and teeth were discretized using three-dimensional hexahedral elements, while the shafts were simplified to rigid representations. It is worthy to point out that the region of the gears, in which no contact was expected, was discretized using a coarse FE grid. Conversely, in the case of teeth for which meshing contact was foreseen, smaller elements were used. The size of the FE mesh in contact region was determined using the convergence analysis, which was carried out on a set of models constructed with different FE mesh refinements" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001785_j.ymssp.2016.11.012-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001785_j.ymssp.2016.11.012-Figure3-1.png", + "caption": "Fig. 3. The active suspension testing platform.", + "texts": [ + " From the composition of (28), the initial value of F\u0394 is included in the \u03f11 and it is always nonzero. Note that predicting the initial data of F\u0394 is not a simple task in practice. Therefore, under this nonzero condition, it needs some finite time to start the sliding mode, while the time could be made arbitrarily small through selecting the proper design parameters c's as [39]. When \u03f11 and \u03f12 reach the sliding mode, and the state of \u03f1\u03071 stays on the sliding surface for all the time. This section is to implement the presented controller to the active suspension plant as shown in Fig. 3, which is a physical setup resembling a quarter-car suspension in the laboratory. By using this experimental setup, some comparative experimental results are provided to verify the validity of the presented control approach in both trajectory tracking performance and disturbance rejection. In the subsequent parts, the model data used are given in Table 1. The experimental setup is mainly composed of three plates/masses in the vertical direction, which can move independently of one another. Driven by a brushed servo motor with a lead screw and cable transmission subsystem, the bottom plate is devoted to produce the road inputs and system disturbance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002007_j.csefa.2012.11.003-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002007_j.csefa.2012.11.003-Figure1-1.png", + "caption": "Fig. 1. Component of (a) Ball and (b) Roller Bearing [2,5].", + "texts": [ + " Ball bearings can be divided into three categories, i.e. radial contact, angular contact, and thrust. Radial-contact ball bearings are designed to support radial loads. Angular contact bearing designed to support combination of radial and axial loads. Thrust bearings designed to support axial loads. Roller bearings have higher load capacities than ball bearings for a given size and are usually used in moderate speed heavy-duty applications. The preliminary types of roller bearings are cylindrical, needle, tapered, and spherical roller bearing. Fig. 1 shows the component of ball bearings and roller bearings [2,5]. The service life of bearings [3] is expressed either as a period of time or as the total number of rotations before the occurrence of failures in the inner ring, outer ring or in rolling element (ball or roller) because of rolling fatigue, due to repeated stress. Rated life of bearing expressed as the period at which equipment or machine element fails under specified condition of use given by its manufacturer. The service life of bearing differs from rated life, where bearing failure may cause by poor lubrication, misalignment, and mounting damage before its actual life" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.35-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.35-1.png", + "caption": "FIGURE 5.35. A one-link m-R( -90) manipulator.", + "texts": [ + " Describe the meaning of a- Bi b- a i [ \u00a2u ] d- s(di ,Bi ,ki-1) e- RIIR(180)c- hu f- i- 1Ti g- @ h- [ Bi~i-l ] i- s(h ,\u00a2, u) j- Pl-R( -90) d; ki- 1 k- d; 1- a; [ a i ii - l ] n- s (ai, ai,ii- l ) 0 - m-R(-90) .m- A ai 2i - l 2. A 4R planar manipulator. For the 4R planar manipulator, shown in Figure 5.34, find the (a) DR table (b) link-type table (c) individual frame transfo rmation matrices i- 1Ti , i = 1,2 ,3 ,4 (d) global coordinates of the end-effector (e) orientation of the end-effector 'P . 3. A one-link RI-R( -90) arm. 256 5. Forward Kinematics For the one-link Rf-R( -90) manipulator shown in Figure 5.35 (a) and (b) , find the transformation matrices \u00b0T1 , ITz, and \u00b0Tz. Compare the transformation matrix ITz for both frame installations. 4. A 2R planar manipulator. Determine the link 's transformation matrices \u00b0T1, ITz, and \u00b0Tz for the 2R planar manipulator shown in Figure 5.36. 5. A polar manipulator. Determine the link 's transformation matrices ITz, zT3 , and IT3 for the polar manipulator shown in Figure 5.37. 6. A planar Cartesian manipulator. Determine the link 's transformation matrices ITz, zT3 , and IT3 for the planar Cartesian manipulator shown in Figure 5.38. 7. Modular articulated manipulators. Most of the industrial robots are modular. Some of them are manu factured by attaching a 2 DOF manipulator to a one-link Rf-R( -90) arm. Articulated manipulators are made by attaching a 2R planar manipulator, such as the one shown in Figure 5.36, to a one-link Rf-R( -90) manipulator shown in Figure 5.35 (a) . Attach the 2R ma nipulator to the one-link Rf-R( -90) arm and make an articulated manipulator. Make the required changes into the coordinate frames of Exercises 3 and 4 to find the link 's transformation matrices of the articulated manipulator. Examine the rest position of the manipula tor. 5. Forward Kinematics 257 258 5. Forward Kinematics 8. Modular spherical manipulators. Spherical manipulators are made by attaching a polar manipulator shown in Figure 5.37, to a one-link Rf--R( -90) manipulator shown in Figure 5.35 (b) . Attach th e polar manipulator to the one-link Rf--R( -90) arm and make a spherical man ipulator. Make the required changes to the coordinate frames Exercises 3 and 5 to find the link 's transformation matrices of the spherical manipulator. Examine the rest position of t he manipulator. 9. Modular cylindrical manipulators. Cylind rical manipulators are made by at taching a 2 DOF Car tesian manipulato r shown in Figure 5.38, to a one-link RI-R(-90) manip ulator shown in Figure 5.35 (a) . Attach the 2 DOF Cartesian ma nipulator to the one-link Rf--R( -90) arm and make a cylindrical ma nipul ator. Make the required changes into the coordinate frames of Exercises 3 and 6 to find t he link 's t ransformation matrices of the cylindrical manipulator. Examin e the rest position of the manipula tor. 10. Disassembled spherical wrist. A spherical wrist has three revolute joints in such a way that their joint axes inte rsect at a common point, called the wrist point. Each revolute joint of the wrist at taches two links" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003836_978-94-007-6046-2_9-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003836_978-94-007-6046-2_9-Figure15-1.png", + "caption": "Fig. 15 Vertical moment control", + "texts": [ + " In an approach similar to that for avoiding slipping, the allowable range for the yaw moment of the ground reaction force with the target gait is determined from the ground load and the coefficient of floor friction. If the yaw moment of the ground reaction force with the target walking pattern is within the allowable range, then both dynamic stability and avoidance of spin can be achieved. If the allowable range is exceeded, then spin can be avoided by causing the upper body to rotate (twist) around the vertical axis (Fig. 15). The development of this new gait generation technology made it possible to assure dynamic stability during running while limiting slipping and spinning at the instants just before the foot lifts off the floor and just after it lands on the floor. There are also cases of movement such as slow jogging when the ground load does not drop completely to zero, or walking on a floor with a low coefficient of friction, or other of various such dynamic walking patterns. These can now be handled in a uniform manner just by changing the allowable range of the floor friction force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure10-1.png", + "caption": "Fig. 10. Schematic illustration of the arrangement for the finite element mesh about contact point P along: (a) profile, inner, and (b) longitudinal directions.", + "texts": [ + " The volume of each tooth of the model is divided into six subvolumes using auxiliary intermediate surfaces 1\u20136 as shown in Fig. 9(b). Step 3. Node coordinates (Fig. 9(c)) are determined analytically considering tooth surface equations, portions of corresponding rims, and the set of variables for mesh refinement control that are described below. Step 4. Discretization of the model by finite elements using the nodes determined in the previous step is accomplished as shown in Fig. 9(d). Step 5. The set of variables for mesh refinement control affects to the number of finite elements around the contact point P (Fig. 10). A sensitive-contact region is defined around the contact point P as follows: (i) A group of elements of regular size with dimension l\u00d7 l\u00d7 l is created in the sensitive-contact region. (ii) The size l of the elements is controlled by dimension b and number Nb. Here, b is the length of the semi-minor axis of the contact ellipse that Hertz theory predicts; Nb is the number of elements that covers dimension b. Length lmay be obtained as l=b/Nb. (iii) The number of elements of regular size that covers a fraction of dimension a is controlled by number Na", + " Since a\u226bb, Na\u226bNb for the whole contact area to be covered by elements of regular size and this is, in practice, computationally expensive. Beside this, it is expected that pressure distribution has a larger scope along dimension b than along dimension a. These are the reasons why Na is the number of elements of regular size that covers just a fraction of dimension a. (iv) The number of elements of regular size underneath the tooth surface is controlled by number Nd. (v) Three more rows of elements of regular size are added along dimension b, up and down (Fig. 10(a) shows just one row up and one row down for the purpose of simplicity). This establishes the number of elements in the sensitive-contact region as (2Nb+6) \u22c5Na \u22c5Nd. (vi) Size of the elements located out of the sensitive-contact region increase exponentially from such a region towards the borders or the intermediate surfaces of the tooth model. Number of elements in profile, longitudinal, and inner directions are controlled by numbers Np, Nl, and Ns, respectively. A summary of the set of variables for mesh refinement control is shown in Table 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000824_iros.2007.4399407-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000824_iros.2007.4399407-Figure4-1.png", + "caption": "Fig. 4. Double inverted pendulum model used in this example. Parameters are m1 = 35kg, m2 = 35kg, L1 = 1m and L2 = 1m", + "texts": [ + " The resultant posture controller becomes uposture = \u2211 i (E\u2217 i T K\u03c4 (\u03c4d \u2212 \u03c4))E\u2217 i (10) where E\u2217 i is a unit basis vector of the null space and K\u03c4 is a gain matrix that determines how closely the integrator tracks the reference torque, \u03c4d. Because the null-space is associated with all joints except for the ankle, Eq.(10) does not change the ankle torque. However, the reference ankle torque is not ignored, because it was used in the calculation of CoP d, which is tracked using Eq.(9). The entire controller is summarized in the block diagram in Fig. 3. This controller is applied to a planar double inverted pendulum robot, shown in Fig. 4. The center of mass of each link is at the center and there are joint torques at both the ankle and hip joints. The linear quadratic regulator controller was derived by writing linearized dynamics about the upright pose, (\u03b8, \u03b8\u0307)T = (0, 0, 0, 0)T , as( \u03b8\u0307 \u03b8\u0308 ) = A ( \u03b8 \u03b8\u0307 ) + Bu For the properties of the model, given in Fig. 4, and the following manually-chosen Q and R matrices, Q = diag[1e4, 1e6, 1, 10] and R = diag[100, 100] the K matrix became KLQR = [ 1383.0 347.6 508.2 151.0 299.2 366.6 131.6 77.62 ] TABLE I CONTROL PARAMETERS Parameter Value kCMp 400 kCMd 50 kCoP 100 K\u03c4 diag[1e4, 1e4] Fig. 6. Performance comparison of various controllers subject to a horizontal impulse. The other parameters used for the controller are given in Table I. Fig. 5 shows the response to an unknown disturbance, in this case an instantaneous 23Ns horizontal impulse to the center of the torso link" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.28-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.28-1.png", + "caption": "Fig. 6.28 Unbalance excitation on a foundation block", + "texts": [ + " Determine the excitation force vector assuming that the centrifugal force remains independent of the vibrations of the foundation block so that the reaction of the foundation vibrations onto it is negligibly small. Centrifugal force of the rotor: F = me\u03a92 Horizontal distances of the rotor axis from the vertical axis through the center of gravity: \u03beA, \u03b7A Distance of the unbalance plane from the horizontal plane through the center of gravity: \u03b6A Reference length l\u2217 (it is introduced so that all generalized coordinates and all load parameters have equal dimensions.) Coordinate vector, see Fig. 6.28: 6.5 Forced Undamped Vibrations 441 qT = [q1, q2, q3, q4, q5, q6] = [xS, yS, zS, l\u2217\u03d5x, l\u2217\u03d5y , l\u2217\u03d5z ]; |\u03d5x|, |\u03d5y |, |\u03d5z | 1 Excitation force vector: fT = [F1, F2, F3, F4, F5, F6] = [Fx, Fy , Fz , MS x /l\u2217, MS y /l\u2217, MS z /l\u2217] Modal matrix: V = [v1, v2, v3, v4, v5, v6] = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u22120.1 0.2 0 0 0 \u22120.3 0 0 0 0 0.7 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (6.309) 1.Excitation forces Fx, Fy , Fz 2.Excitation moments MS x , MS y , MS z 3.Vector h of the modal excitation forces S6.10 The forces acting in the direction of the coordinates are summarized in the vector fT = [F1, F2]", + "888 > 1). These typical dynamic effects cannot simply be captured by a \u201cdynamic coefficient\u201d. This would have to be told to certain \u201cstatic calculation advocates\u201d who absurdly hold the opinion that one only needs to multiply the result of a static calculation by a factor to obtain the loads for the dynamic case. S6.12 The excitation force is rotating, so it has two components in the horizontal direction. The moments result from the product of the load components and the respective leverages, see Fig. 6.28. Note the positive coordinate directions and distances. In all, the excitation vector, with respect to the coordinates mentioned, is f(t) = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 Fx Fy Fz MS x /l\u2217 MS y /l\u2217 MS z /l\u2217 \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 F cos \u03a9t 0 0 0 (\u03b6A/l\u2217)F cos \u03a9t \u2212(\u03b7A/l\u2217)F cos \u03a9t \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 + \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 0 F sin \u03a9t 0 \u2212(\u03b6A/l\u2217)F sin \u03a9t 0 (\u03beA/l\u2217)F sin \u03a9t \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (6.322) Using the given modal matrix V , the modal excitation forces from (6.270) are h = V Tf(t) = \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 h1 h2 h3 h4 h5 h6 \u23a4\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = F \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u23a1\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u22120" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure7.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure7.4-1.png", + "caption": "Figure 7.4.3 Wheel inclination angles relative to the local path surface.", + "texts": [ + " The antisymmetrical component, the difference of (static) camber angle values, arises on a passenger car only because of production tolerances, although it is used deliberately on some racing cars, essentially those that operate on circuits with turns in one direction only, for example US left-turn \u2018oval\u2019 tracks. In suspension roll, there are suspension bump deflections, \u00fe 1 2 TfS on the right and 1 2 TfS on the left, with wheel camber changes, altering the axle inclination and camber values, Figure 7.4.1. The axle roll inclination angle is the mean inclination angle for the two wheels, relative to the road, resulting from suspension roll. The axle roll inclination coefficient \u00abARI is the rate of change of the mean inclination of the twowheelswith respect to suspension roll. It is dimensionless, being the ratio of an angle over an angle, possibly expressed in units rad/rad or deg/deg. It is related to the bump camber coefficient but also depends on the vehicle track. For small roll angles, linearly, the axle roll inclination angle (mean of the two wheels) is GARI \u00bc \u00abARIfS \u00f07:4:1\u00de Considering a suspension roll angle fS, with corresponding suspension bumps 1 2 TfS relative to the body, the single wheel camber and inclination angles due to suspension roll (axle roll accounted separately), relative to the axle line, are gR \u00bc \u00fe fS \u00fe 1 2 TfS\u00abBC \u00f07:4:2\u00de gL \u00bc fS 1 2 TfS\u00abBC \u00f07:4:3\u00de GR \u00bc \u00fe fS \u00fe 1 2 TfS\u00abBC \u00f07:4:4\u00de GL \u00bc \u00fe fS \u00fe 1 2 TfS\u00abBC \u00f07:4:5\u00de Camber and Scrub 147 The axle mean inclination angle is GA \u00bc 1 2 \u00f0GR \u00feGL\u00de \u00bc fS \u00fe 1 2 TfS\u00abBC \u00bc \u00f01\u00fe 1 2 T\u00abBC\u00defS \u00f07:4:6\u00de Hence the fundamental relationship between the linear axle roll inclination coefficient and the linear wheel bump camber coefficient is \u00abARI \u00bc 1\u00fe 1 2 T\u00abBC \u00f07:4:7\u00de Bump camber coefficients are usually made negative in order to reduce \u00abARI, to offset the effect of body roll on wheel inclination, Figure 7.4.2. To be explicit, equation (7.4.7) may be inverted into the design equation for the necessary bump camber for a desired roll inclination coefficient: \u00abBC \u00bc 2 T \u00f0\u00abARI 1\u00de \u00f07:4:8\u00de For example, the axle roll inclination coefficientwould typically be 0.5 (rad/rad), requiring a bumpcamber coefficient value of 1/T (rad/m), about 0.7 rad/m. A rigid axle is not subject to suspension roll inclination or camber, but it does roll because suspension roll leads to axle roll as a result of load transfer on the tyre vertical stiffness", + " Very loosely, then, a solid axle might be said to have an axle roll camber coefficient, typically of about 0.12 (deg/deg) for a passenger car, although this is not a real geometric effect. This axle roll on the tyres is also applicable to independent suspensions. However, this is not normally accounted for as an axle inclination angle change. It is a roll of the wheel-centres axle line: fA \u00bc kfAfSfS \u00f07:4:9\u00de The complete inclination angles of the wheels relative to the path surface are therefore, Figure 7.4.3, including path inclination angles, given by the path angle contact point to contact point, minus the local path inclination angle, plus the axle roll angle plus the wheel inclination relative to the axle: GW=P \u00bc \u00f0fP \u00fefA \u00feGW\u00de \u00f0fP \u00feGP\u00de \u00f07:4:10\u00de 148 Suspension Geometry and Computation where the path inclination angle GP is measured relative to the path bank angle fP. To be specific, noting that the path bank angle is eliminated, the left and right inclination angles relative to the path (road) are: GW;R \u00bc fA \u00feGR GP;R \u00bc fA \u00fe\u00f0gR0 \u00fefS \u00fe 1 2 T\u00abBCfS\u00de GP;R \u00f07:4:11\u00de GW;L \u00bc fA \u00feGL GP;L \u00bc fA \u00fe\u00f0 gL0 \u00fefS \u00fe 1 2 T\u00abBCfS\u00de GP;L \u00f07:4:12\u00de Considering non-linear bump and roll suspension characteristics, and also asymmetrical characteristics, the basic wheel camber angles are gR \u00bc gR0 \u00fefS \u00fe \u00abBC1;RzS \u00fe \u00abBC2;Rz 2 S gL \u00bc gL0 fS \u00fe \u00abBC1;LzS \u00fe \u00abBC2;Lz 2 S \u00f07:5:1\u00de Substituting zS \u00bc 1 2 fTS, the inclination angles are GR \u00bc \u00fe gR0 \u00fe fS \u00fe 1 2 T\u00abBC1;RfS \u00fe 1 4 T2\u00abBC2;Rf 2 S GL \u00bc gL0 \u00fe fS \u00fe 1 2 T\u00abBC1;LfS 1 4 T2\u00abBC2;Rf 2 S \u00f07:5:2\u00de The axle mean inclination angle is GA \u00bc 1 2 \u00f0GR \u00feGL\u00de \u00bc 1 2 \u00f0gR0 gL0\u00de\u00fefS \u00fe 1 4 T\u00f0\u00abBC1;R \u00fe \u00abBC1;L\u00defS \u00fe 1 8 T2\u00f0\u00abBC2;R \u00abBC2;L\u00def2 S \u00f07:5:3\u00de This may be expressed in terms of the axle roll inclination coefficients as GA \u00bc GA0 \u00fe \u00abARI1fS \u00fe \u00abARI2f 2 S \u00f07:5:4\u00de with the three terms GA0 \u00bc 1 2 \u00f0gR0 gL0\u00de \u00f07:5:5\u00de \u00abARI1 \u00bc 1\u00fe 1 4 T\u00f0\u00abBC1;R \u00fe \u00abBC1;L\u00de \u00f07:5:6\u00de \u00abARI2 \u00bc 1 8 T2\u00f0\u00abBC2;R \u00abBC2;L\u00de \u00f07:5:7\u00de The first of these,GA0, is the asymmetrical production tolerance error on static camber" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003476_j.msea.2018.11.001-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003476_j.msea.2018.11.001-Figure1-1.png", + "caption": "Fig. 1. Schematic of the LBM process.", + "texts": [ + " The ultimate tensile strength after annealing reached 2148 \u00b116 MPa along with an elongation at break of 8.8 \u00b11.1 %. The hardness of the LBM-generated material was determined to 737 \u00b116 HV1 after hardening and to 585\u00b1 9 HV1 after annealing. Additive Manufacturing (AM) technologies are becoming increasingly relevant for industrial applications. To produce metal parts, Laser Beam Melting (LBM), also referred to as Selective Laser Melting (SLM) or Laser Powder Bed Fusion (L-PBF), is currently, the most important manufacturing process [1]. A schematic of the process is shown in Fig. 1. One of the major benefits of LBM is a high degree of design freedom that is facilitated by the layerwise generation of the parts. This allows the production of highly sophisticated structures. With respect to tooling applications, the integration of conformal cooling or heating channels is of particular interest. An optimization of the temperature control e.g. in injection moulds results in reduced cycle times [2] and in increased part quality [3]. In addition, for manufacturing compression moulds for processing thermosets [4] or aluminium hot extrusion dies [5] LBM can be beneficial" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002975_s10659-014-9498-x-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002975_s10659-014-9498-x-Figure2-1.png", + "caption": "Fig. 2 Left: Typical morphologies of ribbons subjected to twist and stretching: (a) helicoid, (b, c) longitudinally wrinkled helicoid, (d) creased helicoid, (e) formation of loops and self-contact zones, (f) cylindrical wrapping, (g) transverse buckling and (h) twisted towel shows transverse buckling/wrinkling. Right: (i) Experimental phase diagram in the tension-twist plane, adapted from [3]. The descriptive words are from the original diagram [3]. Note that the twist used in the experiment is not very small; this apparent contradiction with our hypothesis \u03b7 1 (Eq. (2)) is clarified in Appendix A", + "texts": [ + "1 Overview A ribbon is a thin, long solid sheet, whose thickness and length, normalized by the width, satisfy: thickness: t 1; length: L 1. (1) The large contrast between thickness, width, and length, distinguishes ribbons from other types of thin objects, such as rods (t \u223c 1, L 1) and plates (t 1, L \u223c 1), and underlies their complex response to simple mechanical loads. The unique nature of the mechanics of elastic ribbons is demonstrated by subjecting them to elementary loads\u2014twisting and stretching\u2014as shown in Fig. 1. This basic loading, which leads to surprisingly rich plethora of patterns, a few of which are shown in Fig. 2, is characterized by two small dimensionless parameters: twist: \u03b7 1; tension: T 1, (2) where \u03b7 is the average twist (per length), and T is the tension, normalized by the stretching modulus.1 Most theoretical approaches to this problem consider the behavior of a real ribbon through the asymptotic \u201cribbon limit\u201d, of an ideal ribbon with infinitesimal thickness and infinite length: t \u2192 0,L \u2192 \u221e. A first approach, introduced by Green [1, 2], assumes that the ribbon shape is close to a helicoid (Fig. 2a), such that the ribbon is strained, and may therefore become wrinkled or buckled at certain values of \u03b7 and T (Fig. 2b,c,g,h) [4, 5]. A second approach to the ribbon limit, initiated by Sadowsky [6] and revived recently by Korte et al. [7], considers the ribbon as an \u201cinextensible\u201d strip, whose shape is close to a creased helicoid\u2014an isometric (i.e., strainless) map of the unstretched, untwisted ribbon (Fig. 2d). A third approach, which may be valid for sufficiently small twist, assumes that the stretched-twisted ribbon is similar to the wrinkled shape of a planar, purely stretched rect- 1Our convention in this paper is to normalize lengths by the ribbon width W, and stresses by the stretching modulus Y, which is the product of the Young modulus and the ribbon thickness (non-italicized fonts are used for dimensional parameters and italicized fonts for dimensionless parameters). Thus, the actual thickness and length of the ribbon are, respectively, t = t \u00b7 W and L = L \u00b7 W, the actual force that pulls on the short edges is T \u00b7 YW, and the actual tension due to this pulling force is T = T \u00b7 Y. angular sheet, with a wrinkle\u2019s wavelength that vanishes as t \u2192 0 and increases with L [8]. Finally, considering the ribbon as a rod with highly anisotropic cross section, one may approach the problem by solving the Kirchoff\u2019s rod equations and carrying out stability analysis of the solution, obtaining unstable modes that resemble the looped shape (Fig. 2e) [9]. A recent experiment [3], which we briefly describe in Sect. 1.2, revealed some of the predicted patterns and indicated the validity of the corresponding theoretical approaches at certain regimes of the parameter plane (T , \u03b7) (Fig. 2). Motivated by this development, we introduce in this paper a unifying framework that clarifies the hidden assumptions underlying each theoretical approach, and identifies its validity range in the (T , \u03b7) plane for given values of t and L. Specifically, we show that a single theory, based on a covariant form of the F\u00f6ppl\u2013von K\u00e1rm\u00e1n (FvK) equations of elastic sheets, describes the parameter space (T , \u03b7, t,L\u22121) of a stretched twisted ribbon where all parameters in Eqs. (1) and (2) are assumed small", + " Various \u201ccorners\u201d of this 4D parameter space are described by distinct singular limits of the governing equations of this theory, which yield qualitatively different types of patterns. This realization is illustrated in Fig. 3, which depicts the projection of the 4D parameter space on the (T ,\u03b7) plane, and indicates several regimes that are governed by different types of asymptotic expansions. 1.2 Experimental Observations The authors of [3] used Mylar ribbons, subjected them to various levels of tensile load and twist, and recorded the observed patterns in the parameter plane (T ,\u03b7), which we reproduce in Fig. 2. The experimental results indicate the existence of three major regimes that meet at a \u201c\u03bb-point\u201d (T\u03bb, \u03b7\u03bb). We describe below the morphology in each of the three regimes and the behavior of the curves that separate them: \u2022 The helicoidal shape (Fig. 2a) is observed if the twist \u03b7 is sufficiently small. For T < T\u03bb, the helicoid is observed for \u03b7 < \u03b7lon, where \u03b7lon \u2248 \u221a 24T is nearly independent on the ribbon thickness t . For T > T\u03bb, the helicoid is observed for \u03b7 < \u03b7tr, where \u03b7tr exhibits a strong dependence on the thickness (\u03b7tr \u223c \u221a t ) and a weak (or none) dependence on the tension T . The qualitative change at the \u03bb-point reflects two sharply different mechanisms by which the helicoidal shape becomes unstable. \u2022 As the twist exceeds \u03b7lon (for T < T\u03bb), the ribbon develops longitudinal wrinkles in a narrow zone around its centerline (Fig. 2b,c). Observations that are made close to the emergence of this wrinkle pattern revealed that both the wrinkle\u2019s wavelength and the width of the wrinkled zone scale as \u223c(t/ \u221a T )1/2. This observation is in excellent agreement with Green\u2019s characterization of the helicoidal state, based on the familiar FvK equations of elastic sheets [2]. Green\u2019s solution shows that the longitudinal stress at the helicoidal state becomes compressive around the ribbon centerline if \u03b7 > \u221a 24T , and the linear stability analysis of Coman and Bassom [5] yields the unstable wrinkling mode that relaxes the longitudinal compression. \u2022 As the twist exceeds \u03b7tr (for T > T\u03bb), the ribbon becomes buckled in the transverse direction (Fig. 2g), indicating the existence of transverse compression at the helicoidal state that increases with \u03b7. A transverse instability cannot be explained by Green\u2019s calculation, which yields no transverse stress [2], but has been predicted by Mockensturm [4], who studied the stability of the helicoidal state using the full nonlinear elasticity equations. Alas, Mockensturm\u2019s results were only numerical and did not reveal the scaling behavior \u03b7tr \u223c \u221a t observed in [3]. Furthermore, the nonlinear elasticity equations in [4] account for the inevitable geometric effect (large deflection of the twisted ribbon from its flat state), as well as a mechanical effect (non-Hookean stress-strain relation), whereas only the geometric effect seems to be relevant for the experimental conditions of [3]. \u2022 Turning back to T < T\u03bb, the ribbon exhibits two striking features as the twist \u03b7 is increased above the threshold value \u03b7lon. First, the longitudinally-wrinkled ribbon transforms to a shape that resembles the creased helicoid state predicted by [7] (Fig. 2d); this transformation becomes more prominent at small tension (i.e., decreasing T at a fixed value of \u03b7). Second, the ribbon undergoes a sharp, secondary transition, described in [3] as similar to the \u201clooping\u201d transition of rods [9\u201312] (Fig. 2e). At a given tension T < T\u03bb, this secondary instability occurs at a critical twist value that decreases with T , but is nevertheless significantly larger than \u03b7lon \u2248 \u221a 24T . \u2022 Finally, the parameter regime in the (T , \u03b7) plane bounded from below by this sec- ondary instability (for T < T\u03bb) and by the transverse buckling instability (for T > T\u03bb), is characterized by self-contact zones along the ribbon (Fig. 2e). The formation of loops (for T < T\u03bb) is found to be hysteretic unlike the transverse buckling instability (for T > T\u03bb). In a recent commentary [13], Santangelo recognized the challenge and the opportunity introduced to us by this experiment: \u201cAbove all, this paper is a challenge to theorists. Here, we have an experimental system that exhibits a wealth of morphological behavior as a function of a few parameters. Is there anything that can be said beyond the linear stability analysis of a uniform state", + " (ii) A far-from-threshold (FT) expansion of the cFvK equations that describes the state of the ribbon when the twist exceeds the threshold value \u03b7lon for the longitudinal wrinkling instability. (iii) A new, asymptotic isometry equation (Eq. (42)), that describes the elastic energies of admissible states of the ribbon in the vicinity of the vertical axis in the parameter plane (T , \u03b7). We use the notion of \u201casymptotic isometry\u201d to indicate the unique nature by which the ribbon shape approaches the singular limit of vanishing thickness and tension (t \u2192 0, T \u2192 0 and fixed \u03b7 and L). We commence our study in Sect. 2 with the helicoidal state of the ribbon (Fig. 2a)\u2014 a highly symmetric state whose mechanics was addressed by Green through the standard FvK equations [2], which is valid for describing small deviations of an elastic sheet from its planar state. We employ a covariant form of the FvK theory for Hookean sheets (cFvK equations), which takes into full consideration the large deflection of the helicoidal shape from planarity. Our analysis of the cFvK equations provides an answer to question (A) above, curing a central shortcoming of Green\u2019s approach, which provides the longitudinal stress but predicts a vanishing transverse stress", + " This result reflects the remarkable geometrical nature of the FT-longitudinally-wrinkled state, which becomes infinitely close to an isometric (i.e., strainless) map of a ribbon under finite twist \u03b7, in the singular limit t, T \u2192 0. At the singular hyper-plane (t = 0, T = 0), which corresponds to an ideal ribbon with no bending resistance and no exerted tension, the FT-longitudinally-wrinkled state is energetically equivalent to simpler, twist-accommodating isometries of the ribbon: the cylindrical shape (Fig. 5) and the creased helicoid shape (Fig. 2d, [7]). We argue that this degeneracy is removed in an infinitesimal neighborhood of the singular hyper-plane (i.e., t > 0, T > 0), where the energy of each asymptotically isometric state is described by a linear function of T with a t -independent slope and a t -dependent intercept. Specifically: Uj(t, T ) = AjT + Bj t 2\u03b2j , (42) where j labels the asymptotic isometry type (cylindrical, creased helicoid, longitudinal wrinkles), and 0 < \u03b2j < 1. For a fixed twist \u03b7 1, we argue that the intercept (Bt2\u03b2 ) is smallest for the cylindrical state, whereas the slope (A) is smallest for the FT-longitudinallywrinkled state", + " In Table 2, we compare the control parameters and their relevant mutual ratios in both experiments. Green, who used a material with very large Young\u2019s modulus, could address the \u201cultra-low\u201d tension regime, T \u223c Tsm(t) (Fig. 3c), but a simple steel may exhibit a non-Hookean (or even inelastic) response at rather small T , which limits its usage for addressing the regime around and above the triple point (i.e., T > T\u03bb). In contrast, the experiment of [3] used a material with much lower Young\u2019s modulus, which allows investigation of the ribbon patterns in Fig. 2g, but the minimal exerted tension Tmin (associated with the experimental set-up) was not sufficiently small to probe Green\u2019s threshold plateau \u03b7lon(T ) \u2192 10t for T Tsm(t). This comparison reveals the basic difficulty in building a single set-up that exhibits clearly the whole plethora of shapes shown in Fig. 3. In addition to the effect of Tmin and THook, there is an obvious restriction on Lmax (at most few meters in a typical laboratory). Below we propose a couple of other materials, whose study\u2014through experiment and numerical simulations\u2014may enable a broader range of the ratios Tmin/Tsm, THook/T\u03bb and Lmaxt ", + " The far-from-threshold analysis of the cFvK equations revealed a profound feature of the wrinkling instability: assuming a fixed twist \u03b7, and reducing the exerted tension (along a horizontal line in Fig. 3), the formation of longitudinal wrinkles that decorate the helicoidal shape enables a continuous, gradual relaxation of the elastic stress from the strained helicoidal shape at T > \u03b72/24, to an asymptotically strainless state at T \u2192 0. This remarkable feature led us to propose a general form of the asymptotic isometry equation (42), which characterizes the wrinkled state of the ribbon (Fig. 2b, c), as well as other admissible states at the limit T \u2192 0, such as the cylindrical wrapping (Fig. 2e) and the creased helicoid state (Fig. 2d). The asymptotic isometry equation provides a simple framework, in which the transitions between those morphologies in the vicinity of the vertical line (T = 0 in Fig. 3) correspond to the intersection points between linear functions of T (Fig. 6b), whose intercepts and slopes are determined solely by the geometry of each state. Beyond its role for the mechanics and morphological instabilities of ribbons, the asymptotic isometry equation may provide a valuable tool for studying the energetically favorable configurations of elastic sheets" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure3.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure3.3-1.png", + "caption": "Fig. 3.3 Phasor diagrams of a polyphase induction motor. (a) Space diagram of m.m.f.s.", + "texts": [ + " and flux waves due to the balanced polyphase currents in each winding rotate relative to the stator at synchronous speed w 0 and combine to form the resultant air-gap m.m.f. and flux waves. The instant at which the resultant m.m.f. wave, represented by the space phasor F, is on the direct axis (drawn horizontally), is indicated on Fig. 3.2. At the same instant, the component m.m.f.s due to the primary and secondary currents respectively are represented by the space phasors Fl and F2 at angles (- 1) and (1800 - 2) to the vertical. Since the three phasors move round together at speed w 0, they can be related by a stationary phasor diagram (Fig. 3.3a). If core losses are neglected, the resultant flux wave due to F also has its axis on the direct axis, and consequently the internal voltage, opposing that induced in the primary phase AI, has its maximum value at the instant considered. The internal voltage is represented by the phasor V j \u2022 If the primary windings carried polyphase currents such that the current in phase Al was in phase with Vj, they would set up an m.m.f. on the quadrature axis at this instant. Since, however, the phasor FI is displaced by 1 from the vertical axis, the corresponding primary current It actually lags behind V j by the angle CPI (see Fig. 3.3b). In the primary voltage phasor diagram of Fig. 3.3b, which applies to phase AI, (b) Time diagram of primary voltages. (c) Time diagram of secondary voltages. the terminal impressed voltage U is the sum of the internal voltage Uj, the resistance drop RIft and the leakage reactance drop jXI/I . The secondary winding is not located in any definite position relative to the primary winding and in general has a different number of turns per phase. If a per-unit system, defined for the stationary induction motor in the same way as for the transformer on p. 12 is used, the voltage induced in phase A2 by the resultant flux has the same magnitude as Uj if the rotor is at rest. With a slip s the flux induces a slip-frequency voltage, while the phase depends on the rotor position. In Fig. 3.3c the phasor sUj, like Uj in Fig. 3.3b, represents the voltage opposing the induced voltage. If the secondary winding carried polyphase currents such that the current in phase A2 was in phase with the secondary induced voltage, the secondary currents would set up an m.m.f. on the quadrature axis at the instant when the flux is along the direct axis. This relation holds whatever the actual position of the secondary winding may be at that instant. Since, for the operating condition indicated in Fig. 3.2, F2 is displaced from the quadrature axis by the angle (1T - cJ>2), it follows that the secondary current phasor h is displaced by (1T - cJ>2) from sUj , as shown in the time phasor diagram of Fig. 3.3c. In the secondary voltage phasor diagram (Fig. 3.3c), the sum of sUi> the resistance drop R2h, and the leakage reactance drop jsX 21 2, is zero, since the secondary winding is short-circuited. The theory of the induction motor is thus based on three separate phasor diagrams. When a per-unit system is used, the primary and secondary m.m.f.s are in the ratio of the currents producing them. The current in the primary winding which would produce the resultant m.m.f. is called the magnetizing current, and the phasor is denoted by 1m. It lags 90\u00b0 behind U j and is therefore horizontal in Fig. 3.3b. Fig. 3.3a may be considered as a current diagram showing that 1m is the sum of ft and h, since each m.m.f. phasor is proportional to the corresponding current phasor. The phasor equations can be written down from the diagrams The Steady-State Phasor Diagrams of A.C. Machines 47 (Figs. 3.3a-c). The quotient of the magnitudes of Uj and 1m is a constant called the magnetizing reactance X m . The equations are: o =sUj + (R2 +jsX2 )h Uj =jXm/m (3.2) Elimination of Uj and 1m from these equations gives the two voltage equations of the induction motor: (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.10-1.png", + "caption": "FIGURE 2.10. Global yaw.", + "texts": [], + "surrounding_texts": [ + "42 2. Rotation Kinematics\nand the pit ch angle is\n(2.31)\nand the yaw angle is\nprovided that cos (3 =f: O.\n'Y = tan-1 (r21 )\nrll (2.32)\nExample 9 Global roll, pitch, and yaw rotations. Figures 2.8, 2.9, and 2.10 illustrate 45 deg roll, pitch and yaw about the axes of global coordinate frame.", + "2. Rotation Kinematics 43\n2.4 Rotation About Local Cartesian Axes\nConsider a rigid body B with a space fixed at point O. The local body coordinate fram e B(Oxyz) is coincident with a global coordinate frame G(OXYZ) , where the origin of both frames are on th e fixed point O. If the body undergoes a rotation 'P about the z-axis of its local coordinate frame, as can be seen in the top view shown in Figure 2.11 , then coordinates of any point of the rigid body in local and global coordinate frames are related by the following equat ion\nBr = A z,'f' Gr . (2.33)\nThe vectors G r and B r are th e position vectors of the point in global and local frames resp ectively\n[ X Y Z JT [ x Y z f\n(2.34)\n(2.35)\nand A z,'f' is the z-rotation matrix\nA\" ~ [ ~~r:~ :~~~ ~] . (236)\nSimilarly, rotation e about the y-axis and rotation 1jJ about the x-axis are describ ed by the y-rotation matrix Ay,o and t he x -rotation matrix Ax,,p respectively.\n[\ncos e 0 Ay,o = 0 1\nsine 0\n[\n1 0 Ax,,p = 0 cos 1jJ\no - sin 1jJ\n- s~ne ]\ncos e\nsi~ 1jJ ] cos 1jJ\n(2.37)\n(2.38)", + "44 2. Rotation Kinematics\nProof. Vector r l indicates the posit ion of a point P of the rigid body B where it is initially at Pl. Using t he unit vectors (i,5, k) along t he axes of local coordinate frame B(Oxyz) , and (I ,), K) along the axes of global coordinate frame B(OXYZ) , the initial and final position vectors r l and r 2 in both coordinate frames can be expressed by\nB r l xli + Yl1 + zlk (2.39) G r l x .i + Yl } + ZlK (2.40)\nB r2 X2 i + Y25 + Z2 k (2.41) G\nr 2 x.i + Y2} + Z2K. (2.42)\nThe vectors B r l and B r2 are the initial and final positio ns of the vector r expressed in body coordinate frame Oxyz, and G r l and G r 2 are the initial and final positions of the vector r expressed in the global coordinate frame OXYZ.\nThe components of B r2 can be found if we have the components of G r 2 . Using Equation (2.42) and t he definition of the inner product , we may write\nor equivalently\nY2\ni \u00b7 r 2 = i . x21+ i . Y2} + i . Z2K 5\u00b7 r 2 = 5\u00b7 x21+ 5\u00b7Y2} + 5\u00b7 Z2K k. r 2 = k.x 2i + k.Y2 } + k.Z2K\n(2.43)\n(2.44)\n(2.45)\n[ i . Z 5\u00b7J k\u00b7l i \u00b7 } 5\u00b7 } k \u00b7} i \u00b7~ ] 5\u00b7K k \u00b7K\n(2.46)" + ] + }, + { + "image_filename": "designv10_3_0003193_j.triboint.2016.01.027-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003193_j.triboint.2016.01.027-Figure1-1.png", + "caption": "Fig. 1. (a) The six-DOF discrete dynamics model for spur gears, and (b) the tooth meshing interface friction.", + "texts": [ + " However, the methodology of this study is general, allowing the replacement of the dynamic model or the EHL model with other ones of varying sophistication. The spur gear pair that consists of gear 1 and gear 2 is modeled as a rigid disk pair that is composed of disk 1 and disk 2. The mass and the polar moment inertia of disk j (j\u00bc 1;2) are the same as those of gear j and are denoted as mj and Jj, respectively. The radius of disk j, denoted as rj, is equal to the base radius of gear j. The discrete dynamic model that describes both the torsional motion and the translational motions in the x (OLOA) and y (LOA) directions is illustrated in Fig. 1 for a general spur gear pair. The mesh of the two gears is modeled by a spring element (km), a clearance element (2\u2113) and a static transmission error element (\u03b5s) connected in parallel, representing the tooth mesh stiffness, the backlash (\u2113 equals the half backlash) and the geometric deviation from the involute profile caused by manufacturing errors and/or intentional modifications, respectively. The gear mesh damping is introduced through the friction forces exerted along the tooth surfaces in the OLOA direction as shown in Fig. 1(b). To model the bearing support for gear j, a set of spring-damping elements is implemented in the LOA direction (kyj and cyj) and another set is applied in the OLOA direction (kxj and cxj). In addition, the torsional damping of the bearing caused by the viscous power loss is included as ctj for gear j, while not shown in the figure. The equations of the torsional motion in terms of the angular displacement, \u03b8j, and the translational motions in the x and y directions are then arrived for gear j as [8] Jj \u20ac\u03b8j\u00fectj _\u03b8j\u00fe\u03d1jrjWM \u00bc \u03d1j T j\u00fe XN n \u00bc 1 \u00f0Fj\u00den\u00f0Rj\u00den ( ) \u00f01a\u00de mj \u20acyj\u00fe\u00f0WBy\u00dej\u00fe\u03d1jWM \u00bc 0 \u00f01b\u00de mj \u20acxj\u00fe\u00f0WBx\u00dej \u00bc \u03d1j XN n \u00bc 1 \u00f0Fj\u00den \u00f01c\u00de where WM \u00bc km\u03b4 \u00f02a\u00de \u00f0WBy\u00dej \u00bc cyj _yj\u00fekyjyj \u00f02b\u00de \u00f0WBx\u00dej \u00bc cxj _xj\u00fekxjxj \u00f02c\u00de representing the dynamic gear mesh force, the dynamic bearing force in the LOA direction, and the dynamic bearing force in the OLOA direction, respectively", + " The gear dynamics simulation is then repeated to update the dynamic surface velocity and mesh force, the convergence of which stops the iteration process. The design parameters of the example spur gear pair considered in this study are listed in Table 1. For this gear pair, gear 1 and gear 2 are identical, and both have the tip relief of 10 \u03bcm starting at the 20:9 3 roll angle. This micro geometry modification leads to the static transmission error as shown in Fig. 2(a), obtained by using the gear load distribution program (LDP) [22]. The bearing supporting stiffness and damping as specified in Fig. 1 take the same values as those in Ref. [8] of kyj \u00bc 1:15 109 N/m and cyj \u00bc 5360 Ns/m in the LOA direction and kxj \u00bc 8:0 108 N/m and cxj \u00bc 2980 Ns/m in the OLOA direction (j\u00bc 1; 2). The torsional damping of the bearing takes the value of ctj \u00bc 10 N m s=rad [8]. The turbine fluid, Mil-L23699, is used as the lubricant, whose density and viscosity properties were reported in Ref. [18]. To examine the influences of the load and the lubricant viscosity on the flash temperature, two input torques of 700 Nm and 1500 Nm, and two lubricant temperatures of 90 \u00b0C and 60 \u00b0C are implemented" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000319_j.eswa.2008.07.003-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000319_j.eswa.2008.07.003-Figure6-1.png", + "caption": "Fig. 6. Inverted pendulum system.", + "texts": [ + " The tracking error and the modeling error will then both approach zero. Theorem 1. Consider a nonlinear system yi \u00f0ni\u00de \u00bc fi\u00f0x\u00de \u00fe PP j\u00bc1gij\u00f0x\u00de uj \u00fe di\u00f0t\u00de that satisfies the assumptions \u00f0 hj; h\u0302j\u00de. Suppose that the unknown control input u can be approximated by u\u0302j\u00f0S; h\u0302j\u00de as in (14). Now Si is given by (23), and Qi is a symmetric positive definite weighting matrix. In this section, the proposed GA-based MAFSMC is demonstrated with an example of the control methodology. Consider the problem of balancing an inverted pendulum on a cart as shown in Fig. 6. The dynamic equations of motion of the pendulum are given below (Yoo & Ham, 1998): _x1 \u00bc x2 _x2 \u00bc g sin\u00f0x1\u00de amlx2 2 sin\u00f02x1\u00de=2 a cos\u00f0x1\u00de u 4l=3 aml cos2\u00f0x1\u00de ( ; \u00f030\u00de where x1 denotes the angle (in radian) of the pendulum from the vertical; and x2 is the angular vector. Thus, the gravity constant g \u00bc 9:8m=s2, where m is the mass of the pendulum, M is the mass of the cart, l is the length of the pendulum, and u is the force applied to the cart (in Newtons), and a \u00bc 1=\u00f0m\u00feM\u00de. The parameters chosen for the pendulum in this simulation are: m \u00bc 0:05 kg, M \u00bc 1 kg, and l \u00bc 0:5 m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000743_j.jfranklin.2011.11.003-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000743_j.jfranklin.2011.11.003-Figure1-1.png", + "caption": "Fig. 1. The configuration of the X-33 reusable launch vehicle.", + "texts": [ + " These modifications result in a simplified kinematic equations of reusable launch vehicle as follows: _f \u00bc p cos a cos b q sin b r sin a cos b\u00fe _a sin b \u00f05\u00de _a \u00bc p cos a tan b\u00fe q r sin a tan b \u00f06\u00de _b \u00bc p sin a r cos a \u00f07\u00de Let T \u00bc \u00bdT1,T2,T3 T , it is well known that the control torque T is related to the surface deflection vector d, namely, T \u00bc Bd where B 2 R3 m, m is the number of the control surface deflection variable. In this paper, we choose the X-33 reusable launch vehicle as the studied plant. Fig. 1 shows the configuration of the X-33 vehicle. It has four sets of control surfaces: rudders, body flaps, inboard and outboard elevons, with left and right sides for each set. Each of the eight surfaces can be independently actuated with one actuator for each surface. These control surface deflection variables, collectively known as the effector vector, are given by d\u00bc \u00bddrei, dlei, drft, dlft, drvr, dlvr, dreo, dleo T9\u00bdd1, d2, d3, d4, d5, d6, d7, d8 T where drei and dlei are the right and left inboard elevons, drft and dlft are the right and left body flaps, drvr and dlvr are the right and left rudders, dreo and dleo are the right and left outboard elevons" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002447_025003-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002447_025003-Figure1-1.png", + "caption": "Figure 1. Experimental setup. (a) Device 1: rectangular PDMS microchannel with h = 100 and W = 600 \u00b5m. (b) Device 2: circular chamber made from a droplet of the suspension of diameter D = 5 mm confined between two cover glass slides separated by a distance h = 100 \u00b5m. (c) Left panel: snapshot of the suspension (\u03c6 = 0.75%). Right panel: the detected bacterial body is indicated as a circle and its velocity in the x\u2212-y plane is represented with a line. Inset: fluorescently labeled E. coli bacterium; the scale bar is 2 \u00b5m.", + "texts": [ + " coli body length being a = 2 \u00b5m the total length of the bacterium, taking also the flagella into account, can be estimated as l \u2248 3\u20134a = 6\u20138 \u00b5m. In this case, the excluded volume fraction is \u03bd = \u03c6 \u2217 (l/a)3 and for \u03c6 = 8% we reach a value \u03bd = O(1). At a concentration of \u03c6 = 8% a semi-dilute regime is thus reached. When necessary, in order to monitor the flow velocity, a very low concentration of 2 \u00b5m density-matched latex beads are suspended as passive tracers into the suspensions. To contain the suspension, different types of geometries are used: rectangular PDMS channels of height h = 100 \u00b5m and width W = 600 \u00b5m (see figure 1(a)) and circular chambers of diameter 5 mm made from a droplet of the suspension confined between two glass cover slips maintained at a distance of h = 100 \u00b5m by two spacers (see figure 1(b)). The suspensions of bacteria are flown into the microfluidic channel, whereas the droplet of the suspension is directly deposited onto the cover glass. Furthermore, rectangular micro-fluidic channels are made in PDMS, a material known to be transparent to oxygen fluxes (avoiding in this way oxygen shortage for the bacteria), whereas in the droplet, oxygen can permeate through the droplet interface with air but not from the upper and lower edges. The PDMS channels are made using standard soft-lithography techniques", + " Even bacteria swimming perpendicular to the x\u2013y plane do thus not leave the field of observation during this time. This means that we are essentially measuring projections of 3D trajectories. After processing, we obtain at each time step a spatially resolved velocity field EV (Er , t) at time t . We also analyzed the image sequences using a tracking algorithm developed in the group. In this case, the bacteria appearing as a white spot surrounded by a dark edge can easily be tracked at high frame rate if the concentration is not too high. See figure 1(b) and video 1 in the supplementary data (available from stacks.iop.org/NJP/16/025003/mmedia) for an animation of the bacteria tracking. The effective depth of field is here 3.4 \u00b5m. The difficulty is that most of the bacteria stay only fractions of a second in the field, so the lag time during which a bacterium is tracked can act as a filter on the population. For these results, we used the corresponding PIV lag time of 0.04 s. We have checked that varying the lag time slightly did not lead to a modification of the velocity correlations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000604_biorob.2008.4762872-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000604_biorob.2008.4762872-Figure8-1.png", + "caption": "Fig. 8. Distributed load (compresssive and frictional forces) acting on a needle shaft as it interacts with an elastic medium. Inset: Forces acting on the bevel tip, where P and Q are the resultant forces along the bevel edge. qx and qy are the resultant forces along the bottom edge of the needle tip.", + "texts": [ + " The length of the window when the needle tip is interacting and outside the tissue is given by L1. During the phase when the needle tip is outside the tissue and only the needle shaft interacts with tissue, the insertion force is fairly constant. The rupture toughness for the various materials are provided in Table I. The material parameters obtained from the experiments in the previous section were incorporated into FE simulations using ABAQUS [1] in order to evaluate the forces at the needle tip. Figure 8 shows the various forces acting on the needle interacting with an elastic medium. The needle is subjected to compressive and frictional forces along its needle shaft, and forces due to tip asymmetry. In this paper, we investigate the effect of rupture toughness, bevel angle, and tissue elasticity on the forces at the bevel tip. In order to simulate the interaction of the needle tip deforming and rupturing tissue as it travels, we employ a cohesive zone model (Figure 9). Cohesive zone modeling techniques are commonly used to simulate interface failure in composite structures" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000449_0278364907080423-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000449_0278364907080423-Figure7-1.png", + "caption": "Fig. 7. Diagram of vehicle on the stairs. CG is the center of gravity, O is the center of rotation, is the heading direction, and dL , dR are the distances to the left and right of the stairs, respectively. Note in this plot that the dark-grey regions correspond to the \u201cnon-safe\u201d areas close to staircase boundaries, while the white and light-gray regions are considered as \u201csafe\u201d areas. When the vehicle steers away from the stair ends, at a commanded angle r d , it needs to pass through the lightgrey area and move within the white region before the heading controller switches its reference signal r back to the nominal heading direction of 0 degrees.", + "texts": [ + " As previously mentioned, the optimal heading direction for a stair-climbing vehicle is r 0. However, when the robot approaches the staircase boundaries, the threat of collision requires the centering controller to deviate from the optimal heading direction and steer the robot away from the stair sides. The information available to the centering controller for predicting whether the robot is outside a \u201csafe zone\u201d around the centerline, is the ratio of the distances dL dR to the left and right boundaries of the staircase (Figure 7). Since the ratio is a non-symmetric function of the robot location relative to the staircase centerline, the centering controller uses instead as input the normalized ratio min dL dR dR dL , 0 1. Additionally, the sign value s sign dL dR 1 is computed to determine the direction of the deviation from zero heading. The output of the centering controller is the reference signal r provided to the heading controller (Figure 2). The centering controller is implemented as a step function with hysteresis: r 0 c s d c (57) where d 10o is the magnitude of the direction change, and c 3 7 ( c 4 7 ) is the normalized distance ratio threshold for at TEXAS SOUTHERN UNIVERSITY on November 5, 2014ijr", + " A detailed description of modeling techniques for tracked vehicles is presented in Wong (2001) and Bekker (1956). In this work, we have approximated the dynamics of the robot climbing stairs as a second-order linear system. This approximation does not invalidate the model it limits though the range of application of the designed heading controller to small angles ( 30o) of robot heading direction. The main advantage of this linearized model is that it allows for the use of formal control-system design techniques when designing the heading controller (Franklin et al. 1997). As shown in Figure 7, the center of gravity (CG) of the vehicle used in our implementation is above its center of rotation O. The equation that describes the rotation of the vehicle in a plane defined by the stair edges is Iz TO mgdCG sin sin Mr (58) where is the rotational acceleration, is the heading direction, and TO is the torque exerted by the motors about the vehicle\u2019s center of rotation, O. The parameters in the above equation are: (i) Iz is the moment of inertia about the z-axis, computed by weighing the individual subcomponents of the vehicle and measuring their location relative to O, (ii) m is the mass of the robot, (iii) g is the magnitude of the gravitational acceleration, (iv) dCG is the distance of the CG from O, (v) is the inclination of the stairs, and (vi) Mr is the rotational resistance", + " In this run, the robot completed climbing the first step at approximately t 2 7 s, and shortly after, the first reliable distance ratio became available. The robot correctly determined at TEXAS SOUTHERN UNIVERSITY on November 5, 2014ijr.sagepub.comDownloaded from that it was positioned too close to the left wall, and the centering controller commanded the robot to head at an angle of 10o to the right (cf. Figure 9). At approximately t 7 s the robot entered the center zone, and therefore the reference angle of the heading controller became r 0o. However, due to slippage, the robot again moved to the left \u201cnon-safe zone\u201d after 2 s (cf. Figure 7), and the reference angle was set to 10o once again. At approximately t 11 s, the robot\u2019s distance ratio crossed the threshold c 4 7, and the robot remained in the center zone until it reached the top of the stairs, at approximately t 13 s. In Figure 10, we plot the residuals of the line measurements, computed by (38), for all the lines that passed the gating test (cf. (45)) during the run. These residuals are compared to the 3 bounds corresponding to the diagonal elements of S (cf. (47)). We observe that no noticeable bias is present, which indicates that the estimator is consistent, and that the employed sensor noise models are sufficiently accurate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure6.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure6.6-1.png", + "caption": "Fig. 6.6 Jerk: problem 2", + "texts": [ + "102) is the third-order driver matrix of the two-degree-of-freedom parallel manipulator. Meanwhile, MJ D \u02da L1I 0J 5 P fL2IJ Pg T (6.103) is the complementary jerk matrix. 1. The nozzle shown in Fig. 6.5 rotates with constant angular velocity ! about a fixed horizontal axis passing through point O. The velocity of the water relative to the nozzle is v and is constant. Determine the velocity, acceleration, and jerk of a water particle as it passes point A. 2. The slider P can be moved by the string S while the bar OA rotates around the pivot O (see Fig. 6.6). The orientation of the bar is given according to the expression D 0:25 C 0:1t C 0:05t2 C 0:075t3, where the angle is given in radians and the time t is in seconds. The position of the slider is commanded to follow the expression r D 0:6 0:25t 0:025t2 C 0:001t3, where r is given in meters and t in seconds. Determine the velocity, acceleration, and jerk of the slider at time t D 3 s. 3. In the development of cam profiles due to tribological implications and the ability of the actuated body to follow the cam profile without chatter, the jerk must be taken into proper account" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure4.28-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure4.28-1.png", + "caption": "Fig. 4.28 Cam stepping mechanism; a) Schematic, b) Calculation model", + "texts": [ + " Real systems, however, comprise elasticity and backlash so that the actual motion of the driven link deviates from the desired motion program at higher speeds due to interfering vibrations. The typical position function (VDI 2143)[36] of a stepping mechanism is composed of a perfectly straight dwell and a \u201cBestehorn sinoid\u201d for each phase of the motion. This kinematic excitation corresponds to a Fourier series with an infinite number of summands (4.138). HS curve profiles do not use such segment-wise position functions. Instead, Fourier series with a minimum number of summands are applied [4]. The dynamic behavior for the calculation model of a stepping mechanism according to Fig. 4.28b is examined on the one hand for a motion program in the form of a \u201cBestehorn sinoid\u201d and for an HS profile with k = 4 harmonics on the 4.3 Forced Vibrations of Discrete Torsional Oscillators 269 other hand. To be determined is the speed up to which operation is possible if the permissible tolerance range is utilized. The following parameter values are given: x = \u239b\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d US \u03d5\u2217 n J2 cT D \u0394U \u239e\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 = \u239b\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239c\u239d 30\u25e6 200\u25e6 300 rpm 0.22 kg \u00b7m2 5 400 N \u00b7m 0.02 0.3\u25e6 \u239e\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u239f\u23a0 Pivoting angle, see Fig. 4.29 Input angle of rotation per step, see Fig. 4.29 Operating speed Moment of inertia of the output link Torsional spring constant of the output shaft Damping ratio of the torsional oscillator Permissible error of dwell (\u201ctolerance range\u201d) (4.135) The equation of motion of the oscillator with motion excitation according to Fig. 4.28 results from the moment balance at the rotating output mass J2. It is known from (4.120): J2\u03d5\u03082 + bT \u00b7 ( \u03d5\u03072 \u2212 U\u0307 ) + cT \u00b7 (\u03d52 \u2212 U) = 0. (4.136) If the relative angle of the output shaft is used as the generalized coordinate q = \u03d52 \u2212 U ; q\u0308 = \u03d5\u03082 \u2212 U\u0308 = \u03d5\u03082 \u2212\u03a92U \u2032\u2032; ( )\u2032 = d( ) d\u03d5 , (4.137) the equation of motion is obtained. The zeroth-order position function of a stepping mechanism can be interpreted as superposition of a uniform motion and a periodic motion. The velocity and acceleration functions are then periodic functions of the input angle \u03d50, see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002920_j.matdes.2018.06.029-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002920_j.matdes.2018.06.029-Figure1-1.png", + "caption": "Fig. 1. CAD models of grinding wheels: a) octahedron structure wh", + "texts": [ + " Furthermore, grinding performances of the SLM-fabricated wheels and electroplated wheel are evaluated and compared with each other in terms of grinding force, material removal rate, ground surface roughness and hardness. The results reveal that the SLM-fabricated grinding wheels possess excellent dressing and self-sharpening ability, controllable pore structure and porosity, as well as good comprehensive grinding performance. In this study, three kinds of structures for grinding wheels are designed, including one 3D cellular structure \u2013 octahedron structure, one 2D porous structure \u2013 honeycomb structure and one solid structure. The CAD models for three kinds of grinding wheels are depicted in Fig. 1 and design parameters of grinding wheels are clarified in Table 1, including design porosity, outer diameter, inner diameter and wheel height. The dimension of octahedron cellular unit is defined as 2.83 \u2217 2.83 \u2217 2.83 mm and strut diameter is defined as 0.8 mm, making the porosity to a high level. The octahedron structure wheel is obtained by duplicating the cellular unit and then cut into a cylinder. The honeycomb structure wheel is obtained by slotting on the entity with regular hexahedral slot", + " Ground surface hardness is measured by the hardness tester (Qness Q60A+) via measuring the micro Vickers hardness. Test points are hit on the specimen surface by penetrator with a pressing force of 1 kg and duration time of 10 s. Surface topography of grinding wheels is obtained via SEM images shown in Fig. 7. It indicates the surface topography of octahedron structure wheel, honeycomb structure wheel and solid structure wheel in Fig. 7a, b and c respectively. The structures of SLM-fabricated grinding wheels are identical with CAD models depicted in Fig. 1 considering the fabrication accuracy. Fig. 7d and e represents the surface topography of solid structure wheel before and after grinding process respectively. After grinding process, the surface of SLM-fabricated grindingwheel becomes smoother due to the bond wear. Different from traditional hot pressing grinding wheel, during grinding process, chip flute will occur around diamond abrasive grain on the surface of SLM-fabricated grinding wheel. The self-formed chip flute, presented in Fig. 7f, results from the cutting effect of grinding chip" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003309_978-3-319-24729-8-Figure6.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003309_978-3-319-24729-8-Figure6.5-1.png", + "caption": "Fig. 6.5 2D flying robot", + "texts": [ + " In conclusion, we may assume that, in addition to the IMUdata, vehicle i has access to the relative displacement and relative orientation of vehicle j with respect to vehicle i\u2019s local frame. 72 6 Introduction to Flying Robots The flying robots discussed in the introduction have something in common. If we ignore the masses and moments of inertia of the rotors, each robot may be viewed as a rigid body propelled by a thrust vector that has constant direction in the body frame and is endowed with some steering mechanism that induces torques about three body axes. We will now model such a general setup, beginning with the simpler planar case. We begin with the simplified setup of Fig. 6.5, in which the robot flies in a horizontal plane, propelled by a thrust vector f parallel to its heading. The state of the robot is the position x = (x1, x2) of its centre of mass in an inertial coordinate frame, the velocity x\u0307 , the heading angle \u03b8, and the angular speed \u03b8\u0307. There are two control inputs: the magnitude, u, of the thrust vector and the torque, \u03c4 , about the axis coming out of the page. The thrust vector f in inertial coordinates is given by f = u [ cos(\u03b8) sin(\u03b8) ] . Let m denote the mass of the robot" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003185_j.surfcoat.2015.12.031-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003185_j.surfcoat.2015.12.031-Figure1-1.png", + "caption": "Fig. 1. Schematic of V-groove design.", + "texts": [ + "% Cu, and the balance Fe) with the dimension of 180 mm \u00d7 50 mm \u00d7 40 mm. Fe-based self-fluxing alloy powder (0.1 wt.% C, 14.92 wt.% Cr, m/s, Vp = 11 g/min). (a) 1.3 kW, (b) 1.5 kW, (c) 1.7 kW, and (d) 1.9 kW. 4.4wt.% Ni, 2.0 wt.%Mo, and the balance Fe) with the particle size in the range of 45\u2013100 \u03bcm was selected as the repairing material. The repairing zone was designed as V-grooves up to 10 mm in depth. For the purpose of discussing the effects of the V-groove bevel, three different angles (conducted for A1, A2 and A3) were prepared, as shown in Fig. 1. The dimensions of the V-grooves are listed in Table 1. Laser cladding was carried out using a diode laser-based cladding system, consisting of a 3 kW high-power diode laser (DILAS Fig. 5. Liquid penetrant test for cracks in SD3000/S) with 980 \u00b1 10 nm wavelength. The off-axial autofeeding powder equipment was used as the powder feeder and the lateral nozzle was kept at an angle of 45\u00b0 to the horizontal. Both the laser and the nozzle were fixed to a 6-axis KUKA robot system. Finally, an inert gas, Ar, was used as shielding and powder carrier gas" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002560_j.mechmachtheory.2018.11.026-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002560_j.mechmachtheory.2018.11.026-Figure6-1.png", + "caption": "Fig. 6. Meshing process in spur gears.", + "texts": [ + " The critical tooth thickness of the gear increases when using asymmetric teeth profile. Consequently, the stiffness of the teeth profile is increased, and the effects of crack length decrease by using an asymmetric teeth profile. During the rotation of the gears, torque is transmitted by the engagement and disengagement of one and two gear pairs in one mesh cycle, respectively. The torque transfer occurs on the line of action, which is a straight line for involute spur gears. A typical line of action for spur gears is shown in Fig. 6 . The meshing process begins at point A for the first tooth pair. At the same time, the second tooth pair is in contact at point D. Thus, at the beginning of the contact for the first tooth pair, there are two teeth pairs in contact. When the first tooth pair contact reaches point \u201cB \u201d, the second tooth pair leaves the contact and the torque is transmitted by only the first tooth pair, until point \u201cD \u201d. Therefore, point \u201cB \u201d is specially named \u201cLowest point of single tooth contact\u201d and point \u201cD \u201d is named \u201cHighest point of single tooth contact\u201d" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000037_j.ijnonlinmec.2004.08.011-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000037_j.ijnonlinmec.2004.08.011-Figure10-1.png", + "caption": "Fig. 10. A truss model for the Yamaki shell with Z \u2248 200: (a) initial buckling, (b) final buckling.", + "texts": [ + " On the other hand, the longer shells are clearly more able to tolerate large applied twists without much change from the form of initial buckling. This becomes clear from comparing values of in Table 3. At the stage seen experimentally, the long cylinders have peak and valley lines that remain close to being parallel, as demonstrated by the fact that the experimental values of are considerably smaller than those seen in the folding mechanism. The same change in characteristics between long and short cylinders can be seen in the following plots. Fig. 10 shows, for a shell of medium length, two comparative triangular patterns, one based on the simply supported initial buckling mode of Table 3, and the other on the truss mechanism. The increase in orientation angle required to produce a mechanism is clearly seen. On the other hand, Figs. 11(a)\u2013(f) give torque to end-shortening plots for various truss models of all of Yamaki\u2019s [3] shells, relating to all four situations of Table 3. Whereas the \u201cfinal buckling\u201d mechanism shows that the full end-shortening can be achieved with very little torque for short and medium length models, this is not the case for the longer models of the lower two plots" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001711_978-3-319-16310-9-Figure21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001711_978-3-319-16310-9-Figure21-1.png", + "caption": "Fig. 21. Statibilty of the controller", + "texts": [], + "surrounding_texts": [ + "We show the actions of a controller generated with weight (0.9788, 0.0211) by our framework in Plot 20(a). On the x-axis we present the distance to the car in front, while we present the relative velocity on the y-axis. The color indicates the applied acceleration. For example, where the distance is as desired (50 m), and the relative velocity is 0, no further acceleration is applied. Going through this point is a diagonal going from roughly (35, -15) to (65, 15) where applied acceleration equals zero. In this area, the controller judges the relative velocity just right to reach the desired distance quickly enough. As we move horizontally outwards from this narrow band, the acceleration the controller applies rises sharply. Especially, as either distance or relative velocity decreases, the controller increases the applied acceleration. Plot 19(b) shows one trace of the interplay between controller and environment as it happens in the continuous environment (i.e., we run the program defined above as it is). It starts out in position (50,10), i.e., where the distance is as desired but we are closing in too fast. As we follow the trace, we see that the car equipped with an ACC gains on the car in front (as its velocity is greater than that of the other car). The color of the trace shows the applied braking force in each particular moment. As we can see, the controller brakes the car harshly until he reaches a relative velocity of -3 m/s. At this point it slowly decreases the de-acceleration until a relative velocity of about -5 m/s is reached. It now maintains speed until we reach a distance of about 47 m (i.e., the car is 3 meters too close). Would the controller maintain speed here, then it would overshoot the desired distance. Instead, it gently accelerates the car again until it reaches a relative velocity of 0 and is very close to the desired distance. The \u201cball\u201d region around the desired distance and relative velocity 0 shows how the controller reacts to the random behavior of the car in front. In Plot 20(b), we present a controller generated with weight (0.9588, 0.0411). In comparison to the weight above, we have decreased the importance of rewards[0], and increased the importance of rewards[1]. This decreases the importance of the distance to the other car and increases the importance of not applying too much acceleration. This has the effect of growing the band where relative velocity is judged adequate, and also moving the area of increased acceleration further out. These two examples show that the weight chosen when optimizing a controller can have a strong influence on the one hand, and that choosing weights is not intuitive on the other hand, especially as the number of dimension increases. We therefore consider the easy availability of Pareto Curves an asset of our framework. Verification. Once a controller has been selected, we can turn to verification and validation. To that end, we support two systems that complement each other: (1) a classical probabilistic model checking algorithm, and (2) a Bayesian probabilistic model checking algorithm. Correctness of Service Components and Service Component Ensembles 141 142 J. Combaz et al. Correctness of Service Components and Service Component Ensembles 143 Classical Probabilistic Model Checking. We use both systems to judge how the controller behaves if assumptions we made about the environment are not met and how the controller behaves with regard to properties that were not used for its construction. As an example of the latter, we can consider the stability of the system. In control theory, stability is the property of a system to reach a bounded set of states and never leave it. In our case, we define this set as a bound on the deviation of the distance of the two cars from the desired distance. We can easily state a desired bounded set of states via PCTL formula: P=?[G(|d \u2212 50| < c)], where d denotes the distance between the two cars and c is a constant. This formally asks \u201cwhat is the probability of from now on always (denoted by G) seeing states whose deviation from 50 meters is less than c. Our framework takes this formula as input and calculates the probability of being in a stable (i.e., in a state from which only other stable states can be reached) for each state. In Plot 21(a) we plot the probability of being in a stable state, where we arbitrarily judge a state stable if c = 5. Note, first, that any state with a distance not within 5 meters of the desired distance cannot be stable. Note second, that as the relative velocity becomes more extreme, the probability of a state being stable goes towards zero. At the very extreme ends, the controller is unable to maintain control over the relative velocity in a way that guarantees that the distance will stay within 5 meters of the desired distance. Closer to the area where relative velocity is 0, the probability lies between 0 and 1. The reason that there is no sharp threshold between probability 0 and 1 lies in the random acceleration of the car in front. With a certain probability, the car in front will contribute to moving the distance towards the desired distance (braking where the controller needs to accelerate and vice versa). With a certain probability, the car will work against our controller (accelerating where we need to accelerate, braking where the controllers needs to brake as well). Judging the probability of reaching a stable state is an additional task. This can be easily done in our framework by checking the controller against formula P =?(FP=1[G(|d \u2212 50| < c))). Verbally, this means \u201cwhat is the probability of reaching a state such that the state is stable almost surely?\u201d. As it turns out, the probability is 1 for all states of our model, i.e., under the given assumptions the controller is able to reach and maintain a low deviation from the desired distance to the other car almost surely. We can now modify certain parameters of the system, and judge its behavior under these modified assumptions. For example, consider very rainy weather, where we assume that acceleration only works at 70% efficiency of what the controller expects7. In this case, the probability of a state being stable is only about at most 40% (see Plot 21(b))8. Lastly, our framework also allows us to easily turn the tables around and choose actions for the car in front. In this new model, the braking force applied 7 This assumes that we use the same controller in bad weather, and that we cannot compensate 8 Note that there are techniques for dealing with uncertain parameters(e.g., Robust Markov Decision Processes 144 J. Combaz et al. Correctness of Service Components and Service Component Ensembles 145 by the ACC is determined by a controller we previously generated, and we now synthesize worst-case accelerations for the car in front. This is easily achieved by replacing the function next of the Java class ACC (defined previously) by the following implementation. public void next(double acceleration2 , ACC target) { double acceleration = controller.get(this); double nextVelocity = velocity + (accleration + acceleration2) / ticks; double nextDistance = distance - (0.5 * velocity + 0.5 * nextVelocity) / ticks; target.velocity = nextVelocity; target.distance = nextDistance; } Now we can apply the very same techniques we used above to compute the worst-case probability of a state being stable. Bayesian Probabilistic Model Checking. As we have noted before, the models described in Java lend themselves directly to continuous state space simulation. In general, we cannot check PCTL formulas since they may express properties over infinite runs. Instead we have to give time-bound formulas. As an example, we consider a formula expressing the property \u201cWhat is the probability that we reach a state inside 5 meters around the desired distance in 1000 steps (where 1 step is 10 milliseconds long), and stay inside this area for the next 1000 steps.\u201d Bayesian probabilistic model checking allows us to make statements like \u201cgiven the set of samples generated, the probability that this formula is true lies in the interval [a, b] with probability c\u201d. In this framework, the width of the interval b \u2212 a and confidence c are configurable. In our case it turns out, that with 95% confidence the formula holds with probability [0.98, 1.00] from some randomly generated state. We assume that the remaining cases will require longer runs. For comparison, we decreased the efficiency of the applied acceleration to 70%. In this case, we get an interval [0.971297, 0.991297], which shows us that the controller performs well even under adverse conditions. Conclusion. We believe that our framework is the first time that verification and synthesis are present in a loop in the same tool. It allows engineers to (1) quickly model probabilistic environments for controllers in a language they know, (2) study the trade-offs their model possesses and pick a controller that is to their liking, (3) study the robustness of their controller with respect to environment assumptions, (4) study the performance of the controller in criteria for which the controller was not optimized, (5) allow efficient specification of latter criteria via a formal language, (6) judge the effect of discretization on the same criteria via the simulation engine we contribute. (7) effectively compare the influence discretization resolution has on the controllers. In addition to what we presented here, our framework is developer-friendly and open and allows for quick addition of new synthesis and analysis algorithms. It also allows the easy consumption of new input formats. For example, to judge" + ] + }, + { + "image_filename": "designv10_3_0001241_978-3-319-02636-7-Figure5.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001241_978-3-319-02636-7-Figure5.2-1.png", + "caption": "Fig. 5.2 The Tora system", + "texts": [ + " For such systems, we shall propose a strategy to construct stabilizing control laws in the following subsections. In order to illustrate the procedure, let us consider a system that is initially in the tree structure, for example the Tora system. This system is composed of a platform that can oscillate on the horizontal plane without friction. On this platform, an eccentric mass is actuated by a DC motor. Its movement applies a force to the platform, which can be used to dampen the transverse oscillations; see Fig. 5.2. The problem of stabilizing this system was introduced by Wan, Brenstein and Coppola [22] and has recently attracted the attention of many researchers by the fact that it presents a nonlinear interaction between the translational and rotational motions. It has also been used as a benchmark for the nonlinear control of cascaded systems, especially the passivity-based methods [12, 13, 17], backstepping [15, 22], robust control and sliding modes [10, 14, 24], dynamical surfaces [16], LMI (linear matrix inequality) controllers [1, 9], velocity gradient [8], and fuzzy logic [11, 23]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001796_978-3-319-32156-1-Figure2.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001796_978-3-319-32156-1-Figure2.6-1.png", + "caption": "Fig. 2.6 Systems engineering integration of disciplines and technologies [4]", + "texts": [ + " Overseeing these developments we could question what mechatronics actually is or will be. Is mechatronics being disrupted? Has it evaporated already into systems engineering, is it part of the supporting disciplines, does it enlarge to be the backbone of cyber physics? Moreover, if biological systems are also going to have technical devices implemented (Internet of Humans), what is then the role of the mechatronics discipline? How should we educate people in mechatronics thinking, how small or how broad? In Fig. 2.6 the role of systems engineering is used to enable the necessary integration of the disciplinary as well as the technological contributions. In this book many of the mentioned developments will be addressed. We will not have definite answers for the future of mechatronics, nor for its education, but we learn also that this should be robust and adaptable because we cannot predict the future! We know for sure that the pace of technological development is accelerating, hence, so should we! 24 M. Steinbuch 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002105_j.protcy.2014.08.003-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002105_j.protcy.2014.08.003-Figure2-1.png", + "caption": "Fig. 2. Image of the test bearing and the defect (a) test bearing BB1B420204 (b) components of the test bearing (c) circular defect on outer race", + "texts": [ + " A photographic view of the test set up on which experiments have been performed is shown in Fig. 1.The test bearing is mounted on the stepped portion of the cantilevered shaft. A polymer cage deep groove ball bearing with the designation as SKF BB1B420204 has been selected for the creation of defect on the outer race of the bearing. The polymer cage bearing has been selected to enable ease in assembling and disassembling of the bearing elements so that progressive increase of defect size can be created. The image and the details of the bearing are presented in Fig. 2 and Table 1 respectively. Circular defects of varying sizes i.e. 1.3 mm, 1.5 mm, 1.77 mm and 2.02 mm have been achieved through the Electric Discharge Machining (EDM) process. A Br\u00fcel & Kj\u00e6r type 4368 accelerometer with an undamped natural frequency of 39 KHz has been used for acquiring the vibration signal in the form acceleration by mounting it on the top of test bearing housing. The captured signal was stored in ONO SOKKI (CF3200) Fast Fourier Transform (FFT) Analyzer through charge amplifier and analyzed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002573_j.ijfatigue.2019.105301-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002573_j.ijfatigue.2019.105301-Figure1-1.png", + "caption": "Fig. 1. Geometry of the fatigue specimens for load increase and constant amplitude tests.", + "texts": [ + " This is underpinned by the fact that all fatigue failures in the present work originated either at fatigue slip bands or at microstructural defects and in no case any grain boundary damage has been observed. The results of not heat treated bars were already published in [5] and are used as reference (SLM-H; SLM-V). To exclude the influence of surface topography, the bars were turned to the final geometry of the fatigue specimens and subsequently polished in the gauge length. The geometry of the fatigue specimens is in accordance with DIN 50100 [37] and given in Fig. 1. To investigate the influence of additively manufactured surface on the fatigue properties, specimens were manufactured near-net-shape in both building directions (SLM-H-AB; SLM-V-AB). Again, a heat treatment at 650 \u00b0C for 2 h has been performed before built plate removal, to avoid plastic deformation of the specimens. The sector of the SLM-H-AB specimens\u2019 gauge length, which contained the support structure, was polished to exclude the influence of the support structure on fatigue behavior. Consequently, the SLM-H-AB specimens show more or less the half of the additively manufactured surface area compared to the SLM-V-AB specimens" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure15-1.png", + "caption": "Fig. 15. Tresca stress distribution in the pinion tooth model for case A1 and mesh M3without any averaging threshold: (a) slice of the pinion tooth model, and (b) detail A showing points along the normal direction for collecting stress results.", + "texts": [ + " 13(b) shows the overclosures distribution on the pinion tooth surface. A visual comparison of the area of contact in Fig. 13(a) and the area of interference between pinion and gear tooth surfaces in Fig. 13(b) shows a significant difference. Fig. 14 shows the pressure distribution p(x) and p(y) along dimensions a and b, respectively, in case A1, obtained from the Hertz theory and from the finite element method throughmeshM3. Fig. 14 shows that bothmethods provide similar distributions of pressure. Fig. 15(a) shows the Tresca stress distribution on the middle slice of the pinion tooth model. Since no averaging threshold is considered in the representation, discontinuities are observed. Fig. 15(b) shows a detail of the middle slice of the pinion tooth model. Fig. 15(b) shows as well the set of points along the normal direction to the pinion tooth surface for collecting stress results. The start point coincides with the contact point. The end point is 5b far from the start point in the normal direction. The middle points are obtained as the intersections of the normal direction to the pinion tooth surface and the element faces. Fig. 16 shows the Tresca stress distribution obtained for case A1 and mesh M3 when an averaging threshold of 35% is applied. Such an averaging threshold is large enough to smooth the Tresca stress distribution. The set of points considered in Fig. 15(b) is being considered here for representation of averaged values. Fig. 17 shows the variation of principal stresses and Tresca stress along the normal direction z, \u03c3x(z), \u03c3y(z), \u03c3z(z), and \u03c3T(z), in case A1, obtained from the Hertz theory and from the finite element method with mesh M3. The set of points represented in Fig. 15(b) was considered here for collection of the averaged and not-averaged stress results. Fig. 17 shows a good agreement of the stress variations obtained by the Hertz theory and the averaged stress results obtained by the finite element method. The obtained results for case A1, where the Hertz theory should work better than in other cases, confirm that the finite element model provided with mesh M3 is validated. Mesh M3 provides 52,788 elements with 58,697 nodes when one pair of teeth is considered" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000042_s11663-004-0104-7-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000042_s11663-004-0104-7-Figure1-1.png", + "caption": "Fig. 1\u2014Schematic illustration of LENS process.", + "texts": [ + " freeform fabrication process that has the capability of producing dense, near-net-shaped parts through the use of a computer-aided drawing (CAD). Fabrication of these structures is made possible when a continuous wave Nd:YAG laser is coupled with an underlying substrate to create a molten pool. Powder material is then injected into the molten pool through four nozzles and upon solidification, a metallurgical bond is formed between the substrate and the incoming powder. A schematic illustration of the process can be seen in Figure 1. The component is constructed in a line-by-line, layer-by-layer manner in a shape that is dictated by the CAD model. After the deposition of a single layer, the nozzles, as well as the focusing lens of the laser, are incremented in the ( ) z-direction to begin the deposition of subsequent layers, thereby building the three-dimensional form of the component. Successive layers are deposited atop one another until the three-dimensional part is completed in a layer-by-layer manner. Powders that have not been fused to the workpiece can often be recycled since the entire process is performed in an inert argon environment; however, the powder must first be sifted in order to remove unwanted contaminants and agglomerated powder particles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003603_tie.2020.2977578-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003603_tie.2020.2977578-Figure13-1.png", + "caption": "Fig. 13. Experimental devices.", + "texts": [ + " The relative errors of modal frequencies are all below 5%, verifying that the established FE model has sufficient accuracy for vibration calculation. Based on the previous analysis, the 30\u00b0 configuration has less harmonic components of MMF and radial force, and the vibration acceleration is lower in the entire frequency band. Therefore, the 30\u00b0 and 60\u00b0 configurations of the 48-slot/22-pole DTP-PMSMs are fabricated and tested to verify the theoretical analysis and predicted results. The experiments of the electromagnetic performance and vibration behavior are implemented, and the experimental devices are shown in Fig. 13. The predicted and measured of one set of three-phase no-load back-EMF waveforms at the speed of 200 r/min are shown in Fig. 14(a), and their corresponding spectrum analyses are shown in Fig. 14(b). The measured fundamental component Authorized licensed use limited to: UNIVERSITY OF BIRMINGHAM. Downloaded on June 14,2020 at 02:15:09 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003153_j.ymssp.2019.106553-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003153_j.ymssp.2019.106553-Figure2-1.png", + "caption": "Fig. 2. Experiment set-up. (a) Test rig, (b) accelerometer, and (c) localized roller defect.", + "texts": [ + " Firstly, an experiment was carried out to observe the vibration characteristics as a roller defect travels around a race (Section 2). Then, a dynamic model considering roller defects is proposed (Section 3). The proposed model is verified in Section 4. Based on the proposed dynamic model, the vibration characteristics when a roller defect goes around a race is investigated (Section 5). Finally, the conclusion is given in Section 6. In order to investigate the fault diagnosis techniques of cylindrical roller bearings, an experiment was carried out. The test rig is shown in Fig. 2(a). The outer ring of the tested bearing is installed inside the bearing housing, and the housing is bolted to the base plate. Two accelerometers are used to measure the vibrations of the bearing in the y and z axes, as shown in Fig. 2 (b). The accelerometers are 8763B50AB type Kistler ceramic shear triaxial IEPE accelerometers. The tested bearing is a 32,205 cylindrical roller bearing whose basic parameters are listed in Table 1. A defect is produced by wire-electrode cutting as shown in Fig. 2(c). The geometrical property of the roller defect is shown in Fig. 3. The width of the roller defect, wd, is 1.5 mm, and the depth of the defect in the experiment, dd1, is 0.5 mm (the other geometrical parameter dd shown in Fig. 3 can be calculated based on the roller diameter and wd as about 0.083 mm). The acceleration signals were recorded by a Coco-80 dynamic signal analyzer produced by Crystal Instrument. The sampling frequency is 25.6 kHz. The rotation speed of the shaft is 600 r min 1 (rotation frequency f r \u00bc 10 Hz). Based on the geometric property of the investigated bearing, the rolling-element-defect-frequency (REDF) calculated based on pure-rolling assumption [1,52] is about 2:69f r (26.9 Hz) and the cage rotation frequency is about 0:41f r (4.1 Hz). In the experiments, the tested bearing is loaded by rotating the handle (Fig. 2(a)). When rotating the handle, the threaded rod connected to the handle moves vertically, and thus applies a radial force for the shaft. As the inner race is connected to the shaft, the radial force can also be applied to the inner race of the bearing. The magnitude of the radial load is related to the vertical displacement of the threaded rod. The applied radial load is about 50 N. The tested bearing was lubricated by grease. The collected vibration signal of the defective bearing system in the z direction when the roller defect goes around the outer race is shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.8-1.png", + "caption": "FIGURE 2.8. Global roll.", + "texts": [], + "surrounding_texts": [ + "2. Rotation Kinematics 41\nTh e expanded form of the 12 global axes tr iple rotations are presented in Appendix A .\nExample 8 Order of rotation, and order of matrix multiplication. Changing the order of global rotation matrices is equivalent to changing the order of rotations. Th e position of a point P of a rigid body B is located at B r p = [1 2 3 f . Its global position aft er rotation 30deg about X axis and then 45deg about Y -axis is at\n-0.84 0.15 -0.52\nQy,45 QX,30 B r p\n[\n0.53 0.0\n-0.85\n0.13 ] [ 1] [-0.76 ]0.99 2 3.27 0.081 3 - 1.64\nand if we change th e order of rotations then its posit ion would be at\nQX ,30 Qy,45 B r p\n[ 0.53 0.0 -0.84 0.15 -0.13 -0.99 0.85 ] [ 1] [ 3.08]0.52 2 1.02 0.081 3 -1.86\nTh ese two final positions of Pare d = I(Gr p) 1- (Gr p) 21 = 4.456 apart .\n2.3 Global Roll-Pitch-Yaw Angles\nThe rotat ion about the X -axis of the global coordinate frame is called roll, the rotation about the Y-axis of the global coordinate frame is called pitch, and the rot ation about the Z-axis of the global coordinate frame is called yaw. The global roll-p it ch-yaw rotation matrix is\nQ Z ,,,!QY,{3Qx ,o:\n[ e(3q - co:S'y+ q sa s(3 e(3s,,! co:e\"!+ sas(3s,,! -s(3 e(3sa sas\"! + caqs(3 ] - qsa + ea s(3s,,! . (2.29) co:e(3\nGiven the roll, pitch , and yaw angles, we can compute the overall rotation matrix using Equation (2.29). Also we are able to compute the equivalent roll, pit ch, and yaw angles when a rot ation matrix is given. Suppose that r i j indicat es the element of row i and column j of the roll-pitch-yaw rot ation matrix (2.29), then the roll angle is\na = tan- 1 (1'32) 1'33 (2.30)", + "42 2. Rotation Kinematics\nand the pit ch angle is\n(2.31)\nand the yaw angle is\nprovided that cos (3 =f: O.\n'Y = tan-1 (r21 )\nrll (2.32)\nExample 9 Global roll, pitch, and yaw rotations. Figures 2.8, 2.9, and 2.10 illustrate 45 deg roll, pitch and yaw about the axes of global coordinate frame.", + "2. Rotation Kinematics 43\n2.4 Rotation About Local Cartesian Axes\nConsider a rigid body B with a space fixed at point O. The local body coordinate fram e B(Oxyz) is coincident with a global coordinate frame G(OXYZ) , where the origin of both frames are on th e fixed point O. If the body undergoes a rotation 'P about the z-axis of its local coordinate frame, as can be seen in the top view shown in Figure 2.11 , then coordinates of any point of the rigid body in local and global coordinate frames are related by the following equat ion\nBr = A z,'f' Gr . (2.33)\nThe vectors G r and B r are th e position vectors of the point in global and local frames resp ectively\n[ X Y Z JT [ x Y z f\n(2.34)\n(2.35)\nand A z,'f' is the z-rotation matrix\nA\" ~ [ ~~r:~ :~~~ ~] . (236)\nSimilarly, rotation e about the y-axis and rotation 1jJ about the x-axis are describ ed by the y-rotation matrix Ay,o and t he x -rotation matrix Ax,,p respectively.\n[\ncos e 0 Ay,o = 0 1\nsine 0\n[\n1 0 Ax,,p = 0 cos 1jJ\no - sin 1jJ\n- s~ne ]\ncos e\nsi~ 1jJ ] cos 1jJ\n(2.37)\n(2.38)" + ] + }, + { + "image_filename": "designv10_3_0003296_1.4935711-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003296_1.4935711-Figure1-1.png", + "caption": "FIG. 1. Initial setting of computational domain.", + "texts": [ + " Supplementing the three basic conservation laws with the fourth volume of fluid (VOF) equation describing conservation of fluid volume in the simulation grid allows calculation of the transient 3D location of the void-fluid interface shape and hence the shape of the fluid free surface. The commercial software FLOW3D (Flow Science, Inc.) is used to solve the equations. The fundamental fluid volume conservation equations, constitutive equations, and more details of the modeling of process heat and mass inputs are given in a recent paper by the authors.19 The computational domain in Fig. 1 has dimensions of 2.8 cm, 1.5 cm, and 0.9 cm in the X, Y, and Z directions, respectively. The Z direction has 0.5 cm of substrate and 0.4 cm of void region. The domain mesh is divided into two blocks to reduce computational load. The lower block from Z\u00bc 0 cm to 0.4 cm has 26 600 cells with edge length 400 lm and the upper block from Z\u00bc 0.4 cm to 0.9 cm has 262 500 cubic cells with edge length 200 lm. These cell sizes are selected to optimize mesh size independence of simulation results. For the bottom surface of the substrate, continuous heat flow boundary conditions are defined to model a semiinfinite domain" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001273_tie.2010.2050753-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001273_tie.2010.2050753-Figure2-1.png", + "caption": "Fig. 2. Three-dimensional model of the robot.", + "texts": [ + " In this section, the model of the biped robot and the controllers are shown. An overview of the biped robot used in this research is shown in Fig. 1. The robot is a 3-D biped robot with a serial link structure. Each joint has an actuator and an encoder. The responses of the position and the posture are calculated from the encoders with direct kinematics. Additionally, each corner of soles has a force sensor, and the response of the ZMP is calculated from the force sensors. The 3-D model of the robot is shown in Fig. 2. The robot has four degrees of freedom (DOFs) in a frontal plane and six DOFs in a sagittal plane. It is modeled as a rigid body of a system of 11 mass points. Thus, the model for trajectory tracking control is the 11-mass COG model. Moreover, the total COG of the robot is calculated from the 11-mass COG model. Table I shows the parameters of the links. The length of the foot in the forward direction is 0.26 m. The origin of the coordinate is set on the ground just under the ankle joint at the time of the walk start" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000412_s0021-9258(18)54675-5-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000412_s0021-9258(18)54675-5-Figure5-1.png", + "caption": "FIG. 5. EPR spectra of 02-oxidized C24A-FdI (a) and native FdI (b ) at -10 K. C24A-FdI was 74.1 PM and native FdI was 41.4 PM in 100 mM potassium phosphate buffer, pH 7.4. Microwave power, microwave frequency, modulation amplitude, and gain were 1 mW, 9.59 GHz, 5 G, and 1.6 X lo4, respectively.", + "texts": [ + " These are interpreted as being due to inefficient packing in the vicinity of the C24A [4Fe4S] cluster giving rise to a higher B-factor for that cluster. If those peaks had been due to lower iron occupancy in the [4Fe4S] cluster site of the C24A protein, the optical spectra of the C24A protein would have been substantially different from that of the native protein. As shown in Figs. 3 and 4, this is not the case. The EPR of oxidized C24A was also found to be essentially identical in g value, shape, and temperature dependence to that of the oxidized native FdI (Fig. 5), as was the EPR of oxidized C20A (2). This EPR arises from the [3Fe-4S]+ cluster (7,23) confirming that its environment is essentially identical in all three proteins. As with the oxidized native and C20A proteins, no other EPR was observed from g = 1-14. Dithionite at pH 7.4 reduces the g -2.01 EPR to -5% of its oxidized intensity for all three proteins. No new EPR signals appear from g = 1-14 upon dithionite reduction of C24A at pH 7.4, demonstrating that like the native (20) and C20A (2) proteins, the C24A [4Fe-4S] cluster must have a very low reduction potential" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.47-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.47-1.png", + "caption": "Fig. 2.47 Derivation of the balancing conditions for a multicylinder machine", + "texts": [ + " This covers the case of an in-line engine with k cylinders. The interesting case of a V-engine or radial engine in which the piston directions are arranged at a specific angle is excluded from these considera- 166 2 Dynamics of Rigid Machines tions, see [1]. It is also assumed that all rotating masses, that is, the crankshaft with the rotating portions of the connecting rod (see m32, Fig. 2.29), are completely balanced. All cylinders should also be identical (equal masses and geometry) and only have different crank angles, see Fig. 2.47. The angle between the first crank (j = 1) and the jth crank is denoted as \u03b3j . The inertia forces can be stated in the form of a Fourier series, see (2.293). With (j = 1, 2, . . . , J), the following applies to each mechanism: Fj(t) = \u221e\u2211 k=1 [Ak cos k(\u03a9t + \u03b3j) + Bk sin k(\u03a9t + \u03b3j)] . (2.343) k identifies the order of the harmonic. If it is assumed that the crankshaft revolves at constant angular velocity, the crank angles are \u03d5j = \u03a9t + \u03b3j . \u03b31 = 0 applies to the first cylinder. The Fourier coefficients (Ak; Bk) of a mechanism are assumed to be known" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001688_bi00912a015-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001688_bi00912a015-Figure2-1.png", + "caption": "FIG. 2.-Ag-AgCl reference electrode with ground glass junction replacing fiber junction of a commercial Beckman electrode.", + "texts": [ + " The microburet was controlled from the out,side of the Faraday cage by means of a long, insulated extension handle. Electrode System.--The Ag-AgCI reference electrode was employed since i t is much more stable and adjust.s more rapidly t o temperature changes than the calome! electrode (Bates, 1954). The fiber liquid junction comrnoply used in reference electrodes shows poor stabiiity even in simp!i: salt aoiutions :Leonard, 1955'. and especially in protein solutions because of adsorption of the proteins on the fiber. Therefore the liquid junction was changed (see Fig. 2 ; to a ground glass one. The junction cmplojreci was Srst suggested by L. Hammett iLaMer and Baker, 1922) and was shown to have a highly reproducible potential. The junction can be readily flushed and cleaned. 1046 JACOB LEBOWITZ AND MICHAEL LASKOWSKI, JR. Biochemistry The leakage rate is very small; in order to reduce it further the hydrostatic head in the electrode was kept very low. In order to minimize instability due to protein systems, the salt concentration in the liquid junction was the same as in the protein solutions; Le" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000855_tie.2011.2159357-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000855_tie.2011.2159357-Figure6-1.png", + "caption": "Fig. 6. Analysis model in this paper.", + "texts": [ + " (32) In this paper, Nh = 4, Nl = 10, and Ns = 14 are selected, and the gear ratio is \u22122.5. The orders of the cogging torque and constraints are shown in Table I. The cogging torque is generated by the two imaginary magnets and one stationary part, but the orders are the same. Moreover, the fundamental order of the cogging torque on the low-speed rotor is 2.5 times higher than that on the high-speed rotor. In order to verify the orders shown in Table I, 3-D FEM was employed. Moreover, the analysis model is shown in Fig. 6, and the major dimensions and material properties are shown in Tables II and III, respectively. The 14 stationary pole pieces are joined to each other by means of a flux path facing the high-speed rotor, whose width is 0.5 mm. This structure helps not only by making assembly easier but also by reducing the cogging torque. However, it is thought that the maximum transmission torque slightly decreases due to the short circuiting of the magnetic flux. The magnetic flux density is computed by employing the magnetic vector potential A in 3-D FEM" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002127_j.addma.2016.10.009-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002127_j.addma.2016.10.009-Figure4-1.png", + "caption": "Fig. 4. Arc deflection due to the action of electromagnetic force: 1 \u2013 arc, 2 \u2013 drops, 3 \u2013 wire, 4 \u2013 contact tube, 5 \u2013 workpiece, 6 \u2013 power source, 7 \u2013 point with stronger electromagnetic field, a1 \u2013 angle of the direction of the drops, a2 \u2013 angle of the welding arc [21].", + "texts": [ + " Lack of fusion (aka, ncomplete fused spots, incomplete fusion, or incomplete penetraion) is often seen in welded joints or products from AM processes nd it is a major reason for part-structural failure. The lack of fusion rack is normally a sign of insufficient welded material overlaps ith the parent material and, for instance in AM, could introduce racks between two adjacent scan lines or between two adjacent ayers. Another cause of lack of fusion crack is the arc blow in a elding process where the electromagnetic force is hard to conrol which gives bad angles of energy input. Fig. 4 shows the arc eflection due the electromagnetic force [21]. Lack of fusion, if not ignificant, is very difficult to find after the manufacturing process. owever, performing a fatigue test will normally initiate the crack s the bonds between welded materials and parent materials are enerally weak. Fig. 5 provides a typical example of cracks initited by lack of fusion during fatigue testing [22]. Lack of fusion can e controlled by conducting ultrasonic inspection, penetrant testng (PT), correcting the energy input angle, edge preparation, and djusting the laser parameters" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure3-1.png", + "caption": "Fig. 3. Simplified PM magnetic circuit of CPM2 and CPM3. (a) CPM2. (b) CPM3.", + "texts": [ + " See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Figs.3 (a) and (b) show the simplified PM magnetic circuit of CPM2 and CPM3, respectively. It can be observed that the end leakage flux is bipolar in the CPM machines with symmetric pole-sequences. It means that the magnetized risk of the mechanical components can be eliminated effectively. Fig.4 (a) shows the further simplified main PM magnetic circuits of CPM2 and CPM3, which are derived based on Fig. 3. It can be seen that the main PM flux does not pass the airgap above the iron-poles, and it is closed through the PMs with different polarity. These are confirmed by the FE predicted flux distributions of their slotless models in Fig.4 (b). Consequently, the airgap flux density of CPM2 and CPM3 have undesirable subharmonics, especially 1st, which will result in the saturation of the stator yoke in practical models, and the reduction of the working airgap flux density (5th) and output torque. Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure1.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure1.5-1.png", + "caption": "Fig. 1.5 Diagram of a primitive machine with four coils.", + "texts": [ + " The general theory given hereafter is developed to cover a wide range of machines in a unified manner. A very important part of this generalization applies to the two-axis theory in which, by means of an appropriate transformation, any machine can be represented by coils on the axes. However, other forms are possible, for example the phase equations of an a.c. machine or those of a commutator machine with brushes displaced from the axis. Kron called the two-axis idealized machine, from which many others can be derived, a primiti]!(' machine. Fig. 1.5 shows the diagram of such a primitive machine with one coil on each axis on each element, viz., F and G on the stationary member and D and Q on the rotating member. Some machines may require fewer than four coils to represent them, while others may require more. The Basis of the General Theory 9 Any machine, however, can be shown to be equivalent to a primitive machine with an appropriate number of coils on each fixed axis. If the coils of the practical machine are permanently located on the axes, they correspond exactly to those of the primitive machine, but, if they are not, it is necessary to make a conversion from the variables of the practical machine to the equivalent axis variables of the corresponding primitive machine, or vice versa", + " The properties are the same as those possessed by a commutator winding, in which the current passes between a pair of brushes, viz., Such a coil, located on a moving element but with its axis stationary, and so possessing the above two properties, may be termed a pseudo-stationary coil. The commutator machine of Fig. 1.4 may be either a d.c. machine or an a.c. commutator machine depending on the nature of the supply voltage. The actual circuits D and Q through the commutator winding not only form pseudo-stationary coils like the coils D and Q of the primitive machine of Fig. 1.5, but have the same axes as these coils. There is thus an exact correspondence between Figs. 1.4 and 1.5, and as a result the two-axis equations derived for the primitive machine of Fig. 1.5 apply directly to the commutator machine of Fig. 1.4. On the other hand, the three moving coils on the armature of the synchronous machine of Fig. 1.3b do not directly correspond to the coils D and Q of Fig. 1.5. In developing the two-axis theory of the synchronous machine, the three-phase coils A, Band C are replaced by equivalent axis coils D and Q, like those of Fig. 1.5, or in other words, the variables of the (a,b,c) reference frame are replaced mathemat- ically by variables of the (d,q) reference frame. The transfonn ation involved in the conversion, which depends on the fact that the same m.m.f. is set up in the machine by the currents of either reference frame, is explained and justified in Section 4.2. In applying the two-axis theory to any type of rotating electrical machine the process may be summarized as follows. The diagram of the idealized two-pole machine is first set out using the smallest number of coils required to obtain a result of sufficient accuracy", + " The conventional theories of electrical machines apply mainly to steady conditions, which are easier to deal with than the more general transient conditions. The steady-state theories are usually developed for particular machines, in terms of phasor diagrams, equivalent circuits, and other devices, while transient conditions are considered quite independently. The general thcory developed in this book embraces all these different conditions and shows the relation between the transient and steady conditions, as well as between the different types of machine. The primitive machine of Fig. 1.5 has on each axis a pair of coils similar to the two coils of the transformer of Fig. 1.6. Since a The Basis of the General Theory 17 stationary coil on one axis is mutually non-inductive with a stationary coil on the other axis, there would, if the machine were at rest, be no voltages induced in any coil on one axis due to currents in coils on the other axis. Hence the equations of each pair separately would be similar to those of the transformer. When the machine rotates, however, there are additional terms in the equations because, as a result of the rotation, voltages are induced in the pseudo-stationary coils D and Q by fluxes set up by currents on the other axis (see p. 9). For the commutator machine of Fig. 1.4, or the alternative representation by four coils as shown in Fig. 1.5, the equations relating the voltages and currents in the four circuits are derived in Section 2.1 and stated in Eqn. 0.5). Parameters in Eqn. (l.5) may be either in actual units or in per-unit. R f + Lffp LdfP ir LdfP Rd +LdP Lrqw Lrgw -LrfW -Lrd W Rq +LqP LqgP LqgP Rg + LggP . ig (l.5) The constants in the equations are resistances R, self-inductances Lff, L d, L q, Lgg and mutual inductances Ldf, Lqg with suffixes indicating the coils to which they refer. Ldf and Lqg are analogous to the mutual inductance L12 in the transformer Eqns. (l.3). Lrd, L rf , L rq , Lrg are additional constants of a similar nature to inductances, determining the voltage induced in an armature coil on one axis due to rotation in the flux produced by a current in a coil on the other axis. In setting down the equations for each circuit in Fig. 1.5, the terms for all the internal voltages are added to the resistance drop and equated to the impressed voltage. The use of the matrix notation makes it easy to compare the different coefficients and shows at a glance which currents have zero coefficients. The four equations given by Eqns. (l.5) refer to a machine represented by the four coils of Fig. 1.5. In general, a machine represented in the diagram by n coils has n voltage equations, relating n voltages to n currents. The impedance matrix of such a machine has n2 compartments. In Eqns. 0.5) some terms contain the derivative operator p, and represent voltages due to changing currents in coils on the same axis as the one being considered. They are called transformer voltages, and are present even when the machine is stationary. Other terms, containing the speed w, represent voltages induced by rotation in the flux set up by the current in a coil on the other axis", + "6) becomes 2H Mt =Me +-pw wo (l.8) The per-unit system has the advantage, as mentioned on p. 13, that the quantities for different machines are of the same order of magnitude. The inertia constant H, which is used mainly for synchronous machines, has a value from two to six seconds for a wide range of designs of different sizes and speeds. The per-unit system, as applied to the mechanical quantities, has the disadvan tage that the dimensional consistency of the equations is lost. Considering only the rotor coil D of Fig. 1.5, the power Pd supplied to this coil is, from Eqn. (l.S) Pd = kpUdid In the above expression for P d, the first term is the ohmic loss, and the second and third terms give the rate of change of stored magnetic energy in the machine. Only the fourth and fifth terms contribute to the output power corresponding to the electrical torque. It therefore follows that the power Pe, corresponding to the torque developed by the interaction between flux and current, is determined by adding together the terms obtained by multiply ing all the rotational voltages by the corresponding currents. Hence for the machine represented in Fig. 1.5: Pe = kpw(Lrqidiq + Lrgidig - Lrriqir - Lrdidiq). 0.9) Using the definition of electrical torque given on p. 19, and the definition of base torque on p. 20, W Pe = --Me wo The negative sign appears because Pe is derived from the electrical power passing into the terminals, whereas Me is defined as a torque applied to the shaft. The following expression is therefore obtained for the electrical torque: Me = Wo kp [Lrriq ir - Lrgidig + (Lrd - Lrq )id iq ] . (1.10) Eqn. (1.10) applies particularly to a machine represented by the four coils in Fig. 1.5, for which the equations are those stated in Eqns. (1.5). In the more general case the same method can be used, although there may be more or fewer terms depending on the number of rotational voltage terms in the equations, and the expression for Me can be written down for any machine in the same way. If then the value of Me is substituted in Eqn. (1.8), an equation is obtained giving M t in terms of the currents and the speed. The assumptions made in Section 1.3 are based on those given by Park [3]", + " machine illustrated by Fig. 2.2. The machine has only two windings. The stator has a field winding on the vertical axis (which is now the pole axis of the d.c. machine) and the rotor has a commutator winding with brushes located so that an armature current sets up a field on the horizontal axis. The vertical axis is chosen as the pole axis in order to avoid having a negative sign in the voltage equations. The diagram represents a separately excited d.c. machine with its brushes in the neutral position. As in Fig. 1.5, the armature circuit through the brushes can be replaced by an axis coil on the direct axis. The coil A then has the pseudo-stationary property discussed on p. 9. The coils F and A of Fig. 2.2 correspond to the coils G and Din the primitive machine of Fig. 1.5 and the equations can be found from Eqns. (1.5) by omitting the first and third rows and columns of the impedance matrix. R = I--R_f_+_L_f_fP----i ____ ---i G LafW Ra + LaP (2.10) These two equations do not depend on any assumption that the flux wave is sinusoidal, since both the rotational voltage Lafwir in the armature winding and the voltage Lffpif in the field winding depend on the total flux regardless of its distribution. Eqns. (2.10) hold whether the quantities are expressed in actual units or in per-units" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002402_s11661-018-4826-6-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002402_s11661-018-4826-6-Figure1-1.png", + "caption": "Fig. 1\u2014Schematic diagram of constitutional liquation and direct liquation (localized melting) of the low-melting-point eutectic.", + "texts": [ + " Many previous works have attempted to explain the cracking mechanisms in the fusion welding of high-(Al+Ti)-content Ni-based superalloys and have confirmed that the cracks are owing to grain boundary (GB) liquation cracking in the HAZ. Further, the mechanisms governing GB liquation have been deemed as localized melting (also called direct liquation) of the c-c\u00a2 eutectic or as constitutional liquation of c\u00a2 particles and carbides.[8\u201312] It is well known, however, that the susceptibility of a secondary phase to constitutional liquation is primarily related to its solid-state dissolution behavior, as shown in Figure 1. Constitutional liquation was first proposed by Pepe and Savage,[8,13] and usually occurs below an alloy\u2019s equilibrium solidus temperature and can be described as follows: During the rapid heating process, the solute concentration in the matrix at the precipitate/matrix interface will increase with the solid-state dissolution of the precipitate (light-red ringed zone in Figure 1). When that solute concentration exceeds the alloy composition at a temperature equal to or above the equilibrium reaction temperature of the precipitate\u2013matrix eutectic, a metastable solute-rich liquid film will be formed at the precipitate/matrix interface, thus inducing the constitutional liquation (i.e., a subsolidus liquation) to occur. Subsequently, the adjacent liquation zones will connect to form a liquid film and will eventually crack under tensile stress (shown in Figure 1). According to a previous work, the solid-state dissolution process of a non-coherent precipitate is typically diffusion-controlled, and constitutional liquation can occur easily. Conversely, the solid-state dissolution of a coherent precipitate is usually interface-controlled, and the constitutional liquation will not occur.[14] Interestingly, once the particles (such as the c\u00a2 phase in nickel-based superalloys) exceed a critical dimension, a coherency loss will occur.[15\u201318] Considering that the sizes of the c-c\u00a2 eutectic, c\u00a2 particles, and carbides in the LSF-fabricated nickel-based superalloys are much smaller than those in cast superalloys,[5,19] however, it remains a controversy whether or not constitutional liquation occurs in LSF-fabricated nickel-based superalloy. Zhao et al.[20] have found that the cracks in LSF-fabricated Rene 88DT alloy (Al+Ti of ~ 5.5) are primarily liquated cracks resulting from the localized melting of the c-c\u00a2 eutectic (shown in Figure 1) in the previously deposited layer owing to the reheating METALLURGICAL AND MATERIALS TRANSACTIONS A from the subsequent laser deposition, and no constitutional liquation is found. In contrast to Zhao et al.\u2019s findings, Yang et al.[21] still attribute the GB liquation to the constitutional liquation of c\u00a2 particles in LSF-fabricated Rene 104 superalloy (Al+Ti of ~ 7.1) and the liquid film separates into cracks under tensile stress, as shown in Figure 1. Importantly, once the cracks are formed, their initial morphology will be affected by the subsequent laser deposition during LSF, in which the thermal history can be very complex, including melting, solidification, remelting, partial-remelting, cyclic annealing, etc. (Figure 1). Thus it is challenging to find direct evidence of GB liquation, which causes the controversy regarding the liquation cracking mechanism during LSF. In the present work, the laser remelting of an IN-738LC alloy deposit fabricated by LSF was carried out. Crack analysis combined with microstructural observation and microsegregation analysis was conducted on the laser remelting of the LSF-fabricated IN-738LC alloy, which will provide theoretical support for future extensive applications of LSF technology in superalloys with a high (Al + Ti) content", + " As shown in Figures 6(c) and (d), the crack, located at the GB according to Figure 5, exhibits the irregular and zigzag morphology typical of liquation cracking. Figure 7 shows the microstructure of GBs away from the RZ in the HAZ. As shown in Figure 7(a), there is an apparent liquation of the c-c\u00a2 eutectic, and a continuous liquid film is thus formed along the GB. The c\u00a2 phases dissolve into the c matrix incompletely while the MC carbides maintain their shape and size almost unchanged compared with that in the substrate deposit shown in Figure 1. A crack is observed to form preferentially along the intergranular liquid film which results from the liquation of the c-c\u00a2 eutectic located at the edge of the crack, as shown in Figure 7(b). The substrate deposit was reheated to 1160 C for 1 second and then was water-quenched in the thermomechanical simulation system, with the goal of simulating the possible microstructure evolution present in the HAZ during laser remelting/reheating. As shown in Figure 8, the liquated c-c\u00a2 eutectic and liquid film formed along the GB can also be found in the reheated deposit" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002819_j.mechmachtheory.2016.11.006-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002819_j.mechmachtheory.2016.11.006-Figure1-1.png", + "caption": "Fig. 1. Displacement increment along the line of action with driving gear eccentricity.in different rotational directions: (a) anticlockwise, (b) clockwise.", + "texts": [ + " If the driving gear has an eccentricity, the meshing point displacement along the line of action will change after rotating each unit angle. Compared with the ideal gear transmission, the displacement increment of meshing point along the line of action is defined as transmission error (TE). The part of transmission error caused only by eccentricity is defined as no load transmission error (NLTE), besides, we have DTE (eccentricity, tooth deformation and backlash are taken into account). The NLTE analysis model with driving gear eccentricity is shown in Fig. 1. For the reason that the formula of NLTE varies in different rotational direction, two kinds of analysis models as shown in Fig. 1 are presented. Where\u0394FLis the displacement increment along the line of action when the left side of driving gear tooth is in meshing state; the positive direction is defined by\u0394FL +, and the subscript 1 denotes driving gear. \u0394FR and\u0394FR + have the similar meaning. The NLTE is expressed as \u0394F e \u03c6 \u03b1 \u03b8 e \u03b1 \u03b8= sin( + \u00b1 ) \u2212 sin( \u00b1 )1 1 1 1 1 1 (1) where \u03c61 is the angular displacement of driving gear;e1and\u03b81are the driving gear eccentricity and its initial phase, respectively;\u03b1is the pressure angle. The upper symbols are available when the driving gear rotates counterclockwise, otherwise the under symbols are available" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000588_036354657700500303-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000588_036354657700500303-Figure3-1.png", + "caption": "FIG. 3. Preliminary deceleration phase.", + "texts": [ + " Preliminary deceleration may be accomplished over several gait cycles. Because all deceleration cycles are similar, however, we can describe the case with just one cycle. Deceleration requires a significant alteration in the normal gait. The cycle starts on the same foot that is to be planted for the cut. First, the foot descent period of the recovery phase is modified. With the knee extended, no backward motion of the foot before foot strike occurs. As the heel touches, the foot immediately plantar flexes to allow the full foot to contact the turf (Fig. 3A). With the body moving forward, a deceleration force develops. The torso becomes more erect and the foot dorsiflexes until the tibia angles ahead of the vertical (Fig. 3B). Now, the deceleration force becomes maximum. Both quadriceps and gastrocnemius provide the muscular power for deceleration. Knee joint flexion compensates for dorsiflexion of the foot so that the center of mass remains posterior to the planted foot. When the center of the player\u2019s mass passes the contact point, the planted foot only supports the player\u2019s weight. In many instances the knee flexes as much as 90\u00b0. Unlike a normal gait step, the second step of the deceleration cycle can be a passive step; that is, no change in velocity occurs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.42-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.42-1.png", + "caption": "FIGURE 5.42. A 2R manipulator, acting in a horizontal plane.", + "texts": [], + "surrounding_texts": [ + "260 5. Forward Kinematics\n14. Cylindrical robots.\nAttach the spherical wrist of Exercise 11 to the cylindrical manip ulator of Exercise 9 and make a 6 DOF cylindrical robot. Change your DR coordinate frames in the exercises accordingly and solve the forward kinematics problem of the robot.\n15. An RIIP manipulator.\nFigure 5.41 shows a 2 DOF RIIP 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 261\n17. SCARA manipulator.\nA SCARA robot can be made by attaching a 2 DOF RIIP manipulator to a 2R planar manipulator. Attach the 2 DOF RIIP manipulator of Exercise 15 to the 2R horizontal manipulator of Exercise 16 and make a SCARA manipulator. Solve the forward kinematics problem for the manipulator.\n18. * SCARA robot with a spherical wrist.\nAttach the spherical wrist of Exercise 11 to the SCARA manipulator of Exercise 17 and make a 7 DOF robot. Change your DH coordinate frames in the exercises accordingly and solve the forward kinematics problem of the robot .\n19. * Modular articulated manipulators by screws.\nSolve Exercise 7 by screws.\n20. * Modular spherical manipulators by screws.\nSolve Exercise 8 by screws.\n21. * Modular cylindrical manipulators by screws.\nSolve Exercise 9 by screws.\n22. * Spherical wrist kinematics by screws.\nSolve Exercise 11 by screws.", + "262 5. Forward Kinematics\n23. * Modular SCARA manipulator by screws.\nSolve Exercise 15, 16, and 17 by screws.\n24. * Space station remote manipulato r system .\nAttach a spherical wrist to the SSRMS and make a 10 DOF robot . Solve the forward kinematics of the robot by matrix and screw meth ods." + ] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure3.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure3.2-1.png", + "caption": "FIGURE 3.2. Axis and angle of rotation.", + "texts": [ + " To find the axis and angle of rotation we introduce the Eul er parameters eo, el , e2, e3 such that eo is a scalar and el , e2, e3 are components of a vector e , and, eo e (3.55) (3.56) (3.57) 3. Orientation Kinematics 89 Then, the transformation matrix G RB to satisfy the equation Gr = G RB B r , can be derived uti lizing the Eu ler parameters where e is the skew-symm etric matrix corresponding to e defined below. (3.59) Euler parameters provide a well-suited, redundant, and nonsingular ro tation description for arbitrary and large rotations. Proof. Figure 3.2 depicts a point P of a rigid body with position vector r , and the unit vector u along t he axis of rotation ON fixed in the global frame. The point moves to P' with position vector r' after an active rotation \u00a2 abo ut u. To obtain the relationship between r and r' , we express r ' by t he following vector equation: ----+ ----+ -7 r' = ON + N Q+ QP' . (3.60) By invest igat ing Figure 3.2 we may describe Equation (3.60) utili zing r , r' , ii, and \u00a2. r ' (r . u) u + u x (r xu) cos \u00a2 - (r xu) sin \u00a2 (r . u)u + [r - (r . u)u]cos \u00a2 + (u x r ) sin \u00a2 (3.61) Rearranging Equation (3.61) leads to a new form of the Rodriguez rotation formula r ' = r cos \u00a2 + (1 - cos \u00a2) (u \u00b7 r ) u + (u x r ) sin \u00a2 . (3.62) Using the Euler parameters in (3.55) and (3.56), along with the following trigonometric relations cos\u00a2 2 2 \u00a2 (3.63)cos - - 1 2 sin\u00a2 2 . \u00a2 \u00a2 (3.64)sm- cos - 2 2 1 - cos\u00a2 2sin 2 ~ (3.65) converts the Rodriguez formula (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.4-1.png", + "caption": "FIGURE 5.4. Illustration of a 3R planar manipulator robot and DR frames of each link.", + "texts": [ + "1, a DH table has five columns fo r fram e ind ex and four DH param eters . The rows of the four DH parameters for each frame will be fill ed by constant param eters and the joint variable. The j oint variable can be found by considering what fram es and links will m ove with each varying active jo int. 204 5. Forward Kinematics Example 126 DH table and coordinate frames for 3R planar manipulator. R stands for revolute, hence , an RIIRIIR manipulator is a planar robot with three parallel revolute joints. Figure 5.4 illustrates a 3R planar ma nipulator robot. The DH table can be filled as shown in Table 5.2, and the link coordinate frames can be set up as shown in the Figure. Example 127 Coordinate frames for a 3R PUMA robot. A P UMA manipulator shown in Figure 5.5 has Rf-RIIR main revolute joints, ignoring the structure of the end-effector of the robot. Coordinate frames attached to the links of the robot are indicated in the Figure and tabulated in Table 5.3. 5. Forward Kinematics 205 The joint axes of an K 1RI IR manipulator are called waist zo, shoulder Zl, and elbow Z2", + " So , we employ the half angle formula 2 0 I-cosO t an - = -----,- 2 1 + cos O to find O2 using an atan2 fun ction O2 = \u00b12 atan2 (h + l2)2 - (X + y)2 (X2 + y 2) - (li + l~) . (6.144) Th e \u00b1 is because of the square root, which generates two solutions. Th ese two solutions are called elbow up and elbow down , as shown in Figure 6.4. Th e first joint variable 01 can be found from (6.145) Th e two different solution s fo r 01 correspond to the elbow up and elbow down configurations. 6. Inverse Kinematics 281 Example 169 * Inverse kinematics and nonstandard DH frames. Consider a 3 DOF planar manipulator shown in Figure 5.4. The non standard DH transformation matrices of the manipulator are [ COS B1 0T _ sinB 1 1 - 0 o (6.146) [ 0089 2 - sinB z 0 l~ ]ITz = sinBz cosBz 0 (6.147) 0 0 1 0 0 0 [ c009 3 - sinB 3 0 ~ ]zT3 = sinB 3 cosB3 0 (6.148) 0 0 1 0 0 0 3TF [ ~ 0 0 l~ ]1 0 (6.149) 0 1 o . 0 0 1 Solution of the inverse kinematics problem is a mathematical problem and none of the standard or nonstandard DH methods for defining link frames provide any simplicity. To calculate the inverse kinematics, we start with calculating the forward kinematics transformation matrix \u00b0T4 r13 r14 ] rZ3 rZ4 r33 r34 o 1 (6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000312_jsen.2005.846173-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000312_jsen.2005.846173-Figure1-1.png", + "caption": "Fig. 1. Schematic illustration of the final microfabricated amperometric biochip device showing the borosilicate glass substrate after electron-gun sputter-deposition of platinum metal and the microdisc array design of the working electrodes showing the hexagonal-close packed arrangement of microdisc array elements.", + "texts": [ + " The composite polymer membrane of the biorecognition layer has been developed to incorporate the interference shielding capabilities conferred by electroactive polypyrrole [30] and the biocompatibility conferred by biomimetic phosphorylcholine derivatives [31]\u2013[33] associated with the natural cell membrane. We demonstrate broader dynamic range and increased stability with our approaches. Our programmatic goal is to achieve stable, continuous, implantable long-term biosensors for the detection and quantitation of clinically important analytes such as glucose and lactate for periods of up to six months. The die of the final implantable biochip is shown in Fig. 1. Using techniques based on standard microfabrication technology, two miniature microdisc array enzyme electrodes, along with their respective platinum counter electrodes and a common Ag/AgCl reference electrode, were prepared on the single biochip substrate of insulating and chemically resistant borosilicate glass. The overall physical dimensions of the biochip substrate are 4.0 2.0 0.5 mm (L W T). The chip was prepared in a multi-stage photolithographic process employing two masks. The first metallization stage involved deposition of 100 of Ti/W (adhesion layer) followed by 1,000 of platinum metal via electron-gun sputtering", + " To define the microdisc array pattern to the circular metallic electrode area, to passivate the various conductive traces, and to reveal the other active metallic areas and bonding pads, the second of two optical photomasks and photopositive photoresist was employed to allow through-holes of diameter 10 m to be fluoro-plasma etched into the silicon nitride layer above each working disk electrode. These bore holes were arranged in a hexagonal-close packed (hcp) array, with the spacing between holes of 20 m from center on center (Fig. 1). Such an arrangement yields the maximum microdisc array hole packing density of 74% within the defined working area. With the hcp arrangement, a total of 127 holes were accommodated within each working electrode area, resulting in an effective working electrode area of 9.98 mm . The silicon nitride layer was also simultaneously etched away at the reference and counter electrode positions to expose the underlying sputtered metal and the bonding pads. The chip was finally completely chemically modified with an organosilane adhesion promoting layer of either methacryloxypropyl trimethoxysilane or -aminopropyl trimethoxysilane followed by coupling to acryloyl (polyethylene glycol) NHS ester" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003857_j.engfailanal.2018.08.028-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003857_j.engfailanal.2018.08.028-Figure3-1.png", + "caption": "Fig. 3. Slice model of a helical gear: (a) slice model; (b) contact line on the plane of action.", + "texts": [ + " For the helical gears without identical slice profile, the proposed method is also applicable but the improvement of the calculation efficiency of the proposed method is not evident. It is obvious that the slice profile of the healthy helical gears is identical, and some fault gears also satisfy this situation, such as the uniform penetrating crack (see Fig. 2a), uniform penetrating spalling (see Fig. 2b) and uniform wear (see Fig. 2c). The slice profile of the healthy helical gears is identical, so the healthy helical gear is taken as an example to illustrate the idea of \u2018offset and superposition\u2019. According to the property of the involute, the arc length of SnHn in Fig. 3a is equal to the length of \u2032 \u2032S Hn n in Fig. 3b. The offset angle of the nth sliced gear relative to the first sliced gear \u03b8n can be expressed as: = \u2032 \u2032 =\u03b8 S H \u03b2 r nL \u03b2 Nr tan tan n n 1 b b1 b b1 (1) where rb1 is the radius of base circle of driving gear; \u03b2b is the helix angle of base circle. L is the face width of the helical gear and the face width of each sliced gear is l= L/N. \u0394\u03b8 is the rotation angle corresponding to a mesh period: =\u03b8 Z \u0394 2\u03c0 1 (2) where Z1 is the teeth number of driving gear. The normalized offset time of the nth sliced gear relative to the first sliced gear \u0394T is: =T \u03b8 \u03b8 \u0394 \u0394 n (3) The normalized time can be defined as \u03c4= \u03b8/\u0394\u03b8 (\u03b8 is the rotation angle of driving gear)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001216_tro.2011.2168170-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001216_tro.2011.2168170-Figure1-1.png", + "caption": "Fig. 1. Cable-driven open chains with various cable routings. (a) Planar open chain with cables attached to the end effector by routing through proximal segments. (b) Spatial open chain with all cables directly attached to the end effector.", + "texts": [ + " The force-closure analysis is aimed at the evaluation of the workspace, its optimization, and the minimization of the number of cables. As one would realize, too many cables will result in control complexity, an increase in system setup cost, and possible cable interference. However, the effort on force closure was mainly focused on single rigid-bodied cable-driven platforms [12]\u2013[18]. The force-closure analysis of open chains that are driven by cables has not been been addressed systematically in the literature. Given several cable routing configurations for an n-DOF open chain (see Fig. 1(a) and (b)), how can the force-closure condition be analyzed systematically to deduce meaningful results? Only recently has this issue begun receiving some interest. In [19] and [20], the authors showed that n + 1 cables can sufficiently restraint an n-DOF cable-driven open chain. However, the open chain had a special structure, in which each cable could only be attached to one link. The approach of their analysis was based on writing force/moment equilibrium equations for each body and then concatenating these to find the representation of the entire chain. Their analysis did not take into consideration the cable force coupling effect when cables may require routing to the distal segments through the proximal segments (see Fig. 1(a)). 1552-3098/$26.00 \u00a9 2011 IEEE In this paper, the authors propose a force-closure analysis based on the concept of reciprocal screw theory. Screw theory, in general, offers the benefit of allowing a geometric description of rigid-body motion, which makes it intuitive. In addition, through the use of reciprocal screws, force closure of the cabledriven open chain problem is analyzed by expressing individual wrench screws acting on the open chain as linear combinations of the reciprocal screws. The net torque at the joints are, then, determined by the superposition of the scalar components in their respective reciprocal screws", + " In the context of kinematic analysis of an open chain, numerous theorems have also been established for different types of open chain, i.e., proper (=d-DOF), deficient (d-DOF), where d is the dimension of the screw system that is available to the end effector [27]. However, this section will present the theorems for \u201cproper\u201d open chains, i.e., chains with just enough joints to fully position and orient the end effector. This means that there will be 3 DOF for a planar open chain, and 6 DOF for a spatial open chain (see Fig. 1). Based on the theoretical contributions given in [32], the following presents the main theorem along with several propositions that will be used in this paper. Theorem 1: For a \u201cproper\u201d open chain, the reciprocal screws \u0302$ir are unique and form a linearly independent set that spans the screws of the relevant wrench system. Note: \u0302$ir is a special screw, such that it is reciprocal to all screws of the chain, except for the ith one. Proposition 1.1: Any external wrench $ext can be uniquely expressed as a linear combination of the reciprocal screws, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure8.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure8.7-1.png", + "caption": "Fig. 8.7 Two-axis phasor diagram for the initial current and", + "texts": [ + "6, flUq = jXd\"fl/d flUd = jXq\"fl/q Hence Uq - jXd \"/d = constant = Cd Ud - jXq \"/q = constant = Cq where the constants Cd and Cq are Ud \" and Uq \" respectively as defined by Eqn. (8.41). Thus for a short period after a sudden change (during which U and I change) brought about by a fault or the operation of a switch anywhere in the system, the voltages Ud\" and Uq \", obtained by adding the 'subtransient reactance drops' (-jXd \"/d) and (-jXq\"/q ) to the components Uq and Ud of the terminal voltage (see Eqn. (8.41\u00bb remain unaltered. The relations are shown on Fig. 8.7, which is a phasor diagram similar to Fig. 3.10, except that the armature resistance Ra is neglected. PL\" is the direct-axis subtransient reactance drop (-jXd \"Id), and L\"N\" is the quadrature-axis sub transient reactance drop (-jXq \"/q ). ON\" is U\", the resultant of Ud \" and Uq \", and is called the voltage behind sub transient reactance. The voltage U\" remains initially unaltered after any sudden change. If the machine has no damper winding, or if the conditions of 188 The General Theory of Alternating Current Machines voltage", + " the problem are such that the rapidly decaying sub transient components of voltage and current can be neglected, the relations between the sudden changes of voltage and current are given by the equivalent circuits Db and Qb of Fig. 8.6, of which the overall reactances are Xd' and Xq respectively. In a similar way to the derivation of Eqn. (8.41) it can be shown that, without a damper winding, Ud -jXqlq = Ud' = constant} Uq -jXd'Id = Uq' = constant (8.42) Thus for the effective initial condition ignoring the sub transient components, the voltages Uq ' and Ud', obtained by adding the 'transient reactance drops' (-jXd'Id) and (-jXqlq ) to the com ponents Uq and Ud of the terminal voltage, remain unaltered. In Fig. 8.7, PL' is the direct-axis transient reactance drop (-jXd'Id) and L'N' is the quadrature-axis synchronous reactance drop (-jXqlq ). ON' isU', the resultant of Ud ' and Uq', and is called the Synchronous Generator Short-Circuit and System Faults 189 voltage behind transient reactance. The voltage U' remains initially unaltered after any sudden change. Fig. 8.7 also shows the steady-state phasor diagram, in which the synchronous reactance drops (-jXd/d) and (-jXq/q ) are added to the tenninal voltage. ON is Uo, the voltage behind synchronous reactance, which remains unaltered for any condition of steady operation. The phasor diagrams for the two alternative types of transient condition are similar to the steady-state diagram, differing only in the values of reactance used. Hence the use of the phasor diagram to detennine the initial currents after a sudden change follows the same lines as the steady-state two-axis method", + "44), is neglected the voltage drops suddenly from the original voltage U to the initial voltage Xe U/(X d' + Xe), which would be calculated by considering the generator to have a voltage U behind its transient reactance. Finally the steady voltage XeU/(Xd + Xe) could be calculated in accordance with ordinary steady-state theory by considering the generator to have a voltage U behind its synchronous reactance. Thus the curve showing the variation of the terminal voltage could be calculated by using the phasor diagram of Fig. 8.7 or Fig. 8.8 to determine the initial transient values and the steady value, and then fitting in appropriate time constants for the components of the change. The transient time constant Td t' depends on the external reactance. It is equal to Td' when Xe = 0 (short-circuit), and is equal to TdO ' when Xe = 00 (open circuit). For any given load impedance, Td t' is intermediate between these two extremes. Similarly the subtransient time constant Td t\" is intermediate between Td \" and TdO \". A calculation of this kind is valuable in studying the action of a voltage regulator used to maintain a constant voltage", + " For an accurate calculation a step-by step solution is necessary. During a load rejection test, in which the load is suddenly disconnected from a generator, the voltage rises, at first rapidly and then more slowly, until a new steady value is reached. The curve of variation of the voltage can be calculated by the method just described. Generally the sub transient effect is too rapid to be of any importance, and it is neglected in the following calculation. If the phasor diagram for the original load condition is that shown in Fig. 8.7, the voltage behind synchronous reactance is Uo. Hence if saturation is neglected, the steady voltage after the load is removed is Uo. The voltage behind transient reactance is U', and is the initial value of the voltage immediately after the load is removed. The appropriate time constant is the open-circuit direct-axis transient time constant Tdo'. Hence the r.m.s. voltage is given by: Ut = U' + (Uo - U')(I - (3- tiT dO ') (8.45) and is plotted on Fig. 8.11. The full line includes also the sub transient component" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002212_s00170-016-9510-7-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002212_s00170-016-9510-7-Figure10-1.png", + "caption": "Fig. 10 3D finite element mesh", + "texts": [ + " The basic geometry of the model used comprises of a rigidly clamped rectangular substrate plate of dimensions 160 \u00d7 160 \u00d7 10 mm. Based on earlier experiments, the width and height of each weld-deposition pass was taken as 4.5 and 1.5 mm, respectively [26]. Length of each pass is 80 mm and the speed of the weld-deposition torch is 2.0 m/min. A onethird overlap between each weld-deposition pass is considered [1]. The FEA model consists of 90,000 3D Solid-70 elements. For saving computational time, the deposition area is fine-meshed, while the rest of the substrate is coarsely meshed, as shown in Fig. 10. The double ellipsoid heat source model discussed in the previous section (Eq. 6 and 7) is used for the analysis. The elements of the depositing passes are deactivated initially before the solution phase and activated gradually during the depositing process. The initial temperatures of all nodes are set at the ambient temperature 300 K. The convergence and stability criterion for heat equation (1) under time marching scheme is ensured if the Courant number, C is less than 0.5, where C is defined as [34]: C \u00bc \u03b1\u0394t=\u0394x2 Where \u03b1=K/(Cp\u03c1) Thermal diffusivity K Conductivity (W/m-K) Cp Specific heat at constant pressure (J/kg-K) \u03c1 Density (Kg/m3) \u0394t Time increment (s) \u0394x Minimum size of the mesh (m) In these simulations,\u0394x is 5 \u00d7 10\u22124 m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000007_tro.2004.842336-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000007_tro.2004.842336-Figure1-1.png", + "caption": "Fig. 1. Reduced system. (a) Actual system. (b) Reduced system.", + "texts": [ + " The traditional approach to solving the inverse dynamics of closed chains is to first solve the inverse dynamics of the reduced system, followed by an application of D\u2019Alembert\u2019s Principle to solve for the actuated joint torques of the closed-chain mechanism. By adopting the Lie theoretic framework, we can exploit the recursive algorithms for the serial-chain case, and derive a similar set of recursive algorithms for exactly evaluating the closed-chain dynamics [32]. To illustrate the approach, let us consider the mechanism of Fig. 1. The motion of this mechanism is generated by the actuator at joint 1 and the external applied force . We can think of another identical mechanism that generates the same motion, 1F is the external force, e.g., tool force, applied to link fng expressed in frame fn + 1g. 2I is calculated with respect to a frame attached at the center of mass, with the same orientation as frame fkg. but and every joint is assumed actuated;3 this is essentially the concept of the reduced system. Note that the internal forces in the reduced system are different from those of the actual system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001805_1.4914606-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001805_1.4914606-Figure5-1.png", + "caption": "FIGURE 5. Scheme of image generation.", + "texts": [ + " In Fig. 4 the wavelength dependent sensitivity of the camera is illustrated. In addition, as an example a interval for a filter is shown. The gray-shaded area in the figure describes the permeable wavelength range of the filter which is detected by the OT-camera. The image data acquired with high frequency are stored in one image at the end of each layer. Between image generation and data storage image operations are performed to reduce noise. A basic online analysis is executed in the same time (Fig. 5). Interference signals are suppressed by means of the adapted spectral filter, so that a correlation between the OT signals and the quality of the welding process becomes possible. Therefore a correlation of potential defects in the component and the OT signal can be achieved. MTU currently operates six machines of the type EOSint M280, which are equipped with OT systems. The expansion of a machine with OT-system is shown in Figure 6. Without major modifications, the system is modular mountable to any SLM machine" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure5.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure5.6-1.png", + "caption": "Figure 5.6.2 Independent suspension steering box with parallelogram linkage, plan view, right-hand drive.", + "texts": [ + " Precision is of great importance in the steering system, and the rack systemhas a superior reputation to the steering box, although it is quite difficult to observe any substantial 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 springloaded.Where the suspension is mounted on a subframewhich has some compliance relative to the body, in the interests of steering precision it is desirable that the steering rackor box alsobemounted on the subframe. On trucks it is still common to use a rigid axle at the front, mounted on two longitudinal leaf springs. Usually thewheel steering arms are connected together by a single tie rod, Figure 5.6.1. Thiswas the system used on passenger cars before the introduction of front independent suspension. Steering is effected by operating a steering control armA on one of thewheels, by the horizontal drag link B from a vertical Pitman armC.This acts from the side of the steering box,which ismountedon the sprungmass.The steering column is inclined to the vertical at a convenient angle, about 20 for commercial vehicles and 50 for cars. For independent suspension, two principal steering systems have been used, one based on a steering box, the other on a rack and pinion. In the typical steering box system, Figure 5.6.2, known as the parallelogram linkage, the steering wheel operates the Pitman armAvia the steering box. The box itself is 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. From appropriate points on the relay rod, the track rodsD connect to the steering armsE" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure19-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure19-1.png", + "caption": "Fig. 19. Prototype.", + "texts": [ + " More importantly, the leakage flux in the end of the CPM11 and CPM1-2 is unipolar, as shown in Figs. 18 (a) and (b). However, in the proposed machines, the unipolar leakage flux does not exist and replaced by the bipolar one, as shown in Figs. 18 (c)-(f). Therefore, the magnetization of the mechanical components in the end of the proposed machines (CPM2, CPM3, HPM1 and HPM2) can be effectively eliminated. V. EXPERIMENTAL VERIFICATION AND DISCUSSION The proposed HPM1 is prototyped for the verification of previous analyses. Fig. 19 show the photos of the 9-slot stator and 10-pole HPM1 rotor. For the tested line-line back-EMF, a DC motor is used to drive the machine to the rated speed. The platform for testing the static torque is shown in Fig. 20 (a), and it is measured based on the reported method [30]. Fig. 20 (b) shows the dynamic test platform. A DC-motor-based dynamometer is adopted as a variable load. Moreover, an encoder is employed to detect the rotor position of the prototype, whilst a torque transducer is built in the experimental platform to measure the dynamic output torque" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003207_s00170-016-9445-z-Figure17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003207_s00170-016-9445-z-Figure17-1.png", + "caption": "Fig. 17 Remanufactured impeller safety test. a Over-speed test. b Dye penetration inspection", + "texts": [ + " According to the test, m is less than 0.3 g which meets the requirements of impeller. As the composition of FeCrNiCu is similar to that of FV520B, there is no difference in density. Meanwhile, the high-precision machining method was adopted after laser cladding. Thus, the m is very small. The safety of remanufactured impeller under bad conditions also should be considered. The over-speed test of impeller can not only test the safety at high speed but also release part of residual stress to enhance safety. Figure 17a shows the over-speed test experiment. By using this experiment, the manufactured impeller was tested 3 min at 115 % rated speed. In order to test the impeller quality after over-speed test, the dye penetration inspection technique (DPIT) was adopted to detect the cracks invisible to the naked eyes of the remanufactured impeller. The result is shown in Fig. 17b after cleaning the remanufactured impeller with the cleaning agent. In overspeed test, no abnormal phenomenon occurred. Further dye penetration inspection shows that there are no cracks on the surface of remanufactured impeller. The centrifugal compressor impeller is widely used in petroleum, chemicals, military, and other important fields. In this paper, the laser cladding remanufacturing process with FeCrNiCu alloy powder for thin-wall impeller blade was studied. Based on present study, several points can be concluded as follows: (1) Thermal mechanism of laser cladding was analyzed by FEA" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000676_s00205-007-0076-2-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000676_s00205-007-0076-2-Figure5-1.png", + "caption": "Fig. 5. A single fold deformation. See also Fig. 1b", + "texts": [ + " Sharp folds, that is, discontinuous gradients, give however, infinite elastic energy. A similar construction with small elastic energy is then obtained by inserting appropriate smooth constructions in place of the sharp folds. It is therefore clear that the crucial point is the analysis of a single fold, which is discussed in the next section. 1.5. The approximation of a single fold Given points a, b, c, and d in R 2, we denote by [abcd], [abc], and [ab] the convex envelopes of the sets {a, b, c, d}, {a, b, c}, and {a, b}, respectively. Definition (single fold, see Fig. 5). We say that a pair ([abcd], v) is a single fold along [ac] if a, b, c, and d are the ordered vertices of a convex quadrilateral in R 2, v \u2208 W 1,\u221e(R2; R 3), and there exist F1, F2 \u2208 O(2, 3) such that \u2207v = F1 on [acb], \u2207v = F2 on [acd]. The continuity of v implies a compatibility condition between F1 and F2, namely, if n is a unit vector normal to [ac], then F1n\u22a5 = F2n\u22a5. As usual, (x1, x2) \u22a5 := (\u2212x2, x1). The angle \u03d5 between F1n and F2n will be called the angle of the fold ([abcd], v), while the length l of [ac] will be called the length of the fold" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001499_j.apm.2015.03.026-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001499_j.apm.2015.03.026-Figure2-1.png", + "caption": "Fig. 2. Wind turbine two-planetary-stage gearbox from GR drivetrains.", + "texts": [ + " The gearbox models in the existing studies are commonly composed of one planetary gear stage and two parallel gear stages [11\u201313,16,17]. Such structure may not be adequate for high capacity wind turbines. It is known that the planetary design of the gearbox provides higher gear ratios and is capable of carrying higher loads compared to the parallel arrangement. By considering this feature, the dynamic model to be developed in this paper is based on the gearbox having two planetary gear stages and one parallel gear stage, as illustrated in Fig. 2 [1]. The dynamic model in this paper takes into account the time-varying mesh stiffness, damping, static transmission error and gear backlash. The static transmission errors are expressed in the form of periodically time-varying displacement functions applied at gear meshes [38]. Damping was neglected in some of the existing studies as this assumption is reasonable for large wind turbines [13]. However, large influence of damping in the nonlinear behaviour was observed during wind turbine emergency stop [39,40]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003857_j.engfailanal.2018.08.028-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003857_j.engfailanal.2018.08.028-Figure11-1.png", + "caption": "Fig. 11. Nephograms of comprehensive deformation: (a) health; (b) crack type 1; (c) crack type 2; (d) crack type 3; (e) crack type 4.", + "texts": [ + " driving gear is still in engagement (observed in FE model), which means that the triple-tooth engagement occurs in theoretical double-tooth meshing duration. This phenomenon is caused by extended tooth contact [11]. 3.2. Model verification of the cracked helical gears The parameters of different crack types are listed in Table 3. The TVMS of the helical gear pair obtained from the proposed method and the FE method under different crack types is shown in Fig. 10. The mesh stiffness at moments D and E is listed in Table 4. The comprehensive deformation at moment E is shown in Fig. 11. It can be observed that the change laws of the TVMS obtained from two methods under different crack types are in consistent (see Fig. 10) and the maximum error is about 5.26% (see Table 4). The deformation caused by the end face penetrating crack is the largest among all crack types due to its minimum healthy part (see Fig. 11e), so the loss of the stiffness is largest under this crack type. It should be noted that the proposed method only costs 2min, while the FE method costs 2.5 h. The TVMS obtained from the proposed method and the FE method under different crack growth distances along face width l3= 9, 19, 29mm and constant q0= 2.5mm, qe= 0.5mm and l1= 3mm is shown in Fig. 12. The comprehensive deformation at moment E under different l3 is shown in Fig. 13. The mesh stiffness at moments D and E is listed in Table 5, and the maximum error is about 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure4-1.png", + "caption": "Fig. 4. Simplified main PM magnetic circuit of CPM2 and CPM3. (a) Equivalent magnetic circuit. (b) Flux lines in slotless model.", + "texts": [ + " 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. Figs.3 (a) and (b) show the simplified PM magnetic circuit of CPM2 and CPM3, respectively. It can be observed that the end leakage flux is bipolar in the CPM machines with symmetric pole-sequences. It means that the magnetized risk of the mechanical components can be eliminated effectively. Fig.4 (a) shows the further simplified main PM magnetic circuits of CPM2 and CPM3, which are derived based on Fig. 3. It can be seen that the main PM flux does not pass the airgap above the iron-poles, and it is closed through the PMs with different polarity. These are confirmed by the FE predicted flux distributions of their slotless models in Fig.4 (b). Consequently, the airgap flux density of CPM2 and CPM3 have undesirable subharmonics, especially 1st, which will result in the saturation of the stator yoke in practical models, and the reduction of the working airgap flux density (5th) and output torque. Fig.5 (a) shows the main PM magnetic circuits of CPM2 and CPM3 with tangential PMs (i.e. HPM2 and HPM3). The tangential PMs represent large reluctances for the SPMs, and they can provide additional flux. Therefore, the main PM flux goes through the airgap above the iron-poles of HPM1 and HPM2, which are confirmed by FE analysis, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000281_elan.1140010203-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000281_elan.1140010203-Figure2-1.png", + "caption": "FIGURE 2. The electrocatalytic oxidation of AA on PB CME. (a) PB-CME, 0.1 M KCI. (b) Naked Pt electrode, 10 rnM AA. (c) PB-CME, 10 rnM AA.", + "texts": [ + " Baldwin and coworkers [23 , 241 detected carbohydrates and sulthydryl compounds at cobalt phthalocyanine-containing carbon paste electrode (CPE) in combination with liquid chromatography or flow injection systems. The significant lowering of the overvoltage offered major improvements in the detection of these compounds, In our laboratory, the electrocatalytic oxidation of ascorbic acid (AA) at a CME immobilized with Prussian blue (PH) [ 61 or with polyvinylferrocene film [ 2 5 ] has been studied. The cyclic voltammogram (CV) of PB-CME in a blank solution is shown in Fig. 2a. When AA is added to the solution it causes a drastic change in the response. The anodic peak appearing at nearly the same potential as PB film itself, 0.2 V vs. Ag/AgCI, is enhanced by 2.5 and 28 times compared to when AA is absent or when the same amount of AA is oxidized at naked electrode at the same potential. This catalytic reaction can be used for the determination of ascorbic acid in aqueo-s solution. Yon Hin and Lowe reported the catalytic oxidation of reduced nicotinamide ademine dinucleotide (NADH) at Fe(CN)jb--modified nickel electrode" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure1.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure1.4-1.png", + "caption": "FIGURE 1.4. Symbolic illustration of prismatic joints in robotic models.", + "texts": [], + "surrounding_texts": [ + "4 1. Introduction\nthe 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.\nA symbolic illustration of revolute and prismatic joints in robotics are shown in Figure 1.3 (a)-(c) , and 1.4 (a)-(c) respectively.\nThe coordinate of an active joint is controlled by an actuator. A passive joint does not have any actuators and its coordinate is a function of the coordinates of active joints and the geometry of the robot arms . Passive joints are also called ina ctive or free joints.\nActive 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.\nRevolute and prismatic joints are the most common joints that are uti lized in serial robotic manipulators. The other joint types are merely im plementations to achieve the same function or provide additional degrees of freedom . Prismatic and revolute joints provide one degree of freedom . Therefore, the number of joints of a manipulator is the degrees-of-freedom (DOF) of the manipulator. Typically the manipulator should possess at least six DOF: three for positioning and three for orientation. A manipula-", + "1. Introduction 5\ntor having more than six DOF is referred to as a kinematically redundant manipulator.\n1.2.3 Manipulator\nThe main body of a robot consist ing of the links, joints, and other st ructural 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 1.5 schematically illustrat es a 3R manipulator.\n1.2.4 Wrist\nThe joints in the kinematic chain of a robot between the forebeam and end effector are referred to as the wrist. It is common to design manipulators", + "6 1. Introduction\nwith spherical wrists, by which it means three revolute joint axes intersect at a common point called the wrist point. Figure 1.6 shows a schematic illustration of a spherical wrist, which is a Rf--Rf--R mechanism.\nThe spherical wrist greatly simplifies the kinematic analysis effectively, allowing us to decouple the positioning and orienting of the end effector. Therefore, the manipulator will possess three degrees-of-freedom for posi tion, which are produced by three joints in the arm. The numb er of DOF for orientation will then depend on the wrist . We may design a wrist having one, two, or three DOF depending on the application.\n1.2.5 End-effector\nThe end-effector is the part mounted on the last link to do the required job of the robot . The simplest end-effector is a gripper, which is usually capable of only two actions: opening and closing. The arm and wrist assemblies of a robot are used primarily for positioning the end-effector and any tool it may carry. It is the end-effector or tool that actually performs the work. A great deal of research is devoted to the design of special purpose end effectors and tools. There is also extensive research on the development of anthropomorphic hands. Such hands have been developed for prosthetic use in manufacturing. Hence, a robot is composed of a manipulator or mainframe and a wrist plus a tool. The wrist and end-effector assembly is also called a hand." + ] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.12-1.png", + "caption": "Fig. 2.12 Examples of rigid-body mechanisms with multiple drives; a) planar Stewart platform (n = 3), b) spatial Stewart platform (n = 6), c) hydraulic drives of a dredging shovel (n = 3), d) lift truck (n = 2), e) cable-guided handling system (n = 6), f) welding robot (n = 3)", + "texts": [ + " This is relevant for understanding the range of applicability of such programs, for their proper use, and for evaluating the results of calculations. For most practical problems, the driving forces are given by the motor characteristic, so that it becomes necessary to integrate the equations of motion, see Sect. 2.4.3. A mechanism consists of I links, of which the frame is given the index 1 and the movable bodies are given the indices i = 2, 3, . . . , I , and index I is usually assigned to an output link. Figure 2.12 shows some examples of rigid-body mechanisms with multiple drives. The gyroscope in Fig. 2.14 can also be interpreted in such a way that the position of the rigid body is determined by the three \u201cinput coordinates\u201d q1, q2, and q3. The center-of-gravity coordinates rSi of the ith link of a mechanism show an (often nonlinear) dependence on the so-called kinematic dimensions and the positions of the n input links: rSi(q) = [xSi(q), ySi(q), zSi(q)]T. (2.141) Their velocities can also be calculated according to the chain rule: d(rSi) dt = vSi = n\u2211 k=1 \u2202rSi \u2202qk q\u0307k = n\u2211 k=1 rSi, k q\u0307k; i = 2, 3, ", + "4 Kinetics of Multibody Systems 103 Y i(q) = \u23a1\u23a3 xSi,1 xSi,2 . . . xSi,n ySi,1 ySi,2 . . . ySi,n zSi,1 zSi,2 . . . zSi,n \u23a4\u23a6 ; Zi(q) = \u23a1\u23a3 u\u03bei1 u\u03bei2 . . . u\u03bein u\u03b7i1 u\u03b7i2 . . . u\u03b7in u\u03b6i1 u\u03b6i2 . . . u\u03b6in \u23a4\u23a6 (2.146) Zi(q) is found by differentiating the angular velocities with respect to the input velocities q\u0307k or simply by a comparison of coefficients, see for example (2.30) from Sect. 2.2.3. Position functions and Jacobian matrices can be explicitly stated in analytical form for open linkages, such as in Examples c, d and f in Fig. 2.12. Mechanisms with a loop structure,, such as in cases a, b and e in Fig. 2.12, in which the constraint equations cannot be solved in closed form, the Jacobian matrices can be numerically calculated as a function of position (using a PC and existing software). The elements of the Jacobian matrices typically depend on the position of the input coordinates. They are also called first-order position functions. A mechanism consists of I \u2212 1 movable rigid bodies whose dynamic properties are captured by 10 mass parameters, respectively, that are contained in the parameter vector pi = [mi, \u03beSi, \u03b7Si, \u03b6Si, JS \u03be\u03bei, JS \u03b7\u03b7i, JS \u03b6\u03b6i, JS \u03be\u03b7i, JS \u03b7\u03b6i, JS \u03be\u03b6i] T; i = 2, 3, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002897_j.engfailanal.2016.12.008-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002897_j.engfailanal.2016.12.008-Figure1-1.png", + "caption": "Fig. 1. The gearbox system.", + "texts": [ + " One recent problem involves the crack failure of gearbox housings during operation, where gearbox housings have failed to reach their designed operating mileage, resulting in diminished operational safety. A gearbox is a key transmission component of a high speed train traction system, which is supported on the axle with bearings through one end and with the other end connected to the bogie frame by means of a C bracket, and the pinion shaft end is connected with the motor by universal couplings, as shown in Fig. 1. The gearbox is used for transmitting the motor torque to the axle, so its reliability is directly related with the operational safety of a high speed train [1]. Extensive gearbox-related studies have been conducted, although most have focused on rotary machines and gear transmission systems [2,3,4]. Some studies have considered the dynamic response of the gearbox housing. Sonsino [5] employed laboratory proof tests to evaluate the structural durability of train gearbox housings under variable amplitude loading" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001720_s00339-017-1194-9-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001720_s00339-017-1194-9-Figure1-1.png", + "caption": "Fig. 1 Physical phenomena during selective beam melting", + "texts": [ + " A randomly packed powder bed was generated using discrete element method (DEM) in the PFC software. The volume of fluid method (VOF) was employed to capture the free surface of the molten pool. The shrinkage of powder bed due to density change was involved in the numerical model. The effect of laser power and scanning speed on the morphology of the scan track was investigated numerically. The simulation results show good agreement with experiments. The SLM process is complex and involves many different physical phenomena (as depicted in Fig. 1). The real physical process has to be simplified in such a way: (1) the fluid of molten pool is assumed to be a laminar and incompressible Newtonian fluid. (2) The flow at the interface between solid and liquid phases defined as mushy zones. (3) Powder size is a Gaussian distribution with sphere shape. Particle Flow Code (PFC) models the assemblies of rigid spherical 3D particles using the distinct-element method (DEM). First, a rectangular substrate with a given size was generated. Then, the powder bed with Gaussian size distribution and a mean diameter of 19 lm were laid onto the substrate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001469_tim.2015.2390958-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001469_tim.2015.2390958-Figure3-1.png", + "caption": "Fig. 3. Connection scheme for the identification of Ld (id ) and Lq (iq ) with the CDT strategy.", + "texts": [ + " (17) CDT is an identification strategy where the magnetic saturation is considered and is based on the current and voltage drop measurement in the stator winding when the rotor is locked and aligned with the measured axis [31]. Solving (1a) and (1b) for the inductance value and assuming that the speed is equal to zero (\u03c9r = 0), the direct and quadrature inductance equations can be written as Ld (id) = (vd \u2212 Rsid)/ d dt id (18a) Lq(iq) = (vq \u2212 Rsiq)/ d dt iq . (18b) To perform the measurement on the d-axis, the rotor should be aligned (\u03b3 = 0\u00b0) with the phase U , and for the measurement of the q-axis, the flux linkage should be perpendicular to the phase U (Fig. 3). Once the rotor is mechanically locked and aligned with the measured axis, voltage test signals are injected into the machine through the Insulated Gate Bipolar Transistor (IGBT). As soon as the current reaches the nominal current of the machine, the voltage injection is halted and the measurement of the current and voltage drop is executed. The values of inductances Ld (id) and Lq(iq) at the instant k are estimated through the discretized equations (18a) and (18b), respectively. The experimental validation is carried out on a 32-bit TMS320F28335 Delfino microcontroller controlCARD [Fig", + " On the other hand, the data acquisition system and the PSO algorithm are not correlated; therefore, the data acquisition system and the PSO algorithm uncertainties have been added to the combined standard uncertainty to obtain the total uncertainty value of the system. Table III summarizes the results of the evaluation of the uncertainty for the identification strategy using the PSO algorithm. As it is observed, the total standard uncertainty indicates small dispersion of the data results, which demonstrates high-accuracy detection and validates the robustness of the PSO algorithm. During the CDT, the machine is connected as shown in Fig. 3 and a test voltage signal is injected to align the rotor into the measured axis. Once the rotor is aligned, it is mechanically locked and the routine in the MCU begins. A train of voltage pulses is generated to saturate the IGBT, and consequently, a current is generated, the voltage injection finishes when the nominal current value is reached, and the measurement of the current and voltage of the machine is performed. Fig. 10 shows the waveforms of the injected voltage and of the produced current in the q-axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001890_17579861111162914-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001890_17579861111162914-Figure1-1.png", + "caption": "Figure 1. Schematic diagram of laser cladding process with side powder injection", + "texts": [ + " The result is formation of a high-quality layer or coating with excellent bonding to the substrate. The process is carried out by either preplacing a powder on the substrate or injecting the powder into the melt pool (Steen, 2003). Injecting is either laterally (side injection) or coaxially with the laser beam. In the former process, the powder is adhered to a material surface by a chemical binder (e.g. alcohol) which evaporates during the heating process. No powder feeding device is required. Powder injection is a sophisticated process that uses a controllable powder feeding system. Figure 1 shows the principle of the laser cladding process using the side powder injection. The powder is delivered at an angle to the melt pool on the surface of the substrate in a stream of argon carrier gas. The laser beam melts the incoming powder to form a melt pool, which contains alloying elements from the substrate and the powder. IJSI 2,3 316 Argon as an inert shielding gas protects the melt metal from oxidation. The process produces a well-defined clad layer consisting of the powder alloy and a HAZ", + " The microhardness measurements were made automatically along a direction from the top of the clad layer into the substrate using a LECO Automatic Nozzle (cross-section view) Nozzle (gas + powder) Gas shield outlets Powder stream outlet Laser beam Scan Micro/Macro-Indentation Hardness Testing System (AMH43) with a Vickers indenter. The applied load was 100 gf and dwell time was set at 15 s. Different spacings between the individual indentations were used for the clad layer and HAZ. Rectangle section tensile specimens (12.7 \u00a3 6.35 mm2) were machined from clad substrates with orientations normal to the clad layer ( y-direction in Figure 1), and parallel to the clad deposition direction (x in Figure 1). The tensile test specimens complied with ASTM Standard E8-90 with a gauge length of 50 mm. The tests in triplicate were conducted on a 10 kN, Instron static testing machine. The fatigue tests used a 100 kN, digitally controlled, MTS testing machine, under load control mode, with a variable amplitude spectrum. This spectrum was representative of the bending moment loads at the wing root of a military fighter aircraft during flight. The loading spectrum consisted of 13,480 turning points per block, with one block equal to 324" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003866_j.rinp.2018.11.075-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003866_j.rinp.2018.11.075-Figure2-1.png", + "caption": "Fig. 2. Diagram of the basic process parameters of the SLM: (a) process parameters and (b) scanning strategy (the red point: at the centre of layer 1, layer 2 and layer 3). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)", + "texts": [ + " Considering the calculation efficiency and the computational precision, the elements of the AlSi10Mg powder bed which interact with the laser beam are finely meshed with hexahedral element sizes equal to 10 \u03bcm, the same as a quarter of the laser spot radius. The laser scan area on the AlSi10Mg powder bed has the dimensions of 0.5 mm\u00d70.5mm\u00d70.075mm, and the layer thickness is 25 um. The EN AW-5083 Al plate with the dimensions of 0.7mm\u00d70.7mm\u00d70.3mm was taken as the substrate for the powder bed. Coarser mesh is used for the solid substrate. The 3D simulation model was meshed into 54,000 elements and 59,617 nodes. The scanning pattern during the SLM process is presented in Fig. 2. The laser plot moves with the specific Exposure Time (ET) and Point Distance (PD) in the X-direction on the powder bed, as is shown in Fig. 2a. When the laser moves to next load step, the previous load step is deleted to account for the cooling cycle. The laser beam stepped in a reciprocating raster pattern in Fig. 2b. In multi-laser AM processing, the zone re-melted is melted two or four times in order to contrasting with single scanning. In SLM processing, the powder bed and its natural surroundings are regarded as a closed and adiabatic system. The spatial and temporal distribution of the temperature field satisfies the differential equation of 3D heat conduction in a domain region D, which can be described as [10,11]: \u239c \u239f \u2202 \u2202 = \u239b \u239d \u2202 \u2202 + \u2202 \u2202 + \u2202 \u2202 \u239e \u23a0 + \u2208\u03c1c T t k T x T y T z Q x y z D, ( , , )p 2 2 2 2 2 2 (1) where \u03c1 is the material density (kg/m3), c is the specific heat capacity (J/kg\u00b7\u00b0C),T is the temperature (\u00b0C), t is the interaction time (s), kp is the effective thermal conductivity of powder bed (ks (W/m\u00b7\u00b0C) and Q is heat generated per volume within the component (W/m3)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.26-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.26-1.png", + "caption": "Fig. 6.26 Effect of absorption on the frame; a) Frame with additional support, b) Frame with vibration absorber", + "texts": [ + "8478\u03c9\u2217 2 (6.307) where \u03c9\u2217 2 = 48EI/ml3 according to (6.134). The roots of the denominator are known from (6.136). The dynamic compliance can thus be written in the form of (6.293): D11(\u03a9) = 64l3 48EI ( 1\u2212 \u03a92 \u03bd2 1 )( 1\u2212 \u03a92 \u03bd2 2 )( 1\u2212 \u03a92 \u03bd2 3 ) ( 1\u2212 \u03a92 \u03c92 1 )( 1\u2212 \u03a92 \u03c92 2 )( 1\u2212 \u03a92 \u03c92 3 )( 1\u2212 \u03a92 \u03c92 4 ) . (6.308) This representation shows both the positions of the natural frequencies and the positions of the absorption frequencies. The absorption frequencies are the natural frequencies of the frame shown in Fig. 6.26a, which is developed from the original frame by providing the right bearing with a rigid support. This bearing ensures that this point cannot move in the vertical direction. If the original frame (not supported at this point), were excited with a harmonic vertical excitation force at the absorption frequency, this point would remain at its equilibrium position and there would be no resonance. The free frame has a node at this point at the absorption frequency. 6.5 Forced Undamped Vibrations 439 To keep the force application point at rest at a given circular frequency of the excitation \u03a9, a vibration absorber in the form of a spring-mass system can be provided as shown in Fig. 6.26b. This additional oscillator causes all natural frequencies of the original frame to shift. The mode shape of the natural frequency that matches the excitation frequency then has a node at the force application point. The condition \u03a92 = c/m5 must be satisfied for vibration absorption to occur. This can theoretically be achieved using a large mass (and a stiff spring constant) or with a small mass (and small spring constant). The force application point remains at rest because the dynamic force of the absorber is at any point in time equal in magnitude and opposite in direction to the excitation force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001216_tro.2011.2168170-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001216_tro.2011.2168170-Figure4-1.png", + "caption": "Fig. 4. Formation of a polyhedron containing the origin for force closure of planar cable-driven open chains.", + "texts": [ + " This relationship between the external wrenches and cable forces acting on the planar 3R cable-driven open chain is reflected in (21), and the force-closure condition of a general n-DOF open chain can be mathematically described as follows: \u2200W \u2208 n ,\u2203ti > 0, AT = W. (22) Proposition: An n-DOF cable-driven open chain must have a minimum of n + 1 cables to achieve force closure. Proof: It is known from the literature that achieving force closure can be equivalently represented as column vectors ai forming a convex hull containing the origin. (The proof can be found in [14] and [17].) Looking at (21), which is the force/moment equilibrium equation of the planar 3R cable-driven open chain, W must be spanned by the column vectors ai (see Fig. 4). For force closure, the convex hull that is formed by ai must enclose the origin. The smallest convex hull is a tetrahedron, which requires a minimum of four vertices. Each vertex is represented by one ai . As seen from Fig. 4, having three or less ai will prevent the formation of a tetrahedron and will not enclose the origin. This shows that a minimum of four cables are necessary for the 3-DOF planar cable-driven open chain to achieve force closure. Looking at a 2-DOF case, the convex hull is now a polygon. The smallest convex hull is a triangle, which requires a minimum of three vertices. Therefore, for force closure of a 2-DOF system, a triangle cannot be formed unless there are three vertices (i.e., three ai). This shows that a minimum of three cables are necessary for the 2-DOF cable-driven open chain to achieve force closure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003825_j.addma.2020.101499-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003825_j.addma.2020.101499-Figure3-1.png", + "caption": "Figure 3: Orientations of the EBM parts on the hatching pattern, with the electron beam moving along the principal directions (x\u2032 and y\u2032 axes). The built sample is oriented 45\u25e6 with respect to principal axes. The red straight arrows denote the scanning direction of the electron beam, the blue curved arrows indicate that the electron beam rotates 90\u25e6 between layers. The coordinate systems (x\u2032, y\u2032, z\u2032) and (x, y, z) are associated to the EBM machine and the built samples respectively.", + "texts": [ + " Note that the217 FO denotes the current used by the focusing coils to focus the electron beam, the SF controls218 the beam speed as a function of the current so that a constant melt depth is maintained. The219 Jo ur na l P re -p ro of powder was heated up to 850\u25e6C for each layer before being melted by the electron beam. Dur-220 ing the hatching, the electron beam moves parallel to the principal directions of the machine221 (x\u2032 or y\u2032), and rotates 90\u25e6 between layers. The samples built with the standard parameters are222 oriented 45\u25e6 with respect to the principal axes of the beam scanning (machine coordinate sys-223 tem (x\u2032, y\u2032, z\u2032) in Fig. 3) so that the scanning length is the same after the rotation of 90\u25e6of the224 electron beam. To evaluate the effect of the parameters on the residual stresses, the FO and SF225 were changed for two additional samples. Note that the change of FO will change the spot size,226 thus the energy density of the electron beam, while the variation of SF will alter the melt pool227 depth [21].228 The four samples, two built with standard parameters and two with modified parameters,229 were made in the same batch: two samples with standard parameters (the same used by de230 Formanoir et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure7.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure7.1-1.png", + "caption": "Fig. 7.1 Example 7.1. Rotating disk", + "texts": [ + "k kvm O C kam O/ : 9>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>= >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>; (7.14) 164 7 Hyper-Jerk Analysis Finally, substituting Eqs. (7.14) into Eq. (7.13) and reducing terms, we obtain Eq. (7.9). \u02d8 Postulate 3. Some terms of Eq. (7.9) may be grouped as follows: hjcor D 4j!k k m O C 4j k kvm O C 8j\u02dbk .j!k kvm O/C 6j\u02dbk kam O C 6j!k .j!k kam O/C 4j!k .j\u02dbk kvm O/C 4j!k \u0152j!k .j!k kvm O/ ; (7.15) where hjcor is termed the Coriolis hyper-jerk. Example 7.1. The disk shown in Fig. 7.1 rotates about a fixed axis passing through point O with angular velocity ! D 5 rad=s, angular acceleration \u02db D 2 rad=s2, angular jerk D 3 rad=s3, and angular hyper-jerk D 2 rad=s4 in the indicated directions. On the other hand, the small sphere A moves in the slot undergoing relative motions with respect to the disk as follows: Pu D 2 m=s, Ru D 1:5 m=s2, \u00abu D 0:5 m=s3, and \u00acu D 3 m=s4 in the indicated directions. We must compute the total instantaneous velocity, acceleration, jerk, and hyper-jerk of sphere A considering that the instantaneous coordinates of A are given by x D 0:75 m and y D 0:5 m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.1-1.png", + "caption": "FIGURE 4.1. Rotation and translation of a local frame with respect to a globa l fram e.", + "texts": [ + " Show that and 43. * Stanley method. Find the Euler parameters of the following rotation matrix based on the Stanley method. [ 0.5449 G RB = 0.3111 -0.7785 -0.5549 0.6285 ] 0.8299 0.4629 -0.0567 0.6249 4 Motion Kinematics 4.1 Rigid Body Motion Consider a rigid bod y with an attached local coordinate frame B (oxy z) moving freely in a fixed global coordinate frame G(OXYZ) . The rigid body can rotate in the global frame, while point 0 of the body frame B can translate relative to the origin 0 of G as shown in Figure 4.1. If th e vector G d indicates the position of the moving origin 0 , relative to the fixed origin 0 , then the coordin ates of a body point P in local and global frames are related by the following equation: G r p = G RB B r p + Gd (4.1) where G r p [ x; Yp z; f (4.2) B r p [ Xp y p Zp f (4.3) Gd [ x, Y o z; f \u00b7 (4.4) 128 4. Motion Kinematics The vector G d is called the displacement or translation of B with respect to G, and G R B is the rotation matrix to map B r to G r when Gd = O. Such a combination of a rotation and a translation in Equation (4.1) is called rigid motion. In other words, the location of a rigid body can be described by the position of the origin 0 and the orientation of the body frame, with respect to the global frame . Decomposition of a rigid motion into a rotation and a translation is the simplest method for representing spatial displacement. We show the translation by a vector, and the rotation by any of the methods described in the previous Chapter. Proof. Figure 4.1 illustrates a translated and rotated body frame in the global frame. The most general rotation is represented by the Rodriguez rotation formula (3.62) , which depends on B r p , the position vector of a point P measured in the body coordinate frame . In the translation G d, all points of the body have the same displacement, and therefore, translation of a rigid body is independent of the local position vector B r . Hence, the most general displacement of a rigid body is represented by the following equation, and has two independent parts: a rotation, and a translation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001463_1.4029461-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001463_1.4029461-Figure2-1.png", + "caption": "Fig. 2 (a) Contact between a ball and normal race and (b) that between a ball and an edge of a defect", + "texts": [ + " The simulation results are compared with those from the previous defect models. An experimental investigation is also presented to validate the proposed model. The relationship between the time-varying contact stiffness and defect sizes is studied here. Localized surface defects on inner and outer races are schematically shown in Fig. 1. It is well known that the contact between a ball and an inner or outer race can be considered as a point contact between two spheres at the beginning when the race is normal, as shown in Fig. 2(a). However, when a defect occurs on the surface of a race, the contact between the ball and race becomes that between the ball and a line when the ball reaches an edge of the defect, as shown in Fig. 2(b). For a normal bearing, the contact stiffness between the ball and race can be calculated using Hertzian contact deformation theory, and the nonlinear load\u2013deformation relationship can be written as [54] F \u00bc Kd1:5 (1) where F is the externally applied force, K is the contact stiffness between the ball and race, and d is the radial deformation of contact surfaces between the ball and race. For an abnormal bearing, the load\u2013deformation relationship is given by F \u00bc Kdd n (2) where Kd is the contact stiffness between the ball and defect, and n is the load\u2013deformation exponent; Kd and n depend on defect sizes", + "org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use For a normal ball bearing, the equivalent contact stiffness between two races can be obtained using [55] K \u00bc 1 1=Ki\u00f0 \u00de1=n\u00fe 1=Ko\u00f0 \u00de1=n \" #n (19) where Ki is the contact stiffness between the ball and inner race, and Ko is the contact stiffness between the ball and outer race. When there is a localized surface defect on the races of a ball bearing, the contact between a ball and the defect will be changed from a point contact to a ball-line contact (Fig. 2). Hence, Eq. (1) cannot be used to formulate the contact force between the ball and defect; a new formulation is proposed here by replacing the Hertzian force\u2013deflection relationship by Fup \u00bc Kupd nup up (20) where the subscript u denotes the defect type discussed earlier and the subscript p is the number of the contact points; Fup, Kup, and dup are the contact force, the contact stiffness, and the radial contact deformation at the defect location, respectively; and nup is the load\u2013deflection exponent" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000657_tmag.2009.2024159-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000657_tmag.2009.2024159-Figure3-1.png", + "caption": "Fig. 3. Magnet eddy current distributions of IPM motor: (a) 28 segmentations, and (b) without segmentations.", + "texts": [ + "2024159 The formulations of the 3-D FEM that considers the carrier of the PWM inverter [3] are as follows: (1) (2) (3) where and are the magnetic vector and electric scalar potentials, respectively. is the permeability and is the conductivity. is the armature current density, is the magnetization of the permanent magnet, and and are the armature voltage and current, respectively. is the armature coil resistance and is the flux linkage of the armature coil. is given due to the theoretical PWM voltage waveform [3] shown in Fig. 2. Fig. 3 shows the calculated eddy current distributions of the magnet in the IPM motor. Fig. 3(a) shows the result when the magnet is subdivided into 28 pieces along the axial length. In 0018-9464/$26.00 \u00a9 2009 IEEE this case, half the axial length of the magnet is shown. Fig. 3(b) shows the result without the segmentation of the magnet. In this case, half the core length of the motor is shown. It can be observed that the eddy currents concentrate at the edges of the magnet, particularly, when the magnet is not segmented. Fig. 4 shows the calculated magnet eddy current loss decomposed into harmonic components in the case of the IPM motor when the number of magnet segmentations is 28. The sixth and twelfth components are caused by the stator harmonics that are due to the number of the stator slots", + " 6 shows the result when the imposed flux density is 10 mT and the frequencies are 5 and 20 kHz, which nearly correspond to the major slot harmonics and carrier harmonics in the analyzed motor, respectively. The result obtained by the finite-element analysis under the same condition is also compared. These results are almost identical. They indicate that the loss becomes maximum when the axial length of the segmented conductor is nearly twice the skin depth . When the number of segmentations is smaller, the eddy currents concentrate at the edges of the conductor, as shown in Fig. 3(b). As a result, the loss increases almost linearly with the number of segmented conductors due to the increase in the total edge length and surface area [3]. On the other hand, when the number of segmentations is larger and the axial length of the conductor is smaller than , the loss decreases with the number of segmentations. The loss characteristics of the IPM motor in Fig. 5 is well expressed by this model. On the other hand, we consider that the differences in the loss-reduction effect due to the rotor types are caused by the differences in reaction fields produced by the magnet eddy currents, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000519_ichr.2005.1573537-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000519_ichr.2005.1573537-Figure1-1.png", + "caption": "Fig. 1. Three types of contact, showing contact normals and friction cones.", + "texts": [ + " We model other types of contact between the robot and the environment by groups of k > 1 point contacts (pR i , pE i ), i = 1, ..., k, occurring simultaneously, where all points pR i belong to the same robot link. When k = 2, we have an edge contact that allows the robot link to rotate freely about the fixed line passing through pR 1 and pR 2 . When k > 2, we have a face contact that fully constraints the link\u2019s orientation. By convention, each point pR i in a face contact is located at a vertex of the convex hull of the overlap between the robot link and the environment. Each type of contact is illustrated in Figure 1. In advance, we designate a set of features (points, edges, and faces) on the robot at which contact is allowed. There is no restriction on this set, but once it has been chosen, no other points on the robot\u2019s surface may touch the environment. A contact is generated by picking a feature and placing it against a point in the environment. This process is repeated many times to construct a discrete set of candidate contacts. This raises the question, \u201cwhich points in the environment should be allowed contact with which robot features" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.14-1.png", + "caption": "Fig. 6.14 Machine frame; a) System schematic with parameters and coordinates, b) Identification of the rigid support, c) Explanation of the constraint (6.217)", + "texts": [ + "215) The natural frequencies and mode shapes of the system stiffened with rigid fasteners result from the solution of the eigenvalue problem (C1 \u2212 \u03c92M1)v = o. (6.216) As a result of the additional constraints, all natural frequencies usually increase. Those frequencies, the mode shapes of which are most obstructed, are most affected. Those frequencies, the mode shapes of which are not affected as a result of the support, remain unchanged. The frame for which the mass and stiffness matrices are given in Table 6.3 (Case 2) is used as an example. A hinged column according to Fig. 6.14b obstructs the motion of the mass m2 in the direction of that support, but it allows the motion perpendicular to it. The horizontal displacement of the mass m2 corresponds to coordinate q3 and its vertical displacement is q2, see Fig. 6.14a and b. As a result of the attached column, q2 and q3 can no longer change independently. The following constraint applies: 6.4 Structure and Parameter Changes 409 q2 = q3 \u00b7 tan \u03b1. (6.217) It was assumed that the change of angle \u03b1 as a result of the displacements q2 and q3 is negligibly small. Only three (n\u2212 r = 3) coordinates are included in the vector qT 1 = [q1, q3, q4]. In matrix notation, (6.217) according to (6.210) takes the form q = \u23a1\u23a2\u23a2\u23a3 q1 q2 q3 q4 \u23a4\u23a5\u23a5\u23a6 = \u23a1\u23a2\u23a2\u23a3 1 0 0 0 tan \u03b1 0 0 1 0 0 0 1 \u23a4\u23a5\u23a5\u23a6 \u00b7 \u23a1\u23a3 q1 q3 q4 \u23a4\u23a6 = T \u00b7 q1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure29-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure29-1.png", + "caption": "Fig. 29. Contact and bending stresses at a contact point of the pinion in examples: (a) 2 and (b) 3.", + "texts": [ + " The total number of elements is 71,460 with 87,360 nodes. The material is steel with the properties of Young s modulus E = 2.068 \u00b7 105MPa and Poisson s ratio 0.29. A torque of 4000Nm has been applied to the pinion in the three cases. Fig. 28(a) and (b) show the formation of the bearing contact on the face-gear tooth surface in examples 2 and 3, respectively. The path of contact is orientated longitudinally and edge contact is avoided. The dimensions of the contact ellipse are increased in example 3. Fig. 29(a) and (b) show the formation of the bearing contact on the pinion surface for examples 2 and 3, respectively. Fig. 29(b) shows that a severe contact area appears in the pinion surface in example 3, but the stresses are still allowable. The variation of contact and bending stresses along the path of contact has been analyzed as well. Figs. 30 and 31 illustrate the variation of contact and bending stresses, respectively, for the three examples. Edge contact is avoided in examples 2 and 3 and this is the reason why high peaks of contact stresses (Fig. 30) do not appear in examples 2 and 3 as in example 1. Bending stresses are higher in example 2 because the load is applied across a smaller area" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000122_0168-1656(93)90147-f-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000122_0168-1656(93)90147-f-Figure1-1.png", + "caption": "Fig. 1 shows cyclic voltammograms of a graphite electrode (RW-0) modified with adsorbed HRP in plain phosphate buffer (a) and in buffer also containing hydrogen peroxide (b). As is clearly evident only the voltammogram obtained in the buffer containing hydrogen peroxide reveals high reduction currents. The corresponding voltammogram of a bare graphite electrode in the HzO2-containing buffer is very similar to a voltammogram obtained previously with a HRP modified electrode in plain buffer (J6nsson and Gorton, 1989). The voltammograms are consistent with a reaction sequence outlined below. The native form of HRP in its", + "texts": [ + " The surface coverage, F (mol cm-2), of the adsorbed compound was determined by cyclic voltammetry, registered with the modified graphite electrode dipped into a 0.25 M phosphate buffer (pH 7.5), by integration of the voltammetric waves. It was assumed for all these substances that the number of electrons, n, participating per adsorbed molecule in the redox reaction at the electrode surface was equal to two. Further modification of these electrodes with adsorbed enzymes followed the procedure outlined above. Results and Discussion E / mV vs SCE Fig. 1. Cyclic voltammograms of HRP modified polished RW-0 electrode in (a) 0.l M phosphate buffer, pH 6.0 and in (b) the same buffer also containing 17 mM H202. The sweep rate was 50 mV s - k The ( + ) indicates the start potential. ferric resting state, containing ferriprotoporphyrin IX as prosthetic group (with the iron in oxidation state +II I , here denoted ferric), is oxidized in a two-electron process whereby compound-I is formed (with the iron in oxidation state + V): H202 + ferric ~ 2 H 2 0 + compound-I (1) In a subsequent electrochemical reaction compound-I is reduced at the electrode surface returning the enzyme to its native active ferric state", + " If the electrodes, both graphite and carbon, are electrochemically pretreated for longer times (~ 30 s) at + 2.5 V (oxygen bubbles on the surface then appear), the oxidation wave will move to even more positive values starting at about + 150-200 mV (data not shown). It should be noted that somewhat different results can be obtained with electrodes identically prepared and pretreated. The cyclic voltammogram of bare polished RW-I (not shown) is very similar to the voltammogram obtained for bare polished RW-0 (Fig. 1). The heat treatment causes a great increase in the background current of the voltammogram as is seen in Fig. 3. When comparing cyclic voltammograms of the different electrode materials and of electrodes differently pretreated and modified with adsorbed HRP, only those prepared from heat-treated RW-I graphite showed a clear tendency of voltammetric peak formation within the investigated potential range A RW-O /I! ' I / il 'I B C D i//'1/ Y/ . ] i u o o 4 ~ 8 e ~ . 4 c ~ o 4 o o o o o 4 ~ o 4 c ~ o e o " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000030_0005-1098(84)90007-4-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000030_0005-1098(84)90007-4-Figure3-1.png", + "caption": "FIG. 3. Variable length pendulum.", + "texts": [ + " In robots with fast dynamics we must tackle the highly nonlinear structure of dynamical equations and the lack of knowledge of the payloads. An effective reduction of the computer burden is achieved by equipping the mechanical structure with an adaptive model reference control (Young, 1978b; Balestrino, De Maria and Sciavicco, 1983b; Slotine and Sastry, 1983). Young and Kwatny (1982) have studied turbine overspeed protection. 7. EXAMPLE In order to illuminate more clearly the three reviewed approaches and the kinship between them, let us consider the position control of the pendulum shown in Fig. 3, where m and l(O) are the mass and the changeable length respectively. Assuming l(O) = lo + l~cos0 (56) the equat ion of mot ion can be writ ten as 0 =/1sin0(1 + llcosO/lo)O2/loA(O) - gsin0(1 + cosO)/loA(O) + T/mlZAiO) (57) 7.1. VSS design procedure. The error e v = (el,Ol) = (0 - 0, (i - 0t (641 during the sliding mode depends on the eigenvalue associated with equat ion v = Ge = glel + el = 0. (65) For sliding we need vb <_ O. Now b = - a o e l + (gl - al)kl + {10(1 + cosO)sinO/OA(O)}O - {a~ + 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000156_1.2958070-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000156_1.2958070-Figure1-1.png", + "caption": "Fig. 1 Proposed elastical model for a ball bearing", + "texts": [ + " Thus load-deformation relationship can be generalized as W = 2 2 3 E 1 \u2212 2 1/2 1 * 3/2 3/2 4 Here, * is the dimensionless deflection factor and is the curvature sum at the contact point. * is given on a graph by Harris as a function of the curvature difference, F . For computational purposes, * may be expressed as 36 * = \u2212 327.6145 + 1883.338 F \u2212 3798.1121 F 2 + 3269.6154 F 3 \u2212 1026.96 F 4 5 The system shaft-ball bearing couple is assumed as a massspring system and the model also incorporates masses of the balls. Additionally, the contacts of balls to the inner and outer races are represented by nonlinear contact springs, as shown in Fig. 1. 2.2 Calculation of Deflections. It is necessary to calculate the deflection of ith ball for the calculation of contact forces acting on the shaft and the ball. Balls continuously contact on the surfaces at different points during rotation. Oi and Oo are, respectively, the centers of curvature of the inner and outer race grooves and move with the balls, as can be seen in Fig. 2. Assuming that the outer race is fixed, then Oo may be considered as a fixed origin 19,21 . Now take an auxiliary plane containing an axis parallel to the z axis at Oo and a radial axis defining the pitch angle of the ith ball center with respect to the x axis", + "org/terms i \u2212 W s D q = r 1 J Downloaded Fr ts superharmonics fbpfi+ fS=466 Hz, fbpfi\u2212 fs=300 Hz, fbpfi 2xfs=217 Hz, fbpfi\u22123xfs=134 Hz, fbpfi+3xfs=632 Hz, etc. . 3.2.3 Effect of Defected Ball Surface on Ball Vibrations. hile the defected ball rotates it causes complex vibrations, as hown in Fig. 11 a , due to defect-ring contact during rotation. efect-ring contact occurs with 0.025 s intervals. Dominant peaks in the frequency spectrum are at the cage freuency 35 Hz , doubles of the ball rotating frequency 2fb 560 Hz , the natural frequency of the shaft 620 Hz , and the adial oscillation frequency of the ball 700 Hz , as shown in Fig. 1 b . Other peaks are 2fb+ fc 595 Hz and 2fb\u2212 fc 525 Hz . ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 07/05/2013 Terms 4 Conclusions In this study, a rigid shaft supported by a pair of angular contact ball bearing model is developed and ball vibrations of the ball bearing with and without defects are investigated. The equations of motion in radial and axial directions were obtained for shaft and rolling elements, and they were solved simultaneously with a computer simulation program and these results were analyzed both in time and frequency domains" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003236_j.jmapro.2018.06.033-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003236_j.jmapro.2018.06.033-Figure3-1.png", + "caption": "Fig. 3. Schematic visualization of possible defects induced during LMD due to thermal effects. A deposited bead with length lhot is deposited (a). The shrinkage due to temperature decrease leads to residual stresses and the deformations of the substrate for single-bead deposition (b). Multi-layer LMD with bead lengths of lhot due to subsequent deposition (c) and cooled down state, which leads to residual stresses in both layers and the substrate in the y\u2013z plane (d) [23,22].", + "texts": [ + " During the LMD process, the laser heat source melts the wire in order to add the material to the substrate or the underlying structure, leading to a high bonding. Owing to the fact that high laser powers have to be used to melt the material, high temperature gradients occur, resulting in residual stresses in the substrate or the previously deposited structure. In case that these stresses exceed the yield strength of the material, plastic deformation of the substrate as well as in the deposited structure develop [19,20]. This mechanism is known as the temperature gradient mechanism and can lead to componential distortions of the processed structure. Fig. 3 depicts the possible reasons for residual stresses within the deposited structures. It is assumed that due to shrinkage effects of the deposited beads, internal compressive stresses occur, whereas high tensile stress intensities especially in the beginning and ending regions of the deposited layer result [21]. During the process, a bead of the length lhot is deposited (shown in Fig. 3(a)) and contracts during solidification to the length lcool (shown in Fig. 3(b)). As a result of strong bonding between the substrate material and the deposited bead, compressive stresses in the substrate occur. These stresses may induce distortions of the structure in y\u2013z plane, as shown in Fig. 3(b). Fig. 3(c) visualizes the deposition of a second bead on top, where the same effect occurs. This leads to compressive stresses in the first bead and the substrate, which additionally increases the development of the distortion angle \u03c61 (as shown in Fig. 5(d)). Owing to the so-called temperature gradient effect, additional distortions occur in the x\u2013z plane occur [22,23]). In addition, these residual stresses may introduce cracking inside the deposited materials or between the layer and the substrate, which is also known as the delamination effect [20,24]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001355_17452751003703894-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001355_17452751003703894-Figure1-1.png", + "caption": "Figure 1. A typical SLM machine layout.", + "texts": [ + " During the SLM process, a powder layer is deposited onto a base plate attached to the building platform of the machine. The laser beam scans the powder bed according to the slice data of the CAD model, and the powder being fully molten forms the first layer on the base plate. Then, the building platform is lowered with an amount equal to the layer thickness and a fresh layer of powder is deposited on the already solidified layer. Successive scanning and lowering the building platform continues until the part is completely made. A typical SLM machine is shown schematically in Figure 1 with its main components. The mechanical properties obtained with SLM might be different from those of bulk material produced by conventional techniques for several reasons. Laser processing of materials generally results in high cooling rates due to the short laser/material interaction time because of high scanning speeds and high thermal gradients. This might lead to the formation of non-equilibrium phases such as glasses, quasi-crystalline phases and new crystalline phases with extended composition ranges (Rombouts 2006)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000017_s11666-007-9026-7-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000017_s11666-007-9026-7-Figure1-1.png", + "caption": "Fig. 1 Laser cladding", + "texts": [ + " Keywords finite element method, inductive preheating and postweld heating, laser cladding, phase transformation, process simulation, residual stress, stellite coating Laser cladding is increasingly used for the generation of corrosion- and wear-protective coatings and for the repair of tools and components. It is able to yield a strong interfacial bond between the substrate and the coating without significant dilution of one material into the other. In the laser cladding process, the pulverized coating material is transported by a carrier gas through a nozzle onto the workpiece surface (Fig. 1). There it penetrates into the melt pool that is generated by the laser beam on the moving substrate. Care must be taken to adjust the temperature field so that a strong metallurgical bond between the deposit and the substrate is achieved with very low dilution of the coating with substrate material. Since the coating material is in the liquid state while being deposited on the cold substrate, thermal contraction of the deposit unavoidably leads to the evolution of residual stresses and workpiece distortion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001740_j.jmatprotec.2015.02.026-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001740_j.jmatprotec.2015.02.026-Figure3-1.png", + "caption": "Fig. 3. (a) FE mesh model used in the sim", + "texts": [ + " The user-written PDL subroutine was developed to model the inclined surface of the olten pool using the following analytical expression (Farahmand t al., 2013): (x, y, z) \u2261 [x \u2212 x0] ( x \u2212 x0 L )2 + ( y w )2 + ( z + z0 \u2212 HC z0 ) \u2212 1 = 0 (11) here is a step function with the values of 1 and 0 in and outside f the molten pool surface, respectively. HC is the clad height, and 0 and z0 are the halves of the interface thicknesses in the X and directions, respectively. The meshing of computational domain, omposition modeling, and element activation process during the ladding is also shown in Fig. 3b. The temperature dependent mateial properties, such as thermal conductivity and specific heat for i, WC, and mild steel (A36) are shown in Fig. 4. 4. Results and discussion 4.1. Molten pool evolution The evolution of the molten pool is a prominent thermal feature affecting the quality characteristics of composite coating. The width and length of the molten pool and penetration depth of the heat along the substrate thickness are compared to the experimental ones shown in Fig. 5. These results show that the simulated molten pool shape and dimensions are comparable to experimental ones" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001578_tmag.2010.2093509-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001578_tmag.2010.2093509-Figure1-1.png", + "caption": "Fig. 1. Wave generation structure based on FSPMLGs.", + "texts": [ + " In this paper, in order to solve the problems created by \u201cmover-PM\u201d generators, a novel FSPMLG is presented for wave energy electric generation. The 2-D finite-element method, combined with an equivalent circuit, is employed to analyze electromagnetic characteristics. Under the constraint of the harmonic components of electromotive force (emf), less cogging force is obtained by optimization. The simulation results are validated by experiments. The system structure used for wave energy extraction is shown in Fig. 1. This system consists of a buoy and four linear FSPM generators. The translator of the generator is connected Manuscript received May 25, 2010; revised August 15, 2010 and October 10, 2010; accepted November 07, 2010. Date of current version April 22, 2011. Corresponding author: H. Yu (e-mail: htyu@seu.edu.cn). 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.2010.2093509 to the buoy, through which the translator is moved with the motion of a sea wave" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.5-1.png", + "caption": "FIGURE 5.5. 3R PUMA manip ulator and links coordinate frame.", + "texts": [ + " The j oint variable can be found by considering what fram es and links will m ove with each varying active jo int. 204 5. Forward Kinematics Example 126 DH table and coordinate frames for 3R planar manipulator. R stands for revolute, hence , an RIIRIIR manipulator is a planar robot with three parallel revolute joints. Figure 5.4 illustrates a 3R planar ma nipulator robot. The DH table can be filled as shown in Table 5.2, and the link coordinate frames can be set up as shown in the Figure. Example 127 Coordinate frames for a 3R PUMA robot. A P UMA manipulator shown in Figure 5.5 has Rf-RIIR main revolute joints, ignoring the structure of the end-effector of the robot. Coordinate frames attached to the links of the robot are indicated in the Figure and tabulated in Table 5.3. 5. Forward Kinematics 205 The joint axes of an K 1RI IR manipulator are called waist zo, shoulder Zl, and elbow Z2. Typica lly, the joint axes Zl and Z2 are parallel, and per pendicular to Zo . Example 128 Stanford arm . A schematic illustration of the Stanford arm, which is a spherical robot R'rR'r P attached to a spherical wrist R'r R'r R , is shown in Figure 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002795_j.apsusc.2014.05.210-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002795_j.apsusc.2014.05.210-Figure1-1.png", + "caption": "Figure 1. The torsional vibration model of gear-pair considering the friction Where: is time-varying contact stiffness, is damping coefficient; is the composite error of gear-pair meshing;", + "texts": [ + " As fractal dimension has a connection with the gear surface morphology, so the fractal method also establish a bridge between the dynamic performance and the gear *Manuscript- new Click here to view linked References Page 3 of 11 Acc ep te d M an us cr ip t micro surface quality, which can be used to indicate the future gear surface design and manufacture. 2. Traditional torsional vibration model review There are several gear dynamics models used commonly, such as dynamic load factor model, torsional vibration model of gear pair, drive system model and gear system model [10]. The torsional vibration model of gear-pair is the most popular, as shown in Figure 1. p \uff0c g) are the basis radius, inertia, torsional vibration displacement, torsion of the pinion and bull gear respectively. 2.1 dynamic differential equation According to reference[11], the gear dynamic equation is represented as follows: Set as the difference of static transmission error, as the external static load; here, me=1/(Rp 2 /Ip+Rg 2 /Ig) is the equivalent mass of gear-pair; Then the formula (1) can be transferred to the following expression. (2) Chosen the first - order harmonic component, is conveyed as follows[2]: (3) Where is average meshing stiffness, is the first-order harmonic component, is gear meshing frequency, is gear comprehensive error" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002922_j.ymssp.2018.05.028-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002922_j.ymssp.2018.05.028-Figure4-1.png", + "caption": "Fig. 4. The interaction between the ball and raceways. (a) Ball-inner raceway interaction, (b) ball-outer raceway interaction, and (c) the relative slip velocity between the ball and raceways in the contact ellipse (including 1 and 2 pure rolling points cases).", + "texts": [ + " 3(a), \u00f0Xor;Yor; Zor\u00de denotes the outer race fixed frame, hbor describes the azimuth of the considered ball relative to the outer race fixed frame and is used to determine the azimuth-in-outer raceway frame \u00f0Xaor;Yaor ; Zaor\u00de. In Fig. 3(b), aor denotes the actual contact angle between the ball and outer raceway; the frame \u00f0Xair ;Yair ; Zair\u00de denotes the azimuth-in-inner raceway frame. Dx denotes the axial relative displacement motion of the bearing inner ring to the outer ring; b denotes the rotational angular displacement of inner ring around axis Yi. The geometrical interaction between the ball and raceways in FDB is shown in Fig. 4. In FDB, the interaction between the ball and outer raceway is similar to that of the ACBB. While, as FDB has a cylindrical roller bearing inner race, the ball-inner raceway interaction relationship is equal to the contact relationship between a ball and a cylindrical surface. Thus, the contact line between the considered ball and the inner raceway passes through the ball center and is perpendicular to the cylindrical surface forever, as shown in Fig. 3(b). In this section, the geometrical interaction relationship between a considered ball and the inner raceway in the azimuth-in-inner raceway frame \u00f0Xair ;Yair ; Zair\u00de is used to more clearly introduce the ball-inner raceway interaction, as shown in Fig. 4(a). In Fig. 4(a), vector rairbir locates the center of the considered ball relative to the center of the inner race in the azimuth-ininner raceway frame. As shown in Fig. 4(a), the Zcir axis of the contact frame \u00f0Xcir;Ycir; Zcir\u00de is parallel with the Zair axis of the azimuth-in-inner raceway frame \u00f0Xair ;Yair ; Zair\u00de but with the opposite direction. Thus, the elastic contact deformation between the ball and inner raceway can be calculated by dbir \u00bc rIRo \u00fe 1 2 d rairbir3 \u00f03\u00de where rairbir3 denotes the 3rd component of the vector rairbir . The normal contact force between the ball and inner raceway can be calculated according to the Hertzian point contact theory as Qbir \u00bc Kbird 1:5 bir dbir > 0; 0 dbir 6 0: ( \u00f04\u00de where Kbir is the Hertzian contact stiffness coefficient, which is related to Modulus of elasticity, Poisson\u2019s ratio, curvature and curvature sum of the two contacting bodies", + " The radii of curvatures of the ball and inner raceway in two main planes can be expressed by rI1 \u00bc d=2; rI2 \u00bc d=2; rII1 \u00bc 1; rII2 \u00bc rIRo; \u00f06\u00de As the Hertz contact coefficient is related to curvature and curvature sum of the two contacting bodies, the differences of the curvature between the ball-inner-raceway contact and the ball-outer-raceway contact should be considered when calculating the Hertz contact coefficients. In this study, the cage is guided by the outer raceway and the effect of the cage is also included in the dynamic model. The ball-cage and cage-outer race interaction are modeled based on the method described in [16,19] for the ACBB. Once the ball contacts with raceways, elastic deformation occurs at the contact zone, as shown in Fig. 4 (b). The semimajor axis and semiminor axis of contact ellipse can be calculated based on the obtained contact load and Hertzian point contact theory. As described by Gupta [16], for most bearings the contact ellipse is quite narrow (a b, as shown in Fig. 4(b)), and the vibration in relative velocity along the Ycor axis can be neglected. Thus, the contact ellipse is divided into several elementary strips to calculate the slip velocity, and the slip velocity of the considered elementary can be calculated by the point lying on the major axis of the contact ellipse. However, there is something that should be noted when calculating the slip velocities and tangential tractive force between the ball-inner-raceway. According to [16], the radius of curvature of the contact deformed pressured surface between the ball and the raceway q (as shown in Fig. 4(b)) can be defined by qj \u00bc 2f jd 2f j \u00fe 1 \u00f07\u00de where j = i or o, which denote the inner and outer raceways, respectively; f i denotes the curvature factor of the inner raceway and is defined as the ratio of the radius of curvature of inner raceway groove to the ball diameter. However, in the FDB, as the radius of the curvature of inner raceway in the \u2018\u2018Plane 1\u201d is 1, (i.e., rII1 \u00bc 1), f i is equal to 1. As a result, for the ball-inner-raceway contact in FDB, the radius of curvature of the contact deformed pressured surface between the ball and inner raceway qi is defined by qi \u00bc 2f id 2f i \u00fe 1 f i\u00bc1 \u00bc d \u00f08\u00de This is much different from the ball-outer-raceway contact condition and should be considered when calculating the relative slip velocity between the ball and raceways. The slip velocity of the raceway relative to the ball at a considered point in the contact frame can be calculated by ucor s \u00bc ucor r ucor b \u00f09\u00de where ucor r and ucor b denote the slip velocity of the raceway and ball, respectively. The relative slip velocity between the ball and the raceways in the contact ellipse is shown in Fig. 4(c). When there is one or two pure rolling points in the contact ellipse, the contact ellipse will be divided into 2 or 3 sub-regions, and the relative slip velocity in two neighboring subregions are opposite, as shown in Fig. 4(c). In this study, the tangential tractive forces between the ball and raceways are calculated based on a four-parameter traction model of lubrication described by Gupta in [16]. This model gives the traction coefficient at a certain relative slip velocity and is expressed by j \u00bc \u00f0A\u00fe Bu\u00de exp\u00f0 Cu\u00de \u00fe D \u00f010\u00de where A, B, C, and D are coefficients for particular lubricant, and the coefficients used in [31] are applied in this study. In this traction model of lubrication, parameters A, B, C, and D are separately set as 7" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure4.21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure4.21-1.png", + "caption": "Fig. 4.21 Minimal models for forced vibrations; a) Two excitation moments, b) Motion excitation", + "texts": [ + "117) The last equation refers to the rotational speeds nim in rpm and the frequencies fi in Hz. This is a necessary (not a sufficient) condition, which can be conveniently represented in a resonance diagram, also known as Campbell diagram. The natural frequencies are plotted on the ordinate and rotational speeds on the abscissa. The lines of the orders then intersect with the natural frequencies at the critical rotational speeds that may occur there, see Figs. 4.24b, 4.27, and 6.31a. The equations of motion for the minimal model in Fig. 4.21a result as a special case from (4.113) for n = 2 or as an extension of (4.23): J1\u03d5\u03081 + bT(\u03d5\u03071 \u2212 \u03d5\u03072) + cT(\u03d51 \u2212 \u03d52) = M1(t) (4.118) J2\u03d5\u03082 \u2212 bT(\u03d5\u03071 \u2212 \u03d5\u03072)\u2212 cT(\u03d51 \u2212 \u03d52) = M2(t). (4.119) If no driving or braking torques Mk(t) are given, but instead a forced motion excitation \u03d51(t) is applied, the magnitude of J1 is not relevant for the motion of \u03d52(t), and the calculation model of Fig. 4.21b is obtained, the equation of motion of which is derived as a special case from (4.119): J2\u03d5\u03082 + bT\u03d5\u03072 + cT\u03d52 = bT\u03d5\u03071(t) + cT\u03d51(t). (4.120) (4.118) can be used to determine the moment M1(t) that maintains the predefined motion excitation. It is sometimes helpful to use the relative angle q = \u03d51 \u2212 \u03d52 as a coordinate. From (4.120), one obtains the following for this angle: q\u0308 + bT J2 q\u0307 + cT J2 q = \u03d5\u03081(t). (4.121) One can obtain a single equation of motion from (4.118) and (4.119) for the internal (\u201celastic\u201d) moment M = cT(\u03d51 \u2212 \u03d52) in the twisted shaft, see also (4", + " The dynamic loads in the vibration system depend on the magnitude and time sequence of such torque jumps. 4.3 Forced Vibrations of Discrete Torsional Oscillators 273 A torque jump is the harshest load case because the load jumps to its maximum value \u201cin zero time\u201d. The other discussions in Sect. 4.3.3.2 will show the conditions under which this extremely high load case can be a useful approximation, even for loads applied over a finite time period. The torsional moments that emerge after several torque jumps in the input shaft will be calculated for the torsional oscillator shown in Fig. 4.21a. The results can be transferred to the systems outlined in Table 4.2 and to any linear oscillator with multiple degrees of freedom if the torsional oscillator is viewed as a modal oscillator, see Chap. 6. The following considerations can therefore also be applied to the load oscillation of a crane, a stepping motor, an asynchronous motor that is controlled via several stages, multiple-step brakes and similar cases, which will not be discussed in detail here, see [4]. The internal moment for an undamped oscillator (bT = 0, D = 0) with a sudden torque jump Man = M10 acting on the disk 1 is to be determined", + "158) They can be used to calculate favorable points in time and magnitudes for the torque jumps, see [4] and Problem P4.5. Loads are not really applied suddenly, as assumed in Sect. 4.3.3.1, but during a finite time that will be called startup time ta here. This subsection is to answer the question of what influence the time function of the input torque M1 = Man(t) has on the torsional moment in the shaft if it increases during the startup time from zero to the maximum value M10. Figure 4.34 shows four different moment curves and their associated equations. Like in Sect. 4.3.3.1, the torsional oscillator from Fig. 4.21a is considered for the torsional moment of which (4.147) applies. This section only exemplifies the calculation for Case 1 from Fig. 4.34. The solution of (4.147) for the initial conditions t = 0: M = 0, M\u0307 = 0 for the linearly increasing input torque M1(t) = M10 t ta ; 0 t ta (4.159) is: M(t) = M10J2 J1 + J2 ( t ta \u2212 sin \u03c9t \u03c9ta ) ; 0 t ta. (4.160) 4.3 Forced Vibrations of Discrete Torsional Oscillators 277 Starting at the time t = ta, the same function is excited once again (at a time offset of ta) using the linearly decreasing moment \u2212M10(t \u2212 ta)/ta so that an excitation at the constant value of M10 remains from this superposition: \u0394M(t) = \u2212M10J2 J1 + J2 ( t\u2212 ta ta \u2212 sin \u03c9(t\u2212 ta) \u03c9ta ) ; t ta" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000269_1.27882-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000269_1.27882-Figure2-1.png", + "caption": "Fig. 2 Quadrotor aircraft configuration.", + "texts": [ + " The quadrotor-based mechanism is generally used for small UAVs such as the Draganfly rotorcraft (see Fig. 1). The front and the rear motors rotate counterclockwise while the other two motors rotate clockwise. As a result, gyroscopic effects and aerodynamic torques tend to cancel in trimmed flight. The gyroscopic moments that occur when rotors are not spinning at exactly the same speed can be neglected. In the following, we include the relations between the control inputs and the motor velocities in the case of the quadrotor aircraft (see Fig. 2). The collective lift u is the sum of the thrusts generated by the four propellers [33]: u X4 i 1 fi X4 i 1 w2 i In fact, propeller thrust and torque are generally assumed to be proportional to the square of the angular velocity. The airframe torques generated by the rotors are given by [1] l w2 2 w2 4 (8) l w2 3 w2 1 (9) D ow nl oa de d by U N IV E R SI T Y O F C IN C IN N A T I on N ov em be r 13 , 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .2 78 82 w2 1 w2 3 w2 2 w2 4 (10) where and are positive constants characterizing the propellers aerodynamics" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000820_s12555-012-0107-0-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000820_s12555-012-0107-0-Figure1-1.png", + "caption": "Fig. 1. The coordinate axes, the rotation directions of the rotors, the lift forces, and the Euler angle descriptions.", + "texts": [ + " For this purpose, a custom experimental test stand is developed and manufactured for the evaluation of the quadrotor flight controllers. The paper is organized as follows. Section 2 describes the mathematical model of a quadrotor. The controllers are presented in Section 3. The simulations supporting the objectives of the paper are presented in Section 4, followed by the experiments in Section 5. Concluding remarks are presented in Section 6. 2. MATHEMATICAL MODELLING OF THE QUADROTOR HELICOPTER A quadrotor (Fig. 1) is an under-actuated aircraft with fixed-pitch angled four rotors. It contains four motors located on the front, back, left and right of the air frame. The rotors connected to these motors provide the necessary lift forces, and these four forces are the inputs to the system to control six degrees of freedom; three Euler angles and three positions. In order to move the quadrotor on the z-axis, the speed of all of the motors should be changed. Forward (backward) motion is maintained by increasing (decreasing) speed of front (rear) motor speed while decreasing (increasing) rear (front) motor speed simultaneously which means changing the pitch angle", + " Left and right motion is accomplished by changing roll angle by the same way, by changing the lift forces which changes the roll angle rate of the vehicle. The front and rear motors rotate counter-clockwise while other two motors rotate clockwise, so yaw command is derived by increasing (decreasing) counter-clockwise motors speed while decreasing (increasing) clockwise motor speeds. This also eliminates the need of a tail rotor. Let us describe the mathematical model of the quadrotor using Newton-Euler equations. Consider a rigid body model of a 3D quadrotor given in Fig. 1, where the coordinate axes, the rotation directions of the rotors, the lift forces, and the Euler angles are provided. Assume a body fixed frame (frame B) is located at the center of gravity of the quadrotor, and an inertial frame (frame A) is located on the ground. The relation of Frame B with respect to Frame A gives the helicopter\u2019s pose, which is composed of six degrees of freedom. The 3D position of any point with respect to axis A can be represented by [ ] T P x y z= also representing the helicopter position" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000056_s0263574707003530-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000056_s0263574707003530-Figure9-1.png", + "caption": "Fig. 9. Bennett mechanism.", + "texts": [ + " A detailed introduction into this interesting topic can be found in McCarthy.6 The mathematical tools used there are closely related to the methods presented within this paper. But there is a difference in the geometric interpretation of the derived equations. We show the application of our methods in the synthesis of a Bennett mechanism. The Bennett mechanism is a closed 4R chain. It is well known that a Bennett mechanism can be synthesized exactly when three poses of the end effector system are given (Fig. 9). Synthesis means that we have to find the design parameters of the mechanism and the location of the axes in the fixed system and the location of the moving body in the moving system. For the synthesis of such a mechanism, we attach two of the revolute axes to the fixed system and two axes to the moving (coupler) system. Now we prize open the coupler link and obtain two open 2R chains. The basic idea of the synthesis is to map the possible displacements of the first 2R chain onto S2 6 . This yields the constraint manifold M1 of the 2R chain in the kinematic image space" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002211_b978-0-08-100433-3.02001-7-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002211_b978-0-08-100433-3.02001-7-Figure3-1.png", + "caption": "Figure 3 (a) Blisks. (b) The cross-sectional profile and deposition strategy for rebuilding a blisk with variable laser beam diameter and power [15].", + "texts": [ + " All powder nozzles feature specific advantages and disadvantages dependent on the powder delivery concept. The choice of a suitable powder nozzle is application specific and, consequently, part and material dependent as well as process specific. The characteristics of the three common powder delivery nozzles used for AM are listed in Table 2 [14]. Under normal AM operation, the laser spot size is preset to maximize the build rate, for example, or minimize the heat buildup in more delicate components. In some cases of part repairdfor example the repair of blisks (Fig. 3), the cross-sectional area of the part varies in the XY plane. To achieve a near-net-shape deposit and avoid bead overlap within a layer with potential defects, a variable beam focus optic has been developed (Fig. 4) that is numerically controlled. This allows a variable beam diameter and, consequently, melt pool with an adjusted powder mass flow rate to be achieved in a single pass. In component repair, in particular where part accessibility is restricted, internal powder deposition nozzles have been developed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001056_asjc.587-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001056_asjc.587-Figure1-1.png", + "caption": "Fig. 1. Quadrotor helicopter configuration frame system.", + "texts": [ + " The vertical velocity is controlled via the overall thrust of the motors, while the lateral and longitudinal velocities are controlled by the cascaded control of the roll and pitch angles. The model of the quadrotor utilized in this article assumes that the structure is rigid and symmetrical, the center of gravity and the body fixed frame origin coincide, the propellers are rigid and the thrust and drag forces are proportional to the square of the propeller\u2019s speed. Two coordinate systems have been utilized, i.e. the body-fixed frame B = [B1, B2, B3]T and the Earth-fixed frame E = [Ex, Ey, Ez]T as presented in Fig. 1. Assuming rigid blades, neglecting blade flapping and coning, one may model a variety of aerodynamic forces and moments that govern the quadrotor\u2019s flight, including the rotor thrust forces, the hub forces, the drag moments and the roll moments. An extended model may be found in [8]. For control issues however, the Euler\u2013Lagrange formulation is more favorable. Such a formulation that also takes into consideration the additive effects of the atmospheric disturbances that has the following nonlinear form: X X U W= +f ( , ) , with U \u2208 R5 the input vector, and X \u2208 R12 the state vector that consists of the translational components x = [x, y, z]T along the Earth\u2013fixed frame E, the corresponding translation velocities \u03be = [ , , ]x y z T" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003230_soro.2017.0035-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003230_soro.2017.0035-Figure6-1.png", + "caption": "FIG. 6. (a) Fabric overlapping under shear load. (b) Fabric/rubber bonding: through-thickness permeation (black, area \u00bc ap) or rubber adhesion or absorption to threads (gray, area \u00bc 1 ap). (c) A unit volume of rubber on top of the fabric loaded with tensile force. (d) A unit volume of rubber on top of the fabric loaded with shear force.", + "texts": [ + " An extra layer of wetted fabric, which we call a \u2018\u2018patch,\u2019\u2019 should be applied if weak areas are anticipated. For example, a patch should be applied if stand-up wrinkles are formed during manufacturing, especially where rubber is squeezed out from under the wrinkle. Likewise, a patch should be applied if there is insufficient overlap between two sections of fabric. Patches can also be applied if failure occurs, but careful surface preparation is required. In all of these cases, \u2018\u2018patches\u2019\u2019 provide an extra layer of reinforcement and ensure reliability. The size of the patch or overlapping fabric, Figure 6, should be large enough to provide shear resistance and limit potential failure caused by fracture propagation. It is related to the bonding strength between the fabric and the rubber substrate. Consider a unit area of a fabric, Figure 6b, the green region in plane with the fabric indicates rubber thread bonding area, which is directly related to the rubber absorbency of the thread. The black area indicates throughthickness permeation of liquid rubber and, thus, is bonded with rubber through the hole. Fabric composite bonding failure occurs when fabric starts to separate from the rubber substrate due to tensile strain, et, Figure 6c, or shear strain, es, Figure 6d. Let ap 0 represent the permeable area in a unit area, then 1 ap represents the rubber thread bonding area. Thus, the tensile bonding strength, Bt, and shear bonding strength, Bs, are dependent on fabric permeable area, ap, and can be represented as follows: Bt ap \u00bc apSt et\u00f0 \u00de\u00fe 1 ap Tt (1) Bs ap \u00bc apSs es\u00f0 \u00de\u00fe 1 ap Ts (2) where St et\u00f0 \u00de is the rubber tensile strength at tension et and Ss es\u00f0 \u00de is the rubber shear strength at shear strain es, which can be determined by tensile and shear material testing, respectively. With Bt, Bs, et, and es, obtained from material tests for a specific fabric weave density, or permeable area ap, thread rubber bonding strength in tension, Tt, and shear, Ts, can be estimated through Equation (1) and Equation (2). Then, the bonding strength of a fabric/rubber composite made of similar fabrics with the same thread but different weave density, or a different permeable area, ap\u00a2, can be estimated. As a result, for an overlapped fold, Figure 5b, or a joint, Figure 6a, to bear a load force F and its corresponding shear deformation Dx, the area of the overlapping, A, and the material shear thickness, t, should satisfy both conditions: F Bs A (3) Dx t es (4) Therefore, it is recommended that the size of the fabric overlap discussed in this section and the previous subsection should be estimated and designed based on these rules. A two-piece 3D-printed clamp is designed to firmly encapsulate the folded fabric directly onto the surface of the Mold Insert, Figure 4c, or a rubber substrate, Figure 4c\u2019-ii, depending on the location of the fabric layer in the composite" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure2.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure2.5-1.png", + "caption": "Figure 2.5.2 Road camber curvature (bank curvature).", + "texts": [ + " For this, really a time-stepped Earth-fixed coordinate analysis should then be used, for clarity, so that pseudo-forces are not needed. With pitch curvature, the road normal direction at the two axles is different, by the wheelbase normal- curvature angle uLN \u00bc LW RN \u00bc kNLW This has a small effect on the tyre-road normal force magnitude and direction, but is probably better neglected as of little importance for normal roads. It may be significant when the pitch curvature is large, arising for off-road applications. Figure 2.5.1 shows a rear view of a vehicle on a straight road with a road bank angle fR, but without any longitudinal gradient or cornering, and having zero lateral acceleration. Figure 2.5.1 Vehicle on a straight banked road. Road Geometry 51 To see the effects, analysis is performed in road-aligned coordinates, so theweight force is resolved into components normal to the road and tangential, down the slope. The result of the reduction of normal component is a reduction of tyre normal forces. The result of the lateral component is a lateral load transfer. There is also some resulting body and axle roll, and the front-to-rear distribution of the lateral load transfer should be considered" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000780_10402004.2011.639050-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000780_10402004.2011.639050-Figure4-1.png", + "caption": "Fig. 4\u2014Radially loaded rolling element bearing. Gr, internal diametral clearance; g, radial clearance; \u03b4max, maximum race deformation: (a) concentric arrangement, (b) initial contact, and (c) interference. Adapted from Hamrock and Anderson (17).", + "texts": [ + " [12] should be 10/9 (typically rounded to 1.11). D ow nl oa de d by [ U ni ve rs ity o f C al if or ni a Sa nt a C ru z] a t 2 0: 36 2 6 O ct ob er 2 01 4 Fig. 3\u2014Loads, P, and deflections between rolling elements and races in radially loaded ball or roller bearings. Dp, bearing pitch diameter; j, rolling element number (index); CF, body force due to centripetal motion. The loads between the rolling elements and the inner and outer races of a bearing are shown schematically in Fig. 3. The initial radial clearance is shown in Fig. 4a. The compression in the normal direction of element j due to inner-ring displacement in a radially loaded ball or roller bearing is \u03b4n j = x sin\u03c8j + y cos\u03c8j \u2212 Gr 2 > 0 [15] where is the displacement of the inner race and \u03c8j is the position angle of element j. A more general treatment, including non-zero contact angle and loading in 5 degrees of freedom was presented by Jones (13), (14) and Houpert (15). The total compression \u03b4nj at rolling element j is the sum of the deflections at the inner and outer race contacts: \u03b4n j = \u03b4oj + \u03b4i j [16] From the force equilibrium on an element, Pij + CFj \u2212 Poj = 0 [17] where Pij = Kij \u03b4 \u03b1 ij [18a] Poj = Koj \u03b4 \u03b1 oj [18b] CFj = k1mj ( Dp 2 ) \u03c92 cage [19] and where K is the stiffness, k1 is the body force conversion constant, Dp is the bearing pitch diameter, m is the mass, and \u03c9 is the rotating speed", + " Check the equilibrium of forces using Eqs. [22a] and [22b]. 6. If the residual forces \u03b5\u2032x and \u03b5\u2032y are larger than a tolerance value, repeat steps 1 to 5 with new estimates for the inner-race displacements x and y. Once this iteration has completed, L10, the 10% fatigue life for the bearing, can be calculated using the classical LundbergPalmgren method from the rolling element loads calculated above (7). The geometry of a radially loaded ball or roller bearing with internal clearance is shown in Fig. 4. Consider that the bearing is initially arranged symmetrically, with the clearance Gr divided equally around the outer race (Fig. 4a). Next, the clearance is taken up by an infinitesimal radial load that shifts the inner ring by a distance Gr/2, as shown in Fig. 4b. Opposite the point of application of the radial load, the position angle \u03c8= 0\u25e6 and the clearance is zero. At any other (non-zero) angle \u03c8there will be a radial clearance g = (1 \u2212 cos \u03c8)Gr/2. At \u03c8 = 90\u25e6, the clearance g will be the initial value of Gr/2. Additional load applied to the bearing causes elastic deformation at the contact between the rolling elements and the races as shown in Fig. 4c. At \u03c8= 0\u25e6, the maximum deformation \u03b4max adds to the clearance take-up Gr/2. The total race displacement \u03b4T = \u03b4max + Gr/2. If the race maintains a circular shape, the elastic compression of the rolling elements is given by Eq. [23]. For Gr > \u22122\u03b4T, the limiting contact angle \u03c8l is given by Eq. [24] (Hamrock and Anderson (17)), where \u03b5 = 1 2 \u2212 Gr/(4\u03b4T). \u03b4\u03c8= \u03b4T cos\u03c8\u2212 Gr/2 [23] \u03c8l = cos\u22121 ( Gr/2 \u03b4T ) = cos\u22121 (1 \u2212 2\u03b5) [24] Harris and Kotzalas (11) provided an iterative procedure to calculate the maximum rolling element load in ball and roller bearings using the load distribution integral Jr(\u03b5)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001596_j.msea.2017.10.064-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001596_j.msea.2017.10.064-Figure1-1.png", + "caption": "Fig. 1. Experimental setup (a) and cutting position of test samples (b).", + "texts": [ + " However, few work has been addressed on the anisotropy in FCGR. This paper then studied this topic to deepen the understanding. The equipment used were Fronius Magic Wave 4000 plasma welder and Fanuc M-710iC robot. The deposition material was 1.2 mm-diameter Ti-6Al-4V wire with the chemical composition (wt%) of Al6.1V4.0-Fe0.15-C0.01-N0.01-H0.002-O0.16-Ti balance. The substrate was hot rolled Ti-6Al-4V plate with the size of 1000 mm in length, 70 mm in width and 20 mm in height. The experiment setup is shown in Fig. 1a, a water cooling cycle device was under the substrate. The experiment was shielded by argon. In order to prevent the oxidation, each layer was deposited when the temperature of previous layer was below 100 \u00b0C. The sample were deposited under the parameters of arc current 115 A, wire feed speed 1.6 m/min, deposition speed 0.18 m/min, vertical build interval 1.1 mm, reversed deposition direction, and interlayer spacing time 180 s. The deposited thin-wall was 835 mm in length, 145 mm in width and 9 mm in thickness. To relieve residual stresses, the deposited thinwall was directly annealed at 550 \u00b0C for 2 h. As shown in Fig. 1b, the metallographic and mechanical samples were taken from the region http://dx.doi.org/10.1016/j.msea.2017.10.064 Received 5 September 2017; Received in revised form 12 October 2017; Accepted 20 October 2017 \u204e Corresponding authors. E-mail addresses: mgao@mail.hust.edu.cn (M. Gao), wfdhust2013@mail.hust.edu.cn (F. Wang). Materials Science & Engineering A 709 (2018) 265\u2013269 Available online 21 October 2017 0921-5093/ \u00a9 2017 Elsevier B.V. All rights reserved. MARK below the top of 5 mm and above the bottom of 2 mm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000966_j.phpro.2011.03.048-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000966_j.phpro.2011.03.048-Figure4-1.png", + "caption": "Figure 4: Hexagonal unit cell Figure 5: Uniaxial compressive testing of specimen", + "texts": [ + " Process capabilities for production of freely suspended structures were examined by fabricating single lattice bars inclined in angles from 0\u00b0 to 80\u00b0 with respect to the base plate. To study additional interrelations length of the bars was also taken into account and varied from 0,5 mm up to 5 mm. All investigated specimens were produced using an energy input per unit length of 0,4 J/mm, which describes a stable region for lattice bar production. On the basis of these principal studies, a lattice structure based on a hexagonal unit cell was developed that incorporates horizontal x-y-bars, cp. Figure 4. Theoretical calculations on the resulting porosity with respect to previously determined lattice bar diameter and geometrical restrictions, such as unit cell height or maximal aspect ratio for cell structures [9], were chosen as development criteria. Cellular structures are typically described by their specific values with respect to the theoretical solid geometry. The specific Young\u2019s modulus is thus defined as E*= */ . The specific stress * can be similarly derived from the orthogonal load F on the theoretical cross sectional area A*, *=F/A* [8]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001521_1077546311411756-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001521_1077546311411756-Figure1-1.png", + "caption": "Figure 1. Tread element.", + "texts": [ + " In this paper, the formula of tire wear is established considering temperature effect and the dynamic characteristics of a vehicle. In addition, the effects of speed, ambient temperatures, tire pressure and sprung mass for tire wear are analyzed. Finally, the main impact factors of tire tread wear are obtained through the parameters sensitivity analysis. Based on friction theory, the friction between tire and pavement will consume energy; therefore, wear quantity can be gained if we calculate the energy loss. We simplify the mass of tire which has contact with the surface of a road into a cuboids\u2019 element, as shown in Figure 1, where a and b are the length and width of the ground contact patch, respectively, and h is tread thickness. The ground contact patch of tire is affected by tire structure, wheel alignment parameters, tire pressure and vertical load. According to the deformation characteristics of the tire, the length and width of ground contact patch can be determined by the following empirical equations, respectively (Zhuang, 2001). a \u00bc 4d 2d s \u00f01\u00de b \u00bc b0\u00f01 e \u00de \u00f02\u00de where b0 is crown thickness; d is the outside radius of tire; is the deformation of tire; s and are empirical coefficients which are related to tire structure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003780_j.optlastec.2018.06.042-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003780_j.optlastec.2018.06.042-Figure3-1.png", + "caption": "Fig. 3. Temperature counters at diverse times during LMD process on the cross-section of the molten pool (X-Z plane): (a) the processing time of N 1track, t = 0.008 s; (b) the processing time of N track, t = 0.04 s; (c) the processing time of N + 1track, t = 0.064 s.", + "texts": [ + "04 s was increased by about 100 C compared with the time of 0.008 s due to the heat accumulation effect The temperature of adjacent part of the N 1 and N deposited track also exceeded the liquidus temperature of Inconel 625, which meant that the N 1 track has been remelted during the process of depositing the N deposited track (Fig. 2b). This phenomenon was beneficial to form good metallurgical bonding between adjacent tracks, improving the relative density of deposition parts. At the time of 0.064 s, the peak temperature was 2590 C (Fig. 2c). Fig. 3 illustrates the transient temperature distribution at different time (0.008 s, 0.04 s and 0.064 s) during LMD process on the cross-section of the molten pool. In the LMD process, the laser energy was attenuated by the absorption and reflection of the MD-processed Inconel 625 superalloy using constant laser power and scan speed of powder before reaching the substrate. The remainder laser energy was absorbed by substrate or previously deposited layers, leading to the rapid heating and resultant local melting and good metallurgical bonding between adjacent tracks and layers. It could be observed that substrate was melted by the high-power laser beam and molten pool with certain depth formed (Fig. 3). The transient temperature distribution consisted of a series of isothermal curves. The dash line was the isothermal line of Inconel 625 powder liquidus temperature. The internal area of the dash line curve was the formative molten pool during the manufacturing process. The laser energy was Gaussian distribution, and as a result, the temperature of the molten pool decreased progressively from the center to the edge. It could be found that the molten pool was symmetry of isotherms along the laser scanning direction and the depth of the molten pool is 0.83 mm (Fig. 3a). As the LMD process continued, the part of previously deposited track has been remelted, giving rise to the formation of the metallurgical bonding between the adjacent deposition tracks (Fig. 3b and c). The depth of the molten pool of the N deposited track was 0.75 mm, which decreased by 0.08 mm compared with that of the N-1 deposited track. There was a slight increase compared with the depth of the N deposited track, and the depth of the molten pool of the N + 1 deposited track was 0.76 mm. When the N deposited track was processed, a part of laser energy was absorbed by the former deposited track, leading to the formation of the decreased depth within the molten pool. The rise of temperature slowed down and the dimension of the molten pool tended to be stable as the deposition process continued, because the energy reached a balance status between the heat input and the heat sink" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.4-1.png", + "caption": "FIGURE 11.4. Intersection of the momentum and energy ellipsoids .", + "texts": [ + "108) In other words, the dynamics of moment-free motion of a riqid body requires that the corresponding angular velocity w(t) satisfy both Equations (11.107) and (11 .108) and therefore lie on the intersection of the momentum and energy ellipsoids. For a better visualization, we can define the ellipsoids in the (Lx ,Ly , Lz) coordinate system as 1. (11.109) (11.110) Equation (11.109) is a sphere and Equation (11.110) defines an ellipsoid with V2IiK as semi-axes. To have a meaningful motion, these two shapes must intersect. The intersection may form a trajectory, as shown in Figure 11\u00b74\u00b7 It can be deduced that for a certain value of angular momentum there are maximum and minimum limit values for acceptable kinetic energy . Assum ing (11.111) 464 11. Motion Dynamics the limits of possible kin etic energy are \u00ab-: Km ax = (11.112) (11.113) and the corresponding motions are turning about the axes hand h respec tiv ely. Example 257 * Alternative derivation of Eul er equations of motion. Th e moment of the small for ce df is dm dm Crdm x df c rdrn x c \" drn dm. (11.114) Th e in ertial angular momentum dl of dm is equal to and according to (11" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000339_s0022112005004829-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000339_s0022112005004829-Figure9-1.png", + "caption": "Figure 9. (a) The wake regions of the two spheres comprising the dumbbell, and the resulting shielding effect. (b) The restricted regime of validity for Harper & Chang\u2019s analysis; the only overlap is with the vanishingly small region of Jeffery orbits with orbit constants C 40% / 10 min) by applying acoustic energy to the microrobot using a high-intensity focused ultrasound (HIFU) transducer. (c) Schematic of the acoustic energy transfer using the HIFU transducer (D = 60 mm, Vpp = 20 V). The acoustic energy (f = 1 MHz) was focused at the focal point (F = 58 mm from the surface) and produced pressure (p = 1.2 MPa). (d) Schematic illustration of the acoustic energy-driven ultrafast drug release by the helical microrobot. Because the DOX molecules were non-covalently bonded to the catechol group of the microrobot, they were efficiently released upon the application of acoustic energy.", + "texts": [ + " Several techniques have been reported for the fabrication of microhelices, including self-scrolling [21], glancing angle deposition (GLAD) [22,23], direct laser writing [7,24], and the coating of biological helical templates [25,26]. In this regard, this study investigated the fabrication of helical microrobots by using a self-folding technique and utilized the microrobots to provide a magnetically controlled drug delivery and provides for highly efficient drug release by ultrasound stimulation (Fig. 1). This concept enables a morphological transformation from two-dimensional (2D) to three-dimensional (3D) shape upon external stimuli [27]. An inhomogeneous reaction occurs in an inhomogeneous membrane or bilayers of a membrane in response to the stimuli. This structure is commonly referred to as having soft and hard layers, with the hard layer consisting of wrinkles and creases, and the soft layer curling and rolling to release internal stress [28\u201330]. The advantages of this self-folding technique include quick, reproducible production and the ability to control the morphology and chemical properties of the structures [29,30]", + " SEM and EDS analyses were performed with a 5-kV potential and 8-mm working distance and a 15- kV potential and 15-mm working distance, respectively. X-ray diffraction (XRD) patterns of the selected specimens were measured by a highresolution XRD (Malvern PANalytical, Malvern, UK) with a Cu target and 1.8 kW of power. A vibrating sample magnetometer (VSM, Lake Shore: 7404, USA) was used at room temperature to analyze the magnetic properties. An electromagnetic actuation (EMA) system consisting of eight electromagnetic coils with soft magnetic cores, as illustrated in Fig. 1a, was used to evaluate locomotion performance. The system could realize a five-degrees-of-freedom heading and force control of the magnetic object by generating rotating magnetic fields (maximum of 75 mT), to facilitate the microrobot\u2019s swimming motion. Eight power supplies were used to control the coil currents, including four MX15 units and four 3001iX units from AMETEK, USA. A digital single-lens reflex (DSLR) camera was installed above the workspace to record the locomotion test, and a light source was placed under the workspace to enhance image quality", + " After being exposed for 10 s, the microrobots and cell medium were transferred into the 96-well plate and placed in the incubator (40 \u25e6C) for 24 h. All quantitative values are presented as means \u00b1 standard deviation. All experiments were performed with at least three replicates for each group, and the Student\u2019s t-test was performed for the statistical analysis. The indication ** represents P < 0.01, which was considered statistically significant. B.A. Darmawan et al. Sensors and Actuators: B. Chemical 324 (2020) 128752 The acoustic energy-driven on-demand drug delivery system was designed, as shown in Fig. 1b. Propelled by the magnetic force produced by the EMA system, the helical microrobot swam to the target region. Thereafter, the drug molecules were efficiently released (>30% / 10 s) by applying acoustic energy to the microrobot using an HIFU transducer (Fig. 1c). As illustrated in Fig. 1d, the DOX molecules were efficiently released upon the application of acoustic energy because they were noncovalently bonded to the catechol group of the microrobot. This study fabricated helical-shaped microrobots from a biocompatible magnetic ink by using a self-folding technique with a directpatterning optical system. As described previously, a mixed biocompatible ink was injected into the 100 \u03bcm thick microchamber. Before the curing process, the objective lens (NA: 0.15) was focused such that the desired position and surface of the membrane were clearly visible" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure7.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure7.5-1.png", + "caption": "Fig. 7.5 Example 7.2. Decomposition of the velocity analysis", + "texts": [ + " Determine (a) the magnitude of the velocity, acceleration, jerk, and hyperjerk of the nozzle N for t D 2 s, and (b) the symbolic expressions for the reduced velocity, acceleration, jerk, and hyper-jerk states of the nozzle N as measured from the fixed link. Solution. Let XYZ be a reference frame with associated unit vectors OiOjOk attached to the fixed body whose origin is located at point O. The velocity of N as measured from body j, the vector vN D jvm N , is computed as jvm N D jvk N C kvm N ; (7.63) where jvk N is the velocity vector of N considering the body m is joined to body k. Furthermore, kvm N is the velocity vector of N assuming that j and k are the same rigid body. With reference to Fig. 7.5, it is evident that jvk N D P Ok rN=O; (7.64) where rN=O D .1:5C l/ h cos. /OiC sin. /Oj i (7.65) is a vector pointed from O to N and P D d dt \u0152 =3C . =6/ sin. t=2/ D . 2=12/ cos. t=2/: (7.66) Furthermore, the relative velocity vector kvm N is given by kvm N D Pl OuN=O; (7.67) where 7.3 Hyper-Jerk Equations in Screw Form 177 OuN=O D cos. /OiC sin. /Oj (7.68) is a unit vector along the arm of the robot. Meanwhile, Pl D d dt \u0152.1=4/ sin. t=2/ D . =8/ cos. t=2/: (7.69) Hence, jvm N D P Ok .1:5C l/ h cos" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003780_j.optlastec.2018.06.042-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003780_j.optlastec.2018.06.042-Figure2-1.png", + "caption": "Fig. 2. Three-dimension temperature distribution at different simulation times during L 800 W and 500 mm/s, respectively: (a) t = 0.008 s; (b) t = 0.04 s; (c) t = 0.064 s.", + "texts": [ + " The microstructure of sample was analyzed by optical microscopy (OM) and field emission scanning electron microscopy (FE-SEM; Hitachi, Tokyo, Japan) at an accelerating voltage of 3 kV. Table 1 Thermal-physical parameters of Inconel 625. T/ C 20 100 200 400 600 800 1300 k [W/(m C)] 9.8 10.9 12.4 15.4 18.3 21.3 28.6 c [J/(kg C)] 410 430 455 505 556 606 732 Table 2 Chemical compositions of Inconel 625 alloy powder (in weight fraction, wt. %). Ni Cr Mo Nb Fe Co Mn Si Al Ti C P S 58 min 20\u201323 8\u201310 3.15\u20134.15 5 1 0.5 0.5 0.4 0.4 0.1 0.015 0.013 Fig. 2 shows the computed temperature distribution at different simulation time (0.008 s, 0.04 s and 0.064 s) during LMD process. As the simulation time progressed, the shape of temperature field changed and temperature was unstable (Fig. 2). The temperature field distribution of the N-1 deposited track presented a towed semi-elliptical, and the shape of temperature field was symmetrical along the laser scanning direction (Fig. 2a). It showed that the temperature field was no longer symmetrical along the laser scanning direction due to the heat accumulation and heat conduction between the two adjacent tracks. Moreover, heat affected zone (HAZ) has become larger as the simulation proceed. The maximum temperature and relatively dense isothermal curves appeared in the front of the molten pool because of the main of heat input focused on a limit area (Fig. 2). The peak temperature increased progressively as the subsequent tracks deposition. At the time of 0.008 s, the peak temperature was 2415 C, which was higher than the liquidus temperature of Inconel 625 (1350 C). The peak temperature at the time of 0.04 s was increased by about 100 C compared with the time of 0.008 s due to the heat accumulation effect The temperature of adjacent part of the N 1 and N deposited track also exceeded the liquidus temperature of Inconel 625, which meant that the N 1 track has been remelted during the process of depositing the N deposited track (Fig. 2b). This phenomenon was beneficial to form good metallurgical bonding between adjacent tracks, improving the relative density of deposition parts. At the time of 0.064 s, the peak temperature was 2590 C (Fig. 2c). Fig. 3 illustrates the transient temperature distribution at different time (0.008 s, 0.04 s and 0.064 s) during LMD process on the cross-section of the molten pool. In the LMD process, the laser energy was attenuated by the absorption and reflection of the MD-processed Inconel 625 superalloy using constant laser power and scan speed of powder before reaching the substrate. The remainder laser energy was absorbed by substrate or previously deposited layers, leading to the rapid heating and resultant local melting and good metallurgical bonding between adjacent tracks and layers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.45-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.45-1.png", + "caption": "Fig. 2.45 Examples of mass balancing by using a compensatory mechanism moving in the opposite direction (solid line: original mechanism; dashed line: compensatory mechanism)", + "texts": [ + " Mechanisms can be found using computer-aided synthesis, in which specific harmonics of the excitation forces and moments have a minimal magnitude. The solution is not always in balancing the first or second harmonics, often balancing of higher harmonics is of practical significance. In addition to complete and harmonic mass balancing, the following practical measures can help to achieve an improvement: 2.6 Methods of Mass Balancing 163 \u2022 Generation of an equivalent countermotion, i. e. compensation by equal and opposite inertia forces of an additional mechanism (Fig. 2.45) or by additional dyad. \u2022 Balancing of specific harmonics using compensatory mechanisms (Fig. 2.45). \u2022 In multicylinder machines by placing counterweights at various crank angles, by offsetting the mechanism planes relative to the axis, and possibly by varying the crank radii and piston masses, see Sect. 2.6.3.3. \u2022 Optimal balancing, taking into account secondary design conditions (requires the use of software). Slider-crank mechanisms are used in many machines for converting rotating into reciprocating motions (and vice versa) so that mass balancing has met with special interest for quite some time", + "Required dimensions (R, \u03b2), mass ma, and moment of inertia JO a of the balancing mass so that both the first harmonic of the frame force Fx is balanced and JO a becomes as small as possible. The materials that can be selected are cast iron, tin bronze, and white metal. Calculate the x component of the bearing force (Fx12) and the input torque Man for a slider-crank mechanism for which the inertia forces are to be balanced using an balancing mass and a compensatory mechanism arranged as shown in Fig. 2.45e. State the balancing conditions for the first and second harmonics of Fx12 and Man in general form. What values should be selected for the angles \u03b1 and \u03b3 and the balancing masses m4 and m5 so that the first two harmonics of these forces are compensated? Assume \u03bb = l2/l3 = l2/l3 1 and \u03d5 = \u03a9t. 2.6 Methods of Mass Balancing 169 The following quantities are up for discussion for balancing individual harmonics in a fourcylinder machine, see Fig. 2.51: Variante a) : \u03b31 = 0\u25e6; \u03b32 = 90\u25e6; \u03b33 = 270\u25e6; \u03b34 = 180\u25e6 Variante b) : \u03b31 = 0\u25e6; \u03b32 = 180\u25e6; \u03b33 = 180\u25e6; \u03b34 = 0\u25e6 Find out which orders of the forces and moments are balanced by these variants if the cylinder distances and cylinders are the same" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure14.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure14.2-1.png", + "caption": "Figure 14.2.1 Spring compression displacement v. suspension bump displacement.", + "texts": [ + " For struts, a slightly different analysis is required. The main notation required here is as in Table 14.2.1. Note that the subscript K is used for the spring because the subscript S has already been allocated to \u2018suspension\u2019. At a given suspension bump position zS from static ride height, the spring compression is xK relative to static. A small further suspension bumpmotion dzS results in a corresponding further spring compression Suspension Geometry and Computation J. C. Dixon \u00a9 2009 John Wiley & Sons, Ltd. ISBN: 978-0-470-51021-6 dxK, Figure 14.2.1. The ratio of these is the displacement motion ratio for the spring at the suspension bump position zS. This is denotedRK/S (spring relative to suspension bump), generally abbreviated to RK: RK=S \u00bc dxK dzS Note that this is the spring compression increment divided by the suspension bump increment, not vice versa. It is the suspension bumpmovement that is considered to be the reference movement. This value of RK will be independent of zS and dzS only if the system is linear, that is, if the motion ratio RK is constant, which is generally not true" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001254_j.mechmachtheory.2012.10.003-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001254_j.mechmachtheory.2012.10.003-Figure1-1.png", + "caption": "Fig. 1. Frame and eccentricity error definition.", + "texts": [ + " The resulting state equations point to a non-linear parametrically excited differential system which is solved iteratively by combining a time-step integration scheme, a fixed-point method and a normal contact algorithm. Finally, a number of results are presented which illustrate the contributions of eccentricity errors and the interest and drawbacks of floating members (i.e., members on very flexible supports in this context) in terms of dynamic tooth load sharing. The modelling principles have been exposed in [12] and only the main lines are presented here for the sake of completeness. Based on the PTG geometry and the coordinate systems shown in Fig. 1, the eccentricity errors on the central members can be characterised using screws of infinitesimal generalised displacements attributed to every solid as [13]: SRk n o uR k Gk\u00f0 \u00de \u00bc OkGk \u00bc ekTk \u03c9R k \u00bc \u03d5kz0;k k \u00bc S;C;R ( \u00f01\u00de in whi where ek is the eccentricity of solid k and \u03d5k represents an additional infinitesimal rigid-body rotation possibly induced by the where errors on the sun-gear (k=S), carrier (k=C) and ring-gear (k=R); superscript R indicates that the perturbations are measured from the errorless configuration of solid k" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000339_s0022112005004829-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000339_s0022112005004829-Figure4-1.png", + "caption": "Figure 4. (a) The Jeffery orbits of a finite-aspect-ratio fibre when projected onto the flow\u2013gradient plane. The O(Re) corrected behaviour of the trajectories: inertial trajectories spiral out crossing successive Jeffery orbits (dotted lines) approaching the stable limit cycle in the shearing plane.", + "texts": [ + " A fibre in this orientation acts, at leading order, as a distribution of force-doublets, leading to a torque that is algebraically smaller, being of O(\u03ba\u22122); for blunt-edged bodies, the contribution to this torque comes from the blunt ends, and thereby precluding the use of slender-body theory (see Cox 1971). may be contrasted with the trajectory configuration in the limit of infinite aspect ratio illustrated in figure 3(a). For Re small enough, the surface of the unit sphere thus transforms from a structurally unstable centre manifold at Re =0 to a structurally stable combination of an attracting limit cycle (the flow\u2013gradient plane) and a pair of spiral repellors (the intersections of the vorticity axis with the unit sphere) for small but finite Re (see figure 4). The evolution of the orbit constant calculated using (3.28) is shown in figure 5, where we have plotted the ratio C/(C + 1) as a function of time for a fibre aspect ratio \u03ba = 20, and for Re = 0.05. The dominant changes are seen to occur in the nearly aligned phases of the Jeffery orbits, with \u03c6 near n\u03c0, where the fibre spends the most time, and for which case the inertial drift in (3.23) attains its maximum value. The otherwise monotonic increase in C/(C +1) is modulated by a secondary wiggle on the scale of a Jeffery period, leading to a pair of short plateaus in a \u03c0 interval of \u03c6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001337_s10846-013-9936-1-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001337_s10846-013-9936-1-Figure8-1.png", + "caption": "Fig. 8 Left to right, MM-UAV arm transition from stowed to fully deployed", + "texts": [ + " In this paragraph, we put the adaptive control to the test, trying to stabilize the same system from our previous work. Matlab was used for simulations and a recursive Newton-Euler dynamics model of the manipulators was implemented using the Robotics Toolbox [31]. Figures 7 and 10 show the results of one of the performed tests where the quadrotors roll controller was tuned close to the stability boundary. The aircraft takes off with arms tucked and stowed. After the vehicles settles to a hover, the arms are deployed down and fully extended (Fig. 8), thus increasing the moments of inertia. This change in the moment of inertia tries to destabilize the system and thus produces undesired oscillations in the roll angle control loop. The oscillations trigger the MRAC that changes the overall control loop gain, and therefore stabilizes the system. According to the stability criteria (8), the adaptive gain \u03b6 needs to increase the derivative gain KD to account for the rise in J. Figure 9 shows how the adaptive gain \u03b6 changes throughout the simulation, and Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003538_978-3-319-26106-5_8-Figure8.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003538_978-3-319-26106-5_8-Figure8.11-1.png", + "caption": "Fig. 8.11 Schematic view of manufacturing process of parallel wire array composite with wire spacing of 3, 7 and 10 mm, respectively (Reprinted with permission from Ref. [86], copyright 2014 AIP)", + "texts": [ + "31 Oe and a saturation magnetisation of 850 Gs. The inset stress-strain curve gives the tensile strength as high as 1297 MPa and the fracture strain of 2.88 %. These results validate the applicability of microwires as highstrength and soft magnetic functional fillers in the composites. The present microwires are embedded into two E-glass 950 aerospace-graded prepregs in a parallel geometry with 3, 7 and 10 mmwire-wire spacing, respectively, followed by adding the other two prepregs on top and bottom of this sandwiched wire-prepreg layer (Fig. 8.11). It should be noted that all the microwires are arranged along the direction of glass fibres to reduce hard contact between them if otherwise. The stacked wire prepregs are then cured in the autoclave to yield a resultant wire composite with dimensions of 500 500 1 mm [3]. The curing conditions are detailed elsewhere [87]. The microwave characterisation is performed by a freespace measurement rig placed in an anechoic chamber in the frequency range of 0.9\u201317 GHz with or without a dc magnetic bias up to 3000 Oe" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000976_rspa.2010.0135-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000976_rspa.2010.0135-Figure3-1.png", + "caption": "Figure 3. (a) Splay\u2013bend director conformation with n varying in the yz-plane on traversing the cantilever. (b) Twist director conformation with n twisting in the xy-plane on traversing the cantilever.", + "texts": [ + " 2008), which is discussed below. Heat release is also important in photo-effects (Hogan et al. 2002; Jiang et al. 2009), but the dependence of polydomain mechanics on light polarization proves that effects are dominated by optical response, and we limit ourselves to either light, or purely thermal effects. Proc. R. Soc. A (2010) (a) Director gradient cantilevers The simplest way to get an asymmetric response is to rotate the director by 90\u25e6 on going from the bottom to the top surface of the cantilever, see figure 3, either by a splay\u2013bend or by a twist conformation. (i) Splay\u2013bend The splay\u2013bend configuration (figure 3a) gives a greater response than that of twist. One does not need a gradient of stimulation to get response\u2014heating or cooling give bend (of opposite signs) and illumination will give bend in the same sense irrespective of which side it is incident from. For splay\u2013bend, the director rotates in the yz-plane from parallel to the bottom boundary (z = \u2212h) through to normal on the top (z = h). As an example, take the angle q(z) the director makes with the y-axis to be q(z) = pz 4h + p 4 . (3.1) The zeroth and first moments of es are easily evaluated and give 1 Ro yy = \u2212 6 hp2 (e\u2016 \u2212 e\u22a5), eyy = 1 2 (e\u2016 + e\u22a5) and 1 Ro xx = 0, exx = e\u22a5", + " One can see that the asymmetry about z = 0 is only thereby reduced and so too is the bend response. Also one could change the phase Proc. R. Soc. A (2010) of the variation while keeping the range at p/2. This too reduces the response. A critical example would be adopting the variation q(z) = pz 4h , where the director splay-bends from \u2212p/4 to p/4. Asymmetry about z = 0 is lost altogether and no curvature is induced. (ii) Twist The second possibility to rotate the director through the cantilever is the twist configuration (figure 3b), explored thermally (Mol et al. 2005) and optically (van Oosten et al. 2007) by the Broer group. As before, one does not need a gradient of stimulation to get response. The director twists uniformly in the xy-plane from being parallel to y at the bottom boundary to parallel to x on the top. The angle f(z) the director makes with the y-axis is given as for q in equation (3.1). The spontaneous strain, equation (2.2), now has off-diagonal components: es = \u239b \u239de\u2016 sin2 f + e\u22a5 cos2 f (e\u2016 \u2212 e\u22a5) sin f cos f 0 (e\u2016 \u2212 e\u22a5) sin f cos f e\u2016 cos2 f + e\u22a5 sin2 f 0 0 0 e\u22a5 \u239e \u23a0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002302_j.ymssp.2017.01.032-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002302_j.ymssp.2017.01.032-Figure1-1.png", + "caption": "Fig. 1. Measurement arrangement.", + "texts": [ + " That is, it is an analytical-mathematical model. Then, there is the lumped-parameter model, or dynamic model, which is based in the numeric resolution of the equations of motion of the system. The study of phenomenological model started three decades ago with the work of McFadden and Smith [1], who contributed to the understanding of the difference between the dominant frequency and gear meshing frequency. They also used the model to explain the asymmetry of the spectrummeasured by a transducer mounted on the outside of the ring gear (Fig. 1). Years after, McNames [2] used the Fourier series to complement the work of McFadden and Smith. Parker and Lin [3] studied the vibration phases of each gear pair inside a PG. Inalpolat [4] and Vicu\u00f1a [5] generalized the previous work by expanding the analysis to different geometries of PG. Both works took the amplitude modulation effect (AM) caused by the carrier rotation into account, but did not consider any frequency modulation effect caused by meshing stiffness variation or gear damage. The latter was included by Feng in the analysis of his work [6]. More recently, Hong [7] used Fourier series analysis to explain the distinct sideband patterns in healthy and faulty PG. All studies mentioned propose models that bring solutions referred to the measurements that the sensor would take placed as in Fig. 1. The first studies of the lumped-parameter model started as a method to determine the natural frequencies and vibration modes of PG. Kahraman [8] presented a torsional model for this purpose. Then Lin [9] worked in modal analysis on an equation of motion with multiple degrees of freedom. Chaari et al. [10] expanded the previous work by studying the influence of manufacturing errors. Additionally, there are works on other research topics like load sharing among planet gears [11,12], nonlinear dynamics and tooth faults [13\u201317]. Among these we highlight the work of Chaari et al. [18], where changes in gearmesh stiffness due to tooth spalling and breakage were studied, although not in PG. Unlike the fixed transducer scheme of Fig. 1, generally all lumped-parameter model solutions are referred to a noninertial reference frame, fixed to and rotating with the carrier. In the case of comparing the solutions with experimental measurements, it is desirable to know the vibration in the inertial basis as seen by a ground-based observer [19]. In brief, solutions of lumped-parameter model are not directly comparable with results from phenomenological model and real vibrations measured on the ring gear. Other works include the lumped-parameter model and present their solutions as representing the fixed transducer response, but no explanation of the method used to obtain the solutions are provided [7,20]", + " Faults considered are local faults on sun gear, planet gear and ring gear. To compare the lumped-parameter model results with the phenomenological model results and experimental measurements (to account for additional frequency components related to the local faults), we propose a method that provides a solution to the decomposition of rotatory frame to fixed reference frame vibrations. In this section, vibration models of the PG used in this study are presented. The configuration and measurement arrangement considered is shown in Fig. 1. According to the classification suggested in [4], the PG pertains to group A, i.e., with N \u00bc 3 equally spaced planet gears at the angular positions wi (where i \u00bc 1;2; . . . ;N and w1 \u00bc 0), and in-phase gear meshes. Tooth number of gears are Zs \u00bc 18 (sun), Zp \u00bc 26 (planet), and Zr \u00bc 72 (ring). This model is presented in detail in [5], and describes directly the measurements as a sensor according to the arrangement of Fig. 1 would take. It models the vibrations of all gear pairs as periodic functions with fundamental frequency equal to the gear mesh frequency f g \u00bc Zr f c (where f c is the carrier frequency). Fig. 2 presents a simulation example of a PG considering planet-ring gear meshing only. Individual planet-ring vibrations v r i \u00f0t\u00de with the corresponding phase difference wi=\u00f02pf c\u00de can be seen in Fig. 2a. Vibration contributions of each planet-ring gear meshing to the transducer measurements, including the amplitude modulation effect ar i \u00f0t\u00de produced by the variable transmission path between the fixed sensor and the planets are presented in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003218_tpel.2017.2710137-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003218_tpel.2017.2710137-Figure13-1.png", + "caption": "Fig. 13 Simple i-\u03a8 loci curves at low speed", + "texts": [ + " T is the sampling period. 2 12 2t t base t k k T T (18) The actual hysteresis width can be expressed: 1 2 1 1 ( ) ( ) max up down dc t t i i i U T L L (19) 1 2 1 2 2 1 2 1 1 1 2 2 1 1 ( ) 2 1 1 ( ) 2 t t avg up down dc t t up down dc t t up down dc base i i i U T L L L i i U T L i i U k T (20) (a) Low speed When the speed is low, current can be controlled very well and large torque is still reachable considering the stable input power. Fig.13 shows the i-\u03a8 loci curves at low speed. The changeable area S1, S2 are restricted by S2=S1. 21 2 em L T i (21) With an advance angle, L would be a little smaller. The phase current would be bigger and the top linkage would be lower to produce the same conversion energy. Thus, advance angle should be equal to zero or be positive when the rotation speed is low. (b) High speed and small torque In this part, as the rotation speed goes high, the variation range of k gets large relative to kbase" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001776_tia.2016.2533598-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001776_tia.2016.2533598-Figure11-1.png", + "caption": "Fig. 11. Calculated (FEM) distribution of iron loss density per unit value in the stator core of tested motor in operation mode I [kW/m3].", + "texts": [ + " At 20 Nm, the carrier harmonic iron loss reduction effect is counterbalanced by the increase of stator iron loss and copper loss. When the torque becomes larger, the increase of stator iron loss and copper loss exceeds carrier harmonic iron loss reduction. Figs. 11 and 12 show calculated (FEM) distribution of iron loss density per unit value in the stator core of tested motor for operation modes I and II, respectively. Calculation conditions are 4000 min-1 speed, 10 Nm torque, 400 V DC voltage, and 15 kHz PWM carrier frequency. In operation mode I (Fig. 11), iron loss density is distributed equally for all teeth and back yoke. On the other hand, iron loss density distribution on non-excited teeth and half of back yoke is reduced in operation mode II (Fig. 12), although that on excited teeth is almost equal to that in Operation mode I. Fig. 13 shows calculated (FEM) loss on excited tooth and non-excited tooth in operation mode II (at 4000 min-1 10 Nm). Carrier harmonic iron loss reduction effect is confirmed from the figure. These results confirm that carrier harmonic current ic does not increase even if phase current increases as long as the hypothesis in (2) is true" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.2-1.png", + "caption": "Fig. 6.2 Calculation model of a frame", + "texts": [ + "25) They can thus be found by performing the following steps: 1. Division of the overall system into R subsystems, the matrices Cr and M r of which are known. 2. Determination of the global coordinates q 3. Expression of the relationships between the local coordinates q(r) of the substructures and the global coordinates q using the transformation matrices T r. 4. Determination of the global matrices of the overall system according to (6.25) The matrices D, C, and M are to be established as an example for the system outlined in Fig. 6.2 consisting of point masses and massless beams. Given parameters are the bending stiffness EI , the length l, the masses m1 and m2 and the coordinates q1 and q2 that are to be used. The relationships between forces and displacements can be expressed in the form (6.4). The influence coefficients can be calculated according to Table 6.1. First, the forces gT = (Q1, Q2) are assumed in the direction of the coordinates qT = (q1, q2). If s1 and s2 are the position coordinates for describing the bending 364 6 Linear Oscillators with Multiple Degrees of Freedom moments (see Table 6", + "31) This yields matrix D, and after brief calculation, its inverse matrix C, see (6.12): 6.2 Equations of Motion 365 D = \u23a1\u23a2\u23a2\u23a3 4l3 3EI l3 2EI l3 2EI l3 3EI \u23a4\u23a5\u23a5\u23a6 = l3 6EI [ 8 3 3 2 ] ; D\u22121 = C = 6EI 7l3 [ 2 \u22123 \u22123 8 ] . (6.32) One can check by numerical calculation that D \u00b7 C = E. The kinetic energy is Wkin = 1 2 m1q\u0307 2 1 + 1 2 m1q\u0307 2 2 + 1 2 m2q\u0307 2 2 = 1 2 m1q\u0307 2 1 + 1 2 (m1 + m2)q\u0307 2 2 . (6.33) Note that the horizontal motion of the mass has to be considered in addition to its vertical motion m1 (Fig. 6.2). It follows as a result of forming the partial derivatives according to (6.15): m11 = m1; m12 = m21 = 0; m22 = m1 + m2. The mass matrix for m1 = 2m and m2 = 4m is therefore: M = [ m11 m12 m21 m22 ] = [ m1 0 0 m1 + m2 ] = m [ 2 0 0 6 ] . (6.34) The stiffness matrix C can also be obtained directly using the beam element discussed in 6.2.2.2, see (6.225). A beam element with interfaces 1 and 2 onto which FL1, FL2, F1, F2, M1 and M2 act forms the starting point. The deformations caused by this in the local coordinate system are depicted in Fig", + "5: a)Load m2 falls with the initial velocity u into the cable of the resting crane (gripper drops into the holding cables) b)Load drops suddenly (breakage of the load handling device) c)Sudden motor shutdown during lifting (uh = const., crane at rest) d)Load m2 is suddenly caught by a rigid obstacle during lifting. What are the equations for calculating the cable force and the bending moment in the center of the crane girder? Note: The coordinate origin of x1 is the static equilibrium position of the unloaded crane, that of x2 is the end of the unloaded cable. For the model shown in Fig. 6.2, calculate the natural frequencies and mode shapes and check whether the orthogonality relations are satisfied. Determine the system matrices as a special case of the example given in Sect. 6.3.4.2. P6.6 Influence of an Elastic Bearing on the Natural Frequencies of a Torsional Oscillator The measured fundamental frequency of a drive deviated significantly from the one that was calculated using the calculation model according to Fig. 4.3a (torsionally elastic shaft and two rotating masses). The observed difference could not be explained by parametric uncertainties alone", + " Since a vibrating conveyor has to be operated at 50 Hz due to the fixed frequency of the electrical power line , the change of the mode shapes when varying the application point of one of the two exciters was investigated. The result of the analysis is shown in Fig. 6.27b. One can see that mounting the exciters at a spacing l3 allows an even flow of the material to be conveyed while at a spacing of l1 one can expect accumulation of material in the center of the trough, and at a spacing of l5 even a counterflow of material in portions of the trough due to a vibration node. What are the equations of motion in terms of modal coordinates for the system shown in Fig. 6.2 if the two excitation forces F1 and F2 act in the directions of the coordinates q1, q2? At what magnitudes of F1 and F2 is the second mode shape not excited? A vertical force is applied suddenly to the beam end of the system discussed in Problem P6.10, i. e. F1 = 0 and F2 = 0. Calculate the time variation of the coordinates q1 and q2 over time and estimate the magnitude of the maximum moment at the clamping point by deriving an equation similar to (6.301) for that case. A rotor with an unbalance U = me rotates at an angular velocity \u03a9 about its vertical axis", + "315) In the static case, the deformations for qst = Dfst would be: qst = l3 6EI [ 8 3 3 2 ][ 1 0 ] F1 = 1 6 [ 8 3 ] F1l3 EI = [ 1.333 0.5 ] F1l3 EI . (6.316) They are obtained in the special case that no vibrations take place: cos \u03c91t and cos \u03c92t do not occur then and should be set to zero. The maximum dynamic deflections then are within the limits 2 \u00b7 1.2179 = 2.4358 \u2264 ( EIq1 l3F1 ) max \u2264 2 \u00b7 (1.2179 + 0.1155) = 2.6668 2 \u00b7 0.5807 = 1.1614 \u2264 ( EIq2 l3F1 ) max \u2264 2 \u00b7 (0.5807 + 0.0807) = 1.3228. (6.317) The fixed-end moment results from the equilibrium of moments, see Fig. 6.2: M = F1l + 2mlq\u03081 + 6mlq\u03082. (6.318) The accelerations in nondimensional form are: mq\u03081 F1 = mv11 \u03b31 \u03c92 1 cos \u03c91t + mv12 \u03b32 \u03c92 2 cos \u03c92t = 0.2972 cos \u03c91t + 0.2028 cos \u03c92t mq\u03082 F1 = mv21 \u03b31 \u03c92 1 cos \u03c91t + mv22 \u03b32 \u03c92 2 cos \u03c92t = 0.1417 cos \u03c91t\u2212 0.1417 cos \u03c92t (6.319) The dynamic fixed-end moment is thus 6.5 Forced Undamped Vibrations 443 M = F1l [ 1 + (2v11 + 6v21) m\u03c92 1 \u03b31 cos \u03c91t + (2v12 + 6v22) m\u03c92 2 \u03b32 cos \u03c92t ] = F1l(1 + 1.444 cos \u03c91t + 0.444 cos \u03c92t) (6.320) The moment is \u201calmost periodic\u201d, and its extreme values can be up to: Mmin = \u22120", + " If, for example, an actuator acted at the node of a normal mode shape of a bending oscillator, it could not excite the respective normal mode shape, i. e. this normal mode shape could not be influenced by that actuator and thus not all types of motion could be implemented. There are mathematical methods and criteria for evaluating the stability, observability and controllability, which are described, for example, in [2], [14] and are recommended for further study. The simple model of a machine frame with two degrees of freedom according to Fig. 6.2, as known from Sect. 6.2.2.1, shall be considered here, however, extended by two interfering excitation forces F1(t) and F2(t) as well as measuring points B and D and a control force FR in the direction of the coordinate q1 that is to reduce the excited vibrations, see Fig. 9.2. The vertical velocity vBv is measured in B and the difference in strain \u0394\u03b5D is measured in D using a strain gauge as the strain has to be determined from both sides to compensate for the influence of the axial force. The mass and stiffness matrices for q = [q1, q2] T are known from Sect" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.13-1.png", + "caption": "Fig. 4.13 Geneva wheel and its geometry scheme", + "texts": [ + "100) where \u2022 The first-order coefficient matrix A of the mechanism is given by A D 2 4 1 1 0 a1 sin q 0 1 a1 cos q d 0 3 5 I (4.101) \u2022 I is the identity matrix of order 3; \u2022 is a matrix containing the passive joint-rate velocities of the mechanism as follows: D 1!1 2 2!1 3 Pd T : (4.102) \u2022 Finally, the first-order driver matrix of the manipulator Pq is defined as Pq D Pq 0 0 T : (4.103) 90 4 Velocity Analysis Expression (4.100) allows us to determine singular configurations of the crankslider linkage mechanism. The issue is left as an exercise. Example 4.7. The Geneva wheel or Maltese cross (see Fig. 4.13) is a mechanism where a driven body undergoes intermittent rotary motion produced by the continuous rotation of a driver body. The name derives from the devices used mainly in mechanical watches, and Geneva is an important center of watchmaking. Prominent applications of this one-degree-of-freedom planar mechanism include movie projectors, the pen change mechanism in plotters, indexing tables in assembly lines, automated sampling devices, tool changers for CNC machines, and banknote counting. The rotating drive wheel A has a pin P and a plate B. The motion of the mechanism is such that wheel D turns one fourth of a revolution for each revolution of the pin P. At the engagement position shown in Fig. 4.13, we have D 30\u0131. For a constant clockwise angular velocity !1 D 2 rad/s of wheel A, it is required to compute the corresponding angular velocity !2 of the driven wheel D and the relative velocity of point P as measured from wheel D. The intention of this example is twofold: (1) The velocity analysis is carried out using the method exposed in standard books; and (2) the velocity analysis is carried out using screw theory. Solution. Let XYZ be a reference frame whose origin is point O1. One classical solution of the velocity analysis of the Geneva wheel is as follows", + " Based on screw theory, determine the velocity of the middle of the coupler platform of the four-bar planar mechanism. 7. Determine in loci form the singular regions of the crank-slider linkage mech- anism. In other words, find an analytic expression to compute the singularities of the mechanism. 8. Using classical methods, Eq. (4.107) leads to a linear system of two equations in the unknowns !2 and v00 P; determine such a system. 9. Apply another classical method to solve the velocity analysis of the Geneva wheel, Example 4.7. Hint: Obtain two closure equations from the triangle O1O2P indicated in Fig. 4.13. Finding the corresponding time derivatives of such equations allows us to solve the velocity analysis. 10. In Example 4.7 we considered that v4 D !2. Give a justification, if any, for this assumption. 11. The Geneva wheel of Example 4.7 is a little case that illustrates how easy it is to formulate the velocity analysis of parallel manipulators when reciprocal screw theory is used. Determine the input\u2013output equation of velocity of the planar parallel manipulators shown in Fig. 4.16 by resorting to reciprocal screw theory", + "100)] is given by A D I Pq; where A D 2 4 1 1 0 a1 sin q 0 1 a1 cos q d 0 3 5 is the first-order coefficient matrix of the mechanism, while I is the 3 3 identity matrix. Thus, since det.I/ D 1, the mechanism is free of singularities concerned with the inverse velocity analysis. On the other hand, in loci form the equation of singularities dealing with the forward velocity analysis is given by det.A/ D a1 cos.q/ d D 0. 8. Using classical methods, Eq. (4.107) leads to a linear system of two equations in the unknowns !2 and v00 P; determine such a system. Solution. With reference to Fig. 4.13, the equation of velocity was derived as follows: !1 rP=O1 D !2 rP=O2 C v00 P OuP=O2 : Taking into account that the fixed reference frame O XYZ has associated unit vectors OiOjOk, we have !1 D !1 Ok and !2 D !2 Ok, while the position vectors rP=O1 and rP=O2 may be written as rP=O1 D r1 cos. /Oi C r1 sin. /Oi and rP=O2 D r2 cos.\u02c7/Oi C r2 sin.\u02c7/Oi. Furthermore, the unit vector OuP=O2 may be written as 328 15 Full Answers to Selected Exercises OuP=O2 D rP=O2=r2. Equating Oi with Oi and Oj with Oj in the aforementioned equation of velocity and reducing terms, one obtains a linear system of two equations given by !2r2 !1r1 cos. C \u02c7/ D 0; v00 P !1r1 sin. C \u02c7/: 9. Apply another classical method to solve the velocity analysis of the Geneva wheel, Example 4.7. Hint: Obtain two closure equations from the triangle O1O2P indicated in Fig. 4.13. Finding the corresponding time derivatives of such equations allows us to solve the velocity analysis. Solution. From the closed loop O1O2P it is possible to write two closure equations as follows: r1 cos. /C r2 cos.\u02c7/ O1O2 D 0; r1 sin. / r2 sin.\u02c7/ D 0; where O1O2 denotes the signed distance between points O2 and O1. Then the time derivatives of the aforementioned equations lead to the following input\u2013 output equation of velocity: r2 sin.\u02c7/ cos.\u02c7/ r2 cos.\u02c7/ sin.\u02c7/ P\u030c Pr2 D r1 P sin. / r1 P cos" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003435_b978-0-12-804782-8.00001-x-Figure1.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003435_b978-0-12-804782-8.00001-x-Figure1.2-1.png", + "caption": "Figure 1.2 GE Aviation\u2019s GEnx is an advanced dual rotor, axial flow high bypass gas turbine engine for use on Boeing\u2019s 787 and 747-8 aircraft and features titanium allow compressor blades and disks. Source: GE Aviation.", + "texts": [], + "surrounding_texts": [ + "CHAPTER 1 The Additive Manufacturing of Titanium Alloys\nABBREVIATIONS AND GLOSSARY\n3D three dimensional AM additive manufacturing CAD computer aided design DED directed energy deposition DMD direct metal deposition DMLS direct metal laser sintering EBM electron beam melting GE General Electric Corporation LENS laser engineered net shaping PBF powder bed fusion P/M powder metallurgy SL stereolithography\nTitanium alloys are among the most important of the advanced materials that are key to improved performance in aerospace and terrestrial systems (Figs. 1.1 1.4) and is even finding applications in the cost conscience auto industry.1 5 These applications result from the excellent combinations of specific mechanical properties (properties normalized by density) and outstanding corrosion behavior6 11 exhibited by titanium alloys. However, negating its widespread use is the high cost of titanium alloys compared to competing materials (Table 1.1).\nThe high cost of titanium compared with the other metals shown in Table 1.1 has resulted in the yearly consumptions as shown in Table 1.2.\nAdditive Manufacturing of Titanium Alloys. DOI: http://dx.doi.org/10.1016/B978-0-12-804782-8.00001-X \u00a9 2016 Elsevier Inc. All rights reserved.", + "In publications over the past few years1 29 the cost of fabricating various titanium precursors and mill products has been discussed (very recently the price of TiO2 has risen to US$2.00/lb and TiCl4 to US $0.55/lb). The cost of extraction is a small fraction of the total cost of a component fabricated by the cast and wrought (ingot metallurgy) approach (Fig. 1.5). To reach a final component, the mill products shown in the figure must be machined, often with very high buy-to-fly\nTable 1.1 Cost of Titanium: A Comparisona Item Material ($/lb) Steel Aluminum Titanium\nOre 0.02 0.01 0.22 (rutile)\nMetal 0.10 1.10 5.44\nIngot 0.15 1.15 9.07\nSheet 0.30 0.60 1.00 5.00 15.00 50.00 a2015 Contract prices. The high cost of titanium compared to aluminum and steel is a result of (a) high extraction costs and (b) high processing costs. The latter relates to the relatively low processing temperatures used for titanium and the conditioning (surface regions contaminated at the processing temperatures, and surface cracks, both of which must be removed) required prior to further fabrication.\nTable 1.2 Metal Consumption Structural Metals Consumption/Year (103 Metric Tons)\nTi 50\nSteel 700,000\nStainless steel 13,000\nAl 25,000" + ] + }, + { + "image_filename": "designv10_3_0001095_rm2010v065n02abeh004672-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001095_rm2010v065n02abeh004672-Figure6-1.png", + "caption": "Figure 6. The bifurcation diagram of the Goryachev\u2013Chaplygin case. The darker colour marks the domain in which to each point there corresponds a pair of invariant tori.", + "texts": [ + " All of them are unstable. This example shows that it is quite possible that isolated \u2018poorly predictable\u2019 integral manifolds appear for which the finiteness condition is violated. On the other hand, the example also shows that such exceptional integral manifolds are easily detected in a precise bifurcation analysis. 4.1. Bifurcation complex of a Goryachev\u2013Chaplygin top. In order to construct the bifurcation complex of a Goryachev\u2013Chaplygin top, we recall that to each point (h, f) in the darker area in Fig. 6 there corresponds a pair of invariant tori, that is, here we have a pair of leaves of the bifurcation complex, and branching occurs at the tangent point P1 (see Fig. 13). The vertical axis in this picture has no physical meaning and is used merely for convenience of visualization of different leaves. Stability of critical solutions is indicated in the picture by the symbols + (stable) and \u2212 (unstable). Thus, we see that for the Goryachev\u2013Chaplygin case in the phase space of the system there are four families of stable periodic trajectories (there are no other stable orbits)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure5.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure5.7-1.png", + "caption": "Figure 5.7.1 Wheel axis geometry, with steer and camber angles: (a) rear three-quarter view; (b) plan view showing steer angle; (c) view on ACD with camber angle.", + "texts": [ + " A steering damper may be helpful. these angles and their relationship to the axis direction cosines. This is complicated, a little, by variations of sign because of the different ISO and SAE axis system definitions, by the left and right sides of the vehicle, and by the choice of two directions for the unit vector along any line, and adjustments must be made to allow for these. Here, generally, the ISO axes will be used (X forwards, Y to the left, Z upwards), with a left-hand wheel, shown from the rear, Figure 5.7.1. It is easiest to think of the wheel beginning with zero steer and camber. In that case the wheel rotation axis is parallel to the vehicle Y axis. The direction cosines of the axis in this case are (0, 1, 0) or (0, 1, 0) depending on the direction chosen for the axis unit vector, inwards or outwards respectively, for the left wheel. Either direction could be used, but here the inward directionwill be preferred; that is, the unit vector points from the wheel generally towards the vehicle centreline", + " At zero steer and camber, the wheel axis direction cosines for a left wheel are therefore l\u00bc 0, m\u00bc 1 and n\u00bc 0. Consider the wheel now to be rotated in steer, and then in camber. The order of these rotations is important, affecting the equations. The steer rotation is first. Toe-out is taken as positive. The wheel is a 114 Suspension Geometry and Computation left-hand one, and positive steer is anticlockwise in plan view, and positive camber (negative inclination for a left wheel) is anticlockwise in rear view. Thewheel is steered by angle d (delta) and then cambered by angle g (gamma); see Figure 5.7.1(b) and (c). In Figure 5.7.1(a), consider a segment AD of the wheel axis, of length L. The triangle ABC is in the horizontal plane, with AB parallel to the Y axis and BC parallel to the X axis, so ABC is a right angle. The five lengths in the figure are: AD \u00bc L CD \u00bc L sin g AC \u00bc L cos g Now it follows directly that the direction cosines (l, m, n) of the wheel axis, which are the (X, Y, Z) components of the unit vector along the line AD, are l \u00bc cos g sin d m \u00bc cos g cos d \u00f05:7:1\u00de n \u00bc sin g l2 \u00fem2 \u00fe n2 \u00bc cos2 g\u00f0sin2 d\u00fe cos2 d\u00de\u00fe sin2 g \u00bc 1 Given particular values for the steer and camber angles, the direction cosines of the wheel axis are thereby easily calculated" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.29-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.29-1.png", + "caption": "Fig. 2.29 Distribution of the connecting rod mass over two equivalent masses", + "texts": [ + " The first harmonic component is called first-order inertia force. The second term in the Fourier expansion varies at twice the frequency and is therefore called second-order inertia force. The first-order inertia force, that is, the first harmonic of the force Fx, is balanced when condition (2.339) is satisfied, i. e. if a balancing mass is attached to the crank only. According to (2.341), the balancing mass is then located on the opposite side of the crank. It is, in practice, often designed as a segment of a circle, 2.6 Methods of Mass Balancing 165 see Fig. 2.29. The first-order inertia force of Fy is balanced when the balancing condition m2\u03beS2 + m3l2 ( 1\u2212 \u03beS3 l3 ) = 0 (2.342) is satisfied. Multicylinder machines in which multiple slider-crank mechanisms are connected by a common shaft are frequently used in engines and compressors . Balancing of some harmonics is possible if the relative position of the individual mechanism planes and the relative orientation of the crank angles are favorably selected. It is assumed for the following derivations that the cylinder axes and the crankshaft axis are in one plane, the y-z plane. This covers the case of an in-line engine with k cylinders. The interesting case of a V-engine or radial engine in which the piston directions are arranged at a specific angle is excluded from these considera- 166 2 Dynamics of Rigid Machines tions, see [1]. It is also assumed that all rotating masses, that is, the crankshaft with the rotating portions of the connecting rod (see m32, Fig. 2.29), are completely balanced. All cylinders should also be identical (equal masses and geometry) and only have different crank angles, see Fig. 2.47. The angle between the first crank (j = 1) and the jth crank is denoted as \u03b3j . The inertia forces can be stated in the form of a Fourier series, see (2.293). With (j = 1, 2, . . . , J), the following applies to each mechanism: Fj(t) = \u221e\u2211 k=1 [Ak cos k(\u03a9t + \u03b3j) + Bk sin k(\u03a9t + \u03b3j)] . (2.343) k identifies the order of the harmonic. If it is assumed that the crankshaft revolves at constant angular velocity, the crank angles are \u03d5j = \u03a9t + \u03b3j ", + " l2 = 40 mm crank length l3 = 750 mm coupler length \u03beS2 = 12 mm distance of the center of gravity of the crank from O 168 2 Dynamics of Rigid Machines JS2 = 6, 1 \u00b7 10\u22123 kg \u00b7m2 moment of inertia referred to the axis through the center of gravity of the crank m2 = 4.8 kg crank mass m4 = 14 kg piston mass r = 20 mm inner radius of the balancing mass Rmax = 140 mm maximum outer radius of the balancing mass (installation space!) b = 40 mm thickness of the balancing mass G = 7250 kg/m3 density of cast iron Z = 8900 kg/m3 density of tin bronze W = 9800 kg/m3 density of white metal Note: The mass parameters of the coupler 3 have been approximately included in the calculation of those of links 2 and 4, see Fig. 2.29. 1.Resultant frame force components Fx and Fy in general form for an arbitrary input motion \u03d52(t), taking into account the balancing mass. 2.Required dimensions (R, \u03b2), mass ma, and moment of inertia JO a of the balancing mass so that both the first harmonic of the frame force Fx is balanced and JO a becomes as small as possible. The materials that can be selected are cast iron, tin bronze, and white metal. Calculate the x component of the bearing force (Fx12) and the input torque Man for a slider-crank mechanism for which the inertia forces are to be balanced using an balancing mass and a compensatory mechanism arranged as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure17-1.png", + "caption": "Fig. 17. Coordinate systems used for the derivation of the worm.", + "texts": [ + " (36) correspond to the application of a right-hand and left-hand worms, respectively. The worm thread surface Rw is determined as an envelope to the family of shaper tooth surfaces Rs. Surface Rw is determined in coordinate system Sw by the following equations: rw\u00f0us; ls;ws\u00de \u00bc Mws\u00f0ws\u00ders\u00f0us; ls\u00de; \u00f038\u00de Ns v\u00f0sw\u00des \u00bc fws\u00f0us; ls;ws\u00de \u00bc 0: \u00f039\u00de Here, vector function rs(us, ls) represents the tooth surface of the shaper. Matrix Mws(ws) describes the coordinate transformation from coordinate system Ss to coordinate system Sw (Fig. 17). Vector function rw(us, ls,ws) represents in coordinate system Sw the family of surfaces Rs of the shaper. Eq. (39) is the equation of meshing between the surfaces of the shaper and the worm. Parameter ws is the generalized parameter of motion considering that the shaper and the worm perform related rotations about the axes za and zc (Fig. 17). These rotations are related by the equation ws ww \u00bc Nw Ns : \u00f040\u00de Eqs. (38) and (39) considered simultaneously represent the worm thread surface by three related para- meters (us, ls,ws). Fig. 18 shows simultaneous meshing of the face-gear, the shaper, and the worm. Discovery of worm singularities is based on application of a similar approach to the one represented in Section 5. The geometric interpretation of the developed approach is based on following considerations: (i) The shaper and the worm are considered in line contact and their lines of contact are represented in the plane of surface parameters (us, ls) of the shaper (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003390_j.vacuum.2020.109314-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003390_j.vacuum.2020.109314-Figure1-1.png", + "caption": "Fig. 1. (a) Printed parts layout (b)\u2013(e) Dimensions for the rectangular bar, square tube, round tube and square bent tube, respectively.", + "texts": [ + "8 \u03bcm, respectively with an average material composition of major elements as: Cr 20\u201323%, Mo 8\u201310%, Fe \ufffd 5%, Nb 3\u20134%, Co \ufffd 1%, Cu \ufffd 0.5%, Mn \ufffd 0.5%, Si \ufffd 0.5% and Ni Bal. All LPBF parts were printed using Renishaw AM 400 (Renishaw plc, Wotton-under-Edge, United Kingdom). An average laser power of 200 W, point distance of 60 \u03bcm, exposure time of 100 \u03bcs, hatch distance of 140 \u03bcm and a layer thickness of 60 \u03bcm was used to print all LPBF samples. The layout of the printed samples (three repetitions each) is shown in Fig. 1a. Four different samples namely; (a) rectangular bar, (b) square tube, (c) round tube, (d) square bent tube were printed for electropolishing. The rectangular bars (Fig. 1b) were printed to calibrate and study the electropolishing process. The square, round and square bent tubes were hollow and were used to study the improvement of internal surface roughness. The polished hollow samples were crosssectioned before measuring the internal surface roughness. A Retsch Camsizer x2 optical particle analyzer (Retsch Technology GmbH, Haan, Germany) was used to find the powder size while the surface roughness (arithmetical mean height - Sa) was measured using a Keyence VK-X250 confocal microscope (Keyence Corporation, Osaka, * Corresponding author", + " 4b shows the as-built and polished optical images. It should be noted that all samples were electropolished for 100 s. The corresponding maximum height (Sz) surface roughness for the as-built and polished samples is also given in Fig. 4a. The un-filled blue bars show the U. Ali et al. Vacuum 177 (2020) 109314 U. Ali et al. Vacuum 177 (2020) 109314 as-build surface roughness, while the filled bars show the polished surface roughness. It should be noted that as the square bent tubes consist of flat and curved sides (Fig. 1e), the flat and the round surfaces were analyzed separately. Results show a significant surface enhancement for a minimal thickness loss for all samples. In addition, the reduction in error bars showed an improved repeatability for the surface roughness of polished parts. The square, round, square bent flat and square bent round tubes show a surface roughness improvement of 65%, 66%, 84% and 60%, respectively with a thickness reduction of 5%, 7%, 14% and 8%, respectively. It should be noted that a lower surface roughness (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000088_tia.2006.870044-Figure15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000088_tia.2006.870044-Figure15-1.png", + "caption": "Fig. 15. Motor #2.", + "texts": [ + " This could be particularly useful especially for starting/low speed and close to rated torque. These findings, although demonstrated on relatively small motors, are explained in the paper in such a way that they are anticipated to be valid, regardless of the motor rating. APPENDIX MOTORS FOR TESTS AND ANALYSIS Three motors were used for the analysis and the tests (Figs. 15\u201317). 1) Motor #1: Four phase; 8/6; rated torque: 2.0 N \u00b7 m; base speed: 2500 r/min; 42 V. 2) Motor #2: Three phase; 12/8; rated torque: 1.0 N \u00b7 m; base speed: 3000 r/min; 42 V (Fig. 15). 3) Motor #3: Four phase; 8/6; rated torque: 0.8 N \u00b7 m; base speed: 2500 r/min; 12 V; 8 turns per pole (Fig. 16). The authors would like to thank L. Frost, E. Nedelcu, and S. Rawski of Delphi Research Labs for their support during experimentation and their colleagues at Delphi-Saginaw Steering Systems, Delphi-E&C Dayton TC, and Delco-Electronics for the hardware and general project support. [1] C. M. Stephens, \u201cFault detection and management system for fault tolerant SR motor drives,\u201d IEEE Trans" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000232_j.phpro.2010.08.080-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000232_j.phpro.2010.08.080-Figure4-1.png", + "caption": "Fig. 4. Principle of the pyrometer registering of the manufacturing process: t0 and tn are the start and end instants of the powder layer processing", + "texts": [ + " In order to continuously monitor the surface temperature, i.e. temperature in the laser impact zone, a twowavelength pyrometer (11, fig. 2) registering surface thermal radiation is connected to the optical unit by optical fiber (10, fig. 2). Fig. 1. Schematic of the SLM process paper. For further discussion, it is necessary to introduce definition of a \u201ctrack\u201d and a \u201chatch distance\u201d. A track is the result of the laser beam scanning along a straight line on the powder bed with a constant speed. Hatch distance, \u03b4, (fig. 4d) is the distance between the neighbour tracks. To study SLM thermal phenomena, 10x10 mm2 surface area was subjected to laser beam scanning. The scanning strategy is presented in fig. 4c: the scanning direction is the same within each layer. The tracks must be codirectional to avoid heat accumulation at their ends fig. 4c. The laser beam jumps between the consecutive tracks with a much higher speed (\u03bdt12 = 7\u00b7103 mm/s) than the beam scanning speed (\u03bdt01 = 120 mm/s) during track formation. The experiments were carried out on Phenix PM100 machine (see SLM schematic in fig. 1). Laser source is YLR-50 continuous wave Ytterbium fiber laser by IPG Photonics operating at 1075 nm wavelength with P = 50 W maximum output power. In the present study, 32 W power was delivered to the powder layer. The laser spot size on the surface of the powder bed is 70 \u03bcm in diameter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000492_0301-679x(81)90058-x-FigureI-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000492_0301-679x(81)90058-x-FigureI-1.png", + "caption": "Fig I Dub-off and crown profiles", + "texts": [], + "surrounding_texts": [ + "R oiler bearings under radial and eccentric loads P.M. Johns and R. Gohar*\nThe influence of the roller axial profile on the contact pressure distributions is discussed for the cases of aligned and misaligned rollers. The results of numerical solutions show that careful profil ing using radial arcs can result in a more even distr ibution of pressure. A design method employed by Harris for predicting pressures on misaligned rollers can underestimate the maximum value. However, its use in a shaft and roller bearing system enables the maximum misalignment angle to be predicted for the worst loaded roller with fair accuracy. Numerical methods are then used to find the detailed pressure distr ibution, thus allowing bearing selection to be made, based upon the maximum pressure present\nNumerical solutions have been given for the pressure distribution and footprint shape for a roller bearing roller subjected to a radial load, or a moment and a radial load I . A knowledge of this pressure distribution is necessary in order to estimate the maximum stresses within the rolling elements. A proper choice of its axial profile (the reduction in its diameter near its ends) can thus be made so as to reduce these stresses. Now, roller bearings normally support loads that lie between them, so their design should be considered with reference to a complete system and not in isolation. In the work reported below, the effect on the pressure distribution of various roller prof'des is first considered under both radial and eccentric loads. These results are then incorporated into the design of a simple shaft and bearing system.\nCylindrical roller profiles\nThe two most popular methods employed by the bearing manufacturers for reducing roller edge stress concentrations are dub-off and crown profiling (Fig 1). These are approximations to a profile first suggested by Lundberg 2 which gives a pressure distribution uniform axially, elliptical transversely, and acting upon a rectangular footprint when the roller is subjected to a pure radial load. Lundberg's profile may be written as:\n1 (1) b ( 0 , ~ ) = ~ In (1 _~2)\nwhere P is the dimensionless profile, and .~ = y/b, b being the footprint half length (see Nomenclature). Unfortunately, Eq (1) gives an infinite dimension at the roller ends and is also independent of load. A modified version can be written a s :\n7r 1 (2) P(0,fi) = ~ In 1 - K I ~ 2\nwhere Ka = KI (ao/b), ao being the footprint half width, itself depending on the load applied. The derivation of Ks is shown in Appendix 1. Ks is given by:\na o Ks = 1 - 0.3033 ( -b-- ) (3)\n*Department o f Mechanical Engineering, Imperial College o f Science and Technology, London SW7 2BX, UK\nNomenclature (7 o al (X), b C d\nE I\nK Ks l L M Mi p\nPm Pm Po e ( O ,y ) Ps P2\nPm q\nqo O R Rs ,R~ S W x,y XS , Y l\nZ 6 O,c~ P %\nU3 09 o\nFootprint half width at 0,y Footprint half width and half length Pressure element half base length Deflection due to a pressure element = (zrdE)/(al Pm (1 - ~,2)) Young's modulus Shaft second moment of area Dimensionless influence coefficient Roller and race stiffness factor Lundberg's profile factor Shaft length between bearings Roller length Total shaft reaction moment at a roller bearing Reaction moment on ith roller Pressure at x,y Pressure at 0,y = Pm/Po Pressure at 0,0 Roller axial profile Roller axial profile at end of R1 Roller axial profile at end of R2 = (PnE)[(aopo(1 - u ~)) Modified misaligned roller profile Force per unit length on a roller a ty Force per unit length on a roller at y = 0 Total force on a roller Roller radius Roller profile arcs Axial coordinate defining juncture ofRs and R2 Shaft load Coordinates of deflection Coordinates of pressure = y /b Number of rollers in a bearing Total roller bearing deflection Roller and shaft misalignment angles Poisson's ratio Angle subtended by ith roller from bottom roller Roller or race deflection at 0,y due to a distributed pressure = Or ~E)/(aopo (1 - ~ ) ) Roller or race deflection at 0,0\n0301-679X/81/030131-06 $02.00 \u00a9 1981 IPC Business Press TRIBOLOGY international June 1981 131", + "Johns and Gohar - Rol ler bearings under radial and eccentr ic loads\nIn Lundberg's theory the full length of the roller, L, is utilised, L = 2b, so the actual profile is:\n2Q (1 - v 2) 1\nP = 7rLE In [ 1 - (1 - 0.3033 ao/b)(2y/L) 2 ] (4)\nIt is, however, difficult to machine such a logarithmic shape. To give some idea of its dimensions, for a steel roller 0.025 m diameter, 0.025 m long having a load which produces a b/ao ratio o f 25 (derived from Hertz's theory), the maximum value of P is 2.16 x 10-Sm (at the roller ends). Thus, the machining process must remove a negligible amount of material to tight tolerances. It is for this reason that approximate profiles following radial arcs are utilised. A close approximation to Lundberg's profile can be achieved by means of two arcs. Their radii can be approximated as follows (see Appendix 2):\n(b - S ) 2 R, - ( 5 ) 2P1\nwhere Pa is derived from Eq (4) at some chosen point, distance S from the roller ends, and:\n[(P2 - Pl )2 + S 2 ] R2 =R1 (6)\n2(P2 - P~ )(R ~ - Pt ) - ZS( b - S )\nwhere P2 is again derived from Eq (4) at the roller ends. Its value depends on the radial load. The two radii are tangential to each other at distance S, but R2 intersects the roller end, being much less than R 1. Under the design load, the roller and race deflect so that point B just contacts the race. The approximate profiles are compared with Lundberg's in Fig 2 for two values of S/b. The 10% value of S/b is more accurate towards the roller ends where stress concentrations may act.\nPressure distribution Knowing the axial profile of a roller and the load applied, the pressure distribution over the footprint can be found by solving a set of linear equations J \u2022\n(Pm j ) = [ d i j ] - ' (~Ji) (7)\nwhere the deflection vector, ~ i , is found from the equation:\n= - (8) ~(0 ,0 ) and e being prescribed. Each element of the matrix [-dij ] is calculated from:\ndi] = ( a ) ) ( l i / ) (9) ao\nwhere Iij are influence coefficients derived from the potential equation J :\n1 - v 2 a, c p ( x l , y l ) d x l dyl f f ( ( x _ x l ) 2 + ( y _ y l ) 2 ) l : 2 (10) d(x ,y)= 1 r E - a , - c\nThis relates the local deflection d(x,y) due to an element of pressure formed by P(x 1 ,Y x ) which is elliptical transversely, is an isosceles triangle longitudinally and acts on a base of local width 2al with length\" 2c. These bases constitute the footprint, whilst the overlapping triangular pressure elements form the wanted pressure distribution, Prn/, of the local maxima alongxl = 0. When the roller is subjected tO a misalignment angle 0, Eq (8) has a modified profile, Pm, to account for the altered geometry. Full descriptions of this theoretical method are also given a : . A computer program has been written which shows the effect of load, roller geometry and misalignment on the contact pressure distribution. Some results from this numerical method are shown in Fig 3 for a centrally loaded roller using the modified Lundberg profile and also two radial arc combinations. The arc profiles yield an approximately uniform axial pressure distribution, the one with the most end profiling 3 causing the most fall off in pressure towards the ends. When a single generous dub-off is used near the roller ends, Fig 4 results. There is now a rise of pressure at the ends and a corresponding footprint spread there. The effect of load increase raises pressure and footprint dimensions but does not appreciably sharpen the end pressures, presumably because of thegenerous end relief. Fig 5 shows the effect of various misalignment angles under a single load. At the highest misalignment, the footprint has been truncated, with the maximum pressure almost twice the central pressure.\nShaft and bearing systems Rolling element bearings are usually used to support a rotating shaft which can be loaded in a variety of ways, depending upon the engineering application. The general effect on the bearings is to subject them to combinations of forces and moments which themselves depend on the way the shaft is loaded. Under certain circumstances, the\n132 TRIBOLOGY international June 1981", + "Johns and Gohar - Roller bearings under radial and eccentric loads\n'~E z\n494.5 kq Load\n1 . 5 - -\nI 1.0 ~-\n0.5\n- 4 -2 Axial 0 distance, rn x I0 \"3\n~x392.2 kg Load\n~xl96,4 kg Load\n2 4\n494.5 kg Load z o _\n196.4 kg Load l'O\n~__~ -2 0 -I.0\n-Z0\n:o\ni d\nAxial distance, m ~ I\n\" ~ 3 9 2 z k~ Loo~~-~\nbearings may have to resist axial loads (as in gas turbines and helical gear boxes). In that case, combinations of ball thrust bearings or angular contact bearings, roller bearings, or a pair of taper roller bearings may be used. For low axial loads, roller bearings alone can suffice. In the simple design procedure to be described, it is assumed that there is a two roller bearing and shaft system with a steady, unidirectional radial load at the shaft mid-span. In a later publication, it is hoped to describe procedures for more complex multi-roller bearing systems. Harris 5 has described a general design procedure for such shaft and bearing systems. The solution of the problem always requires relationships between roller load, moment, deflection and angular misalignment. Such additional information is needed to solve a problem which is normally statically indeterminate. Harris postulated that in roller bearings under pure radial forces only, each roller load is evenly distributed along its effective length. Thus, at any roller location, for a local total load on it of Q, the load intensity (force per unit length) is given by:\nqo = Q (11)\nIf the bearing rings are misaligned due to the shaft load intensity, q(y) is no longer constant but differs from qo along the roller length. Harris, quoting Lundberg 2 , gives an approximate relationship between roller load and deflection at an interface as:\nWo = 4 . 3 6 x 10 -7 Q0.9 LO.a (12)\nzE 2.O OO5* / - - ' X Aligned w l misolignment J \\\nroller ~ I / /~ \\\nf / miso,gnmeot Ill\nI I O . 5 - - I I\n-4 -2 0 2 4\nAxial distance, mxllff 3\nAligned ' ~ o 0.1' roller c x l misolignment\nin which K is a constant depending on material properties. He then considers that the roller is divided into a series of laminae, each behaving independently (plane strain), so that under a moment and load:\nw ( y ) = wo + Oy (14)\nwhere 0 is the roller misalignment, and the limits o f y cannot exceed +--L/2. Therefore, from Eqs (13) and (14):\n1 q(Y)= ~ (~o +Oy) (15)\nNow, let the contact conditions be according to Hertz with the pressure elliptical transversely, ie:\nX 2 p(x , ) ' ) =pro(0,) ' ) (1 - ( ~ - - , ) )I/2 (16)\na u ' )\n*The figure 4.36 X 10-7 is obtained from the general expression for the mutual approach of a finite roller and a half-space = :\nQ0.9 ,2(1_o2) 09 ~ o ~ 3.81 1-Zz;-.~, ~ ~\nTherefore: QO.9\nCO o = k - - ] . 0 .8\nFor steel on steel, k = 4.36 X 10 -7 (in.lbf.s). so that K = (kL \u00b0'~ )/Q 0.2 or alternatively K = (L w o )/Q\nTRIBOLOGY international June 1981 1 3 3" + ] + }, + { + "image_filename": "designv10_3_0000360_13506501jet656-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000360_13506501jet656-Figure1-1.png", + "caption": "Fig. 1 A parabolic Hertzian contact pressure (upper image) acting on a circular point contact surface of radius a. Contours of constant principal shear stress (\u03c41) and trajectories of principal stress (\u03c31, \u03c32) directions (left image in the middle) and sub-surface stress distribution along the axis of symmetry (right image in the middle) under elastic Hertzian contact pressure in steel with \u03bd = 0.3 [10, 11], and principal stress planes at points A and B (lower image)", + "texts": [ + " Furthermore, if a bearing becomes subjected to wear instead of rolling contact fatigue, the lifetime cannot be mathematically predicted on a statistical basis. JET656 Proc. IMechE Vol. 224 Part J: J. Engineering Tribology at TOBB Ekonomi ve Teknoloji \u00dcniversitesi on April 26, 2014pij.sagepub.comDownloaded from When two non-conforming solids of geometrically ideal shapes are brought into contact, the initial contact is a point or a line, which can be analysed with the Hertzian contact theory [10]. The contact pressure from the normal load causes principal stresses and shear stresses beneath the contact surface (Fig. 1). Three features of the contact mechanics can be seen in Fig. 1. First, under normal static loading, the angle of principal or maximum shear stress is \u00b145\u25e6 in the middle of the normal pressure (however, in a rolling and sliding contact, tangential forces affect the angle of the principal shear stress). Second, under the Hertzian contact pressure, the shear stress reaches its maximum below the surface at a depth of 0.48a and the maximum shear stress value is 0.31 \u00d7 p0 with steel. Third, in the surface (z = 0) at the centre of contact (r = 0), the radial stress \u03c3r is 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure5.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure5.1-1.png", + "caption": "Fig. 5.1 Nomenclature in the calculation model of a symmetrically supported shaft with one disk", + "texts": [ + " Identification of causes for vibrations in real designs. It is known from Sect. 2.6.2 that there is virtually always a residual unbalance in rotors because complete balancing cannot be achieved. This section will demonstrate the effect of an unbalance excitation in a simple rotor with a disk. For the sake of simplicity, it is assumed that the disk is located at the center of a shaft with two bearings and a constant bending stiffness EI so that only a symmetric mode shape occurs and the influences of the gyroscopic effect are eliminated. Figure 5.1 shows the disk, which is displaced from the static equilibrium position, in a fixed coordinate system. The disk rotates at the angular velocity \u03a9. The deflections in the co-rotating reference system are denoted as r. The center of gravity of the disk S is away from the shaft center point W (eccentricity e). A torque M is applied at the disk. The disk mass is m, the moment of inertia about the axis of rotation is Jp. The massless shaft is isotropic, i. e., its spring constant c is the same in the x and y directions. Since there is no shaft inclination, no other spring constants are required. The equilibrium of forces at the center of gravity of the disk rotating in the horizontal plane results in, see Fig. 5.1: mx\u0308S + cxW = 0 (5.1) my\u0308S + cyW = 0. (5.2) From the equilibrium of moments about the axis through the center of gravity, it follows that 5.2 Fundamentals 313 Jp\u03d5\u0308 + cxWe sin \u03d5\u2212 cyWe cos \u03d5 = M. (5.3) If one considers the constraints, see Fig. 5.1, xW = xS \u2212 e cos \u03d5, yW = yS \u2212 e sin \u03d5 (5.4) the following equations of motion result: The natural circular frequency in this minimal model can be calculated from the static deflection (f = mg/c) at the mass m due to its weight (mg): \u03c91 = \u221a c m = \u221a cg mg = \u221a g f . (5.8) If one denotes the ratio of angular frequency to natural circular frequency \u03b7 = \u03a9/\u03c91, the particular solutions of (5.5) and (5.6) with \u03d5 = \u03a9t (harmonic excitation) are: 314 5 Bending Oscillators xS = e\u03c92 1 \u03c92 1 \u2212\u03a92 cos \u03a9t = e 1\u2212 \u03b72 cos \u03a9t = r\u0302S cos \u03a9t yS = e\u03c92 1 \u03c92 1 \u2212\u03a92 sin \u03a9t = e 1\u2212 \u03b72 sin \u03a9t = r\u0302S sin \u03a9t" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002096_j.mechmachtheory.2014.10.011-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002096_j.mechmachtheory.2014.10.011-Figure5-1.png", + "caption": "Fig. 5. Two operation modes of a variable-DOF single-loop mechanism with 1 to 2 DOF: Mechanism 1.", + "texts": [ + " (2), (5) and (6)) is not possible using Maple or Singular directly. By calculating a Gr\u00f6bner basis with respect to a lexicographic ordering, we obtain the following \u201cunivariate\u201d polynomial y3 25v41v 2 7 \u00fe 16 ffiffiffi 3 p v31v7 \u00fe 48v41\u221246v21v 2 7 \u00fe 144v1 ffiffiffi 3 p v7 \u00fe 64v21 \u00fe 25v27\u2212112 \u00bc 0: \u00f07\u00de Eq. (7) can be decomposed into the following two equations 25v41v 2 7 \u00fe 16 ffiffiffi 3 p v31v7 \u00fe 48v41\u221246v21v 2 7 \u00fe 144v1 ffiffiffi 3 p v7 \u00fe 64v21 \u00fe 25v27\u2212112 \u00bc 0 \u00f08\u00de and I I y3 \u00bc 0: \u00f09\u00de Eq. (8) corresponds to the 1-DOF spatial 7R operation mode of the mechanism (Fig. 5a), in which the axes of R joints 1 and 2 are usually not parallel to those of R joints 4\u20136. Due to space limitation, the solutions to the remaining variables are omitted in this paper. Now let us investigate the operation modes associated with Eq. (9). After the substitution of Eq. (9) into the ideal I ((Eqs. (2), (5) and (6)), a primary decomposition can be obtained using Singular as I \u00bc\u2229 4 j\u00bc1 I j \u00f010\u00de where 1 \u00bc \u00bdv7; x2; y2v21 \u00fe 75x3v 2 1 \u00fe 40x0v1 \u00fe y2 \u00fe 35x3; \u221225x2v 5 1 \u00fe 176x2v 3 1 ffiffiffi 3 p \u2212377x2v 3 1 \u00fe 176x2v1 ffiffiffi 3 p \u2212328x2v1 \u00fe 24x1; y3; \u2212625x2v 5 1 \u00fe 4400x2v 3 1 ffiffiffi 3 p \u22129425x2v 3 1 \u00fe 4400x2v1 ffiffiffi 3 p \u22128800x2v1 \u00fe 24y0; 625x2v 5 1\u22124400x2v 3 1 ffiffiffi 3 p \u00fe 9425x2v 3 1\u22124400x2v1 ffiffiffi 3 p \u00fe 12y2v1 \u00fe 900x3v1 \u00fe 8800x2v1 \u00fe 12y1 \u00fe 900x0 2 \u00bc \u00bd25v41\u2212176v21 ffiffiffi 3 p \u00fe 352v21\u22129;75v31 ffiffiffi 3 p \u00fe 100v31 \u00fe 373v1 ffiffiffi 3 p \u00fe 33v7\u2212148v1; 25x2v 2 1 ffiffiffi 3 p \u00fe 25x2v 2 1 \u00fe 105x2 ffiffiffi 3 p \u00fe 64x3\u221271x2; \u2212375x2v 3 1 ffiffiffi 3 p \u00fe 175x2v 3 1\u22126407x2v1 ffiffiffi 3 p \u00fe 10159x2v1 \u00fe 528x0; \u221213125x2v 2 1 ffiffiffi 3 p \u221213125x2v 2 1\u221235925x2 ffiffiffi 3 p \u00fe 704y2 \u00fe 56475x2; \u221225x2v 5 1 \u00fe 176x2v 3 1 ffiffiffi 3 p \u2212377x2v 3 1 \u00fe 176x2v1 ffiffiffi 3 p \u2212328x2v1 \u00fe 24x1; y3; \u2212625x2v 5 1 \u00fe 4400x2v 3 1 ffiffiffi 3 p \u22129425x2v 3 1 \u00fe 4400x2v1 ffiffiffi 3 p \u22128800x2v1 \u00fe 24y0; 625x2v 5 1\u22124400x2v 3 1 ffiffiffi 3 p \u00fe 9425x2v 3 1\u22124400x2v1 ffiffiffi 3 p \u00fe 12y2v1 \u00fe 900x3v1 \u00fe 8800x2v1 \u00fe 12y1 \u00fe 900x0 I3 \u00bc \u00bdv21 \u00fe 1;2v1 ffiffiffi 3 p \u00fe 3v7; x3; x0;50x2 ffiffiffi 3 p \u00fe y2; \u221225x2v 5 1 \u00fe 176x2v 3 1 ffiffiffi 3 p \u2212377x2v 3 1 \u00fe 176x2v1 ffiffiffi 3 p \u2212328x2v1 \u00fe 24x1; y3;\u2212625x2v 5 1 \u00fe 4400x2v 3 1 ffiffiffi 3 p \u22129425x2v 3 1 \u00fe 4400x2v1 ffiffiffi 3 p \u22128800x2v1 \u00fe 24y0; 625x2v 5 1\u22124400x2v 3 1 ffiffiffi 3 p \u00fe 9425x2v 3 1\u22124400x2v1 ffiffiffi 3 p \u00fe 12y2v1 \u00fe 900x3v1 \u00fe 8800x2v1 \u00fe 12y1 \u00fe 900x0 I4 \u00bc \u00bdx2; x3; x0; y2;\u221225x2v 5 1 \u00fe 176x2v 3 1 ffiffiffi 3 p \u2212377x2v 3 1 \u00fe 176x2v1 ffiffiffi 3 p \u2212328x2v1 \u00fe 24x1; y3;\u2212625x2v 5 1 \u00fe 4400x2v 3 1 ffiffiffi 3 p \u22129425x2v 3 1 \u00fe 4400x2v1 ffiffiffi 3 p \u22128800x2v1 \u00fe 24y0; 625x2v 5 1\u22124400x2v 3 1 ffiffiffi 3 p \u00fe 9425x2v 3 1\u22124400x2v1 ffiffiffi 3 p \u00fe 12y2v1 \u00fe 900x3v1 \u00fe 8800x2v1 \u00fe 12y1 \u00fe 900x0 : The last ideal, I4, yields solutions with xi = 0 for all i = 0, \u2026, 3 which are not valid solutions since Eq", + " The third one, I3, yields complex solutions with v1 = \u00b1 I which are of no relevance in the context of motion. The first ideal, I1, has solutions of the form fv1 \u00bc v1; v7 \u00bc 0; x0 \u00bc \u2212 1 40 75v21x3 \u00fe v21y2 \u00fe 35x3 \u00fe y2 v1 ; x1 \u00bc 0; x2 \u00bc 0; x3 \u00bc x3; y0 \u00bc 0; y1 \u00bc 1 8 525v21x3 \u00fe 7v21y2 \u00fe 525x3 \u00fe 15y2 v1 ; y2 \u00bc y2; y3 \u00bc 0g: \u00f011\u00de The vanishing set of this ideal has dimension 3, therefore the mechanism has 2 DOF. Since v7 = 0, we have \u03b87 = 0, which leads to configurations where the axes of joints 6 and 1 are parallel. Therefore, Eq. (11) represents a 2-DOF planar 5Rmotion of Mechanism 1 (Fig. 5b). The second ideal, I2, of Eq. (10) has two complex solutions and the following two real solutions fv1 \u00bc 1 5 g1; v7 \u00bc \u2213 1 55 g2g1 ffiffiffi 3 p \u2212 4 165 g2g1\u2212 197 165 g1 ffiffiffi 3 p \u00fe 4 11 g1; x0 \u00bc 1 2640 g1 \u22124967\u00fe 3151 ffiffiffi 3 p \u00fe 15 ffiffiffi 3 p g2\u22127g2 x2; x1 \u00bc 1 120 g1x2 \u221288 ffiffiffi 3 p \u00fe 161\u00fe g2 ; x2 \u00bc x2; x3 \u00bc \u2212 1 64 ffiffiffi 3 p g2 \u00fe g2 \u00fe 17 ffiffiffi 3 p \u00fe 17 x2; y0 \u00bc 5 24 g1x2 \u221288 ffiffiffi 3 p \u00fe 185\u00fe g2 ; y1 \u00bc \u2213 5 264 g1 \u22123745\u00fe 2426 ffiffiffi 3 p \u00fe 18 ffiffiffi 3 p g2 \u00fe 7g2 x2; y2 \u00bc 75 704 \u2212137\u2212137 ffiffiffi 3 p \u00fe 7 ffiffiffi 3 p g2 \u00fe 7g2 x2; y3 \u00bc 0g \u00f012\u00de where g2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 54433\u221230976 ffiffiffi 3 pq ; g1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u2212176\u00fe 88 ffiffiffi 3 p \u00fe g2 q : \u00f013\u00de The above two real solutions are nothing but the configurations of the mechanism undergoing the 1-DOF spatial 7R motion with the restriction that y3 = 0 holds. This can be verified by substituting these solutions into the input\u2013output equation (Eq. (8)) of the above 1-DOF spatial 7R operation mode. In summary, Mechanism 1 has two operation modes: 1-DOF spatial 7R operation mode (Eq. (8) and Fig. 5a) and 2-DOF planar 5R operation mode (Eq. (11) and Fig. 5b). 3.2.2. Transition configurations Transition configurations between the 5R-planar-mode (Eq. (11) and Fig. 5) and the 7R operationmode (Eq. (8) and Fig. 5) can be computed as the common roots of the ideals corresponding to these twomodes. Two transition configurations (Fig. 6) have been obtained and are given below: fv1 \u00bc 1; v7 \u00bc 0; x0 \u00bc 0; x1 \u00bc 0; x2 \u00bc 0; x3 \u00bc \u2212 1 55 y2; y0 \u00bc 0; y1 \u00bc 4 11 y2; y2 \u00bc y2; y3 \u00bc 0g: \u00f014\u00de In a transition configuration, the axes of R joints 3 and 7 are coplanar, and all the axes of the R joints in themechanism are parallel to the same plane. The wrench system to the twist system composed of all the joint twists is a 1-\u03b6infty \u2212 1 \u2212 \u03b60-system. The above analysis shows that Mechanism 1 has two operation modes, including one 2-DOF planar 5R operation mode (Eq. (11) and Fig. 5b) and one 1-DOF spatial 7R operation mode (Eq. (8) and Fig. 5a), and it can switch between these two operation modes through two transition configurations (Eq. (14) and Fig. 6). In this subsection, all the operation modes of Mechanism 2 will be determined. Using Singular, one can obtain a primary decomposition of the ideal I (Eqs. (2), (5) and (6)) as: I \u00bc\u2229 5 i\u00bc1 J i \u00f015\u00de where J 1 \u00bc \u00bdv7; x2; x1; y3;75v21x3 \u00fe v21y2 \u00fe 40v1x0 \u00fe 35x3 \u00fe y2; \u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0;50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 J 2 \u00bc \u00bdv21 ffiffiffi 2 p \u00fe 2v1v7\u2212 ffiffiffi 2 p ; v21x1\u22122v1x2\u2212x1; v7x1 \u00fe ffiffiffi 2 p x2;\u221220v1x1 \u00fe 15x2 \u00fe y3; v21x2 \u00fe v21x3 \u00fe 2v1x1\u2212x2\u2212x3; v7x2 \u00fe v7x3\u2212 ffiffiffi 2 p x1; x 2 1 \u00fe x22 \u00fe x2x3; x0; \u221220v1x1 \u00fe 70x2 \u00fe 55x3 \u00fe y2;\u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0; 50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 J 3 \u00bc \u00bd\u22123v21 ffiffiffi 2 p \u00fe 4v1v7\u22127 ffiffiffi 2 p ; x1;\u221225v21x2 \u00fe v21y3 \u00fe 15x2 \u00fe y3; \u221255v1 ffiffiffi 2 p x2 \u00fe v1 ffiffiffi 2 p y3 \u00fe 15v7x2 \u00fe v7y3; x3 \u00fe x2;3v 2 1x0\u22124v1x2 \u00fe 7x0; v7x0\u2212 ffiffiffi 2 p x2;25v1x 2 2\u2212v1x2y3\u221255x0x2 \u00fe x0y3;\u221230v1x0 \u00fe 15x2 \u00fe y2; \u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0;50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 J 4 \u00bc \u00bdv21 \u00fe 1; v1 ffiffiffi 2 p \u00fe v7; v1x2 \u00fe x1; x3; x0; y2 \u00fe 50x2;\u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0; 50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 J 5 \u00bc \u00bdx2; x1; y3; x3; x0; y2;\u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0;50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 : The last ideal, J 5, does not yield valid solutions because in the solutions all xi are equal to zero and Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002517_1.4033662-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002517_1.4033662-Figure1-1.png", + "caption": "Fig. 1 Illustration of the ellipsoidal heat distribution and the local heat source coordinate system with the origin at the start of the heating path. For vs > 0, the heat source moves in the local 2z direction.", + "texts": [ + "url=/data/journals/jmsefk/935392/ on 02/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Ui\u00fe1 \u00bc Ui dR dU i 1 Ri (11) 3.1 Single Ellipsoid and LI. The Goldak\u2019s ellipsoidal distribution Q is [41] Q \u00bc 6 ffiffiffi 3 p Pg abcp ffiffiffi p p exp 3x2 a2 3y2 b2 3 z\u00fe vst\u00f0 \u00de2 c2 (12) where P(W) is the heat source power, g is the efficiency, a(m), b(m), and c(m) are the width, depth, and length, respectively, of the ellipsoid, and vs\u00f0m=s\u00de is the speed of the source. The orientations of the local coordinates x, y, and z are illustrated in Fig. 1. Because the heat source moves in the local z direction, c is the relevant parameter to use when determining the time increment size. When c is small, a large number of time increments is required to accurately simulate the continuous motion of the source along a line. Specifically, if the simulation time increment Dt\u00bds does not satisfy the relation Dt c=vs, then Goldak\u2019s model will skip over some elements. To overcome this restriction, Eq. (12) is averaged over the duration of the time increment Q \u00bc 1 Dt \u00f0t0\u00feDt t0 Q dt (13) where t0 is the time at the beginning of the increment" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000765_978-3-540-30301-5_15-Figure14.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000765_978-3-540-30301-5_15-Figure14.9-1.png", + "caption": "Fig. 14.9 Redundant parallel drive shoulder joint", + "texts": [ + " One problem is to eliminate unsensed degrees of freedom. The calibration index is now applied based on the number of loops. 2 loops: A two-loop mechanism has three arms or legs, attached to a common platform. An example is the RSI Research Ltd. Hand Controller [14.21], which employs three 6-DOF arms with three sensed joints each. The mobility of this mechanism is M = 6. As S = 9, therefore C = 3 and closed-loop calibration is possible. 4 loops: Nahvi et al. [14.22] calibrated a spherical shoulder joint, driven redundantly by four prismatic legs (Fig. 14.9). In addition, the platform is constrained to rotate about a spherical joint; with the four legs, four kinematic loops are formed. For this system, M = 3 and S = 4, so that C = 1. Hence self-calibration is possible. Without the extra leg and the sensing it provides, one would have C = 0 and calibration would not be possible. 5 loops: Wampler et al. [14.2] calibrated the six-legged Stewart platform (M = 6) via a closed-loop procedure. In addition to leg length measurements, all angles on one of the legs were measured (S = 11)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001191_978-3-642-28572-1_22-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001191_978-3-642-28572-1_22-Figure2-1.png", + "caption": "Fig. 2 Theoretical field magnitude (a, c) and orientation (b, d) at z = 0 of the workspace when the system is commanded to a 15 mT field along the positive z-axis at [0.000, 0.000, 0.000] (a, b) and at [0.005, 0.000, 0.000] (c, d). The figure illustrates a more homogeneous region when the set point is at the center of the workspace than toward the extremities, which reduces the need for closed-loop feedback when working with a small workspace.", + "texts": [ + " The n electromagnet currents are mapped to a field and gradient through a 6 \u00d7 n actuation matrix A(B\u0302,P) which depends on the orientation of the magnetic field and the set point. For a desired field/gradient vector, the choice of currents that best solves for the target can be found using the pseudoinverse: I = A(B\u0302,P)\u2020 [ B \u2207 ] (5) This derivation can be similarly extended for controllers that require torque and/or force control as opposed to the field and gradient control and is discussed in full in [10]. For open-loop control experiments, the set point can be left at the origin of the system, Fig. 2(a, b), which limits the effective workspace due to the magnetic field varying from the desired set value toward the extremities of the workspace. In the case of objects ranging on the order of nanometers or tens of micrometers, this phenomenon is not a problem due to the small size of the workspace. For applications that require the use of a larger workspace, a vision feedback system can be used to close the loop for setting the magnetic field at the exact location of the agent, Fig. 2(c, d). This will be discussed in the experimental section. Whereas the OctoMag was designed to optimize the manipulability of the magnetic field, the MiniMag has been designed to restrict the locations of the electromagnetic coils to a single hemisphere. This is accomplished by moving the intersection point of all the coils\u2019 axes as shown in Fig. 1(a), which enables less physical restrictions in the workspace as well as allows the system to be compatible with an inverted microscope. Using a design process similar to that detailed in [10], but with the added hemispherical limitation, core radii of 7 mm and orientation angles of 64\u25e6 and 42" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002517_1.4033662-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002517_1.4033662-Figure8-1.png", + "caption": "Fig. 8 Temperature contours ( C) at the end of the first scan (top) and final scan (bottom)", + "texts": [], + "surrounding_texts": [ + "4.1 Numerical Implementation. In order to verify the accuracy and efficiency of the proposed heat input models, simulations are performed for the same process with Goldak\u2019s model and each of the new models with various time increment sizes. An 18 18 1.5 mm3 Ti\u20136Al\u20134V substrate is heated by five heat source passes, each proceeding in the \u00fex direction (see Figs. 5 and 6). The substrate\u2019s density is 4430 kg/m3, its Young\u2019s modulus is 200 GPa, its Poisson\u2019s ratio is 0.3, and its coefficient of thermal expansion is 9 lm/m K. The temperature-dependent conductivity, specific heat, and yield strength are shown in Fig. 7. Outside the illustrated range of properties, the closest value is used. The complete stress relaxation is simulated at 690 C [42]. The heat source parameters are efficiency g\u00bc 0.45, width a\u00bc 0.1 mm, depth b\u00bc 0.06 mm, and length c\u00bc 0.1 mm. The power is P\u00bc 100 W, the length of each scan is 10 mm, and the scan velocity is vs\u00bc 450 mm/s. These values are taken from Ref. [7], which investigates a selective laser-melting process. For the thermal model, a uniform natural convection of 10 W/m2 K and radiation with emissivity 0.5 are applied to all the free surfaces. The ambient temperature and initial temperature for the substrate are both 30.5 C. For the mechanical model, six displacement constraints are applied to prevent the rigid body translations and rotations. A nonconforming mesh is automatically generated with the eight-node linear hexahedral elements for both thermal and mechanical analysis. The analysis code is CUBES by Pan Computing LLC, State College, PA, described in Ref. [13]. The lengths of the finest elements are 0.047 mm, roughly half the heat source radius. The time increment size is set such that the heat source moves approximately one fine element length each increment. 4.2 Results. The final temperature and displacement contours are shown in Figs. 8 and 9 for Goldak\u2019s model. The remainder of 111004-4 / Vol. 138, NOVEMBER 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935392/ on 02/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use this section compares Goldak\u2019s model to the two new models. The temperature results are compared along a line in the middle of the substrate. The displacement results are compared along a free edge of the substrate and are compared at node 1 on the free corner. These verification locations are illustrated in Fig. 10. Temperature versus x location is compared with the Goldak\u2019s model in Fig. 2(a) for LI and Fig. 2(b) for EE. The Ds\u00bc 0.5 curves in Figs. 2 and 11 are the results of the Goldak\u2019s model (Eq. (12)), while the other curves are the results of the new heat source models. As expected, the results for both models converge monotonically toward that of the Goldak\u2019s model as the time increment decreases. To facilitate comparison of different models, a dimensionless time increment size Ds is introduced Ds \u00bc vsDt c (19) Because Goldak\u2019s model requires Ds 1, this parameter provides a measure of how large the time increments used for the new models are relative to those used for the Goldak\u2019s model. Equivalently, it also measures the length of the segments in terms of the heat source radius. Note the stairsteps in the temperature profiles of LI, which motivate the use of EE. The longitudinal distortion is shown in Fig. 11. As expected, the results for LI converge monotonically toward that of Goldak\u2019s as Ds decreases. However, the EE models do not converge monotonically. Specifically, the largest time increment size Ds\u00bc 100 yields more accurate longitudinal distortion results than Ds\u00bc 25. Simulation wall times and percent errors are shown in Table 1. The percent errors for mechanical results are calculated as enode 1 \u00bc 100 uz u\u0302z uz (20) eRMS \u00bc 100 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 L \u00f0L 0 uz u\u0302z uz 2 dx s (21) where uz and u\u0302z are the z displacements calculated from the Goldak\u2019s model and one of the new models, respectively, and L\u00bc 18 mm is the length of the part. Equation (20) represents the error at the point of maximum displacement, while Eq. (21) averages errors along the displacement profile shown in Fig. 11. The error in residual stress is evaluated as estress \u00bc 100 j\u00f0rmax r\u0302max\u00de=rmaxj, where rmax and r\u0302max are the maximum von Mises stresses calculated from the Goldak\u2019s model and one of the new models, respectively. Percent errors for the thermal results are averaged over the heated region shown in Fig. 2 etherm% \u00bc 100 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Dx \u00f0x0\u00feDx x0 T T\u0302 T 2 dx vuut (22) Journal of Manufacturing Science and Engineering NOVEMBER 2016, Vol. 138 / 111004-5 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935392/ on 02/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use where T and T\u0302 are the temperatures calculated from the Goldak\u2019s model and one of the new models, respectively, x0 4.03 mm, and Dx 9.94 mm. These values of x correspond to the nodes closest to the beginning and end of the scan path. As expected, the simulations run faster as Ds increases. Even the slowest of the new models (LI with Ds\u00bc 10) runs nearly eight times faster than the Goldak\u2019s model. The percent errors generally increase as Ds increases. An LI usually gives more accurate mechanical results, likely because of the consistency with the Goldak\u2019s model as shown in Eq. (15). Despite its smoother and more accurate thermal results, EE gives less accurate displacements for small Ds. A convenient feature of LI is that each point in space receives the same incident energy as in Goldak\u2019s model, although distributed differently in time. However, EE differs from Goldak\u2019s model in both time and space, giving only the same total energy integrated over the volume of the part. These observations suggest that the 111004-6 / Vol. 138, NOVEMBER 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/935392/ on 02/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use displacement is more sensitive to where heat is added to the part and less sensitive to when heat is added." + ] + }, + { + "image_filename": "designv10_3_0001774_j.surfcoat.2016.03.083-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001774_j.surfcoat.2016.03.083-Figure1-1.png", + "caption": "Fig. 1. Illustration of a laser cladding process for coaxial powder feeding.", + "texts": [ + " This powder is characterized by its high temperature properties, showing high strength, hardness, corrosion and wear resistance at elevated temperatures. It is mainly used in high requirement applications, e.g., in free lubricating equipment due to its low friction coefficient. In this study, the CO2 laser beam was used with a coaxial powderfeeding laser cladding system, which indicates that the CO2 laser beam, metal powder and shielding gas were injected simultaneously from the nozzle during the process. A schematic drawing of the process is shown in Fig. 1. The cladding quality is generally characterized by the profile of the clad coatings, depth of the heat affected zone, thermal stresses, porosity, micro cracks, etc. Process parameters, e.g., the laser power, powder feed rate, nozzle scanning velocity and the spot diameter, are deemed the main factors that influence the cladding quality. To study the influence of the laser power, the experiment was conducted under different laser powers, whilst the scanning velocity, the powder feed rate and the laser spot diameter were constant for all specimens" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000960_j.conengprac.2010.02.007-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000960_j.conengprac.2010.02.007-Figure2-1.png", + "caption": "Fig. 2. Flaps subsystem: anti-torque (above) and lateral/longitudinal control flaps (below). The notation c.p. denotes the center of pressure of the aerodynamic forces on the flaps.", + "texts": [ + " Following Stengel (2004), the propeller generates both a thrust force T = kTwP 2, with wP the angular speed velocity of the propeller and kT a constant parameter, and a resistance aerodynamic torque N = kNT, with kN a constant coefficient collecting aerodynamical parameters. From Froude\u2019s theory, see Thwaites (1960), the induced air velocity inside the duct is given by Vi \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T 2rSdisk s in which Sdisk is the area of the propeller\u2019s disk and r the air density. For the sake of simplicity, the velocity Vi can be thought to be perpendicular to the propeller disk, i.e. aligned with the body z-axis (see also Fig. 2). The rotational component of such velocity, caused by the fan\u2019s angular speed, is in fact compensated by the vanes positioned just below the propeller. By considering each control vane as a wing immersed into a relative wind Vi, see for example Stengel (2004), the aerodynamic lift and drag forces, L and D, can be computed as L\u00bc 1 2 rSCLV2 i ; D\u00bc 1 2rSCDV2 i ; \u00f03\u00de where S is the vane\u2019s surface and CL, CD are, respectively, the lift and drag coefficients (see also Fig. 2). For reasonably small angles of attack, it turns out that CL \u00bc cLa; CD \u00bc cDa2\u00fecD0 \u00f04\u00de with cL, cD, cD 0 constant parameters which depend on the airfoil profile (which in this case is the same for all the control surfaces) and a the vane\u2019s angle of attack. The configuration considered in this paper has been built as a cascade of two different levels of control vanes, respectively, (c1) and (c2) in Fig. 1. In the first level, depicted on top of Fig. 2, the vanes are disposed radially around the propeller spin axis and are constrained to have the same angle of attack c with respect to the airflow. In this way, recalling (3) and (4), the aerodynamic lift forces turn out to generate a torque contribution Nc \u00bc \u00f01=2\u00dercLSL1V2 i c\u00f0dT=2\u00de, with dT/2 the lever arm of the lift, which is applied by definition in the so-called center of pressure of the vane, and SL 1 the overall surface. The role of the first level is to control the yaw attitude dynamics and, in turn, to counteract the aerodynamic torque N. The second level, at the bottom of Fig. 2, is composed of two independent control vanes, whose angles of attack are denoted, respectively, by a and b. By construction the resultant lift forces, denoted by FL x and FL y, are directed, respectively, along the body x- and y-axes of the vehicle and their points of applications form, with respect to the center of mass of the vehicle, a lever arm of length d (see also Fig. 1). In this way two torques are generated to control the roll and pitch attitude dynamics. In summary, by considering the contributions of the control vanes and of the propeller, the forces and torques which govern the system dynamics are given by f b \u00bc Fx L Fy L T\u00feFD 2 64 3 75\u00feRT 0 0 Mg 2 64 3 75; tb \u00bc Fy L d Fx L d N\u00feNc 2 64 3 75\u00feRT wPGo; \u00f05\u00de where g is the gravity acceleration, Fx L \u00bc \u00f01=2\u00dercLSL2 a V2 i and Fy L \u00bc \u00f01=2\u00dercLSL2bV2 i , in which SL2 is the surface of each independent control vane in the second level, FD denotes the sum of all the drag forces of the control vanes in both levels, which can be obtained by using (3) and (4), and finally G = Skew(col(0, 0, Irot)) with Irot the inertia of the propeller with respect to its spin axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000491_978-3-540-79029-7-Figure1.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000491_978-3-540-79029-7-Figure1.1-1.png", + "caption": "Fig. 1.1 Formation of the stator current vector from the phase currents", + "texts": [ + " These are the field-orientated coordinate system for the 3- phase AC drive technology or the grid voltage orientated coordinate system for generator systems. The orientation on a certain vector for modelling and design of the feedback control loops is generally called vector orientation. The three sinusoidal phase currents isu, isv and isw of a neutral point isolated 3-phase AC machine fulfill the following relation: using three-phase AC machines These currents can be combined to a vector is(t) circulating with the stator frequency fs (see fig. 1.1). ( ) ( ) ( ) 22 with 2 3 3 j j s su sv swi t i t e i t e= + + =i (1.2) The three phase currents now represent the projections of the vector is on the accompanying winding axes. Using this idea to combine other 3- phase quantities, complex vectors of stator and rotor voltages us, ur and stator and rotor flux linkages s, r are obtained. All vectors circulate with the angular speed \u03c9s. In the next step, a Cartesian coordinate system with dq axes, which circulates synchronously with all vectors, will be introduced" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003153_j.ymssp.2019.106553-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003153_j.ymssp.2019.106553-Figure6-1.png", + "caption": "Fig. 6. Coordinate frames of a roller and a race. (a). The inertial frame Oixiyizi , the race-fixed frame Orxryrzr , the roller-fixed frame Obxbybzb , the roller-raceazimuth frame Oarxaryarzar , the roller-azimuth frame Oaxayaza , (b) the contact frame Ocxcyczc at roller-inner race, and (c) the contact frame Ocxcyczc at rollerouter race.", + "texts": [ + " In the current investigation, the dynamic model of the healthy bearing is modeled based on Gupta\u2019s dynamic model [50,53]. As the roller-race interaction is the main focus of and is essential to the current investigation, only the part determining the roller-race interaction is discussed here. The determinations of cage-roller and cage-guiding ring interactions have been well discussed in Refs. [50,53,54], and will not be provided here. The interaction between a roller and a race (take inner race for instance) is shown in Fig. 6. For convenience, the interaction is only determined in the yz plane (the x axis is the bearing rotation axis). The direction of the x axis can be determined by the right-hand rule. In Fig. 6, the following coordinate frames are established (These frames are also essential to the determination of the interaction between a roller defect and a race which will be discussed in Section 3.2. Therefore, it is important to discuss these frames clearly here. The directions of the x axes of the following coordinate frames are all the same as each other). Inertial frame Oixiyizi. All of the interactions between bearing components are determined based on the inertial frame. Roller-fixed frame Obxbybzb. The origin Ob is located at the roller center. This frame is fixed in the roller. In Fig. 6(a), frame Obxbybzb can be obtained by rotating the inertial frame along the zi axis by the attitude angle of the roller relative to the inertial frame, gb. The transformation matrix from frame Oixiyizi to frame Obxbybzb is Tib \u00bc T gb; 0;0\u00f0 \u00de (the basic theory of the transformation matrix can be found in Ref. [50]). Race-fixed frame Orxryrzr . The origin Or is located at the race center. This frame is fixed in the race. When the attitude angles of the race relative to the inertial frame are gr 0 0f gT, the transformation matrix from frame Oixiyizi to frame Orxryrzr can be written as Tir \u00bc T gr ;0;0\u00f0 \u00de. Roller-azimuth frame Oaxayaza. The origin Oa is located at the roller center. The za axis is parallel to the radial component of the vector rb locating the position of the roller center relative to the inertial frame. This frame will be used to calculate the orbital position of the roller in the inertial frame (hb shown in Fig. 6(a)). The transformation matrix from frame Oixiyizi to frame Oaxayaza can be written as Tia \u00bc T hb;0;0\u00f0 \u00de. Roller-race-azimuth frame Oarxaryarzar . The origin Oar is located at the roller center. The zar axis is parallel to the vector rbr which locates the roller center relative to the race center. This frame is used to determine the azimuth angle of the roller relative to the race-fixed frame (hbr shown in Fig. 6(a)). Based on angle hbr , the transformation matrix from frame Orxryrzr to frame Oarxaryarzar can be written as Trar \u00bc T hbr; 0;0\u00f0 \u00de. Contact frame Ocxcyczc. The origin Oc is located at the contacting point between the roller and the race. The zc axis is along the direction of the zar axis for the inner race, and is along the negative direction of the zar axis for the outer race (refer to Fig. 6(b) and (c)). The transformation matrices from the roller-race-azimuth frame to the contact frames for the inner and the outer races can be written as Tarc \u00bc T 0; 0;0\u00f0 \u00de and Tarc \u00bc T p;0;0\u00f0 \u00de, respectively. Now, the geometric interaction between the roller and the race (dbr in Fig. 6(a)) is dbr \u00bc rbrj j dm\u00f0 \u00de \u00f01\u00de where dm is the bearing pitch diameter and signs \u2018\u2018\u00b1\u201d refer to the outer race and the inner race, respectively. Then, the contact force can be calculated by Hertzian contact theory [52]: Qbr \u00bc Kdnbr dbr > 0 0 dbr 6 0 \u00f02\u00de where K is the Hertzain contact coefficient. Coefficient n is 1.11 for line contact type. Moreover, the direction of the contact force Qbr is along the zc axis. The traction force significantly relies on the relative sliding velocity. The relative sliding velocity is described in the contact frame to calculate the traction force based on the contact force and lubricant models" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000442_rnc.1561-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000442_rnc.1561-Figure8-1.png", + "caption": "Figure 8. Overactuated marine vessel\u2014A schematic of a marine vessel.", + "texts": [ + " Bu (t)u(t)\u2212Bvv(t), is reported for the two proposed F-TCAP algorithms. Those are Copyright q 2010 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control 2010; 20:1958\u20131980 DOI: 10.1002/rnc two important indexes to evaluate the estimation and reconfiguration performances, the lower the better (at zero one has exact estimation and allocation). Notice in this viewpoint, how WIN F-TCAP performs slightly better than the LMS-based algorithm. We consider here the ship model presented in [37] and [38]. Earth-fixed positions (x, y) and yaw angle (see Figure 8) are represented by the vector = [x, y, ]T and the body-fixed velocities are expressed by =[v,u,r ]T, where v is the forward velocity (surge), u the transverse velocity (sway) and r the angular velocity in yaw (rate of turn). In order to normalize the variables, the following bis-scaling change of variables is accomplished: = diag{L , L ,1} \u2032\u2032 = diag{\u221agL, \u221a gL, \u221a g/L} \u2032\u2032 (36) where g is the gravity acceleration and L the length of the ship. Time was bis-scaled too and the resulting Copyright q 2010 John Wiley & Sons, Ltd" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002571_j.ymssp.2019.106275-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002571_j.ymssp.2019.106275-Figure6-1.png", + "caption": "Fig. 6. The interaction model of the outer ring and pedestal.", + "texts": [ + " At this time, the center of the bearing outer ring coincides with the coordinate system center. When the bearing is loaded, relative movement occurs between bearing outer ring and pedestal as shown in Fig. 5(b). O1 y; z\u00f0 \u00de is the geometric center of the bearing outer ring in the Cartesian inertial coordinate system-yoz. OO1 ! is the relative displacement between bearing outer ring and pedestal, cAB is the contact area. The contact deformation d hpi at the angular position hpi can be expressed as: d hpi \u00bc ycoshpi \u00fe zsinhpi do hpi 2 cAB 0 hpi R cAB ( \u00f09\u00de A spring-damper model shown in Fig. 6 is proposed to calculate the interaction force between the bearing outer ring and pedestal. As shown in Fig. 6, a serial of spring-damper elements distribute equably in radial direction. The pedestal is modeled as lumped mass. The interaction force between the pedestal and rack is modeled by 2 spring-damper elements distributed in horizontal (y) and vertical (z) directions, respectively. The motion equations of bearing outer ring can be written as: mor\u20acy\u00fe PNp i\u00bc1 kpid hpi \u00fe cpi _ycoshpi \u00fe _zsinhpi coshpi \u00bc Fy mor\u20acz\u00fe PNp i\u00bc1 kpid hpi \u00fe cpi _ycoshpi \u00fe _zsinhpi sinhpi \u00bc Fz ( \u00f010\u00de wheremor is the mass of the bearing outer ring, Np is the number of the spring-damper element, hpi is the angular position of the ith spring-damper element, kpi and cpi are the stiffness and damping, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001007_1.4025219-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001007_1.4025219-Figure2-1.png", + "caption": "Fig. 2 Compositional units for planar parallel manipulators: (a) Spherical CU _R _R, (b) Planar CU R R R R, (c) Bennett CU, and (d) Supplement joint of a Bennett CU", + "texts": [ + " In this section, all the CUs [10,14] for planar parallel kinematic chains composed of only R joints will be presented. Several classes of CUs are defined by their geometric characteristics in Ref. [10]. These CUs can also be regarded as generators of displacement subgroups [1,3] of dimension 1\u20134, the subchains of these generators and kinematically redundant generators of these displacement subgroups. For example, a spherical CU is composed of at least two R joints whose axes pass through a common point (Fig. 2(a)). Each R joint within a spherical CU is denoted by _R. Spherical CUs cover the generator composed of three R joints, and its subchain composed of two R joints as well as the kinematically redundant generators composed of four or more R joints of the spherical displacement subgroup. Among the CUs in Ref. [10], there are only three classes of CUs [10] composed of only R joints: planar CUs (see Fig. 2(b), for example) composed of at least two R joints, spherical CUs (see Fig. 2(a), for example), and coaxial CUs (serial kinematic chains composed of one or more coaxial R joints). In the planar CU shown in Fig. 2(b), all the R joints have parallel axes and are denoted by R. 041015-2 / Vol. 5, NOVEMBER 2013 Transactions of the ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use In addition to the above CUs for PMs, there are also CUs derived from paradoxical four-bar linkages [14]. Among these CUs, the only class of CU composed of only R joints is the Bennett CU (Fig. 2(c)), which is composed of three successive R joints derived from a Bennett linkage by removing one R joint. A Bennett CU is denoted by gRRR. For simplicity reasons, we define the R joint which forms a Bennett linkage with a Bennett CU as the supplement joint (Fig. 2(d)) of the Bennett CU. It is noted that the Bennett CU was called Bennett joint in constructing singleDOF single-loop kinematic chains in [25]. In summary, only the above four classes of CUs can be used to construct planar PMs composed of only R joints and the associated 3-DOF single-loop kinematic chains involving an (RRR)E virtual chain since all the other CUs include other types of joints. 2.3 Type Synthesis of Legs for Planar Parallel Kinematic Chains. Type synthesis of legs for planar parallel kinematic chains is to obtain the types of legs with a given wrench system, which is a subsystem of the wrench system of the E virtual chain", + " For clarity and simplicity, slmn, which implies that R joints l, m, and n have parallel axes and denotes a unit vector parallel to the axes of these R joints, is represented by a solid round arrow. Ak denotes the axis of R joint k, which is not parallel to the axes of the other joints within the same leg. It is noted that in constructing 3-DOF single-loop kinematic chains with a 1-f0-system (such as the 00 R gRRR 00 R (RRR)E kinematic chain in Fig. 3(b)) by combining one planar 5R CU (5-6-7-8-1 in Fig. 3(b)) and one gRRR Bennett CU (2-3-4 in Fig. 3(b)), the axis of the supplement R joint of the gRRR CU (Fig. 2(d)) must be parallel to the axes of the 00 R joints. The axis of the basis f01 of the 1- f0-system is parallel to the axes of the 00 R joints and intersects the axes of the three R joints within the Bennett CU gRRR. For simplicity reason, this basis f01 is not shown in Fig. 3(b). The existence of the above f01 can be proved using the concept of reciprocal screws as in the case of a 3-DOF single-loop kinematic chain involving a Bennett CU and a spherical CU [14] or using the properties of a hyperboloid of one sheet" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003514_j.addma.2020.101428-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003514_j.addma.2020.101428-Figure2-1.png", + "caption": "Fig. 2 shows the internal channels built on the AM powder bed in the vertical direction,", + "texts": [], + "surrounding_texts": [ + "2.1. Internal channel: Dimensional specifications Three sets of internal channels were designed with the geometric complexity adopted from fuel nozzles, space rocket injectors, and conformal cooling channels. Rolls-Royce is currently adopting unique internal channel designs for the next generation fuel nozzles. The geometric details of Rolls-Royce fuel nozzles are proprietary information and are not included in this manuscript. However, L-PBF rocket injectors developed by NASA include similar geometries. The rocket injectors were built using Inconel 625 and contain internal holes and passages of diameter up to 1 mm [21]. Non-linear internal channels built at 90-degree orientation without support structures were also used. Fig. 1(a-c) shows the L-PBF rocket injector prototype with complex internal passages. Adopting such real-world complex geometries from rocket injectors, fuel nozzles, and cooling channels would enable us to understand the full potential of the multi-jet hydrodynamic surface finishing approach proposed in this study. J ur na l P re -p r of Fig. 1. (a) L-PBF rocket injector prototype, (b) front view of the nozzle with dimensions, (c) isometric cross-sectional view of the nozzle showing internal channels. Fig. 1d depicts the internal channels used for surface finishing. The linear, stepped, and nonlinear channels of varying diameter and radius of curvature are investigated. Table 1 details the dimensions and nomenclature of the internal channels. The wall thickness of the channels was within 3 mm. The channels are referred to using their nomenclature throughout the paper. D, R, and L represent the diameter, mean radius of curvature, and the total length of the channel. For example, D1R10L100 represents the channel with a diameter of 1 mm, a mean radius of curvature of 10 mm and a total length of 100 mm. Fig. 1. (d) Internal channels for surface finishing: (1) linear, (2) stepped, and (3) non-linear channels. Jo ur na l P re -p ro of powder bed fusion technique. The EOS M290 (EOS Electro optical systems, Germany) additive manufacturing machine was utilized for the build process. with XY-plane as the base. Z-axis represents the channel length. The linear and stepped internal channels possess the surface characteristics of 90\u00b0 build orientation. In non-linear channels, the La zone possesses the characteristics of 90\u00b0 (vertical) build orientation; the Lb zone possesses the characteristics of 0\u00b0 (horizontal) build orientation. The side surfaces of a 90\u00b0 build orientation are referred to in-skin; top and the bottom surface of a 0\u00b0 build orientation are referred to as upskin and downskin. Appropriate support structures were designed outside the channels to prevent component distortion (refer to section-1 in the supplementary data for more information on the support structure design). No support structures were provided inside the channels (self-supported by the powders beneath). A 40 \u00b5m layer thickness, 50 \u00b5m laser hatch Jo spacing, and an optimal laser scanning strategy were deployed to achieve the best build quality. The metal powders were sintered using a 400 W Yb-fibre laser in an argon gas atmosphere and annealed at 870 \u00b0C for one hour. 2.2.3. Materials The internal channels were manufactured using a Nickel-based superalloy: Inconel 625. A powder size of 35 \u00b1 6 \u00b5m with D50 distribution per ISO 13320 was used for the build process. Inconel 625 possesses excellent oxidation resistance, fatigue, and thermal-fatigue strength. The stiffening effect of molybdenum and niobium on the nickel-chromium matrix strengthens the alloy. Table 2 details the alloy composition of the Inconel 625 powders used. This combination of elements is responsible for the alloy\u2019s superior resistance to corrosive environments as well as to high-temperature effects such as oxidation and carburization. As such, fuel transfer, heat exchanger, and combustion system pipelines are manufactured using Inconel 625 [22]. Table 2 Alloy composition Element Cr Mo Nb Fe Ti Al Co Si Mn C Ni Mass (%) 23 10 4.15 5 0.4 0.4 1 0.5 0.5 0.1 Balance" + ] + }, + { + "image_filename": "designv10_3_0001216_tro.2011.2168170-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001216_tro.2011.2168170-Figure7-1.png", + "caption": "Fig. 7. Determination of the reciprocal wrench for twist $4 through geometric observations.", + "texts": [ + ", zero pitch) in the inertial frame are described as follows: \u0302$i = [ n\u0302i ri \u00d7 n\u0302i ] (25) where n\u0302i is the unit direction vector of the ith screw axis in the inertial frame, and ri is the positional vector from the origin of the inertial frame to a point on the ith screw axis (which is taken at the joint center locations). For a \u201cproper\u201d spatial cable-driven open chain, it will have six linearly independent reciprocal wrenches (based on Theorem 1). Unlike the planar case, it is challenging to identify the reciprocal wrenches of spatial open chains through geometric observations. For the seven-cable S-R-U spatial open chain, the zero-pitch wrenches of twists 4 and 5 (i.e., $4r \u2013$6r ) can be easily identified through geometrical observations.2 As shown in Fig. 7, $4r passes through the centers of the spherical and universal joints. For $5r , it passes through the center of the spherical joint and intersects screw axes \u0302$4 and \u0302$5 , while $6r passes through the center of the spherical joint and intersects screw axes \u0302$4 and \u0302$5 , as shown in Fig. 8. 2See [34], where a clear explanation of geometrically identifying reciprocal screws of basic kinematic pairs and common kinematic chains is given. For the remaining reciprocal wrenches (i.e., $1r \u2013$3r ), it will be determined numerically, as it is challenging to find it geometrically" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002597_1.4811838-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002597_1.4811838-Figure13-1.png", + "caption": "FIG. 13. Functional prototypes with complex geometry fabricated by SLM: part of the combustion engine with specially textured surface to reduce friction (a); model with complex internal channels (b).", + "texts": [ + " Redistribution subject to LIA license or copyright; see http://jla.aip.org/about/about_the_journal The understanding of the correlations between the major SLM parameters such as particle size, laser power, scanning speed, hatch distance, and scanning strategy allows to develop functional surfaces. Thus, the obtained data can be used in SLM manufacture of complex products with a wide range of functional surfaces for various industrial applications: aerospace, automotive, biological, chemical, and so on (Fig. 13). The study was supported by the grant of the Government of Russian Federation (decree N220). 1I. Etsion, \u201cState of the art in laser surface texturing,\u201d in Proceedings of CIST2008 & ITS-IFT-MM2008, Advanced Tribology, edited by J. Luo, Y. Meng, T. Shao, and Q. Zhao (Springer and Tsinghua University Press, China, 2010). 2T. Hua, Y. Zhang, and L. Hu, \u201cTribological investigation of MoS2 coatings deposited on the laser textured surface,\u201d Wear 278\u2013279, 77\u201382 (2012). 3W. Zhitong and Y. Mingjiang, \u201cLaser-guided discharge texturing for cold mill roller,\u201d J" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002096_j.mechmachtheory.2014.10.011-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002096_j.mechmachtheory.2014.10.011-Figure6-1.png", + "caption": "Fig. 6. Transition configurations of a variable-DOF single-loop mechanism with 1 to 2 DOF: Mechanism 1.", + "texts": [ + " This can be verified by substituting these solutions into the input\u2013output equation (Eq. (8)) of the above 1-DOF spatial 7R operation mode. In summary, Mechanism 1 has two operation modes: 1-DOF spatial 7R operation mode (Eq. (8) and Fig. 5a) and 2-DOF planar 5R operation mode (Eq. (11) and Fig. 5b). 3.2.2. Transition configurations Transition configurations between the 5R-planar-mode (Eq. (11) and Fig. 5) and the 7R operationmode (Eq. (8) and Fig. 5) can be computed as the common roots of the ideals corresponding to these twomodes. Two transition configurations (Fig. 6) have been obtained and are given below: fv1 \u00bc 1; v7 \u00bc 0; x0 \u00bc 0; x1 \u00bc 0; x2 \u00bc 0; x3 \u00bc \u2212 1 55 y2; y0 \u00bc 0; y1 \u00bc 4 11 y2; y2 \u00bc y2; y3 \u00bc 0g: \u00f014\u00de In a transition configuration, the axes of R joints 3 and 7 are coplanar, and all the axes of the R joints in themechanism are parallel to the same plane. The wrench system to the twist system composed of all the joint twists is a 1-\u03b6infty \u2212 1 \u2212 \u03b60-system. The above analysis shows that Mechanism 1 has two operation modes, including one 2-DOF planar 5R operation mode (Eq. (11) and Fig. 5b) and one 1-DOF spatial 7R operation mode (Eq. (8) and Fig. 5a), and it can switch between these two operation modes through two transition configurations (Eq. (14) and Fig. 6). In this subsection, all the operation modes of Mechanism 2 will be determined. Using Singular, one can obtain a primary decomposition of the ideal I (Eqs. (2), (5) and (6)) as: I \u00bc\u2229 5 i\u00bc1 J i \u00f015\u00de where J 1 \u00bc \u00bdv7; x2; x1; y3;75v21x3 \u00fe v21y2 \u00fe 40v1x0 \u00fe 35x3 \u00fe y2; \u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0;50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 J 2 \u00bc \u00bdv21 ffiffiffi 2 p \u00fe 2v1v7\u2212 ffiffiffi 2 p ; v21x1\u22122v1x2\u2212x1; v7x1 \u00fe ffiffiffi 2 p x2;\u221220v1x1 \u00fe 15x2 \u00fe y3; v21x2 \u00fe v21x3 \u00fe 2v1x1\u2212x2\u2212x3; v7x2 \u00fe v7x3\u2212 ffiffiffi 2 p x1; x 2 1 \u00fe x22 \u00fe x2x3; x0; \u221220v1x1 \u00fe 70x2 \u00fe 55x3 \u00fe y2;\u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0; 50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 J 3 \u00bc \u00bd\u22123v21 ffiffiffi 2 p \u00fe 4v1v7\u22127 ffiffiffi 2 p ; x1;\u221225v21x2 \u00fe v21y3 \u00fe 15x2 \u00fe y3; \u221255v1 ffiffiffi 2 p x2 \u00fe v1 ffiffiffi 2 p y3 \u00fe 15v7x2 \u00fe v7y3; x3 \u00fe x2;3v 2 1x0\u22124v1x2 \u00fe 7x0; v7x0\u2212 ffiffiffi 2 p x2;25v1x 2 2\u2212v1x2y3\u221255x0x2 \u00fe x0y3;\u221230v1x0 \u00fe 15x2 \u00fe y2; \u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0;50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 J 4 \u00bc \u00bdv21 \u00fe 1; v1 ffiffiffi 2 p \u00fe v7; v1x2 \u00fe x1; x3; x0; y2 \u00fe 50x2;\u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0; 50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 J 5 \u00bc \u00bdx2; x1; y3; x3; x0; y2;\u221225v1x2 \u00fe v1y3\u221225x1 \u00fe y0;50v1x2 \u00fe 75v1x3 \u00fe v1y2 \u00fe 75x0 \u00fe 50x1 \u00fe y1 : The last ideal, J 5, does not yield valid solutions because in the solutions all xi are equal to zero and Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002288_acs.2662-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002288_acs.2662-Figure1-1.png", + "caption": "Figure 1. Experimental system.", + "texts": [ + " 0 in finite time (as it is the case for the observer (16)), we can conclude (see the proof of Theorem 1) also that \u00b4.t/! 0 and x.t/! 0 in finite time. When e D 0 and x D 0, both gains will stop growing and they will remain constant. Some experiments have been carried out to test the performance of the proposed control strategy. The closed loop controller (13)\u2013(14), (9)\u2013(11) was implemented in a commercial experimental mass\u2013spring\u2013damper setup (Educational Control Products (ECP), Model 210), and it is shown in Figure 1. It consist of one mass (m), two springs (k1; k2), one damper (bd ), one DC motor, and an encoder. As illustrated in the diagram in Figure 2, the DC motor applies a force u to the mass m, which is attached to the springs and the damper. The nominal values for the parameters are m D 1:05 [kg]; k1 D 780 [N/m]; k2 D 450 [N/m]; bd D 15 [N s/m] : (78) The dynamics of the experimental system can be represented by the following dynamical model Pp1 D p2 Pp2 D a.p; t/C b.p; t/u ; (79) Copyright \u00a9 2016 John Wiley & Sons, Ltd" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001310_j.ins.2013.12.026-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001310_j.ins.2013.12.026-Figure3-1.png", + "caption": "Fig. 3. A mass\u2013spring\u2013damper system.", + "texts": [ + " the observer with KSM\u00f0~e1\u00de \u00bc lCT\u00f0Csign\u00f0~e\u00de\u00de satisfies the condition (9) for l P 1 2 supt j~e1j. This condition on the gain l is commonly used in the control literature [1,39]. Simulation studies are carried out to show the effectiveness of the proposed adaptive fuzzy observers. Two observation problems are considered to this end. The first one concerns a mass\u2013spring\u2013damper system, while the second one concerns a half-car suspension system. Example 1. Consider the mass\u2013spring\u2013damper system shown in Fig. 3 whose dynamics are described by [25]: _x1 \u00bc x2 _x2 \u00bc fk\u00f0x\u00de fB\u00f0x\u00de \u00fe u\u00fe d M \u00f041\u00de where x \u00bc \u00bdx1; x2 T is the state vector, y \u00bc x1 represents the displacement of the mass, x2 represents its velocity, fk\u00f0x\u00de is the spring force due to spring constant K , fB\u00f0x\u00de is the friction force due to friction constant B, M is the body mass, u is the applied force and d denotes the disturbances. In the following simulation, the nominal parameters and their corresponding uncertainties are selected as follows: M0 \u00bc 1Kg;K0 \u00bc 2 and B0 \u00bc 2 and DM \u00bc 0:1 sin\u00f0x1\u00de kg, DK \u00bc 0:5 and DB \u00bc 0:5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002005_j.ijfatigue.2014.01.029-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002005_j.ijfatigue.2014.01.029-Figure6-1.png", + "caption": "Fig. 6. (a) Equivalent plastic strain accumulation (PEEQ) in the submodel domain, and (b) magnified view of strain accumulation near the carbide particle.", + "texts": [ + " The ratio of carbide area to unit cell will determine the carbide volume fraction. Since carbide particles in M50-NiL are circular and are uniformly distributed [35] with minimal interaction, modeling a single carbide within a unit cell is appropriate. For this submodel, the time varying stress fields obtained from the global model are applied as boundary conditions on its edges (see Fig. 3c). The incorporation of carbide particles in the submodel thus introduces heterogeneity into the domain. Fig. 6 shows the equivalent plastic strain field in the vicinity of carbide particle inside the submodeling domain. The maximum strain accumulation in the steel matrix surrounding the carbide particle ( 1.6%) is an order of magnitude greater than the nominal strain away from particle ( 0.24%), thus clearly manifesting the effect of strain amplification. It should be noted that such strain amplification is significantly higher in high strength bearing steels because of their low strain hardening exponents and higher percentage of carbide particles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003637_j.mechmachtheory.2016.09.017-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003637_j.mechmachtheory.2016.09.017-Figure3-1.png", + "caption": "Fig. 3. Gear mounting errors: (a) misalignments (b) eccentricities.", + "texts": [ + " In this paper, gear tooth local scale errors are denoted as ef1(Mj) and ef2(Mj) for the driving gear and driven gear, respectively (as shown in Fig. 2(d)). The overall profile error of the gear pair ef(Mj) is defined as the sum of ef1(Mj) and ef2(Mj). (b) Global scale errors Two typical types of mounting errors of a gear pair are misalignments and eccentricities. Misalignments of the gears are modeled by small constant angles of \u03b8 \u03b8,xi m yi m relative to the X-axis and the Y-axis [14] as shown in Fig. 3. Therefore, the corresponding normal deviations in Mj due to misalignments can be expressed as: V ue M M( )= ( )m j m j mT (15) where Vm(Mj) is a subset of V(Mj) which includes only the components related to bending slopes \u03b8xi and \u03b8yi, and um is the misalignment vector: u \u03b8 \u03b8 \u03b8 \u03b8={ }m x m y m x m y m 1 1 2 2 T (16) Eccentricity of a gear i is defined as the distance ei between the center of rotation and the center of inertia (as shown in Fig. 3(b)) with an initial phase angle \u03b8i e with regard to the positive X-axis. Therefore, the perturbations along the X-axis and Y-axis due to eccentricities will be ei x and ei y, namely: \u23a7\u23a8\u23a9 e e t \u03b8 \u03b8 e e t \u03b8 \u03b8 = cos (\u03a9 + + ) = sin (\u03a9 + + ) i x i i zi i e i y i i zi i e (17 - a, b) where \u03b8zi is the rotational perturbation of the gear i along the Z-axis. According to geometric relationships in Fig. 3(b), the corresponding normal deviations in Mj due to eccentricities can be expressed as: \u23a7\u23a8\u23a9 \u23ab\u23ac\u23ade M \u03b2 t \u03b8 \u03b8 \u03c8 t \u03b8 \u03b8 \u03c8 e e( )=cos *{sin (\u03a9 + + \u2212 ) sin (\u03a9 + + \u2212 )}e j z e z e 1 1 1 2 2 2 1 2 (18) (a) Total error The total error at the contact point Mj is the sum of the abovementioned individual errors, namely: e M e M e M e M e M( )= ( )+ ( )+ ( )+ ( )j f j f j m j e j1 2 (19) Lagrange's equations were used in [14] to derive the un-damped equations of motion for the gear pair, namely: M u K u u F F F ut t t\u00a8+ ( , ) = + ( ) + ( , )g g 0 1 2 (20) where: M m m m I I I m m m I I I=diag( , , , , , , , , , , , )g p p1 1 1 1 1 1 2 2 2 2 2 2 (21 - a) \u2211K u V Vt k M M( , ) = ( ) ( )g j N t j j j T =1 ( )c (21 - b) F T T={0, 0, 0, 0, 0, ,0, 0, 0, 0, 0, }T 0 1 2 (21 - c) F t m e m e m e m e( ) = {\u2212 \u00a8 ,\u2212 \u00a8 ,0, 0, 0, 0, \u2212 \u00a8 ,\u2212 \u00a8 ,0, 0, 0, 0}T x y x y 1 1 1 1 1 2 2 2 2 (21 - d) \u2211F u Vt k e M M( , ) = ( ) ( ) j N j j j2 =1 c (21 - e) wheremi, Ii, Ipi are the mass, transverse moment of inertia and the polar moment of inertia of the ith gear, respectively; kj is the cell stiffness at the contact pointMj;Kg(t, u) is the nonlinear stiffness matrix which depends not only on time t, but also onMj; F0 is the force vector produced by the nominal input and output torques; F1(t) is the force excitation coming from the centrifugal and tangential inertial force due to gear eccentricities; F2(t, u) is the force excitation due to the unloaded static transmission error, which is also time and position dependent" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000472_s00170-009-2265-7-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000472_s00170-009-2265-7-Figure1-1.png", + "caption": "Fig. 1 a Integrally bladed rotor disk\u2014blisk; b typical cross-sectional geometries of a blisk airfoil", + "texts": [ + "eywords Laser powder deposition . Net shape manufacturing . Adaptive toolpath . Inconel 718 . Compressor airfoils . Blisk Integrally bladed rotor disks (blisks) are increasingly being used in the compressors of advanced gas turbine engines for improved performance and efficiency. Such parts are typically made from expensive high-performance alloys, i.e., Ti\u20136Al\u20134V, Inconel 718, and forged from one continuous piece of metal and then machined to the final geometry (Fig. 1a). Blisks are subjected to foreign object damages on the airfoils during engine service and are typically repaired by mechanical blending technique. When the airfoils are damaged beyond the blendable limits, the entire bladed rotor had to be removed from service and replaced with a new blisk. This is extremely costly in terms of raw material and labor expense. For cost effectiveness, it is definitely necessary to provide a repair technique that is capable of restoring severely damaged blades. Laser net shape manufacturing (LNSM) is a laser cladding or laser powder deposition-based technique which uses a laser beam as a precise high-energy heat source to melt metal powders and make solidified deposit on base material", + " Parts made by this technique have unique advantages, such as fine microstructures, small heat-affected zone, and superior-to-cast material properties due to the inherently fast solidification rates [1\u20134]. The near net shape deposition provides flexible repair capabilities to restore the damaged compressor blades and enables a costeffective repair process with minimum post machining work. Compressor airfoils typically have slim and long crescent-like cross-sections along the chordwise direction (Fig. 1b) where the thickness usually varies from submillimeter at the edges to several millimeters in the middle of the cross-section. Depositing on this geometry requires H. Qi (*) :M. Azer : P. Singh Material Systems Technologies, General Electric Global Research Center, One Research Circle, Niskayuna, NY 12309, USA e-mail: qih@research.ge.com variable bead widths adaptively produced along the chordwise deposition toolpath. Such geometric adaptive deposition is necessary to improve the geometric accuracy of the repair, save raw materials and processing time, and minimize the thermal problems that are typically associated with constant bead width deposition, such as overheating (at thin edges) or undercut (at thick midsections) defects" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.52-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.52-1.png", + "caption": "Fig. 2.52 Mechanism with additional unbalances", + "texts": [ + "384) and its angular position is defined as: cos \u03b22 = \u22120, 994 07; sin \u03b22 = 0, 108 72 \u21d2 \u03b22 = 173, 76\u25e6. (2.385) The following results for the corresponding quantities at the rocker: U4\u03be = \u22123, 9735 kg \u00b7m; U4\u03b7 = \u22120, 686 67 kg \u00b7m. (2.386) This provides the basis for calculating the magnitude of the unbalance at the rocker: U4 = ma4 \u00b7 ra4 = 4, 0324 kg \u00b7m (2.387) at an angular position: cos \u03b24 = \u22120, 985 39; sin \u03b24 = \u22120, 170 29 \u21d2 \u03b24 = 189, 8\u25e6. (2.388) The mechanism is shown true to scale with additional unbalances in Fig. 2.52. The design of the balancing masses depends on the specific conditions, such as the available installation space. Balancing masses are often designed so that their moments of inertia are minimized. In the four-bar linkage, complete mass balancing can be achieved by adding one additional unbalance each to the crank and to the rocker. Their influence on the input torque as well as the individual bearing and joint forces should be checked by proper calculations. Chapter 3 Unfortunately, machines often cause vibrations at their mounting site and, consequently, interruptions, damages and disturbances to people" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001987_s11071-015-2475-5-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001987_s11071-015-2475-5-Figure8-1.png", + "caption": "Fig. 8 The dynamic response using normal distribution (\u03bc = 0.2517, \u03c3 = 0.1491): a phase diagram and b Poincar\u00e9 map", + "texts": [ + " It can be seen in the table that the phase diagram calculated by fixed backlash value (Fig. 5) failed to match any phase diagrams of the four sensors. The correlation degree was below 0.23. This means that the fixed backlash value method was not reasonable to estimate the gear tooth characters and hence was not able to establish a reliable link between the simulation and experimental results. As for the normal distribution method, the correlation degree was very low and the best correlation degree was 0.55 between Fig. 8a and the sensor 2. However, by checking Figs. 8a and 14a, the shape and scale of the chaotic attractors did not look similar. Unlike the fixed value and normal distribution methods, it can be seen that the phase diagram obtained by the fractal backlash at D = 1.9 provided the highest correlation degree of 0.76 to that of the sensor 3. By checking Figs. 11 and 15, it suggested that the scale of the chaotic attractors between the simulation and experiment is very close and although strong noise appeared in the experiment in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001725_17452759.2015.1008643-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001725_17452759.2015.1008643-Figure5-1.png", + "caption": "Figure 5. (a) Schematic of samples of varying thickness \u2013 1 mm, 5 mm and 10 mm. (b) Optical micrograph of micropores. (c) OM image of lack-of-fusion defects observed in EBM-built Ti-6Al-4V.", + "texts": [ + " Based upon our current experience, circular or complex-shaped parts with thin walls are preferable when using EBM additive manufacturing. Figure 4 shows the industrial impeller that has been successfully built by our EBM machine, with a base diameter of 100 mm and a height of 43 mm. The thinnest part of the impeller can be 0.8 mm. Its total build time is around 8 hours, which is much longer than the simulation time obtained through the EBM Control. The extra time should be due to the triple raking mode used. Nevertheless, the EBM has provided a high productivity mainly due to its high beam speed and the MultiBeamTM technology. Figure 5(a) shows the as-built samples with different thicknesses with a 5 mm spacing between them. It is assumed that the spacing is sufficient to thermally separate them. These three samples could represent the features with different thicknesses in the impeller. For simplicity, the samples were built with block shape for microstructural and mechanical investigations of EBM-built Ti-6Al-4V. Figure 5(b) shows the near-spherical pores after polishing. Their occurrence is attributed to the inherent Argon gas trapped during the gas atomised titanium alloy powder (Gaytan et al. 2009). Mechanical properties are thought to be unaffected by such kinds of micropores (Safdar et al. 2012). In addition to the inherent porosity, some lack-of-fusion defects, e.g., unmelted powder and layer gaps (as revealed in Figure 5(c)) were also seen, which is likely due to inconsistent raking or a non-optimised melting process parameter. It should be pointed out that more porosity would occur inside the 1 mm sample due to the fast contour melting that leads to numerous lack-of-fusion defects. Figure 6(a) shows the XRD patterns for the EBM-built Ti-6Al4V samples with thicknesses of 1 mm and 10 mm. The XRD peak positions are basically consistent for these two samples. Figure 6(b) shows enlarged XRD patterns of Figure 6(a) with the indexing of the major XRD peaks" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003398_j.msea.2020.140002-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003398_j.msea.2020.140002-Figure2-1.png", + "caption": "Fig. 2. CAD model sectional cutaways of three experimental specimen geometries used to induce powder spreading errors: a) overhanging features, b) internal cylindrical cavities and c) internal cylindrical cavities and overhanging features.", + "texts": [ + " To provide an effective platform for assessment of the effect of powder bed quality on defect formation, an experiment was devised to intentionally create a high number of powder spreading irregularities. This was accomplished by designing part geometries that were likely to cause these errors during recoating. Three different geometric variations of standard rectangular (20 mm \ufffd 20 mm in-plane and 6 mm tall) parts were used, which featured: 1) internal cylindrical cavities (2 mm in diameter) at a variety of spatial locations and relative spacings, 2) overhanging features (extending 1.5 mm at 45\ufffd) and 3) internal cavities plus overhanging features. Fig. 2 displays the three geometries produced. All parts were produced upon 2 mm of support structure connecting the base plate; no supports were used for the overhanging features. Three different energy density levels were used to explore the relationships between defect formation and powder inconsistencies for differing energy levels, resulting in nine total parts (three geometries with three separate power levels). The volumetric energy density has been a standard relationship used in the literature to better understand propensity for defect formation based on processing parameters" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000036_robot.1992.220061-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000036_robot.1992.220061-Figure3-1.png", + "caption": "Figure 3: A robot with a steering wheel", + "texts": [], + "surrounding_texts": [ + "We use a lower index notation to identify the quantities relative to each wheel. We consider here the particular case where the 2 front wheels (index 2 and 3 ) have a fixed orientation but the two motors provide the torques for their rotation, while the orientation of wheel 1 is varying, wheel 1 being self-aligning. The reference point Q is the center of the segment B2B3 (see Fig. 2). The basis vector 2 1 is aligned with B2B3. The geometric characteristics are : R 1 = R 2 = R 3 = R , l 1 = l 2 = l 3 = L d l = d , d 2 = d 3 = O 3n 2 O1=-,O2=O,O3=n n & = P I p 2 = @ 3 = 0 , ? \u2018 I = - , 72=73=0 2 The robot motion is then completely described by the following vector of 7 generalized coordinates : Using (9)-(10) and (ll)-(l2)the pure rolling and non slipping conditions can be deduced. We easily check that the matrix A(P, e ) has rank 5, consequently this robot has 2 degrees of freedom. Moreover, using the notations of section 1, we can compute the matrix S(q) defined in (3) (see [l]). The two actuators providing the rotation of wheels 2 and 3, it is then easy to check that the input matrix S\u2019(q B P has full rank and we to obtain the form (6) which !an be reduced in this particular case, noticing that p and d, are uniformly bounded provided that 77 is bounded : can apply the general met 1 6 6 io escribed in section 1, x = -q1sint9 s = qlcose 9 = 772 (14) 71 = v1 772 = v2" + ] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure9.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure9.9-1.png", + "caption": "Figure 9.9.1 Rigid axle coordinates, with forces and moments, for compliance analysis.", + "texts": [ + " For tractive forces the shear centre is again rather closely aligned with the kingpin axis, so in practice steering not far removed from centre-point steering is used. For front drive, careful tuning of the system is required to prevent power steer, although the situation is complicated by the dominant influence of the driveshaft torque component. A complete rigid axle may be analysed for compliance steer effects in the same way as an independent suspension. The axis origin is taken at the centre of the axle at ground level, Figure 9.9.1. The characteristics naturally depend very much on the particular type of link location system adopted, or the use of leaf springs. Just as for independent suspensions, there has been considerable development of link systems and carefully controlled compliance to achieve desired handling characteristics. Compliance Steer 187 Various rigs have been built for the measurement of suspension compliance, typically combined with measurement of geometric bump steer and bump camber. Basically, such a rig comprises a rigid frame replacement of the vehicle body, to which the suspension arms are connected in the usual way" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure2.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure2.5-1.png", + "caption": "Fig. 2.5 Illustration of the Jacobian for a 2 DOF planar limb. For the posture shown, the columns of the 2 \u00d7 2 Jacobian show the expected instantaneous endpoint linear and angular velocity for isolated angular velocities of 1 rad/s at each of the joints. If both joints are actuated, then their contribution to instantaneous endpoint velocity simply add. The limb parameters are, as per the convention in Fig. 2.3, li = 25.4 cm, l2 = 30.5 cm, q1 = 135\u25e6, and q2 = \u2212120\u25e6", + "texts": [ + " This will make the presentation of concepts easier to describe and illustrate. In the case of a planar 2-link, 2-joint system as in Fig. 2.3, the 2D forward kinematic model for the endpoint is x = \u239b \u239d x y \u03b1 \u239e \u23a0 = \u239b \u239d Gx (q) G y(q) G\u03b1(q) \u239e \u23a0 = \u239b \u239d l1c1 + l2c12 l1s1 + l2s12 q1 + q2 \u239e \u23a0 (2.30) Taking the appropriate partial derivates produces J (q) = \u23a1 \u23a2\u23a2\u23a2\u23a3 \u2212l1s1 \u2212 l2s12 \u2212l2s12 l1c1 + l2c12 l2c12 1 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 (2.31) where x\u0307 = \u239b \u239d x\u0307 y\u0307 \u03b1\u0307 \u239e \u23a0 = \u23a1 \u23a3 \u2212l1s1 \u2212 l2s12 \u2212l2s12 l1c1 + l2c12 l2c12 1 1 \u23a4 \u23a6 ( q\u03071 q\u03072 ) (2.32) As shown in Eq. 2.32, and graphically in Fig. 2.5, each column of the Jacobian is the instantaneous endpoint velocity vector produced by one unit of the corresponding joint angular velocity (i.e., the first column of the Jacobian is the endpoint velocity vector produced by an angular velocity of 1 rad/s at the first joint if other joint angular velocities are zero, the second column is the endpoint velocity vector produced by a etc.). If there are simultaneous angular velocities at both joints, their instantaneous effects at the endpoint simply add linearly. The last row says that the angular velocity of the endpoint is simply the sum of the angular velocity at each joint. But let us look at the planar arm example in Fig. 2.5 and Eq. 2.32 in detail. First, we notice that (other than the last row) the values of the elements of the Jacobian matrix can be posture dependent (i.e., they change as the posture\u2014or angles q1 and q2\u2014change). Second, we are therefore forced to always speak of instantaneous endpoint velocities because these values only hold for that posture, and the posture is changing\u2014by definition\u2014given that the joints have angular velocities. And third, given that the forward kinematic model and the Jacobian involve trigonometric functions, the mapping from angular velocities to endpoint velocities changes in nonlinear ways as the motion progresses", + " We can use Newton\u2019s first law stating that the sum of forces and torques equals zero to find joint torques needed to exert a static 1 N force in the negative y-direction. The simplified scalar version of this equation is \u03c4i = di ||f||, where ||f|| is the magnitude of the force applied, and di is the perpendicular distance from the line of action of the force to the center of rotation of the joint. Using this equation, we see that \u03c41 = d1 ||f|| = \u22120.115 Nm and \u03c42 = d2 ||f|| = \u22120.295 Nm. However, we can also do this by simple matrix multiplication using the Jacobian seen in Fig. 2.5. After selecting the first two rows as in Sect. 3.3, and using Eq. 3.9 we obtain, \u03c4 = J T f = \u23a1 \u23a3 \u22120.259 0.115 \u22120.0787 0.295 \u23a4 \u23a6 ( 0.0 \u22121.0 ) = (\u22120.115 \u22120.295 ) Try this same comparison using the example in Sect. 3.3, or any other of your choosing. What is clear is that J T encapsulates Newton\u2019s first law for static equilibrium. Impressive, right? Later on you will also see that the various forms of the Jacobian encapsulate many inherent kinematic and mechanical properties of the limb. The critical issue here is to clearly define the independent internal versus external kinematic DOFs of the system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure13.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure13.5-1.png", + "caption": "Figure 13.5.1 Rigid axle with steer governed by two parallel longitudinal links (other links not shown).", + "texts": [ + " Arguably, then, it may be better to use an arrangement in which the roll centre is lowered as the load increases, giving preference to the more critical limit-state handling. The axle characteristics can usefully be investigated by direct analysis of the links, particularly with some simple configurations. Consider a rigid axle with a single-point upper lateral location and two lower parallel longitudinal members, along the lines of Figure 1.7.4 or 1.9.1, such that the lower longitudinal arms govern the steer angle of the axle, as illustrated here in Figure 13.5.1. The longitudinal links are characterised by their length, static angle to the horizontal, and spacing. Consider then a body roll giving a suspension roll angle fS on such a system. Relative to the axle, the front of the left link will rise and the front of the right link will fall. In conjunction with the link static inclination in side view, this will give a linear roll steer effect. Also, the non-infinite length of the linksmay give a secondary steer effect. The resulting understeer angle, dUS, for a rear axle, will be given by dUS \u00bc dxL dxR B where x is the forwardmovement of the axle point", + " due to manufacturing tolerances), dxL \u00bc LL\u00f01 cos uL\u00de LL\u00f0 1 2 u2L\u00de \u00bc LL 1 2 1 2 BfS LL 2 giving dxL \u00bc 1 8 B2 LL f2 S Then, in terms of the link shortnesses S\u00bc 1/L, dUS \u00bc 1 8 B\u00f0SR SL\u00def2 S so the resulting quadratic understeer coefficient is \u00abRU2 \u00bc 1 8 B\u00f0SR SL\u00de Evidently, then, the first understeer coefficient arises from any difference in the static arm angles, asmight occur due to manufacturing tolerances or to asymmetrical loading. The second understeer coefficient arises fromdifferences of the arm lengths,which is just amatter ofmanufacturing tolerance, usually small. Figure 13.5.2 shows a simple example axle in side view for two cases. The change of axle pitch angle can be analysed in a very similar way to the analysis of camber angle on an independent suspension. In the first case, for a bump dz the longitudinal displacement of the end of the link is dx \u00bc dz tan u dz u Considering both links then, the change of pitch angle is du \u00bc dxU dxL HA dz HA \u00f0 uU uL\u00de Rigid Axles 259 The result is a linear axle heave pitch coefficient \u00abAHP1 \u00bc uU uL HA For links of different lengths, LU and LL, initially horizontal, dx \u00bc L 1 cos dz L L 1 2 dz2 L2 \u00bc 1 2 S dz2 The pitch angle change is then D u \u00bc SU SL 2HA dz2 with a consequent quadratic axle heave pitch coefficient \u00abAHP2 \u00bc SU SL 2HA Further analysis along these lines may be applied to obtain the longitudinal scrub of the bottom of the wheel in bump, which is held to be significant in braking quality on rough roads, as any bump scrub at this point is likely to cause deterioration of the braking quality", + " The criterion applied here is of course a rather rigorous one, and from the point of view of engineering accuracy, an equivalent link of say 1000 m would probably be adequate. Whatever the configuration, a numerical analysis by computer can obtain the various characteristics of the axle, provide that suitable software is available, or written for the purpose, and small details, such as the effect of manufacturing tolerances of mounting points, are also easily investigated. 260 Suspension Geometry and Computation The basic rigid axle, as in Figure 13.5.1, is mounted on four links. This is the simplest form. Other more complex types, such as a Watt\u2019s linkage location, require a specialised program or the use of equivalent links, as discussed earlier. In principle, this could be solved by writing equations for the link spaces in terms of the axle position variables, and setting these equal to the physical link lengths. In practice the equationswould be unwieldy, and non-linear, and iteration would be required for a practical solution. In practice, then, there is really no way to avoid doing an iterative solution" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001700_s00170-015-7932-2-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001700_s00170-015-7932-2-Figure3-1.png", + "caption": "Fig. 3 A biomedical impeller geometry used as 3D complex freeform geometry in the simulations", + "texts": [ + " The developed model can simulate transient temperature fields for any given complex freeform structures. Figure 2 illustrates the implementation scheme of transient thermal modeling approach for additive manufacturing of 3D complex structures with freeform. The modeling approach considers the interactions between 3D CAD model, material properties, ALM process parameters, mathematical modeling, and finite element analysis. The simulation of the proposed modeling approach is demonstrated in an example of mini impeller of a blood pump in a biomedical application. Figure 3 shows a 3D CAD of the biomedical impeller. For the freeform implementation procedure, one main module (Mathematical Modeling Module) and its two submodules (CAD Module and Material Module) have been developed. In the CADModule, the 3D part data from any solid model-based CAD package is taken and converted to the STL format. An off-the-shelf slicer program is used to slice the geometry and to generate the laser path (Fig. 4). In the Mathematical Modeling Module, scanning lines are broken into laser position points according to the laser beam diameter", + "1 mm along the Y-axis are caused due to the material properties are considered as powder in the simulation after the melting occurs (1941 K). Hence, the heat is not conducted as it should be as in the experimental values. On the other hand, the simulation results of X- and Yprofile agree for the molten pool zone and previously non- melted zones, which is crucial to the additive layer manufacture process, with the temperature measurements obtained by Kolossov et.al [9]. In order to perform the transient thermal analysis of ALM for 3D complex structures with freeform geometries, the impeller (shown in Fig. 3) of a biomedical application was utilized for the simulations. A steel block with the dimensions of 3\u00d73\u00d7 1.5 mm was selected as the base. In the laser-based ALM, 3\u00d7 3\u00d70.1 mm Ti-6Al-4V powder layers were deposited on the steel base. Argon was selected as the inert gas. Six layers were placed onto the steel base in an argon-filled chamber and scanned by the laser. Process parameters and powder properties are listed in Tables 2 and 3, respectively. Fifty-seven seconds of manufacturing simulation of sixlayered impeller geometry was performed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002855_j.msea.2019.138078-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002855_j.msea.2019.138078-Figure4-1.png", + "caption": "Fig. 4. (a) XRD patterns of the different layers of CP-Ti. (b) Schematic illustration of SLM processing under the reactive atmosphere. (c) Schematic diagrams of the heat history. TL is liquidus temperature, TS is solidus temperature, T\u03b2 is \u03b2 transus temperature, and MS is martensite transition start temperature.", + "texts": [ + " A nitrogen mass transfer occurred from the atmosphere to laserheated regions [42]. The diffusion of nitrogen into titanium resulted in the formation of Ti\u2013N compounds (mainly in droplets and particles) and a solid solution (mainly in molten pool). XRD analysis revealed that the top surface of the as-printed CP-Ti was a thin layer of \u03b1/\u03b1\u2032-Ti with TiN and non-stoichiometric compound TiN0.3 [43] in it. The diffraction peaks corresponding to TiN and TiN0.3, however, disappeared after surface polishing (Fig. 4(a)). Owing to the dilute N2 environment, N contents of all the as-printed components (\u22642.16 at%) were well below the maximum solubility of nitrogen in \u03b1-Ti at RT (~9 at%) [39]. Hence the disappearance of the aforementioned diffraction peaks might be attributed to the decomposition of TiN and TiN0.3 compounds. The layered structure and heat history of the as-printed CP-Ti are illustrated in Fig. 4(b) and (c). Notably, the superficial compound layer would not influence the mechanical properties of hardness/tensile specimens since it had been removed before the mechanical tests through polishing. Microscopic features of the CP-Ti printed in various atmospheres are displayed in Fig. 5. Refined acicular \u03b1\u2032-Ti grains with a hierarchical structure were distributed in a zigzag form due to the \u03b2\u2212\u03b1\u2032 phase transition under very high cooling rates (103\u2212108 K/s) [6]. The EBSD orientation maps (Fig. 5(d)\u2212(g)) of four representative samples (printed in Ar + 3/5/7/10 vol% N2 atmospheres) demonstrated that over 99% of the grain boundaries were high-angle grain boundaries (HAGBs, \u226510\u00b0)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003382_s00170-020-05027-0-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003382_s00170-020-05027-0-Figure5-1.png", + "caption": "Fig. 5 Part-level model: active and inactive elements [115]", + "texts": [ + " In the quiet element method, or sometimes called dummy material method, the elements representing material deposition regions are present from the beginning, whose properties are manually set so that the overall results will not be affected significantly. In the inactive element method, the elements representing material deposition regions are added and connected to the existing elements at each time step. The number of elements to be added at each time step is determined by the amount of material entering melt-pool in that time step. Only active elements are considered in solution process but related boundary conditions and solver information need to be updated frequently. A typical part-level model can be seen in Fig. 5, where active and inactive mesh elements are separated by a virtual interface. Naturally thermal boundary conditions such as convection and radiation should be specified at this interface. However, this is generally neglected because the interface is hard and expensive to be captured, which may lead to inaccurate results [115]. Quiet element method Quiet element method has been used in many numerical part-level models. Wang et al. [116] developed a 3D model that employed a constant mesh to analyze the thermal field in LENS" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003544_tr.2016.2590997-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003544_tr.2016.2590997-Figure8-1.png", + "caption": "Fig. 8. (a) Illustration of the rotation of a faulty planet gear and (b) its influence on time-varying GMS of ring-planet and sun-planet meshes (indicated with dotted squares).", + "texts": [ + " Therefore, it is possible to detect and differentiate the failure modes by monitoring the TE in gear systems. Consequently, the overall behaviors of TE from other types of faults are expected to be similar. Also, we assumed that the faults exist in a planet gear. A faulty tooth in a planet gear would contact with both a sun and a ring gear repeatedly in a half-planet rotation. Therefore, the stiffness reductions appear with a phase difference equal to a half-planet rotation (like that shown in Fig. 8). In Fig. 8(b), the faulty tooth of the planet gear was parameterized by reducing the magnitudes of GMS in time-varying profiles of GMS. The phase difference of faulty time-varying GMS is a half-planet revolution. Then, the time-varying profiles of GMS in normal and faulty gears were parameterized into a dynamic model, as described in Section III-B. As the planetary gear used in this study is a spur planetary gear, we ignored the translational displacements in the x- and y-axes, which are related to a helical angle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003309_978-3-319-24729-8-Figure6.15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003309_978-3-319-24729-8-Figure6.15-1.png", + "caption": "Fig. 6.15 Coordinate representations of the thrust axes of robots i and j", + "texts": [ + " As in the 2D case, if we set u1 = \u00b7 \u00b7 \u00b7 = un = u\u0304 > 0 and we make Ri e3 converge to a common constant vector, then the velocities x\u0307i converge to a common constant vector as well, and flocking is achieved. The problem has thus been reduced to the synchronization of the vectors Ri e3, i = 1, . . . , n, whichwewill refer to as the thrust axes of the robots. For the design of flocking controllers we focus our attention on the rotational dynamics R\u0307i = Ri S(\u03c9i ) Ji \u03c9\u0307i + \u03c9i \u00d7 (Ji\u03c9i ) = \u03c4i , i = 1, . . . , n. (6.12) Before continuing our development,we introduce someuseful notation, illustrated in Fig. 6.15. We let qi := Ri e3 denote the thrust axis of robot i represented in the common inertial frame I, and by Ri j := RT i R j the relative orientation of robot j with respect to robot i . Operationally, Ri j transforms a vector in frame j to its representation in frame i . We let qi j := Ri j e3 denote the representation of robot j\u2019s thrust axis in the local frame of robot i . For flocking we would like to have qi j = e3 for all i, j . Finally, we denote by \u03d5i j the angle between the third axis of frame Bi and qi j " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003834_s11837-020-04469-x-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003834_s11837-020-04469-x-Figure2-1.png", + "caption": "Fig. 2. (a) Schematic of the x-ray experiment. The home-built directed energy deposition system at Northwestern University consists of an environmental chamber, powder hopper, and laser scanning system. (b) Photo of the deposition setup. A linear stage is used to move the optics assembly and powder nozzle to fabricate a single clad on top of the thin substrate.", + "texts": [ + " The advantages of the large-scale system include: representative of the industry process, ability to manufacture thin walls and small parts, evaluation of bulk mechanical properties in materials, and study of multi-particle impacts. In all, the limitations within the large-scale system are met by the small scale, and vice versa. Both systems were set up at the beamline closely following the previous LPBF experiments with the same high-speed camera and x-ray conditions and the same laser setup in the small-scale DED system.29 Schematics of the high-speed x-ray imaging setup are presented in Figs. 1 and 2, where Fig. 2 shows how the x-ray beam aligned with the the DED system, the LuAG scintillator, and high-speed camera. A short period (18 mm) undulator with the gap set at 16 mm was used to generate the polychromatic x-ray beam. The first harmonic of the x-ray energy was centered around 24 keV. The x-rays passed through the substrate as the laser and powders were deposited on top. The transmitted x-rays were converted to visible light using a single-crystal scintillator (LuAl5O12 : Ce; 100lmthick; /10mm, Crytur Czech Republic)", + " Remotely controlled parameters for the system were disc speed, pulse width duration of disc movement (time duration of disc movement), and pulse width duration of shield gas flow (time duration that the argon shield gas entered the nozzle), which were set to 1 rpm, 400 ms, 0.1 ms, and 172 kPa, respectively. The large-scale DED setup for x-ray experiments consisted of a deposition system housed in an environmental chamber and a multi-material commercial powder hopper (PF 2/2, GTV, Germany). The overall beamline setup is shown in Fig. 2. The commercial powder hopper ensured powder flow rates that are similar to those used in commercially available DED machines while also enabling the study of many AM materials that have dissimilar thermo-physical properties. The deposition system used a linear stage for laser and powder delivery on a gantry-like structure and a drum sample holder underneath. The drum was remotely controlled such that moving to the next sample only required a small rotation. A dichroic mirror (DMSP900L, Thorlabs, USA) was used to deliver the collimated laser to the top of the substrate through a planoconvex focusing lens (LA1509, Thorlabs, USA)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure12.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure12.11-1.png", + "caption": "FIGURE 12.11. A planar slider-crank machanism.", + "texts": [ + " Find an equation to relate the acceleration of link (i) to the accelera tion of link (i - 2), and the acceleration of link (i) to the acceleration of link (i + 2). 5. Even order recursive angular acceleration. Find an equation to relate the angular acceleration of link (i) to the angular acceleration of link (i - 2), and the angular acceleration of link (i) to the angular acceleration of link (i + 2). 6. Acceleration in different frames. For the 2R planar manipulator shown in Figure 12.5, find ~az, &az, \u00b0 z z dOzaI, oal, oaz, an laI \u00b7 7. Slider-crank mechanism dynamics. A planar slider-crank mechanism is shown in Figure 12.11. 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 5.37. Eliminate the joints' constraint force and moment to derive the equations for the actuators' force or moment. 558 12. Robot Dynamics 9. Global differential of a link momentum. In recursive Newton-Euler equations of motion , why we do not use the following Newton equation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000952_cpa.3160230402-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000952_cpa.3160230402-Figure13-1.png", + "caption": "Figure 13. Graphs of t ( 0 ) for P =' 6 x and the same sequence of values of k as in Figure 12.", + "texts": [ + " In the thick sphere case this is P, . At this pressure it may be possible for the sphere to deviate from perfect sphericity without jumping by merely deforming continuously into the bifurcated mode of solution. In general, if the bifurcation branch branches up (down) this smooth transition can occur only for P increasing (decreasing). Thus since B5,1 branches down from P5 such a smooth transition cannot occur at P5 as P increases.8 For other values of k , e.g., k = 1.2 x the lowest eigenvalue is symmetric (see Figure 13). Therefore, a smooth transition into the bifurcation branch as P increases is possible. 562 L. BAUER, E. L. REISS AND H. B. KELLER We recall that for the bifurcation branches B2m,l passing through each symmetric eigenvalue P,, , the energy e2m. l ( P ) is monotone decreasing. Thus as P increases beyond some P,, the unbuckled state has more energy than the state on B2m,l . If we make the reasonable assumption that at a bifurcation point states with least energy are preferred, then the thick sphere smoothly deforms into the state on B,,l as P goes from P, past P, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003816_j.ymssp.2020.106903-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003816_j.ymssp.2020.106903-Figure5-1.png", + "caption": "Fig. 5. Roller/Raceway defect Interactions.", + "texts": [ + " The dynamic equations of bearing chock can be shown as: mh\u20acyh \u00fe cy _yh \u00fe kyyh \u00bc Fhy mh\u20aczh \u00fe cz _zh \u00fe kzzh \u00bc Fhz \u00f024\u00de where Fhy and Fhz are horizontal and vertical loads acting on the bearing chock; mh is the weight of outer raceway; \u20acyh and \u20aczh are the accelerations of bearing chock on axes OiYi and OiZi in inertial frame; _yh and _zh are velocities of bearing chock in corresponding directions; yh and zh are displacements in the same directions as above; cy and cz are damping coefficients; ky and kz are stiffness coefficients. The mathematical description methods of inner raceway defect, outer raceway defect and roller defect are introduced in this section from two aspects: additional clearance and change in direction of contact load. 2.2.1. Localized defect on raceway 1) Additional deflection Fig. 5 is a schematic diagram of the interaction between roller and raceway defect. wd and hd are the width and depth of defect; he is half of the central angle corresponding to the damaged area on raceway and its value is subjected by wd. hb is the angle at which roller turns, hd represents the angle that defect has rotated. To determine if the roller has entered the damaged area, it is necessary to calculate the difference hbd between hb and hd. Since the outer raceway is fixed and the inner raceway rotates, hbd for outer raceway damage and inner raceway damage can be calculated by Eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002721_0278364916640102-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002721_0278364916640102-Figure5-1.png", + "caption": "Fig. 5. Compensation of the virtual leg angle \u03b8virtual by \u03b8imu measured by an IMU sensor.", + "texts": [ + " (2006). In our control scheme, this orientation regulation allows the robot to maintain the prescribed angle of attack and exert impulse to the ground in a proper direction. We implement active regulation on top of the original framework in order to achieve stable gallop. The leg trajectory generator computes the equilibrium-point foot-end trajectories with respect to the body coordinate. While computing the trajectory, the body orientation measured by an IMU sensor, \u03b8imu, is compensated as shown in Figure 5. The leg impedance controller allows reflex responses to external forces according to the predefined compliance. We used the fixed virtual leg compliance referring to the biological observation (Blickhan and Full, 1993) which addresses relationship between the body mass and the effective leg compliance. Also, stable and robust walking of a biped compliant-leg walker can be achieved with a combination of fixed stiffness and proper angle of attack (Rummel et al., 2010). The leg compliance is pre-tuned in the dynamic simulator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure7.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure7.5-1.png", + "caption": "FIGURE 7.5. A rigid body with an at tached coordinate frame B (oxyz) moving freely in a global coordinate frame G(OXYZ) .", + "texts": [ + " dt dt Now B r = RI ,'P [ti] = t cosspi- t sin Rec. To analyse the change in orbit constant due to migration across inertialess meridional trajectories, it is necessary to consider fluid motion induced orthogonal to the fibre-flow plane" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000036_robot.1992.220061-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000036_robot.1992.220061-Figure2-1.png", + "caption": "Figure 2: A robot with a free wheel", + "texts": [ + " the fact that the component of the velocity of the contact point, orthogonal to the plane of the wheel is zero, are of the form : c1 ( P ) W ) i + c2P = 0 (11) where C1 and C2 are given by : (C l ) i l (P ) = cos(% +Pi + Yi) (12) We note that these constraints (9)-( 11) are in the general form of kinematical constraints (1) . We use a lower index notation to identify the quantities relative to each wheel. We consider here the particular case where the 2 front wheels (index 2 and 3 ) have a fixed orientation but the two motors provide the torques for their rotation, while the orientation of wheel 1 is varying, wheel 1 being self-aligning. The reference point Q is the center of the segment B2B3 (see Fig. 2). The basis vector 2 1 is aligned with B2B3. The geometric characteristics are : R 1 = R 2 = R 3 = R , l 1 = l 2 = l 3 = L d l = d , d 2 = d 3 = O 3n 2 O1=-,O2=O,O3=n n & = P I p 2 = @ 3 = 0 , ? \u2018 I = - , 72=73=0 2 The robot motion is then completely described by the following vector of 7 generalized coordinates : Using (9)-(10) and (ll)-(l2)the pure rolling and non slipping conditions can be deduced. We easily check that the matrix A(P, e ) has rank 5, consequently this robot has 2 degrees of freedom" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002066_j.ymssp.2018.06.054-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002066_j.ymssp.2018.06.054-Figure12-1.png", + "caption": "Fig. 12. RIP with additional pendulum.", + "texts": [ + " ANN was used in system identification of twin RIP in Ref. [16]. Some researchers implement their controllers on another type of double RIP, as shown in Fig. 11. In this case, the first pendulum is connected to the arm and the second pendulum is connected to the free end of the first pendulum. The multiple feedback delay was used to control this kind of RIP in Ref. [126]. Pujol et al. [30] generated a disturbance to the RIP by incorporating another inverted pendulum to the major inverted pendulum. This is done using semi-rigid spring as shown in Fig. 12. The system center of mass was changing when the motion was induced in the second pendulum. This creates a perturbation analogous to that of transportation units of mobile inverted pendulum. LMI controller was designed considering only the main pendulum. Consequently, the whole closed-loop system\u2019s behavior and the performance of the controller were analyzed experimentally [30]. The stabilization problem for triple RIP was addressed in Ref. [127]. The triple RIP has three inverted pendulums positioned at direct drive motor, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003886_j.mechmachtheory.2019.103693-Figure14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003886_j.mechmachtheory.2019.103693-Figure14-1.png", + "caption": "Fig. 14. Controller schematics of T-Bot.", + "texts": [ + " Two identical spiral grooves were machined out on the surface of the drum to wind the cables and ensure the synchronized motion of the parallel cables. Cables were made of the 8-strand Kevlar braided rope. Kevlar cable has the advantages of reduced weight, high strength, and high Young\u2019s modulus compared to steel cable [46] . The cable was guided by V-groove pulleys on the base. Two V-groove pulleys were tangentially rolled, and the cable was pulled from the middle hole. This design allows the cable to achieve a large swing angle. The controller schematics of the T-Bot are displayed in Fig. 14 . The PMAC Clipper was the controller, which carried out the following tasks: 1) edit and solve the inverse and forward kinematics; 2) data acquisition and storage, including the position, speed, acceleration, and following error of each motor; 3) trajectory generation and interpolation. The proportional-integralderivative (PID) position control method was adopted in the experiments. The controller outputs the position control signal to the servo driver to actuate the motors, and the encoder feeds back the real-time motor position signal, forming a closedloop position control" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000856_tmag.2009.2021666-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000856_tmag.2009.2021666-Figure1-1.png", + "caption": "Fig. 1. Schematic of 12/10 FSPM machine.", + "texts": [ + " A simple 1-D analytical model is developed and validated by the finite element analysis to accurately estimate the level of proximity losses and then used to determine the optimal number and diameter of conductors. Index Terms\u2014Brushless machine, flux-switching, permanent magnet, proximity loss. I. INTRODUCTION M ODULAR flux-switching permanent magnet (FSPM) machines usually have high number of stator and rotor poles and limited armature slot area due to the inclusion of both permanent magnets and armature windings within the stator, Fig. 1. Consequently, the current density in FSPM machines is usually higher than that in a surface-mounted PM machine having an equivalent electrical loading. High pole number in FSPM machines also results in high frequency and dictates narrow stator slots resulting in high slot leakage across the coils, which causes large eddy currents in the conductors [1], [2]. For the specific application of the FSPM machine that will be discussed in this paper, the high speed operation will also result in low number of turns [3]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001025_1.3005147-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001025_1.3005147-Figure2-1.png", + "caption": "Fig. 2 Simulations were started with the trailing limb in an upright configuration and the forward limb oriented at the impact angle. The double support phase started when the leading limb contacted the ground and then continued until the trailing limb length reached its undeflected length. The second single support phase continued until the limb reached an upright configuration, signaling the end of the half gait cycle. We searched for limit cycle solutions in which the limb length, forward velocity, and vertical velocity at the end of the half gait cycle replicated the initial conditions.", + "texts": [ + "org/about-asme/terms-of-use w p o 0 Downloaded Fr MR sin 1 M ML1 2 + 2ML1R cos 1 + MR2 MR sin 1 \u03081 L\u03081 = \u2212 MR\u03071 2 cos 1 + ML1\u03071 2 + M\u03071 2R cos 1 \u2212 Mg cos 1 + KL0 \u2212 KL1 + KL0 \u2212 KL2 L2 cos 1 \u2212 2 + R cos 1 L2 + R cos 2 \u2212 2ML1L\u03071\u03071 \u2212 3ML\u03071\u03071R cos 1 + ML1\u03071 2R sin 1 + ML\u03071R\u03071 cos 1 + MgL1 sin 1 + KL0 \u2212 KL2 RL2 sin 2 \u2212 L1L2 sin 1 \u2212 2 \u2212 RL1 sin 1 L2 + R cos 2 1 here g represents the gravitational acceleration and L0 represents the spring slack length. For each simulation, the model was initially positioned in upright single support with the point mass at its apex and the swing limb ositioned out in front of the stance limb at a prescribed impact angle Fig. 2 . During the initial single support period, the equations f motion Eq. 1 were numerically integrated forward in time until contact of the leading limb with the ground was detected. We 11013-2 / Vol. 131, JANUARY 2009 Transactions of the ASME om: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use a l 2 D d i f l w s r c c s T c p w a n m a l e s d i l l s q g c p d e t c w J Downloaded Fr ssumed that there was no slip between either of the rollers and ground during contact", + " 2 resulted in the following relationship Eq. 3 between the accelerations of the leading and trailing limbs uring double support: L\u03082 \u03082 = L2\u03071 L2\u03072 cos 1 \u2212 2 \u2212 L\u03072 sin 1 \u2212 2 \u03072 2 \u2212 L2 L2\u03072L1\u03071 sin 1 \u2212 2 \u2212 L2\u03072L\u03071 cos 1 \u2212 2 + L\u03072L1\u03071 cos 1 \u2212 2 + L\u03072L\u03071 sin 1 \u2212 2 \u03072 2 \u03071\u03072 sin 1 \u2212 2 L2 \u03072 L1\u03071 cos 1 \u2212 2 + L\u03071 sin 1 \u2212 2 L2 L\u03081 \u03081 3 Double support continued until the trailing limb spring reached ts slack length. At this point, the trailing limb was then reset in ront of the body at the limb impact angle Fig. 2 . This swing imb motion incurred no energetic cost since the limb and foot ere assumed massless. Numerical integration continued into the ubsequent single limb support phase until the leading limb eached an upright configuration, and the half cycle of gait was omplete. Throughout this process, integration was stopped in the ase of circumstances not representative of gait i.e., take-off in ingle limb support, falling backward, or the mass bottoming out . he total system energy TE for the conservative system was alculated by summing kinetic, spring potential, and gravitational otential energies, TE = 1 2 M v 2 + 1 2K L0 \u2212 L1 2 + 1 2K L0 \u2212 L2 2 + Mg R + Li cos i kinetic spring potential gravitational potential 4 here v is the velocity of the point mass Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure1.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure1.8-1.png", + "caption": "Figure 1.8.1 De Dion axle: (a) front three-quarter view; (b) rear elevation; (c) plan view (1969 Opel).", + "texts": [ + " Generally, the torque tube arrangement is a superior but more costly design used on more expensive vehicles. Figure 1.7.5 Rear axle with torque tube and Panhard rod (Opel). Figure 1.7.6 Axle with torque tube and Watt\u2019s linkage (Rover). 22 Suspension Geometry and Computation ThedeDiondesign is an old onegoingback to the earliest days ofmotoring. In this axle, the twowheel hubs are linked rigidly together, but the final drive unit is attached to the body, so the unsprung mass is greatly reduced compared to a conventional live axle, Figure 1.8.1. Driveshaft length must be allowed some variation, for example by splines. The basic geometry of axle location is the same as that of a conventional axle. Figure 1.8.2 shows a slightly different version in which thewheels are connected by a large sliding tube permitting some track variation, so that the driveshafts can be of constant length. In general, the de Dion axle is technically superior to the normal live axle, but more costly, and so has been found on more expensive vehicles. Undriven rigid axles, used at the rear of front-drive vehicles, have the same geometric location requirements as live rigid axles, but are not subject to the additional forces and moments of the drive action, and can be made lower in mass" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003582_j.ijfatigue.2019.02.041-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003582_j.ijfatigue.2019.02.041-Figure6-1.png", + "caption": "Fig. 6. Case ii), two diametrically opposed cracks down the bore of the hole. Here c is referred to as the crack depth.", + "texts": [ + " Since it is unclear what the effect of machining a hole in an AM Ti-6Al-4V structure will have on the fatigue critical location two cases, which both had A=62MPa \u221am, were analysed: (i) The hole was assumed to contain four cracks, with two diametrically opposed quadrant cracks (EIFS) at the intersection of the bore of the hole with each of the two free surfaces, see Fig. 5. (ii) The hole was assumed to contain two diametrically opposed semicircular cracks (EIFS) at the intersection of the bore of the hole with the free surface, see Fig. 6. In both analyses the EIFS assumed was a 1.27mm radius crack. The resultant computed lives are shown in Table 3 where we see that Case i), i.e. two diametrically opposed quadrant cracks (EIFS) at the intersection of the bore of the hole with each of the two free surfaces, was the most severe. The analysis was then repeated for values of A= 36.6, 75 and 128MPa \u221am. The resultant crack depth versus simulated flight hours histories are shown in Figs. 7 and 8 and the associated fatigue lives are shown in Tables 4 and 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000902_0959651812455293-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000902_0959651812455293-Figure1-1.png", + "caption": "Figure 1. The Qball-X4 UAV configuration and attitude motions.18", + "texts": [ + " The experimental setup of the Qball-X4 system and the experimental flight testing results and comparisons are given thereafter. Finally, conclusions are drawn. The groundwork of a controller design process is always based on a mathematical model of the system to be controlled. In this paper, a dynamic model is needed because the forces generated by four propellers provide the main power for the quadrotor to fly and these propellers need to be controlled in appropriate ways for different flight modes and flight conditions, even under actuator faults and propeller damage cases. Qball-X4 is a rigid body, as shown in Figure 1, and two sets of reference frames have been used to at LAURENTIAN UNIV LIBRARY on November 25, 2014pii.sagepub.comDownloaded from formulate the system dynamic equations. One frame is the body-fixed frame in which the origin is located at the centre of the mass of the Qball-X4. The other reference frame is the earth-fixed frame (known as the global frame) in which the origin can be chosen as desired. The coordinates xq, yq, zq are defined in body-fixed frame, and x, y, z are defined in the earth-fixed frame", + " The experimental tests have been carried out in the Qball-X4 quadrotor helicopter testbed available at the Networked Autonomous Vehicles (NAV) lab of Concordia University. The testbed includes six cameras as the indoors global positioning system for providing the position of the Qball-X4 during the flight in real time, a joystick as the safety control and a desktop computer as the ground control station. The reason for the name \u2018Qball-X4\u2019 is because of the ball-shaped protection cage surrounding the quadrotor to protect the four propellers and also the person who is using the Qball-X4 for flight tests. The four propellers are lined up orthogonally as shown in Figure 1. The black-box at the centre has all the control hardware devices that send control signals to control the attitude and motion of the Qball-X4 during flight, to generate different pulses to each rotor for pitch, roll and yaw commands with the control algorithm implemented in software format in the on-board Gumstix single-chip microcomputer (control device). For the system, not only are there inertial sensors on the HiQ board which is located inside the black-box, but also vision sensors of the OptiTrack camera system from Natural Point, Inc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003197_s11661-016-3478-7-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003197_s11661-016-3478-7-Figure1-1.png", + "caption": "Fig. 1\u2014Shapes as drawn (top) and fabricated (bottom): (a) tube, (b) t-shape, (c) reduction, and (d) 45-deg angle. Inner tube diameter: 10 mm.", + "texts": [ + " Therefore, an internal channel cross-sectional shape of a round with a self-supporting cone with a 45-deg angle (Figure 2) described by Thomas[3] was chosen to be the best shape investigated as an internal channel possibility for building on the xy-plane at the 0 deg. During slicing of a round cross section into 2D sections, a SLM machine appoints different build parameters to different areas of the slices. These are core, up-skin, down-skin and contour.[21] Changing parameters helps to control the build more efficiently. These build parameters affect the piece roughness. Four different tubing shapes (Figure 1) with round cross sections of 10 mm were designed according to shapes commonly used in the hydraulic manifold. Aluminum tubing with an inside diameter between 5 to 10 mm was used, from which the 10-mm diameter was chosen as it is in the upper end of tubes commonly used. The shapes are tube (Figure 1(a)), t-shaped divider (Figure 1(b)), reduction piece (Figure 1(c)), and 45-deg angle piece (Figure 1(d)). These pieces were produced by tilting the parts 5-deg in comparison to the recoating direction from EOS AlSi10Mg and EOS Ti64 powders with EOS\u2019s EOSINT M270 DUAL Mode machine. Parameters used for AlSi10Mg and Ti6Al4V are compiled in Table I. The layer thickness is 0.03 mm for both materials, and the building platform temperature for aluminum is 373 K (100 C) and for titanium is 353 K (80 C). Pieces were manufactured from AlSi10Mg with different building angles of 0, 35, 40, 45, 60, 80, and 90 deg with respect to the building platform (Figure 3)", + " These slight differences are characterized in the research. The dimensional accuracy was measured to check the distortions during the building of the internal channels. It was done by measuring the roundness from the bottom to the top of all of the specimens in stereomicrographs by fitting an ellipse. The results are presented in Table II. No large variances in distortions were measured in the fabrication angles, since roundness was near one; the major and minor axes aspect ratios were similarly close to one. In one shape (Figure 1(c)), a decrease in dimensional accuracy was noticed, indicating a problem in low building angles. The deformation was in the reduction piece (Figure 1(c)) at a 40-deg incline. The bottom diameter aspect ratio (minor/major axes) was decreased from 1 to 0.94. Halves were cut horizontally from the middle to reveal the top internal surfaces built with down-skin parameters and bottom internal surfaces produced with up-skin parameters. Both top and bottom surfaces have different evolutional structures depending on the build orientation. On the top half of the teardrop cross section of the self-supporting cone, the joint has a dross formation that is similar to a slight cave-in of the unsupported top surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002693_j.applthermaleng.2014.08.005-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002693_j.applthermaleng.2014.08.005-Figure3-1.png", + "caption": "Fig. 3. 3D finite element model build", + "texts": [ + " The deposit was the solidified form of powderparticles added into themeltpool, so itwasmodeledontopof the heat source to simulate the volume of added powder particles. As the beam moved to a new location after a time t \u00fe dt, the heat flux correspondingly moved to the location Lt \u00fe dt, with vdt being the length of deposited material over the incremental time dt. The analysiswas divided into several steps in order tomove theheatflux from the laser over the nodes in the laser path. In order to predict the temperature distribution of the deposited thin wall in the DLD process, a 3D finite element and meshes were built using Hypermesh software, as shown in Fig. 3. The mesh on the geometry, which represents its discretization into the elemental form, is made of thermal 8-node linear brick type elements. It was generated such that the wall region, where fusion occurs and more severe temperature gradients are expected, was assigned the finest mesh, and regions further from the wall were assigned a relatively coarse mesh [13e16]. The DLD process was simulated using ABAQUS/CAE. The structure of the deposited thinwall in the model was built by depositing multi-layer and single-layer tracks on top of each other with a length of 30mm, total height of 14 mm, and width of 2", + " The influence of the laser parameters on the shape and size of the lasermelting pool was evaluated by specifying the actual power (P), travel speed (v) and beam diameter (Db) as the specific energy (Es) by means of Eq. (5). Fig. 4 illustrates the transient temperature distribution contour plot for the first deposited layer for the case of Q \u00bc 600 W and V\u00bc 300mm/min. The location of the laser beam is evident from the intensity of the temperature distribution, where the maximum contour limit of 1996 C signifies the melt pool. The thermal history was essentially independent of the vertical free edges once the laser reached the center of the wall, where the mesh was highly refined, as shown in Fig. 3, for accurate extraction of the thermal gradient and cooling rate. Fig. 5a and b illustrates the temperature distribution along the deposited layers and substrate simulated using the defined laser parameters. The temperature of each nodal point within the solid Fig. 4. Temperature contours for Q \u00bc was calculated as a function of time. The bottom of the deposited layers cooled faster than the top because of heat conduction to the substrate, while showing significant temperature gradients along the height of the deposited layers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002730_tie.2016.2644598-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002730_tie.2016.2644598-Figure2-1.png", + "caption": "Fig. 2 Geometry of rotor models. (a) Initial model. (b) Equivalent model.", + "texts": [ + " For the paths which are close to bridges, the cross area for leakage fluxes is progressively smaller, which makes the magnetic flux density bigger. Therefore, the permeability of these areas, i.e. the bridges and their neighbors, is very small. Although the permeability of the saturation region varies with position, the error is small. For the sake of simplicity, the rotor is segmented into two pieces: saturation region with a constant permeability and non-saturation region with infinite permeability. Fig. 2 shows the rotor model, where \u03b21 and \u03b22 are the width angle of outer and inner magnetic bridges in the saturation region, respectively. The width angle of the saturation region has great influence on the pole-arc angle. As the leakage fluxes broaden the fan-shaped saturation regions, the incremental length of the saturation regions is almost double the bridge thickness. The equivalent width angle \u03b21 and \u03b22 are considered and obtained by 1 1 2 2 2 2 r m m r m f f R d h R d R R (1) B" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.9-1.png", + "caption": "FIGURE 11.9. A simple pendulum .", + "texts": [ + " We th us have n second order ordi nary differential equations in which ql, qz, q3, .. . , qn are the dep endent vari ab les and t is t he independent variable. The coordinates ql , qz , q3, ' \" , qn are called generalized coordinat es and can be any measurab le parameters to prov ide the configuration of the system. Since the number of equations and the number of dependent variables are equal, the equations are theoreti cally sufficient to determine t he motion of all mi. \u2022 Example 268 A simple pendulum. A pendulum is shown in Figure 11.9. Using x and y for Cartesian posi tion of m , and using 8 = q as the generalized coordinate, we have and therefore, x Y K f(8) = Isin8 g(8) = l cos 8 1 2 2 1 2 \u00b72 - m (x + y ) = - m l 8 2 2 (11.247) (11.248) (11.249) d(OK) o\u00ab d 2' 2 \" dt 00 - 08 = dt (ml 8) = ml 8. The external force compon ents, acting on m, are o mg (11.250) (11.251) (11.252) 482 11. Motion Dynamics and therefore, of og . Fe = Fx oe + Fyoe = -mgl sm e. Hence, the equation of motion for the pendulum is (11.253) ml2e= - m gl sin e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure4-1.png", + "caption": "Fig. 4. For determination of surface \u03a3r: (a) tangent plane \u03a0, (b) surfaces \u03a31 and \u03a32, and (c) surface \u03a3r.", + "texts": [ + " Position vector r1(P) and unit normal n1 (P) are determined in coordinate system S1, rigidly connected to the pinion tooth surface (Fig. 3). (ii) A new reference system Sp is defined as follows (Fig. 3). Origin Op is located at point P. Axis zp results collinear to unit normal n1 (P). Axes xp and yp are collinear to vectors \u2202r1(P)/\u2202 l and \u2202r1(P)/\u2202u, respectively, wherein u and l are the surface parameters for profile and longitudinal directions. Axes xp and yp define a common tangent plane \u03a0 to the pinion and gear tooth surfaces (Fig. 3). (iii) A new surface \u03a3r is formed from pinion and gear tooth surfaces as follows (Fig. 4) (a) A point A on the plane \u03a0 is given in system Sp by vector position rp(A)(x,y) (Fig. 4(a)). (b) Two projections of point A, A1 and A2, on tooth surfaces \u03a31 and \u03a32, respectively, are obtained as (Fig. 4(b)) r A1\u00f0 \u00de p x; y\u00f0 \u00de = r A\u00f0 \u00de p x; y\u00f0 \u00de + \u03bb1 x; y\u00f0 \u00den P\u00f0 \u00de p \u00f01\u00de r A2\u00f0 \u00de p x; y\u00f0 \u00de = r A\u00f0 \u00de p x; y\u00f0 \u00de + \u03bb2 x; y\u00f0 \u00den P\u00f0 \u00de p \u00f02\u00de wherein \u03bb1 and \u03bb2 are scalar coefficients and np (P)=Lp1n1 (P) is the unit normal at the contact point P in system Sp. Here, Lp1 is a matrix 3\u00d73 for coordinate transformation from system S1 to system Sp. Scalar coefficients \u03bb1 and \u03bb2 are determined wherein Ar is a new point that belongs to the new surface \u03a3r. Function (|\u03bb1(x,y)|+|\u03bb2(x,y)|) is designated as h(x,y) for the purpose of simplicity and represents the gap between pinion and gear tooth surfaces when these surfaces are in contact at point P" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003707_j.addma.2020.101265-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003707_j.addma.2020.101265-Figure3-1.png", + "caption": "Fig. 3. (a) Illustration of the process chain and (b) WAAM robot system.", + "texts": [ + " It puts forward an analysis of the waviness and achievable wall thickness in single and double-bead strategies, showing that to achieve a certain wall thickness in ribs, two or more overlapping beads per layer are needed. Moving from a single bead to a double-weld bead strategy is shown to pave the way for creating Eulerian paths from any connected rib-web structure. This forms the basis of the tool path strategy detailed in section 3. The last section presents conclusions of the proposed method and the outlook. All WAAM experiments were conducted on the robot system shown in Fig. 3. A six-axis FANUC welding robot was used, which was synchronized with a two-axis positioner. As power source, a Fronius TPS500i welding system was utilized. To operate the WAAM system, CAM (computer-aided manufacturing) programs are needed. The proposed tool path strategy contains two modules that are the tool path generation and the robot program generation. The tool path generation was developed in the software Rhinoceros\u00ae, which outputs continuous tool paths. The control points (vertices) from these paths are exported to an ASCII file" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000759_s1560354708050079-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000759_s1560354708050079-Figure7-1.png", + "caption": "Fig. 7. Ball with a displaced center on a plane.", + "texts": [ + " As before consider two nonholonomic models of rolling motion: 1) rolling without sliding, dut spinning is allowed (marble ball); 2) both sliding and spinning are prohibited (rubber ball). Assume that there are no external forces. REGULAR AND CHAOTIC DYNAMICS Vol. 13 No. 5 2008 10.1. Marble Ball By analogy with problem on the motion of a Chaplygin ball we write the equations of motion of this system as M\u0307 = M \u00d7 \u03c9 + mr\u0307 \u00d7 (\u03c9 \u00d7 r), r\u0307 = (r \u2212 a) \u00d7 \u03c9, M = I\u03c9 + mr \u00d7 (\u03c9 \u00d7 r), (10.1) where a is the vector from the center of mass to the geometric center, r = \u2212R\u03b3 \u2212 a (Fig. 7), and m is the mass of the ball. The system (10.1) (as any body on an absolutely rough surface) has an energy integral and the geometric integral F1 = \u03b32 = 1, H = 1 2 (M ,\u03c9). (10.2) Besides these (obvious) integrals, the system (10.1) admits one quadratic integral F2 = (M ,M) \u2212 m(r, r)(M ,\u03c9). (10.3) This integral is a generalization of the integral M2 = const in the problem of motion of a Chaplygin ball (Section 7). We see that to achieve integrability by the Euler\u2013Jacobi theorem and additional integral and invariant measure are needed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000549_tfuzz.2010.2051447-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000549_tfuzz.2010.2051447-Figure1-1.png", + "caption": "Fig. 1. TRMS [22].", + "texts": [ + " The dynamics of the TRMS is described in Section II. In Section III, 1063-6706/$26.00 \u00a9 2010 IEEE the pseudodecomposed model of the TRMS is introduced. The FSFISC is designed in Section IV. In Section V, the reaching conditions and the stability of the TRMS with the proposed controller are guaranteed. Section VI presents the simulation results to demonstrate the effectiveness of the FSFISC. Concluding remarks are provided in Section VII. II. MODEL DESCRIPTION OF THE TWIN-ROTOR MULTI-INPUT\u2013MULTI-OUTPUT SYSTEM The nonlinear TRMS, as shown in Fig. 1, primarily comprises the main and tail propellers that are driven by the independent main and tail dc motors, respectively. The propellers are perpendicular to each other and are joined by a beam that can rotate freely on the horizontal plane and on the vertical plane. The pitch (yaw) angle can be adjusted by changing the input voltage of the main (tail) motor to control the rotation speed of the main (tail) propeller. Because of the mutual interference between two propellers, it is not trivial to design an effective controller for the TRMS to reach the desirable yaw and pitch angles", + " 4, it is easy to see that (21) can be simplified as ufsh = 7\u2211 i=1 ghiMhi (\u03c3h) = \u2212 7\u2211 i=1 |ghi | sign (\u03c3h) Mhi (\u03c3h) (22) where sign(\u03b3) = { 1, if \u03b3 > 0 0, if \u03b3 = 0 \u22121, if \u03b3 < 0. Substituting ueqh and ufsh into (16), the output of the FSC is given by uh = ueqh + (Ch2Bh2) \u22121 ufsh = \u2212 (Ch2Bh2) \u22121 [ Ch1 (Ah11eh1 + Ah12eh2) + Ch2 (Ah21eh1 + Ah22eh2) + 7\u2211 i=1 |ghi | sign (\u03c3h) Mhi (\u03c3h) ] . (23) It will be shown in Section V that the sliding mode of TRMSHS with uh in (23) is guaranteed. B. Design of a Fuzzy-Integral-Sliding Controller From Fig. 1, it can be seen that the TRMS weighs asymmetrically, where the main propeller is heavier than the tail propeller, i.e., the pitch angle would not stay in the desired state under the uncontrolled situation. In this case, it is not easy to control the VS of the TRMS to achieve zero position error for the pitch angle by using a simple FSC. In order to eliminate the effect of the asymmetrical weight at ev1 = 0, an FISC is designed in this section. Let a sliding function for the TRMS-VS be \u03c3v = Cv1ev1 + Cv2ev2 + Cv3 \u222b ev1dt (24) where Cv1 = [Cv11 Cv12 ] \u2208 R2 , Cv3 = [Cv31 Cv32 ] \u2208 R2 , with Cvij > 0, i = 1 and 3, j = 1 and 2, and Cv2 > 0 and Cv2 \u2208 R" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001226_cdc.2009.5400466-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001226_cdc.2009.5400466-Figure5-1.png", + "caption": "Fig. 5. 3D Time convergence", + "texts": [], + "surrounding_texts": [ + "In this paper a procedure for constructing a family of quadratic-like Lyapunov functions for the STA has been presented. Surprisingly, the procedure is reduced to the solution of an algebraic Lyapunov equation, as in the LTI case!. It has been shown also that there is a minimal estimation of the convergence time among the Lyapunov functions in the family, and a procedure for obtaining it has been presented in the unperturbed case. For unperturbed case the sufficient conditions are found ensuring that the optimal value is obtained with the Lyapunov function calculated from the algebraic Lyapunov equation with the matrix Q = I, a result expected from the LTI case. The procedure of selection of the Lyapunov function is discussed ensuring the minimal estimation of the convergence time among the proposed functions of the family in the presence of uncertainties." + ] + }, + { + "image_filename": "designv10_3_0001436_j.mechmachtheory.2013.10.014-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001436_j.mechmachtheory.2013.10.014-Figure1-1.png", + "caption": "Fig. 1. A planetary gear set with 4 planets and a sensor mounted on the fixed annulus gear.", + "texts": [ + " The effect of local faults on the sidebands in the measured vibration spectrum picked by a fixed sensor mounted on the annulus gear reveals important frequency features, which can be useful for developing an early detection algorithm of a damaged tooth and diagnosing the source of faults in a planetary gear system. The derived conclusions are validated by both dynamic simulations and experiments on a 750 kW gearbox similar to those installed in wind turbines. The gearbox used for experimental validation had faults in the annulus and sun gears that could be correlated to the dominant vibration response predicted at the frequency components determined by the Fourier series analysis presented in this work. Fig. 1 illustrates a typical equally spaced planetary gear set configuration with 4 planets wherein the sun gear s and the planet carrier c act as the input and output respectively. The ith planet in this gear set is located at angular position \u03c8i \u00bc 2\u03c0 i\u22121\u00f0 \u00de P , where P = number of planets. If P planets rotate counter-clockwise with angular rotation frequencies of \u03c9p, the sun gear s and the carrier cwill rotate clockwise with an angular rotation frequency of\u03c9s and\u03c9c respectively. The annulus gear a is stationary, which implies \u03c9a = 0", + " Therefore, multiple accelerometers can bemounted around the circumference of the gear housing to help improve the monitoring capability. As several identical planets are employed andmultiple teethmesh in a planetary gear set, themesh phasing properties of phasing between the various sun-planet meshes and phasing between the various annulus-planet meshes for general planetary gear sets must be carefully considered to avoid analysis and simulation results' error [17]. Fig. A2 illustrates a scenario that considers the planetary gear set (given by Fig. 1 of the paper) in a rotary reference frame,which has been fixed to the carrier. In this reference frame, the carrier becomes stationary, annulus rotates counter-clockwise with \u2212\u03c9c and the sun gear rotates clockwise with \u03c9s \u2212 \u03c9c. Thus, the vibration contribution from planet i meshing with the annulus gear can be expressed as xi t\u00f0 \u00de \u00bc x t\u2212 \u03c8i \u03c9c \u00f0A7\u00de e vibration contribution from planet i meshing with the sun gear can be represented as xi t\u00f0 \u00de \u00bc x t \u00fe \u03c8i \u03c9s\u2212\u03c9c : \u00f0A8\u00de Fig. A2. (a) Annulus gear meshes with planets in the rotary reference frame, (b) Sun gear meshes with planets in the rotary reference frame" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001796_978-3-319-32156-1-Figure10.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001796_978-3-319-32156-1-Figure10.7-1.png", + "caption": "Fig. 10.7 Recalled GM ignition switch", + "texts": [ + " Design changes and optimizations can occur in each discipline with not full appreciation of the effect on the other. A very good example can be seen in the following case. While there have been many valuable attempts to model mechatronics from a number of different authors, the design and modelling of mechatronics is still a considerable challenge [18]. In product development, an incorrect product integration within a system is clearly seen in the media. For instance, in 2014 the GM ignition switch (see Fig. 10.7) recall was headline news, with record breaking costs/damages to the company of around $1.2 billion involving the recall of 28 million vehicles. The basic failure mode meant that the switch was unable to provide the torque to hold the key in the ON position while the vehicle was running, and in some circumstances the switch would slip from the ON to the (ACC)ESSORY position. The failure to identify and remedy the issues in this case were quite systemic and reported at length by Valukas [19]. First, it is important to point out that this was a component provided to GM by a supplier and which had to fit on multiple GM vehicles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure12.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure12.7-1.png", + "caption": "Figure 12.7.1 Double transverse arms with arm length difference.", + "texts": [ + " The divergence angle is given, approximately, in radians, by uYD \u00bc HBJD RS so the swing arm radius is approximately gB \u00bc 2zS tan 1 2 uYD HBJD zS uYD HBJD Double-Arm Suspensions 231 Substituting for uYD, then gB \u00bc zS RS and the consequent linear bump camber coefficient is \u00abBC1 \u00bc 1 RS uYD HBJD Therefore the linear bump camber coefficient may be adjusted by control of the convergence angle of the arms, or, amounting to the same thing, by the length of the swing arm. If the convergence angle is negative, then the arms converge outwards, the swing arm radius is negative, and the linear bump camber coefficient is positive. For unequal arm angles from horizontal, and small angles, continue to take the difference of the arm angles. In Figure 12.6.1(a), it is apparent that converging the arms will also affect the bump scrub rate (roll centre height), but subsequently thismay be changed independently as desired by adding the same slope to both arms. Figure 12.7.1. It is usual for the upper arm to be the shorter one. Figure 12.7.1(b) shows the bumped position, with associated lateral movement of the ball joints because of the arm inclinations. Then yU \u00bc LYU\u00f01 cos uYU\u00de 232 Suspension Geometry and Computation Approximating the arm angle by uYU \u00bc zS LYU and using cos uYU 1 1 2 u2YU \u00bc 1 z2S 2L2YU then yU \u00bc z2S 2LYU and yL \u00bc z2S 2LYL Consequently, the bump camber angle is gB \u00bc yU yL HBJD \u00bc 1 2HBJD 1 LYU 1 LYL 0 @ 1 Az2S In terms of the arm shortness S\u00bc 1/L, this is gB \u00bc 1 2HBJD \u00f0SYU SYL\u00dez2S Using the arm shortness difference SYD \u00bc SYU SYL the bump camber angle is simply expressed as gB \u00bc SYD 2HBJD z2S Hence, the arm length difference causes a quadratic bump camber coefficient \u00abBC2 \u00bc SYD 2HBJD and the arm length difference may be used to control this aspect of the geometry as required" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000802_j.mechmachtheory.2010.03.010-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000802_j.mechmachtheory.2010.03.010-Figure1-1.png", + "caption": "Fig. 1. Coordinate systems for the universal face-hobbing hypoid gear generator.", + "texts": [ + " The feasibility of this proposed flank modification method is clearly illustrated by a numerical example that uses a Gleason's Triac Formate\u00ae hypoid gear set cut by a Cartesian-type hypoid generator. The numerous different mathematical models proposed for individual simulation of face-milled or face-hobbed hypoid gears, all bound to a specific cutting process, make it difficult to program a universal design and evaluation software for hypoid gears. To resolve this problem, earlier work established a mathematical model of a universal face-hobbing hypoid gear generator for spiral bevel and hypoid gears [9]. As Fig. 1 shows, this machine is a virtual cradle-type machine with a cutter tilt, cradle, and work gear support mechanisms that can simulate existing face-milling and face-hobbing cutting systems with or without AFM motions, including Oerlikon's face-hobbing Spiroflex and Spirac methods, Klingelnber's face-hobbing cyclo-palloid method, and Gleason's face-milling (SGM/SFT/SGDH/HGM/HFT/HGDH) and face-hobbing (Triac) methods. As shown in Fig. 1, the coordinate systems St(xt, yt, and zt) and S1(x1, y1, and z1) are rigidly connected to the cutter head and the work gear, respectively. According to Ref. [9], the transformation matrices St to S1 yield the following surface locus for the cutting tool in coordinate system S1: where r U\u00f0 \u00de 1 u;\u03b2;\u03d5c\u00de = M U\u00f0 \u00de 1f \u03d51\u00de\u22c5M U\u00f0 \u00de fa i;j;\u03b8c;SR;Em;\u0394A;\u0394B;\u03b3m;Ra;\u03d5c\u00de\u22c5M U\u00f0 \u00de at \u03b2\u00f0 \u00de\u22c5rt \u03b10;rc;\u03b1h;\u03b40;r0;\u03b2i;u\u00de\u00f0 \u00f01\u00de M U\u00f0 \u00de 1t \u03d51;\u03b2;\u03d5c\u00f0 \u00de = 1 0 0 0 0 cos \u03d51 sin \u03d51 0 0 sin \u03d51 cos \u03d51 0 0 0 0 1 2 66664 3 77775\u22c5 cos \u03b3m 0 sin \u03b3m \u0394A 0 1 0 0 sin \u03b3m 0 cos \u03b3m 0 0 0 0 1 2 66664 3 77775\u22c5 1 0 0 0 0 1 0 Em 0 0 1 \u0394B 0 0 0 1 2 66664 3 77775 \u00d7 cos \u03b8c + \u03d5c\u00f0 \u00de sin \u03b8c + \u03d5c\u00f0 \u00de 0 0 sin \u03b8c + \u03d5c\u00f0 \u00de cos \u03b8c + \u03d5c\u00f0 \u00de 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775\u22c5 sin j cos j 0 SR cos j sin j 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775 \u00d7 cos i 0 sin i 0 0 1 0 0 sin i 0 cos i 0 0 0 0 1 2 66664 3 77775\u22c5 cos \u03b2 sin \u03b2 0 0 sin \u03b2 cos \u03b2 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775 The newly developed Cartesian-type machines, however, introduce a novel manufacturing method for spiral bevel gears, a sixaxis Cartesian-type structure that produces the minimum sufficient degrees of freedom for the operation of existing spiral bevel gear cutting methods" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003179_tie.2015.2442216-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003179_tie.2015.2442216-Figure3-1.png", + "caption": "Fig. 3. Notional sketch of the planet gearbox structure.", + "texts": [ + " The driving motor is a three-phase 10-hp induction motor with a motor controller. A Hall effect sensor was used as the tachometer paired with a toothed wheel mounted on the motor shaft. The output shaft of the gearbox is connected to a generator and a grid tie to serve as a load generator. The structure of the PGB test rig is similar to those used in a wind turbine. In this paper, the PE strain sensor was glued on the housing of the ring gear, as shown in Fig. 2(c), and a commercially available single-stage PGB with a 5:1 speed reduction ratio was used. In Fig. 3, a notional sketch of the PGB structure is provided. Among the three different PGB types, a specific PGB with standstill ring gear was used in this paper. For this type PGB, the number of teeth is linear to the radius of each gear pitch circle. This indicates that the gear ratio is also related to the angular velocity (\u03c9) of the gears. The gear ratio can be defined as R = \u03c91 \u03c9A = 1 + z3 z1 (4) where \u03c9i is the angular velocity of the ith gear component; zi is the number of teeth on the ith gear component; and gear component index subscripts 1, 2, 3, and A correspond to sun gear, planet gear, ring gear, and arm (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000132_1.1691433-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000132_1.1691433-Figure4-1.png", + "caption": "Fig. 4 Illustration of sliding distance of a point ap on gear p at different positions r", + "texts": [ + " The sliding distance (si j k )r\u2192r11 p ,g is defined as the distance by which a point represented by node ij on one gear slides with respect to its corresponding point on the mating gear as gears rotate from position r to position r11 after k th geometry update. Consider a fixed point ap on the active tooth surface of gear p. Assume that the leading edge of contact reaches the point at a particular rotational position r5m and contact zone passes through the point ap in following incremental rotations. The sliding distance calculation becomes a matter of tracking the relative position of this point with respect to its mating point on the other gear. Focusing in the circled contact zone shown in Fig. 4~a! in the transverse plane of gears, Fig. 4~b! shows the start of wear cycle of a given point ap at node ij on gear p as well as its mating point ag on gear g. At this rotational position r5m , both ap and ag are at the leading edge of the 600 \u00d5 Vol. 126, JULY 2004 rom: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Term contact zone, experiencing a nonzero pressure for the first time since the beginning of loading cycle. Position vector of point ap that lies on node ij of the fixed surface grid on gear p can be written as ~Xap", + "r5m p 5@xi j , yi j , zi j#r5m p (8) Since points ap and ag overlap in space at position r5m , the position vector of point ag on the mating gear will be the same as that of point ap ~Xag!r5m g 5~Xap!r5m p (9) When the gears are rotated by one incremental rotation to position to r5m11, point ap rotates about the center Op of gear p. If one incremental rotation of gear p amounts to angle Dup, the position vector of ap at r5m11 is given simply by a coordinate rotation transformation ~Xap!r5m11 p 5F cos Dup sin Dup 0 2sin Dup cos Dup 0 0 0 1 G ~Xap!r5m p (10) As illustrated in Fig. 4~c! at position r5m11, point ag on gear g no longer overlaps with point ap on gear p as gear g rotates about its center Og. Position vector of point ag can be obtained by first translating the coordinate frame from Op to Og ~see Fig. 4!, then rotating it by Dug, and finally translating it back to Op where Dug52(Zp/Zg)Dup. Here, Zp and Zg are the number of teeth of gears p and g, respectively. Accordingly, the position vector of point ag on gear g at position r5m11 is given by ~Xag!r5m11 g 5F cos Dug sin Dug 0 2sin Dug cos Dug 0 0 0 1 G H ~Xag!r5m g 1F 0 2E 0 G J 1F 0 E 0 G (11) where E is the center distance. Thus, relative sliding distance of point ap defined on a fixed grid node ij on gear p while moving from position r5m to r5m11 is given by ~sap k !m\u2192m11 p 5i~Xag!r5m11 g 2~Xap!r5m11 p i (12) In order to generalize the above equation, consider the contact zone at the next position r5m12 as shown in Fig. 4~d!. Here, as gears rotate more the points of interest ap and ag move further away from each other. Relative sliding distance increment as gears rotate from position r5m11 to r5m12 is equal to the distance between ap and ag minus (sap k )m\u2192m11 p . If point ap enters the contact zone at position r5m and remains within contact zone until position r5t , the sliding distance that occurs when gears rotate from any position r to r11 can be given in general terms as ~sap k !r\u2192r11 p 55 UI ~Xag!r11 g 2~Xap" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000320_ip-b.1988.0042-Figure49-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000320_ip-b.1988.0042-Figure49-1.png", + "caption": "Fig. 49 Cross-section through running gear and vehicle of M-Bahn 1 = Guideway cross-section", + "texts": [], + "surrounding_texts": [ + "The rectified output of the pole-face generator winding supplies a 440 V battery required for low speed operation. At a velocity of 110 km/h the generator is capable of supplying all on-board requirements, and above this speed the batteries are recharged.\nTable 11 gives some basic data of the Transrapid 06. Initial tests have been performed using sections 11 to 57 (Fig. 39) which were the first to be built. Figs. 45 and 46 show some of the characteristics during acceleration to 355 km/h. F, in these Figures is the load force including gradients, windage and drag force. The discontinuity at DT/SB on Fig. 45 is due to the change from direct inverter supply to sypply via the output transformers. Evaluation of these graphs shows the following performance data:\nMaximum motor active power 11.5 MW Maximum motor apparent power 15 MVA Power factor 300 km/h constant) 0.6-0.9* Efficiency (300 km/h constant) 0.8-0.95* Acceleration distance up to 355 km/h 8980 m Maximum acceleration 0.85 m/s Mean acceleration 0.6 m/s\nAt a steady running speed of 245 km/h, the following performance is given:\nMotor active power 2.1 MW Motor apparent power 2.2 MW Power Factor 0.95 Overall efficiency (including feeder cables) 0.8\nThe complexity of the above system is considerable, and it is an excellent engineering achievement to have obtained the results above. The main future objectives are to achieve the top design speed of 400 km/h after commissioning the southern reversing loop, and to then sell the technology in the high-speed transport market, competing with both aircraft and high-speed wheel-onrail systems.\nA comparison of the Transrapid system with high speed wheel on rail and aircraft is presented in a paper by Hessler and Wackers [45]. Fig. 47, taken from this paper, is a graph of average door-to-door speed versus straight line distance of travel, and shows that the Transrapid is faster than either an aeroplane or high speed wheel-onrail (TGV) up to a distance of 700 km. From the same paper, Table 12 gives the relative cost/km for guideway control, guideway installations (stators and reaction rails) and power supply costs. The civil engineering costs, at 1986 prices, for the guideway shell is larger by about 500% than the guideway installations or power supplies.\n* Depending on the length of the motor feeder section\nIEE PROCEEDINGS, Vol. 135, Pt. B, No. 6, NOVEMBER 1988\nThese installation costs are claimed by Blumstein and Brand [50] of TGV Ltd., (the French high-speed wheel\n- 400km/h\ngradient 35%\nO_JL - I 1200A\n* \\\n1200A\nDTj SB\nx\nIi q o DO\n12OOA t r-innnnnnnnnnnnnn 24 28 32 36\n12 14 16 18 20 22 26 30 34 38 42~ motor sections", + "on rail system) to be 50% higher than a wheel-on-rail system for top speeds of 240 km/h respectively (compared with 400 km/h for Transrapid).\n* = 200 km between stops\nDoor-to-door travelling speeds of different transportation\nFuture developments [46] will include changes in the power supply to the stator sections, using either a series connection and/or a staggered switch-over, to eliminate the need for two sets of inverters at each inverter station. The series connection involves connection of the incoming section in series with the outgoing one across the single inverter. This changeover would result in half the inverter voltage across each section during the time which the vehicle straddles both sections. The staggered arrangement arranges the left and right winding junction points to be at different points along the guideway as shown in Fig. 48.\nFor long guideways, several substations are used along its length (these are required no matter which of the above systems is used). Proposed routes using Transrapid have maximum substation intervals of 30 km [45, 46] in their design. Further design aspects under consideration are concerned with cabin noise and ride comfort. Peak to peak vertical passenger acceleration of 1.3 m/s2 have been measured on the Emsland test track and it is stated that this rather high value for passenger comfort could be improved by reducing friction in the combined rollstabilisation secondary suspension. Noise levels in the cabin at low speeds were measured at 57 dbA and increased up to about 80 dbA at 355 km/h [51]. External noise measurement at 25 m from the guideway for the TR 06 vehicle has been measured at between 73 dbA at 100 km/h and 88 km/h at 250 km/h. Improvements to the rough surfaces of the undercarriage and general aerodynamics shape are being considered, and it is thought possible that relatively simple changes to the cabin floor will improve cabin noise.\n3.5 M-Bahn System An interesting variant of active track linear synchronous motor transport known as the M-Bahn has been developed and built in West Germany. Figs. 49 and 50 shows the arrangement. Magnetbahn Gmbh started development of the M-Bahn in 1973, and has been funded by the Federal German ministry of research and technology since 1975. A test facility exists at Braunschweig University and a track for public service has been constructed in Berlin. Vehicle length is 12 m, and width is 2.3 m, with a capacity for 80 passengers (peak 132), and maximum gross weight of 17800 kg.\n2 = Emergency escape path 3 = Switch guidance wheels 4 = Vertical guide wheels 5 = Permanent magnets 6 = Travelling field stator 7 = Horizontal guide wheels 8 = Vertical guide wheels 9 = Primary suspension/airgap control 10 = Secondary suspension/airspring\n398 IEE PROCEEDINGS, Vol. 135, Pt. B, No. 6, NOVEMBER 1988", + "Two 3-phase stator windings in laminated steel cores are positioned down each side of the guideway with the\nFig. 50 M-Bahn: underneath view of vehicle\nactive surfaces facing downwards. Permanent magnet poles on the vehicle bogies are attracted upwards to the stator core and are coupled by an ingenious mechanical lever and spring suspension to lightweight wheels resting on the top and bottom surfaces of the guideway. These wheels act as a reference for the suspension and as the pay load varies, the magnetic gap is changed by the action of the lever system to vary from 15 mm at maximum load to 25 mm at minimum load. The majority of the vehicle weight is supported by the magnetic field in the airgaps of the synchronous motor with enough pressure between the guideway and guide wheels to control the motor airgaps within the above limits. The attractive force between stator and secondary magnets is therefore used to both levitate and propel the vehicle. The vehicles weight is claimed to be less than 50% [52] of a conventional steel wheel on steel rail vehicle with heavy bogies, motors, alternators and control equipment on board.\nThe price paid for this decrease in vehicle weight is the active track, which must be supplied from variable frequency inverters at regular intervals. Secondary position is calculated from the emf induced in the stator windings by the permanent magnets and the inverters are synchronised to this signal. At low speeds, AC signals from antennae installed between the poles are used to determine pole position. Stator sections of between 40 and 200 m are supplied in sequence as the vehicle moves along the guideway. A DC supply is connected to inverters spaced several kilometres apart, their output being connected to sections via switches. The number of inverters depends on the number of trains travelling independently of one another. Switching of the inverters from one section to another occurs when the midpoint of the train passes the junction between those sections. Frequencies up to 100 Hz are used and regenerative braking can be achieved through the inverters.\nLittle information has been published on the performance of the system but Reference 52 gives measured energy consumption figures of 1.0 kWh/vehicle mile with an acceleration capability of 1.3 m/s2.\n3.6 Superconducting systems Superconducting magnets for both levitation and synchronous motor poles have the advantage of being able to operate at large airgaps, suitable for high speed Maglev transport systems. Japanese National Railways has built a test track for such vehicles with vehicle mounted superconducting magnets, and Canadian design\nIEE PROCEEDINGS, Vol. 135, Pt. B, No. 6, NOVEMBER 1988\nstudies have been undertaken for a traffic corridor between Toronto and Montreal. The cryogenic equipment is obviously a disadvantage from a financial and reliability consideration, but recent inventions of ceramic superconductors capable of operating at liquid nitrogen temperatures and above will obviously give this type of motor a renewed attraction.\n3.6.1 Japanese MLU001: Japanese National Railways have for some time been developing a high speed Maglev train employing an active track linear synchronous motor with superconducting poles on the vehicle. Levitation is provided above a lift off speed by superconducting magnets reacting with a set of short circuit coils on the track in the electrodynamic principle (EDS). Currents induced in these coils act to repel the vehicle mounted lift magnets.\nA test track at Miyazaki has been in operation for several years. The first system used a 13.5 mile long inverted T guideway with a 10 tonne test vehicle (ML 500) and a speed of 517 km/h was achieved in 1979. The second system [53] (MLU001) uses a U shaped guideway and a three sectional vehicle as shown in Figs 51, 52, 53 and 54.\nFig. 51 MLU001 three-unit train" + ] + }, + { + "image_filename": "designv10_3_0003721_s11665-020-05125-w-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003721_s11665-020-05125-w-Figure13-1.png", + "caption": "Fig. 13 Acoustic monitoring array design including a) posts for clearance to allow for sensor array (FRONT view), b) transducer arrangement including transducer 4 attached directly to the build plate (TOP view), c) detail drawing showing the transducer mounting plate, transducers, and posts for temperature mitigation, and d) the array attached to the underside of the build plate. Arrows indicate the direction of the front of the assembly in all plots (Ref 17)", + "texts": [ + " (Ref 16) used the AE sensor which could eliminate background noise and was attached to the side surface of the extruder and connected to a preamplifier, and data acquisition device (Ref 59). In a study by Koester et al. (Ref 17) where titanium alloy (Ti-6Al-4V) was deposited by a direct energy deposition (DED) system, an array of acoustic sensors (commercial sensors; digital wave, B1025-MAE) was installed below the baseplate with a customized arrangement. High-temperature ultrasonic couplant was used to keep the transducers in an acceptable temperature range, and the data were collected in five different building conditions (Ref 17). The setup is shown in Fig. 13. During defect monitoring of laser metal deposition (LMD) by Gaja and Liou (Ref 18), distinguishing the type of defects in the LMD process has been done by the clustering of AE signals. Corrective action could be done, such as machining and remitting, based on the results. Also, a classification method for analyzing AE was used for the identification of defects based on types of defects. AE sensors were connected to a substrate for recording the signals. These sensors were used for capturing AE signals and then transferring them to the computer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure5.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure5.9-1.png", + "caption": "Fig. 5.9 Milk centrifuge; a) Drawing; 1 Inlet device, 2 Drum cover, 3 Drum, 4 Frame, 5 Neck bearing, 6 Mandril, 7 Footstep bearing; b) Calculation model", + "texts": [ + " The shaft rotates in bent condition and is under a quasi-static load. It is important for the strength calculation of such rotating shafts that no reversed bending occurs and thus no material damping by the shaft is acting. Figure 5.2 shows that the shaft centers itself at high rotating speeds. The disk rotates about its axis through the center of gravity at speeds above the critical (\u03a9 \u03c91). This fact is utilized in centrifuges and other machines in which balancing is not an option due to the eccentric stock (Fig. 5.9). The system is tuned to run above the critical speed using soft springs in neck bearings. The disk rotates about its axis through the center of gravity, i. e. the springs in the neck bearings are deflected at the rotational frequency by the magnitude of eccentricity and apply a corresponding force to the frame. It is considerably smaller for a soft neck bearing than the respective unbalancing force that would occur with a rigid bearing. Many drives are operated at speeds above the critical, i.e", + " In the case of bending oscillators, the natural frequencies and mode shapes are calculated based on the influence coefficients. Table 5.1 lists the influence coefficients for shafts in two bearings, taking into account the bearing elasticity. Rigid support results as a special case (1/c1 = 0 or 1/c2 = 0, respectively). Case 4 in Table 5.1 takes into account that the rotor-shaft joint does not coincide with the center of gravity of the rotor, as is the case, for example, for centrifuge drums and mandrils. The milk centrifuge shown in Fig. 5.9 is used to separate liquids. The elastic neck bearing was introduced in 1889 for steam turbines, textile mandrils, and centrifuges after realizing that supercritical operation is feasible and beneficial. Questions relating to the set-up and sizing of mandril, neck bearing, and drum play an essential part in the optimal sizing of the design. The shaft can be considered perfectly rigid and massless (bearing stiffness bending stiffness, shaft mass rotor mass). The minimal model is a hinged rigid body with a single elastic isotropic bearing, see Fig. 5.9b. If the rotor is displaced from its static equilibrium position at \u03c8x = \u03c8y = 0, the forces and moments shown in Fig. 5.10 occur due to inertia, see Fig. 5.4. The positive directions of the small angles \u03c8x and \u03c8y have been specified here so that the respective angular velocities point in the positive axis directions (right-hand system). The force components shown represent \u2022 the restoring forces of the elastic bearing (cl\u03c8x, cl\u03c8y) \u2022 the inertia forces from translating the center of gravity (mL\u03c8\u0308x, mL\u03c8\u0308y) that should be plotted in opposite direction of the positive coordinate direction 5", + "57) there are a \u201cpositive\u201d and a \u201cnegative natural circular frequency\u201d since the root expression is larger than the first summand. If one inserts the negative root in (5.54), one will see that it corresponds to another direction of rotation (\u201copposite direction of rotation\u201d: rotation of the rotor in opposite direction of 332 5 Bending Oscillators the vibration direction) than the positive root (\u201csame direction of rotation\u201d: rotation of the rotor in the same direction as the vibration direction). For the milk centrifuge shown in Fig. 5.9a, the speed-dependent natural frequencies shown in Fig. 5.12 were calculated using the model from Table 5.1, Case 4. This model with four degrees of freedom has four natural frequencies. The intersection of the straight line ni with the curve n2 provides the critical speed of synchronous rotation in the opposite direction that is generated in the event of unbalance excitation. Curves n1 and n3 correspond to the mode shapes of rotation in opposite direction. However, not all dynamic phenomena found in experiments on such centrifuges can be explained with this simple model" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003775_j.ijheatmasstransfer.2018.04.092-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003775_j.ijheatmasstransfer.2018.04.092-Figure4-1.png", + "caption": "Fig. 4. Three dimensional of (a) temperature isoterms (b) velocity field and (c) mixing phenomena (iron mixture) in the weld pool of case 1.", + "texts": [ + " The achieved nodes displacements are linearly extruded to top surface of the 3D computational domain using deformed geometry interface. Finally, half of the computational domains is taken account due to symmetry. To verify the numerical results, three bead-on-plate depositions are performed using the GTA-CWT welding parameters shown in Table 4. The effects of change in travel speed and wire feed rate on the mixing process are investigated. A three-dimensional view of the numerical prediction of the temperature field, velocity field and mass distribution for case 1 is shown in Fig. 4. In Fig. 4a, the arc travel speed causes compressed isotherms at front of the WP and expanded isotherms behind the WP. In cold wire feeding, the droplet temperature is lower than the pool temperature. The isotherms are affected by the cold droplet contact with the hot molten pool surface at the front part of the WP. The free surface of the weld is deformed under arc pressure while solidified zone is elevated due to wire material addition as shown in Fig. 4a. The mushy zone is also visible along the fusion boundary. The three-dimensional velocity field is illustrated in Fig. 4b. It shows that the two toroidal vortices within the flow; around the wire inlet the surface flow is toward the wire. This flow pushes the molten wire material downward into the WP. The wire material is then circulated toward the top surface of the WP in the upwelling region that separates this secondary vortex from the primary vortex flow field that dominates the back of the WP. Subsequently, this strong vortex creates a well-mixed region at rear of the WP which is solidified as the clad layer shown in Fig. 4c. The velocity fields for the three cases examined are described in more detail in the next section. The velocity field of case 1 is presented in Fig. 5. The color bar indicates the velocity magnitude in m/s. The normalized arrows in this figure show the planar direction of the flow fluid. The length of the WP (x-direction) is about 6.9 mm and the half width (ydirection) is 2.5 mm. The molten metal circulates in the WP within the two opposing toroidal vortices. Fig. 5a shows the velocity field on the top surface of the WP", + " This vortex is developed around the wire inlet due to the thermal gradient that occurs in CWT. A part of this vortex is visible as a counterclockwise (CCW) vortex just after wire inlet in center of the WP in Fig. 5b. It circulates the metal in the WP from middle of the pool toward the molten wire inlet. This vortex is smaller in cross section at front side of the WP. The depth of the WP below the wire inlet is affected by heat absorption from filler wire as shown in Fig. 5b. Over all, the molten metal circulates from the front part of the pool to the rear part as shown in Fig. 4b. The effect of flow circulation on mass distribution is illustrated in Fig. 4c. The molten clad flow begins to mix with the substrate just under the wire inlet. The mixture of the solidified clad layer is made up of about 70% of the wire material and about 30% of the substrate material (this mixture of the cladding is about the same for cases 2 and 3 as well). Hence, the solidified clad layer is the result of an additive layer materials process. Fig. 6 illustrates the velocity field of case 2. The fluid flow is similar to case 1 as illustrated by the free-surface flow. The length and half width of the WP is essentially the same as predicted for case 1 because the amount of heat input is equal in both cases", + " The maximum temperature of heat affected zone (2 mm from the weld boundary) on top surface (Fig. 9 a and c) is elevated from 600 C to 850 C with decrease of the travel speed from 4 mm/s to 3 mm/s. The deviation of numerical temperatures at bottom surfaces is in result of the coarse mesh used in the solid domain (see Fig. 9 b and d). To study the mass transport in the cold wire feed cladding, three major chemical elements, viz., iron (Fe), nickel (Ni) and chromium (Cr), are the only constituents considered. Fig. 4c shows a three-dimensional view of Fe distribution with the filler wire immersed in the WP in case 1. The black line illustrates the fusion boundary between solid and liquid. The concentration of Fe in the substrate and wire are assumed to be 78 wt% and 20 wt%, respectively. It is observed that the filler wire is a significant part of the mixture with the substrate at rear part of the WP. Fig. 10 represents the distribution of the element Fe, Ni and Cr in the solidified WZs at yz-plane. This plane is located just behind the weld pool where the material is in the solid phase" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure8.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure8.1-1.png", + "caption": "FIGURE 8.1. A planar polar manipulator .", + "texts": [ + "32) This prob lem is solved by finding the 6 x n transformation matrix J (q) where n is the number of joint variables. The matrix J (q) is called Jacobian. It is possible to break the forward velocity problem into two sub problems to find the t ranslation and angular velocities of the end frame independently. (8.33) (8.34) X= [ ~Vn ] = [ J D ] q = J q W n J R (8.35) 8. Velocity Kinematics 347 From t he forwar d kinematics we know that 0Tn(q) = [ O~n O~n ] and t herefo re, J (q) = 8T (q) 8q (8.36) (8.37) Example 211 Jacobian matrix for a planar polar manipulator. Figure 8.1 illustrates a planar polar manipulator with the following for ward kinematics. \u00b0T2 = \u00bbr, lT2 [ cosO - sin () 0 ~ ][ ~ 0 0 ~ ] sin () cos () 0 1 0 0 0 1 0 1 0 0 0 0 0 [ NS O - sin () 0 rcoo O ] sin e cos () 0 r sin () (8.38) 0 0 1 0 0 0 0 1 The tip point of the manipulator is at [ X ] =[ r C?S e ] (8.39)Y rsm () and therefore, its velocity is [ ~] =[ C?S () - r sin () ] [ ~ ] (8.40 )Y sm() r cos () () 348 8. Velocity Kinematics which shows that J = [ cos 8 - r sin 8 ] D sin 8 r cos 8 . (8.41) Example 212 Jacobian matrix for the 2R planar manipulator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002005_j.ijfatigue.2014.01.029-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002005_j.ijfatigue.2014.01.029-Figure1-1.png", + "caption": "Fig. 1. Schematic of the RCF ball-on-rod test.", + "texts": [ + " The present manuscript is structured as follows: Section 2 describes the ball-on-rod RCF test and microstructural details of the case-hardened bearing steel used in FE simulations. Section 3 presents the constitutive model used for bearing steel and details of the FE model. The primary observations from FE simulations and the origin of ratcheting phenomenon in the vicinity of a single carbide particle are discussed in Section 4. The manuscript is concluded with an investigation of the ratcheting behavior at various orientations around the carbide particle. In order to study the response of bearing steels to RCF, an accelerated ball-on-rod test is widely used [30\u201332]. Fig. 1 shows a schematic of the test setup. The test specimen is a cylindrical bearing steel rod (of M50, M50-NiL, P675, etc.) supported and radially loaded by three silicon nitride (Si3N4) balls [30\u201332]. The radial load can be varied to control the maximum Hertzian stress induced between the ball-rod contact area. The rod diameter is 9.5 mm (3/8 in.) while the balls are 12.7 mm (1/2 in.) in diameter. The test-rod is driven by an electric motor at 3600 rpm such that roughly 8600 RCF cycles are accumulated per minute during the test [30]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002823_s11071-017-3451-z-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002823_s11071-017-3451-z-Figure1-1.png", + "caption": "Fig. 1 Quadrotor aircraft concept", + "texts": [ + " 4, a novel adaptive and robust control scheme is proposed to cope with input saturation and parameter uncertainties. In Sect. 5, simulation results are provided to demonstrate the effectiveness and robustness of the proposed methods for sys- tems with input saturation and sustained disturbances. Finally, the conclusions of this paper are drawn in Sect. 6. In this section, position coordinate is selected to describe the motion situations of the quadrotor model. This kind of aircraft system can be modeled by Euler formalism. As depicted in Fig. 1, a quadrotor is a cross rigid frame with four rotors to generate the driving forces, where \u03a9i denotes the angle velocity of the i th propeller. Based on the simplified rotor model, we can use rotational speed vector \u03a9 \u2208 R4 to obtain a mapped control inputs uT , u\u03c6 , u\u03b8 and u\u03c8 , defined as [27] \u23a7 \u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 uT = b 4\u2211 i=1 \u03a92 i u\u03c6 = lb(\u03a92 1 \u2212 \u03a92 3 ) u\u03b8 = lb(\u03a92 2 \u2212 \u03a92 4 ) u\u03c8 = \u03ba(\u2212\u03a92 1 + \u03a92 2 \u2212 \u03a92 3 + \u03a92 4 ), (1) where uT \u2208 R is thrustmagnitude, u\u03c6 , u\u03b8 and u\u03c8 represent roll, pitch and yawmoments, l denotes the distance from the mass center to each rotor, \u03ba > 0 and b > 0 are thrust and drag coefficients, respectively. Finally, the thrust magnitude uT and three rotational moments u\u03c6 , u\u03b8 and u\u03c8 are considered as the real control inputs to the dynamical system. Let B = [Bx , By, Bz] be the body fixed frame shown in Fig. 1, and denote E = [Ex , Ey, Ez] an earth fixed inertial frame.Define the vector [p, q, r ]T to represent the quadrotor\u2019s angular velocity in the body frame. A quadrotor system has six state variables, three translational motions \u03be = [x, y, z]T and three rotational motions \u03b7 = [\u03c6, \u03b8, \u03c8]T. The orientation of the quadrotor from the inertial frame to the body fixed frame can be obtained via three successive rotations about the three axes, and the transformation matrix from [p, q, r ]T to [\u03c6, \u03b8, \u03c8]T is given by [28] \u23a1 \u23a3 \u03c6\u0307 \u03b8\u0307 \u03c8\u0307 \u23a4 \u23a6 = \u23a1 \u23a3 1 sin\u03c6tan\u03b8 cos\u03c6tan\u03b8 0 cos\u03c6 \u2212sin\u03c6 0 sin\u03c6sec\u03b8 cos\u03c6sec\u03b8 \u23a4 \u23a6 \u23a1 \u23a3 p q r \u23a4 \u23a6 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001245_tac.2012.2223351-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001245_tac.2012.2223351-Figure4-1.png", + "caption": "Fig. 4. (a) Bouncing ball system (21). (b) Sets", + "texts": [ + " The Lyapunov function decreases monotonically to zero during flow, and, after the first jump, is not affected by jumps of the hybrid system. After the first hysteretic reset, the control feedback action , i.e., , is always negative, such that the plant trajectory \u201cwaits\u201d for the reference trajectory, as explained using the analogy between system (1) and a clock hand. The tracking error evaluated in , depicted in Fig. 3(d), does not display the \u201cpeaking\u201d of the Euclidean tracking error of these trajectories, shown in Fig. 1. We consider the bouncing trajectories of a ball on a table, see Fig. 4(a), as an elementary though representative model in for two points and , where is given in (22). the class of hybrid models for mechanical systems with impacts. Assuming that non-impulsive forces can be applied on the ball with unit mass, the flow of the system is described by (19a) where contains the vertical position and velocity of the ball, respectively, is the gravitational acceleration, is a force that can be applied to the system, and the contact force between the ball and the table, with , for , and , for , avoids penetration of the table by the ball, cf", + " To distinguish when the distance or should be considered, we use the minimum of both, such that the novel distance measure is given by (22) To recognize that this distance function satisfies the conditions posed in Definition 1, first, note that , such that when , implying that , such that is equivalent to . Since for , the condition can be rewritten to , such that directly follows and relation (6a) is satisfied. As required in (6b), for given , the set is compact, as it is the union of the bounded sets and . Since for , relation (6c) holds, as , which equals . An analogue argument shows that (6d) holds. Since, in addition, is continuous, the tracking error measure is compatible with the hybrid system (19). In Fig. 4(b), the neighborhoods of two different points , are shown. Essentially, the tracking error measure allows to compare a reference trajectory with a plant trajectory, \u201cas if\u201d both of them already jumped. For example, in Fig. 4(b), the gray domain with positive is considered close to , since will experience a jump soon, and after this jump, will arrive in this domain. We design a tracking control law for system (21) using a reasoning that exploits the design of the tracking error measure in (22). Analogously to the design approach in the previous section, observe that in (22) is given by the minimum between the two functions, and . When the trajectory is sufficiently close to and neither of them experiences a jump in the near future or past, then the tracking error given in (22) is given by " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003816_j.ymssp.2020.106903-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003816_j.ymssp.2020.106903-Figure4-1.png", + "caption": "Fig. 4. The Model of Bearing Chock.", + "texts": [ + " Since only the rotation around the axis of cage is considered and the tilt and skew are ignored, the differential equation of cage rotating around the centroid is: Icx _xc \u00bc Mrc \u00feMbc \u00f022\u00de where Mrc and Mbc represent the moment between cage/guiding raceway and roller/cage, respectively; Icx is the moment of inertia of cage, xc is the angular velocity of cage. The inner raceway is fixed with rotor, and the angular velocity is constant. So only the translation of inner raceway centroid is calculated here, it can be described in inertial frame as: min\u20acyin \u00bc Fcry \u00fe Fbryi min\u20aczin \u00bc Fcrz \u00fe Fbrzi \u00f023\u00de where Fcry and Fcrz represent the two components of resultant force between cage and inner raceway in the inner raceway guiding mode; Fbryi and Fbrzi are components of resultant force between roller and inner raceway; min is the weight of inner raceway. As Fig. 4, assuming that the outer raceway is fixed in bearing chock with no rotation. In order to study the vibration response, two translation freedoms are added to bearing chock to simulate the measure results of acceleration sensors. The dynamic equations of bearing chock can be shown as: mh\u20acyh \u00fe cy _yh \u00fe kyyh \u00bc Fhy mh\u20aczh \u00fe cz _zh \u00fe kzzh \u00bc Fhz \u00f024\u00de where Fhy and Fhz are horizontal and vertical loads acting on the bearing chock; mh is the weight of outer raceway; \u20acyh and \u20aczh are the accelerations of bearing chock on axes OiYi and OiZi in inertial frame; _yh and _zh are velocities of bearing chock in corresponding directions; yh and zh are displacements in the same directions as above; cy and cz are damping coefficients; ky and kz are stiffness coefficients" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.29-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.29-1.png", + "caption": "Fig. 6.29 Forced mode shapes of a beam (s = 3) at times tk = (k \u2212 3)T/4 for k = 1 to 5; a) Undamped, b) Damped", + "texts": [ + " The dynamic compliances do not become zero for the damped oscillator at any excitation frequency, i. e., the amplitudes have finite values at the resonance points as well. The forced mode shapes, which result from the totality of the coordinates qk, have no fixed nodes for the damped oscillator, unlike the undamped oscillator. One can recognize that since all phase angles are the same for the undamped oscillator, see (6.288) and Fig. 6.24, but they are of different magnitude for the damped oscillator. Figure 6.29 illustrates this fact using a simple example. It shows the synchronously changing deflections for an undamped bending oscillator as compared to a damped bending oscillator during half a period of the forced oscillation (0 < t < \u03c0/\u03a9 = T/2). The graphic representation of a complex frequency response Hlk(j\u03a9) provides an planar curve called locus, see Fig. 6.30c. It contains important information about the behavior of an oscillator. 6.6 Damped Vibrations 451 Loci are commonly used in aircraft design, machine design, rotor dynamics and other fields", + " The motion is approximately proportional to the ith mode shape: qk(t) \u2248 vkivsiF\u0302sm sin (m\u03a9t + \u03b1im) 2\u03b3iDi \u223c vki sin (\u03c90it + \u03c8km) . (6.364) (6.364) can also be used for the case of higher-order resonance to estimate velocities, accelerations, forces, moments and other mechanical parameters. Note that the phase angles for coordinates qk differ from each other, see (6.362). The forced mode 454 6 Linear Oscillators with Multiple Degrees of Freedom shapes do not have fixed nodes for damped oscillators, even in the case of resonance, see also Fig. 6.29b. A typical resonance curve is shown in Fig. 6.31b. It is not identical with an amplitude frequency response, since it represents the amount of the maximum value of a coordinate qk that results from multiple harmonics that do not all reach their maximum at the same time, see (6.362). There are, however, resonance peaks at points that satisfy the condition (6.363), that is, at integral fractions of natural frequencies (i. e. if \u03a9 = \u03c9i/m). Compare in this respect Figs. 3.5, 4.22, 4.23, 4.31, and 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003945_j.addma.2019.05.012-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003945_j.addma.2019.05.012-Figure2-1.png", + "caption": "Fig. 2. Scheme of the scan pattern with multiple contour lines followed by inner bidirectional scanning.", + "texts": [ + " To reduce the field of influencing factors, state of the art scan strategies were used with a contour-hatch strategy in a bidirectional hatching pattern on a SLM\u00ae280 machine by SLM Solutions. The manufacturing of the samples was under argon atmosphere. Cubes of 10\u00d710\u00d710 mm edge length were produced with an Yb:YAG fiber laser featuring a maximum beam energy of 400 W with a focus diameter of 80 \u03bcm at a wave length of 1030 nm. The layer height was set to 30 \u03bcm and the orientation of the hatching is rotated by 67\u00b0 per layer. A schematic diagram regarding the scan strategy is given in Fig. 2. As the powder fabrication is time consuming and the percentage of usable powder particles after production is low, the decision was made to use a horizontal buildup of the tensile specimens, even though it is known that this can lead to higher residual stress and bending of the specimens. A preheating of the base plate was set to 200 \u00b0C in order to reduce possible cracks due to the martensitic transformation. As an initial starting point the work from [9] was taken into account. We selected a region of interest (ROI) in the parameter space with hatch distances H=100/120/140 \u03bcm, laser powers PL=275/ 325/375 W and scan speed =v 550\u2013950 mm/s in steps of 50 mm/s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure7.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure7.3-1.png", + "caption": "Fig. 7.3 Calculation model of an oscillating conveyor in displaced position", + "texts": [ + " The resonance range is very narrow when using a linear spring. The resonance range of linear oscillators is highly sensitive to variations in the parameter values (load, excitation frequency, spring stiffnesses). 7.2 Nonlinear Oscillators 477 The amplitudes would change considerably for small parameter changes and the conveyor would not work reliably. It is therefore advantageous and common for robust operation to use nonlinear spring systems (with stepped springs) to achieve large amplitudes over a wide range of frequency ratios. Figure 7.3 shows a lever-guided oscillating conveyor, that is driven by a slider crank (l3 l2) with an elastic push rod. The calculation model, which actually has 12 degrees of freedom due to the two coupled rigid bodies, is simplified to a model with 3 degrees of freedom using the following assumptions: 478 7 Simple Nonlinear and Self-Excited Oscillators \u2022 Symmetry with respect to the drawing plane is assumed. \u2022 The tilting motion is neglected (since it is not excited). \u2022 The direction of thrust is perpendicular to the direction of motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001216_tro.2011.2168170-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001216_tro.2011.2168170-Figure10-1.png", + "caption": "Fig. 10. \u201cNon-proper\u201d cable-driven open chains. (a) Planar 2R deficient open chain. (b) Planar 4R redundant open chain.", + "texts": [ + ", \u0302$ei , which are reciprocal to the n joint twists of the chain. For a set of n \u2212 1 joint screws (without \u0302$i), there exists a [d \u2212 (n \u2212 1)] system of screws reciprocal to every joint screw in this set. This set is labeled as Ri . Every screw \u0302$ir\u2217 in Ri \u2212R is a possible choice for \u0302$ir because such a screw is reciprocal to every joint screw in the chain except \u0302$i . \u0302$ir is now expressed as follows: \u0302$ir = \u03b3i \u0302$ir\u2217 + \u03bdi1 \u0302$e1 + \u00b7 \u00b7 \u00b7 + \u03bdinr \u0302$enr (52) where scalars \u03b3i and \u03bdinr are real, and \u03b3i is nonzero. As an illustration, Fig. 10(a) presents a planar 2R deficient open chain. It has only two twists, i.e., \u0302$1 and \u0302$2 . For this case, there will be one independent reciprocal screw, i.e., \u0302$e1 , which will be reciprocal to these two twists. There will also exist a two-system of screws, i.e., \u0302$1r\u2217 and \u0302$2r\u2217, which will be reciprocal to all twists except its own. These are a pencil of screws passing through the rotation axes of the twists and lying in the X\u2013Y plane. Any one of the screws in the set can be selected as the reciprocal screw", + " The first d screws can be chosen to form the linearly independent set, while the remaining n \u2212 d screws form the dependent set. These screws are then labeled as \u0302$1 , . . . , \u0302$n , where the first d screws are linearly independent. The remaining n \u2212 d screws are expressed in terms of the independent set as follows: \u0302$k = \u03bdk1 \u0302$1 + \u00b7 \u00b7 \u00b7 + \u03bdkd \u0302$d , (k = (d + 1), . . . , n). (55) The d reciprocal screws \u0302$ir are then identified correspondingly to the first d linearly independent screws \u0302$i , based on Theorem 1. As an illustration, Fig. 10(b) presents a planar 4R redundant open chain. It has four twists, i.e., \u0302$1\u2013\u0302$4 . For this case, the first three twists, i.e., \u0302$1 , \u0302$2 , and \u0302$3 , will be selected as the independent set, and \u0302$4 will be expressed in terms of the independent screws. The selection of screws in the independent set is arbitrary, provided these screws are independent. The three reciprocal screws, i.e., \u0302$1r , \u0302$2r and \u0302$3r , will be determined based on Theorem 1. The reciprocal screws for spatial-redundant openchain cases can be similarly determined" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003603_tie.2020.2977578-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003603_tie.2020.2977578-Figure11-1.png", + "caption": "Fig. 11. Predicted and measured modal shapes. (a) 2nd-order with 1023 Hz by FE method. (b) 4th-order with 1702 Hz by FE method. (c) 2nd-order with 992 Hz by test. (d) 4th-order with 1761 Hz by test.", + "texts": [ + " Because the \u2164 stator core is aligned with the z-axis, the value of Young\u2019s modulus in z-direction is smaller than that in x- and y-direction. In addition, the windings contribute more to mass than stiffness because of the small value of Young\u2019s modulus in all direction. The frequency response function of the fixed motor is measured. As can be seen in Fig. 10, the first 6 modal frequencies and modal damping are marked in red and in blue, respectively. The lower order modes contribute most to the motor vibration, and the first 6 modes are enough for vibration calculation. Fig. 11 shows the 2nd-order and 4th-order modal shapes, which are obtained by FE method and experiments, respectively. The comparison of the first 6 modal frequencies by the test and FE method is shown in Fig. 12. The relative errors of modal frequencies are all below 5%, verifying that the established FE model has sufficient accuracy for vibration calculation. Based on the previous analysis, the 30\u00b0 configuration has less harmonic components of MMF and radial force, and the vibration acceleration is lower in the entire frequency band" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000597_j.bios.2011.06.029-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000597_j.bios.2011.06.029-Figure1-1.png", + "caption": "Fig. 1 shows the fuel cell assembly consisting of the laccaseathode (lower plate), two counter electrodes (platinum mesh), he dehydrogenase-anode and a reference electrode. The cell was etup in this configuration so that both the anode and cathode ould be studied independently and their individual polarization urves determined before measuring the output of the complete, unctioning fuel cell. For the ADH-laccase fuel cell, the fuel solution onsisted of 475 mM ethanol and 1.5 mM NAD+, and for the MDHaccase fuel cell, the fuel solution contained 500 mM l-malate and .5 mM NAD+. Polarization curves were constructed for the cathde (under potentiostatic regime) and for the complete biofuel cell under potentiostatic and galvanostatic regimes). The anodic polarzation curve was determined by subtracting the cathodic curve rom the fuel cell curve. The fuel was pumped to the fuel cell using peristaltic pump at a flow rate of 3 mL/min and the fuel was recyled back into the fuel cell. This flow speed was chosen as optimal fter different trials. It provides enough flow of the fuel, without ompromising the mechanical stability of the electrodes.", + "texts": [], + "surrounding_texts": [ + "nd Bio\nI e d w 2 p m 2 r f t ( 1 r t r ( F p 2 X a p\ne o o t a p p e a u s p m a\no i l t e t r l o B t c f e L c f ( a e s a\no s c f\nR.A. Rinc\u00f3n et al. / Biosensors a\nvnitski et al., 2008, 2010; Ivnitski and Atanassov, 2007; Solomon t al., 1996). Laccase belongs to the group of multicopper oxiases that catalyze the four-electron reduction of oxygen to water, hile oxidizing a wide range of aromatic substrates (Piontek et al.,\n002). In addition, laccase enzymes possess high thermodynamic otential and catalytic parameters that are optimal for the developent of cathodes for biofuel cells (Barton et al., 2004; Mano et al.,\n006; Solomon et al., 1992, 1996). Spectroscopic studies and Xay crystallography reveal that laccase proteins include a minimal unctional unit containing one blue copper, Type 1 (T1) site, and a rinuclear cluster that has one Type 2 and two Type 3 copper atoms T2/T3) (Piontek et al., 2002; Shleev et al., 2005; Solomon et al., 992, 1996). The T1 center provides long-range intramolecular apid electron transfer from the substrate, redox mediator or elecrode to the trinuclear T2/T3 redox copper center, where oxygen eduction to water takes place, via intermolecular electron transfer Piontek et al., 2002; Solomon et al., 1992, 1996; Xu et al., 1996). ungal laccases in particular, are capable of reducing oxygen at high otentials (680\u2013850 mV) (Barton et al., 2004, 2002; Morozova et al., 007; Piontek et al., 2002; Reinhammar, 1972; Shleev et al., 2005; u et al., 1996) but their activity is often optimal at low pH (4\u20135) nd reduced, or even inactive, at neutrality; the desirable operating H for biofuel cells (Barton et al., 2004).\nFor biofuel cell anode design a wide range of enzymes can be xplored, since a variety of fuels can be used. Considering the xidation of glucose as a model fuel, for example, a multitude f enzymes is able to catalyze the first-step of glucose oxidaion. These enzymes utilize different cofactors (e.g., nicotinamide denine dinucleotide, NAD+; flavin adenine dinucleotide, FAD; or yrroloquinoline quinone, PQQ), which define the reaction redox otentials. NAD+-dependent enzymes are known to have the lowst redox potential. Since one would like to work at the lowest node potential in order to obtain the maximum cell voltage, the se of NAD+-dependent enzymes is highly desirable. There are everal NAD+-dependent enzymes that are involved in metabolic athways like the Kreb\u2019s cycle and glycolysis. We have selected two odel enzymes for this research: malate dehydrogenase (MDH) nd alcohol dehydrogenase (ADH). Historically, the use of NAD+-dependent enzymes as the anode f biofuel cells has been limited by the need to reoxidize NADH n order to regenerate the enzyme cofactor. Mediators and cataysts have been demonstrated in order to address this issue, but o date have only been used in biofuel cells that operate in a \u201cquiscent\u201d mode, which results in insufficient transport of fuels and hus limited conversion (Palmore et al., 1998). We have recently eported the development of poly-(methylene green) electrocataysts for NADH oxidation, however, that can be fabricated directly nto 3-dimensional (3D) electrode materials (Rinc\u00f3n et al., 2011). y combining such structures with defined enzyme immobilizaion techniques we have been able to obtain anodic electrodes that an support continuous flow regimes. The use of 3D chitosan scafolds, for example, makes it possible to entrap NAD+-dependent nzymes and retain catalytic activities (Cooney et al., 2008, 2009; au et al., 2008, 2010). Moreover, chitosan can be combined with arbon nanotubes (CNTs) to obtain micro-porous polymeric scafolds that provide a high residence time for the diffusive cofactor NAD+), resulting in efficient electrochemical conversion of NADH nd in turn, good conversion of the fuel (Martin et al., 2010; Rinc\u00f3n t al., 2011). This immobilization technique has been previously tudied and chosen due to its ability to provide enhanced enzymatic ctivity and stability.\nFor the research described herein, we utilize a standardized labratory platform that serves as a stackable, flow-through, fuel cell ystem (Svoboda et al., 2008) in which both bio-anode and bioathode were integrated with the purpose of generating power rom biological fuels.\nelectronics 27 (2011) 132\u2013 136 133\nCompleting a fully enzymatic biofuel cell requires the design of an anode that is functional in flow-through mode of the fuel (and potentially the electrolyte) with a cathode capable of operating in a gas-flow mode. It is preferred those flow modes to impose as low parasitic loss as possible. In this research the air-breathing gasdiffusion enzyme-catalyzed electrode of hydrophobic type is being incorporated as a passive cathode. This paper presents the effort and investment of our team in engineering both anode and cathode for an enzymatic biofuel cell that is able to operate in a continuous flow mode. The following sections describe the development of a cathode that can undergo DET and a 3D anode that is based on NAD+-dependent enzymes.\n2. Material and methods\n2.1. Materials\nMethylene green (Fluka Cat. 66870), l-(\u2212)-malic acid (Sigma Cat. M1000), NADH (Sigma Cat. N6005), NAD+ (Fluka Cat. 43407), alcohol dehydrogenase (ADH) from Saccharomycescerevisiae (pI: 5.4\u20135.8, Sigma Cat. A3263, 347 U mg\u22121), laccase from Trametes versicolor (pI: 4.1\u20134.7, Sigma Cat. 53739, 25.5 U mg\u22121), chitosan (CHIT) (medium molecular weight, Aldrich Cat. 448877), ethanol (200 proof, VWR Cat. 89125172), multi-walled carbon nanotubes (MWCNTs) (20\u201330 nm outer diameter, 10\u201330 m length, 95 wt% purity from www.cheaptubesinc.com), dimethyl sulfoxide (DMSO, Sigma), 1-pyrenebutyric acid N-hydroxysuccinimide ester (PBSE 95%, Sigma\u2013Aldrich Cat. 457078), carbon black (XC72R, Cabot), and concentrated acetic acid (EMD Chemicals Cat. EMAX0073P5) were used without further purification. All other chemicals were reagent grade quality. Malate dehydrogenase (MDH) from porcine heart (pI: 6.1\u20136.4, USB products from Affymetrix Cat. 18665, 2580 U mg\u22121) was purified by dialysis (Slide-A-Lyzer MINI dialysis units 10,000 MWCO, and concentrating solution from Thermo Scientific) with TRIS buffer (pH 7.0, 50 mM) in three steps (30 min, 1 h and 30 min) against 500 mL of the same buffer. The final MDH stock solution contained 1 mg MDH/10 L TRIS buffer (pH 7.0). Chitosan was pretreated to achieve a final deacetylation degree of 95% by initially autoclaving (20 min at 121 \u25e6C in 40 wt% NaOH), followed by filtration and washing with DI water and phosphate buffer (pH 8.0, 0.1 M) before drying in a vacuum oven at 50 \u25e6C for 24 h. A MWCNTs/CHIT suspensionwas prepared by combining 1 wt% CHIT (in 0.25 M acetic acid) stock solution and MWCNTs (final concentration of 2.5 wt%). NADH stock solutions were prepared for each buffer. l-malic acid was prepared with distilled water and its pH was adjusted to 7.4 with concentrated NaOH.\nElectrochemical measurements were carried out using a stackable flow through electrochemical cell (Svoboda et al., 2008) with a platinum mesh (100 mesh, Alfa Aesar Cat. 10282) counter electrode and Ag/AgCl/sat KCl reference electrode (CH Instruments Inc.) when working in the three-electrode setup. For the fuel cell experiments (two-electrode setup) the cathode was connected to the potentiostat as the working electrode and the anode was connected as the counter and reference electrodes. All potential values are reported against Ag/AgCl.\n2.2. Preparation of dehydrogenase anodes\nReticulated vitreous carbon (RVC) of a defined porosity (60 pores per linear inch, ppi) was used for the anode supporting material and was pretreated with oxygen plasma cleaning for 15 s to achieve hydrophilization of the surfaces. Enzymatic anodes were prepared by modifying 60 ppi RVC with poly-(MG) as previously described, with10 deposition cycles (Rinc\u00f3n et al., 2011). The immobilization technique for both enzymes (MDH and ADH)", + "1 nd Bioelectronics 27 (2011) 132\u2013 136\nw p ( e t a F f e o a t t\n2\ns T t t c t 1 p D t c i o\n2\nc t s c c f c l 1 o ( i f a c a c\nf p\nf t o p o t\n34 R.A. Rinc\u00f3n et al. / Biosensors a\nas direct entrapment in the MWCNTs/CHIT scaffolds according to rocedures presented by Cooney et al. (2008, 2009) and Lau et al. 2008, 2010). Briefly, materials were prepared by filling the RVC lectrodes with CHIT/MWCNTs/NAD+/MDH (500 L of immobilizaion solution in which every10 L of chitosan contain 0.35 mg NAD+ nd 1 L MDH or 3 L ADH) and then frozen at \u22124 \u25e6C overnight. reeze-drying was performed for 4 h in order to eliminate water rom the scaffold. The stock solutions of enzymes contained 1 mg of nzyme per 10 L of buffer, hence the MDH anode contained 5 mg f enzyme, and the ADH anode contained 15 mg of enzyme. The mount of ADH immobilized to electrodes was calculated based on he amount of enzyme units in order to obtain comparable results o those for MDH.\n.3. Preparation of laccase cathode\nThe gas-diffusion cathode consists of two layers: a gas diffuion layer and a catalytic layer. 80 mg of carbon black XC72R with a eflon content of 35 wt% were placed into a round dye (2 cm diameer) and pressed by hand onto a nickel mesh (Alfa Aesar Cat. 39704) hat serves as current collector. 10 mg of teflonized multi-walled arbon nanotubes (3.5 wt% PTFE) were evenly distributed on top of he gas diffusion layer. The layers were fused by pressing (1 min at\nkp) in a hydraulic press to a final thickness of 0.5 mm. PBSE (1- yrenebutyric acid N-hydroxysuccinimide ester) (4 mg in 0.5 mL MSO) was allowed to soak into the catalytic layer for 2 h, before\nhe electrode was rinsed with DMSO and then with DI water. Lacase was immobilized by physical adsorption onto the electrode by ncubating 0.5 mL of the enzyme (4 mg mL\u22121 in PBS, pH 6.3) at +4 \u25e6C vernight. The electrode was rinsed with DI after incubation.\n.4. Enzymatic biofuel cell construction\nThe working parameters of a functional fuel cell can be defined rom polarization curves, obtained under both galvanostatic and otentiostatic regimes.\nInitially, an open circuit voltage (OCV) of 0.584 V was observed or the MDH-laccase biofuel cell (Fig. 2). The shape of the polarizaion curve for the anode indicates that the MDH-anode is limited by hmic losses and transport limitations. The laccase-cathode in comarison, demonstrates minimal kinetic losses within the current peration range of the anode. The biofuel cell polarization curve, herefore, shows a kinetic-limited behavior for currents lower than", + "R.A. Rinc\u00f3n et al. / Biosensors and Bioelectronics 27 (2011) 132\u2013 136 135\nF a\n1 c a t\nu e c s t\nl ( A a d\n\u223c i r t c\n3\na t o A I 0 c o\n( s t i a p\nterms of volumetric density, the corresponding maximum power was \u223c21 W cm\u22123. This result is one order of magnitude higher than the one reported by Stoica et al. (2009) and at least double the\nig. 3. Power curves of MDH-laccase biofuel cell in 500 mM l-malate normalized to node volume and cathode area: ( ) galvanostatic, ( ) potentiostatic.\n0 A where the sustained voltage is almost independent of the urrent. At currents higher than 10 A, ohmic losses are observed nd the limitations of the anode dictate the overall performance of he biofuel cell and restrain maximum current to about 65 A.\nClearly, for the case of biofuel cells, evaluation of the system nder galvanostatic regime is more informative, as we are intersted in observing the voltage output that the complete fuel cell an sustain. It was necessary, however, to perform the potentiotatic experiments in order to determine the operational range of he device, in respect to current.\nFig. 3 shows power curves that were constructed for the MDHaccase biofuel cell, represented with the volume of the anode \u223c1.5 cm3)and area of the cathode (\u223c1.3 cm2)taken into account. maximum power density of \u223c9 W cm\u22122 was observed, in good greement with reports for enzymatic biofuel cells based on a single ehydrogenase enzyme in mediated systems (Stoica et al., 2009).\nThe maximum power per unit volume (of the anode) was 8 W cm\u22123. Current biofuel cell methodologies often report maxmum current and power outputs based on per unit area, but eporting outputs per unit volume is more significant for 3-D archiectures and provides a design parameter for scale-up of the biofuel ell technology.\n.2. ADH-laccase biofuel cell\nA second biofuel cell was designed with the laccase-cathode as bove but with an ADH-anode. Fig. 4 shows the open circuit potenials obtained for each electrode, as well as the cell voltage data. The pen circuit potential (OCP) of the anode approached \u22120.05 V vs. g/AgCl while the OCP of the cathode approaches 0.58 V vs. Ag/AgCl. n combination, this provides a theoretical maximum cell voltage of .63 V for the biofuel cell. In fact, Fig. 4 shows a cell voltage of 0.61 V lose to steady-state and demonstrates a system with minimal loss f enzymatic activity.\nFig. 5 shows the polarization curves of the anode and cathode obtained in potentiostatic regime) and the biofuel cell (galvanotatic regime). In the current operating range the cathode shows he typical behavior of an air breathing electrode with kinetic limtations at low currents, ohmic losses between 30 and 150 A and very sudden drop in potential at higher currents due to transort limitations imposed by the diffusion of air through the cathode\narchitecture. This biofuel cell sustained an OCV of 0.618 V, slightly higher than that of the MDH-laccase biofuel cell.\nFor both of the biofuel cell configurations studied the anode is the limiting electrode, and performance degradation mainly dictated by ohmic losses. The limitation is a consequence of various design aspects. Firstly, the supporting electrolyte contains a total salt concentration of 0.4 M, which compared to other electrochemical devices (e.g., batteries) is low. Enzymes however, could be inactivated at high salt concentrations, and as such, electrolyte optimization is a design parameter that could be addressed, but may inherently constrain the working limits of the system. Second, the 3D design and dimensions of the anode significantly separate the electrodes. This macroscopic separation (\u223c1 cm) between the anode and the cathode and the flow of low conductive ions significantly contribute to the ohmic losses in the biofuel cell.\nFig. 6 shows power curves for the ADH-laccase biofuel cell in the same way as for the MDH-laccase. The maximum power density was determined to be \u223c25 W cm\u22122 which is almost three times higher than that obtained for the MDH-laccase biofuel cell. In" + ] + }, + { + "image_filename": "designv10_3_0000156_1.2958070-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000156_1.2958070-Figure4-1.png", + "caption": "Fig. 4 Dimension definitions of the defect on the running surface \u201ethe inner race, outer race, and ball surface\u2026", + "texts": [ + "5 Defects on the Rolling Surfaces. First, a model is estabished for a single defect on the outer race surface, then a single efect on the inner race surface, and finally a defect on the ball urface is modeled. The combination of these defects is then aplied in the simulation. 2.5.1 Defect on the Outer Race Surface. Let there be a defect n the surface of the outer race at the angle from the horizontal xis X. If ct+ i coincides with the defect angle , a ball at its ontact will have additional deflection d, as shown in Fig. 4. For the computational convenience, the following definitions re made 37 . 1. Since the defect is not a single point, to define the defect at a certain angle may cause problems in computation. Thus, a tolerance band is placed on the angles. For example, for the outer race defect, the defect angle is defined as d = d 2ro 22 where d is the width of the defect. 2. Since ct+ i increases continuously, its sine and cosine angles are simultaneously checked with those of the defect angle. 2.5.2 Defect on the Inner Race Surface. Let there be a defect n the surface of the inner race. This defect will rotate at the shaft peed as the inner ring is forced fitted to the shaft. If the defect ngle, t d /2ri , coincides with one of the balls, ct+ i , i 1,m, the deflection on that ball will be see Fig. 4 id = i + d 23 2.5.3 Defect on the Ball Surface. The defect was assumed to e rotating around an axis passing through its center and parallel o bearing axis; hence the defect passed the same points on the nner and outer raceways at regular intervals. From Fig. 4 it can be een that when the sine of the angle bt equals to zero for that articular ball the deflection will be id = i + d 24 ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 07/05/2013 Terms 3 Results and Discussion In this study, the shaft is assumed to be perfectly rigid and uniform supported by two precision angular contact ball bearings. The specifications of the bearings and the shaft were chosen as Aini\u2019s experimental arrangement 38 since the particulars of both the shaft and bearings were readily available", + "2 Vibrations of Balls for Faulty Ball Bearings. A crack or debris was assumed to be located on the running surface inner race, outer race, and ball surface . It was assumed to have 3 m depth and 1 deg width 1 . The combination of these defects was then input to the simulation program and ball vibrations were obtained. The results were discussed in the following sections. 3.2.1 Effect of Defected Outer Raceway on Ball Vibrations. The defect was assumed to be located on the outer raceway at 15 deg angular position see Fig. 4 . This means that the defect was located where the load is maximum for an 18 N preload. Ball vibration takes a sinusoidal form for this preload because Ball 1 is completely in the loaded region. The vibration amplitude increases when Ball 1 approaches the defect due to entering relatively more rigid region, as shown in Fig. 9 a . The amplitude shows an increase for a short period during the ball-defect contact when the ball contacts with defect and decreases again upon leaving the defect. Figure 9 b shows the frequency spectrum of Ball 1 with defected outer race surface bearing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002780_icra.2015.7139416-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002780_icra.2015.7139416-Figure4-1.png", + "caption": "Fig. 4: Tilt-torsion decomposition. For any current (Red) and target (Blue) rotations, add an intermediate (Green) rotation. Then execute a two-stage control action.", + "texts": [ + " But for yaw control, the rotors must change significantly to generate needed rotational torque. Some pitch and roll control is always applied faster than yaw control. In our experiments we found that the response time of pitch or roll controller to 10 \u25e6 is around 60ms, but the yaw controller will take more than 150ms to rotate 10 \u25e6 around the yaw axis. Therefore, we add a planner to process target rotation. For any target rotation input either by user command or controller regulator, we calculate the error rotation Re = RtR \u22121 c , and decompose Re as: Re = RtorsionRtilt as plotted in Figure 4. The calculation of Rtilt takes the inner product and cross product of the yaw axes of the current frame and the target frame. Let zc = zt = [0 0 0]T be the yaw axis of the target frame, then RTe zt is the coordinate of this yaw axis in the current frame. The cross product of zc and RTe zt is the rotation axis r of Rtilt. And the angle \u03c6 between this two axes is the rotation angle. Hence, Rtilt = er\u0302\u03c6 The purpose of Rtilt is to align the yaw axis of the current frame with yaw axis of the target frame" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.11-1.png", + "caption": "Figure 4.11 (a) illustrates the configuration of a wedge. The coordinates of the corners of the wedge in its body frame B are collected in the matrix P.", + "texts": [ + " Hence , the position of 02 in the base coordinate frame is at (4.98) Example 91 Object manipulation. The geometry of a rigid body may be represented by an array containing the homogeneous coordinates of some specific points of the body described 4. Motion Kinematics 151 in a local coordinate frame. The specific points are usually the corners, if there are any . The configuration of the wedge after a rotation of -90 deg about the Z axis and a translation of three units along the X -axis is shown in Figure 4.11(b). The new coordinates of its corners in the global frame G are found by multiplying the corresponding transformation matrix by the P matrix. DX ,3RZ ,90 [~ ~ ~ ~] [~~~ =~~ o 0 1 0 0 o 0 0 1 0 [ ~1 ~ ~ ~] o 0 1 0 . o 0 0 1 - sin -90 cos -90 o o (4.100) 152 4. Motion Kinematics Example 92 Cylindrical coordinates. There are situation in which we wish to specify the position of a robot end-effector in cylindrical coordinates. A set of cylindrical coordinates, as shown in Figure 4.12, can be achieved by a translation r along the X -axis, followed by a rotation ip about the Z -axis , and finally a translation z along the Z-axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001890_17579861111162914-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001890_17579861111162914-Figure3-1.png", + "caption": "Figure 3. Schematic of cooling system for laser cladding on a thin aluminium plate", + "texts": [ + " Al-12Si powder was selected because it delivers an excellent combination of corrosion and wear-resistance properties while the 7075 Al powder matches the substrate composition and should minimise any stresses at the interface. The powder was heated to 1008C before cladding to eliminate any moisture. The cladding was carried out using argon as an inert shielding gas with a flow rate of 3 L/min. A water-cooled copper block was placed under the substrate to quickly remove heat from it produced during cladding (Figure 3). The detail of the water-cooled system is shown in Figure 4. The microhardness measurements were made automatically along a direction from the top of the clad layer into the substrate using a LECO Automatic Nozzle (cross-section view) Nozzle (gas + powder) Gas shield outlets Powder stream outlet Laser beam Scan Micro/Macro-Indentation Hardness Testing System (AMH43) with a Vickers indenter. The applied load was 100 gf and dwell time was set at 15 s. Different spacings between the individual indentations were used for the clad layer and HAZ" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure12.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure12.8-1.png", + "caption": "Figure 12.8.1 Double transverse arms, general case, front view of right wheel or rear view of left wheel.", + "texts": [ + " A negative quadratic bump camber coefficient is usually desired, in which case SYD must be positive, requiring the upper arm to be the shorter one. The foregoing equations are a useful guide to the effect of various geometrical changes, but with arm convergence the bump scrub effects are not handled accurately enough for design purposes, so an improved analysis will now be given here. However, the resulting equations are more complex, and the Double-Arm Suspensions 233 effects of design changes are not as clear as in the previous very simple equations. Figure 12.8.1 shows the geometry, which now simultaneously includes different arm lengths, different arm angles, the ball joint static vertical spacing HBJD, and the mean static ball joint height HBJM. The individual static-position heights of the upper and lower outer ball joints are HBJU and HBJL. Table 12.8.1 summarises the definitions and relationships for related variables. The values ofHBJU,HBJL, HBJS, HBJD, HBJM and fBJH are constant for a given design. Their use simplifies subsequent equations. The front-view equivalent link lengths are LYU and LYL", + "1 Outer ball joint height relationships The sum and difference are HBJS \u00bc HBJU \u00feHBJL HBJD \u00bc HBJU HBJL The individual ball joint heights are HBJU \u00bc 1 2 \u00f0HBJS \u00feHBJD\u00de HBJL \u00bc 1 2 \u00f0HBJS HBJD\u00de The mean outer ball joint static height is HBJM \u00bc 1 2 HBJS The ball joint height factor is the ratio of the sum to the difference: fBJH \u00bc HBJS HBJD which, more explicitly, is fBJH \u00bc HBJU \u00feHBJL HBJU HBJL Note that fBJH is not the ratio of the height of the individual ball joints. The shortness sum and difference are SYS \u00bc SYU \u00fe SYL SYD \u00bc SYU SYL The initial (static position) link angles are uYU0 and uYL0, positive as shown in the figure, clockwise. These arm angles are defined positive such that they increase in bump. Table 12.8.2 summarises useful arm angle equations. In Figure 12.8.1, the long triangle gives, approximately, HBJD \u00bc RS uYD so the swing arm radius is RS \u00bc HBJD uYD \u00bc HBJD uYD0 \u00fe SYDzS The linear bump camber coefficient is \u00abBC1 \u00bc 1 RS0 \u00bc uYD0 HBJD As before, the quadratic bump camber coefficient is \u00abBC2 \u00bc SYD 2HBJD Table 12.8.2 Arm angle relationships The static arm angle sum and difference are uYS0 \u00bc uYU0 \u00fe uYL0 uYD0 \u00bc uYU0 uYL0 At suspension bump position zS, the link angles become uYU \u00bc uYU0 \u00fe SYUzS uYL \u00bc uYL0 \u00fe SYLzS The sum and difference of these angles are uYS \u00bc uYU \u00fe uYL uYD \u00bc uYU uYL The individual angles are uYU \u00bc 1 2 \u00f0 uYS uYD\u00de uYL \u00bc 1 2 \u00f0 uYS uYD\u00de By substitution, the sum and difference are uYS \u00bc uYS0 \u00fe SYSzS uYD \u00bc uYD0 \u00fe SYDzS Double-Arm Suspensions 235 The height of the swing centre is HS \u00bc HBJM 1 2 uYSRS \u00bc HBJM 1 2 HBJD uYS uYD This gives HS \u00bc HBJM 1 2 HBJD uYS0 \u00fe SYSzS uYD0 \u00fe SYDzS The local lateral bump scrub rate (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure6.30-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure6.30-1.png", + "caption": "Fig. 6.30 Frequency responses of the two-mass oscillator of Fig. 4.40 for \u03bc = 0.2, \u03b6 = 1, D = 0.1; a) Amplitude frequency response Dlk, b) Phase frequency response \u03c8lk, c) Loci of the complex frequency responses Hlk", + "texts": [ + "24) The coupling that exists between the 4 equations is caused by the gyroscopic moment. One can see that decoupling occurs for \u03a9 = 0 (non-rotating shaft) so that only the displacement and tilt in one plane influence each other (y and \u03c8x or x and \u03c8y , respectively). The vibrations in the planes that are offset by 90\u25e6 can then be examined separately. The gyroscopic moments for rotors in which Jp Ja are relatively small as compared to other moments so that they can be neglected without any substantial loss in accuracy (e. g. textile mandrils), see Fig. 5.5a and Fig. 6.30. In the case of isotropic support, it is permissible and useful to use the rotating plane (r; z) formed by the z axis and the elastic line rather than the two fixed planes (x, z; y, z). The radial displacement r of the shaft center and the angle \u03c8 of the cone formed by the rotating tangent can be used as coordinates. The shaft shown in Fig. 5.4 corresponds to case 6 in Table 5.1, the influence coefficients being \u03b1 = d11, \u03b2 = d22, \u03b3 = \u03b4 = d12. The following equations apply likewise to cases 3 to 5", + " One can recognize that since all phase angles are the same for the undamped oscillator, see (6.288) and Fig. 6.24, but they are of different magnitude for the damped oscillator. Figure 6.29 illustrates this fact using a simple example. It shows the synchronously changing deflections for an undamped bending oscillator as compared to a damped bending oscillator during half a period of the forced oscillation (0 < t < \u03c0/\u03a9 = T/2). The graphic representation of a complex frequency response Hlk(j\u03a9) provides an planar curve called locus, see Fig. 6.30c. It contains important information about the behavior of an oscillator. 6.6 Damped Vibrations 451 Loci are commonly used in aircraft design, machine design, rotor dynamics and other fields. Loci are obtained by plotting in the complex plane Dlk(\u03a9) as radius and \u03c8lk(\u03a9) as angle in polar coordinates. It is often sufficient to plot the amplitude frequency response Dlk(\u03a9). Unlike for the undamped system, it has no singular points at resonance in the damped vibration system. The number of its maxima at most equals n and is often much smaller than n", + " One can reduce these findings to the classic statement that \u201cresonance occurs when the excitation frequency equals the natural frequency\u201d if one considers all excitation frequencies that are contained in the periodic excitation (and all natural frequencies). The resonance curves of damped systems always remain finite. The resonance curve differs only slightly from that of the undamped system in areas outside resonance, if the damping ratios Di are small. Damping frequently becomes supercrit- 6.6 Damped Vibrations 455 ical at higher natural frequencies (Di > 1) so that no resonance peaks form, see e. g. Figure 6.30. Amplitude frequency responses can be calculated for each harmonic of qk(t) and recorded as functions of \u03a9 as so-called cascade diagram. Textile mandrils work at high speeds and belong to the machine sub-assemblies that cannot be designed or improved without an exact dynamic analysis. Figure 6.32 shows the design drawing of a textile mandril and the corresponding calculation model. Note that hydraulic dampers with a damping spiral (sleeve spring) as shown in Fig. 6.32c are used at both bearings", + "391) If one introduces the dimensionless characteristic parameters according to the problem statement, and in addition \u03be2 = \u03b3/\u03bc and \u03b7 = \u03a9/\u03c9\u2217, it follows that \u0394(j\u03b7) = c2T1 \u03b32 { \u03b74\u03bc\u2212j2\u03b73D\u03bc(1+\u03bc)\u2212\u03b72 [\u03b3+\u03bc(1+\u03b3)]+j2\u03b7D\u03bc+\u03b3 } \u039422(j\u03b7) = cT1 \u03be2 (\u2212\u03b72+j2\u03b7D+\u03be2 ) . (6.392) 464 6 Linear Oscillators with Multiple Degrees of Freedom Using the abbreviations a1 = \u03be2 \u2212 \u03b72, a2 = \u03b74\u03bc\u2212 \u03b72 [\u03b3 + \u03bc(1 + \u03b3)] + \u03b3, a3 = 2\u03b7D, a4 = 2\u03b7D\u03bc [ \u03b72(1 + \u03bc)\u2212 1 ] (6.393) one finds H22 = \u039422 \u0394 = \u03b3\u03bc cT1 a1 + ja3 a2 \u2212 ja4 = \u03bc cT2 [ a1a2 \u2212 a3a4 a2 2 + a2 4 + j a3a2 + a1a4 a2 2 + a2 4 ] . (6.394) The curves for the amplitude and phase frequency response shown in Fig. 6.30a and b and the locus in Fig. 6.30c correspond to the solution for the numerical values from the problem statement. One can recognize the two resonance frequency ratios \u03b71 = 0.8; \u03b72 = 1.25 and the absorption frequency (antiresonance) at \u03b7 = 1.02. S6.16 One can use the following heuristic approach: The natural frequencies at resonance according to (6.363) are always an integral multiple of the fundamental excitation frequency f0, i. e. the measured resonance frequencies are the quotients of the natural frequencies fi and small integers m, that is f0R = fi/m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003523_j.msea.2020.140606-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003523_j.msea.2020.140606-Figure2-1.png", + "caption": "Fig. 2. Finite element mesh of the L-DED-processed Al\u2013Mg-Sc-Zr deposit (a); Schematic showing the points located at the center position of the deposit for analysis of temperature field. A, B, C indicate the positions with the distance from the substrate of 0, 4, and 8 mm, respectively (b).", + "texts": [ + " The temperature-dependent physical properties are summarized in Table 2. The \u03b5, h, and T\u221e were set to 0.21, 20 W/(m2\u22c5\u25e6C), and 25 \u25e6C, respectively [33]. The laser energy absorptivity of Al at the wavelength of the diode laser (970 nm) was retrieved from the work of Kennedy et al. and set to 0.25 [34]. In addition, the boundary condition on the bottom surface of the substrate was assumed to be maintained at the ambient temperature (25 \u25e6C) during the simulation of the L-DED process using the WC substrate. Fig. 2a presents the finite-element mesh of the L-DED-processed Al\u2013Mg\u2013Sc\u2013Zr deposit. In the central region of the deposit, three points (A, B, and C) were selected along the deposition direction to analyze the temperature field during the L-DED process. Points A, B, and C correspond to positions with distances of 0, 4, and 8 mm from the substrate, respectively, as illustrated in Fig. 2b. The grain structures of the top and middle zones in the AC sample are presented in Fig. 3a and c, respectively. Unlike the reported epitaxial columnar grain structure of an L-DED-processed 5083 Al\u2013Mg alloy [35], a fully equiaxed grain structure was obtained in the L-DED-processed Al\u2013Mg\u2013Sc\u2013Zr alloy using the AC substrate, while a heterogeneous grain structure consisting of a fine grain (FG) band at the fusion boundary and a fan-shaped coarse grain (CG) domain in the inner region of the molten pool, was formed using the WC substrate (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000036_robot.1992.220061-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000036_robot.1992.220061-Figure4-1.png", + "caption": "Figure 4: A robot with omnidirectional wheels", + "texts": [ + " The two actuators providing the rotation of wheels 2 and 3, it is then easy to check that the input matrix S\u2019(q B P has full rank and we to obtain the form (6) which !an be reduced in this particular case, noticing that p and d, are uniformly bounded provided that 77 is bounded : can apply the general met 1 6 6 io escribed in section 1, x = -q1sint9 s = qlcose 9 = 772 (14) 71 = v1 772 = v2 The description of the wheels is quite analogous to that of Section 2.1, except for wheel 1 which is described as follows (see Fig. 4) : 37r R1 = R, 11 = L , d l = 0 , 0 1 = 2, pi = p, 71 = 0 . The robot motion is also described by the following vector of 7 generalized coordinates : q ( t ) = (. Y 0 P $1 $2 $3)) (15) The pure rolling and non slipping conditions can be obtained as previously and it is easy to check that this robot has also 2 degrees of freedom and to compute the corresponding matrix S(q). Moreover, the 2 motors providing both orientation and rotation of wheel 1, the matrix S\u2019(q)B(P) has full rank and we can apply once more the general method described in section 1, to obtain the representation (6) which can be written in reduced form in this particular case, noticing that $ i , i = 1 , ", + " Proof : Computing h we obtain : where w1 = &VI + d8\u2019 Differentiating h twice and delaying w1 twice : $1 = w2 we obtain : (37) Considering w2 and 0 2 as input variables we achieve full linearization for the extended system with extended state vector X = (2, Y, 8 , X, 6 , 4, wi, $1)\u2019 by static state feedback w2(x) and v 2 ( X ) , and diffee morphism : (39) the linearizing feedback law is singular when w1 is zero, from (36) the linearization is also not possible at equilibrium points XO = (20, yo, 80, 0, 0, 0, 0 , 0)\u2019. Once more this is not surprising since the tangent linearization of system (34) is not controllable when the tangent linearization of system (18) (with each wheel controlled) is controllable and therefore system (18) is static feedback linearizable as previously mentioned. 0 Remark 1 hl and h2 are in fact the Cartesian coordinates in the reference frame (0, I I , I 2 } of a point P o n the z1 azis, P having coordinates ( -d,O) in the (x1,xz) basis attached to the trolley, see Fig. 4 . Ackiiowledgeiiieiits : The authors would like to thank Alain Micaelli from CEA Fontenay-aux-Roses, for interesting discussions concerning dynamical modelling of mobile robots. REFERENCES [l] B. d\u2019AndrCa-Novel, G. Bastin, G. Campion, Mo- delling and Control of nonholonomic Wheeled Mobile Robots, IEEE Conf. on Robotics and Automation, Sacramento, April 1991. [a] B. d\u2019AndrCa-Novel, P. Martin, R. Sepulchre, Full Dynamic Feedback Linearization of a class of Mechanical Systems, proceedings of MTNS 1991, Kobe" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure14.8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure14.8-1.png", + "caption": "Figure 14.8.2 Rigid arm suspension with spring\u2013damper unit, shown in elevation.", + "texts": [ + " Rising rate also causes an important additional stiffness term even with a linear spring (see Section 14.14). Rigid-arm suspensions, such as a trailing arm, have a single arm from a pivot axis, thewheel camber angle being rigidly fixed relative to the arm. It is possible, but unusual, to have steeringwith such a system. Rigid arms may be classified in various ways. From the geometric point of view, the important distinction is the angle, cA, between the arm pivot and the vehicle centreline in plan view, Figure 14.8.1(a). Sometimes there is a non-zero angle of the arm pivot, fA, in rear view, Figure 14.8.1(b), as discussed in Chapter 11. The basic classifications by cA are: (1) trailing arm (90 ); (2) semi-trailing arm (e.g. 70 ); (3) leading arm (90 ); 282 Suspension Geometry and Computation (4) swing axle (0 ); (5) transverse arm (0 ); (6) semi-trailing swing axle (e.g. 45 ). The spring and damper usually act directly on the arm. In any case, it is necessary to obtain the relationship between the suspension bump velocity, that is, of the vertical wheel velocity at the contact patch, relative to the body, and the angular velocity of the arm. The radius of action of the wheel is lWP in plan view, Figure 14.8.1(a). For an arm angular speedv, the tangential speed of thewheel isvlWP, but this is not vertical in rear view, so the actual suspension wheel bump velocity VS is VS \u00bc vAlWP cosfA The velocity ratio of arm to wheel RA/W is therefore RA=W \u00bc vA VS \u00bc 1 lWP cos fA rad s 1=m s 1 Note that the pivot axis plan angle uA does not appear in this expression. Neither does any influence of the angle of the arm in side view, because this has been incorporated by using the plan length lWP, which may in fact vary somewhat through bump movement, because lWP \u00bc lW cos uA For any given bump position, uA follows, whence lWP and RA/W: RA=W \u00bc 1 lW cos uA cosfA With some consideration, the above can be applied to any of the rigid-arm suspensions listed above. The second part of themotion ratio then follows from the position of the spring or damper. Figure 14.8.2 shows the rigid arm in elevation viewed along the pivot axis. The spring may not be in the plane of the elevation, but will be close to it, with out-of-plane angle aK. Installation Ratios 283 The rigid-arm analysis is now easily completed as for analysis of the output of the rocker: V2 \u00bc vAl2 cos c2 Allowing for the out-of-plane angle aK, the spring compression velocity is VK cos aK \u00bc V2 so VK \u00bc l2 cos c2 cos aK vA \u00bc l2 cos c2 cos aK VB lWcos uA cos fA Hence, the spring motion ratio RK is RK \u00bc VK VS \u00bc l2 lW cos c2 cos uA cosfA cos aK This is very similar to the expression for a simple rocker, but includes effects from the angles fA and aK" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000443_j.elecom.2006.06.019-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000443_j.elecom.2006.06.019-Figure1-1.png", + "caption": "Fig. 1. Image of the screen-printed carbon strip (SPCS) consisting of a carbon working electrode, a carbon counter electrode, and Ag/AgCl reference electrode.", + "texts": [ + " Solutions were prepared and diluted using ultra-pure water from the Millipore Milli Q system. Electrodeposition and measurements in connection with cyclic voltammetry (CV) and chronocoulometry (CC) were performed using a potentiostat model 660 A (Bioanalytical Systems Inc., Japan). The planar screen-printed carbon strip (SPCS) consisted of a carbon working electrode, a carbon counter electrode, and Ag/AgCl reference electrode. SPCSs were provided from Bio Device Technology Ltd. (Ishikawa, Japan). Total length of the strip was 11 mm, and the geometric working area was 2.64 mm2 (Fig. 1). Electrochemical measurements were performed in 30 lL of the solution covering all three electrodes in a horizontal position. All measurements were carried out at room temperature (23 \u00b1 2 C). Scanning electron micrographs (SEM) of the electrode surface were obtained using a VE-7800 (Keyence, Japan) at an acceleration voltage of 8 kV. Energy dispersion X-ray spectrometry (EDS) of the deposited metals was monitored using JED-2200 (JEOL, Japan). Gas chromatographic determination of hydrogen was performed using G-5000 (Hitachi, Japan) in connection with the column of Molecular Sieve 13X (GL Science Inc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003603_tie.2020.2977578-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003603_tie.2020.2977578-Figure9-1.png", + "caption": "Fig. 9. Modal test. (a) Stator core. (b) Stator core with windings. (c) Entire motor. (d) Nodes distribution.", + "texts": [ + " Since the 30\u00b0 configuration suppresses the most stator MMF and radial force harmonics compared to other configurations, the 30\u00b0 configuration has lower vibration over the entire frequency band. V. EXPERIMENTAL VERIFICATION In order to verify the accuracy of the structural FE model, modal test of stator core, stator with coils and entire motor are implemented. The stator core and stator core with coils are suspended by elastic ropes as shown in Figs. 9(a) and 9(b). In this way, the natural modal parameters of the structure can be obtained. In Fig. 9(c), the motor is fixed to the test bench. The modal frequency of the motor in fixed state provides more accurate parameters for the vibration prediction of the motor. To record the vibration response of the stator and the stator assembly, 72 vibration picking points were selected on the surface as shown in Fig. 9(d). Then, an estimation of the modal parameters of the stator and the stator assembly is completed automatically by commercial software, which is based on the frequency response functions obtained by the modal test. The testing software can gather natural frequencies, modal shapes, and damping ratios from the peaks of the frequency response functions. Afterwards, modal damping parameters are used to predict the vibration of the electric motor. DTP-PMSMs with different phase shift angles have different windings topologies, but their geometric parameters are consistent" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002073_978-3-319-06698-1-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002073_978-3-319-06698-1-Figure12-1.png", + "caption": "Fig. 12 Simulation of the three-dof DM: compacted configuration (a); partial expansion in one (b) and two (c) directions; deployed configuraion (d)", + "texts": [ + " Mechanisms with Decoupled Freedoms Assembled from Spatial Deployable Units 523 Using the same assembling method, by linking the three-dof deployable units, threedof DMs can be obtained. The mechanism can be deployed in three directions independently. An unlimited number of unit mechanisms can be assembled together while the degree of freedom of the assembly stays three. As in the planar case, the scissor linkage is used to transmit motion between units. Two simulated models of two DMs, with two and eight units, respectively, are shown in Fig. 11. Each becomes a cube when fully deployed. The deployment process of the 8-unit DM is illustrated in Fig. 12. 524 S. Lu et al. Mechanisms with Decoupled Freedoms Assembled from Spatial Deployable Units 525 A family of unit-based mechanisms able to deploy and compact in two or three directions independently has been reviewed. In the deployable unit, Sarrus linkages provide the motion directions, and the scissor linkages connect the units, while maintaining the dof of the whole system constant. The DUs are connected by merging links and adding revolute joints. Thus, DMs with various boundary outlines and different dof are obtained" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003707_j.addma.2020.101265-Figure14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003707_j.addma.2020.101265-Figure14-1.png", + "caption": "Fig. 14. CAD model of the case study: (a) perspective view of the CAD model; (b) a typical intersection.", + "texts": [ + " It turned out that there was no occurrence of valleys and voids. The training was performed using MATLAB\u00ae with the nntraintool tool. Fig. 13 depicts the ANN architecture. The ANN has three layers: input, hidden, and output layer. The ANN has five inputs and one output. From computational experiments, it was found that two hidden layers with 7 neurons showed a suitable network architecture. The training algorithm used was Bayesian Regularization [34], which showed the best performance among several tested algorithms. Fig. 14 shows the CAD model of a validation case for the proposed tool path generation method. The part is 45.0 mm high. The dimensions of the rib-web structure are detailed in Fig. 14b. The tool path for printing the part was generated using the developed algorithm. Tool path generation proceeds layer by layer. The slicing plane slices the CAD model from the bottom to the top with uniform distance in Z + direction. Based on the intersection between the slicing plane and the CAD model, inner and outer contours are obtained. The developed algorithm computes offset curves from inner and outer part contours, and then establishes the continuous tool path for each layer according to the proposed algorithm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure2.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure2.1-1.png", + "caption": "Fig. 2.1 a Human arm modeled as planar 2 DOF serial manipulator. The angle of each DOF is often described as the qi variable, where i is the index of the DOF. b Human thumb modeled as 3D serial manipulator with 5 rotational DOFs contained in the carpometacarpal (CMC with 2 DOFs), metacarpophalangeal (MCP with 2 DOFs), and interphalangeal (IP with 1 DOF) joints. Note the axes of rotation of the different DOFs need not be parallel or perpendicular to each other [10]", + "texts": [ + " In general, there are two kinds of engineered DOFs that are convenient to define and use mathematically: the linear or prismatic DOF like telescoping tubes that change the lengths of a link in the limb; and the revolute or rotational DOF like a hinge that changes the orientation of adjacent links in the limb. This allows us to use the state of each DOF to define a specific limb configuration, shape, and size. In addition, by having motors act on each DOF using linear or rotational motors, we can produce specific limb forces and accelerations. I will focus on rotational joints because most vertebrate limbs are approximated as behaving in this way,1 as in Fig. 2.1. Universal joints, such as those used to represent 2 DOF rotational joints like the metacarpophalangeal (MCP) joint of the index finger (which is the base knuckle of the finger), consist of two pin joints with intersecting and perpendicular rotational axes. Ball-and-socket joints, like the shoulder or hip, consist of three intersecting and perpendicular rotational joints. Other joints like the 1In biological systems, joint kinematics arise from the interaction of the contact of bony articulating surfaces held by ligamentous structures", + " This situation highlights the unavoidable conceptual struggle in neuromechanics between mathematical rigor and expediency versus biological realism. 4Actuator is the generic engineering term for a motor or some other device that produces forces or mechanical work. The forward kinematics of a limb determine the location and orientation of its endpoint with respect to its base, given the relative configurations of each pair of adjacent links of the limb [6]. The base is usually the origin of the fixed, reference coordinate system\u2014(x, y) or (x, y, z) in Fig. 2.1\u2014chosen to represent the Cartesian coordinates of the workspace of the limb. The endpoint is the final, functional part of the limb. It is the point of interest, such as the hand when we speak of the arm for reach tasks, the foot when we speak of the legs for locomotion, or the fingertips when we speak of the hand for manipulation. Here I briefly present a simplified version of well-established methods to calculate forward kinematics of limbs. These simple kinematic formulations are common in neuromechanics studies, and sufficient to address important debates of motor control. In [6, 7] you can find an in-depth and generalized treatment of these topics. This basic kinematic problem is: given a mathematical representation of the robotic or biological limb, and its joint angles and angular velocities, what is the position and velocity of its endpoint? To do so we must first understand how to create a mathematical representation of the forward kinematics of the limb. Consider the example of a human arm, modeled as the planar 2 DOF serial manipulator shown in Fig. 2.1a. It is called a planar model because it is constrained to lie on a 2D plane; in contrast to a spatial model like the thumb model in Fig. 2.1b that allows motion in 3D space. The parameters of the arm model needed to calculate the position of the hand (i.e., the endpoint) are the lengths of the forearm and upper arm, and the angles of the shoulder and elbow joints as shown in Fig. 2.1a. Using the sample parameter values shown in the figure, it requires only basic knowledge of geometry to calculate the endpoint location by inspection as (x, y) = (25.4 cos(135\u25e6) + 30.5 cos(15\u25e6), 25.4 sin(135\u25e6) + 30.5 sin(15\u25e6)) (2.1) (x, y) = (11.5, 25.9) in cm (2.2) That was simple enough. However, now consider the 3D model of the thumb shown in Fig. 2.1b, in which there is a universal joint at both the carpometacarpal (CMC) and metacarpophalangeal (MCP) joints, and one hinge joint at the IP (interphalangeal) joint [10]. Say the metacarpal bone (closest to the wrist) has length 5.08 cm, the proximal phalanx (middle bone) has length 3.18 cm, and the distal phalanx (the bone on the thumbtip) has length 2.54 cm, and the joint angles are as in Table 2.1. Where is the endpoint then? The mathematical expression for calculating the thumb endpoint coordinates for any set of joint angles is quite complicated, and even difficult to calculate by inspection", + " But there are no DOFs between frames N \u2212 1 and N as both frames are fixed to the same rigid body. The addition of such extra (or \u2018dummy\u2019) frames of reference is sometimes necessary to define the forward kinematic model of the limb. To avoid confusion, the end of a range will always be a capital letter like N . Thus, T N 0 = T 1 0 T 2 1 . . . T N\u22121 N\u22122 T N N\u22121 (2.4) where T N 0 = \u23a1 \u23a3 RN 0 p0,N 0 0 0 1 \u23a4 \u23a6 (2.5) If there are 2 or more DOFs between two rigid bodies, like the CMC joint at the base of the thumb in Fig. 2.1, then intermediate frames of reference, and their respective homogeneous transformations, are needed to represent these DOFs. Appendix A and Sect. 2.4 discuss the importance of defining and allocating the DOFs of a limb in a specific order. See, for example, the kinematic models of the thumb in [10, 11]. 2. Extract the position of the endpoint from the homogeneous transformation T N 0 . Note that in Eq. 2.5 the vector pN 0 is the location of the endpoint with respect to the base. 3. Extract the orientation of the endpoint from the homogeneous transformation T N 0 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003846_j.renene.2018.01.072-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003846_j.renene.2018.01.072-Figure1-1.png", + "caption": "Fig. 1. Dynamic model of a single stage planetary gear train.", + "texts": [ + " Based on the dynamic analyses, a resultant vibration signal model is developed as the summation of weighted vibration signals along the action lines of both sun-planet and ringplanet pairs by considering the effects of transmission paths. Then, a numerical example is used to demonstrate the vibration features of a single stage planetary gear trainwith incipient crack on the sun gear working under slow-speed and varying load condition in both time domain and frequency domain. In the last, an experimental test rig is set up to validate the simulations. A lateral-torsional-coupled dynamic model of a single stage planetary gear train is shown in Fig. 1. The system is composed of one sun gear \u2018s\u2019, one ring gear \u2018r\u2019, one carrier \u2018c\u2019 and N identical planet gears denoted as pn. Herein, Oxy is defined as the general coordinate system rotating at the speed of the carrier uc with x axis passing through the center of the 1st planet. Each component i (i\u00bc s,r,c, pn) has three degree of freedoms, i.e., two lateral motions (xi, yi) and one torsional motion (ui). The supporting stiffness for each component is represented by a lumped virtual spring with constant stiffness kij (j\u00bc x,y,u)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000625_tro.2011.2173835-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000625_tro.2011.2173835-Figure4-1.png", + "caption": "Fig. 4. Free-body diagram of a microsphere in its environment.", + "texts": [ + " To enable the accurate and efficient positioning of a micro-object using this manipulation method, a relation must be determined between Dg and Ds . To achieve the assembly of multiple micro-objects, a Mag\u03bcBot must push one of the objects to the other so that they contact. However, because of fluid effects, this task cannot be achieved by simple contact pushing, as shown in Fig. 3. A pushing method that compensates for this fluid effect is necessary to achieve assembly. When a Mag-\u03bcBot manipulates a microsphere, the sphere experiences forces from the environment. Fig. 4 displays a schematic of these forces, which includes the microrobot\u2019s contact pushing force Fc , fluid drag forces from the environment F (U, u), friction forces from the surface Ff , adhesion forces P between the sphere and the surface, as well as the sphere\u2019s own weight Wb . In this study, we primarily focus on manipulations due to fluid interactions and, thus, ignore Fc in analyses. We develop much of the theoretical background of these interactions in [20] and summarize the formulations in this section" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002467_j.triboint.2017.01.035-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002467_j.triboint.2017.01.035-Figure2-1.png", + "caption": "Fig. 2. Deformation relationship between ball and rings.", + "texts": [ + " z i i e c i i e r e e (2) Here, Fr and Fz are the radial and axial loads of bearing respectively, and the contact loads Qi and Qe are calculated by Hertzian theory for spherical contact, \u23aa \u23aa \u23a7 \u23a8 \u23a9 Q K \u03b4 Q K \u03b4 = = ,i i i e e e 3/2 3/2 (3) where Ki and Ke are the load-deflection parameters, \u03b4i is the contact deformation between ball and inner ring, and \u03b4e is the contact deformation between ball and outer ring. \u23a7\u23a8\u23a9 \u03b4 l l \u03b4 l l = \u2212 = \u2212 ,i i oi e e oe (4) where loi and loe are the initial center lengths, while li and le are the center lengths during operation for inner and outer ring respectively as shown in Fig. 2, \u23a7 \u23a8\u23aa \u23a9\u23aa l \u03b5 l \u03b1 u v \u03b5 u l \u03b1 u v l \u03b5 l \u03b1 v \u03b5 l \u03b1 v = + ( cos + \u2212 + + ) + ( sin + \u2212 ) = + ( cos + \u2212 ) + ( sin + ) i b oi o r r ir cent oi o z z b oe o r er oe o z 2 2 e 2 2 (5) where vr and vz are the ball center motions as well as the output of the ball equilibrium solution, ur and uz are the inner ring motions, \u03b5ir and \u03b5er are the ring thermal expansions, and ball thermal expansion \u03b5b and inner ring centrifugal expansion ucent can be estimated by the following two equations [25]. \u03b5 \u03b1 \u0394T r= ,b b bb (6) u \u03c1\u03c9 E d D v d v= 32 [ (3 + ) + (1 \u2212 )]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-FigureA.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-FigureA.3-1.png", + "caption": "Fig. A.3 The rotation of the rigid body on the plane of the page about the kinematic DOF of a pin joint can be described as the rotation of frame 1 with respect to frame 0. Frame of reference 0 is fixed and attached to ground, and frame 1 is attached to the rigid body, and they both share the same origin. As the link rotates by an angle q1, the location of the endpoint, Eq. A.12, does not change in frame 1, but changes in frame 0. The angle q1 is defined to be zero when both frames are aligned, and is positive when rotating as per the right-hand rule: If your right thumb is pointing along the axis of rotation (out of the page in this case), then the fingers curl in the direction of a positive rotation", + "texts": [ + "3 Rotation of Frames of Reference Expressing vectors in a variety of frames of reference is critical to the mathematical analysis of limb kinematics and dynamics. This is because each rigid link of a limb is described mathematically by a frame of reference attached to it. From then on, you do not work with the links themselves, but only with the frames of reference that represent them. Some thorough sources for these fields are [2, 3, 10]. Here, I only present a short introduction to essential concepts from these very extensive topics. Figure A.3 shows the example of frame 0 defined by i0, j0, and k0 attached to ground (which is also a rigid body), and frame 1 attached to a link that rotates about a pin joint attached to ground. Thus this is a 1 DOF kinematic chain as defined in Chap. 2. By convention, the two frames of reference share the same origin, and in their default configuration their basis vectors are aligned with each other. Then, frame 1 rotates an angle q1 about the axis k0 (which is collinear with k1 as per the definition of default configuration)", + " Therefore, unless there is ambiguity, I will not write such subscripts for the vectors to simplify notation. For example, Eq. A.25 becomes \u239b \u239d a b c \u239e \u23a0 = Rn+1 n \u239b \u239d d e f \u239e \u23a0 (A.30) It is important that you try out these rotation matrices by doing exercises like the one shown in Fig. A.5 by hand. This way you can convince yourself of how they work and how to use them. These will become crucial to your ability to create kinematic models of limbs (Fig. A.6). A.6 Translation and Rotation of Frames of Reference Let us consider an extension of Fig. A.3 that includes a second link, and therefore the need to both rotate and translate frames of reference. Figure A.7 shows the example Fig. A.6 Figure showing the isolated right-handed rotation about the collinear basis vectors kn and kn+1 by an angle q that produces the rotation matrix in Eq. A.29 q q i n+1 j n+1 j n i n k n , k n+1 of a planar 2 DOF limb where we need to define and place a frame of reference at the limb\u2019s endpoint. Figure A.8 shows the general case of two frames of reference displaced and rotated with respect to each other" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure12.11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure12.11-1.png", + "caption": "Figure 12.11.2 Side view of double transverse arms for two-dimensional numerical analysis.", + "texts": [ + " It may be concluded that the algebraic method is useful, but not precise because of the modelling assumptions, for example neglect of the ball joint lateral position from the wheel centre plane, a detail which is easily included in the numerical model. The algebraic model could be made more accurate, of course, but then the clarity of the equations would be reduced. As in the case of the lateral properties, which can be analysed approximately in two dimensions using an equivalent front view, the pitch properties, namely bump scrub (anti-dive, etc.) and bump caster variation, can be analysed approximately in a two-dimensional equivalent side view, as in Figure 12.11.1. The rear effective pivot points of the arms are the points at which the pivot axes penetrate the longitudinal vertical plane of the wheel centre. Themathematical analysis of the side view follows verymuch along the lines of the front-view analysis, but with changes of notation and some changes of sign. The variables shown are the ball joint height difference HBJD, the mean ball joint height HBJM, the upper arm equivalent longitudinal length LXU and angle uXU, the latter positive as shown in the figure and increasing in bump, and the lower arm length LXL and angle uXL", + "2): SXS \u00bc fBJHSXD 2\u00abBScd1;X with SXU \u00bc 1 2 \u00f0SXS \u00fe SXD\u00de SXL \u00bc 1 2 \u00f0SXS SXD\u00de and the lengths follow immediately as reciprocals. In a practical design it may be that the secondary coefficients are set to zero, \u00abBScd1;X \u00bc 0 \u00abBcas2 \u00bc 0 in which case SXD \u00bc 0; SXS \u00bc 0 LXU \u00bc \u00a5; LXL \u00bc \u00a5 The infinite lengths in sideviewmean that the pivot axes are parallel to thevehicle centre plane. The angles are still evaluated as above, and the axes will generally be inclined to the horizontal. As an alternative to the analytical solution in pitch, a two-dimensional numerical solution is a possibility, Figure 12.11.2, similar in general terms to the front view. The lower arm is rotated from the static position and the consequent caster angle, longitudinal scrub and suspension bump are solved and curve fitted for coefficients. The difference is that the ground contact point is the point initially directly below thewheel centre, and for longitudinal scrub analysis thewheel must be treated as locked in rotation. The angle FBE will normally be positive as shown, in the other direction from in the front view, and the perpendicular EF is also probably in the other direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003409_j.mechmachtheory.2015.06.004-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003409_j.mechmachtheory.2015.06.004-Figure2-1.png", + "caption": "Fig. 2. Lumped parameter model of the spur planetary gear: (a) in-plane motions; (b) axial motions.", + "texts": [ + " All components are modeled as rigid bodies with moments of inertia Ic, Ir, Is, Ip and massmc,mr,ms,mp. Because of bedplate tilt angle, the gear plane and vertical plane do not coincide (Fig. 1). The tilt angle affects the components of gravity in the gear plane and the direction perpendicular to the gear plane. Therefore, the axial motion has to be taken into account. Based on the typical rotational-translational dynamic model [17], the rotational-translational-axial lumped parameter model is presented (Fig. 2). Each component has one rotational, two translational and one axial degree of freedom, and the system has 4(N + 3) degrees of freedom, where N is the number of planets. The gravity, backlash, backside contact, bearing clearance and bedplate tilt angle are considered. Compared with the gear motion, the bedplate tilt angle \u03b3 varies relatively slowly [19]. In the following derivation process, the change of tilt angle is treated as a static process. For spur gears, the dynamic mesh force only acts in the gear plane, and the axial motion is not coupled with the translational and rotational motions in the gear plane" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000721_j.ymssp.2008.08.015-Figure11-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000721_j.ymssp.2008.08.015-Figure11-1.png", + "caption": "Fig. 11. UNSW gear test rig.", + "texts": [ + " The amount of delay between the inverted echo peaks is measured by examining the negative peaks appearing in the cepstrum, to perform a DD. Fig. 10, (d) shows the presence of the first rahmonic peak which appears in the position (in number of samples) corresponding to the amount of delay between the inverted echo impulses. Theoretical assessment of the technique based on simulated signals showed promising results [6]. Now the method is evaluated by using experimentally measured signals. Vibration and transmission error (TE) signals measured from the gear test rig (Fig. 11) at the University of New South Wales were used to evaluate the practicality of the DD technique in practice. The TE was obtained by taking the difference of the phase demodulated encoder signals attached to input and output gears [20] (see Fig. 11 for picture of the encoder and accelerometer settings). Three sets of steel gears with tooth spalls of different sizes and a pair of plastic gears with an artificially cut TFC were considered. The gears with the seeded faults are shown in Fig. 12, (1a)\u2013(1d) and the dimensions of the faults are given in Table 2. Vibration (acceleration) signals on the gearbox casing were measured while running the gears at a constant speed of 168 rpm. It was found from the measured TE of steel gears that the effect of the TFC was not as clear as the result expected based on the static simulation study" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure4.12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure4.12-1.png", + "caption": "Fig. 4.12 Crank-slider linkage mechanism", + "texts": [ + " This example consists of computing the velocity and displacement analyses of the crank-slider linkage mechanism, a planar mechanism widely used in reciprocating engines where cranks (with connecting rods) are used to transform the back-and-forth motion of the pistons into rotary motion, and vice versa. The cranks usually are incorporated into a crankshaft. Prominent applications of this mechanism include internal combustion engines, steam trains, pumps, compressors, and of course robotics applications. Solution. A crank-slider linkage is a four-bar mechanism where one of the pin joints is substituted by a sliding joint (see Fig. 4.12). In a standard arrangement, the line connecting two adjacent pin joints is parallel to the axis of the sliding joint. The purpose of the planar mechanism at hand is to convert the rotational motion of the crankshaft (1) into oscillatory motion of the slider (3), or vice versa. With reference to Fig. 4.12, d denotes the nominal position of the slider with respect to the origin O of the reference frame XY , which is quickly determined as d2 D a2 1 C a2 2 2a1a2 cos \u02c7; (4.97) 4.3 Equations of Velocity in Screw Form 89 where \u02c7 D q is the orientation of the coupler bar with respect to the crankshaft in which D arcsin .a1 sin q=a2/ is the orientation of the coupler bar measured clockwise from the X-axis. Furthermore, the velocity state of the slider (3) as observed from the base link (0), the vector 0V3 O D 0 0 0 Pd 0 0 T ; (4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure2.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure2.9-1.png", + "caption": "FIGURE 2.9. Global pitch.", + "texts": [], + "surrounding_texts": [ + "2. Rotation Kinematics 41\nTh e expanded form of the 12 global axes tr iple rotations are presented in Appendix A .\nExample 8 Order of rotation, and order of matrix multiplication. Changing the order of global rotation matrices is equivalent to changing the order of rotations. Th e position of a point P of a rigid body B is located at B r p = [1 2 3 f . Its global position aft er rotation 30deg about X axis and then 45deg about Y -axis is at\n-0.84 0.15 -0.52\nQy,45 QX,30 B r p\n[\n0.53 0.0\n-0.85\n0.13 ] [ 1] [-0.76 ]0.99 2 3.27 0.081 3 - 1.64\nand if we change th e order of rotations then its posit ion would be at\nQX ,30 Qy,45 B r p\n[ 0.53 0.0 -0.84 0.15 -0.13 -0.99 0.85 ] [ 1] [ 3.08]0.52 2 1.02 0.081 3 -1.86\nTh ese two final positions of Pare d = I(Gr p) 1- (Gr p) 21 = 4.456 apart .\n2.3 Global Roll-Pitch-Yaw Angles\nThe rotat ion about the X -axis of the global coordinate frame is called roll, the rotation about the Y-axis of the global coordinate frame is called pitch, and the rot ation about the Z-axis of the global coordinate frame is called yaw. The global roll-p it ch-yaw rotation matrix is\nQ Z ,,,!QY,{3Qx ,o:\n[ e(3q - co:S'y+ q sa s(3 e(3s,,! co:e\"!+ sas(3s,,! -s(3 e(3sa sas\"! + caqs(3 ] - qsa + ea s(3s,,! . (2.29) co:e(3\nGiven the roll, pitch , and yaw angles, we can compute the overall rotation matrix using Equation (2.29). Also we are able to compute the equivalent roll, pit ch, and yaw angles when a rot ation matrix is given. Suppose that r i j indicat es the element of row i and column j of the roll-pitch-yaw rot ation matrix (2.29), then the roll angle is\na = tan- 1 (1'32) 1'33 (2.30)", + "42 2. Rotation Kinematics\nand the pit ch angle is\n(2.31)\nand the yaw angle is\nprovided that cos (3 =f: O.\n'Y = tan-1 (r21 )\nrll (2.32)\nExample 9 Global roll, pitch, and yaw rotations. Figures 2.8, 2.9, and 2.10 illustrate 45 deg roll, pitch and yaw about the axes of global coordinate frame.", + "2. Rotation Kinematics 43\n2.4 Rotation About Local Cartesian Axes\nConsider a rigid body B with a space fixed at point O. The local body coordinate fram e B(Oxyz) is coincident with a global coordinate frame G(OXYZ) , where the origin of both frames are on th e fixed point O. If the body undergoes a rotation 'P about the z-axis of its local coordinate frame, as can be seen in the top view shown in Figure 2.11 , then coordinates of any point of the rigid body in local and global coordinate frames are related by the following equat ion\nBr = A z,'f' Gr . (2.33)\nThe vectors G r and B r are th e position vectors of the point in global and local frames resp ectively\n[ X Y Z JT [ x Y z f\n(2.34)\n(2.35)\nand A z,'f' is the z-rotation matrix\nA\" ~ [ ~~r:~ :~~~ ~] . (236)\nSimilarly, rotation e about the y-axis and rotation 1jJ about the x-axis are describ ed by the y-rotation matrix Ay,o and t he x -rotation matrix Ax,,p respectively.\n[\ncos e 0 Ay,o = 0 1\nsine 0\n[\n1 0 Ax,,p = 0 cos 1jJ\no - sin 1jJ\n- s~ne ]\ncos e\nsi~ 1jJ ] cos 1jJ\n(2.37)\n(2.38)" + ] + }, + { + "image_filename": "designv10_3_0003497_j.triboint.2019.105960-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003497_j.triboint.2019.105960-Figure2-1.png", + "caption": "Fig. 2. Geometrical dimensions of a double-row TRB.", + "texts": [ + " Section 3 first presents the formulation of contact pressure and discusses the distribution of contact pressure in tapered roller with and without crowned roller profiles, and then investigates the effect of angular misalignment on the contact pressure. Brief conclusions are presented in Section 4. In order to determine the internal force and pressure distribution of rolling elements, this section presents a novel quasi-static model subjected to the combined loading, angular misalignment and frictional force. The typical cross-section of a double-row TRB is illustrated in Fig. 2, where \u03b1i is the contact angle of inner ring, \u03b1m is the mean contact angle, \u03b1o denotes the contact angle of outer ring, \u03b5 represents the roller semi-cone angle, lwe denotes the roller effective length, Dmax represents the diameter of roller large-end, Dmin is the diameter of roller small-end, Dm stands for the mean roller diameter. In addition, \u03b1f is the inner ring flange angle, ri is the inner raceway radius in the middle of contact length, rm represents the pitch radius and ro is the radius of outer raceway in the middle of contact length" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure5.13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure5.13-1.png", + "caption": "Fig. 5.13 Impact of a beam; Model parameters: c, m, l, EI", + "texts": [ + "2 Fundamentals 333 elastic set-up of the housing, the resilience of the drum and other effects is required to accurately clarify all dynamic influences. A flap with a horizontal axis of rotation is slammed shut. The first three natural frequencies during free rotation (c = 0) and after the impact (c = 0) are to be calculated and represented as a function of the characteristic parameter c = 2EI/(cl3). The flap is modeled as a bending oscillator with 4 degrees of freedom and the point of impact is modeled as a massless spring, see Fig. 5.13. Figure 5.13 shows the bending oscillator prior to the impact. The absolute displacements can be combined in the coordinate vector q = [q1; q2; q3; q4] T . (5.59) The equation of motion corresponds to (5.43). The elements of the compliance matrix D are determined from Table 5.1. For example, the influence coefficients according to case 1 there for l1 = l2 = l3 = l; c1 \u2192\u221e; c2 = c are: d11 = 1 9c + 4l3 9EI ; d12 = 2 9c + 7l3 18EI ; d22 = 4 9c + 4l3 9EI . (5.60) Case 2 provides the influence coefficients for l1 = l3 = l; l2 = 2l; c1 \u2192 \u221e and c2 = c: d14 = 4 9c \u2212 4l3 9EI ; d44 = 16 9c + 4l3 3EI ", + " The critical speed for the same direction of rotation (\u03a9/\u03c9 = 1) is nk = 6127 \u00b7 rpm (=\u0302fW = 102.1 Hz). S5.6 The continuous model is obtained by evenly \u201cspreading\u201d the four masses over the beam length. The beam then has a constant mass distribution A = m/l. Table 5.7, Case 2 provides the eigenvalues for this continuous model, in which the beam is hinged at one end and free at the other: \u03bb1 = 0; \u03bb2 2 = 15.4; \u03bb2 3 = 50.0. (5.103) Note when comparing the natural circular frequencies to (5.94) that the flap in Fig. 5.13 has the length L = 4l and the mass 4m. The natural circular frequencies for this model of the continuum beam are therefore: \u03c9 (K) i = \u03bb2 i \u221a EI AL4 = \u03bb2 i \u221a EI A44l4 = \u03bb2 i 16 \u221a EI ml3 . (5.104) The natural frequencies of the free-falling flap in Fig. 5.14 are asymptotic on the right margin (c \u2192 0) as early as at c = 100. The values \u03c91 \u221a ml3 EI \u2192 0; \u03c92 \u221a ml3 EI \u2248 0.89; \u03c93 \u221a ml3 EI \u2248 2.8 (5.105) can be obtained for the four-mass system. (5.104) with (5.103) provides the following for the continuum \u03c9\u2217 1 \u221a ml3 EI = 0; \u03c9\u2217 2 \u221a ml3 EI \u2248 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.32-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.32-1.png", + "caption": "FIGURE 5.32. Illust rat ion of a screw joint to define Shet h coordinate transfor mation.", + "texts": [ + " A cylindrical joint provides two DOF, a rotational and a translational about the same axis . Two links connecte d by a cylindrical joint are shown in Figure 5.31. The transform ation ma trix for a cylindrica l joint can be described by combining a revolute and a prismatic joint. Therefore, the 252 5. Forward Kinematics Sheth parameters are a = 0, b = 0, c = d, 0: = 0, (3 = 0, \"( = e , and - sine 0 0 j cose 0 0 Old . o 0 1 (5.180) Example 161 * Sheth transformation matrix at a screw joint. A screw joint, as shown in Figure 5.32, provides a proportional rota tion and trans lation motion, which has one DOF. The relationship between translation h and rotation () is called pitch of screw and is defined by h p = o\u00b7 (5.181) The transformation for a screw joint may be expressed in terms of the relative rotation e [ cosO - sin e 0 ~ jiTj = sine cos e 0 0 0 1 0 0 0 or displacement h rcoo' . h 0 ~ ] - SlIli _sin K p cos !l 0 T j - P P 0 0 1 0 0 0 (5.182) (5.183) The coordinate frames are installed on the two connected links at the screw joint such that the axes Wj and z; are aligned along the screw axis, and the axes Uj and Xi coincide at rest position" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001663_piee.1968.0265-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001663_piee.1968.0265-Figure1-1.png", + "caption": "Fig. 1 Magnetic circuits and terminals a Simple linked circuits b Distributed circuits c System boundary and terminals", + "texts": [], + "surrounding_texts": [ + "Synopsis The possibilities of using magnetic, instead of electric, equivalent circuits for eddy-current devices, which have recently been pointed out by Laithwaite, are here explored further. Couplings between distributed flux paths and windings can be expressed in terms of a generalised linkage parameter N, which is associated with flux linkage in electric circuits, and with an analogous current linkage in the magnetic equivalent. The magnetic-circuit treatment extends to rotating, as well as to static, devices, and leads to a view ofinduction machines as nonpassive magnetic elements. The relationships between the energy flow through the terminals, the mechanical forces and the magnetic terminal parameters are examined, and an alternative equivalent circuit, in which the analogue of current is not the flux but its rate of change, is shown to be in many respects a more useful one. The force equations are applicable, in particular, to devices in which induced currents are important. List of symbols B = magnetic flux density ^\u2014 magnetic analogue of capacitance '\u00a3= electric field 2F= m.m.f. 5?= magnetic analogue of conductance / \u2014 instantaneous current / = r.m.s. current 1, then \u03b4j = \u2016x \u2212 jv3\u2016. Step 7: As explained previously, the robot is represented by a set of surface vertices. Let the vertex coordinates be xl i , i = 1, . . . , Vl , where Vl is the number of vertices on link l. The deviation distance of a single coordinate xl i from the constraint segments {\u03a9k+1 , . . . ,\u03a9k+\u0394k} can be computed as follows: l i\u03b4k,\u0394k = min j { \u03b4k+1(xl i), \u03b4k+2(xl i), . . . , \u03b4k+\u0394k (xl i) } (8) where \u0394k is the number of segments involved in the calculation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000966_j.phpro.2011.03.048-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000966_j.phpro.2011.03.048-Figure2-1.png", + "caption": "Figure 2: Schematic representation of the two dimensional transformation of a unit cell", + "texts": [ + " On the other hand it concentrates on the investigation of manufacturing lattice bars contradicting conventional design rules to allow the build-up of tilted unit cells and whole structures. Results of the study are implemented in the development and manufacture of an innovative implant featuring a modified surface with osseointegrative characteristics. For the modification of the implant\u00b4s surface a unit cell approach was used. In order to avoid the errors discussed above when approximating a complex surface by cells, the unit cell has to be transformed. This transformation can be described by a set of mathematical operations. Figure 2 shows the combination of the operations scaling (S), distortion (D), rotation (R) and transformation (T) which are necessary to describe the surface by a combination of several cells. The order of these operations is dependent on the choice of the coordinate system and the routine chosen for software-related realization. To simplify matters, the possibility to describe any surface by an alignment of unit cells is only exemplified in two dimensions and on the basis of a circle. The starting point is a quadratic unit cell, or its bounding box, with the edge length a" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.22-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.22-1.png", + "caption": "Fig. 1.22 Dampers as sub-assemblies; a) VISCO damper (Source: GERB [33]), b) Single pipe damper (VDI 3833) (Source: Fichtel & Sachs), c) Spiral bearing damper (VDI 3833)", + "texts": [ + " If the mass m is known, the damping constant can be determined from b = m(\u03a92 \u2212\u03a91) = 2\u03c0m(f2 \u2212 f1). (1.110) A major advantage of this procedure is that the magnitude of the excitation force does not have to be known. 1.4 Damping Characteristics 51 The classical way is to measure the parameter values of those components that serve as dampers. This is done for sub-assemblies that were produced as dampers, such as the torsional vibration dampers described in Sect. 4.4 or the commercial dampers, some of which are described in VDI Guideline 3833 [36], see the examples in Fig. 1.22. Many dampers use the effect that a velocity-dependent force is created when squeezing a viscous medium through a small gap. Proven damping media include oils, bitumen, polybutene and silicone. Some dampers also use friction, see Figs. 4.42 and 4.44. Characteristics and parameter values are available for most commercial dampers. One can request these from the manufacturers. If a free-response test is analyzed, in most cases a dependency of the logarithmic decrement on the amplitude will be found", + " None of the measures should impair any one of the technological requirements (such as good forging efficiency). Forging hammers typically require large reinforced concrete foundations (Fig. 3.18a) to absorb the high dynamic loads of the hammer. Figures 3.18b and c show alternative mountings of a forging hammer. By comparing the volumes of the concrete bodies, it can be deduced that the cost for a foundation can vary. It 212 3 Foundation and Vibration Isolation is very beneficial to provide a resilient support for such equipment. Using VISCO dampers (in parallel to the springs), according to Fig. 1.22a, can considerably reduce the mass of the spring-mounted foundation block as compared to a firm mounting. The system shown in Fig. 3.18c has proven its worth for hammers with a work capacity of up to 400 kJ. The basic structure is shown in Fig. 3.19. The frame of the forging hammer is firmly mounted onto the foundation block. It houses the lifting or accelerating mechanism for the hammer (ram). One can distinguish between drop hammers and hammers that are accelerated by a drive system (such as compressed air)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000526_tmag.1977.1059627-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000526_tmag.1977.1059627-Figure2-1.png", + "caption": "Figure 2. Superposition of wedges to obtain finite gap, finite width head.", + "texts": [ + " The rectangular field components are given by: H4 = (Ho/n)[Fq(u+)-F4(~_)1 (74 with u+ as in (6b) and Fqx = tan-l [sinh(u/2)/sin('p/2)] (7b) Fqy = -2cosh(u/2)sin(rp/2) (7c) Fqz = 2cosh(~/2)cos('p/2)-ctnh-~ [cosh(u/2)/cos(~/2)] (7d) with 'p as shown in Figure lb , and defined by tan-l(z/y), zo, y g/2, the maximum field error does not exceed 8%. If field points closer than about g/2 from the head are evaluated by superposition, the error increases. This occurs because in the subtraction, Figure 2c, just the right values of potential are preserved on the surfaces where the excess material is removed, but there are slight discontinuities in the fields normal to these boundaries. This is equivalent t o a small magnetic charge density in the y=O plane for Ixi>g/2 and izl>w/2 but localized near the gap corners. By restricting y>g/2, the effect of these charges cannot exceed 8% field error for w>O and indeed vanishes as w+m. Another reason to restrict yBg/2 is that even in two dimensions the assumption of linear potential drop in the gap is only approximately correct" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001863_j.optlaseng.2017.07.008-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001863_j.optlaseng.2017.07.008-Figure3-1.png", + "caption": "Fig. 3. A schematic view of the cross-section of a single track cladding.", + "texts": [ + " The geo- etrical characteristics (clad height, clad width, clad area, etc.) of the ross-section in each cladding layer were measured using the optical miroscopy (OM). For each geometry parameter of the clad beads, every easurement was repeated three times and their averages were calcuated. According to Farahmand and Kovacevic [27] , the dilution depth s too shallow (less than 10 \u03bcm) in laser cladding using HPDL, and it ould not be measured by OM. Therefore, the dilution depth would not e chosen as the geometry characteristics of the cross-section. Fig. 3 hows the cross-section of the single track cladding. . Results and discussion The cross-section diagram of 27 STCs at different process parameters P, T and V ) are depicted in Fig. 4 . It can be seen from the figure that here are no porosity and crack in the clad zone of all cross-sections. able 2 lists the process parameters and results of the geometry charac- eristics parameters of each cross-section measured by OM. The detailed nalysis will be carried out in the following sections. .1. Effect of process parameters on geometrical characteristics of the ross-section " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002059_s00466-017-1528-7-Figure17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002059_s00466-017-1528-7-Figure17-1.png", + "caption": "Fig. 17 Predicted temperature distributions during building a bridge sample a Heat layers before forming a bridge; b Heat a layer near the top surface of the bridge", + "texts": [ + " There are three numerical steps for one layer: depositing a layer, heating the layer, and cooling down. This three-step approach was repeated for all layers. It took 9.1 h to get one complete solution including a thermal analysis to predict temperature and a mechanical analysis to prediction distortion. It should be pointed out that the laser scan direction and scan path within each layer cannot be considered in this simplifiedmodeling approach. These two factorsmay have small effects on distortion prediction which will be studied in a future project. Figure 17 shows predicted temperature distributions on the bridge sample after heating one layer to material melting temperature. A high temperature gradient was formed near the heating layer, which is critical to predict the deformation correctly. Figure 18 shows the predicted deformation shape and vertical deformation magnitudes. Because of the shrinkage of built materials, the sample was bent down in the middle. Note that the deformation was magnified by five times for better visualizing the deformation shape" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001874_tmech.2018.2818442-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001874_tmech.2018.2818442-Figure5-1.png", + "caption": "Fig. 5. Design of the manipulator", + "texts": [ + " In a similar way, the winding pulley 2 will make the grippers open or close. The driving module is a 1083-4435 (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. TMECH-07-2017-6836.R1 4 modular design which can be replaced during the operations. To meet the requirements of operational space, sinus robot is designed with the DOFs of rotation and translation as shown in Fig. 5. Rotation enables the end-effector to reach the top and alveolar recess of maxillary sinus while translation enables it to reach the front and back of maxillary sinus. The base of the manipulator is connected to the shaft of the motor 2 by coupling to realize the rotary motion. A linear actuator (HIWIN\u00ae KK6005PE-500A1-F0CS1) as shown in Fig. 5 is adopted so that the sinus robot can achieve translation motion. This kind of translation mechanism has higher parallel movement precision than the translation mechanism of screw rod and guide rail assembly. The driving module is mounted on the linear actuator. The designed sinus robot is shown in Fig. 5. The control infrastructure of sinus robotic system is based on a traditional setup for remote operation. One haptic device (Novint\u00ae Falcon\u2122) is connected to a host PC. It possesses 4 DOFs (translation, rotation, deflection, gripper) and then can be bent into maxillary sinus for surgical tasks. Table I shows the specifications of the sinus robot. In this section, piecewise constant curvature hypothesis enables the kinematics of continuum module to analyze the deflection of manipulator. In order to describe the kinematics, three coordinate systems of the robot shown in Fig. 5 are defined. Global joint coordinate system is fixed to the base joint, and its XY-plane is defined in accord with the base joint\u2019s upper surface, the origin of XY-plane is at the base joint\u2019s center. The direction of b x is from the base joint\u2019s center to first deflection cable, and the direction of b z is normal to the base joint. Local joint coordinate system designated as , , i i i x y z is attached to each joint to describe the system\u2019s kinematic configuration, whose origin is at center of each joint", + " Due to the negligible mass of joint, the inertial force and moment seem close to zero, inertial effects and gravitational loading have little effect on the total external loading. Then all external forces and moments are defined, the equilibrium equations are as follows: , , 0 0 eq i j f i T F F + F e (14) , , 0 i ela i eq M M M (15) In this section, the experiments and results analysis are presented. The experiments comprise kinematics validation, bending test, payload test, scissoring and skull phantom test. The overall configuration of platform is shown in Fig. 5. A master device which is used for inputs control is connected to a host PC. Four controllers (Maxonmotor\u00ae EPOS2 24/5, EPOS2 70/10) which control four motors respectively are also connected to the host PC using CANopen and USB protocols for signal outputs control. The host PC runs a Windows operating system (OS). Three types of motors (Maxonmotor\u00ae RE40 motor, HEDL500 encoder; RE-max24 motor, GP22C gearhead, HEDL500 encoder; RE16 motor, GP16C gearhead, MR32 encoder) are used in the sinus robot. In Microsoft Visual Studio, a customized program sends commands to controllers to control four motors as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003785_j.jmapro.2018.09.007-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003785_j.jmapro.2018.09.007-Figure1-1.png", + "caption": "Fig. 1. Diagram of the vertically and horizontally built samples and dimensions for the tensile specimens.", + "texts": [ + " At least twenty measurements were made at X, Y and 45\u00b0 direction, respectively. Tensile tests were carried out with an electronic testing machine (SANS XYA105C) at room temperature with measuring length of 66mm, according to EN 10002-1. The vertically and horizontally built samples were tested along their axis and the tensile velocity was 0.5 mm/min. Three tensile test results were collected for every type of specimen and the average values were adopted as results. The dimensions for the tensile specimens were made in two build direction, as illustrated in Fig. 1. Typical microstructures of the AlSi10Mg parts perpendicular to building directions produced by P-SLM are shown in Fig. 2. The interlayer microstructure features (as seen in Fig. 2(a)) created by the pulsed laser beam has distinguished difference with the elongated teardrop shape molten pool microstructures caused by continuous-wave laser beam movement reported in previous literature [17], the obvious layered structure can be observed, and the elliptical molten pools overlapping each other toward the direction of laser movement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure3.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure3.3-1.png", + "caption": "Fig. 3.3 A 3-link, 3 DOF planar serial kinematic chain. The details of the individual frames of reference are not shown for clarity as they follow the convention in Fig. 2.2", + "texts": [ + " In the case where you have more than 6 internal DOFS (think of a snake robot with many links), you can still control the 6 kinematic DOFs of the last link, but your system is kinematically redundant in that there is an infinite number of possible configurations q that can produce the same endpoint position and orientation (and you can do internal work that does not produce external work, in violation of the derivation in Sect. 3.1). We will discuss many versions of redundancy at length in later chapters. But, for the sake of expediency, in this chapter we will focus on limbs with at most 6 internal DOFs. Note that the last link of a planar limb has 3 external kinematic DOFs, as mentioned above. So let us move beyond the simpler systems shown in Fig. 2.3 and consider the system in Fig. 3.3. In this case, we have enough internal DOFs to control the 3 external DOFs at the last link: its location and orientation. The forward kinematic model is then x = \u239b \u239d x y \u03b1 \u239e \u23a0 = \u239b \u239d Gx (q) G y(q) G\u03b1(q) \u239e \u23a0 = \u239b \u239d l1c1 + l2c12 + l3c123 l1s1 + l2s12 + l3s123 q1 + q2 + q3 \u239e \u23a0 (3.16) and its Jacobian is J = \u23a1 \u23a2\u23a2\u23a2\u23a3 \u2212l1s1 \u2212 l2s12 \u2212 l3s123 \u2212l2s12 \u2212 l3s123 \u2212l3s123 l1c1 + l2c12 + l3c123 l2c12 + l3c123 l3c123 1 1 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 (3.17) Note that J \u2208 R 3 \u00d7 3 has the possibility of being full rank. Not all square matrices are full rank, and in this case it is full rank except for those postures that lead to singularities (more on this details later)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002721_0278364916640102-Figure18-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002721_0278364916640102-Figure18-1.png", + "caption": "Fig. 18. Pitch versus CoM Height of the MIT Cheetah I during the robot\u2019s trotting, gait-transition and galloping at 3.2 m/s.", + "texts": [ + " The controller resulted in an increase in CoM height and nose-down pitch after the gait transition, similar to the simulation result shown in Figure 12. The variations of the CoM height and the pitch are both increased with the gallop gait. The experiment clearly represents the characteristics of the transverse gallop (Bertram and Gutmann, 2009). The transition of the motion of the robot from downward-forward to upward-forward is initiated by the front legs, while the landing is achieved by the back legs. Extension 1 shows the experimental results. In Figure 18, we project the robot dynamics onto the phase plane of which the axes are the body pitch and the CoM height of the robot, respectively. These states are considered as the most representative ones to describe the robot\u2019s dynamics. Figures 16 and 18 illustrate periodic patterns we found in the entire state space; similar periodic patterns can be found from other phase planes. A large fluctuation in the robot states during the gait transition and convergence on the stable periodic orbit are more notable in Figure 18. foot-end trajectories. Figure 20 compares the equilibriumpoint foot-end trajectories and the actual foot-end trajectories with respect to the inertial reference frame during trotting at 3.2 m/s. The actual foot-end trajectories are reconstructed from encoder measurements at each joint and pitch data given from the IMU sensor over 2 s (\u2248 6 strides). The objective of the swing phase foot-end trajectory design is to re-position foot-ends to the desired angle of attack before the legs\u2019 touchdown with enough ground clearance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003327_j.ijfatigue.2017.10.004-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003327_j.ijfatigue.2017.10.004-Figure6-1.png", + "caption": "Fig. 6. Relationship between up-skin angle and down-skin angle and roughness Ra for SLM [17].", + "texts": [ + " These surfaces separate the solid part from the unmelted powder and their relative position, i.e. powder over the melted material as in Fig.5a or below the melted material as in Fig.5b define different solidification conditions for the processed material because local heat transfer, cooling velocity, etc. are influenced. According to the scheme of Fig. 5 up-skin and down-skin surfaces can be readily identified and characterized by the respective angles \u03c5 and \u03b4. The roughness vs surface orientation diagram of Fig. 6 is taken from a DIN norm, [17], and uses the angles defined in Fig. 5 to qualitatively map the expected surface roughness (in terms of Ra). Apparently, the surface orientation \u03b4 = \u03c5 = 90\u00b0 has the lowest roughness, \u03b4 = 0\u00b0 has the highest roughness and \u03c5 = 0\u00b0 has an intermediate roughness. In this study both the flat and the notched surfaces are tested in fatigue. Surface roughness of the as-built flat surfaces was measured in the longitudinal direction on a Mitutoyo SJ 210 machine, [10]. The results are summarized in Table 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.6-1.png", + "caption": "FIGURE 5.6. Stanford arm RI-RI-P:RI-RI-R.", + "texts": [ + "5 has Rf-RIIR main revolute joints, ignoring the structure of the end-effector of the robot. Coordinate frames attached to the links of the robot are indicated in the Figure and tabulated in Table 5.3. 5. Forward Kinematics 205 The joint axes of an K 1RI IR manipulator are called waist zo, shoulder Zl, and elbow Z2. Typica lly, the joint axes Zl and Z2 are parallel, and per pendicular to Zo . Example 128 Stanford arm . A schematic illustration of the Stanford arm, which is a spherical robot R'rR'r P attached to a spherical wrist R'r R'r R , is shown in Figure 5.6 and tabulated in Table 5.3. The DH parameters of the Stanford arm are tabulated in Table 5.4. This robot has 6 DOF: 81 , 82 , d3 , 84 , 85 , 86 . 206 5. Forward Kinematics Example 129 Special coordinate frames . In a robotic manipulator , some frames have special names. The base frame Eo or G is the grounded link on which the robot is installed. It is in the base frame that every kinematic information must be calculated because the departure point, path of motion, and the arrival point of the end effector are defined in this frame" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002156_978-3-642-27482-4_8-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002156_978-3-642-27482-4_8-Figure5-1.png", + "caption": "Fig. 5 Miniskybot Robot. Version 1.0", + "texts": [ + " They are all attached to the servos by means of M3 bolts and nuts. Standard O-rings are used as wheel tires. For making the robot stable, the rear part has two support legs that slide across the floor. Therefore this prototype is only valid for moving on smooth flat surfaces. The goal of this first design was to show the students a minimal fully working mobile robot for stimulating their minds. They were encouraged to improve this initial design. 11 http://www.thingiverse.com/thing:7989 The version 1.0 chassis is an evolution of the previous design (figure 5). It consist of nine printable parts: the front, the rear, two wheels, the battery compartment, the battery holder and the castor wheel. An important feature is that the parts have been parameterized, just changing some parameters new parts are obtained. For example the battery compartment is automatically changed if the parameter battery type is set from AAA to AA. In this case a new compartment capable of holding AA batteries (instead AAA) is generated. The parametric feature is possible thanks to the open source Openscad12 software used for designing the pieces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002212_s00170-016-9510-7-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002212_s00170-016-9510-7-Figure4-1.png", + "caption": "Fig. 4 Schematic of double ellipsoidal heat source for twinwire (arc-arc distance =6 mm)", + "texts": [ + " The net heat input rate is given by the equation (5) for a basic welding process: Q \u00bc \u03b7VI \u00f05\u00de Where Q Heat input rate (W) \u03b7 Arc efficiency (%) V Voltage (V) I Current (A) This basic heat input rate equation does not fully capture the entire process of arc generation and distribution. Hence, a series of heat source models were put forward in the literature to depict the heat source equation to realistically fit the welding process. Double ellipsoidal heat source model, presented by Goldak et al. consisting of Gaussian distribution has excellent feature of power density distribution control in the weld pool and HAZ [7]. The heat input rate is defined separately over two ellipsoidal regions; one region in front of the arc center and the other behind (Fig. 4). The power distribution of front and rear quadrants of the heat source of welding arc can be expressed as: qf \u00bc 6 ffiffiffi 3 p Qf f \u03c0 ffiffiffi \u03c0 p af bc e \u22123 x2 a2 f \u00fe y2 b2 \u00fe z2 c \u00f06\u00de qr \u00bc 6 ffiffiffi 3 p Qfr \u03c0 ffiffiffi \u03c0 p arbc e \u22123 x2 a2r \u00fe y2 b2 \u00fe z2 c n o \u00f07\u00de ar , af , ff , fr , b , c are characteristic parameters of heat source. As per Goldak et al., the values of af, ar, b, and c can be obtained from shape of the weld bead andmolten zone. The recommended estimate for the parameters b and c will be the width and penetration of the weld bead, while those for af and ar will be around one-half and twice the weld bead width" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure5.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure5.7-1.png", + "caption": "Fig. 5.7 Disk motion; a) Synchronous rotation in the same direction (\u03c9 = \u03a9), b) Synchronous rotation in opposite direction (\u03c9 = \u2212\u03a9), c) Loading of the shaft rotating at angular velocity \u03a9 = \u03c0n/30 and vibrating circular frequency \u03c9", + "texts": [ + "6 (natural circular frequencies are independent of the direction of rotation of the rotor). The negative sign in the case presented here indicates that the shaft center rotates in the opposite direction of the shaft rotating at \u03a9 during the vibration at \u03c91 or \u03c93, see (5.26). This is called rotation in opposite direction. The direction of rotation of the shaft vibration and the direction of rotation of the rotating shaft are the same for the positive values of the natural circular frequencies \u03c92 and \u03c94. This is called rotation in the same direction, see Fig. 5.7. The four natural circular frequencies that the shaft has at an angular velocity \u03a91 are depicted in Fig. 5.6 as small full circles. The associated mode shapes, which indicate the ratio of radial to angular amplitude at the respective natural frequency, are obtained by inserting the calculated \u03c9i in (5.29). One can see from Fig. 5.6 that both for opposite and same directions of rotation there are two natural frequencies of the rotating shaft, the magnitude of which depends on the angular velocity \u03a9", + " milk centrifuges and spin driers), for which Ja/Jp depends on the load status and may come close to one, resonance occurs at all higher speeds, and passing through the second critical speed becomes impossible. The designer should avoid such phenomena by selecting favorable system parameters. Resonance during rotation in the same direction is dangerous because the shaft deformation does not produce damping. The shaft rotates in bent condition and is, as it were, exposed to static loading only. Only bearing damping is effective. The mode shapes of opposite rotation are exposed to stronger damping because material damping becomes active due to the alternating deformation of the shaft that occurs, see Fig. 5.7. If the rotating shaft is not excited by the unbalance, but from outside by other forces or motions, it is called secondary or external excitation. Secondary excitations are, for example, motions of the mounting site that act onto the shaft as support motion(such as a shaft on a vibrating frame, centrifuges or fans in vibrating vehicles). Secondary excitations can also be caused by the input or output forces of a rotor, e. g. the forces with the meshing frequency of gear teeth or of the drive chain, the inertia forces of a linkage (crankshaft in reciprocating engines) et", + " The influence of the gyroscopic effect on the position of the first critical speed depends on the ratio Jp/Ja and on whether the rotor tilts strongly (e. g. when overhung) or weakly (e. g. when centered between bearings) perpendicular to the axis of the shaft. This is determined by the influence coefficients. If it is positioned exactly symmetrically between the bearings, \u03b3 = \u03b4 = 0 and thus the gyroscopic effect exerts no influence on \u03c91 at any Jp. 5.2 Fundamentals 325 It helps to imagine the forces and moments acting onto the disk that result from (5.17) and (5.18) at the natural frequencies according to (5.26). They are depicted in Fig. 5.7c. The centrifugal force then acts in the direction of the displacement F\u0303 = Fx + jFy = m\u03c92r\u0302ej\u03c9t = m\u03c92r\u0302(cos \u03c9t + j sin\u03c9t) (5.37) and a moment that depends on the ratio \u03a9/\u03c9, see (5.30), acts in the perpendicular direction: M\u0303 = My \u2212 jMx = JR\u03c92\u03c8\u0302ej\u03c9t = JR\u03c92\u03c8\u0302(cos \u03c9t + j sin\u03c9t). (5.38) Both rotate with the bent shaft. The center of the disk rotates at an angular velocity \u03c9, the disk at an angular velocity \u03a9 about its axis through the center of gravity. 326 5 Bending Oscillators The basis for the following is a calculation model that consists of massless shaft sections with n disks mounted on them, see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000764_tnn.2009.2030748-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000764_tnn.2009.2030748-Figure3-1.png", + "caption": "Fig. 3. Visualization of -modification with modeling errors.", + "texts": [ + " In this case, integration of the system uncertainty over the time interval gives (33) where the term can become very large over time. Hence, (33) cannot be used effectively in the update law (12) with the appropriate modifications. Alternatively, if the system uncertainty is integrated over a moving time window , , then the unknown weights satisfy (34) where the term is bounded by . By choosing appropriately, one can guarantee that is sufficiently small. Note that (34) defines a collection of parallel affine hyperplanes in , or a boundary layer, where the ideal weights lie. Fig. 3 shows such a collection of affine hyperplanes for the case where . Note that in Fig. 3 the width of the boundary layer, that is, the distance between points and , is . In the subsequent sections, we consider the case of nonperfect parametrizations of the system uncertainty and show how the -modification technique can be used to develop static and dynamic neuroadaptive controllers using (34). For illustrative purposes, in this section, we considered a simplified version of an adaptive control problem wherein the system uncertainty is a scalar function and the adaptive weight is a vector" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002033_j.jsv.2016.01.041-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002033_j.jsv.2016.01.041-Figure8-1.png", + "caption": "Fig. 8. Planet bearings with different faulty components. (a) Faulty outer race (b) Faulty rolling element (c) Faulty inner race.", + "texts": [ + " To illustrate this, two loading conditions are verified via applying a torque to the planet carrier shaft by the magnetic powder brake respectively. One is no-load, and the other is 38.75 Nm that the magnetic powder brake can provides stably. In this paper, our purpose is to understand the characteristics of fault vibration and to reveal the fault symptoms. Therefore, we introduced relatively severe defect to the planet bearings to better show the vibration signal features. A slot is introduced to the inner and outer races, and one of the rollers respectively, to simulate bearing localized fault, as shown in Fig. 8. Table 5 lists the defect geometry. Using the above faulty bearings and healthy ones, we carried out four types of tests, i.e. (1) baseline when all planet bearings are healthy, (2) outer race fault, (3) rolling element fault, and (4) inner race fault. 6.2 Resonance frequency identification Rolling element bearing fault usually excite the resonance of mechanical system, and the fault information is carried by such resonance. Therefore, the modal frequency of mechanical system is a key parameter for fault diagnosis of rolling element bearings" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002897_j.engfailanal.2016.12.008-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002897_j.engfailanal.2016.12.008-Figure10-1.png", + "caption": "Fig. 10. Fatigue strength simulation analysis of the gearbox housing.", + "texts": [ + " The connection between the C-bracket and the housing was simplified to be an elastic structure (a linear line element in ABAQUS). A rigid connection between the housing and the rings was assumed. The center point of the rings couples to the contact area between the rings and the bearings. Full constraints (UX = UY = UZ = ROTX = ROTY = ROTZ = 0) were applied on the linear line element. Meanwhile, partial constraints (UX = UZ = 0) were applied on the center point of the wheel-axis rings. Fatigue strength analysis was conducted according to the European standard EN 13749 [12]. Fig. 10 shows the stress response of the failure region with a combined load of traction torque and shocks in all directions. A fairly large structural stress concentration is observed at the inner surface of the inspection window corner, which is consistent with observed gearbox-housing failures. Partial constraints (UX = UZ = 0) were applied on the center point of the wheel-axis rings. The results are shown in Figs. 11 and 12, and are listed in Table 1. The first order resonant mode of the gearbox housing is the lateral bending mode with a natural frequency of 579 Hz, and the second order mode is the axial opening mode with a natural frequency of 618 Hz" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002025_jfm.2014.8-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002025_jfm.2014.8-Figure1-1.png", + "caption": "FIGURE 1. Oblate (a) and prolate (b) spheroids translating at a liquid\u2013gas interface. Although it is not shown, we also consider the translation of the prolate spheroid in the y direction.", + "texts": [ + " Happel & Brenner 1965) can be used to facilitate the calculations by eliminating the need for developing the detailed flow field (e.g. Nadim, Haj-Hariri & Borhan 1990; Stone & Samuel 1996). Following this idea, in \u00a7 2, we derive closedform expressions for the translational speed of spheroidal particles. We also present simplified expressions for the limiting cases of spheres, discs and rods. Consider a solid spheroid located at a flat surface (z= 0) that bounds a half-space of Newtonian liquid with viscosity \u00b5 (see figure 1). The spheroid translates with the velocity U=Ue due to a non-uniformity in the surface tension \u03b3 stemming from the release of a rapidly diffusing insoluble agent. Here, e is the unit vector in the direction of motion. Also, the direction of unit vectors in the xyz coordinate system (ex, ey, ez) coincides with the principal axes of the spheroid whose semi-lengths are, respectively, a, b and c (see figure 1). The relations between the semi-lengths for oblate and prolate spheroids are, respectively, a= b> c and a> b= c. To ensure that the self-propelling motion is restricted to translation, we assume that the release from the spheroid is symmetric about the direction of motion. Let u and \u03c3 denote, respectively, the velocity and stress fields, in z 6 0, corresponding to the Marangoni-driven motion of the spheroid. Also, let u\u0302 and \u03c3\u0302 denote, respectively, the velocity and stress fields corresponding to the translation with the velocity U\u0302 = U\u0302e of an identical spheroid at an otherwise clean interface (i.e. with no surface tension gradient). Then, in the absence of inertia, according to the reciprocal theorem\u222b Ssp (n \u00b7 \u03c3 ) \u00b7 u\u0302 dS+ \u222b SI (n \u00b7 \u03c3 ) \u00b7 u\u0302 dS= \u222b Ssp (n \u00b7 \u03c3\u0302 ) \u00b7 u dS+ \u222b SI (n \u00b7 \u03c3\u0302 ) \u00b7 u dS, (2.1) where Ssp is the surface area of the spheroid in contact with the liquid, SI is the liquid\u2013gas interface area (see figure 1) and n is the unit outward normal toSsp and 741 R4-2 SI . Integrals over bounding surfaces at infinity are zero since velocities decay at least as fast as the inverse distance in the far field. Owing to the no-slip condition, u= Ue and u\u0302= U\u0302e on Ssp. Given that all surface motions are planar, the balance of shear stress at the interface (i.e. the Marangoni stress condition) requires (n \u00b7 \u03c3 ) \u00b7 u\u0302=\u2212\u2207s\u03b3 \u00b7 u\u0302 and (n \u00b7 \u03c3\u0302 ) \u00b7 u= 0 on SI , where \u2207s is the surface gradient operator. Since no net external force is applied on the spheroid, the viscous force \u222b Ssp n \u00b7 \u03c3 dS exerted on Ssp is balanced by the surface tension force Fste= \u222b `sp \u03b3 t d` acting along the triple-phase contact line `sp, where t is the unit vector tangent to SI and normal to `sp" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure4.22-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure4.22-1.png", + "caption": "Figure 4.22 (a) shows a cub e at initial configurations. Label the cor ners of the cube, at the final configuration shown in Figure 4.22 (b), and find the associated homogeneous transformation matrix. The length of each side of the cube is 2.", + "texts": [], + "surrounding_texts": [ + "4. Motion Kinematics 193\nThe orientation of B1 in B2 can be found by a rotation of 60 deg about\n2U = [1 -2 4]\nand the orientation of B2 in the global frame G can be found by a rotation of 30 deg about\nGu = [4 3 -4] .\nCalculate the transformation matrix GT2 and GT21\n10. Rotation about an axis not going through origin .\nFind th e global position of a body point at\nB r p = [ 7 3 2 r after a rotation of 30 deg about an axis parallel to\nG u = [4 3 -4]\nand passing through a point at (3,3,3) .\n11. Inversion of a square matrix.\nKnowing that the inverse of a 2 x 2 matrix\n[AJ = [~ ~]\nis\n(4.299)\n_adb;t be ] ,\n-ad+ be\n(4.300)\nuse the inverse method of splitting a matrix [T] into\n[T] = [~ ~]\nand applying the inverse technique (4.61) , verify Equation (4.300), and calculate the inverse of", + "194 4. Motion Kinematics\n12. Combination of rotations about non-central axes.\nConsider a rotation 30 deg about an axis at the global point (3,0,0) followed by another rotation 30 deg about an axis at the global point (0,3,0) . Find the final global coordinates of\nB r p = [ 1 0 f to\n13. Transformation matrix from body points.", + "4. Motion Kinematics 195\nafter a screw motion G SB (h , < >: ; \u00f014\u00de where Hi \u00bc R Ti T0 q\u00f0Ti\u00dec\u00f0Ti\u00dedT is the enthalpy; Ti is the temperature in the substrate region (i = 1) and bead region (i = 2), respectively", + " Note that the bead material density, providing that there is no mixing with the substrate, coincides with the density of the powder particle material: qs2 \u00bc qsp, qm2 \u00bc qmp, where qsp;qmp are the densities of the solid and liquid state of the particle material, respectively. The thermal balance equations on the curved boundary z \u00bc h\u00f0t; x; y\u00de of the clad bead and also on the flat part of the substrate z \u00bc 0 look like: ki @Ti @n z\u00bch z\u00bc0 \u00bc AiI\u00f0x; y; z\u00de cos c kg 2r0 Nu\u00f0Ti T0\u00de eirb\u00f0T4 i T4 0\u00de \u00f0Hi H0 p\u00deVn Lei _mei; \u00f015\u00de where index i \u00bc 1;2 means the boundaries of the bead and substrate regions X1;X2, Fig. 1; Ai are the coefficients of laser radiation absorption governed by the absorbing properties of the materials; r0 is the laser beam radius, Vn is the normal component of the bead surface motion velocity, H0 p \u00bc c\u00f0~Tp\u00de\u00f0~Tp\u00f0x; y\u00de T0\u00de is the heat content of adherent particles calculated by the distribution of the mean-mass particle temperature ~Tp\u00f0x; y\u00de on the substrate; Lei is the enthalpy of vaporization, _mei is the mass flow rate of vapors as per [24]: _mei \u00bc qmiV0ie Ui=Ti where Ui \u00bc liLei=Nar, li is the molar mass, Na is the Avogadro constant, V0i is the acoustic speed in the melted material" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000770_j.jmps.2012.09.017-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000770_j.jmps.2012.09.017-Figure1-1.png", + "caption": "Fig. 1. The director basis represents the orientation of the material cross section along the rod.", + "texts": [ + " In order to study the motion of elastic filamentary structures, we need to generalize the notion of space curves to rods. Geometrically, a rod is defined by its centreline r\u00f0S,T\u00de where T is the time and S is a material parameter taken to be the arc length in a stress free configuration \u00f00rSrL\u00de and two orthonormal vector fields d1\u00f0S,T\u00de,d2\u00f0S,T\u00de representing the orientation of a material cross section at S (Coleman et al., 1993; Antman, 1995; Maddocks, 2004). We define the stretch by a\u00bc @s=@S, where s is the current arc length as above. A local orthonormal basis is obtained (see Fig. 1) by defining d3\u00f0S,T\u00de \u00bc d1\u00f0S,T\u00de d2\u00f0S,T\u00de and a complete kinematic description is given by @r @S \u00bc v, \u00f07\u00de @di @S \u00bc u di, i\u00bc 1,2,3, \u00f08\u00de @di @T \u00bcw di, i\u00bc 1,2,3, \u00f09\u00de where u,v are the strain vectors and w is the spin vector. Note that the orthonormal frame \u00f0d1,d2,d3\u00de is different, in general from the Frenet\u2013Serret frame. The components of a vector a\u00bc a1d1\u00fea2d2\u00fea3d3 in the local basis are denoted by a\u00bc \u00f0a1,a2,a3\u00de. 1 The first two components v1,v2 of the stretch vector v represent transverse shearing of the cross sections while v340 is associated with stretching and compression" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure2.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure2.1-1.png", + "caption": "Fig. 2.1 Possibly the first parallel robot, an invention credited to Gwinnett", + "texts": [ + " Imaginary solutions of the forward displacement analysis of the Stewart platform. . . . . . . . . . . . . . . . . . . . . 288 Table 14.1 Example 14.3. Inverse displacement analysis . . . . . . . . . . . . . . . . . . . . . 309 xvii List of Figures Fig. 1.1 The portrait of the work Discorso matematico sopra il rotamento momentaneo dei corpi (Mozzi 1763) . . . . . . . . . . . . . . . . . . . 4 Fig. 1.2 Book cover of the work The Screw Calculus and Its Applications in Mechanics (Dimentberg 1965) . . . . . . . . . . . . . . . . . . . . 5 Fig. 2.1 Possibly the first parallel robot, an invention credited to Gwinnett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Fig. 2.2 Pollard\u2019s spray painting machine (U.S. Patent No. 2,286,571) . . . 21 Fig. 2.3 Three parallel manipulators and a polemic discussion about their origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Fig. 2.4 The Delta robot (U.S. Patent No. 4,976,582) ", + " In the 1800s, Augustin-Louis Cauchy, a brilliant French mathematician, investigated the stiffness of an articulated octahedron. It seems that the hexapod geometry was first specially studied by Bricard (1897) during the nineteenth century. One of the first well-documented parallel manipulators was precisely a lowermobility mechanism. After World War I, the cinematography industry became one of the most lucrative businesses in America. Hence, Gwinnet (1931) proposed a spherical parallel manipulator as a cinema motion simulator, the Oxymoron, and was granted the corresponding patent (Fig. 2.1). However, at that time the industry was not ready for Gwinnett\u2019s invention. Several years later, a more practical application of a parallel manipulator was introduced by Pollard (1940): a spray painting machine (Fig. 2.2). Pollard\u2019s creative invention, a simple five-bar parallel robot, for which he was granted the corresponding patent, is considered the first industrial application of 2.1 Typical Parallel Manipulators 21 a parallel robot. Although Gwinnett and Pollard had pioneering contributions, undoubtedly the most celebrated parallel manipulator is the universal tyre testing machine credited to Dr" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002483_s00170-018-2207-3-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002483_s00170-018-2207-3-Figure6-1.png", + "caption": "Fig. 6 The residual stress nephogram. (1) layer 1; (2) layer 2; (3) layer 3. a, d, g Residual stress along x-direction. b, e, h Residual stress along ydirection. c, f, i Residual stress along z-direction. Process parameters shown in Table 3", + "texts": [], + "surrounding_texts": [ + "oxygen content below 0.01 vol%. The chemical composition of AlSi10Mg alloy powder is presented in Table 4.\nThe equipment for this experiment was \u201cSpace M200 type\u201d SLM manufacturing systems, and as shown in Fig. 3a, the additive manufacturing process parameters were laser power 400 W, the scanning speed was 200 mm/ s, the powder layer thickness was 50 \u03bcm, and the scan spacing was 150 \u03bcm. At present, the methods of measuring residual stress are X-ray method, hole-drilling method, neutron diffraction method, and so on. Among them, X-ray method is widely used and has no destructive effect on the quality of workpiece surface. In order to detect the residual stress distribution on the surface of the formed workpiece, the residual stress measurement was carried out by using the Tec4000 equipment shown in Fig. 3b. The workpieces in Fig. 3c are placed on the platform of the x diffractometer, and the X-ray emitted by the X-ray tube is used to test the residual stress of the test points identified in Fig. 3c.\nLocal uneven heating is the main reason for stress and deformation in the SLM process. Because the rapid\nscanning speed of laser causes the short interaction between laser and material, the region irradiated by laser undergoes rapid heating, melting, rapid cooling, and solidification. This part of the material is inflated by heat, but the low-temperature region limits the expansion of the material, which leads to thermal stress. In the meantime, the yield limit of the material in the laser area is decreased with the increase of temperature. As a result, the thermal stress of partial region is greater than the yield limit of the material, and the plastic thermal compression deformation occurs. Under the constraint by cooling in surrounding area, residual stress occurs.\nIn Fig. 4, the heated material and the solid surrounding material can be assimilated to a structural unbalance that effectively restrains the movement of the heated metallic material when the latter changes in state. During the cooling, a complex contraction of the irradiated region takes place that is a tension state, while the material that surrounds the irradiated zone undergoes an expansion that results in a compression state. The volumetric shrinking of the material melted during the cooling induces compression stresses in the surrounding material, which is under the influence of the temperature gradient.\nFigure 5 shows that the calculated thermal cycle agrees well with the experimentally measured values for a 80- mm-long AlSi10Mg build, the location of test points as shown in Fig. 3c. The residual stress was experimentally", + "measured using the X-ray diffraction method. As shown in Fig. 5, the distribution of residual stress is obviously related to the position of the specimens. The excellent agreement between the experimental and theoretical calculations shows the importance of considering the conduction, convection, and radiation in the simulation. The agreement between the experimental and numerical also indicates that the simulation can be used for the residual stress and strain calculations with confidence.\nFigures 6 and 7 show the changes in deformation and residual stress in each part of the specimen with the increasing thickness of the powder layer. In order to explore the thermal", + "effects of the temperature field between the laser scanning channels on the adjacent channels and to establish the relationship between the stress field and the temperature field during the SLM process, the relevant investigation is carried out (Fig. 8).\nAccording to the comparison between the temperature of the selected point and the residual stress in Fig. 9, it can be found that the formation process of residual stress in the material can be divided into three phases with the rise and fall of temperature." + ] + }, + { + "image_filename": "designv10_3_0001597_tnnls.2017.2766283-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001597_tnnls.2017.2766283-Figure10-1.png", + "caption": "Fig. 10. Electromechanical system.", + "texts": [ + " We change x(0) by setting x(0) = [0.5,\u22120.2]T , [1.0,\u22120.4]T and [1.5,\u22120.6]T , respectively. The first sensor suffers fault at t = 0.5 s, and the failure factor is set as \u03c11(t) = 0.5| sin(2t)| + 0.5. The state variables x1 and x2 and the control u is presented in Figs. 7\u20139. It is seen that the maximum overshoot of states and the magnitude of u increase with increased \u2016x(0)\u2016. Example 2: To further show the effectiveness of the proposed adaptive fuzzy controller in practice, the electro mechanical system [37] shown in Fig. 10 is considered. The dynamics of the system can be described in the following form: x\u03071 = x2 x\u03072 = 1 M x3 \u2212 N M sin(x1)\u2212 B M x2 x\u03073 = 1 L u \u2212 K B L x2 \u2212 R L x3 (32) where M = J K\u03c4 + mL2 0 3K\u03c4 + M0 L2 0 K\u03c4 + 2M0 R2 0 5K\u03c4 N = mL0G 2K\u03c4 + M0 L0G K\u03c4 , B = B0 K\u03c4 and u is the input control voltage, and x1 is the angular motor position (and hence the position of the load), x2 is the motor angular velocity, and x3 represents the motor armature current. These three state variables are measured by three different types of sensors, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000056_s0263574707003530-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000056_s0263574707003530-Figure5-1.png", + "caption": "Fig. 5. Canonical 2R-mechanism.", + "texts": [ + " We demonstrate the computation for the parameter u1. The other two possibilities can be found in the work of Pfurner.18 Fixing the first revolute axis u1 = u10 (the zero in the index indicates a fixed value), the corresponding 2R chain has the matrix representation D = F \u00b7 M2 \u00b7 G2 \u00b7 M3 \u00b7 G3 where F is a fixed transformation, given by M1(u10) \u00b7 G1. F and G3 are coordinate transformations in the base respectively moving frame of this 2R chain. Neglecting F and setting d2 = 0 transforms the chain into a canonical one as shown in Fig. 5. Setting d2 = 0 means no loss of generality, because a transformation in the direction of the second revolute axis can be achieved later directly in the kinematic image space. Omitting G3 transforms the end effector frame such that the z-axis coincides with the second axis of this 2R chain, and the x-axis is aligned with the common normal of the two revolute axes. Then, the matrix representation of the remaining 2R chain becomes D = M2 \u00b7 G2 \u00b7 M3. (15) The parametric representation of the constraint manifold, computed with Eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001663_piee.1968.0265-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001663_piee.1968.0265-Figure7-1.png", + "caption": "Fig. 7", + "texts": [ + " Nevertheless, the torque of the electrical generator, expressed in a form which is independent of speed, is T = KT<&i (12) where O is the flux per pole, and / is the output current; and exactly the same expression is valid for the 'magnetic generator', but / is now the 'current per pole' and 50 HZ). The value of x is measured by the transducer system and fed into the PID (proportional-differentialintegral) controller, which has a power output", + " Although the actual stimulus cannot by measured, the oscillation is also a controlled output because it has a fixed functional relationship to the displacement (dynamic interferences such as resonance frequency of the lever system and hysteresis of the mechanics etc. are negligible). Thus within the chosen frequency range (0 ... 10 Hz) the stimulator produces a feedback controlled rotation stimulus. In pitch and roll the rotational axes do not cross the animal's body, so that the stimulus includes a small translatory component in addition to the rotation (Fig. 3). The possible significance of this will be discussed in part II of this investigation (MShl and Zarnack, 1977). R e s u l t s Basic Problems. A l t h o u g h al l d i r e c t d o w n s t r o k e m u s c l e s a r e s y n e r g i s t i c a l l y ac t ive d u r i n g f l i gh t (F ig . 4 ) , t h e i r a c t i o n p o t e n t i a l s a r e n o t a b s o l u t e l y s y n c h r o n i z e d left 97 98 99 127 128 1291 1292 right 97 I ! I. ~ ! I IL~ I '4 ~ I t , . llJL . I . . I I~_ .L k . - k . i i ~ " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.20-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.20-1.png", + "caption": "FIGURE 5.20. T he position of the final frame in the base frame.", + "texts": [ + " Th is problem can be solved by determining transformation matrices DT; to describe t he kinemat ic information of link (i) in the base link coordinat e frame. The traditional way of producing forward kinemat ic equa tions for robo tic manipulators is to proceed link by link using t he Denavit-Hartenberg not ations and frames. Hence, the forward kinematics is basically t ransformation 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 mat rices i - i T; are uniquely det ermined. Therefore, the position and orientation of the end-effector is also a unique funct ion of the joint variables. The kinematic information includes: position, velocity, accelerat ion, and jerk. However, forward kinematics generally refers to the position analysis. So the forward position kinematics is equivalent to a det ermination of a combined transformation matrix (5.58) 5. Forward Kinematics 227 to find the coordinates of a point P in the base coord inate frame, when its coordi nates are given in the final frame" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure5.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure5.7-1.png", + "caption": "Fig. 5.7 Example 5.5. Trucks in relative motion and its kinematically equivalent mechanism", + "texts": [ + " 102 Fig. 5.2 Example 5.2. Planar two-degree-of-freedom serial manipulator . . 109 Fig. 5.3 Example 5.3. Acceleration analysis of the Geneva wheel . . . . . . . . . 112 Fig. 5.4 Example 5.4. 2RRR+PPR planar parallel manipulator and its geometric scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Fig. 5.5 The gradual improvement of a planar parallel manipulator . . . . . . . 115 Fig. 5.6 2RRR+PPR planar parallel manipulator. Infinitesimal screws . . . . 118 Fig. 5.7 Example 5.5. Trucks in relative motion and its kinematically equivalent mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Fig. 5.8 6-PSU parallel manipulator. A Hexaglide-type robot . . . . . . . . . . . . . 127 Fig. 5.9 Planar timing mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Fig. 6.1 Example 6.1. Rocket fired vertically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Fig. 6.2 Example 6.2. Two trucks in relative motion ", + " Meanwhile, QC D hn QL1IL1 o n QL2IL2 o n QL3IL3 oiT (5.104) 5.3 Equations of Acceleration in Screw Form 121 is the complementary matrix of acceleration. Since the terms of the Coriolis acceleration are self-contained in matrix QC, it could be named something like the Coriolis/centripetal matrix. Example 5.5. This example shows that although rigid bodies are physically disconnected, it is possible, in some cases, to simulate the kinematic analysis of multibody mechanical systems by introducing kinematically equivalent mechanisms. With reference to Fig. 5.7, truck A is rounding a curve of radius r1 D 120 m at a constant speed of 70 km/h while truck B is rounding a curve of radius r2 D 130 m at a constant speed of 75 km/h. We must determine the velocity and acceleration that car B appears to have for the driver of car A when A D 30\u0131 and B D 45\u0131. Solution. The standard solution is presented first. To this end, let XY be a reference frame attached to the center of curve 1, the point O1, with associated unit vectors OiOj. If we use college kinematics, the velocity of truck B as observed from body A, the vector vB=A, is given by vB=A D vB vA D vB h sin" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure9.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure9.3-1.png", + "caption": "Fig. 9.3 Normal mode shapes of the original system", + "texts": [ + "8), however, it would then also be a function of the controller constants \u03ba1 and \u03ba2. 520 9 Relations to System Dynamics and Mechatronics The real parts of the eigenvalues of (A\u2212 SKRY ) provide insight whether the controlled-loop system will behave stably or not. It will be assumed for simplification that only one harmonically variable excitation or disturbance force acts in the minimal model of a machine frame shown in Fig. 9.2 so that: F1(t) \u2261 0; F2(t) = F\u0302 sin \u03a9t. (9.30) This excites both normal mode shapes, as can be seen from Fig. 9.3. Both normal mode shapes can be influenced using an actuator that generates a control force FR in the direction of the coordinate q1 because the free beam end oscillates in the direction of action of FR for both shapes. The task is to determine the controller force FR of the actuator (to be exact: the controller constants) from the two measured signals in such a way that the vibration amplitude q2(t) is reduced. To obtain a general result, dimensionless characteristic parameters (see (9.34)) and three fundamental parameters are introduced for the calculation model: length l, bending stiffness EI and mass m", + " The use of dimensionless characteristic parameters has the advantage that one obtains results for mechanically similar objects. In addition, the numerical results become more precise if there are no major differences in magnitude for the numerical values used in the calculation operations that are performed by the simulation program. The two natural circular frequencies for the undamped system without a controller are known from (6.160): \u03c901 = \u221a 0.244 07 48 \u221a 48EI ml3 = 0.071 308\u03c9\u2217, \u03c902 = \u221a 1.755 93 48 \u221a 48EI ml3 = 0.191 264\u03c9\u2217. (9.31) The normal mode shapes shown in Fig. 9.3 are associated with them. It is useful for the further analysis to introduce the dimensionless time \u03c4 = \u03c9\u2217t as well as a dimensionless state vector x, which is connected as follows to the state vector x containing dimensionless components used so far: x = [ q q\u0307 ] = l \u00b7 diag [ 1, 1, \u03c9\u2217, \u03c9\u2217 ] \u23a1\u23a2\u23a2\u23a3 x1 x2 x3 x4 \u23a4\u23a5\u23a5\u23a6 = T x. (9.32) For the differentiation with respect to time, one finds: 9.2 Closed-Loop Controlled Systems 521 d dt (. . .) = (. . .) \u00b7 = d (. . . ) d\u03c4 \u03c9\u2217 = (. . .) \u2032 \u03c9\u2217 The differentiation with respect to \u03c4 is indicated by a prime" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002522_j.ymssp.2016.03.014-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002522_j.ymssp.2016.03.014-Figure1-1.png", + "caption": "Fig. 1. Mechanical model of spur gear pair.", + "texts": [ + " For example, when shaft deflection or gear wear arrives at a certain degree, impact component may also be visible in the gear vibration signal. Therefore, during the fault diagnosis, impact component can be used as the main basis for judging whether a fault happens in the gear system. Based on the classification above, the vibration mechanisms of gear system suffering from different kinds of faults are discussed as follows. The dynamic model of the engaged spur gear pair investigated in the present study is shown in Fig. 1, which has been employed in previous research work [1,10]. Here Tp and Tg denote the input and output torques respectively, Rp and Rg denote the radius of the base circles respectively. e(t) is the relative displacement on the mesh point caused by the steadytype fault, and can be omitted for the perfect meshing gear. According to Lagrange theorem, the dynamic differential equation of the adopted system can be expressed by \u00a8 ( ) + \u0307 ( ) + ( )[ ( ) + ] = ( )Mx t Cx t k t x t E W 10 where x(t) is the linear displacement along the action line, E is the average static elastic deformation of gear teeth after loading, C is the damping factor which has been simplified as a constant, ( )k t is the time-varying mesh stiffness, M is the equivalent inertia mass of the gear pair and = ( + )M I I I R I R/p g p p g g 2 2 , = =W T R T R/ /p p g g0 , where W0 is the static load" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002225_j.vacuum.2017.12.034-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002225_j.vacuum.2017.12.034-Figure1-1.png", + "caption": "Fig. 1. (a) The schematic diagram of the manufacturing process, (b) surface morphology of the thin-walled parts.", + "texts": [ + " The inter-layer temperature was controlled at 150 C to minimize the impact of molten pool and temperature field. This was achieved by determining the temperature of the middle point in the top layer using a infrared thermometer. The staggered deposition process and pulse current mode were used to decrease the bead dimension of the thin-walled parts. During the fabrication process, the torch direction was always maintained perpendicular to the substrate and elevated in direction of z (as illustrated in Fig. 1a) to keep the distance between the torch and the surface of thin-walled parts remains 11.5mm. A 65 layers thin-walled part was deposited via this process, can be seen in Fig. 1b. Microstructure and hardness properties, which can be used for further evaluating whether the as-deposited part can be used directly and providing design reference for structure optimization. Surface morphology of the thin-walled parts was provided in Fig. 1b. It is evident that the surface appearance is very smooth which has little spatter and distortion. Transverse sections were taken from the deposited thin-walled parts by means of wirecutting polished, and etched with a mixed solution of 75% concentrated hydrochloric acid and 25% concentrated nitric acid. Macro images of the parts were obtained using an optical microscope as reported in Fig. 2. The layers were well formed, no clear delineations were observed between layers, a variety of microstructures were found", + " Vickers hardness of the thin-walled parts was tested from top to bottom as presented in Fig. 3. The mean value of the upper part of the thin-walled parts hardness was 353HV, and was 315HV of the lower part. It is reasonable to concluded that the hardness of the thin-walled parts was uniform from top to bottom, which was between 300 and 360HV. Since many design criteria are based on the yield and tensile strength of materials, tensile tests were performed on the printed die steel at room temperature. As an overlay in Fig. 1, a total of 11 specimens were cut from the die steel wall. Mechanical properties were measured for two different orientations with respect to the deposition direction. When loading in the direction of parallel (x in Fig. 1a) and perpendicular (z in Fig. 1a) to deposit direction, the mechanical properties were anisotropic (as illustrated in Fig. 4). The mean tensile strength/elongation of horizontal specimens were 1085MPa/10%, and 871 MPa/7.8% of vertical specimens. When comparing specimens taken at different locations within the walls, an increasing tensile strength was observed in specimens as welded (1#, 3#, 5#, 6#, 7#, 9#, 11#) from 850MPa to 1187.5MPa. But elongations of the samples were rise at first and then fall, from 7.4% to 11.36% of 9# sample, to 7" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001469_tim.2015.2390958-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001469_tim.2015.2390958-Figure2-1.png", + "caption": "Fig. 2. Connection scheme for the identification of Ld (id ) and Lq (iq ) with the PSO algorithm.", + "texts": [ + " 4) Update pbest and gbest: Update pbest and gbest according to if Fj (ai (k + 1)) < Fj (api) then api = ai(k + 1) (10a) if Fj (api ) < Fj (ag) then ag = api . (10b) 5) Increase: k = k + 1, go back to step 2, and finish in a maximum time of tkmax . It is well known that the stator inductances Ld(id) and Lq(iq) are functions of the current in the same axis, and therefore, the measurement of the inductances should be realized at different current levels [28]. The machine is connected as shown in the scheme shown in Fig. 2, with the rotor locked and aligned with the measured axis. Thus, by considering that the rotor is aligned with the d-axis, (1a) can be simplified as vd = Rsid + Ld (id) d dt id . (11) By discretizing (11), the calculated id stator current in the instant k can be obtained as id(k) = t [ vd (k \u2212 1) Ld(id) \u2212 Rs Ld (id) id(k \u2212 1) ] + id(k \u2212 1). (12) The parameter identification can be addressed as an optimization problem where the system response to a known input is used to find the unknown parameter values of a model", + " Identification of the PM Flux Linkage To measure the flux linkage, the PMSM has been mechanically coupled to an induction machine. The induction machine is powered by a variable frequency drive at different speeds, and the line to line voltage generated by the PMSM is measured and then the flux linkage of the PM is calculated [32]. The value of the flux linkage of the PM at different speeds is listed in Table I. To perform the identification of the stator inductances using the PSO, one phase of the machine is connected to a single-phase voltage source (Fig. 2) during a short period of time and measurements of currents and voltages are carried out. The parameters necessary for the PSO are the population size, maximum number of generations, the acceleration constants, and the inertia factor; the parameters used for parameter identification are listed in Table II. Fig. 5 shows the optimization of the current id using PSO; during the Iterations, the approximated current curve is adjusted according to the measured current curve. Fig. 5(a) shows the current curve in the first iteration; Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000221_1.2991291-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000221_1.2991291-Figure3-1.png", + "caption": "Fig. 3 Sample smooth surfa", + "texts": [ + " Actually, on the highest level of mesh density in the present cases, the number of nodes used in the x-direction is 1537 and the mesh size is x=0.002929 a accordingly. This is sufficiently small to guarantee satisfactory accuracy with minimal numerical errors in film thickness solutions see explanation in Ref. 18 . Central and minimum film thickness results from the present 3D L-EHL model are summarized in Table 1, and film thickness and pressure distributions for four sample cases are shown in Fig. 3. It can be seen that, as the rolling speed continues to decrease from 50 m/s to 0.0005 m/s, the central film thickness gradually decreases from about 1700 nm down to zero, and the minimum film thickness reaches zero even earlier. At high speeds, the solutions show thick lubricant films with typical EHL characteristics, while at ultralow speeds contact occurs with zero film thickness in the Hertzian contact zone, and the pressure distribution and deformed contact geometry are very close to those of a typical Hertzian dry-contact, as demonstrated in Fig. 4. The sequential graphs in Fig. 3 and the comparison in Fig. 4 also indicate that the developed 3D L-EHL model is capable of solving problems in a wide range of operating conditions and handling the entire transition from thick-film EHL to thin-film EHL and all the way down to contact. It is interesting to see the detailed comparison of the 3D linecontact EHL solution at u=0.0005 m /s with the analytical solution from the dry Hertzian contact theory, as shown in Fig. 4. The pressure distribution in the infinite length direction is found to be perfectly flat, while that in the finite contact width direction demonstrates an excellent agreement with that from the Hertzian theory with no visible difference observed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000007_tro.2004.842336-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000007_tro.2004.842336-Figure2-1.png", + "caption": "Fig. 2. Exactly actuated closed-loop manipulator.", + "texts": [ + " In the case of steepest descent, the number of iterations was forcefully terminated after 229 after the algorithm failed to meet the stopping criterion. The final value of the objective function was 314.069. For the BFGS quasi-Newton method, the algorithm was forcefully terminated after 45 iterations, and convergence was extremely slow near the solution. The total elapsed time was 1.27 s, and the final value of the objective function 314.069. The BFGS method, on the other hand, approached the vicinity of the solution in the shortest time among the three methods. We now consider the exactly actuated closed chain of Fig. 2. Joints 1\u20133 are actuated, where joint 2 rotates both and together, and joint 3, lying coaxially with joint 2, rotates only . The actuated joint angles in the initial pose are given by , while in the final pose, the angles are ( , , ). We seek the minimum torque motion such that the manipulator moves between two poses symmetrically situated about the workspace in exactly 1 s. For our test case, the Modified Newton method converged after seven iterations, with a total computation time of 6.94 s. The convergence speed and number of iterations are compared for the steepest descent, Newton method, and the BFGS quasi-Newton method" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000697_rsbl.2007.0049-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000697_rsbl.2007.0049-Figure1-1.png", + "caption": "Figure 1. Mechanics of tree sway. P is the position of the orangutan at height h from the ground and d is the distance the animal must vibrate the sapling to cross the gap.", + "texts": [ + " Orangutans repeatedly crossed from the vertical trunk of a young tree to a vine that was out of reach, by swaying the tree. Calibration of the height of the animal on the sapling and the amplitude of the vibrations was possible from the measurements made on support lengths and diameters at ground level. Video sequences were recorded with a digital video camera (Sony DCR-TRV 900E) at a speed of 25 frames per second. (a) Calculations of energy expenditure Consider an orangutan at point P on the trunk of a sapling, who wishes to move to a nearby sapling or vine that is out of reach by a distance d (figure 1). It makes its sapling vibrate at its resonant frequency, building up the amplitude to the value d that enables it to move across. Free vibrations of the sapling continue after the ape has left it. The motion of point P can be modelled as that of a linear, lightly damped harmonic system, in which case the frequency, f, of the vibrations is given by f w\u00f01=2p\u00deO\u00f0S=m\u00de; \u00f03:1\u00de This journal is q 2007 The Royal Society (e.g. Alexander 1983), where S is the stiffness of the sapling to horizontal forces applied at P and m is the effective mass (the mass which, located at P, would have the same inertia as the tree)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000348_gamm.200890000-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000348_gamm.200890000-Figure2-1.png", + "caption": "Fig. 2 Performance funnel F\u03d5.", + "texts": [], + "surrounding_texts": [ + "depicted in Figure 3.1. Note that (6) is a particular case of this general structure. The concept of \u03bb-tracking is implicit in [33], albeit is a somewhat different context to that considered here. The concept as described above was introduced for the linear class (1) in [18], for infinitedimensional linear systems in [15], for the nonlinear class (1) in [1, 13], for the nonlinear class (7) in [19], and, for systems modelled by differential inclusions in [38]. Discussion on contributions to systems of higher relative degree are postponed until Section 6.\nWhilst we have now addressed the shortcomings (HG3), (HG4), and (HG6), the following questions remain.\n(\u03bb1) How to tackle systems of relative degree \u03c1 \u2265 2?\n(\u03bb2) How to counteract the disadvantages of monotonically non-decreasing gain (which, whilst theoretically convergent, is susceptible to unwarranted increase generated by perturbations to the system)?\n(\u03bb5) How to influence transient behaviour?\n4 Funnel control\nTo resolve (\u03bb2) and (\u03bb5), we first make the following observation. Loosely speaking, the high-gain property, alluded in the Introduction, ensures that the output y(t) or the error e(t) is decaying if the gain is sufficiently large. If k is a time-varying function, we may \u201ctune\u201d its values k(t) to be large only when required: k need not be a monotonically increasing function.\nWith this in mind and to address the issue of transient behaviour, we introduce the concept of a performance funnel. Let \u03d5 be a function of the following class\n\u03a6 := { \u03d5 \u2208 W 1,\u221e(R+, R) \u2223\u2223 \u03d5(0) = 0, \u03d5(s) > 0 for all s > 0 and lim inf s\u2192\u221e \u03d5(s) > 0 } .\nc\u00a9 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim", + "With \u03d5 \u2208 \u03a6, we associate the set\nF\u03d5 := { (t, e) \u2208 R+ \u00d7 R m \u2223\u2223 \u03d5(t)\u2016e\u2016 < 1 } ,\nwhich we refer to as the performance funnel, see Figure 4.1. This terminology arises from the fact that, if a control structure can be devised which ensures that the tracking error evolves within F\u03d5, then we have guaranteed transient behaviour (control objective (TO3)) in the sense that\n\u2016e(t)\u2016 < 1/\u03d5(t) \u2200 t > 0,\nand, moreover, if \u03d5 is chosen so that \u03d5(t) \u2265 1/\u03bb for all t sufficiently large, then control objective (TO2) is achieved.\nTo ensure error evolution within the funnel, the controller (4) is replaced by\nu(t) = \u2212k(t) e(t), e(t) = y(t) \u2212 yref(t)\nk(t) = [1 \u2212 \u03d5(t)\u2016e(t)\u2016]\u22121.\n} (8)\nIn view of the high-gain property, intuitively we see that, in order to maintain the error evolution within the funnel, high gain values may only be required when the error is close to the funnel boundary. This intuition underpins the choice of the gain function in (8). The structure (8) has two advantages: k(t) is not determined by a dynamical system (differential equation); the control (8) is a time-varying proportional output feedback of striking simplicity. This structure was introduced for the class of nonlinear systems (7) in [20]: modifications to mollify controller behaviour near the funnel boundary are contained in [23].\n5 Applications\nWhereas there are few applications of the high-gain control approach described in Section 2, the \u03bb-tracking approach has found several applications (including experimental implementation in the regulation of the pH-value of a biogas tower reactor [17]).\nTheoretical results and simulations for mostly biotechnological applications of \u03bb-tracking are\nc\u00a9 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim", + "as follows: in anesthesia in [3]; for continuous stirred tank reactors in [1, 6]; for exothermic chemical reactors under input constraints in [24]; for chemical reaction models with sampleddata in [25]; for activated sludge processes in [14].\nFunnel control under input constraints for chemical reactor models has been investigated in [26].\nRecently, funnel control has been applied to electrical devices [39, 40] modelled as a two mass system, and the aim is to control the speed of the load mass in the presence of load disturbances and sensor noise.\n6 The obstacle of higher relative degree\nIf a (linear) system has a higher relative degree and derivative feedback is not feasible, then a filter or observer is frequently used to obtain approximations of the output derivatives. However, it is not straightforward to determine how to combine a filter/observer with a high-gain controller.\nA first attempt to achieve stabilization for linear systems of higher relative degree is due to Mareels [31]; however, a counterexample to the main result is presented in [9]. Unless otherwise stated, all results cited below relate to single-input, single-output systems. Hoagg and Bernstein [9, 10] solve the problem of adaptive stabilization of linear systems with higher relative degree. Bullinger and Allgo\u0308wer [2] introduce a high-gain observer in conjunction with an adaptive controller to ensure tracking with prescribed asymptotic accuracy \u03bb > 0 (\u03bb-tracking). This is achieved for a class of systems which are affine in the control, of known relative degree, and with affine linearly-bounded drift term; so they are close to linear. Paper [44] considers linear minimum-phase systems with nonlinear perturbation; the control objective is (continuous) adaptive \u03bb-tracking with non-decreasing gain; the class of allowable nonlinearities is considerably smaller than that encompassed by (7). Stabilization for systems of maximum relative degree in the so-called parametric strict feedback form is achieved in [45] via a piecewise constant adaptive switching strategy. Both these contributions use a backstepping procedure.\nThe concept of funnel control is applied to linear systems of known relative degree in [21] and generalized to a class nonlinear systems (7) in [22]. However, in both contributions, a backstepping procedure is used which complicates the feedback structure. An alternative approach might be to combine a simple high-gain observer with a funnel-type controller.\n7 Robustness\nAs we have seen, high-gain control is applicable to large classes of nonlinear systems. However, if a system of the underlying class is subjected to perturbations which take it outside the class, then it is not clear if the controller continues to maintain performance. This problem of robustness has been investigated for the class of linear systems (1).\nIn particular, exploiting the concept of the nonlinear gap metric (graph topology) (see, e.g. [7]) from the theory of robust stability, in [5] it is shown that the canonical high-gain controller (3) maintains its efficacy in the presence of L2-input and L2-output disturbances. It is\nc\u00a9 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim" + ] + }, + { + "image_filename": "designv10_3_0002338_ac60183a025-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002338_ac60183a025-Figure4-1.png", + "caption": "Figure 4. Filter photometer layout", + "texts": [ + " Mechanical chopping requires very careful machining and alignment of parts; considerable noise results unless the slit illumination is very uniform, and unless the slits are placed symmetrically about the center of rotation of the sector wheel. The principal limitation of the Polaroid sheets is the spectral cutoff around 400 mw. However, this limitation does not preclude the assay of systems involving the reduction of diphosphopyridine nucleotide (DPN) or triphosphopyridine nucleotide (TPK), since coupled enzyme reactions may be used. Such an application to the assay of isocitric dehydrogenase is under way in this laboratory. Construction of the Filter Photometer. The layout of the filter photometer is shown in Figure 4. The light source ( A ) is operated from a 6-volt storage battery. The bulb is mounted on an adjustable backplate, which in turn is mounted on a movable base to permit focusing. Rigidity is essential; otherwise movement of the light source causes instability and drift. The collimating lens and interference filter are mounted in an aluminum block (B). The lens is held in position by two diametrically placed drops of epoxy resin. The filter is held by two bronze spring clamps to permit easy interchange", + " 150 volts electrolytic capacitor 1 N 3 4 A crystal diode 50,000 ohms. 2-watt. 1 0-turn Dotentiometer -_ . Rec. VI, Vz. 12AT7 10-mv. Varian recorder, Moddl G-1 1 A fier is supplied currently by a bench power supply (Kepco, Model 510B). Any regulated power supply should suffice. There are two variable controls on the amplifier: Rjo is a sensitivity adjustment, and R9 is a zero control. Their setting is described below. Adjustment of Photometer. First, the parts of the optical system are aligned as shown in Figure 4. The photo cathode is placed a t the focal point of the focusing lens, and then the lamp position is adjusted to give the sharpest image of the filament on a white card held just before the multiplier phototube. In this adjustment, power is supplied only to the lamp, and the flowing cells and stationary Polaroids are out of the system. All parts are rigidly fixed to the base except the lamp, which is left loose a t the base to permit small adjustments later. The fixed Polaroids are positioned in a dark room, with the photometer housing removed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002091_s11071-013-1060-z-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002091_s11071-013-1060-z-Figure2-1.png", + "caption": "Fig. 2 Dynamics model of multistage planetary gear train", + "texts": [ + " Each gear body is assumed to be rigid, and the flexibilities of the gear teeth at each gear mesh interface are modeled by a spring with periodically time-varying stiffness acting along the gear line of action. This mesh stiffness is subject to a clearance element representing gear backlash. 2. Each gear and the planet carrier are assumed to move in the torsional direction only. 3. Each planet gear on the planet carrier distributes uniformly with the same parameters. 4. Gears and carriers are considered to be free of any eccentricities or run-out, roundness errors, and meshing friction on tooth surface. The torsional dynamic model of the planetary gear train of stage n is shown in Fig. 2. The central elements s, r , and c are constrained by torsional linear springs of stiffness magnitudes k (n) st , k (n) rt , and k (n) ct , respectively. The magnitudes of these stiffness constraints can be chosen according to simulated different power flow arrangements with different fixed central members. A particular central member is held stationary by assigning a very large constraint stiffness value to it. Likewise, a zero value for the constraint stiffness indicates that this central member is not connected to the gearbox" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure3.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure3.6-1.png", + "caption": "Fig. 3.6 Calculation model of a foundation block", + "texts": [ + " The force propagated to the ground decreases, if the natural frequency of the spring-mass system is lowered, i.e., if the mass m is increased or the spring rate c is decreased. Every elastically mounted rigid machine has six degrees of freedom. A calculation model with six degrees of freedom has six natural frequencies. If low tuning is required, it must be ensured that the highest natural frequency is smaller than the lowest excitation frequency. For mixed tuning, all natural frequencies have to be far enough away from the excitation frequencies. The calculation model is shown in Fig. 3.6. The following assumptions are made: 1. The coordinate origin is at the center of gravity of the rigid system, composed of rigid machine and foundation mass (in short: foundation block), which is in its static equilibrium position. 2. In the equilibrium position, the body-fixed coordinate system \u03be-\u03b7-\u03b6 is identical with the fixed x-y-z system in which the displacements x, y, z and the small angles \u03d5x, \u03d5y, \u03d5z about these axes are measured. \u03d5 x cz 3. All external forces and moments are referred to this coordinate system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001278_tie.2010.2087299-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001278_tie.2010.2087299-Figure4-1.png", + "caption": "Fig. 4. Effects of selecting different switchings under dynamic condition. (a) Stator voltage vector in stator flux. (b) Comparison of the load angles \u03b4sr generated by the same magnitude of appropriate voltage vectors.", + "texts": [ + " The relationship between the rotor and stator flux vectors in the rotor flux reference frame can be written as \u03a8r r = Lm/Ls 1 + p\u03c3\u03c4r \u03a8r s (10) where \u03c4r is the rotor time constant. If the ohmic drop in (1) is neglected, then we can approximate the change in stator flux as \u0394\u03a8s = vs\u0394t. (11) Equation (11) indicates that an instantaneous angular velocity of the stator flux is irregular due to the switching voltage vectors. According to (10), the rotor flux will follow the stator flux, however with the irregular motion removed due to the lowpass-filtering action. Fig. 4 shows the space vectors of the stator and rotor flux linkages moving in the counterclockwise direction. The motion of the stator flux is dictated by the voltage vectors vk+1 and vk+2. Case 1 is when the stator flux is about to enter sector k (at \u03b1k = 0 rad), while case 2 is when the stator flux is about to leave sector k (at \u03b1k = \u03c0/3 rad). The dynamic torque response can be studied by looking at the effects of applying the possible two voltage vectors on the angle \u0394\u03b4sr. For this purpose, the vectors are redrawn as shown in Fig. 4(b). From Fig. 4(a) and (b), it can be seen that vk+1 has a larger tangential component to the circular flux locus, while the component of vk+2 has a larger radial (negative) component in case 1. On the other hand, vk+1 has a larger radial component, while vk+2 has a larger tangential component to the circular flux locus in case 2. Fig. 4(b) shows the effect of selecting different switching states on \u0394\u03b4sr. Based on the continuous rotation of the rotor flux as compared to the irregular rotation of stator flux, it can be seen that \u0394\u03b4sr,1 is larger when vk+1 is switched for case 1, and on the other hand, \u0394\u03b4sr,2 is larger when vk+2 is switched for case 2. In fact, if the sector is subdivided into subsectors (i) and (ii) based on (12), vector vk+1 will result in a larger \u0394\u03b4sr throughout subsector (i), and vk+2 will give a larger \u0394\u03b4sr throughout subsector (ii) 0 \u2264\u03b1k < \u03c0/6 rad, for subsector i \u03c0/6 \u2264\u03b1k < \u03c0/3 rad, for subsector ii" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure16-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure16-1.png", + "caption": "Fig. 16. Schematic illustration of tangency of face-gear, shaper and worm at point P.", + "texts": [ + " The new design of the worm (for a face-gear drive with a helical pinion) cover: (i) Design for two types of geometry of the pinion and shaper. (ii) Avoidance of worm singularities. (iii) Limitation of worm application caused by the magnitude of pinion helix angle. (iv) Determination of face-gear tooth surface generated by the worm. The derivation of the crossing angle is performed as follows: (i) Surfaces Rs of the shaper, Rw of the worm, and R2 are considered in tangency at common point P of pitch surfaces of the shaper, worm and the face-gear (Fig. 16). (ii) The shortest distance Ews (Fig. 16) is Ews \u00bc rpw rps; \u00f035\u00de where rpw and rps are the radii of respective pitch cylinders. (iii) The sliding velocity v(sw) is collinear to vector ii of the common tangent to the helices of the shaper and the worm. After derivations, we obtain cws \u00bc 90 b kw; \u00f036\u00de kw \u00bc arcsin rpsNw cos b Ns\u00f0Ews \u00fe rps\u00de : \u00f037\u00de Here, Ns and Nw are the tooth number of the shaper and number of threads of the worm, respectively. The upper and lower signs in Eq. (36) correspond to the application of a right-hand and left-hand worms, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001382_j.mechmachtheory.2011.01.014-Figure3-1.png", + "caption": "Fig. 3. Coordinate system Sp defined at contact point P.", + "texts": [ + " Two approaches for application of the Hertz theory are considered for a whole crowned spur gear drive with localized bearing contact: (i) contact at a single point, when the load is shared by just one pair of contacting teeth, and (ii) contact at two points, when the load is shared by two consecutive pairs of contacting teeth. 3.1. Contact at a single point The application of the Hertz theory at a single contact point is based on the following algorithm: (i) Pinion tooth surface \u03a31 and gear tooth surface \u03a32 contact at a single point P. Position vector r1(P) and unit normal n1 (P) are determined in coordinate system S1, rigidly connected to the pinion tooth surface (Fig. 3). (ii) A new reference system Sp is defined as follows (Fig. 3). Origin Op is located at point P. Axis zp results collinear to unit normal n1 (P). Axes xp and yp are collinear to vectors \u2202r1(P)/\u2202 l and \u2202r1(P)/\u2202u, respectively, wherein u and l are the surface parameters for profile and longitudinal directions. Axes xp and yp define a common tangent plane \u03a0 to the pinion and gear tooth surfaces (Fig. 3). (iii) A new surface \u03a3r is formed from pinion and gear tooth surfaces as follows (Fig. 4) (a) A point A on the plane \u03a0 is given in system Sp by vector position rp(A)(x,y) (Fig. 4(a)). (b) Two projections of point A, A1 and A2, on tooth surfaces \u03a31 and \u03a32, respectively, are obtained as (Fig. 4(b)) r A1\u00f0 \u00de p x; y\u00f0 \u00de = r A\u00f0 \u00de p x; y\u00f0 \u00de + \u03bb1 x; y\u00f0 \u00den P\u00f0 \u00de p \u00f01\u00de r A2\u00f0 \u00de p x; y\u00f0 \u00de = r A\u00f0 \u00de p x; y\u00f0 \u00de + \u03bb2 x; y\u00f0 \u00den P\u00f0 \u00de p \u00f02\u00de wherein \u03bb1 and \u03bb2 are scalar coefficients and np (P)=Lp1n1 (P) is the unit normal at the contact point P in system Sp" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.18-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.18-1.png", + "caption": "Fig. 1.18 Identification of the position of the three axes through the center of gravity", + "texts": [ + "9, by angles \u03b1I, \u03b2I, and \u03b3I that can be calculated from the three directional cosines cos \u03b1I, cos \u03b2I, and cos \u03b3I. The orientations of the other two principal axes II and III can be determined analogously. The calculation becomes simpler when the real body has a plane of symmetry, which in the case on hand is assumed to be the \u03be-\u03b6 plane. Each axis that is perpendicular to the plane of symmetry is a principal axis of inertia, and determining the elements of the moment of inertia tensor becomes simpler, see Fig. 1.18. Figure 1.10 shows a car engine that is suspended for the determination of the principal axes of inertia. The engine is in a frame that can be mounted in various positions to the torsion rod. It is important to meet the conditions on which the equations are based when performing these tests. These conditions primarily include the linear equation of motion and the neglecting of the damping. Since both the pendulum equations and the equation of motion can only be considered linear for small deflections when an object is suspended using several filaments, the angular amplitude or filament angle, respectively, must not exceed 6\u25e6", + " At frequencies greater than 20 Hz, kdyn \u2248 2.8 to 3.2. The moment of inertia of a crankshaft with respect to its axis of rotation is to be determined experimentally using a torsion rod suspension system (Fig. 1.8). The following applies to the torsion rod: length l = 380 mm; diameter d = 4 mm; shear modulus G = 7.93 \u00b7 104 N/mm2. A time of T = 41.5 s was measured for 50 full vibrations. The moment of inertia tensor of a symmetrical body is to be determined by experiment. Pendulum tests about the three axes shown in Fig. 1.18 (k = 1, 2 and 3), which are in the symmetry plane, were performed, from which the three moments of inertia about the axes 1, 2 and 3 could be determined. Given: Moments of inertia about these axes: JS 11, JS 22, and JS 33 Find: 1. Principal moments of inertia JS I , JS II, JS III 2. Angles of principal axes \u03b11, \u03b31, \u03b11I, \u03b31I 1.3 Spring Characteristics 39 The static characteristic for a rubber compression spring was determined as shown in Table 1.7 and Fig. 1.19. What spring value can be expected in a linear vibration system if the spring load at the static equilibrium position is 9 kN, and the frequency is approximately 20 Hz (Shore rubber hardness larger than 80)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000918_12.2018412-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000918_12.2018412-Figure3-1.png", + "caption": "Figure 3. Exploded schematic view of the Kapton Film based shutterless window protection system.", + "texts": [ + " Also visible in the image are several \u201ccomet-like\u201d bright dots with bright tails. These dots are the Ebeam showing up in various different locations during the 1ms exposure of the IR camera. The window became too opaque for imaging 3 minutes after this image was acquired due to metallization build-up on the inside. In order to over come the metallization of the window, a shutterless window protection system was developed. In order to protect the inside of the window from metallization, a film-based system was developed (see Figure 3). A thin Kapton film is spooled across the vacuum side of the window during the E-beam melting process. With each new layer of the build a new area of Kapton film is positioned in front of the window, while the partially metalized area of the film is spooled onto the film take-up reel. The Kapton film based shutterless window system was originally designed similar to the windows used on the front door; A thick disk of quartz, due to the high vacuum inside the chamber, and a thick disk of leaded glass to eliminate X-rays produced when the E-beam strikes the metal powder" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001207_s10846-010-9395-x-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001207_s10846-010-9395-x-Figure1-1.png", + "caption": "Fig. 1 Rotation sequence to transform global coordinate to body-fixed coordinate for underwater vehicle [24]", + "texts": [ + " To verify this idea, simulation of a type of UUV , Deep Submergence Rescue Vehicle (DSRV) using SIFLC is carried out. The results are compared to the CFLC applied on the same system. The notation used in this paper is in according to SNAME, 1950 [24]. The DSRV modeling is based on the Newton\u2013Euler approach as suggested by Fossen, 1994 [25]. Conveniently it can be developed using two coordinate system or frames; where the first one is a global reference frame (XYZ) and the second is a body-fixed frame (X0Y0Z0). This is shown in Fig. 1. The body-fixed frame has components of motion modeled by six velocities components: [u v w p q r] that represent translation and rotation motion: [surge, sway, heave, roll, pitch, yaw]T respectively. The velocity vector is represented as: v = [u v w p q r]T (1) Using Euler angles the position and orientation of the vehicle may be described as a vector \u03b7 relative to the global reference frame: \u03b7 = [x y z \u03c6 \u03b8 \u03c8]T (2) The mapping between the two coordinate systems is given by the Euler angle transformation: \u03b7\u0307 = J(\u03b7)v (3) where J is the Euler angle transformation matrix which can be described by three rotations in a fixed order. The coordinate system obtained by translating the global reference frame to the origin of the body-fixed frame can be shown in Fig. 1. It illustrates the roll angle (\u03c6), pitch angle (\u03b8), and yaw angle (\u03c8).The nonlinear vehicle dynamics can be expressed in a compact form as: M v\u0307 + C(v)v + D(v)v + g(\u03b7) = B(v)u (4) where, M is the 6 \u00d7 6 inertia matrix including hydrodynamic added mass. C(v) is the Matrix of the Coriolis and centripetal forces. D(v) is the Hydrodynamic damping matrix. g(\u03b7) is the Vector of restoring forces and moments. B(v) is the 6 \u00d7 3 control matrix. The simplified rigid-body equations of motion in heave and pitch can be written according to the following criteria by assuming the origin coincides with the centre of gravity and sway (v) and yaw (r) are zero: m(w\u0307 \u2212 u0q) = Z (5) Iyq\u0307 = M (6) The external forces and moments are described by hydrodynamic added mass, linear damping, and effects of the stern plane deflection equations, respectively written as follows: Z = Zw\u0307w\u0307 + Zq\u0307q\u0307 + Zww + Zqq + Z\u03b4\u03b4s (7) M = Mw\u0307w\u0307 + Mq\u0307q\u0307 + Mww + Mqq \u2212 mg(zG \u2212 zB) sin \u03b8 + M\u03b4\u03b4s (8) M \u2248 Mw\u0307w\u0307 + Mq\u0307q\u0307 + Mww + Mqq \u2212 W BGz\u03b8 + M\u03b4\u03b4s (9) For a vehicle operating in the vertical plane, the following assumptions can be made: forward speed is constant, sway and yaw modes can be neglected and in steady state, \u03b80 = constant and (q0 = \u03c60 = 0)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003497_j.triboint.2019.105960-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003497_j.triboint.2019.105960-Figure4-1.png", + "caption": "Fig. 4. Free body diagrams of rollers: (a) on the left row (Row 2), (b) on the right row (Row 1).", + "texts": [ + " Tribology International 141 (2020) 105960 fuMg T \u00bc fuM;r; uM;z; \u03b8Mg and fuM;\u03b1mg T \u00bc fuM;\u03be; uM;\u03b6; \u03b8Mg; in local cylin- drical and inclined coordinate systems can be calculated by using transformation matrices as fuMg \u00bc \u00bdRM \ufffdf\u03b4Mg (3) \ufffd uM;\u03b1m \ufffd \u00bc \u00bdKM \ufffdfuMg (4) Meanwhile, the relationship of roller displacement vectors, fvMg T \u00bc fvM;r; vM;z; \u03c6Mg and fvM;\u03b1mg T \u00bc fvM;\u03be; vM;\u03b6; \u03c6Mg; in local cylindrical and inclined coordinate systems can be described by \ufffd vM;\u03b1m \ufffd \u00bc \u00bdKM \ufffdfvMg (5) Here, the transformation matrices, [KM] and [RM] are given by \u00bdKM \ufffd \u00bc 2 4 cos\u03b1m sin\u03b1m 0 sin\u03b1m cos\u03b1m 0 0 0 1 3 5 (6) \u00bdRM \ufffd \u00bc 2 4 cos \u03c8 sin \u03c8 0 \ufffdzp sin \u03c8 \ufffdzp cos \u03c8 0 0 \ufffd1 \ufffdrp sin \u03c8 \ufffdrp cos \u03c8 0 0 0 \ufffdsin \u03c8 \ufffdcos \u03c8 3 5 (7) where the signs \u201c\u00fe\u201d and \u201c-\u201ccorrespond to different rows. Specifically, the upper sign is used for the right row (M \u00bc 1) and the lower sign for the left row (M \u00bc 2), respectively. The free-body diagrams of the rollers located on the left and right rows are shown in Fig. 4(a) and (b), respectively. The contact area along a roller can be divided into ns identical slices using the slicing technique [25]. The contact deformations of the kth slice on the right and left rows, \u03b4M;N;k, are given by \u03b4M;N;k \u00bc \u03b4M;N \u00fe \u03b2M;Nlk hk (8) where N \u00bc i; o indicate the inner and outer rings, respectively. The position of kth slice, lk, varies from 0:5lwe to 0:5lwe. This paper considers the logarithmic crowned profile and flat raceways. As for the modified roller profile, the crowned drop, hk, at kth lamina is described by the function [25]", + " \u03b4M;f \u00bc\u0394M;\u03be sin\u03bco \u00fe \u0394M;\u03b6 cos\u03bco \u00fe lf \u00bdcos\u03bco cos\u00f0\u03bco \u00fe \u03b2M;i\u00de\ufffd (18) where the contact angle, \u03bco, is defined between the axis of roller and the contact line of roller-flange, lf is the straight-line distance between PM and intersection points between flange forces and roller center line, as shown in Figs. 3 and 4. As the main shaft double-row TRB in a gearless wind turbine commonly operates at low speed, the influence of inertial forces in bearing elements can be neglected. However, the thrust frictional force at roller-raceway contact may have a significant effect on the static equilibrium under the combined operating conditions in the \u00f0\u03beM;\u03b6M\u00de plane [27], as shown in Fig. 4. The thrust contact friction can be given by FtM;N \u00bc sgn\u00f0\u0394uv\u00deQM;N\u03bcz (19) where sgn\u00f0\u0394uv\u00de indicates the sign of \u0394uv. Specifically, \u0394uv \u00bc \u00f0vM;\u03b6 uM;\u03b6\u00de is used for the frictional force between roller and inner race, and \u0394uv \u00bc vM;\u03b6 for the frictional force between roller and outer race. \u03bcz is J. Zheng et al. Tribology International 141 (2020) 105960 the frictional coefficient between roller and races. For the case of low speed and heavily loaded bearing, the fluid-film friction is negligible. Therefore, only Coulomb friction is considered in this study by assuming the frictional coefficient as a constant which is equal to a dry frictional coefficient of 0.2. The quasi-static mathematical model of a double-row TRB can be developed from the equations of equilibrium for rollers and raceways. The modeling process and solution approach will be presented in this section. From Fig. 4, the equations of equilibrium for rollers can be written as: where \u03bco is the nominal angle between the center line of a roller and the flange contact line of inner ring, \u03bcM is the angle transformed by \u03bco to account for the shift of contact points between the big-end of roller and the flange of raceway under low-speed and heavy-load conditions [19]. Eq. (20) will be solved for the unknown roller displacement vector fvM;\u03b1mg, by the iterative Newton-Raphson method using the algorithm: \ufffd FM;r \ufffd \u00fe \u00bdJM;r\ufffd \ufffd \u0394\u03bdM;\u03b1m \ufffd \u00bc f0g (21) where \u00bdJM;r\ufffd is the Jacobian matrix, and f\u0394vM;\u03b1mg is the incremental vector of fvM;\u03b1mg" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001803_17452759.2013.868005-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001803_17452759.2013.868005-Figure8-1.png", + "caption": "Figure 8. Temperature field results of successive layers during model processing.", + "texts": [ + " heating, and once reaching the melting point the powder material was assigned with the material properties of the solid IN718 with the aid of a phase transformation model during the thermal analysis. The model layers were processed one after the other until the whole component was built. After the layer build-up, the phase transformation and cooling, the model attained its final thermal and structural equilibrium. The results of the temperature field during processing of each model layer are shown in Figure 8. Figure 7. Twin cantilever model for the simulation of shape distortions after SLM processing. D ow nl oa de d by [ H er io t- W at t U ni ve rs ity ] at 0 8: 22 0 2 Ja nu ar y 20 15 The transient temperature field including the change of phase from powder into solid was used as a load for the mechanical analysis. The mechanical model is fixed on the bottom side on the substrate (Figure 7). After the thermal processing and cooling to ambient temperature the structural model reached its equilibrium" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure5.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure5.3-1.png", + "caption": "Fig. 5.3 Graphical interpretation of linear programming. Solving the linear programming problem is equivalent to finding out whether or not there exists a unique point in the feasible solution space for which the cost is greatest if maximizing, or smallest if minimizing. If it exists, that point is x\u2217. Otherwise, the problem may be infeasible or unbounded, and have no such unique optimal solution", + "texts": [ + "32) the latter version being in the more commonly known slope-intercept form, with a slope of \u2212 1 2 and intercept of the ordinate axis at the value of b 2 . In Fig. 5.2b we see an example where some portion of the cost function line lie within the feasible solution space. Note that in that case all points on the cost function line that also lie within the feasible solution space are valid, and produce the same cost. This is another interpretation of an underdetermined system (i.e., redundancy): There can be infinitely many valid solutions (i.e., x points in the feasible solution space) that produce a same result (i.e., a same cost). Last, Fig. 5.3 shows the purpose of linear programming: Find a value of the cost (i.e., slide the cost function up and down in value) in the direction of increasing value if maximizing (or decreasing value if minimizing) until you find a unique solution for which the vector x is admissible, and for which the cost is at an extreme value (its maximum in this case). Some consequences and implications of this graphical interpretation include the following: \u2022 Linear programming can be thought of as finding the unique point where the cost function first touches the feasible region", + ", there is redundancy), but a point on the edges (or a vertex itself) has a unique representation as in Figs. 7.6 and 7.8. But for a polyhedron, a point on a face (which is a polygon by definition) does not have a unique representation (why?). Only points along the edges or vertices themselves have unique representations. This concept extends to polytopes in higher dimensions and even serves as the basis for the simplex method that relies on finding edges and following them to a unique vertex as shown in Fig. 5.3 [13]. These concepts serve to motivate the connection between the structure and properties of convex sets, and the choices the nervous system has to produce a particular mechanical output. Exercises and computer code for this section in various languages can be found at http://extras.springer.com or found by searching the World Wide Web by title and author. 1. F.J. Valero-Cuevas, F.E. Zajac, C.G. Burgar, Large index-fingertip forces are produced by subject-independent patterns of muscle excitation", + " We see that the results of the Hit-and-Run algorithm are the probability density functions of the points that create the feasible activation set, Fig. 9.7e, f. Were we to use the bounding box approach, all we would know are the extremes of these distributions. We now see that those bounds apply, but that the distribution of neural activation within those bounds is far from uniform. That is, not all values of activation for each muscle are equally likely. Increasing or decreasing the target magnitude of force output simply translates the plane in a direction orthogonal to it, much as in in Fig. 5.3 when changing the value of a cost function (why?). Figure9.7f shows that, as the plane moves toward the back corner of the unit cube (in this view) to represent a new target output force magnitude of 2 N, the probability distributions change. When producing maximal feasible force magnitude, the solution is a unique point as the plane P shrinks to 9.5 Probabilistic Neural Control 151 152 9 The Nature and Structure of Feasible Sets Fig. 9.8 Iterative stochastic sampling using the Hit-and-Run algorithm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002281_tmag.2013.2239977-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002281_tmag.2013.2239977-Figure1-1.png", + "caption": "Fig. 1. No-load magnetic field distributions for different number of slots used in machines. (a) 1-slot. (b) 3-slot. (c) 6-slot. (d) 6 slot with slot-opening shifted.", + "texts": [ + " For those values, (7) could be simplified to (8) The total cogging torque will be the number of groups multiplying single group cogging torque given in (8), as (9) As defined before, index should take the value of and its multiples, which result in an integer number of as required. Given and is a positive integer index representing integer multiples of , (9) becomes (10) A 12-slot, 8-pole surface-mounted PM motor (with , , , and ) is studied as an example to validate the analysis presented previously. The fundamental model is a machine with only 1-slot, as shown in Fig. 1(a). For this 12-slot, 8-pole machine, the required number of slots forming one group is 3 . Therefore, according to the analysis given in Section II, each slot group should produce the same cogging torque. This may be validated by studying the 3-, 6-, 9-, and 12-slot machines (the 3-slot and 6-slot machine models are given in Fig. 1 as examples). The cogging torque for the machines with different numbers of slots is shown in Fig. 2. It may be observed from Fig. 2 that though the cogging torque produced by a 1-slot machine and that produced by a 3-slot machine behave quite differently, by combining 3 slots into one group (which corresponds to one period of the cogging torque waveform per pole, as ), the cogging torque produced by 3-, 6-, 9-, and 12-slot machines is all in phase and the magnitude is proportional to the number of groups", + " Based on the special feature of the cogging torque profiles viewed in groups, a simple but effective cogging torque reduction method may then be introduced. By shifting the slot-openings belonging to the same group, the cogging torque waveform of this group will also be shifted. Since the cogging torque produced by each group (containing 3 slots in this case) is in phase, therefore, by shifting the slot-openings for one group in one direction and shifting the slot-openings in the other group in the opposite direction, the total combined cogging torque of these two groups will be reduced. Fig. 1(c) shows a 6-slot machine with no slot-opening shift. Fig. 1(d) shows that the slot-openings of the right three slots are shifted 1/8 tooth pitch in the anti-clockwise direction while the slot-openings of the left three slots are shifted 1/8 tooth pitch in the clockwise direction. Those two groups form one pair of groups when considering cogging torque reduction. The resultant cogging torque for those two cases are shown in Fig. 3, where significant cogging torque reduction offered by slot-opening shift can be observed. It is easy to find that in order to reduce effectively the cogging torque, the relative angle shift between the two cogging torque waveforms produced by one pair of groups should be 180 el" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.22-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.22-1.png", + "caption": "FIGURE 11.22. A compound pendulum attached with a linear spring at the tip point.", + "texts": [ + " Convert the moment of inertia B I and the angular velocity gw B to the global coordinate frame and then find the differential of angular momentum. It is an alternative method to show that Cd (B B )dt I CWB Bt+gwB x BL Iw + wx (Iw) . 16. Equations of motion for a rotating arm . Find the equations of motion for the rotating link shown in Figure 11.21 based on the Lagrange method. 11. Motion Dynamics 501 17. Lagrange method and nonlinear vibrating system. Use the Lagrange method and find the equation of motion for the link shown in Figure 11.22. The stiffness of the linear spring is k. 502 11. Motion Dynamics e---~----.. X FIG URE 11.23. A pendulum with a vibrating pivot . (a) the pivot 0 has a dictat ed motion in X direction X o = asin wt (b) t he pivot 0 has a dictat ed motion in Y direction Yo = bsin wt (c) the pivot 0 has a uniform motion on a circle ro = R coswt i + R sin wt J. 19. Equations of mot ion from Lagrangean. Consider a physical syst em with a Lagrangean as I:- = ~m (ax + biJ )2 - ~k (ax + by)2 . The coefficients m , k, a, and b are constant " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000108_i2008-10388-1-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000108_i2008-10388-1-Figure6-1.png", + "caption": "Fig. 6. Stroboscopic snapshots of the filament at different times during the beating cycle for \u03b5 = 0.9. The trajectory of the top bead during one beating cycle is also indicated. In the slow transport stroke the filament rotates clockwise, the fast recovery stroke occurs to the left, as indicated by the arrows. A pronounced bending of the filament occurs only at intermediate sperm number Sp and magnetic-field strength Bs.", + "texts": [ + " Hence, equation (30) constitutes a suitable measure for characterizing the pumping performance of the magnetically actuated artificial cilium. Figure 5a) shows the pumping performance \u03be of a single filament as a function of the sperm number Sp and the asymmetry parameter \u03b5 at a fixed strength of the magnetic field Bs = 2.5. The most striking feature is that the performance is strongly peaked for \u03b5 close to one and at Sp \u2248 3. Such a peak is also observed in the swimming velocity of the artificial micro-swimmer [8,15,18]. The corresponding stroke pattern for Sp \u2248 3 is illustrated in the middle picture of Figure 6a). In the slow transport stroke the filament rotates clockwise being nearly straight. It uses the high friction coefficient of a rigid rod dragged perpendicular to its axis to pump fluid. In the fast recovery stroke, the filament bends due to the large hydrodynamic friction forces that scale with velocity and then relaxes back to the initial configuration. As Figure 3a) illustrates, fluid transport is also noticeable in the recovery stroke. So, the pumping performance, even for the most efficient stroke pattern, is the result of a small asymmetry in the amount of fluid transported to the right or left", + "3% of the total amount of moved fluid are effectively transported in the positive y-direction. As a result, the maximum pumping performance in Figure 5a) is only 6% of the reference stroke. As expected, the pumping performance vanishes for symmetric beating about the z-axis, i.e., when \u03b5 = 0. The same is true for Sp \u2192 0: The filament follows the actuating magnetic field instantaneously. Aside from the base, the filament therefore remains straight and the stroke is reciprocal. The left picture in Figure 6a) gives an example of such a stroke. A reversal of the pumping direction (\u03be < 0) occurs at Sp \u2248 5.5, albeit only with a rather weak performance. Finally, the pumping performance goes to zero for increasing Sp or frequency since the filament can no longer follow the actuating field as illustrated in the right picture of Figure 6a). In summary, an optimal pumping performances is only achieved for intermediate values of Sp. Let us add a further remark. Naively, one might anticipate that the closer \u03b5 is to one, the more pronounced the incurred bending during the fast part of the actuation cycle, giving rise to better pumping performance. However, a limit on the maximal speed with which the filament manages to follow the field exists. The extreme case of instantaneous switching of the direction of the magnetic field in the recovery stroke (\u03c4s = 0) is not conducive to generating fluid transport", + " Surprisingly, it does not display such a pronounced behavior as the pumping performance. Particularly, there is hardly any dependence on the asymmetry parameter \u03b5 visible. Being proportional to the square of the beads\u2019 velocities, one could assume \u03bd \u223c \u03c92 and therefore \u03bd \u223c S8 p (recall that Sp \u223c \u03c91/4). At small Sp, the data shown in Figure 5b) do show a steep incline. However, they do not increase as S8 p , because already at Sp around 2 the filament does not completely follow the actuating field as the snaphots in Figure 6a) illustrate. This effect becomes more pronounced for increasing Sp, and the data clearly deviate from the naive assumption of \u03bd \u223c S8 p . The third picture in Figure 6a) demonstrates that already at Sp = 5 the filament lags significantly behind the actuating magnetic field. As illustrated by the three-dimensional plot of Figure 7a), there exists a pronounced dependence of the pumping performance \u03be on the strength Bs of the actuating magnetic field which has also been observed in the swimming velocity of the artificial micro-swimmer [8,15, 18]. Figure 7b) shows this behavior for different constant values of Sp. Increasing the magnetic field from zero, the pumping perfomance stays close to zero and then, beyond a certain threshold value, it grows until it reaches a maximum. It finally decreases and even becomes negative. The snapshots in Figure 6b) again explain this behavior. Small field strengths Bs are not high enough to overcome the hydrodynamic friction forces and therefore the motion of the filament is very limited. On the other hand, at large strengths Bs the filament is always straight and therefore performs a reciprocal motion. An optimal stroke only exists in an intermediate regime for the strength Bs. Clearly, the optimal performance shifts with increasing Sp to larger values of Bs since a larger field is needed to move the filament through the fluid" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001990_j.phpro.2014.08.100-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001990_j.phpro.2014.08.100-Figure2-1.png", + "caption": "Fig. 2. Application of a defined powder layer: Detect build platform (a), apply an oversized layer and detect powder surface (b) and remove excessive powder material (c).", + "texts": [ + " To adjust the SLM machine setup according to this requirement surface scans of different focal positions are performed and compared manually. The LCI based sensor could be used to execute this task automatically by analyzing the profiles of single weld beads. Application of the first powder layer: The application of the first powder layer is until now an imprecise procedure that strongly depends on the operating personnel as it is done by visual inspection. By comparison of several reference measurements the sensor could perform this task automatically. Figure 2 shows one possible way to proceed: Before applying the powder the platform is placed at a level significantly lower than the expected position. The optical sensor now measures the distance A to the surface (2a). Afterwards a powder layer is applied and the level B of the surface which coincides with the level of the coater tip is sampled (2b). A defined thickness D can now be achieved by moving the platform upwards based on the values measured before. Finally the excessive powder volume will be removed by the coating unit (2c)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003245_access.2019.2906345-Figure14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003245_access.2019.2906345-Figure14-1.png", + "caption": "FIGURE 14. (a) Quadcopter experimental setup and (b) experimental target.", + "texts": [], + "surrounding_texts": [ + "To verify the feasibility of the proposed Moving TargetTracking algorithm, several experiments were performed VOLUME 7, 2019 38415 indoor and outdoor with varying speed. Initially, the quadcopter is hovering at a fixed altitude of 2.5 meters. Once the target is detected, the IR-Camera will send the position of the detected target in pixels to the Arduino DUE every 20 msec. The received data is used as input to the Fuzzy-PI controller to calculate the required angle for tracking the moving target. This process is executed every 22 msec inside the Arduino DUE. For calculating the absolute position of the quadcopter in meters, a GPS can be used. However, since the GPS provides inaccurate localization in indoor environments. A vision-based algorithm is used to obtain the absolute position between the detected target and the drone. The algorithm uses the pinhole camera model and the captured images to build a metric map. The coordinate of a point in 3D (X, Y, Z) can be computed from its projection pixel in the 2D (x, y) image and the projection matrix. Firstly, a reference object is used to measure the pixels per metric ratio. In the algorithm, a MarkOne beacon with a known width and height is used as a reference object. An image of the reference object is captured from a defined height of 2.5 meters using the IR Camera equipped on the drone. Then, the reference object is detected in the image, either based on the placement of the object or via appearances, such as its color or shape. In our case, a distinctive color is used to locate the object in the image and a contour technique is used to define the boundaries of the object, as shown in Fig.16. Thus, the width and height of the reference object in pixels are obtained. The pixels per metric can be calculated as follow: p = h w (9) where p denotes the pixels per metric ratio, h and w are the reference object width in pixels and metric, respectively. The distance between the drone and the detected target is computed as shown in Equation (10, 11): x\u0302 = A1 \u2217 x + B1 (C (x \u2212 100)2 + D (y\u2212 160)2 \u2212 1) (10) y\u0302 = A2 \u2217 y+ B2 (C (x \u2212 100)2 + D (y\u2212 160)2 \u2212 1) (11) Where x\u0302 and y\u0302 are the distance in meter, x and y are the distance in pixels. As shown in the previous equations, each equation has four unknowns, and therefore four known points are used to generate four equations for each axis to identifies these unknowns. Table. 3 shows the identified parameters that are obtained using regular simultaneous equation solving methods, such as substitution and elimination. The experimental target is moving in two trajectories, a rectangular trajectory, and a triangular trajectory. The trials were executed indoor and outdoor. Figures (17-20) shows the results of the performed trials. Figure 17 compares between the Gain-Scheduled PID controller and the Fuzzy-PI controller under variable target speed indoor in a rectangular trajectory. Figure (17-a) shows that both controllers have 38416 VOLUME 7, 2019 close results in the X position. However, in Fig. (17-b), Fuzzy-PI shows a better response than the other controller in the Y position. Figure (17-c) shows the behavior of the quadcopter in the XY plane under varying speed. As shown in this figure, Fuzzy-PI has better response and faster settling time than Gain-Scheduled PID controller. Figure 18 evaluates the performance of the GainScheduled PID controller and the Fuzzy-PI controller under different target speed outdoor in a rectangular trajectory. Figure (18-a) shows that both controllers have close results in X position, while in Fig. (18-b), Gain-Scheduled PID controller depicts feeble response and stability in the Y position. Figure (18-c) illustrates the performance of the quadcopter in the XY plane under varying speed. As it is easily seen in the Figure, the Gain-Scheduled PID has poor performance, poor stability and failed to reach the center of the detected target. Figure 19 shows comparison results between the two controllers under varying target speed indoor in a triangular trajectory. Figure (19-a & 19-b) shows that both controllers have close results in X and Y positions. However, Figure (19-c) indicates that the Fuzzy-PI controller has better response and faster settling time compared to the Gain-Scheduled PID controller in the XY plane under varying speed. Figure 20 evaluates the performance of the GainScheduled PID controller and the Fuzzy-PI controller under variable target speed outdoor in a triangular trajectory. Figure (20-a & 20-b) shows that the Gain-Scheduled PID controller has poor stability and longer settling time than the Fuzzy-PI controller in X and Y positions. Figure (20-c) demonstrates that under variable speed, Fuzzy-PI has better response and faster settling time than theGain-Scheduled PID controller. According to the previous evalutioan of the experimental results, the Fuzzy-PI controller has proven that it has better response, and shorter settling time compared to the GainScheduled PID controller. Although the Gain-Scheduled PID controller is working well compared to the typical PID controller, since the proportional gain is continuously changed according to the position and change of position of the detected target, the output of theGain-Scheduled PID is either increasing or decreasing linearly, which is the reason of the slow response of this controller. In contrast, the Fuzzy-PI controller has proved it has better control because according VOLUME 7, 2019 38417 to the position and change of position values, we can control how much we need to increase or decrease the output of the Fuzzy-PI controller. Thus, it can rapidly minimize the error between the position and the center of the detected target as much as possible, where it gives us more accurate output to adjust the final P and I gain of the PID controller. As a result, the Fuzzy-PI can be thought of an auto-tuningmethod for PID controller. VI. CONCLUSION In this paper, a Moving Target-Tracking algorithm has been proposed. Target-Tracking algorithm based on Fuzzy-PI controller is developed to track a moving target under varying speed and during day and night. Furthermore, the relatively cheap embedded controller was used for real-time applications such as target tracking. The proposed algorithm can be used in many applications such as traffic supervision, autonomous robot navigation, and landing to a moving target. Several experiments are performed indoor and outdoor. The obtained results show that the proposed system works well indoor and outdoor for tracking the moving target. Furthermore, this system is currently being improved to land on a moving target such as a car and also an unstable target such as a ship during the night. Moreover, it can be further improved by using a deep learning algorithm such as CNN (Convolutional Neural Network) and train it to detect a target during day and night then apply the proposed algorithm for tracking and landing. REFERENCES [1] G. Hoffmann, D. G. Rajnarayan, S. L. Waslander, D. Dostal, J. S. Jang, and C. J. Tomlin, \u2018\u2018The stanford testbed of autonomous rotorcraft for multi agent control (STARMAC),\u2019\u2019 in Proc. 23rd Digit. Avionics Syst. Conf., vol. 2, Oct. 2004, pp. 12.E.4\u2013121-10. [2] ICAO\u2019s Circular 328 AN/190: Unmanned Aircraft Systems, ICAO, Montreal, QC, Canada, Feb. 2016. [3] J. Stafford, \u2018\u2018How a Quadcopter works | Clay Allen,\u2019\u2019 Univ. Alaska Fairbanks, Jan. 2015. [4] M. Bhaskaranand and J. D. Gibson, \u2018\u2018Low-complexity video encoding for UAV reconnaissance and surveillance,\u2019\u2019 in Proc. IEEE Military Commun. Conf., Nov. 2011, pp. 1633\u20131638. [5] T. Tomic et al., \u2018\u2018Toward a fully autonomous UAV: Research platform for indoor and outdoor urban search and rescue,\u2019\u2019 IEEE Robot. Autom. Mag., vol. 19, no. 3, pp. 46\u201356, Sep. 2012. [6] L. Merino, F. Cabalero, J. R. Mart\u00ednez-de Dios, J. Ferruz, and A. Ollero, \u2018\u2018A cooperative perception system for multiple UAVs: Application to automatic detection of forest fires,\u2019\u2019 J. Field Robot., vol. 23, nos. 3\u20134, pp. 165\u2013184, 2006. [7] J. Liu, C. Wu, Z. Wang, and L. Wu, \u2018\u2018Reliable filter design for sensor networks using type-2 fuzzy framework,\u2019\u2019 IEEE Trans. Ind. Informat., vol. 13, no. 4, pp. 1742\u20131752, Aug. 2017. [8] M. Talha, F. Asghar, A. Rohan, M. Rabah, and S. H. Kim, \u2018\u2018Fuzzy logicbased robust and autonomous safe landing for UAV quadcopter,\u2019\u2019 Arabian J. Sci. Eng., vol. 44, no. 3, pp. 2627\u20132639, Mar. 2019. [9] P. Doherty and P. Rudol, \u2018\u2018A UAV search and rescue scenario with human body detection and geolocalization,\u2019\u2019 in AI 2007: Advances in Artificial Intelligence. Berlin, Germany: Springer, 2007, pp. 1\u201313. [10] H. Lim and S. N. Sinha, \u2018\u2018Monocular localization of a moving person onboard a Quadrotor MAV,\u2019\u2019 in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), May 2015, pp. 2182\u20132189. [11] H. Huang, L. Zhang, C. Fu, Y. Zhou, and Y. Tian, \u2018\u2018Ground moving target tracking algorithm for multi-rotor unmanned aerial vehicle,\u2019\u2019 inProc. IEEE Chin. Control Decis. Conf. (CCDC), Jun. 2018, pp. 1214\u20131219. [12] R. P. George and V. Prakash, \u2018\u2018Real-time human detection and tracking using quadcopter,\u2019\u2019 in Intelligent Embedded Systems, vol. 492. Singapore: Springer, 2018, pp. 301\u2013312. [13] C. Pei, J. Zhang, X. Wang, and Q. Zhang, \u2018\u2018Research of a non-linearity control algorithm for UAV target tracking based on fuzzy logic systems,\u2019\u2019 Microsyst. Technol., vol. 24, no. 5, pp. 2237\u20132252, 2018. [14] A. Joukhadar, M. AlChehabi, C. St\u00f6ger, and A. M\u00fcller, \u2018\u2018Trajectory Tracking Control of a Quadcopter UAV Using Nonlinear Control,\u2019\u2019 in Mechanism,Machine, Robotics andMechatronics Sciences, vol. 58. Cham, Switzerland: Springer, 2018, pp. 271\u2013285. [15] H. Bolandi, H. Nemati, R. Mohsenipour, and M. Rezaei, \u2018\u2018Attitude control of a quadrotor with optimized PID controller,\u2019\u2019 Intell. Control Automat., vol. 8, no. 3, pp. 335\u2013342, 2013. [16] D. K. Tiep and Y. J. Ryoo, \u2018\u2018An autonomous control of fuzzy-PD controller for quadcopter,\u2019\u2019 Int. J. Fuzzy Logic Intell. Syst., vol. 17, no. 2, pp. 107\u2013113, 2017. [17] M. Islam, M. Okasha, and M. M. Idres, \u2018\u2018Trajectory tracking in quadrotor platform by using PD controller and LQR control approach,\u2019\u2019 IOP Conf., Mater. Sci. Eng., vol. 260, no. 1, pp. 2451\u20132456, 2017. [18] Z. Zuo, \u2018\u2018Trajectory tracking control design with command-filtered compensation for a quadrotor,\u2019\u2019 IET Control Theory Appl., vol. 4, no. 11, pp. 2343\u20132355, Nov. 2010. [19] P. Chen, Y. Dang, R. Liang, W. Zhu, and X. He, \u2018\u2018Real-time object tracking on a drone with multi-inertial sensing data,\u2019\u2019 IEEE Trans. Intell. Transp. Syst., vol. 19, no. 1, pp. 131\u2013139, Jan. 2018. [20] A. Samir, A. Hammad, A. Hafez, and H. Mansour, \u2018\u2018Quadcopter trajectory tracking control using state-feedback control with integral action,\u2019\u2019 Int. J. Comput. Appl., vol. 168, no. 9, p. 8887, 2017. 38418 VOLUME 7, 2019 [21] M. Rabah, A. Rohan, Y.-H. Han, and S. H. Kim, \u2018\u2018Design of fuzzy-PID controller for quadcopter trajectory-tracking,\u2019\u2019 Int. J. Fuzzy Logic Intell. Syst., vol. 18, no. 3, pp. 204\u2013213, 2018. [22] M. Rabah, A. Rohan, M. Talha, K. H. Nam, and S. H. Kim, \u2018\u2018Autonomous vision-based target detection and safe landing for UAV,\u2019\u2019 Int. J. Control, Autom. Syst., vol. 16, no. 6, pp. 3013\u20133025, Dec. 2018. [23] H. Wang, B. Chen, X. Liu, K. Liu, and C. Lin, \u2018\u2018Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints,\u2019\u2019 IEEE Trans. Cybern., vol. 43, no. 6, pp. 2093\u20132104, Dec. 2013. [24] H.Wang, P. X. Liu, and B. Niu, \u2018\u2018Robust fuzzy adaptive tracking control for nonaffine stochastic nonlinear switching systems,\u2019\u2019 IEEE Trans. Cybern., vol. 48, no. 8, pp. 2462\u20132471, Aug. 2018. [25] Y. Yin, G. Zong, and X. Zhao, \u2018\u2018Improved stability criteria for switched positive linear systems with average dwell time switching,\u2019\u2019 J. Franklin Inst., vol. 354, no. 8, pp. 3472\u20133484, May 2017. [26] V. Vesel\u00fd and I. Adrian, \u2018\u2018Gain-scheduled PID controller design,\u2019\u2019 J. Process Control, vol. 23, no. 8, pp. 1141\u20131148, 2013. [27] A. Rohan, F. Asghar, and S. H. Kim, \u2018\u2018Design of fuzzy logic tuned PID controller for electric vehicle based on IPMSM using flux-weakening,\u2019\u2019 J. Elect. Eng. Technol., vol. 13, no. 1, pp. 451\u2013459, 2018. [28] L.-X. Wang and J. M. Mendel, \u2018\u2018Fuzzy basis functions, universal approximation, and orthogonal least-squares learning,\u2019\u2019 IEEE Trans. Neural Netw., vol. 3, no. 5, pp. 807\u2013814, Sep. 1992. MOHAMMED RABAH received the B.S. degree in electronics and telecommunication engineering from the AL-SAFWA High Institute of Engineering, Cairo, Egypt, in 2015, and the M.S. degree in electronics and information engineering from Kunsan National University, South Korea, in 2017, where he is currently pursuing the Ph.D. degree. His research interests include UAV\u2019s, fuzzy logic systems, and machine learning. ALI ROHAN received the B.S. degree in electrical engineering from The University of Faisalabad, Pakistan, in 2012, and the M.S. degree in electronics and information engineering from Kunsan National University, South Korea, in 2017, where he is currently pursuing the Ph.D. degree. His research interests include renewable energy systems, power electronics, fuzzy logic, neural networks, EV systems, and flywheel energy storage systems. SHERIF A. S. MOHAMED received the B.S. degree in electrical, electronics, and communication engineering from Ain Shams University, Egypt, in 2011, and the M.S. degree in electronics and information engineering from Kunsan National University, South Korea, in 2016. He is currently pursuing the Ph.D. degree with the University of Turku, Finland. His research interests include vision-based navigation algorithms for autonomous vehicles, embedded systems, swam intelligence, and machine learning. SUNG-HO KIM received the B.S. degree in electrical engineering from Korea University, in 1984, and the M.S. and Ph.D. degrees in electrical engineering from Korea University, in 1986 and 1991, respectively. He has completed the Postdoctoral Research from Japan Hiroshima University, in 1996. He is currently a Professor with Kunsan National University. His research interests include fuzzy logic, sensor networks, neural networks, intelligent control systems, renewable energy systems, fault diagnosis systems. VOLUME 7, 2019 38419" + ] + }, + { + "image_filename": "designv10_3_0000824_iros.2007.4399407-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000824_iros.2007.4399407-Figure1-1.png", + "caption": "Fig. 1. The two strategies mimicked by our balance controller. The ankle strategy causes the robot to behave like a single inverted pendulum while the hip strategy allows the robot to use the gravitational force to help it balance", + "texts": [ + " We believe that balance is achieved by a set of decoupled controls that regulate the center of pressure and simultaneously ensure that the humanoid balances upright. In human balance experiments, it has been observed that people use a mixture of strategies for dealing with these disturbances. The ankle strategy fixes all joints except the ankle, and balances like a single inverted pendulum. The hip strategy is characterized by a large bending at the hips, which results in a repositioning of the center of mass [1]. These two strategies are illustrated in Fig. 1. In Section II, we present a controller that is inspired by these human balance strategies and accounts for the limits on the location of the center of pressure to ensure that the robot can stand with its feet flat on the ground and withstand large disturbances. We begin by ignoring the presence of the feet and pretend there are no constraints on the joint torques. The torques generated by the balance controller determine the ideal positioning of the center of pressure. This information is fed into an integral controller which maintains the constraints on the center of pressure and keeps the robot standing upright" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002360_s0926-6593(66)80062-0-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002360_s0926-6593(66)80062-0-Figure2-1.png", + "caption": "Fig. 2. ATP and NH.OH-dependent reduction of exogenous NADP+ by Nitrosomonas cell-free extracts. Reaction mixture in a final volume of 3.0 ml contained 0.05 m! cell extracts corre sponding to 500 fIg enzyme protein, 33 mM Tris-H'Cl (pH 9.0). 1.5 mM NH.OH, I,5 rnM MgCl., I mM PMS, 5 mM NaF, and 55 ,LIM mammalian cytochrome c. The test cuvette received, in addition, I mM ATP. After evacuating and gassing the cuvettes with oxygen-free nitrogen (repeated three times), 300 11M NADP+ was tipped into both cuvettes to start the reaction. The following enzymatic trap was used in both cuvettes at the end of the reaction (see arrow): 3 mlVl glutathione (oxidized form) and '30 fJ.g glutathione reductase (type III 'Sigma Chemica! Co.].", + "texts": [ + " I did not effectively reduce the endogenous cytochrome systems but added mammalian cytochrome c was rapidly reduced by succinate. Here again, the addition of 7 mM ATP resulted in the rapid oxidation of the cytochrome c reduced by succinate. These results indicate that in the terminally inhibited Nitrosomonas respiratory chain the oxidation of endogenous or exogenous cytochrome c is energy dependent. Cell-free extracts of Nitrosomonas catalyzed the reduction of added NAD+ or NADP+ in the presence of added ATP. The reducing equivalents were supplied under anaerobic conditions by added cytochrome c reduced by NH20H (Fig. 2), or by Biocliim, Biopbys. Acta, II3 (1966) 216-224 REVERSAL OF ELECTRON TRANSFER IN NITROSOMONAS 2Ig succinate (Fig. 3). The reduction of NAD+ or NADP+ was confirmed by the decrease in absorbance at 340 m;.t upon the addition of the pyruvate-lactate dehydrogenase (EC 1.1.1.27) or the GSSG-glutathione reductase (EC 1.6+2) trapping systems (Fig. 3). Addition of I mM PMS was found quite effective for the reduction of pyri dine nucleotides when glucose and glucose oxidase (EC 1.1.3.4) were used to cause anaerobiosis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003816_j.ymssp.2020.106903-Figure18-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003816_j.ymssp.2020.106903-Figure18-1.png", + "caption": "Fig. 18. Schematic diagram of bearing with six-defects on inner raceway.", + "texts": [ + " If not, the dynamic model of healthy bearing will be used. With the model updated in Section 3.2.1, the vibration responses of bearing with multi-defects on inner raceway and outer raceway can be simulated. Because the methods of modeling, simulation and experiment are similar for multidefects on inner raceway or outer raceway. The vibration responses of bearing with six-defects on inner raceway are analyzed here only. The schematic diagrams of bearings with six-defects on inner raceway are shown in Fig. 18. 1) Six defects of random distribution Parameters of bearing used in this part can be found in Table 3. Six defects are set on the inner raceway, and the angle between the defects and the Z-axis positive direction are 23 , 47 , 79 , 128 , 220 and 281 . The width and depth of the defects are 0.5 mm. The test rig is shown in Fig. 10 and the rotation speed is 600 r/min. The acceleration responses and envelope spectra of bearing in vertical direction are displayed in Fig. 19 and Fig. 20. From the acceleration responses of experiment and simulation, the time interval corresponding to the impacts caused by the same defect is the reciprocal of RPFI" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure3.23-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure3.23-1.png", + "caption": "Fig. 3.23 Functions of foundation force and vibration velocity for two different frequency ratios; a) \u03b7 = 0.7, b) \u03b7 = 1.1", + "texts": [ + "111), two linear equations for the two unknown quantities x0 and v0: x0 cos \u03c9T0 + v0 \u03c9 sin \u03c9T0 = x0 \u2212x0\u03c9 sin \u03c9T0 + v0 cos \u03c9T0 = v0 \u2212 \u0394I m . (3.113) Due to sin \u03c9T0/(1\u2212cos \u03c9T0) = cot (\u03c9T0/2) their solution provides the sought-after initial values: x0 = \u0394I 2m\u03c9 cot ( \u03c9T0 2 ) ; v0 = \u0394I 2m . (3.114) The foundation force function in the interval 0 < t T0 is thus: FB(t) = c \u00b7 x(t) = \u03c9 \u00b7\u0394I 2 ( cot ( \u03c9T0 2 ) cos \u03c9t + sin \u03c9t ) . (3.115) The function of the foundation force and the velocity are shown for some values of \u03c9T0 = \u03c9 \u00b7 2\u03c0/\u03a9 = 2\u03c0/\u03b7 in Fig. 3.23. One can see that there is a kink in the foundation force function at the end point of each interval. This is due to the jump in the velocity of the foundation mass. The foundation force has the amplitude F\u0302B = \u03c9 \u00b7\u0394I 2 \u221a\u221a\u221a\u221a1 + ( cot ( \u03c9T0 2 ))2 = FS\u03c0 \u0394t T 1 |sin (\u03c0/\u03b7)| (3.116) Figure 3.24 shows the amplitude of the foundation force as a function of the frequency ratio, and one can recognize the resonance points at \u03b7 = 1/k for k = 1, 2, 3, 4. (3.115) provides the same time function as the solution (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001971_s00339-018-1737-8-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001971_s00339-018-1737-8-Figure3-1.png", + "caption": "Fig. 3 Thermophysical phenomena at the interface of molten pool in the SLM process", + "texts": [], + "surrounding_texts": [ + "Thermal dynamic behavior during\u00a0selective laser melting of\u00a0K418 superalloy: numerical\u2026\n1 3\nPage 3 of 16 313\npowder particles are assumed to be spatially fixed and the 3D randomly packed powder bed is only solved for the pure thermal problem based on an irradiation of Gaussian laser beam during SLM. Different thermophysical properties and laser absorption of the substrate and powder are not considered, and the wetting behavior of the liquid metal on the solid substrate has not been modeled. Also, the surrounding argon phase and the fluid dynamics induced in this phase have not been modeled.\nA three-dimensional finite difference method (FDM) was developed to investigate the dynamic thermal behavior of the randomly packed K418 powder bed under an irradiation of Gaussian laser beam during SLM. The free surface of the solid\u2013liquid in the molten pool was tracked by the volume of fluid (VOF) method. Generally, the dynamic flow field within the molten pool was governed by Navier\u2013Stokes and energy equations, which is expressed as follows according to [32, 33]:\nMass continuity equation: For incompressible fluid with constant volume, the density\nis constant, the mass continuity equation is\nwhere \u03c1 is the liquid density, u, v, and w represent the components of the velocity vector along X, Y, and Z axes, respectively.\nMomentum conservation equation:\nwhere is the fluid viscosity, P is the hydrodynamic pressure, g is the gravitational acceleration, Tm is the melting temperature of the K418 material, T is the fluid temperature,\n(1) u\nt +\n( u)\nX +\n( v)\nY +\n( w)\nZ = 0,\n(2)\n\ud835\udf15V\u20d7 \ud835\udf15t + ( V\u20d7 \u22c5 \u2207 ) V\u20d7 = \u2212 1 \ud835\udf0c \u2207P + \ud835\udf07\u22072V\u20d7 + g\u20d7 [ 1 \u2212 \ud835\udefd ( T \u2212 Tm )] ,\nis the volumetric thermal expansion coefficient of the K418 material.\nEnergy conservation equation: The conservation of energy satisfies the following\nequation\nwhere k is the thermal conductivity, SU is the energy source term, H is the enthalpy which is considered to be a linear function of temperature T, depending on the solid fraction of the fluid.\nwhere Cp is the specific heat of the liquid metal, Lsl is the solid\u2013liquid phase change latent heat, fs is the phase change fraction. In this work, the latent heat L associated with metal melting is controlled by fs between the liquidus temperature Tl and the solidus temperature Ts. Fs is expressed as\nTo simplify the calculation, the enthalpy is expressed as a function of temperature, which can be calculated according to the following formula\nwhere Hs and Hl are the saturation enthalpy of the solid phase and liquid phase; Cs and Cl are the specific heat capacity of the solid and liquid phase; Ts and Tl are the solidus and liquidus temperature of K418, respectively, \u03b5 is the phase change radius ( = ( Tl \u2212 Ts ) \u22152 ) .\nThe VOF method defines a fluid volume function F, which represents the fraction of the volume fraction of the liquid metal filled in the cell, as shown in Fig.\u00a02. F = 1 indicates that the grid is full of liquid, and F = 0 is completely empty. 0 < F < 1, suggesting that the grid is on a free surface.\nVOF method was applied to reconstruct the evolution of the free surface when particles are penetrated into the molten pool.\n(3) \ud835\udf15H \ud835\udf15t + ( V\u20d7 \u22c5 \u2207 ) H = 1 \ud835\udf0c (\u2207 \u22c5 k\u2207T) + SU,\n(4)H = \u222b CpTdT + Lslfs,\n(5)fs = \u23a7 \u23aa\u23aa\u23a8\u23aa\u23aa\u23a9 0 T \u2a7d Ts T \u2212 Ts Tl \u2212 Ts 1 T \u2a7e Tl Ts \u2a7d T \u2a7d Tl\n(6)T \u2212 Tm = \u23a7 \u23aa\u23aa\u23aa\u23a8\u23aa\u23aa\u23aa\u23a9 H \u2212 Hs Cs \u2212 H \u2a7d Hs H \u2212 CpTm \u2212 Lsl\u22152 Cp + Lsl\u22152 Hs \u2a7d H \u2a7d Hl H \u2212 Hl\nCl\n+ H \u2a7e Hl,", + "Z.\u00a0Chen et al.\n1 3\n313 Page 4 of 16\nThe VOF function was originally derived by Hirt and Nichols [34]. The following equations are satisfied:\n(7) DF\nDt =\nF t +\n(uF)\nx +\n(vF)\ny +\n(wF)\nz = 0.\nThere is a complex energy exchange between the free interface and argon atmosphere, which includes the input of laser energy, the absorption of heat by the powder bed, the heat dissipated by heat convection and heat radiation, and the heat taken away by melt evaporation, as shown in Figs.\u00a03.\nThe thermal boundary condition of the free interface is given by Dai et\u00a0al. [35]:\nwhere A is the laser absorptivity of K418 powder, q(x,y,z,t) is the energy input of the Gauss laser beam, hc is the natural convection heat transfer coefficient, r is the thermal radiation coefficient and s is the Stefan\u2013Boltzmann constant, qev is the heat taken away by melt evaporation, T0 is the ambient temperature.\nIn this work, a rotating volumetric Gaussian distributed laser source with a wavelength of 1064\u00a0nm for ytterbium fiber laser (IPG, YLR-500-WC, Germany) was used in the SLM process,\u00a0Fig.\u00a04 shows the Gaussian distributed laser heat source modele adopted\u00a0in this work. The moving beam described by a Gaussian surface heat equation is given by Yin et\u00a0al. and Gu et\u00a0al. [30, 36, 37]:\n(8)\nT z = Aq(x, y, z, t) \u2212 hc\n( T \u2212 T0 ) \u2212 r s ( T4 \u2212 T4\n0\n) \u2212 qev,\n(9)q(x, y, z) = 2AP\n2 exp\n( \u22122 r2\n2\n) ,", + "Thermal dynamic behavior during\u00a0selective laser melting of\u00a0K418 superalloy: numerical\u2026\n1 3\nPage 5 of 16 313\nwhere P is the laser rated power, is the radius of the Gaussian laser beam, q(r) means the heat flux at a distance r from the center of the circle\nwhere |x| and |y| denote the distance along the X and Y axes, respectively, and v is the laser scanning speed.\nThe absorptivity of the material to the laser beam is relative to the thermal physical parameters of the material, material porosity, the laser wavelength, and laser incident angle. Due to the smaller laser scanning area of 100\u00a0mm \u00d7 100\u00a0mm and the larger focal length (H = 330\u00a0mm) of the F \u2212 \u03b8 lens as seen in Fig.\u00a05, the laser beam can be approximately considered as perpendicularly irradiate on a substrate pass through an F \u2212 \u03b8 lens, i.e., the incident angle is 90\u00b0in simulation. In this work, the absorptivity A of the fiber laser beam by nickel-based alloy powder bed was settled as 0.6 according to Gusarov et\u00a0al. [38].\nThe full heat-flux boundary condition at the free surface is given by\nwhere the Stefan\u2013Boltzmann constant s is 5.67 \u00d7 10\u2212 8\u00a0W/ (m2\u00a0K4).\nDuring the SLM process, at higher energy inputs, some liquid metal evaporates and accumulates above the molten pool, forming a so-called Knudsen layer [39, 40]. The vaporized metal vapor takes away part of the heat and exerts a recoil pressure on the molten pool, affecting the dynamic properties of the molten pool. The heat evaporated by the metal is given by the expression [40]\n(10)r = \u221a (|x| \u2212 |v \u22c5 t|)2 + |y|2,\n(11)qin = Aq(x, y, z, t) \u2212 hc ( T \u2212 T0 ) \u2212 r s ( T4 \u2212 T4\n0\n) ,\nwhere R is the ideal gas constant, P0 is the ambient pressure, M is the molar mass, \u0394H* is the enthalpy of escaping metal vapor, Tlv is the boiling point of the metal melt.\nThe computational region with the temperature between liquid and solidus temperature can be considered as a mushy zone. The volume change associated with phase transitions is ignored, and the drag coefficient is approximated as a function of the local solids fraction and is used to solve the solid\u2013liquid phase change. When the material is in the solid phase, the drag should be effectively infinite. In the mushy zone, the resistance should be an intermediate value. The drag coefficient Fd is expressed as Carman\u2013Kozeny equation, which is derived from Darcy model as given by Voller and Prakash [41]:\nwhere F0 is a constant drag coefficient, fs is the solid fraction in a given cell. The solid free surface of the grid is considered as the wall boundary condition\nIn order to investigate the Marangoni flow caused by the temperature gradient on the free surface in the molten pool, the shear stress should be balanced with the free surface boundary conditions, as given by Cho et\u00a0al. [42]:\nwhere is the dynamic viscosity, \u2215 T is the surface tension gradient. The surface pressure boundary condition is expressed by Masmoudi and Coddet [33]\nwhere PLaser is the laser recoil pressure, v\u20d7n is the normal velocity vector, is the surface tension, and x and y represent the curvature radius along the X and Y directions, respectively.\n(12)qev = 0.82 \u0394H\u2217\n\u221a 2 MRT P0 exp\n\ufffd \u0394H\u2217 \u22c5 T \u2212 Tlv\nRTTlv\n\ufffd ,\n(13)Fd = F0 f 2 s(\n1 \u2212 fs )3 ,\n(14)k T\nn = hc\n( T \u2212 T0 ) .\n(15) \u2212\nu z = T T x\n\u2212 v\nz = T\nT y ,\n(16)\u2212P + 2\ud835\udf07 \ud835\udf15v\u20d7n \ud835\udf15n\n= \u2212PLaser + \ud835\udf0e ( \ud835\udf0cx + \ud835\udf0cx ) ,\n(17)Plaser = 0.54P0 exp ( Llv \u22c5 T \u2212 Tlv\nRTTlv\n) ." + ] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.28-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.28-1.png", + "caption": "Fig. 2.28 Basic structure of a crank press and function of the forming force", + "texts": [ + " N = 2m grid points and the algorithm of the Fast-Fourier transform (FFT) are used in practical calculations. Figure 1.25 shows the curves for the first seven harmonics into which a periodic function f(\u03a9t) was expanded. The higher harmonics (k 8) are decreasing with increasing order and are not shown. The function value f(\u03a9t) at each point in time results from the sum of the harmonics, see (1.113). For a slider-crank mechanism, the Fourier coefficients of the input torque Man needed to overcome the inertia forces (the torque MT = \u2212Man acts on the crankshaft) can be stated analytically, see Fig. 2.28, Fig. 2.48, and (2.279). The following is found with an oscillating mass m, a crank radius l2, a connecting rod length l3, a crank ratio \u03bb = l2/l3 < 1 and an angular velocity \u03a9 of the crankshaft: Man = \u2212MT = \u2212ml22\u03a9 2(D1 sin \u03a9t + D2 sin 2\u03a9t + D3 sin 3\u03a9t + \u00b7 \u00b7 \u00b7 ) (1.120) with the amplitudes of the harmonics D1 = \u03bb 4 + \u03bb3 16 + 15 \u03bb5 512 + \u00b7 \u00b7 \u00b7 D4=\u2212 \u03bb2 4 \u2212 \u03bb4 8 \u2212 \u03bb6 16 \u2212 \u00b7 \u00b7 \u00b7 D2 = \u22121 2 \u2212 \u03bb4 32 \u2212 \u03bb6 32 \u2212 \u00b7 \u00b7 \u00b7 D5=5 \u03bb3 32 + 75 \u03bb5 512 + \u00b7 \u00b7 \u00b7 (1.121) D3 = \u22123 \u03bb 4 \u2212 9 \u03bb3 32 \u2212 81 \u03bb5 512 \u2212 \u00b7 \u00b7 \u00b7 D6=3 \u03bb4 32 + 3 \u03bb6 32 + \u00b7 \u00b7 \u00b7 Non-periodic excitation primarily occurs during start-up, clutch-engaging, and braking processes", + "8 Influence of the Flywheel in a Forming Machine The forming force only acts in a small range of the operating cycle of presses, cutting machines and other forming machines. The drives of forming machines are therefore equipped with flywheels, which release kinetic energy during the forming process and are \u201crecharged\u201d in the remaining time of each cycle. The input torque at the motor and the function of the angular velocity of the motor shaft are to be determined for the steady-state operation of a crank press with a basic structure as shown in Fig. 2.28. To simplify the problem, friction can be neglected. It is assumed that the mass of the connecting rod has already been distributed over the adjacent links. Link lengths of crank and coupler (connecting rod) l2 = 0.22 m, l3 = 1m Gear ratio u = \u03d5\u0307M/\u03d5\u03072 = 70 Mass of the ram m4 = 8000 kg Moment of inertia of the flywheel on motor shaft (2 variants) JS = { 3, 5 kg \u00b7m2, variant A 39, 5 kg \u00b7m2, variant B Moment of inertia of the motor armature JM = 0.5 kg \u00b7m2 Moment of inertia of the gear mechanism (referred to the motor shaft) JG = 0.5 kg \u00b7m2 Breakdown moment MK = 19.5 N \u00b7m Breakdown slippage, see (1.126) sK = 0.12 Synchronous speed of the motor n0 = 1500 rpm (\u03a91 = 157.1 s\u22121) Angular range of the acting forming force \u0394\u03d5 = \u03c0/12=\u030215\u25e6 Forming force (at 2k\u03c0 \u2212\u0394\u03d5 \u03d52 2k\u03c0), with k = . . . , \u22122, \u22121, 0, 1, 2, . . . (Fig. 2.28) F0 = 3.2 MN 136 2 Dynamics of Rigid Machines 1.Using the approximations given in Table 2.1, analytical solutions for 1.1the moment of inertia J(\u03d52) referred to the crank angle 1.2the crank moment MSt = MK (\u03d5\u03072 = 0) required for \u03d5\u03072 \u2248 0 and the forming work W to be performed per cycle 1.3the mean moment MStm in the shaft between gear mechanism and crank for \u03d5\u03072 \u2248 0 2.The functions (for steady-state operation) of 2.1the input torque MM of the motor 2.2the angular velocity \u03d5\u0307M of the motor shaft for both flywheel variants using the SimulationX R\u00a9 [34] program S2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001623_tro.2012.2226382-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001623_tro.2012.2226382-Figure4-1.png", + "caption": "Fig. 4. (a) Three sets of variables (m, qc ): (\u22120.13, \u221255\u25e6), (\u22120.23, \u2212109.7\u25e6), and (\u22120.18, \u2212119.7\u25e6) generate three bending configurations with ascending curvature through the actuation of odd joint axes in one direction. (b) Two bending configurations corresponding to the actuation of even joint angles in opposite directions, parameterized as +ve: (0.31, 112.9\u25e6), \u2212ve: (\u22120.11, \u221234.7\u25e6). (c) Motion planes spanned by even and odd joint angle actuation are perpendicular to each other. Their intersection is aligned with the robot axis in the straight configuration q = 0. Four primitive bending directions are indicated. (d) Four primitive bending configurations with (m, qc ) = (0, \u00b15\u25e6) are represented in solid color. The other four configurations displayed in semitransparent color are generated between the four primitive configurations by assigning (\u03b1, \u03b2) = (0.25, 3.35).", + "texts": [ + " We consider that only a certain number of distal joints L are directly manipulated by the user, while the proximal joint values are determined through the shape conformance algorithm introduced in Section III-A as q\u0303 L\u2212 L +1...L . The optimal configuration of the distal joints is instead denoted by \u0394q := [\u0394q1 , . . . ,\u0394q L ]T \u2208 2 L \u00d71 , where \u0394qi = [\u0394q2i\u22121 ,\u0394q2i ]T and L \u2265 L. As shown in Fig. 2, each universal joint comprises two DoFs with odd and even joint indices. Since the corresponding joint axes are parallel to each other when the robot is in a straight configuration, actuation of either odd or even joint angles along the robot structure yields a planar motion, as shown in Fig. 4(a) and (b). These two motion planes are orthogonal to each other, as shown in Fig. 4(c). For panoramic exploration, the linear combination of such independent odd- and even-joint angles actuation can generate a wide range of configurations in different bending directions, as shown in Fig. 4(d). Each of these configurations can be represented by a linear gradient. The main advantage of this model is that only two parameters, namely the slope m and the intercept of angular value qc , are required to control the amount of bending. Therefore, to conform to different parts of the navigation channel, the joint values \u0394q are modeled and adjusted by the two variables (m, qc) according to \u0394qe i (m, qc) = { m(i \u2212 2 L) + qc , if i is even 0, otherwise (10) where \u0394qe = [\u0394qe 1 ,\u0394qe 2 , . . . ,\u0394qe 2 L ]T represents the bending configuration applied to the joint angles with even indices and contains all zeros for the joint angles with odd indices. Assuming the robot is in a straight configuration when q\u0303 = 0, we can derive the end-effector position lxeff \u2208 3 relative to the link frame {l = L \u2212 L} given by \u0394qe as follows: [ lxeff , 1 ]T = l LT (\u0394qe(m, qc)) [ 0, 1 ]T . (11) The corresponding displacement of the end-effector can then be expressed as follows: deff = lxeff (\u0394qe(m, qc)) \u2212 lxeff (\u0394qe(0, 0)) . (12) With m = 0 and a small value \u00b1\u03b5 assigned to qc , we have de\u00b1 eff = deff (\u0394qe(0, qc) |qc =\u00b1\u03b5 ) . (13) Fig. 4(b) shows that the two resultant configurations are bending in opposite directions. With the condition of i being odd applied to (10)\u2013(12), this odd-index bending effect spans perpendicularly to the one given by even angles, as shown in Fig. 4(a). In total, four basic displacements {de+ eff ,do+ eff ,de\u2212 eff ,do\u2212 eff } are defined to determine the optimal amount of bending in different quadrants [see Fig. 4(d)], thus allowing panoramic exploration by manipulating the camera at the robot tip. 2) Constrained Optimization of Robot Configuration: In addition to panoramic exploration, robot bending must be confined within the anatomical channel to avoid discomfort [30], [31] to the patient, especially during unsedated endoscopy. The constraint pathway closely fitting with the anatomical structure can be implemented as a safety margin to optimize the bending angles, thus providing diversified viewing directions while ensuring safe navigation", + " By averaging two consecutive optimal bending configurations \u0394 q(r,\u03d1j ) and \u0394 q(r,\u03d1j + 1 ) , we obtain \u0394q\u0304(r,\u03c6j ) = 1 2 ( \u0394 q(r,\u03d1j ) + \u0394 q(r,\u03d1j + 1 ) ) , j = 1, . . . , n s.t. \u03d1 n +1 := \u03d11 and \u03c6j := 1 2 (\u03d1j + \u03d1j+1) . (18) Finally, by introducing two parameters (\u03b1, \u03b2) to scale every value of \u0394q\u0304(r,\u03c6j ) , we can devise a new bending configuration \u0394q(r,\u03c6j ) as \u0394q (r,\u03c6j ) i = [ (\u03b2 \u2212 \u03b1) i 2 L + \u03b1 ] \u0394q\u0304 (r,\u03c6j ) i i = 1, . . . , 2 L, \u03b1 > 0 and \u03b2 > 0. (19) By restricting \u03b1 and \u03b2 to be positive, we ensure that the new configuration will bend in a consistent direction between the two consecutive control bending configurations. Fig. 4(d) shows four intermediate bending configurations at polar angles \u03c6j of 45\u25e6, 135\u25e6, 225\u25e6, and 315\u25e6. The optimal parameters \u03b1 and \u03b2 can be found by minimizing the same cost function as in (14) and considering the deviation constraint (17) but performing the search in a different domain ( \u03b1, \u03b2 ) = arg min \u03b1,\u03b2>0 { lzeff ( \u0394q(r,\u03c6j )(\u03b1, \u03b2) )} s.t. Dk,\u0394k i ( q\u0303l+1...l+i + \u0394q(r,\u03c6j ) 1...i (\u03b1, \u03b2) ) \u2264 bi, i = 1, . . . , L (20) where the same optimization solver used to find (m, qc) is adopted. With a new bending configuration \u0394 q(r,\u03c6j )( \u03b1, \u03b2 ) optimized as in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002386_s11665-017-2710-y-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002386_s11665-017-2710-y-Figure1-1.png", + "caption": "Fig. 1 Schematic diagram of the tensile bars printed using direct metal laser sintering. The orthogonal coordinate system that will be used in this paper are indicated", + "texts": [ + " Samples were printed at a laser power of 340 W, scanning speed of 1.25 m/s, a hatch spacing (the distance between two adjacent scan vectors) of 1.29 10 4 m (120 lm) and a layer thickness of 69 10 5 m (60 lm). Layers were scanned using a zigzag-scanning strategy and rotated 90o between each layer. This alternating scanning strategy was used to obtain highly dense part. The Ti-6Al-4V parts were printed directly in the shape of tensile testing bars based on ASTM standard as schematically shown in Fig. 1 (the orthogonal coordinate will be further used in this work). The as-printed samples (designated as AP) were degreased in acetone before annealing treatments in a vacuum furnace under three different temperatures: 700, 750 and 799 C for 14,400 s (4 h), and followed by air-cooling. The post-annealing treatment procedures and sample designations are listed in Table 1. The AP and annealed samples were cut using an abrasive sectioning machine with SiC blade into cubes with dimension of 0.01 m9 0.01 m9 0.008 m, and mounted by epoxy resin. The mounted specimens were sequentially ground up to 1200-grit silicon carbide paper, followed by final finish with colloidal silica suspension on ChemoMet polishing cloth to achieve a mirror surface. To reveal the microstructure, the polished samples were etched for 30 s using Kroll s reagent (0.002 L HF, 0.005 L HNO3 and 0.1 L H2O). Because of the layer-wise building process, the building planes (XZ and YZ planes in Fig. 1) and deposition plane (XY plane in Fig. 1) are considered during metallographic investigation. The hot forged and mill-annealed Ti-6Al-4V (Grade 5) alloy with equiaxed microstructure will be addressed as the reference material in the following discussions. A Nikon optical microscope (Nikon Instrument Inc.) was used for examination of the microstructure. A JEOL JSM7000F scanning electron microscopy (SEM) was used for high magnification characterization of the microstructure. Size distribution of the pre-alloyed powder particles and surface porosity of the bulk samples were analyzed using ImageJ. Crystallography and phase analysis were conducted on a PANanalytical Empyrean 2 x-ray diffractometer (XRD) with Cu-Ka radiation at 45 keV and 40 mA. The XRD measurements were taken over a range of 2h angle equals 20 to 80 under a step size of 0.05. Phase identifications and Rietveld refinement were carried out using HighScore Plus software (Ref 17, 18). Uniaxial tensile tests were performed on the AP and 799HT samples along X-axis (as indicated in Fig. 1) to determine the stress-strain behavior of the materials. The yield strength and Young s modulus were determined based on ASTM A1011 and ASTM E111, respectively. Four tensile tests were conducted for each condition to determine the mechanical properties. The Vickers hardness measurements were conducted on the as-polished sample surface, and measured with a microhardness tester at a force of 200 gf. The hardness measurements were duplicated for ten measurements on each sample. A Cu wire was attached to the back of the tested sample (0", + " It possesses relatively smooth topography compared to the morphology of AP, and the equiaxed dimples feature indicates ductile failure. The highlighted region in Fig. 10(a) is enlarged in Fig. 10(b) indicates a localized pore-induced fracture. In Fig. 10(b), the hollow arrow refers to the overload direction during tensile test, and the short arrows point out the scanning contours during DMLS. The shell-like crater shown in Fig. 9(c) and (d) is absent in the 799HT parts. Since the uniaxial tensile tests were conducted along X-axis in Fig. 1, so the shell-like features are on the building plane and are unlikely caused by layered sintering. Noticed the acicular features in the craters, they may be caused by pulling out the loosely bound powder particles during tensile testing. The dimension of the shell-like craters is comparable to the starting Ti-6Al-4V particle size of around 2.79 10 5 m (27 lm). After post- annealing treatment, this feature is absent probably because the loosely bound particles were re-sintered by this treatment" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000155_j.cma.2004.09.006-Figure20-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000155_j.cma.2004.09.006-Figure20-1.png", + "caption": "Fig. 20. Illustration of meshing of: (a) the shaper and the face-gear and (b) the worm and the face-gear, wherein the worm diameter is chosen lesser than the shaper diameter.", + "texts": [ + " The maximal magnitudes of ws must be greater than 2p/Ns, whereNs is the number of teeth of the shaper, and 2p/Ns is the angle of rotation of the shaper for one tooth of the shaper. In the case of a large magnitude of the helix angle of the shaper, the permissible area of ws may become less than 2p/Ns, and the angle of rotation of the worm will be less than 2p/Nw, where Nw is the number of worm threads. This means that such a worm cannot be applied for generation of the face-gear. Decrease of the helix angle of the worm, and decrease of the diameter of the generating worm enable to avoid the worm undercutting and apply the worm for generation of the face-gear. Fig. 20(b) shows a grinding worm of special shape wherein the diameter of the worm is smaller than the diameter of the shaper (Fig. 20(a)) for the purpose of avoidance of singularities. Undercutting and contact lines are represented on the plane of parameters of the shaper in Fig. 21 for this case, which shows the existence of an envelope E to the contact lines. Graph of Fig. 22 illustrates the permissible helix angle of the shaper as a function of the ratio of radii rpw/rps of the pitch cylinders of the worm and the shaper. The design data are shown in Table 1. The increased permissible area corresponds to the modification of the geometry of the shaper based on application of parabolic rack-cutters (a parabola coefficient as = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure8.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure8.4-1.png", + "caption": "Figure 8.4.1(a) shows the tyre normal (Z) and lateral (Y) force components on the two wheels of an independent-type axle. This is after removal of forces that support and accelerate the unsprung mass, so it is for the forces supporting and accelerating the sprung mass (body) only. The coordinate system used here is the standard ISO one, with X forward, Y to the left, and Z upwards. The tyre forces are shown in vehicle coordinates. The tyre forces are usually expressed in road normal and lateral coordinates. The road surface is in general rotated by the roll angle, and also by the two road camber angles. The vehicle-axis components shown are easily derived. Figure 8.4.1(b) shows these forces resolved instead along (F2) and perpendicular (F1) to the swing arms. The F1 parts, perpendicular to the swing arms, must be supported by the springs (and dampers in unsteady state). The F2 parts act through the links, and, as may be seen in the figure, will exert no moment about the intersection point of the swing arm lines. This conclusion may be drawn, for a double-wishbone suspension for example, on the basis that the swing arm is the intersection of the lines of the links, and the links carry link-aligned forces only, that is, that the joints at the ends of the links are free of stiffness moments (e.g. rubber bushes) and free of friction moments (e.g. rotating metal sleeve bushes). This is a standard principle of the analysis of pin-jointed structures. These are evidently engineering approximations, which could be improved upon in a more detailed analysis, including bush friction or stiffness moments. The lateral position of the GRC is B, positive to the left.", + "texts": [ + " The problem is the complication introduced by the track change of an independent suspension in roll. The swing arm defines the motion of each wheel relative to the body, sowith some approximations it is reasonable to take the intersection point of the swing arms (i.e. the GRC), as the putative KRC, and then neglect any a lateral offset (i.e. again to take the height of the KRC as being the same as the height of the GRC, in vehicle coordinates). The height of the FRC controls two important factors: Figure 8.4.1(c) shows the link force alone resolved back into normal and lateral components. The link jacking force, which is the total vertical force in the links, relieves the springs of load, causing jacking of the body. This link jacking force is FLJ \u00bc F2;R sin uSA;R F2;L sin uSA;L \u00f08:4:1\u00de 162 Suspension Geometry and Computation The lateral transfer of normal force through the links (colloquially, the link load transfer) is half of the difference between the upwardly-directed link normal forces: FLT \u00bc 1 2 \u00f0F2;R sin uSA;R \u00feF2;L sin uSA;L\u00de \u00f08:4:2\u00de The link-only upward normal forces for each side are then FZ2;R \u00bc 1 2 FLJ \u00feFLT FZ2;L \u00bc 1 2 FLJ FLT \u00f08:4:3\u00de Figure 8.4.1(d) shows the resultant of the link forces, combined vectorially at their intersection point (nominally the GRC). Considering the line of action of the resultant, where this crosses the vehicle centreline the resultant can be resolved into vertical (jacking) and lateral components, FLJ and FY, respectively. This point on the centreline is the one usually accepted as the FRC. The angle of the total resultant link force to the horizontal is u \u00bc atan FLJ FY \u00f08:4:4\u00de so the height of the FRC is HFRC \u00bc HGRC B FLJ FY \u00f08:4:5\u00de In Figure 8.4.1(d), B is positive, so HFRC is less than HGRC. The roll moment exerted by the lateral link force about a central axis at ground level is MFYL \u00bc FYHFRC \u00bc FLTT \u00f08:4:6\u00de so the FRC height is HFRC \u00bc MFYL FY \u00bc FLTT FY \u00f08:4:7\u00de The load transfer factor fLT is defined as fLT \u00bc FLT FY \u00bc HFRC T \u00f08:4:8\u00de so HFRC \u00bc fLTT FLT \u00bc fLTFY \u00f08:4:9\u00de This is sufficient not only to illustrate the close relationship between the FRC and the GRC, but also to illustrate that they are not identical because of the necessary assumptions and approximations, and the lateral offset", + " The actual distribution of forces left and right depends on the tyre characteristics, so only the approximate position of the FRC can be calculated on the basis of the links alone, the height difference from the GRC depending on the inclination of the link force resultant. The anti-roll coefficient JAR is defined as JAR \u00bc HFRC HB \u00f08:4:10\u00de and is usually expressed as a percentage, JARpc\u00bc JAR 100%. The GRC has already been mentioned several times. Its basic definition is simply as follows: The geometric roll centre is a point in the transverse vertical plane of the suspension, being the intersection point of the two swing arm lines, one from each side. Therefore, once the geometric constructions for the swing arms are understood, theGRC follows easily, as in Figure 8.4.1(b). Difficulties arise with the above simple definition when the swing arms are parallel. This divides into two cases. The first case is as for simple unrolled trailing arms \u2013 the swing arms may be overlaid in the ground surface, with the intersection point anywhere along the swing arm lines. The second case arises, for example with simple trailing arms in the rolled position, when the swing arms are parallel and do not intersect at any point. This may occur with or without infinitely long swing arms, which is not important in this context" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000406_ma1003979-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000406_ma1003979-Figure7-1.png", + "caption": "Figure 7. Film with a curvature of 1/r and a thickness of t. The neutral plane with zero strain corresponds to z = zn.", + "texts": [ + " Their glassy films have a finite gradient of thermal expansion coefficient in the thickness direction but without pronounced coupling of local nematic order with macroscopic shape. In contrast, the temperature change considerably influences the nematic order in the present elastomeric films with a Young\u2019s modulus on the order of 104 Pa. The strong coupling between nematic order and strain in LCEs boosts a change in the strain gradient driven by temperature variation. Correlation of the T Dependencies of Curvature in HNEs and Uniaxial Strain in PNEs and VNEs. In the case of elastically isotropicmaterials with sufficiently small thickness (t, r) (Figure 7), the strain \u03b5x is expressed as \u03b5x\u00f0z\u00de \u00bc z - zn r \u00fe zn z - zn r \u00f03\u00de where zn is the position of a neutral plane with \u03b5x = 0. Equation 3 assumes that \u03b5x varies linearly with the distance from the neutral plane. Equation 3 was employed to analyze the bending deformation of LCEs induced by light irradiation20 and temperature gradient.12 The following simple expression for the curvature is obtained from eq 3 t r \u00bc \u03b5x\u00f0t\u00de - \u03b5x\u00f00\u00de \u00bc \u0394\u03b5 \u00f04\u00de Equation 4 directly relates the curvature (1/r) with the gradient of strain (\u0394\u03b5/t), and it explains that the curvature increases as the film is thinner if \u0394\u03b5 is the same" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000566_tro.2006.889485-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000566_tro.2006.889485-Figure1-1.png", + "caption": "Fig. 1. Illustration of an untethered swimming microrobot.", + "texts": [ + " Shoham are with the Department of Mechanical Engineering, Technion\u2014Israel Institute of Technology, 32000 Haifa, Israel (e-mail: mekosha@tx.technion.ac.il; shoham@tx.technion.ac.il). M. Zaaroor is with the Neurosurgery Department, Rambam Medical Center, 31096 Haifa, Israel (e-mail: m_zaaroor@rambam.health.gov.il). Digital Object Identifier 10.1109/TRO.2006.889485 large effect on such a microrobot, and the flow must be analyzed by the Stokes equation [14]. In this paper, a novel method of microrobot propulsion is described that involves tails made of piezoelectric actuators (see Fig. 1), where the propulsion is achieved by creating a traveling wave in the tail. In contrast to the situation with macro-size swimmers, standing waves cannot be used to advance a microrobot in Stokes flow [14]. The combined fluidic-elastic problem was modeled analytically and the model used to optimize the propelling microactuator. This theoretical model was verified experimentally using an upscaled swimming tail. As shown in Fig. 1, the suggested microrobot is comprised of a main body, which encompasses the payload, and two tails. Each tail is divided into three segments of piezoelectric material that are excited at a different phase and amplitude. Thus, traveling waves are created that mediate the propulsion motion. In order to analyze the motion created by a piezoelectric beam in a viscous liquid, one has to decompose the coupled electric-elastic-fluidic domains. The electric and elastic decoupling can be solved using Euler\u2013Bernoulli assumptions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003040_j.optlastec.2019.105678-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003040_j.optlastec.2019.105678-Figure2-1.png", + "caption": "Fig. 2. Raster and orthogonal scanning.", + "texts": [ + " The substrate used in experiment is a 45# steel thin plate, whose composition meet international standard ISO 683-1 C45E4. Its major compositions include (wt.%): C (0.42\u20130.48%), Si (0.15\u20130.35%), Mn (0.60\u20130.90%), P (\u22640.030%), S (\u22640.035%), Cu (\u22640.30%), Ni (\u22640.20%), Cr (\u22640.20%), Fe (Bal.). The machine parameters used within testing were maintained throughout all builds: laser power 150 W, scanning speed 800 mm/s, layer thickness 30 \u03bcm, hatch spacing 80 \u03bcm, the raster and orthogonal scanning strategy as shown in Fig. 2 was adopt. And the chamber oxygen content was controlled below 100 ppm. In order to study the influence of residual powder spatters on the mechanical properties of the manufactured parts, the virgin powders and the gradually contaminated powders were used to fabricate small squares and elongated samples. The CoCrW alloy powders were used for I-VI cycles. During each cycle, the power of the gas circulating system (Fig. 1a) in the DiMetal-100 SLM equipment was reduced to 50% of the normal level. In this way, the light smoke that arises from the laser molten pool will be blown away without affecting the optical lens, but part of the large spatter will still fall within the non-radiated powder bed region" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure4.51-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure4.51-1.png", + "caption": "Fig. 4.51 Calculation model of a spur gear mechanism; a) System schematic, b) Side view, c) Free-body diagram", + "texts": [ + " In a helical gear mechanism, the variations are small as compared to spur gear mechanisms, which means that a few Fourier coefficients suffice to describe them. The meshing frequency is the product of the angular velocity and the number of teeth. The meshing frequency occurs at the contact point of two gear wheels (shaft 304 4 Torsional Oscillators and Longitudinal Oscillators 1: angular velocity \u03a91, number of teeth z1 and shaft 2: angular velocity \u03a92, number of teeth z2) fz = zf = z1\u03a91 2\u03c0 = z2\u03a92 2\u03c0 . (4.237) Note the standard work by Linke [22] for all problems relating to gear mechanisms. In the simplest case of a one-step spur gear mechanism (Fig. 4.51), the angles of rotation \u03d51 and \u03d54 of the two rotating masses, the angles \u03d52 of the pinion and \u03d53 of the gear as well as the torsional stiffnesses cT1 and cT3 between the disks are taken into account when modeling. The gearing errors that are modeled as motion excitation s(t) and the gearing stiffness c(t) are periodically variable. The equations of motion for the calculation model result from the equilibrium of moments on each part of the free-body diagram, see Fig. 4.51 J1\u03d5\u03081 + cT1(\u03d51 \u2212 \u03d52) = M1(t) (4.238) J2\u03d5\u03082 \u2212 cT1(\u03d51 \u2212 \u03d52) + r2c(t)[r2\u03d52 + r3\u03d53 \u2212 s(t)] = 0 (4.239) J3\u03d5\u03083 + r3c(t)[r2\u03d52 + r3\u03d53 \u2212 s(t)] + cT2(\u03d53 \u2212 \u03d54) = 0 (4.240) J4\u03d5\u03084 \u2212 cT2(\u03d53 \u2212 \u03d54) = M4(t). (4.241) 4.5 Parameter-Excited Vibrations 305 (4.238) to (4.241) describe a forced vibration as a result of parametric excitation by c(t) and the motion excitation due to s(t). Such equations cannot be solved analytically in closed form. Many companies provide software for this. The torsional vibration system shown in Fig. 4.51 will be analyzed for given parameter values here. It will also be shown what major influence the selected calculation model has. The following parameter values for the SimulationX R\u00a9 models shown in Fig. 4.52 are given: Rotating masses J1 = 0.2 kg \u00b7m2, J2 = 0.2 kg \u00b7m2, J3 = 1kg \u00b7m2, J4 = 3kg \u00b7m2, Tooth numbers z1 = 23, z2 = 57, module m = 3, contact ratio = 2.3; Mean tooth stiffness cm = 49 \u00b7 106 N/m, Damper constant of the gearing b = 2000N \u00b7 s/m; Torsional spring constants cT1 = 5 \u00b7 105 N \u00b7m; cT2 = 3 \u00b7 105 N \u00b7m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003542_1.4034304-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003542_1.4034304-Figure1-1.png", + "caption": "Fig. 1 Sample refined mesh: (a) isometric view and (b) top view", + "texts": [ + " First, a coarse mesh is generated within Patran (by MSC Software). Then, during simulation, the mesh is refined by CUBES VR according to user inputs. Past simulations have shown that thermal behavior converges with a mesh having one element per laser radius. However, to improve the resolution in the melt-pool region, the adaptive subroutine controls are set to yield a mesh with four elements per laser radius. A sample refined mesh for deposition of Inconel VR 718 under varying laser power and a fixed laser scan speed (see Sec. 3.3) is displayed in Fig. 1. 2.2.2 Melt Pool Convection. In the lumped model, the heat conduction into the substrate at the liquid\u2013solid boundary of the melt pool is modeled as a convection with a coefficient as in Eq. (12). The finite-element model is used to compute the convection as by equating the conductive heat loss from the FE model to the convective heat loss of the lumped model\u00f0 As q nda \u00bc Asas\u00f0Tpool Tm\u00de (19) where As denotes the surface of the liquid\u2013solid boundary, n denotes the normal direction vector to As, and Tpool is the mean 021013-4 / Vol" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000056_s0263574707003530-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000056_s0263574707003530-Figure1-1.png", + "caption": "Fig. 1. 3RPR-platform.", + "texts": [ + " From the algebraic point of view, we have then a system of polynomial equations I = (g1, . . . , gn), which corresponds to an algebraic variety V = V (g1, . . . , gn). The algebraic varieties are the constraint surfaces. With this interpretation it is possible to use all the progress, which was made in recent years, in solving systems of polynomial equations (see Dickenstein and Emiris2). We show this idea with a simple example (see Husty9): consider a planar parallel manipulator consisting of a base and a platform linked by three RPR-legs (Fig. 1). In the direct kinematics, we are given the design of the manipulator, i.e., the design of base and platform (the coordinates B1, C1, C2, a1, a2, b1, b2, c1, c2 and the lengths of the legs r1, r2, r3). The task is to find all assembly modes. Geometric preprocessing transforms the direct kinematics problem now into the following task: given a triangle and three circles, place the triangle such that its three vertices are on the circles (vertex A on circle k1, etc., Fig. 2). The circles constitute now the mechanical constraints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure11.13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure11.13-1.png", + "caption": "FIGURE 11.13. An ideal model of a 2R planar manipulator.", + "texts": [ + " Assume that there is viscous friction in the joint where an ideal motor can apply the torque Q to move the arm. The rotor of an ideal motor has no moment of inertia by assumption. 11. Motion Dynamics 489 y Q The generalized force M is the contribution of the motor torque Q and the viscous friction torque - cO. Hence , the equation of motion of the ma nipulator is Q = Ie + cO + mgl sin O. (11.318) Example 276 The ideal 2R planar manipulator dynamics. An ideal model of a 2R planar manipulator is illustrated in Figure 11.13. It is called ideal because we assumed that the links are massless and there is no friction . Th e masses ml and m2 are the mass of the second motor 490 11. Motion Dynamics (11.319) to run the second link and the load at the endpoint. We take the absolute angle 0] and the relati ve angle O2 as the generalized coordina tes to express the configuration of the manipulator. Th e global posit ion of m] and m 2 are [ ~: ] = [ ~: ~~: ~~ ] [ X2 ] = [!r COSO] +l2cos (O] +(2) ] Y2 l] sinO] + l2sin (0] + (2) and therefore, the global velocity of the m asses are (11" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.42-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.42-1.png", + "caption": "Fig. 2.42 Examples for methods of mass balancing on rotors; a) Cutting from fan blade, b) Inserting lead wire into groove, c) Screwing in bolts of various lengths, d) Breaking off segments inside, e) Milling off molded-on studs from front end, f) Breaking off segments from specially designed outside disks", + "texts": [ + "41 Distribution of the bending moment for various selected balancing planes; a) Rotor without balancing; b) Balancing planes at the front surfaces of the rotor; c) Balancing planes inside of the rotor ods in three or more planes were developed that require a considerable amount of extra computational and experimental effort, as compared to the balancing of rigid rotors. The following aspects should be taken into account when selecting the balancing planes: 1. The balancing planes should be as far away from each other as possible. 2. When balancing assembled rotors with balancing planes on different compo- nents, it should be ensured by appropriate means that the unique relative positioning is ensured (positive-locking fastening of the parts against each other, e. g. using pins). 3. Balancing should not impair the strength of the component. Figure 2.42 gives an overview of the adjustment options when balancing: cutting off, grinding or milling off material (Fig. 2.42a, e). Breaking off segments from disks provided for balancing inside (Fig. 2.42d) or outside (Fig. 2.42f) are examples of subtractive adjustment. Dosing the adjustment unbalance by screws of various lengths or diameters (Fig. 2.42c) or by inserting lead wire into rotating grooves (Fig. 2.42b) are some of the additive methods. The technological conditions of mass production should be taken into account when selecting a method. It may also be useful to weld or solder on strips of sheet metal. The designer has to specify the balancing planes from the outset and cannot leave the selection of the balancing method to chance. In practice, alancing is performed using balancing machines with which the position and magnitude of the unbalance is determined from the bearing responses of the rotor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.48-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.48-1.png", + "caption": "Fig. 2.48 Slider-crank mechanism without offset", + "texts": [ + " Figure 1.25 shows the curves for the first seven harmonics into which a periodic function f(\u03a9t) was expanded. The higher harmonics (k 8) are decreasing with increasing order and are not shown. The function value f(\u03a9t) at each point in time results from the sum of the harmonics, see (1.113). For a slider-crank mechanism, the Fourier coefficients of the input torque Man needed to overcome the inertia forces (the torque MT = \u2212Man acts on the crankshaft) can be stated analytically, see Fig. 2.28, Fig. 2.48, and (2.279). The following is found with an oscillating mass m, a crank radius l2, a connecting rod length l3, a crank ratio \u03bb = l2/l3 < 1 and an angular velocity \u03a9 of the crankshaft: Man = \u2212MT = \u2212ml22\u03a9 2(D1 sin \u03a9t + D2 sin 2\u03a9t + D3 sin 3\u03a9t + \u00b7 \u00b7 \u00b7 ) (1.120) with the amplitudes of the harmonics D1 = \u03bb 4 + \u03bb3 16 + 15 \u03bb5 512 + \u00b7 \u00b7 \u00b7 D4=\u2212 \u03bb2 4 \u2212 \u03bb4 8 \u2212 \u03bb6 16 \u2212 \u00b7 \u00b7 \u00b7 D2 = \u22121 2 \u2212 \u03bb4 32 \u2212 \u03bb6 32 \u2212 \u00b7 \u00b7 \u00b7 D5=5 \u03bb3 32 + 75 \u03bb5 512 + \u00b7 \u00b7 \u00b7 (1.121) D3 = \u22123 \u03bb 4 \u2212 9 \u03bb3 32 \u2212 81 \u03bb5 512 \u2212 \u00b7 \u00b7 \u00b7 D6=3 \u03bb4 32 + 3 \u03bb6 32 + \u00b7 \u00b7 \u00b7 Non-periodic excitation primarily occurs during start-up, clutch-engaging, and braking processes", + " Thus there are four transcendental equations for each order k for calculating the crank angles \u03b3j and the distances zj (these are 2J \u2212 1 unknown quantities for J mechanisms) that are required for complete mass balancing. The inertia forces that occur in mechanisms with a varying transmission ratio can be the cause of frame vibrations. Particularly dangerous are those components of the excitation spectrum, the frequency of which matches the natural frequency of the frame. The additional balancing mass ma in the form of an annulus segment of constant thickness, to be attached to the driving crank of the compressor (slider-crank mechanism without offset, see Fig. 2.48), is to be sized in such a way that the first harmonic of the resultant frame force component Fx is completely balanced at constant input angular speed. l2 = 40 mm crank length l3 = 750 mm coupler length \u03beS2 = 12 mm distance of the center of gravity of the crank from O 168 2 Dynamics of Rigid Machines JS2 = 6, 1 \u00b7 10\u22123 kg \u00b7m2 moment of inertia referred to the axis through the center of gravity of the crank m2 = 4.8 kg crank mass m4 = 14 kg piston mass r = 20 mm inner radius of the balancing mass Rmax = 140 mm maximum outer radius of the balancing mass (installation space", + "26a, the first-order position functions can be taken directly from Table 2.1; the prerequisite stated there regarding the crank ratio \u03bb is satisfied. \u03bb = l2/l3 = 0, 04 m/0, 75 m = 0, 0533\u0304 1 is obtained for the given parameter values. Using the functions from Table 2.1, and after another differentiation with respect to \u03d52, one obtains: x\u2032\u2032 S2 = \u2212\u03beS2 \u00b7 cos \u03d52; y\u2032\u2032 S2 = \u2212\u03beS2 \u00b7 sin \u03d52 x\u2032\u2032 S4 = \u2212l2 \u00b7 (cos \u03d52 + \u03bb cos 2\u03d52) (2.349) The balancing mass has the following center-of-gravity coordinates in the fixed system, see Fig. 2.48: xSa = ra \u00b7 cos (\u03d52 + \u03c0) = \u2212ra \u00b7 cos \u03d52 ySa = ra \u00b7 sin (\u03d52 + \u03c0) = \u2212ra \u00b7 sin \u03d52 (2.350) The derivatives with respect to the crank angle are x\u2032 Sa = ra \u00b7 sin \u03d52; x\u2032\u2032 Sa = ra \u00b7 cos \u03d52 y\u2032 Sa = \u2212ra \u00b7 cos \u03d52; y\u2032\u2032 Sa = ra \u00b7 sin \u03d52 (2.351) If one inserts the expressions from (2.349) and (2.351) into the relationship (2.348) for the forces, the following is obtained: Fx = [( m2\u03beS2 \u2212mara + m4l2 ) \u00b7 sin \u03d52 + m4l2 \u03bb 2 \u00b7 sin 2\u03d52 ] \u00b7 \u03d5\u03082 + [( m2\u03beS2 \u2212mara + m4l2 ) \u00b7 cos \u03d52 + m4l2\u03bb \u00b7 cos 2\u03d52 ] \u00b7 \u03d5\u03072 2 (2.352) Fy = \u2212 ( m2\u03beS2 \u2212mara ) \u00b7 (\u03d5\u03082 cos \u03d52 \u2212 \u03d5\u03072 2 sin \u03d52 ) The equation for the force Fx is an approximation because due to \u03bb 1, the terms that contain higher powers of \u03bb have already been neglected in the equations for x\u2032 S4 , x\u2032\u2032 S4 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001328_j.rcim.2015.06.003-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001328_j.rcim.2015.06.003-Figure1-1.png", + "caption": "Fig. 1. The 3D CompuGauge measurement system and attachment (tool) [75].", + "texts": [ + " The MH6 is a similar 6DOF serial robot that is used for alike applications as the HP20D [48]. We made use of the MH6 manipulator and DX100 controller to validate our 1DCAL method [48,35]. Specifications of the MH6 robot can be found in [48,35]. Its DH Table is shown in Table 2. For the purpose of measuring the Cartesian coordinates of the calibration points for our 3DCAL system, we made use of 3D CompuGauge [75]. CompuGauge is a system that allows 3D measurement and performance testing of robot positioning. It is composed of hardware and software. As shown in Fig. 1, the hardware consists of two triangulation beams. The \u201cmeasurement attachment\u201d (tool zoomed-in in Fig. 1) is mounted on the robot. The four \u201cmeasurement cables\u201d originating from both triangulation beams are connected to the tool. High resolution, low inertia optical encoders are used to constantly measure the extension of the cables. The data is interpreted by the software to deduce an accurate measurement of the test point with respect to the user-defined reference frame [75]. Note that only three out of the four cables that originate from the fixed triangulation beams are utilized to calculate the coordinates of a given test point", + " Hence, estimating that particular error parameter will only translate and/or rotate all calibration points while the Euclidean distances among those observations remain unchanged. Since that will bring about undesired redundancy, in our approach we shall not perturb the error parameter associated with the first joint angle \u03b81 during calibration as well. Finally, another aspect of kinematic calibration is the need to determine the tool transform when necessary. The provided measurement-attachment/tool shown in Fig. 1 is well defined and ideally is to be mounted directly onto the robot. Unfortunately, for the HP20D, we used a fabricated mounting plate due to hardware incompatibility and hence the error parameters of A etool tool( ) in Eq. (3) need to be identified. More will be said about the experimental procedure that we performed to obtain an initial tool definition in Section 4. What needs to be emphasized here is the guidelines that need to be set in order to attain a good estimate after an initial guess of the tool specifications" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001473_j.talanta.2011.07.054-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001473_j.talanta.2011.07.054-Figure1-1.png", + "caption": "Fig. 1 depicts the CV responses for the electrochemical oxidation f 50.0 mol L\u22121 NAC at unmodified CPE (curve b), CNPE (curve ), 2,7-BFCPE (curve e) and 2,7-BFCNPE (curve f). As it is seen, hile the anodic peak potential for NAC oxidation at the CNPE, nd unmodified CPE are 740 and 790 mV, respectively, the correponding potential at 2,7-BFCNPE and 2,7-BFCPE is \u223c320 mV. These esults indicate that the peak potential for NAC oxidation at the 2,7- FCNPE and 2,7-BFCPE electrodes shift by \u223c420 and 470 mV toward egative values compared to CNPE and unmodified CPE, respecively. However, 2,7-BFCNPE shows higher anodic peak current for", + "texts": [ + "1 M phosphate buffer solution (pH 7.0) at can rate of 10 mV s\u22121; (b) as (a) + 50.0 mol L\u22121 NAC; (c) as (a) at the surface of ,7-BFCNPE; (d) as (b) at the surface of CNPE; (e) as (b) at the surface of 2,7-BFCPE; f) as (b) at the surface of 2,7-BFCNPE. the oxidation of NAC compared to 2,7-BFCPE, indicating that the combination of CNTs and the mediator (2,7-BF) has significantly improved the performance of the electrode toward NAC oxidation. In fact, 2,7-BFCNPE in the absence of NAC exhibited a well-behaved redox reaction (Fig. 1, curve c) in 0.1 M phosphate buffer (pH 7.0). However, there was a drastic increase in the anodic peak current in the presence of 50.0 mol L\u22121 NAC (curve f), which can be related to the strong electrocatalytic effect of the 2,7-BFCNPE toward this compound [44]. The effect of scan rate on the electrocatalytic oxidation of NAC at the 2,7-BFCNPE was investigated by linear sweep voltammetry (Fig. 2). As can be observed in Fig. 2, the oxidation peak potential shifted to more positive potentials with increasing scan rate, confirming the kinetic limitation in the electrochemical reaction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001619_tmag.2013.2285017-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001619_tmag.2013.2285017-Figure5-1.png", + "caption": "Fig. 5. CFD calculation results of the HSPM under the rated condition. (a) Velocity vector distribution. (b) Temperature distribution (half model).", + "texts": [ + " Then a new estimation Ti is obtained based on the last estimation Ti\u22121 and calculated average temperature Ti\u22121(calc) Ti = Ti\u22121 + \u03baa(Ti\u22121(calc) \u2212 Ti\u22121) (8) where \u03baa is an acceleration factor. The iteration stops when the difference between the estimated and calculated average temperature of each part is less than a preset requirement. Loss density of each part is calculated and mapped to the CFD model. The flow rate of the cooling air under the rated condition is set as 0.067 m3/s. The temperature solution converges after several iterations. Calculated stream lines and temperature distribution of the HSPM are shown in Fig. 5. It can be seen from Fig. 5(a) that most axial coolant flows through the inner and outer slots while few enter the air gap. The highest winding temperature is found near the outlet, which is approximately 96.0 \u00b0C. The hottest spot in the rotor, however, occurs in the middle of the rotor, which is 125.5 \u00b0C. To verify the CFD model, several Pt100 resistance temperature detectors (RTDs) are installed in different parts of the motor winding [see Fig. 6(a)]. Winding temperatures are monitored while the HSPM is driven by the rated current under the same cooling condition with that set in the CFD model" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002280_s12206-012-0627-9-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002280_s12206-012-0627-9-Figure1-1.png", + "caption": "Fig. 1. A schematic diagram of a typical rolling element bearing.", + "texts": [ + " The model validity is proven by the comparison of our results to those of Harris and as well as to experimental results. The transient motion of rolling elements and skidding is then investigated during acceleration using the new model. The paper is organized as follows. The model to investigate skidding in rolling element bearings during acceleration is presented in Section 2. The model is validated in Section 3. The numerical results for a deep groove ball bearing are analyzed in Section 4. Finally, the paper is then concluded in Section 5. A schematic diagram of a typical rolling element bearing is shown in Fig. 1. The outer race is fixed in a rigid support and the inner race rotates with the shaft (angular velocity i\u03c9 ). A constant vertical radial force (W) acts on the bearing. Ri is inner raceway radius, Ro is outer raceway radius, Rm is pitch radius of bearing, Rr is radius of rolling element, r\u03c9 represents angular velocity of rolling element about its axis, c\u03c9 represents angular velocity of cage, l\u03c8 represents angle range of load zone, j\u03b8 represents angle position of jth rolling element. Elastic deformation between races and rolling elements gives a nonlinear force deformation relationship, which is obtained by the Hertzian theory" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003983_j.bios.2020.112428-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003983_j.bios.2020.112428-Figure1-1.png", + "caption": "Figure 1: Roll-to-roll processing technique: (A) homemade roll-to-roll machine; (B) shim with dimensions H (height), w (width) and d (depth); (C) slot-die head and coating film; (D) meniscus between slot-die head and substrate; (E) screen-printed carbon electrodes (SPCEs); (F) SPCEs made with scotch tape masks on top.", + "texts": [ + "05% was used to obtain a surface tension necessary for printing. The optimized performance was achieved using the ink containing 0.5 mg mL\u02d71 CB, 1.5 mg mL\u02d71 CMC, 2000 U mL\u02d71 Tyr, and 0.05% triton X-100. The optimization steps for the ink formulations were performed using SPCEs modified via drop casting, and by depositing 10 \u00b5L of the dispersion onto the working electrode and letting it dry at room conditions for 2 h. Totally-printed sensors and biosensors were fabricated using a homemade R2R machine as shown in Figure 1A, in which thin films with up to 1.0 m in length and with different thicknesses can be deposited onto flexible substrates(Cagnani et al., 2020). The thickness of the printed film mainly depends on processing parameters, such as scrolling speed and flow rate, and on the printing technique. For the system shown in Figure 1A, the scrolling speed can be adjusted using a digital controller within a speed range from 1.0 to 90 cm min\u22121. The drying hot plate can reach temperatures up to 200 6 \u00b0C, and the flow rate can be chosen according to the syringe pump capacity, which ranges from 0.75 \u03bcL h\u22121 to 1257 mL h\u22121 for the NE-300 equipment (New Era\u00ae). The slot-die coating technique was selected here, and the deposition occurred by pumping the ink into the slot-die head, where it leaked through a shim (Figure 1B). After forming the meniscus, at the exit of the printing head the ink covers the substrate. The film is then obtained by rotation of the rubber rolls used for tensioning the substrate (Figure 1C and 1D). CB-PAA and Tyr-CB inks were deposited only onto SPCEs working electrodes by using an attached adhesive template containing the working electrode pattern as the negative mask. Hence, only the area of the working electrode becomes exposed, as shown in Figures 1E and 1F. The inks were deposited through optimized processing parameters, including scrolling speed of 50 cm min\u22121 and flow rate of 0.03 cm\u00b3 min\u22121. For the fabrication of SPCEs modified with CB-PAA ink, they were heated at 60 \u00b0C for 2 min after each deposited layer to reach a faster solvent evaporation", + " The quality of film deposition using the slot-die technique can be affected by operational parameters such as surface tension of the deposited liquid, which must be sufficiently low to allow spreading onto a substrate surface for forming uniform layers. The two surfactants studied here, viz. non-ionic triton X-100 and anionic SDS, were effective in decreasing surface tension of CB-PAA inks. SDS was selected because it yielded a stable and electroactive voltammetric response for base CB-PAA, as observed in Figure S3. Therefore, a final ink formulation containing 1.0 mg mL\u22121 CB, 0.5 mg mL\u22121 PAA and 0.05% SDS was used in the slot-die coating delimited by adhesive, scotch tape templates (See Figure 1F). Prior to the deposition of CB-PAA ink onto the working electrode, we confirmed the feasibility of the methodology by printing two patterns onto clean PET sheets. The patterns were selected to yield circular and square working electrodes, the most used geometries in SPCEs. The adhesive negative template containing the patterns was attached to the PET substrate, and the ink was deposited under optimized parameters (scrolling speed=50 cm min\u22121 and flow rate=0.03 cm\u00b3 min\u22121). Figure 2A shows the pictures of PET substrates after depositing 10 layers of CB-PAA inks, and with welldefined geometries achieved using the adhesive mask" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001732_coase.2012.6386343-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001732_coase.2012.6386343-Figure4-1.png", + "caption": "Fig. 4. Kinematics of the KUKA KR 210-2 industrial robot", + "texts": [ + " Thus, the param eter vector comprises 115 elements, describing a complete robot trajectory (cf. section III-A). Therefore, realistic joint angle profiles generated by the robot controller software are utilized. As the termination conditions, a fixed number of iterations and a termination tolerance on the function value Joe are defined. In this section, the optimization results for different ex emplary PTP trajectories of an n = 6 axis industrial robot are shown. Therefore, the model described in section II is applied to the KUKA KR 210-2 industrial robot shown in Fig. 4. Additionally, a tool load of 50 kg mounted on the robot EE is assumed for all trajectories. Many high-payload robots like the KR 210-2 comprise a counterbalancing sys tem that is mounted between the first and the second robot link. Thus, excessive torque values caused by gravitation and lever effects are compensated during configurations with a sprawled robot arm. Hence, the position-dependent additional torque on axis 2, which is induced by the count erbalancing unit, is included in the dynamic model" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003857_j.engfailanal.2018.08.028-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003857_j.engfailanal.2018.08.028-Figure6-1.png", + "caption": "Fig. 6. FE model of the helical gear pair with spatial crack.", + "texts": [ + " The stiffness of the cracked tooth can be calculated as: = + + k \u03c4_ _ ( ) 1 _ _ _ _ _ i n k \u03c4 k \u03c4 k \u03c4 t1 crack 1 ( ) 1 ( ) 1 ( )i n i n i n b1 crack s1 crack a1 (17) where kb1_crack_in(\u03c4) and ks1_crack_in(\u03c4) denote the bending and the shear stiffness of cracked gear tooth. And the detailed calculation can be found in Ref. [42]. The flow chart of the TVMS calculation of the cracked helical gears is shown in Fig. 5. 3. Model verification and discussion In order to verify the proposed method, an FE model of the helical gear pair with spatial crack is established in ANSYS software (see Fig. 6). The similar modeling process can be found in Ref. [42]. It is noted that the influence of axial force can not be taken into consideration in the proposed method. Hence, two end faces of the helical gear pair are constrained in axial direction. It is difficult to generate the hexahedral meshes on the gear tooth with crack, so tetrahedral meshes are used for gear teeth of the driving gear, and hexahedral meshes are used for the rest part of the FE model. In order to analyze the influences of the mesh types on the TVMS, the FE model of healthy helical gear pair is established using pure hexahedral meshes and tetrahedron-hexahedral mixed meshes respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002193_j.measurement.2014.04.024-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002193_j.measurement.2014.04.024-Figure1-1.png", + "caption": "Fig. 1. A schematic of the machinery-fault simulator.", + "texts": [ + " Subsequently, the training and the testing were performed at rotational speeds other than at measured ones, i.e. at the intermediate and extrapolated rotational speeds. This has a practical advantage in that it is not feasible to have measured data at all speed of interest. Predictions are excellent and the results are compared with results of purely time domain features of previous published work [22]. Experiments were conducted on a Machinery Fault Simulator\u2122 (MFS) and a schematic drawing of it is depicted in Fig. 1. This setup could be considered for the replication of a variety of machine faults, for example in the gearbox, shaft misalignments, rolling element bearing damages, resonances, reciprocating mechanism effects, motor faults, pump faults, etc. In the MFS, a 3-phase induction motor was connected to a rotor that in turn was coupled to the gear box through a pulley and belt device. The gear box and its assemblage are illustrated in Fig. 2. In the analysis of faults in gears, three different types of faulty pinion gears to be precise the ND, CT, MT and WT were considered and are depicted in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.34-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.34-1.png", + "caption": "FIGURE 5.34. A 4R planar manipul ator.", + "texts": [ + " The matrix 3T6 is the wrist t ransformat ion matri x and 6T7 is t he tool s t ransformat ion matrix. Decomp osing \u00b0T7 into submatrices enables us to make the forward kinemati cs modular . 5. Forward Kinematics 255 Exercises 1. Notation and symbols. Describe the meaning of a- Bi b- a i [ \u00a2u ] d- s(di ,Bi ,ki-1) e- RIIR(180)c- hu f- i- 1Ti g- @ h- [ Bi~i-l ] i- s(h ,\u00a2, u) j- Pl-R( -90) d; ki- 1 k- d; 1- a; [ a i ii - l ] n- s (ai, ai,ii- l ) 0 - m-R(-90) .m- A ai 2i - l 2. A 4R planar manipulator. For the 4R planar manipulator, shown in Figure 5.34, find the (a) DR table (b) link-type table (c) individual frame transfo rmation matrices i- 1Ti , i = 1,2 ,3 ,4 (d) global coordinates of the end-effector (e) orientation of the end-effector 'P . 3. A one-link RI-R( -90) arm. 256 5. Forward Kinematics For the one-link Rf-R( -90) manipulator shown in Figure 5.35 (a) and (b) , find the transformation matrices \u00b0T1 , ITz, and \u00b0Tz. Compare the transformation matrix ITz for both frame installations. 4. A 2R planar manipulator. Determine the link 's transformation matrices \u00b0T1, ITz, and \u00b0Tz for the 2R planar manipulator shown in Figure 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000491_978-3-540-79029-7-Figure2.7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000491_978-3-540-79029-7-Figure2.7-1.png", + "caption": "Fig. 2.7 Temporal (a) and spacial (b) representation of the utilizable area for the voltage vector us", + "texts": [ + " Because the moduli of ur and ul are always positive, and because the term b changes its sign at every sector transition, b can be tested on its sign to determine to which sector of the thus found quadrant the voltage vector belongs. For practical application to inverter control, the vector modulation algorithm (VM) has certain restrictions and special properties which implicitly must be taken into account for implementation of the algorithm as well as for hardware design. The geometry of figure 2.2 may lead to the misleading assumption that arbitrary vectors can be realized in the entire vector space which is limited by the outer circle in fig. 2.7b, i.e. every vector us with 2 3s DCUu would be practicable. The following consideration disproves this assumption: It is known that the vectorial addition of ur and ul is not identical with the scalar addition of the switching times Tr and Tl. To simplify the explanation, the constant half pulse period which, according to fig. 2.3, is available for the realization of a vector is replaced by 2 2p pT T= . After some rearrangements of equation (2.2) by use of (2.5) the following formula is obtained. ( )0 23 cos 30s r l p DC T T T T U = + = u (2.8) In case of voltage vector limitation, that is 2 3s DCU=u , it follows from (2.8): ( )0 0 0 max 2 2 cos 30 with 0 60 3pT T= (2.9) The diagram in figure 2.7a shows the fictitious characteristic of T\u03a3max with excess of the half pulse period Tp/2. By limitation of T\u03a3 to Tp/2 the actual feasible area is enclosed by the hexagon in fig. 2.7b. In some cases in the practice - e.g. for reduction of harmonics in the output voltage - the hexagon area is not used completely. Only the area of the inner, the hexagon touching circle will be used. The usable maximum voltage is then: 26 Inverter control with space vector modulation Restrictions of the procedure 27 max 1 3s DCU=u (2.10) Thus the area between the hexagon and the inner circle remains unused. Utilization of this remaining area is possible if the voltage modulus is limited by means of a time limitation from T\u03a3 to Tp/2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure1.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure1.2-1.png", + "caption": "Fig. 1.2 A typical electrical machine. (a) Sectional drawing. (b) Developed diagram.", + "texts": [ + " The secondary factors not covered by these assumptions are dealt with under the heading of 'leakage', which is discussed in some detail in later sections. Because the radial length of the air-gap is small it is possible to speak of a definite value of air-gap flux density at any angular position. The essential arrangement of the machine can thus be repre sented on a drawing of a section perpendicular to the axis of the The Basis of the General Theory 3 cores. The two-dimensional drawing can then be further simplified to a developed diagram showing the air-gap circumference devel oped along a straight line. Fig. 1.2a shows, as an example, a sectional drawing of a six-pole machine having salient poles on the outer member and a core on the inner member which is continuous if the slots are ignored. Fig. 1.2b shows the corre sponding developed diagram and indicates the fundamental sine wave of flux density. The developed diagram is exemplified in practise by the linear motor. In the developed diagram the distribution of flux density and current repeats itself every two poles, whatever the actual number of poles may be. (Slight variations due to fractional-slot windings or staggered poles are ignored in working out the theory.) Hence any machine can be replaced by an equivalent two-pole machine and only such machines need be considered", + " In this book the theory is developed entirely in terms of two-pole machines. The number of poles must of course be introduced when calculating the constants of the machine, particularly when considering mechanical quantities such as torque and speed. The windings of electrical machines are of three main types: The winding consists of coils similarly placed on all poles, and connected together by series or parallel connection into a single circuit. Usually the coils are wound round salient poles as indicated in Fig. 1.2, but sometimes, as in a turbo-generator field winding, a coil winding may lie in slots. The individual conductors are distributed in slots and are connected into several separate circuits, one for each phase. The groups of conductors forming the phase bands are distributed in regular sequence over successive pole pitches. The conductors are located in slots and are connected to commutator segments in a continuous sequence. The current flows from the external circuit into and out of the winding through brushes pressing on the commutator surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000196_ls.23-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000196_ls.23-Figure1-1.png", + "caption": "Figure 1. Typical EHL engineering contacts.", + "texts": [ + " The author apologizes for this and acknowledges that there exist many significant contributions to our understanding of EHL additional to those mentioned and referenced here. Two previous reviews by Dowson5 and by Dowson and Ehret6 provide further details of EHL, and two useful books on the subject are those by Hamrock and Dowson7 and by Gohar.8 The regime of lubrication known as elastohydrodynamic lubrication occurs in lubricated, nonconforming contacts, such as are present in gears, rolling element bearings and cam-tappet systems (Figure 1). In such contacts, the fluid flow behaviour and thus entrainment caused by motion of the surfaces can be described by the Reynolds equation, just as for conforming journal and pad bearings. However, because of the non-conforming geometry, for high elastic modulus solids such as metals and ceramics there is a very high pressure in the contact region since the applied load is concentrated at a \u2018point\u2019 or \u2018line\u2019 and this has two additional effects which impact on the lubrication behaviour. Firstly, the high pressure elastically deforms the contacting surfaces to form a locally conforming, elliptical or rectangular-shaped contact region", + " Another problem with many EHL systems is that the temperature of the lubricant to be used for film thickness and friction calculation is unknown, unlike in most hydrodynamic contacts where the oil supply temperature is known or measurable. This is more of a problem with cams and gears than with rolling bearings, which may be why EHL analysis is more often applied to the latter. Perhaps most important, however, is that most EHL-based machine components operate both in transient conditions of load, speed and/or geometry (including all of those shown in Figure 1) and in mixed lubrication. However, as described earlier in this review, solutions for transient and mixed EHL lubrication have only just started to become available, and they have not yet been translated into equations that are simple and straightforward enough to be used by non-specialists in tribology. What engineers really need are equations and methodologies based on EHL lubrication theory that predict not film thickness (most engineers care little about this per se), but rather performance in terms of wear, scuffing or fatigue life" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000802_j.mechmachtheory.2010.03.010-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000802_j.mechmachtheory.2010.03.010-Figure2-1.png", + "caption": "Fig. 2. Coordinate systems for the six-axis Cartesian-type bevel gear cutting machine.", + "texts": [ + " [9], the transformation matrices St to S1 yield the following surface locus for the cutting tool in coordinate system S1: where r U\u00f0 \u00de 1 u;\u03b2;\u03d5c\u00de = M U\u00f0 \u00de 1f \u03d51\u00de\u22c5M U\u00f0 \u00de fa i;j;\u03b8c;SR;Em;\u0394A;\u0394B;\u03b3m;Ra;\u03d5c\u00de\u22c5M U\u00f0 \u00de at \u03b2\u00f0 \u00de\u22c5rt \u03b10;rc;\u03b1h;\u03b40;r0;\u03b2i;u\u00de\u00f0 \u00f01\u00de M U\u00f0 \u00de 1t \u03d51;\u03b2;\u03d5c\u00f0 \u00de = 1 0 0 0 0 cos \u03d51 sin \u03d51 0 0 sin \u03d51 cos \u03d51 0 0 0 0 1 2 66664 3 77775\u22c5 cos \u03b3m 0 sin \u03b3m \u0394A 0 1 0 0 sin \u03b3m 0 cos \u03b3m 0 0 0 0 1 2 66664 3 77775\u22c5 1 0 0 0 0 1 0 Em 0 0 1 \u0394B 0 0 0 1 2 66664 3 77775 \u00d7 cos \u03b8c + \u03d5c\u00f0 \u00de sin \u03b8c + \u03d5c\u00f0 \u00de 0 0 sin \u03b8c + \u03d5c\u00f0 \u00de cos \u03b8c + \u03d5c\u00f0 \u00de 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775\u22c5 sin j cos j 0 SR cos j sin j 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775 \u00d7 cos i 0 sin i 0 0 1 0 0 sin i 0 cos i 0 0 0 0 1 2 66664 3 77775\u22c5 cos \u03b2 sin \u03b2 0 0 sin \u03b2 cos \u03b2 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775 The newly developed Cartesian-type machines, however, introduce a novel manufacturing method for spiral bevel gears, a sixaxis Cartesian-type structure that produces the minimum sufficient degrees of freedom for the operation of existing spiral bevel gear cutting methods. These machines' state-of-the-art CNC technology also enables precise simultaneous six-axis movements. They are therefore acknowledged to be the most compact structures capable of providing high efficiency and precision without limiting the implementation of the above-mentioned cutting methods. As Fig. 2 shows, the coordinate systems of a Cartesian-type spiral bevel gear cuttingmachine are arranged like those of the Gleason Phoenixmachine, which has three rectilinear motions (Cx, Cy, and Cz) and three rotational motions(\u03c8a, \u03c8b, and \u03c8c). However, the settings for Cartesian-type machines cannot be derived directly like cradle-type machine settings but rather must be converted from these latter. As Fig. 2 shows, the coordinate systems St(xt, yt, and zt) and S1(x1, y1, and z1) are rigidly connected to the cutter head and the work gear, respectively. According to Ref. [11], the transformation matrices St to S1 yield the following surface locus for the cutting tool in coordinate system S1: r C\u00f0 \u00de 1 u;\u03b2;\u03d5c\u00f0 \u00de = M C\u00f0 \u00de 1d0 \u03d51\u00f0 \u00de\u22c5M C\u00f0 \u00de d0a0 Cd;Cx;Cy;Cz;\u0394\u03c8a;\u03c8b;\u0394\u03c8c \u22c5M C\u00f0 \u00de a0t \u03b2\u00f0 \u00de\u22c5rt \u03b10;rc;\u03b1h;\u03b40;r0;\u03b2i;u\u00f0 \u00de \u00f02\u00de where where from t setting Becau matrix spatia type o where univer matric where axes a terms where machi polyno [11]) t M C\u00f0 \u00de 1t \u03d51;\u03b2;\u03d5c\u00f0 \u00de = 1 0 0 0 0 cos\u03d51 sin\u03d51 0 0 sin\u03d51 cos\u03d51 0 0 0 0 1 2 66664 3 77775\u22c5 1 0 0 0 0 cos\u0394\u03c8a sin\u0394\u03c8a 0 0 \u2212sin\u0394\u03c8a cos\u0394\u03c8a 0 0 0 0 1 2 66664 3 77775\u22c5 1 0 0 Cd 0 1 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775 \u00d7 cos \u03c8b 0 sin\u03c8b 0 0 1 0 0 sin \u03c8b 0 cos \u03c8b 0 0 0 0 1 2 66664 3 77775\u22c5 1 0 0 Cx 0 1 0 Cy 0 0 1 Cz 0 0 0 1 2 66664 3 77775\u22c5 cos\u0394\u03c8c sin\u0394\u03c8c 0 0 sin\u0394\u03c8c cos\u0394\u03c8c 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775\u22c5 cos \u03b2 sin\u03b2 0 0 sin \u03b2 cos \u03b2 0 0 0 0 1 0 0 0 0 1 2 66664 3 77775 rt(u) is the position equation of the cutter blade with cutter parameters (\u03b10\u223c\u03b2i) and Md\u2032\u2019a\u2032 (C) is the transformation matrix he origin of the cutter to the origin of the work gear, which consists of the machine constant Cd and the six-axis machine s (Cx\u223c\u0394\u03c8c)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure5-1.png", + "caption": "Figure 5. Selected vibration modes of the gearbox housing.", + "texts": [ + " The position vector at any point Pi on the gearbox housing due to the internal and external excitations is defined with respect to the inertia system, such as15 ri \u00bc Ri \u00fe Ai \u00bdui0 \u00fe u0\u00f0u, t\u00de \u00f01\u00de where Ri is the position vector of the body reference frame, Ai is the transformation matrix from the body reference frame to the inertia frame, ui0 is the undeformed local position of point Pi, and u0 u, t\u00f0 \u00de is the deformation vector at this point. Dynamic deformation of the gearbox is obtained by the modal superposition method u0\u00f0u, t\u00de \u00bc F q\u00f0t\u00de \u00f02\u00de where q\u00f0t\u00de is the generalized coordinate vector, and is the modal matrix of the gearbox housing. In this study, the FE model is established in the ANSYS environment by using 111,639 solid 45 elements, and the modal matrix is obtained by modal analysis. A total of 10 vibration modes occurring at frequencies up to 1570Hz are considered to determine the gearbox response as shown in Figure 5. To improve the calculation, substructure analysis via ANSYS is necessary before integrating the flexible gearbox housing with the vehicle system.14 Since the main degree of freedom (DOF) node needs to be set at the position where the constraint or the force is applied, it is necessary to establish a node at the centre position of the bearing hole in the finite model and couple it with the nodes around the bearing hole. Therefore, there is a node at the point connecting with the other components, and it must be included in the main DOF nodes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000993_j.jsv.2011.12.010-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000993_j.jsv.2011.12.010-Figure2-1.png", + "caption": "Fig. 2. Schematic graph of spall.", + "texts": [ + " [6], G\u00f0t\u00de can be simplified as G\u00f0t\u00de \u00bc k0F\u00f0t\u00deD\u00f0t\u00deP\u00f0Z\u00de (4) where k0 represents the mesh stiffness per unit contact length, F\u00f0t\u00de represents the defect morphology whose value lies between 0 and 1, D\u00f0t\u00de represents the instantaneous defect width along the contact line, P\u00f0Z\u00de represents the defect depth along the contact line, and Z is the abscissa of a point inside the instantaneous defect width. healthy teeth), then Eq. (5) can eventually be put in the normalized form X00 \u00fe2mX0 \u00fek\u00f0t\u00deX \u00bc f 0\u00feF1\u00f0t\u00de\u00fek0F\u00f0t\u00deD\u00f0t\u00deP\u00f0Z\u00de (6) where o\u00bcoe=o0,m\u00bc cm=2meo0,k0 \u00bc k0=km,f 0 \u00bc F0=meo2 0 ,F1\u00f0t\u00de \u00bc f 1o2cos\u00f0ot\u00de According to the actual datum [15,18], the spalling defect usually develops near the pitch line of the gear, and peels off in sheets. Therefore the spalling defect in this paper is modeled near the pitch line as a rectangular indentation having the dimensions A D P as shown in Fig. 2. The numerical parameters of the gear system are given in Table 1. It is assumed in this investigation that the model is for the big gear defected with a unique tooth having the spall. The mesh stiffness will be affected by spall, and the mesh stiffness can be computed by the method given in [9]. The effect of spall on mesh stiffness is shown in Fig. 3, where P\u00bc2 mm. Fig. 3 shows that the length and width of spall affects the mesh stiffness seriously, and the mesh stiffness of the defected tooth is found to be reduced proportionally to the severity of the spalling defect" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003670_j.optlastec.2018.06.012-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003670_j.optlastec.2018.06.012-Figure3-1.png", + "caption": "Fig. 3. Observation of a cross section of a pure copper bead produced on a 304 SS plate.", + "texts": [ + " To confirm whether continuous beads were produced, the pure copper beads produced on the substrate were observed optically from above using a confocal laser scanning microscope. In this study, the efficiency of the formed coating was defined as the coating amount. The coating amount was the cross-sectional area (CSA) derived from the profile measurements of the beads using a confocal laser scanning microscope. The measurements were performed in the same range of the optical observations, the average CSA was evaluated along a bead. Continuous beads were cut (Fig. 3). The bonding between the bead and the substrate (i.e., bonded interface) was observed by SEM. EDX analysis was carried out to identify the dilution near the bonded interface on the cross section. Figs. 4 and 5 show the top view of pure copper beads produced on the 304 SS plate with blue and IR diode lasers, respectively. As shown in Fig. 4, a continuous bead without bumps was obtained at the laser intensity of not less than 56 kW/cm2 using blue diode lasers (Fig. 4(b) and (c)). As shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002275_j.mechmachtheory.2012.05.002-Figure6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002275_j.mechmachtheory.2012.05.002-Figure6-1.png", + "caption": "Fig. 6. Contact analysis of the spur gear pair in experiments. Relative twist is \u03b3=0.01\u00b0. Tip relief starts at \u03b1=20.9\u00b0. The applied torque is 85 Nm. (a) Contact forces from the finite element model. Dots indicate theoretical contact lines, bars indicate contact pressure. (b) Contact pattern averaged over a mesh cycle from the finite element model. (c) Contact pattern averaged over a mesh cycle from the analytical model.", + "texts": [ + " The contact from both models spans a larger area of the gear tooth surface with increasing torque. At all three torques there is partial contact loss because parts of the tooth surface are out of contact. The mesh deflection is not large enough to compensate for the separation from tooth surface modifications. The analytical model can treat misaligned gears (that is, gears with a specified relative twist angle). The contact pressure from the finite element model at an instant when the misalignment (relative twist angle) \u03b3=0.01\u00b0 is shown in Fig. 6(a). Fig. 6(c) and (b) compares contact patterns from the analytical and finite element models at 0.01\u00b0 misalignment. Contact patterns from both models indicate severe partial contact loss. The analytical model effectively captures partial contact loss. The equivalent model captures the nonlinearity in the gear mesh from the deflection-dependent changes of the translational stiffness km, spread-twist stiffness kt, and center of stiffness b; c . The nonlinear behaviors of these quantities are explored by examining the displacement and stiffness curves obtained by applying torque and twisting moments on the gear pairs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003722_j.optlastec.2020.106627-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003722_j.optlastec.2020.106627-Figure2-1.png", + "caption": "Fig. 2. Schematic of the geometric parameters for bead morphologies for a single bead.", + "texts": [ + " According to the energy conservation law [32]: Then it yielded as: m = P\u2219Ak\u2219t c(Tm \u2212 T0) + \u0394HF (4) According to mass conservation law, the melted wire generated the same amount of the cladding layer, which gave: P\u2219Ak\u2219t c(Tm \u2212 T0) + \u0394HF = \u03c0r2\u2219\u03c1Vf\u2219t (5) where Vf is the wire feeding speed,r is the radius of the wire. The wire feeding speed is given as: Vf = P\u2219Ak \u03c0r2\u2219\u03c1[c(Tm \u2212 T0) + \u0394HF ] (6) In this paper, the geometry characteristics of the single cladding layer were defined by its width W, and the height H. According to [33], the outline of the deposited bead was very close to an arc shape with a radius R, as shown in Fig. 2. The radius can be expressed as: R = W2 + 4H2 8H (7) Meanwhile, the height H of the cladding layer could also be expressed as: H = R \u2212 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 R2 \u2212 (W/2)2 \u221a (8) To express the relation between the bead width and bead height, the so-called aspect ratio RBthe bead is defined as RB = W H (9) The wire feeding direction has a great influence on the quality of deposited metal. From Fig. 3(a), it is shown that the wire is transfer into the welding pool through a molten metal bridge. At the front feeding, the energy of melting the wire mainly comes from the laser irradiation (PL), the plasma and metallic vapor radiation (PM), and weld pool radiation (PW)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003982_j.optlastec.2020.106328-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003982_j.optlastec.2020.106328-Figure4-1.png", + "caption": "Fig. 4. Variation of the laser focal plane position in the powder stream.", + "texts": [ + "2 mm, the focal length of 200 mm, and the Rayleigh length of 2 mm was operated in continuous wave. Cobalt-base super-alloy stellite 6 powder was deposited on the DIN1.2714 hot work tool steel substrate. The length of AMed wall was 4 cm. Laser additive manufacturing experimental works were performed in two strategies, as presented in Table 2. In A series, the effects of variations of the laser focal plane position in the powder stream were surveyed in a single cladding layer. By varying this parameter, the laser energy absorption by the substrate and the stellite powder was investigated. Fig. 4 illustrates the laser focal positions in different modes. The powder concentration plane is located on the surface of the substrate. As shown in Fig. 4 in mode \u22124, the laser spot point is located 4 mm above the powder concentration plane while in +4 mode, it is located 4 mm lower down the powder concentration plane. In zero-mode, the laser spot point is positioned on the substrate and powder concentration plane. In B series, one of the best results of A-series is selected, and the Table 1 Chemical composition of the stellite 6 powder and DIN 1.2714 substrate. Mo Ni S Si C Mn P Fe W Cr Co Element \u2013 \u2013 \u2013 \u2013 1.3 0.22 0.42 1.21 3 31 Bal. Powder (wt. %) 0", + " The higher melted content caused the lower perpendicularity and lower the accurate height of the layers. In our measurements we have considered the vertical height of all samples and we did not consider the tilted wall in the measuring the height. Based on a proverb it is said that: A good beginning makes a good ending. Or in another way: All\u2019s well that ends well. According to Fig. 9 (a), it is evidence that in mode +4 of the focal point position in which the laser focal position is below the surface, see Fig. 4, the width of the deposited layer is the largest case. Because in this mode, a wider area of the laser beam interacts with the substrate surface, and then more volume of the powder is melted and deposited on the substrate. In Fig. 9 (b), we understand that it is cleared that, when the laser beam is placed above the substrate (mode \u22124) while the larger laser beam area has interacted with the powder stream in comparison with the other modes, it causes more powder to be melted and create a longer height" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002940_j.jcrysgro.2019.05.027-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002940_j.jcrysgro.2019.05.027-Figure1-1.png", + "caption": "Fig. 1. FEM model for thermal history calculation during SLM.", + "texts": [ + " The thermal history during solidification is predicted using the commercial FEM package ABAQUS. Different laser beam configurations are incorporated into the FEM model using a subroutine function compiled in Fortran programming language. In the FEM model, the workpiece has dimensions of 5\u00d71\u00d71mm3 and the laser beam scans along the length direction (i.e., the 5mm edge). Non-uniform tetrahedral elements are used to mesh the part, and the finest grid size is used in the melt pool region (about 5 \u00b5m). The construction of the FEM model is shown in Fig. 1. Since the PF simulation is extremely computationally intensive, it is performed only on the YZ plane of the melt pool region. The mesh of the calculated temperature history from the FEM model is refined to 10 nm grid size for the PF simulation, based on a linear interpolation scheme, as shown in Fig. 1. In SLM, the deposited material experiences cyclic melting, solidification, and re-melting, to reduce computation cost, the PF simulation is performed only in the solidification region by using the complete cooling history, as shown in Fig. 2(a). Fig. 2(b) shows the thermal history of different points in the melt pool during the cyclic heating/cooling process. The interested area for microstructure calculation is chosen between point 2 and point 3 so that the interested region does not experience re-melting in the subsequent laser scans" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001148_1.4003501-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001148_1.4003501-Figure8-1.png", + "caption": "Fig. 8 Schematic view of the bearing with an inner ring directed nozzle: \u201ea\u2026 ceramic bearing \u201eouter ring landing\u2026 and \u201eb\u2026", + "texts": [], + "surrounding_texts": [ + "Table 1 lists the specifications of the tested angular contact ball bearings. The values of fixed parameters during experiments are shown in Table 2. The ambient temperature is kept as a constant value by an air-conditioner during the test. The oil-air lubrication hematic view and \u201eb\u2026 photo \u2026 sc should be started about 15 min prior to the beginning of the ex- Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use B B I O W B N C P O A J Downloaded Fr earing type 7006C/P4 B7006C/P4 all material GCr15 bearing steel Si3N4 ceramic nner diameter mm 30 30 uter diameter mm 55 55 idth mm 13 13 all diameter mm 7.144 5.998 o. of balls 14 16 ontact angle deg 15 15 Table 2 Fixed parameters during experiments arameter Value il volume per injection 0.025 cm3 ir pressure of distributor outlet 0.2 MPa ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms brication point. A pipe in an optimum length can get a balance of dispersing the injected oil and reducing the air pressure loss by the inner wall flow resistance. In this test, the oil-air supply pipe adopted is made of polyurethane resin, which has an outer diameter of 10 mm and a wall thickness of 1.75 mm. The operation parameters of the lubrication system are 20,000 rpm of rotation speed, 300 N of preload, and 3 min of lube interval. 46 cSt antiwar hydraulic oil was used, which is offered by the China Great Wall Lubricant Corporation No. 22, Fucheng Road, Haidian District, Beijing, China . The nozzle with two outlets 180 deg apart positioned each side was adopted; the length to outer-diameter ratio of the outlet is 1.6 and the diameter of the outlet is 1.5 mm. Figure 3 shows the relationship between the temperature rises of tested bearings and the oil-air supply pipe length. For the steel ball bearing, there exists a pipe length of 1.5 m for the lowest temperature rise; a longer or shorter pipe will increase the temperature rise. A possible explanation is that the lubricant is not dispersed adequately when it reaches the bearing with a pipe shorter than the 1.5 m used; consequently, a higher temperature will appear due to no uniform lubrication. With a longer pipe used, the pipe flow resistance increases; consequently, the air flow rate will be slightly decreased, resulting in a relatively high temperature rises of the tested bearing. However, the trend does not hold for a hybrid ceramic ball bearing. It can be seen from Fig. 3 that the temperature rise of the hybrid ceramic ball bearing increases smoothly with increase in the pipe length. This can be explained that the ceramic ball of silicon nitride Si3N4 has a self-lubricating property; thus, the dispersion of droplet of inject oil is not sensitive to the temperature rise of this bearing; meanwhile, as the pipe length increases, the inner wall flow resistance will increase also; consequently, the bearing temperature rise increases monotonously. In the following experiments, the pipe length of 1.5 m is used to investigate the effects of bearing preload, lube interval, oil viscosity, oil type, nozzle design, and rotation speed on temperature rise of both types of bearings, and the corresponding measured flow rate of the compressed air is 11.25 m3 /h. 4.2 Effect of Bearing Preload on Temperature Rise. Since an appropriate preload is important for the good performance of ball bearings, the effects of the preload on the temperature rise under different rotating speeds were investigated. In the experiments, 46 cSt antiwar hydraulic oil was used, and lube intervals of 2 min, 1.5 min, and 1 min were applied for the rotating speeds of 10,000 rpm, 20,000 rpm, and 30,000 rpm, respectively. The APRIL 2011, Vol. 133 / 021101-3 of Use: http://www.asme.org/about-asme/terms-of-use d r o s d t t p p p p t e c p c p b r a b t o 0 Downloaded Fr The results also show that, as the preload increases, the temerature rise of the hybrid ceramic bearing at 10,000 rpm dereases slightly, and the tested bearing has a lower temperature for reloads in a wide range 200\u2013600 N; however, as the preload is eyond 600 N or decreases from 200 N to 100 N, the temperature ise increases slightly. The variation in the temperature rise under speed of 20,000 rpm is somewhat similar as that of the steel ball earing; but the trend does not hold for that at a higher speed, here exists an apparent fluctuation in temperature rise for a speed f 30,000 rpm, and no appropriate preload can be used to ensure 21101-4 / Vol. 133, APRIL 2011 om: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms the bearing has a lower temperature rise. It is necessary to put forward a design criterion for selecting the appropriate axial preload. Based on the experimental data acquired, the recommended value of the axial preload N in the case of the angular contact ball bearing at a high speed is estimated as much as ten times that of the inner diameter in mm . To this bearing, the dimension of the inner diameter is 30 mm; therefore, the recommended value of the axial preload should be 300 N. This design criterion has been proven by the author\u2019s recent applied research on the oil-air lubrication for the high speed grinding motorized spindle. 4.3 Effect of Lube Interval on Temperature Rise. The effect of the lube interval on the bearing temperature rise under three rotating speeds is shown in Fig. 5. The oil supply quantity was 0.025 cm3 for each lube interval; 46 cSt antiwear hydraulic oil was also used as the lubricant, and the axial preload load was 300 N. The nozzle with two outlets 180 deg apart positioned each side was adopted; the length to outer-diameter ratio of the outlet is 1.6 and the diameter of the outlet is 1.5 mm. As shown in Fig. 5, except that of the rotational speed of 30,000 rpm, the temperature rises tend to be less sensitive to oil quantity. There exists a proper amount of lubricant for a lower temperature rise at each rotational speed. With an oil quantity larger than the appropriate amount, the higher flow rate will lead to a higher temperature rise. Meanwhile, an oil flow rate less than the appropriate amount will also lead to a higher temperature rise. Fig. 5 Effect of lube interval on temperature rise of tested bearings: \u201ea\u2026 steel ball bearing and \u201eb\u2026 ceramic ball bearing The results also indicate that the appropriate amount of lubricant Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use l o r m 1 e r t t l o c d t l c J Downloaded Fr ube oil quantity. 4.4 Effect of Oil Viscosity on Temperature Rise. The effects f the oils with different viscosities on the bearing temperature ise under three rotating speeds were investigated. In the experient, ten types of oils rating for 32 cSt, 46 cSt, 68 cSt, 80 cSt, 00 cSt, 130 cSt, 150 cSt, 200 cSt, 250 cSt, and 320 cSt were xamined, the lube intervals of 3 min and 2 min were used for otating speeds of 20,000 rpm and 30,000 rpm, respectively, and he preload of 300 N was applied for all the tests. The nozzle with wo outlets 180 deg apart positioned each side was adopted; the ength to outer-diameter ratio of the outlet is 1.6 and the diameter f the outlet is 1.5 mm. ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms increase the bearing temperature rise. From the EHL theory, a higher viscosity will not only increase the oil-film thickness but also generate more churning losses. Consequently, a higher temperature rise is produced. It also appears that a lower viscosity will generate more heat although the same oil flow rate is supplied. This can be explained that, as the oil viscosity decreases from the viscosity grade of 100 cSt to 32 cSt, the minimum oilfilm thickness will decrease and reach a level at which the surface asperities begin to contact. When the surface asperities come into contact, the frictional force and heat generation will increase. For the hybrid ceramic bearing at 20,000 rpm, the trend of temperature rise does not hold for lower viscosities in the range 32\u201348 cSt, and the temperatures fluctuate with decreasing of the viscosity. A possible explanation is that EHL film thickness is related to the entrainment velocity, the lubricant viscosity, and the elastic modulus of the bearing materials. In contrast, the much higher hardness of the ceramic ball is not helpful for deformation of the EHL film, in particular, as the ball bearing is under a relatively lower running speed. 4.5 Effect of Oil Types on Temperature Rise. The effects of the oil types on the bearing temperature rises under different rotating speeds were investigated. In the experiments, three types of oils with a viscosity of 46 cSt were examined, which are the automobile oil, slide way oil, and antiwear hydraulic oil, the lube intervals of 3 min and 2 min were used for rotating speeds of 20,000 rpm and 30,000 rpm, respectively, and the preload of 300 N was applied for all the tests. The nozzle with two outlets 180 APRIL 2011, Vol. 133 / 021101-5 of Use: http://www.asme.org/about-asme/terms-of-use d d 1 t f i o v b t s m 8 r b c n f o e t i t 0 Downloaded Fr eg apart positioned each side was adopted; the length to outeriameter ratio of the outlet is 1.6 and the diameter of the outlet is .5 mm. A possible explanation as to why the ceramic bearing is not ensitive to the distance may be the fact that the cage landing ethods of two types of bearings are different as shown in Fig. ; in detail, the ceramic ball bearing is controlled by the outer ing; in this case, the cage landing on the outer ring, hereinafter to e referred as \u201couter ring landing,\u201d while the steel ball bearing is ontrolled by the inner ring \u201cinner ring landing\u201d . It should be oted that part of the oil-air mixture maybe impinged on the cage or the steel ball bearing with the inner ring landing, so there is an ptimum distance of 6.4 mm where the majority of lubricating oil nter the contact area between rolling element and raceway, and he bearing temperature is at its lowest; otherwise more lubricatng oil will impinge the cage, resulting in being thrown out due to Table 3 Effect of type of oil on Rotation speed rpm Ceramic ball bearing \u00b0C Automobile oil Antiwear hydraulic oil S 20,000 6.9 7.1 30,000 10.3 9.7 he effect of centrifugal force. For the ceramic ball bearing, suffi- 21101-6 / Vol. 133, APRIL 2011 om: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms cient oil is supplied to adequately lubricate the contact area for the hybrid ceramic ball bearing with the outer ring landing. In summary, the oil nozzle should be correctly positioned to avoid difficulty for the oil to enter the bearing, especially for the bearing controlled by the inner ring. To verify the above conclusion, a new nozzle design was considered Fig. 9 , which has also the outlet jet 15 deg to the spindle axis; the only difference is that the outlet directs the oil/air mixture at the intersection of the outer ring inside diameter and the raceway, called \u201couter ring directed nozzle.\u201d The effect of distance between ball surface and nozzle outlet on the temperature rise of tested bearings with an outer ring directed nozzle used is shown in Fig. 10. Test results in this case are different from that under the inner ring directed nozzle. In detail, for the steel ball bearing, the temperature rise keeps lower under a short distance range, where more oil will enter the contact area. However, the operating temperature of the steel bearing increases as the distance between the ball surface and the nozzle outlet increases. These results indicate that, for distance longer than the proper value, lower quantity of lubricant will enter the contact area, resulting in a higher temperature rise. Meanwhile, for the hybrid perature rise of tested bearings Steel ball bearing \u00b0C way il Automobile oil Antiwear hydraulic oil Slide way oil .9 11 11 9.6 .7 20.6 21.5 20.5 tem lide o 6 9 steel bearing \u201einner ring landing\u2026 Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use c a f t t r t t a l f t d v n b m 1 n f a a h w c t F r s J Downloaded Fr eramic ball bearing under the outer ring directed nozzle, there is n apparent decrease in temperature rise as the distance increases rom 4.8 mm to 5.9 mm, and the temperatures keep constant when he distance is beyond 5.9 mm; this phenomenon is contrary to hat under the inner ring directed nozzle, where the temperature ise of the ceramic bearing is hardly affected by the distance. As a result, the oil nozzles should be correctly positioned to jet he lubricant into the contact area easily, and the distance between he ball surface and the nozzle outlet, together with the outlet jet ngle are closely related to the bearing cage landing manner. 4.6.2 Length to Outer-Diameter Ratio of the Outlet. Since the ength to outer-diameter ratio of the outlet is another important actor to affect the temperature rise of ball bearings, the effect of he length to outer-diameter ratio on the temperature rise under ifferent rotating speeds was investigated. Figure 11 shows the ariation in the temperature rises under different ratios, where the ozzle with two oil/air outlets each side was used, the distance etween the nozzle outlet and the ball surface is a constant of 5.4 m, and the diameter of the outlet is 1.5 mm. As shown in Fig. 1, for the steel ball bearing, the temperatures decrease monotoously with the increase in the ratios, while the different trend is or the ceramic ball bearing, except for that under the ratio of 3.2 t a speed of 30,000 rpm, all the temperature rises are lightly ffected by the variation of the ratios. This can also be attributed to the fact that two types of bearings ave different cage landing manners. For the steel ball bearing ith the inner ring landing, the bigger ratios can be helpful to onverge oil-air flow and ensure more lubricant to enter the conact area, while, for ceramic ball bearing with the outer ring land- ig. 9 Schematic view of the bearing with an outer ring diected nozzle: \u201ea\u2026 ceramic bearing \u201eouter ring landing\u2026 and \u201eb\u2026 teel bearing \u201einner ring landing\u2026 ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms ing, the bigger gap between the inner side of cage and the outer side of the inner ring can \u201cswallow\u201d all the oil-air mixture by every ratio. 4.6.3 Number of Outlet. By maintaining the same total oil flow rate but varying the number of nozzles, it was possible to determine the effect of the number of outlets on bearing temperature. Figure 12 illustrates the differences in temperature rise for two types of bearings with two, three, and four outlets circumferentially equispaced on each side of the nozzle. In the experiments, the length to outer-diameter ratio is 3.2, and the distance between the outlet and the ball surface is 5.4 mm. The results show that the number of outlets has a minimal effect on the temperature rises for two types of the bearings at 20,000 rpm; this may be due to the lower heat generation by bearing at this speed. At a speed of 30,000 rpm, using two compared with three and four outlets can reduce the temperature rise by approximately 2\u00b0C. It is well known that the higher rotational speed will generate a larger amount of heat. A possible explanation as to why this reduction in temperature occurs at 30,000 rpm may be the fact that using two outlets can increase the air flowing speed, which can be beneficial for converging the oil-air mixture and injecting more lubricant into the contact area. Fig. 11 Effect of the length to outer-diameter ratio of the outlet on temperature rise of tested bearings APRIL 2011, Vol. 133 / 021101-7 of Use: http://www.asme.org/about-asme/terms-of-use 1 r f o o t e o p t t o t t s i d s r b c g r 5 t d o h p r F b 0 Downloaded Fr 4.7 Effect of Rotation Speed on Temperature Rise. Figure 3 shows the variations in the temperature rise of the hybrid ceamic and steel ball bearings under different operating speeds rom 5000 rpm to 30,000 rpm. In the experiments, two types of ils rating for 46 cSt and 68 cSt were examined, the lube intervals f 2 min was used, and the preload of 300 N was applied for all he tests. The nozzle with two outlets 180 deg apart positioned ach side was adopted; the length to outer-diameter ratio of the utlet is 1.6 and the diameter of the outlet is 1.5 mm. The temerature rise of the tested bearings increases with the increase in he rotation speed, and the hybrid ceramic ball bearing has a lower emperature rise than that of the steel ball bearing at the same perating condition. As the rotation speed increases, the temperaure difference between two types of bearings also increases; and he rate of temperature rise increases sharply when the rotation peed exceeds 20,000 rpm. From the viewpoint of rolling bearing theory, dynamic loading ncluding centrifugal force and gyroscopic moment increases rastically with the rotating speed, especially for the super-highpeed condition. The dramatic increase in dynamic loading will esult in a pronounced increase in temperature rises of the tested earings. For the hybrid ceramic ball bearing, the lower density of eramic ball leads to a lower dynamic loading; in addition its ood self-lubrication property, thereby, lowers the temperature ise. Summary and Conclusions In this study, an experiment setup has been developed to invesigate the tribological behavior of the high speed ball bearing uner the oil-air lubrication; the effects of the operational parameters f an oil-air lubrication system on the temperature rise of both the ybrid ceramic ball bearing and steel ball bearing have been comaratively investigated. From this investigation, the authors can each the following conclusions. 1 For the steel ball bearing, as the pipe length is 1.5 m, the bearing has the lowest temperature rise; with a longer or shorter pipe applied, the temperature rise will increase; however, the temperature rise of the hybrid ceramic ball bearing increases smoothly and monotonously with increase in the pipe length. Thus, the appropriate pipe length for the oil-air lubrication system is about 1.5 m. 2 The temperature rises of the ceramic ball bearing are apparently lower than those of the steel ball bearing for each rotating speed under different preloads. For the steel ball bearing under the high speed operation, an appropriate pre- ig. 13 Effect of rotation speed on temperature rise of tested earings load is required; deviated from the conclusion in the exist- 21101-8 / Vol. 133, APRIL 2011 om: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms ing literature, the recommended axial preload decreases with increasing of the rotational speed. For the hybrid ceramic bearing under a small rotation speed, a lower temperature rise appears for the preload in a wide range 200\u2013 600 N, but the trend does not hold under the high speed of 30,000 rpm. Based on the experimental data acquired, the recommended value of the appropriate axial preload N in the case of the angular contact ball bearing at a high speed is about ten times that for the inner diameter in mm . To this bearing, the dimensions of the inner diameter is 30 mm; therefore, the recommended value of the axial preload is 300 N. 3 There is a proper amount of lubricant for a lower temperature rise for each rotational speed. The temperature rises of both the ceramic ball and the steel ball bearing at the lower rotation speeds tend to be less sensitive to oil quantity, and the difference of temperature rises of the hybrid ceramic ball bearing between the two speeds is much smaller than that of the steel ball bearing. This can be attributed to the fact that the hybrid ceramic ball bearing with a lower mass density not only reveals the self-lubricating property, but also produces a lower dynamic loading including centrifugal force and gyroscopic moment. The test results show that the appropriate lube oil quantity increases with the increasing of the rotational speed. Besides the rotational speed, the author thinks that oil quantity is closely related to the bearing size and bearing type e.g., ball bearing or roller bearing, and steel bearing or ceramic bearing, etc. . In this paper, only one type of bearing, 7006C/P4, has been measured; the experimental data are finite. At the present stage, it is difficult for the author to propose a calculation algorithm for the necessary lube oil quantity. 4 Under the lubricant with the viscosity of 100 cSt, the tested bearings under different speeds have almost the lowest temperature rise. The temperature increases rapidly as the oil with a higher or lower viscosity grade is adopted; however, there exists a fluctuation of the temperature rise, as the hybrid ceramic bearing is a under lower viscosity oil and a lower speed of 20,000 rpm. This phenomenon can be attributed to the fact that EHL film thickness is related to the entrainment velocity, the lubricant viscosity, and the elastic modulus of the tribopair materials. In contrast, the much higher hardness of the ceramic ball is not helpful for the EHL film deformation, in particular, for the condition of a relatively lower running speed. However, one thing is certain: The oil with a viscosity of 100 cSt is strongly recommended for both the steel ball bearing and the hybrid ball bearing. 5 It is impracticable to examine the effect of the types of lubricants on temperature rises by using the test method in this paper; it is because the EHL film can form easily at the high speed over tens of thousands; thus, the rolling balls and the raceways are separated completely or mostly by the oil film. Under this lubrication condition, the oil properties such as the effectiveness of oil additives, etc., cannot be assessed. 6 It should be pointed out that the nozzle design is an important factor to affect the temperature rise of the ball bearing, however, which has not been regarded seriously and reported in the existing literature. The proper distance between the ball surface and nozzle outlet, the length to outerdiameter ratio, the number and the outer diameter of the outlet, together with the outlet jet angle is closely related to the cage landing method of the bearing. Based on these results, inner ring directed nozzle is strongly recommended for the oil-air lubrication system; and for the bearing 7006C/P4, the preferred nozzle design is two outlets for each side with a length to outer-diameter ratio of 4:1, an Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use A N 5 m J N R J Downloaded Fr outlet diameter of 1.5 mm, and a distance between ball surface and nozzle outlet of 6.4 mm. 7 Under the same testing conditions, temperature rise of tested bearings increases with the increasing of the rotation speed; and the hybrid ceramic ball bearing always has a lower temperature rise than that of the steel ball bearing. As the rotation speed increases, the temperature difference between two bearings increases; and the rate of temperature rise increases sharply when the rotation speed is beyond 20,000 rpm. 8 Traditionally, the dip lubrication including the grease lubrication and oil jet spray lubrication has been widely used for the rolling bearing. The previous test study by author indicated that the temperature rise under the grease lubrication or the oil jet spray lubrication is much higher than that of the oil-air lubrication, and it took a long time for the bearing to reach the thermal equilibrium 16 . Therefore, the oil-air lubrication is a best choice for the high speed rolling bearing due to the advantages of high cooling efficiency, high lubricating efficiency, environmental benefit, and precise oil quantity control. cknowledgment The authors gratefully wish to acknowledge the supports of the ational Science Foundation through Grant Nos. 50475073 and 0775036, the National High Technology Research and Developent Program through Grant No. 2006AA05Z237, and the iangsu Province Science and Technology Program through Grant os. BG2006035 and BK2009612. eferences 1 Yeo, S. H., Ramesh, K., and Zhong, Z. W., 2002, \u201cUltra-High-Speed Grinding ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms Spindle Characteristics Upon Using Oil/Air Mist Lubrication,\u201d Int. J. Mach. Tools Manuf., 42 7 , pp. 815\u2013823. 2 H\u00f6hn, B. R., Michaelis, K., and Otto, H. P., 2008, \u201cMinimised Gear Lubrication by a Minimum Oil/Air Flow Rate,\u201d Wear, 266 3\u20134 , pp. 461\u2013467. 3 Nguyen, T., and Zhang, L. C., 2003, \u201cAn Assessment of the Applicability of Cold Air and Oil Mist in Surface Grinding,\u201d J. Mater. Process. Technol., 140 1\u20133 , pp. 224\u2013230. 4 Ramesh, K., Yeo, S. H., Zhong, Z. W., and Akinori, Y., 2002, \u201cUltra-HighSpeed Thermal Behavior of a Rolling Element Upon Using Oil-Air Mist Lubrication,\u201d J. Mater. Process. Technol., 127 2 , pp. 191\u2013198. 5 Bossmanns, B., and Tu, J. F., 2001, \u201cA Power Flow Model for High Speed Motorized Spindles-Heat Generation Characterization,\u201d ASME J. Manuf. Sci. Eng., 123 3 , pp. 494\u2013505. 6 Kim, J. D., Zverv, I., and Lee, K. B., 2010, \u201cThermal Model of High-Speed Spindle Units,\u201d Intelligent Information Management, 2, pp. 306\u2013315. 7 Willenborg, K., Klingsporn, M., Tebby, S., Ratcliffe, T., Gorse, P., Dullenkop, K., and Wittig, S., 2008, \u201cExperimental Analysis of Air/Oil Separator Performance,\u201d ASME J. Eng. Gas Turbines Power, 130 6 , p. 062503. 8 Dudorov, E. A., Ruzanov, A. I., and Zhirkin, Y. V., 2009, \u201cIntroducing an Oil-Air Lubrication System at a Continuous-Casting Machine,\u201d Steel in Translation, 39 4 , pp. 351\u2013354. 9 Yamazaki, T., Muraki, T., Matsubara, A., Aoki, M., Iwawaki, K., and Kawashima, K., 2009, \u201cDevelopment of a High-Performance Spindle for Multitasking Machine Tools,\u201d Int. J. of Automation Technology, 3 4 , pp. 378\u2013384. 10 Szydlo, Z. A., 2007, \u201cEffective Oil/Air Ratio in Industrial Oil Mist Lubricating Systems,\u201d Ind. Lubr. Tribol., 59 1 , pp. 4\u201311. 11 Jeng, Y. R., and Huan, P. Y., 2000, \u201cTemperature Rise of Hybrid Ceramic and Steel Ball Bearings With Oil-Mist Lubrication,\u201d Lubr. Eng., 56 12 , pp. 18\u2013 23. 12 Jeng, Y. R., and Gao, C. C., 2001, \u201cInvestigation of the Ball-Bearing Temperature Rise Under an Oil-Air Lubrication System,\u201d Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 215 2 , pp. 139\u2013148. 13 Wu, C. H., and Kung, Y. T., 2005, \u201cA Parametric Study on Oil/Air Lubrication of a High Speed Spindle,\u201d Precis. Eng., 29 2 , pp. 162\u2013167. 14 Xie, J., Jiang, S. Y., Wang, X. S., and Feng, Y. D., 2006, \u201cExperimental Research on Oil-Air Lubrication for High Speed Ball Bearing,\u201d Lubr. Eng., 181 9 , pp. 117\u2013119. 15 Hamrock, B. J., 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York, Chap. 2, p. 4. 16 Jiang, S. Y., Zhu, B. K., and Wang, L. M., 1994, \u201cThe Investigation of the Rolling Bearing Under a Grease Lubrication,\u201d Bearing, 5, pp. 28\u201329. APRIL 2011, Vol. 133 / 021101-9 of Use: http://www.asme.org/about-asme/terms-of-use" + ] + }, + { + "image_filename": "designv10_3_0001172_iros.2011.6094477-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001172_iros.2011.6094477-Figure1-1.png", + "caption": "Fig. 1: Continuum arm schematics", + "texts": [ + " Then, the length of the any actuator at any time is LiO + lij (t) where LiO is the original length of actuators and t is time (Fig. la). Length variables, defined as lij(t) E [li,min, li,max], can be positive or negative to represent extension and contraction where i E [1, N] is the section number, j E [1,3] is the actuator number, li,max E jR+ is the mean maximum extension for extending actuators, and li,min E jR- is the mean maximum contraction for contracting actuators. Following a similar procedure as in [15], as shown in Fig. 1 b, the spatial orientation of section i upon actuation can be defined by {Ai, \u00a2ii, Bd with respect to the local coordinate system (coordinate set 0iXiYiZi in Fig. la) as given in (2) where Ri is the section radius. This approach can be applied to any geometrically constrained variable length continuum arm structures, planar or spatial, with a differing number of actuators per section by deriving {Ai, \u00a2ii, Bd (in planar case, {Ai, \u00a2id) in variable actuator lengths. By employing standard homogeneous rotational and trans lation matrices, the homogeneous transformation matrix (HTM), T, for points along the neutral axis of the ith section is derived as (3) where Ai = Ai (qi) , qJi = \u00a2i (qi) , and ()i = ()i (qi) \u00b7 Rz, Ry are rotational matrices about the Z and Y axes", + " Therefore both the forward and inverse kinematics can be easily computed without the need for separate singularity resolving methods such as those used in [9], [12]. Further, in this method, without having multiple MSFs to cover the workspace, the errors, eij, of T and T ep elements are simply calculated as eij = tij - tepij. Therefore, this approach eliminates (i) the requirement for mode switching schemes, (ii) mapping complications (\" .. it is solved directly in joint space), (iii) possible modal singularities [12], and (iv) complicated error models. Having obtained the MTM for any ith section, the result can now be extended to multiple arm sections. Fig. 1 b depicts a general multi section arm schematic. By employing classical coordinate transformation techniques, the MTM for any point along the neutral axis of the full continuum arm is derived with respect to global coordinates OXY Z (Fig. Ib), to which the base section of the continuum arm is attached, as N rr N {k } oTcp(e,q) = k=l k-ITcp(\ufffdk,qk) Tk = [ Rcp (e,q) Pcp (e,q) ] Olx3 1 (6) where q = {[ qi qf qrv V : q E R.3Nx I} is the joint space vector that uniquely describe configuration of the entire arm and Tk is any joint transformation present at the section joints", + " This is an appealing feature for computer implementations because MSFs can be defined as functions that take {qi' LiD, Ri} as the input for the ith section. As previously mentioned, this means that only 9 such modular functions (6 from CPR and 3 from cPp) are required to completely define the position and orientation of any geometrically constrained variable length multisection continuum robotic arm with any number of sections. Due to the geometrically constrained design, our model is only capable of rotations about the x' and y' axes of the neu tral axis reference frame 0' x' y' z ' (Fig. 1 b), and incapable of torsional (rotations about the z ' axis) movements. Defining the rotating Euler angle vector 'P = [a (3]T, where a and (3 are the rotations about the X and Y axes at e respectively, the following relationship can be derived. (7) Orientation angles a and j3 are easily computed as a(e, q) = arctan2(r32' r22) j3(e, q) = arctan2(r13' -rl1) (8) where rij are elements ofR and {a, j3} E [-7r, 7r]. In the case of torsional movements, this is easily accommodated using an additional Euler angle parameter \" to represent rotation about the Z axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000433_tmag.2006.871637-Figure8-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000433_tmag.2006.871637-Figure8-1.png", + "caption": "Fig. 8. Order 2 mode of the PMSM.", + "texts": [ + " The motion differential equation determined by state vector method is follows [5]: (7) where is the mass matrices, is the damping matrices, is the stiffness matrices, is the displacement vector, and is the electromagnetic force vector. An associate equation is introduced. Equation (7) is rewritten into (8) (8) Equation (8) is simplified into (9) (9) According to the orthogonal characteristics, can be expressed as follows: (10) where is the complex vibration shape vector and is the corresponding eigenvalue. can be expressed as follows: (11) The transfer function is given by (12) The order 2 mode of the 11-kW PM motor computed numerically is shown in Fig. 8. The modal frequencies of the first five orders are 384.26, 899.20, 969.00, 1687.5, and 1959.3 Hz, respectively. The order 2 modal frequency is 899.203 Hz which coincides with 900 Hz of the noise spectrum of the PM motor. The purpose of modal analysis is building a mathematical model to predict the respond of a structure excited by complex forces. A period electromagnetic force can be decomposed into Fourier series with period (13) It can be rewritten as complex forces if ignoring constant force " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002897_j.engfailanal.2016.12.008-Figure9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002897_j.engfailanal.2016.12.008-Figure9-1.png", + "caption": "Fig. 9. Finite element model of the gearbox housing.", + "texts": [ + "2 mm, and greater fracture complexity is observed. A comparison of these two metallographic analyses indicate that the number of porosity-type casting defects in the crack initiation region are significantly greater than those in the area outlying the crack initiation region. The crack initiation region occurs within an area of variable cross section, where larger porosity-type casting defects are more readily formed in greater abundance, which would reduce the fatigue strength. 3. Finite element analysis and field testing Fig. 9 shows the finite element model of the housing and rings. The housing model includes 224,098 elements and 419,826 nodes (C3D10M element in ABAQUS). The rings model includes 237,672 elements and 131,851 nodes (C3D10 element in ABAQUS). The gearbox housing was modeled as a cast aluminum alloy. The Young's elastic modulus, Poisson's ratio, and density of the models were 74,000 MPa, 0.34, and 2.65 g/cm3, respectively. The connection between the C-bracket and the housing was simplified to be an elastic structure (a linear line element in ABAQUS)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000360_13506501jet656-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000360_13506501jet656-Figure2-1.png", + "caption": "Fig. 2 Micro-slip zones in a deep-groove ball bearing, the Hertzian contact pressure p(x, y) and the traction q(x, y) between a ball and a plane when a ball is rolling on a flat plane under a coefficient of friction \u03bc without any influence of a liquid lubricant", + "texts": [ + " Third, in the surface (z = 0) at the centre of contact (r = 0), the radial stress \u03c3r is 0.8 \u00d7 p0 [11, 12]. When a rolling surface is compressed in one direction, its material tends to expand in the transverse directions according to Hooke\u2019s law and Poisson\u2019s ratio, and this creates tangential forces and local slip between contact surfaces at the trailing edge of the rolling surface [10, 13]. In deep groove ball bearings, the raceway geometry is a semi-conforming groove, and the contact area is a curved ellipse with three slip zones (see Fig. 2); a central zone with a micro-slip in the direction of rotation of the ball and two outer zones with a micro-slip in the opposite direction [10]. Similarly, micro-slip zones Proc. IMechE Vol. 224 Part J: J. Engineering Tribology JET656 at TOBB Ekonomi ve Teknoloji \u00dcniversitesi on April 26, 2014pij.sagepub.comDownloaded from occur in spherical roller bearings but not in cylindrical roller bearings. Real bodies have form errors, surface waviness, and surface roughness due to the surface manufacturing and previous operation", + " Under favourable running-in conditions, a \u2018roll polishing\u2019 effect occurs in rolling bearings, mainly through plastic deformation of surface asperities. The roll polishing effect gradually disappears as the surface roughness decreases and a transition from mixed lubrication into EHD lubrication conditions occurs. The running-in process can be re-activated by changed operational conditions [24, 25, 29, 43, 50]. Each incident of plastic deformation of a surface asperity during running-in forms a dynamic stress field and a vibration source. Micro-abrasive and sliding fatigue wear in the micro-slip regions (Fig. 2) of rolling contacts are responsible for part of the surface alterations, for rolling contact wear, and for wear particle formation in the running-in of rolling bearings [51]. The plastic deformation caused by abrasion and the micro cracking caused by fatigue are weak sources of vibrations. Abrasive wear and surface indentations are caused by particles in the oil during the running-in stage of the bearing [52]. Abrasive wear by contaminant particles during the running-in stage of a bearing usually roughens the rolling surfaces and produces more wear particles, and therefore weakens the preconditions for subsequent operation of the bearing [25]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002973_024001-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002973_024001-Figure10-1.png", + "caption": "Figure 10. 7-axis freeformmachining center.", + "texts": [ + " The surface condition was superior to that of the flat EBM sample. Figure 9(b) shows a rendering of the corresponding CAD model, with the area to be finished in blue. It can be noticed that this shape includes convex, concave, and saddle areas. The surface curvature ranged from 30mm radius (concave) to 10 mmradius (convex). A 7-axis CNC controlled machine built by Zeeko ltd was used for grinding this freeform sample. The SAG tools were mounted such that the center of the machine A and B rotary axes coincided with the center of the spherical tool, as shown infigure 10. This mounting allows for motion of the grinding spot around the workpiece with high precision of the tool offset (which control the grinding area), because the spherical tool remained static (varying only its orientation) while the workpiece is accurately translated along theX,Y, andZ axes. In order to characterize and compensate the deviation between CAD model and actual workpiece, an on-machine probing system was used. A soft probe was mounted on the tool spindle, and used to detect the surface by touch/trigger sensing mode" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure11.6-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure11.6-1.png", + "caption": "Figure 11.6.1 The basic semi-trailing arm,with pivot axis sweep anglecAx: (a) rear three-quarter view; (b) planview; (c) rear view.", + "texts": [ + " This is as would be expected, as the angle changes are basically a property of the lack of parallelism of the wheel axis and the pivot axis. Therefore the sloped-axis trailing arm, for a reasonably small inclination angle, has the properties of Table 11.5.1. The bump scrub coefficients included in the table follow easily by inspection of the rear view. The semi-trailing arm has its pivot axis swept in planview, at the sweep anglecAx, considered positivewhen thepivot axis isangled rearwardswhilstpassing towards thecentreline,asGHinFigure11.6.1.For simplicity, in the initial analysis, the pivot axis is considered to be in the horizontal plane, that is, at zero slope angle at wheel centre height. Also, the wheel initial toe and camber angles are taken as zero. Single-Arm Suspensions 207 As the suspension arm rotates, for angle analysis the wheel axis AB may be considered to rotate about the axis AJ parallel to the real pivot axis GH, with B rotating about J. The basic dimensions are AB \u00bc L BJ \u00bc L sin cAx Relative to the line AJ, point B moves in a circle, with coordinates, relative to AJ, of ZB \u00bc L sin cAx sin uA The bump steer and camber angles are given by sin d \u00bc XB L \u00bc sin cAx\u00f01 cos uA\u00de sin g \u00bc ZB L \u00bc sin cAxsin uA Using the usual small-angle approximations, as in previous sections, the angles may be expressed approximately as d \u00bc cAx 1 2 u2A g \u00bc cAx uA and in terms of the suspension bump as d \u00bc cAx 2R2 P z2S g \u00bc cAx RP zS so the effects introduced by the axis sweep angle are a quadratic bump steer coefficient and a linear bump camber coefficient: \u00abBS2 \u00bc cAx 2R2 P \u00abBC1 \u00bc cAx RP The small-angle approximations on the pivot axis anglemay not be so good in this case, as sweep angles up to 30 may be used, but the results of this simple analysis give an excellent insight into the effects of pivot axis sweep \u2013 specifically, a second-order bump steer and a first-order bump camber" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001017_physreve.80.041922-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001017_physreve.80.041922-Figure2-1.png", + "caption": "FIG. 2. Schematic representation of a bacterium left , bacterium with orientation , , alternatively described by the unit vector d\u0302 right .", + "texts": [ + " At random times depending on conditions, the average time between tumbling events varies from 1 to 60 s; see 14 , the flagella unbundle and rotate separately, causing the bacterium to reorient, until the next bundling event. This effectively results in a random reorientation of the bacterium that can be modeled as a random walk on the unit sphere 15 . It should be noted that not all bacteria are propelled in such a manner, and our results are not expected to hold for bacteria that do not tumble. We model a bacterium as a rigid prolate spheroid with semiaxes a, b see Fig. 2 subject to no-slip boundary conditions in a Stokesian fluid of viscosity whose velocity is denoted by u and pressure by p. The bacterium translates with linear velocity v and rotates with angular velocity . On the container boundary, the fluid is subject to boundary conditions u=E \u00b7x+ x, where E is a given symmetric and trace-free matrix and is a given vector. Selfpropulsion is modeled by means of a rigidly attached point force of magnitude c and direction d\u0302 located at x f, displaced by b 1+ d\u0302 from the center of the bacterium xc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002783_1.4030676-Figure12-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002783_1.4030676-Figure12-1.png", + "caption": "Fig. 12 ACL Variable-pitch quadrotor. The servos that actuate the variable-pitch propellers are visible under each of the motors. The quadrotor frame measures 0.35 m across.", + "texts": [ + " Attitude constraints embedded in the path formulation are utilized to command a path similar to the backflip demonstrated on the Stanford STARMAC quadrotor [8]. Simulation results of the path are presented in Fig. 11. The flipping motion is prescribed by embedding a 290 deg roll constraint just before the apex of the path and a 90 deg roll constraint just after the apex. The variable-pitch quadrotor used in this project was designed and built at MIT\u2019s ACL using mostly off-the-shelf components. A closeup of the vehicle is shown in Fig. 12. The frame is cut from a sheet of carbon fiber sandwich material with a balsa wood core. The square shape is designed to minimize vibrations induced by the propellers, motors, and servos because the vibrations cause the attitude estimate by the on-board sensors to quickly deteriorate. The pitch control mechanisms are commercial parts designed for small remote-controlled airplanes (see Fig. 13(a)). They use a carbon fiber pushrod routed through the center of a hollow motor shaft. A servo is mounted beneath the motor to actuate the propeller pitch" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003778_j.ymssp.2018.06.018-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003778_j.ymssp.2018.06.018-Figure1-1.png", + "caption": "Fig. 1. Illustration of cage instability.", + "texts": [ + " Thus, the aim of this study was to evaluate the bearing stability, torque, cage whirling amplitude, and wear loss as functions of the inner race speed and cage clearances in cryogenic conditions. Based on the results, the effects of the clearances and rotation speed on the cage stability and performance were analyzed using probability density functions (PDFs). In practice, the cage intermittently collides with the ball bearing elements during rotational motion, and these collisions reduce the cage stability. Fig. 1 illustrates the mechanism responsible for the cage instability caused by these intermittent collisions as well as the relative movements of the various elements involved in its functioning. The repeated collisions between the cage and balls generate forces in the radial, axial, and rotational directions in the cage. Further, the collisions cause the cage to rotate in different planes away from the center of the axial plane. Repetitive collisions between the cage and bearing elements increase the cage instability" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure1.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure1.3-1.png", + "caption": "Fig. 1.3 Determination of the center of gravity by determining the mass distribution (1 Filament; 2 Scales)", + "texts": [ + " If there are two suspension points that are not located on the same axis through the center of gravity, the center of gravity will be at the point where these axes intersect. The point of intersection of the vertical axes can be determined using photos (or photogrametrically) after suspending the object on two points. Balancing can be used for small parts. When putting the part onto a sharp edge, it can be clearly felt when the center of gravity is above the edge. For larger bodies, such as cranes and motor vehicles, the mass distribution is frequently determined by measuring the support forces. Figure 1.3 shows the measurement on a connecting rod. If the support force m1g has been determined, the centroidal distance is 16 1 Model Generation and Parameter Identification \u03beS = m1l m . (1.5) For a symmetrical connecting rod, an axis through the center of gravity is provided by the symmetry line. Otherwise, the missing second axis through the center of gravity can be found by tilting the body axis. This will be demonstrated using the example of a motor vehicle. According to Fig. 1.4, the following are given: l = 2450 mm; h = 500 mm; d = 554 mm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure5.9-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure5.9-1.png", + "caption": "Figure 5.9.1 Geometry of the steering axis of a wheel.", + "texts": [ + " The lengths are: LAC \u00bc R tan g LAB \u00bc R sin g LAD \u00bc LAC cos g \u00bc R cos2 g sin g LCD \u00bc R cos g LBD \u00bc R sin g In a three-dimensional computation, with the axis direction cosines to the inner side of the wheel, use the factor f \u00bc 1 l2 \u00fe m2 With the direction cosines from C towards A, the camber angle is given by tan g \u00bc nffiffi f p and LAC \u00bc R tan g \u00bc R ffiffi f p n The coordinates of point A then follow: xA \u00bc xC \u00fe l LAC; yA \u00bc yC \u00fe mLAC; zA \u00bc zC \u00fe n LAC Point D has the same x and y coordinates as C, and zD\u00bc zA. Point B is then given vectorially by PB \u00bc PA \u00fe f \u00f0PD PA\u00de expressed in the three coordinates. In implementing this, the possibility of negative camber angle must be considered, and the possibility that the direction cosines are away from A. For all systems, thewheels and hubs are pivoted about a steering axis, commonly called the \u2018kingpin\u2019 axis, Figure 5.9.1. Nowadays, on cars at least, physical kingpins are no longer used, the steering axis now usually being defined by upper and lower ball joints on a double-wishbone suspension, or by one ball joint and the upper pivot point of the strut on a strut system. In front view, the axis is at the kingpin inclination angle uKI, usually from zero to 20 , giving a reduced kingpin offset b at the ground, measured from the undistortedwheel centre plane. The inclination angle helps to give space for the brakes", + " Sometimes a negative offset is used, this giving straighter braking when surface friction varies between tracks. Zero offset is called centrepoint steering. If the kingpin inclination angle is also zero, it is called centreline steering. Centrepoint steering gives no steeringmoment from longitudinal FX forces at the contact patch; centreline steering gives, in addition, zeromoment for longitudinal forces at thewheel axle height. This latter effect is important because of the variation of rolling resistance on rough roads, and traction effects. In the side view of Figure 5.9.1(b), the kingpin axis is slanted at the kingpin caster angle uKC, with a value generally in the range of 0 \u2013 5 . This introduces a mechanical trail, called the caster trail, which acts in concert with the tyre pneumatic trail. On cars and trucks it is usual for the kingpin axis to pass through the wheel spin axis C in side view, but this is not essential, and some offsetting of the axis from the centre enables the caster angle and trail to be independently varied. The caster angle and the associated caster trail are important in the feel of the steering" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003010_0954409717752998-Figure21-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003010_0954409717752998-Figure21-1.png", + "caption": "Figure 21. Stress distribution in the gearbox housing.", + "texts": [ + " To determine the position with low structural strength under resonance of the gearbox housing, a stress analysis of the gearbox housing with the boundary condition obtained from vehicle systems induced by the 20th-order polygonal wear at the speed of 300 km/h was performed. The boundary condition mainly considers the forces acting between the components connected to the gearbox housing. The vertical motion at the position where the gearbox housing is connected to the bogie frame is fixed, coupling constraints of the pinion bearing hole and the gearwheel bearing hole are adopted, and all DOFs of the gearwheel bearing hole are restrained, except for the rotation around the axle. Figure 21 shows the equivalent stress distribution of the gearbox housing. It can be concluded that the stress near the position of the oil level sight glass is relatively high, which means cracking is more likely to occur at that location due to the resonance caused by the 20th-order polygonal wear. Moreover, the stress analysis results are consistent with the frequent cracking positions of the gearbox during operation. In the present investigation, severe vibration, especially the resonance of the gearbox housing due to polygonal wear, is more likely to accelerate cracking of the gearbox housing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003404_j.jmapro.2020.09.002-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003404_j.jmapro.2020.09.002-Figure1-1.png", + "caption": "Fig. 1. The snapshot of powder bed generation process.", + "texts": [ + " A computational fluid dynamics (CFD) model, in which the recoil pressure and the Marangoni effect were considered, was developed to investigate the formation mechanism of common defects and analyze the forming quality of the single melt track. Meanwhile, corresponding experiments were conducted for the fabrication of melt tracks to validate the numerical model. This paper is expected to provide the guidance for reducing or eliminating common defects during the SLM process. The DEM software YADE in this work was utilized to simulate the powder bed generation process of 316 L stainless powder particles. A powder bed was formed by discrete metal particles instead of treating the powder bed as an equivalent region. Fig. 1 shows a snapshot of the powder bed generation process. According to the SEM image in Fig. 2(a), the individual powder particle can be considered as spherical in good approximation. The particle size distribution was considered to follow the experimental measurement, the particle sizes were found to follow Gaussian distribution with D10, D50, and D90 of 7, 22 and 40 \u03bcm in diameter, respectively. Fig. 2(b) shows the particle size distribution used in the simulation. The simulation of powder bed generation process could mainly be divided into two steps: firstly, a collection of powder particles dropped vertically onto the plate to form a particle pile; secondly, the blade moved along the plate at a specified speed, some particles were pushed into the building chamber to form the powder bed used to manufacture the parts, and others fell into the container" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001143_978-3-540-89940-2-Figure2.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001143_978-3-540-89940-2-Figure2.10-1.png", + "caption": "Fig. 2.10 Forces and moments at a pivoting frame with a rotor", + "texts": [ + "36) and the angular accelerations known from (2.37): 96 2 Dynamics of Rigid Machines MS kin \u03be \u2261 JS \u03be\u03be\u03c9\u0307\u03be \u2212 (JS \u03b7\u03b7 \u2212 JS \u03b6\u03b6)\u03c9\u03b7\u03c9\u03b6 = JS a (\u03b1\u0308 cos \u03b3 \u2212 \u03b1\u0307\u03b3\u0307 sin \u03b3) + (JS a \u2212 JS p )\u03b1\u0307\u03b3\u0307 sin \u03b3 = JS a \u03b1\u0308 cos \u03b3 \u2212 JS p \u03b1\u0307\u03b3\u0307 sin \u03b3 (2.108) MS kin \u03b7 \u2261 JS \u03b7\u03b7\u03c9\u0307\u03b7 \u2212 (JS \u03b6\u03b6 \u2212 JS \u03be\u03be)\u03c9\u03b6\u03c9\u03be = JS a (\u2212\u03b1\u0308 sin \u03b3 \u2212 \u03b1\u0307\u03b3\u0307 cos \u03b3)\u2212 (JS p \u2212 JS a )\u03b1\u0307\u03b3\u0307 cos \u03b3 = \u2212JS a \u03b1\u0308 sin \u03b3 \u2212 JS p \u03b1\u0307\u03b3\u0307 cos \u03b3 (2.109) MS kin \u03b6 \u2261 JS \u03b6\u03b6 \u03c9\u0307\u03b6 \u2212 (JS \u03be\u03be \u2212 JS \u03b7\u03b7)\u03c9\u03be\u03c9\u03b7 = JS p \u03b3\u0308. (2.110) The forces and moments are shown in the opposite direction to the body-fixed coordinate directions in Fig. 2.10c. They are transformed into the x\u2217-y\u2217-z\u2217 coordinate system and balanced with the applied moments and reaction moments: 2.3 Kinetics of the Rigid Body 97 MS kinx\u2217 \u2261 \u2212MS kin \u03b7 sin \u03b3 + MS kin \u03be cos \u03b3 =JS a \u03b1\u0308 = \u2212MS x\u2217 (2.111) MS kiny\u2217 \u2261 MS kin \u03b7 cos \u03b3 + MS kin \u03be sin \u03b3 =\u2212JS p \u03b1\u0307\u03b3\u0307 = MS y\u2217 (2.112) MS kinz\u2217 \u2261 MS kin \u03b6 =JS p \u03b3\u0308 = MS z\u2217 = M\u03b3 an (2.113) See the depiction in Fig. 2.10a. The moment M\u03b3 an causes the angular acceleration \u03b3\u0308 and supports itself against the frame. The components of the kinetic moments of the moving rotor with respect to the x\u2217-y\u2217-z\u2217 coordinate system are entered in the opposite direction to the positive coordinate directions. The same sign convention as explained before in Sect. 2.3.2 was also applied to the inertia forces, which can be calculated using (2.107). The following applies at the rotor (and due to the equilibrium of forces at the frame as well) for the reaction forces: Fy = my\u0308S = m [\u2212\u03b1\u0308(l sin \u03b1 + h cos \u03b1)\u2212 \u03b1\u03072(l cos \u03b1\u2212 h sin \u03b1) ] (2.114) Fz = mz\u0308S = m [ \u03b1\u0308(l cos \u03b1\u2212 h sin \u03b1)\u2212 \u03b1\u03072(l sin \u03b1 + h cos \u03b1) ] . (2.115) From the equilibrium conditions for the frame, one finds the reaction moments relative to the origin O, see Fig. 2.10a: MO x = M\u03b1 an = \u2212Fy(l sin \u03b1 + h cos \u03b1) + Fz(l cos \u03b1\u2212 h sin \u03b1)\u2212MS x\u2217 = [ m(l2 + h2) + JS a ] \u03b1\u0308 (2.116) MO y = MS y\u2217 cos \u03b1\u2212MS z\u2217 sin \u03b1 = \u2212JS p (\u03b1\u0307\u03b3\u0307 cos \u03b1 + \u03b3\u0308 sin \u03b1) (2.117) MO z = MS y\u2217 sin \u03b1 + MS z\u2217 cos \u03b1 = JS p (\u2212\u03b1\u0307\u03b3\u0307 sin \u03b1 + \u03b3\u0308 cos \u03b1). (2.118) It can be seen from (2.116) that the expression in the square brackets represents the moment of inertia about O (parallel-axis theorem). The terms that depend on \u03b1\u03072 do not exert any influence on the moment about the origin since the resultant centrifugal force acts in radial direction and has no leverage with respect to O" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002162_s10846-013-9813-y-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002162_s10846-013-9813-y-Figure1-1.png", + "caption": "Fig. 1 Qaudrotor helicopter scheme", + "texts": [ + " Therefore, dynamic equations of UAV are as follows: \u23a7 \u23aa\u23aa\u23a8 \u23aa\u23aa\u23a9 m\u03be\u0308 + mg \u23a1 \u23a3 0 0 Ez \u23a4 \u23a6 = f\u03be + Funcertain(\u03be\u0307 ) H(\u03b7)\u03b7\u0308 + C(\u03b7, \u03b7\u0307)\u03b7\u0307 = \u03c4\u03b7 + \u03c4uncertain(\u03b7\u0307) (4) As a propeller rotates in the air, it produces a force (thrust) and a moment (drag). Thrust and drag are denoted by T and D respectively. The direction of drag is opposite of rotation\u2019s direction. Both of them are proportional by square of rotational speed in the hover condition. We denote the force produced by rotors by T1, T2, T3 and T4. Moments produced by rotors are denoted by D1, D2, D3 and D4. Since propellers 1 and 3 rotate in the opposite direction of propellers 2 and 4, then the signs of D1 and D3 are the opposite signs of D2 and D4 (See Fig. 1). When all rotors have the same rotation speed and the lift force is equal to the weight of the vehicle, then quadrotor has a fixed altitude and stable attitude. In this condition, the orientation of body frame with respect to the inertial frame is fixed, and the quadrotor is in the hovering mode. In order to change the altitude of quadrotor we must change the lift force which is defined by: U = 4\u2211 i=1 Ti (5) If T1 and T3 are not equal, the roll angle changes. Longitudinal movements also are achieved by change in roll angle. Thus the roll control input is defined as follows: \u03c4\u03c6 = l(\u2212T1 + T3) (6) where l is the distance between center of rotor and center of vehicle (see Fig. 1). If T2 and T4 are not equal, the pitch angle changes. Lateral movements also are achieved by change in pitch angle. Thus the pitch control input is defined as follows: \u03c4\u03b8 = l(\u2212T2 + T4) (7) Yaw movement is obtained by change in sum of D1, D2, D3 and D4. As it mentioned previously, the signs of D1 and D3 are the opposite signs of D2 and D4. The yaw control input is defined as follows: \u03c4\u03c8 = D1 + D2 + D3 + D4 (8) So \u03c4\u03b7 can be expressed as follows: \u03c4\u03b7 = \u23a1 \u23a3 l(\u2212T1 + T3) l(\u2212T2 + T4) D1 + D2 + D3 + D4 \u23a4 \u23a6 = \u23a1 \u23a3 \u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8 \u23a4 \u23a6 (9) By using the rotation matrix between the body fixed frame and the inertial frame, f\u03be can be expressed as follows [1]: f\u03be = \u23a1 \u23a2 \u23a3 (S\u03c8S\u03c6 + C\u03c8S\u03b8C\u03c6)U m (\u2212C\u03c8S\u03c6 + S\u03c8S\u03b8C\u03c6)U m (C\u03b8C\u03c6)U m \u23a4 \u23a5 \u23a6 (10) Due to high power and low weight and fast response, brushless DC motors (BLDC) are normally types of motors that are used in commercial UAV\u2019s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000952_cpa.3160230402-Figure10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000952_cpa.3160230402-Figure10-1.png", + "caption": "Figure 10a. Graphs of ()e)'I3 vs. P for the thin sphere, k = for the solutions branching from the lowest 5 symmetric eigenvalues. As in Figure Za, the P-axis is horizontal and the circles on the P-axis indicate the eigenvalues. Some of the branches and critical loads are labeled. The branch B,,,, is not completely shown in the figure. I t is shown in Figure lob.", + "texts": [], + "surrounding_texts": [ + "For both the sphere and the hemisphere problems, we must solve (2.9) subject to boundary conditions of the form For the hemisphere, L = ?pi-, and for the full sphere, L = T. These problems are solved numerically by the shooting method for the hemisphere, and a parallel shooting method for the full sphere. A crucial step is a continuation procedure used to get good estimates of the proper initial data. First we describe our method for the hemisphere problem and then indicate how that procedure is employed to solve the full sphere case. The numerical procedures and the continuation scheme are analyzed rather thoroughly in [14]. AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 537 4.1. Shooting for hemispheres. Consider the initial value problem, with fixed P and k, (4.2b) u(0) = [ ) a We denote the solution of (4.2) by u = u(0; 11, t2). If this solution exists in 0 5 8 5 3. for initial parameters El and E2 such that (4.3) u d h ; El 3 52) = 0 9 udB..; 61 , t 2 ) = 0 , then, by (4.1), y(0) = u(0; 11, t2) is a solution of the hemisphere problem. The number of distinct solutions of the hemisphere problem is equal to the number of distinct real roots (El , t2) of (4.3). These roots are numerically determined using Newton\u2019s method, and a continuity procedure. For this purpose we introduce the vectors (4.4a) Then it follows by differentiation in (4.2) that the U(j) satisfy the linear variational systems : Here A is the fourth order Jacobian matrix, (4.4d) Given an initial estimate ( E F ) , 6;)) for a root of (4.3), the sequence of Newton iterates (5:\u2019) , tp)) is defined by (4.5a) ,:+l) = 6:) + AEP), =1,2, v = O , 1 , 2 , . - * , 538 L. BAUER, E. L. REISS AND H. B. KELLER where (At?) , AE;)) is the solution of the linear system U ~ \u2019 ( $ T ) At?\u2019 + Ui\u201d((3~) At:\u2019 = - u,($T; tp\u2019 , [p\u2019) , (4.5b) U ~ \u2019 ( $ T ) Alp\u2019 + U ~ \u201c ( & T ) At;\u2019 = - u ~ ( ~ T ; tp\u2019 , Ep)) . The coefficient elements U;\u201d(&T) in (4.5b) are the corresponding elements in the solution of (4.4) in which u(8; 6:) , E ; ) ) is used in the evaluation of A(u, 0) . A Runge-Kutta method is employed to solve the three initial value problems (4.2), (4.4b) and (4.4~) . The singularity at 0 = 0 requires special starting procedures. In (4.2a) we simply use the limiting relations obtained from (2.9b) and (4.2) by requiring continuous derivatives at 0 = 0. In (4.4b) and (4 .4~) the first step in the integration is done with the centered scheme : (4.7) U(h) = U(0) + BhA(&[u(O) + Wl, frh) * [up) + U(h)l , where h is the step width. The error is O(h3) since we use this second order scheme only at one point. The interval 0 < 0 < 4.r is divided into 100 equal subintervals and the integrations are performed, starting at 8 = 0, over each subinterval with spacings h , = 7r/200, and h, = =&, , If the maximum relative difference in the two integrations at the end of a subinterval is not less than we halve the step width, and repeat the procedure over the subinterval. When agreement is achieved we proceed to the next subinterval, starting with the original mesh widths h , and h, . The iterates in Newton\u2019s method (4.5) are terminated when max IA[lV)/EIv)( < In most of the calculations M = 7. Occasionally a larger value of M is used. i = 1 , 2 4.2. Continuation method for parameter variation. After a solution is determined for some value of P with k fixed (or for some value of k with P fixed), accurate estimates of the initial iterates 6:) to use for P f AP (or for k f Ak) can be obtained by finding aE,/aP (or i3tj/ak). With k fixed let tj(P) denote the exact initial values for any given P. Then the boundary conditions (4.3) yield the identities in P : U z ( h ; EI(P), E2(P)> P ) = 0 2 %(bG E,(P), E,(% PI = 0 . (4.3\u2019) AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 539 In rewriting (4.3) we have indicated the dependence of u on P which was previously ignored to simplify the notation. Differentiating each of these identities with respect to P, we obtain, recalling (4.4a), U P \u2019 ( $ T ) i l ( P ) + U 3 4 T ) i 2 ( P ) = - U y ( $ T ) , u:\u2019(:n) t l (P) + U P \u2019 ( b ) i B ( P ) = - Uk\u201c\u2019($n) , (4.8) where we have introduced (4.9a) i = 1 , 2 . By differentiating in (4.2) we find with the aid of (2.9b) and (4.4d) that 1- u 4 ( q (4.9b) U(5)(0) = 0 . The coefficients in (4.8) are already computed for use in the final Newton iterate (4.5b). Thus only the additional system (4.9b) is solved to evaluate kl and i2 from (4.8). Then for initial estimates we use the first two terms in the Taylor expansion : (4.10) t y \u2019 ( P f A P ) = E j ( P ) & t j ( P ) A P , j = 1 , 2 . The derivatives l j ( P ) are of physical interest, especially when P is near a bifurcation point or near a local maximum or minimum point of P(5;). The corresponding continuation analysis and computation for variation of the geometric parameter k follow in an obvious manner. In fact, to replace P by k only the right-hand side in (4.8) need be changed by using the components of (4.11a) Proceeding the same way as in the derivation of (4.9b) we find that (4.llb) , U(S\u2019(0) = 0 . 540 L. BAUER, E. L. REISS AND H. B. KELLER 4.3. Parallel shooting for the full sphere. We treat the full sphere by employing the previous procedure for two hemisphere^.^ We integrate from each pole to the equator and adjust four parameters in order to satisfy four continuity conditions at the equator. Consider the two initial value problems, (4.12a) (4.12b) o S e j g T , Here the ti are the four initial parameters, two for each of the two initial value problems. The solutions of these problems are denoted by u(0; t1 , Ez) and v(0; E 3 , la). If we can find ti such that (4.13) U j ( h E l , t 2 ) = % ( B G 5 s , E , ) Y j = 1,2,3,4, then a solution of the full sphere problem is given by (4.14) For fixed P and k, the number of distinct solutions of Problem S is equal to the number of distinct real roots (tl , l2 , 5 , E4) of (4.13). The equations (4.13) are also solved by Newton's method. Now however there are two nonlinear systems (4.12) and four linear variational systems to be solved for each Newton iteration step. The numerical integration of the initial value problems is done in the same way as for the hemisphere. All convergence criteria are the same as in the hemisphere calculations. Corresponding continuity methods in both k and P are also used for obtaining initial iterates. It is inconvenient to treat the full sphere by integrating from 0 = 0 and adjusting El and t2 to satisfy the two boundary conditions at 8 = v. Some of the derivatives are indeterminate a t 0 = v, and the derivatives of some of the auxiliary variables U(') and U(2) are infinite there. Numerically, these singularities are handled more readily by the special starting procedure, (4.6) and (4.7), than by integrating up to v - E, and then using special formulas. AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 541 4.4. Parallel shooting for hemispheres. For some of the solution branches for the hemisphere problem boundary layers occur at 8 = 0 or 8 = BT; see the discussion in Section 5. When a boundary layer occurs at 8 = in, the solution varies rapidly in a small neighborhood of 8 = BT. Thus small variations in the parameters El and t2 produce large variations in the solution of (4.2) a t 0 = $T. When a boundary layer occurs at 8 = 0, u, and up essentially vanish in an interval a < 8 2 +T. Then relatively large changes in El and E2 produce small changes in the solution at 8 = QT. In both cases the simple shooting method of subsection 4.1 is unsatisfactory for an accurate determination of the roots of (4.3) and parallel shooting is employed. Thus we select a point 8 , in the interval 0 < 0, < $7 and integrate from 8 = 0 to 8 , and from 8 = $7 to 8,, . The corresponding four initial parameters are determined from continuity requirements anaIogous to (4.13). The procedure is completely analogous to the parallel shooting for the full sphere described in subsection 4.3. Appropriate values of 0 , are determined from numerical experiments. 5. Presentation of Results Extensive numerical solutions of Problem S have been obtained for shells with k = (the thin sphere) over a wide range of P values. For k = 1.2 x a less extensive P range has been covered. At the fixed pressure P = 6 x solutions have been obtained for various k in the range low5 k 2 2 x We shall describe the thick sphere results that seem most relevant to buckling and briefly mention significant differences for the thin sphere case. The implications of these results for axisymmetric buckling are discussed in Section 6. The thick sphere computations are summarized in Figures 1 and 2 where we plot P vs. A(P) and e ( P ) . The quantity (the thick sphere) and k = is a measure of the amplitude of the deviation of the deformation at load P from the uniformly compressed state, w = 0. Similarly e (P) , defined in (2.19), is proportional to the difference between the potential energies of the buckled and unbuckled states at the same load, P. The circles and crosses on the P-axis denote, respectively, the symmetric and unsymmetric eigenvalues of the linear theory (see Table IA in Section 3). Each point ( A ( P ) , P) with A(P) > 0 on the graphs in Figure 1 represents buckled states, i.e., nontrivial solutions of Problem S. If the point corresponds to a symmetric state, then it represents a single solution. If it corresponds to an unsymmetric state, then it represents a pair of solutions. The graphs show that for fixed values of P, Problem S may have many solutions. To describe and 542 L. BAUER, E. L. REISS AND H. B. KELLER Figure la. Graphs of P vs. the amplitude A , which is defined in equation (5.1), corresponding to the 7 lowest symmetric eigenvalues and the 4 lowest unsymmetric eigenvalues for the thick sphere k = 0.001. The circles on the P-axis indicate the symmetric eigenvalues and the crosses the unsymmetric eigenvalues. Several of the lower symmetric branches BaSj and the lower unsymmetric branches B , 2 j are explicitly labeled in the graph. Several of the upper P X j and lower P$,J critical loads are also shown. The branches B& , j = 1, 2, * . . , 7, and and B6,0 are not completely shown in the figure since the corresponding values of A are too large. They are shown in Figure 1 b. The circles on the graphs indicate the pressures a t which unsymmetric branches merge with symmetric branches. dicates the pressure at which Bsf, merge with BSel. 544 L. BAUER, E. L. REISS AND H. B. KELLER values of - (&e)lI3 are too large. They are shown in Figure 2b. discuss this multiplicity, we decompose the graphs of A(P) into single-valued segments of maximal extent and denote each such segment by Bn,, with integers n and j . The procedure for choosing appropriate values of n and j is described in subsection 5.1. This is equivalent to decomposing the graph of e(P) in Figure 2 into monotone segments of maximal extent. The P coordinates of the end points of the segments are denoted by Pt,, and PEj . We call them, respectively, the lower and upper critical points of the segment. If each point on Bn,i corresponds to a symmetric (unsymmetric) solution, then we denote the branch of solutions corresponding to Bn,j as Bn,j(P) (B;,j(P)). The P-axis corresponds to the unbuckled states. We shall not include this branch in our discussion of the multiplicity. Buckled solutions of Problem S are said to bifurcate from the unbuckled solution at or from a pressure Po if there is a solution branch, y(0 , P), depending AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 545 546 L. BAUER, E. L. REISS AND H. B. KELLER continuously on P such that y(0, Po) = 0 and y(0, P ) $ 0 for P # Po but IP - POI sufficiently small. This solution branch is called a bifurcation branch. The bifurcation branch need not exist for P in a full neighborhood of Po . If it exists, locally, for P > Po ( 0.05; compare Figures 3a and 4a with Figures 3c and 4c. However, for P near PL 6.1 = P t o = 0.0105 the shapes on both branches are quite similar. Thus there 548 L. BAUER, E. L. REISS AND H. B. KELLER ----- Graph 9 Number 1 2 3 4 5 6 7 8 Branch B, , l + * %.l B6v0 550 L. BAUER, E. L. REISS AND H. B. KELLER 4 AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 55 1 is no abrupt change in mode (see Figures 3b and 4b). As P increases the states on B,,, develop a boundary layer near 8 = $7~. For example, at P = 0.10, t ( 8 ) is almost constant over 0 s 0 s and then changes rapidly over in < 8 < $7 to satisfy the boundary conditions. The graph of w(0) is approximately a parabola with maximum at 8 = 0 so that the deformed sphere is essentially two pushed-in hemispheres joined at the equator. The development of the boundary layer and the simple pushed-in shape of the sphere on B6,, suggests that this mode and branch of solutions continue to exist as P + + 00. The rapid decay of energy e,,,(P) would seem to be consistent with this assumption. The results shown in Figures 3 and 4 and elsewhere indicate that the amplitudes of the solutions on B,,, and on parts of other branches may be so large that the shell theory is not applicable. Therefore, these results do not have significance for real shells. A real shell would deform plastically at these large stresses. These remarks also apply to corresponding branches for the thin sphere. I n Figures 5 and 6 we show four solutions on the branches B6,1, Be,, and B6,3 E B4,1 . One of these solutions is for P = 0.0712594, near the critical pressure PZl = P z 2 , and another is for P = 0.0678672 near the critical pressure P t 2 = P t l . The other solutions are for P near the bifurcation loads P, and P, . These solutions have distinct mode shapes and relatively small amplitudes since P is close to P, or P, . This behavior is typical for all even n since the solutions on different symmetric bifurcation branches Bn,l have distinctly different deformation and stress modes for P near P,, and as P varies the solutions continuously change on each branch and merge with the solutions on some other branch which is usually not a bifurcation branch.6 Thus all symmetric solutions are connected as P varies up and down on the appropriate symmetric branches. The energy variation on all branches is, as previously noted, monotone decreasing. However, for P < P, , the energy on most symmetric branches is mainly positive but, for P > P, , the opposite occurs (the notable exception is B 6 , , , see Figure 2a and Table 11) . merge continuously at the eigenlvalues P = P, for n odd. The branches B:l bifurcate down from the lowest eigenvalue P, = 0.0675 and merge, respectively, with BSfz at P f , = 0.0128. Similarly, BZ2 joins BC3 which joins BZ, which joins BL5 which joins BL6 which joins B17 which finally joins BL7 at P f 7 = 0.0124; see Figure 2b and Table IIB. The obvious mergers also occur for the B;, . Since BL7 and BL7 join at P f 7 i.e., The pairs of unsymmetric bifurcation branches B;, yf(e, \u2018 t 7 ) = y-(. - 8, \u2018 t 7 ) = y\u2019(. - e, \u2018 6 7 ) J B&(P) must be symmetric at P = P t 7 . Furthermore, the results show that The only symmetric bihrcation branches to merge directly with each other were B,,,, and B12,1 * 552 L. BAUER, E. L. REISS AND H. B. KELLER P near the critical loads PEl and Pg2. Graph Number P Branch l / 2 l 1 4 i 0.070 I 0.0712594 I 0.678672 1 0.074 I this symmetric state lies on the branch . The value Pk, is not a critical pressure for B6,1. see Table 11. Equal energy loads are found on the branches B t 2 and B& . Graphs of typical solutions on branch B21 are shown in Figures 7a and 8a. Solutions a t some of the upper and lower critical loads P z j and P k j are shown in Figures 7b and 8b. The transition from one branch to another is indicated by these graphs. We note that on BZ1 the \u201csouthern\u201d hemisphere is less distorted than the \u201cnorthern\u201d hemisphere which suffers a relatively large indentation, or dimple, around the pole. Similar features occur in all the B& branches. In fact, we find that P& < P t , < PCl ; AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 553 At each of the unsymmetric eigenvalues P, , for n = 7 , 3 and 9, the solutions B$,l bifurcate up and go through a series of mergers with intermediate branches. Finally, B:, joins BGi for some j at P = P x j or P = Again the symmetric state into which the unsymmetric pairs of solutions finally merge is found to lie on some symmetric branch of solutions. For example, B t 3 join B4,4 at PF3 = 0.0646. Thus we find the amazing result that all bifurcation branches, for both symmetric and unsymmetric modes, are connected to each other by means of intermediate branches. The energies on the bifurcation branches B2#l for n = 7, 3, 9 are negative for P > P , . They are also negative on BnS2 for a limited range of P values. 554 L. BAUER, E. L. REISS AND H. B. KELLER AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 555 is close to P t , & 0.0123971, this solution is nearly symmetric. 5.2. The thin spheres. The results for the thin sphere, k = 10-5, are summarized in Figures 9 and 10. For this value of k the lowest eigenvalue is also unsymmetric. The eigenvalues for k = low5 (see Table IB of Section 3) , are closely spaced. For example a 10% change in P from P = P,, spans seven additional eigenvalues. A 1 yo change includes two additional eigenvalues. The solutions for the thin sphere are qualitatively similar, in many respects, 556 L. BAUER, E. L. REISS AND H. B. KELLER to those previously discussed for the thick sphere.? All the branches bifurcating from symmetric eigenvalues are continuously connected in the same way as for the thick sphere. The solution branch bifurcates down from the lowest eigenvalue P I , . The solution branches bifurcate up from the next two unsymmetric eigenvalues P,, and P I , and have negative energy for P near the eigenvalues. We have not completely investigated the unsymmetric branches of the solution for the thin spheres. However, numerical results that are not shown in the graphs indicate that the unsymmetric solutions connect with the symmetric ones in the same way as for the thick sphere. The formation of boundary layers as P varies on B16,j is more pronounced for the thin sphere than for the corresponding branch of the thick sphere. A feature of the thin sphere that has not been observed for the thick sphere is the existence of isolated solution branches. They are branches that are not connected to any of the solutions which bifurcate from the eigenvalues. For example, one of these occurs for P in the interval 0.006005 < P < 0.010338. 7 Perhaps the most significant difference is the increase in the multiplicity of the solutions as k decreases. For example, for the thick sphere, 7 different symmetric solutions were determined at P = 0.07. For the thin sphere, 46 different symmetric solutions were determined at P = 0.007. AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 557 There are critical loads at P = 0.007760, 0.006095, 0.010338 and 0.006005. The energies on this branch are in the interval 0.119 < (se)ll3 < 0.232. Since the energy is large and positive this branch is not shown in Figure 9. We have not found any isolated branches with negative energy. 558 I (e l27 ( -.I( - .2 - .3' - .4 L. BAUER, E. L. REISS AND H. B. KELLER k = 10-5 Figure lob. Graphs of ( 4 ~ ) ~ ' ~ vs. P for the lower part of El,,, and for the branches B,,,, , BI6,- , and a part of E16 , -2 . 5.3. Boundary layers. We have observed in subsection 5.1 (see Figures 3 and 4) that for the bifurcation branch from the lowest symmetric eigenvalue, a boundary layer forms at 8 = &r. A second boundary layer was observed to develop at 8 = 0 as k -+ 0 ; the solution is small everywhere except at 8 = 0. In Figures 1 2 and 13 we show the formation of this boundary layer by presenting graphs of solutions for a sequence of decreasing values of k (compare with AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 559 P,, &0.0073640, P I , t 0.007392. Figures 3 and 4). These results partially substantiate Friedrichs\u2019 conjectures in [4] about the formation of \u201cdimples\u201d as k -+ 0." + ] + }, + { + "image_filename": "designv10_3_0001241_978-3-319-02636-7-Figure3.5-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001241_978-3-319-02636-7-Figure3.5-1.png", + "caption": "Fig. 3.5 Acrobot and Pendubot systems", + "texts": [ + " The inertia matrix M(q) and the potential energy V (q) are given by M(q) = [ m1 + m2 m2r cosq2 m2r cosq2 m2r 2 + I2 ] and V (q) = 1 2 k1q 2 1 + m2gr cosq2 where q1 is the platform displacement, q2 is the pendulum angular, m1 is the mass of the cart, m2 the mass of the eccentric mass, r the radius of the rotation, k the spring constant, I2 the inertia of the arm, g the gravity acceleration, and \u03c4 is the torque input. Consider a two-arm robot with a single control input. The actuation of the variable q1 or q2 yields two different UMSs: the Acrobot [7, 16], Fig. 3.5(a), where q2 is actuated and the Pendubot [32], Fig. 3.5(b), whereby q1 is actuated. In reality, these two systems represent the same system when the latter is fully actuated. Any actuator failure or suppression of an actuator leads to two different structures. The inertia matrices of the two systems are given by m11 = I1 + I2 + m1l 2 1 + m2 ( L2 1 + l2 2 )+ 2m2L1l2 cosq2 m12 = m21 = I2 + m2l 2 2 + m2L1l2 cosq2 m22 = I2 + m2l 2 2 and the corresponding potential energyV (q) is given by V (q) = (m1l1 + m2L1)g cosq1 + m2l2g cos(q1 + q2) 2Translational Oscillator Rotational Actuator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure10.4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure10.4-1.png", + "caption": "Fig. 10.4 Diagram of a semi-infinite slab and its co-ordinate axes.", + "texts": [ + " Above a certain frequency it can be assumed that the distribution of flux, current and loss in a region just below a small element of the surface is the same as it would be if the element was part of an infinite plane surface bounding a semi-infinite slab. The same approximation can be made at any curved surface, as indicated by Fig. 10.3, if the effective skin depth 'Y is small compared with the radius of curvature. Since the concentration of the flux means that saturation may become important even when the mean flux density is low, the theory of the semi-infinite slab is developed below for both saturated and unsaturated conditions. Fig. 10.4 is a diagram of a semi-infinite slab of permeability fJ. and resistivity p, bounded by the yz-plane and extending to infinity in the x-direction. Both fJ. and p are assumed to be constant. Uniformly distributed alternating currents, flowing in the z direction near to the yz-surface, set up a surface magnetic field strength H 0 = Hmo cos w t in the y-direction. Fig. 10.4 corresponds to Fig. 10.2 with the centre line (shown dotted) moved to infinity. Inside the slab the magnetic field strength H, the flux density B, and the current density J all vary with x. From symmetry Hand B are in the y-direction at every point, and they vary only with x and t. Thus Also from symmetry J x =Jy = O,J=Jz = F(x,t). The electric field strength E = pJ, is also in the z- P ) = 0 2 %(bG E,(P), E,(% PI = 0 . (4.3\u2019) AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 539 In rewriting (4.3) we have indicated the dependence of u on P which was previously ignored to simplify the notation. Differentiating each of these identities with respect to P, we obtain, recalling (4.4a), U P \u2019 ( $ T ) i l ( P ) + U 3 4 T ) i 2 ( P ) = - U y ( $ T ) , u:\u2019(:n) t l (P) + U P \u2019 ( b ) i B ( P ) = - Uk\u201c\u2019($n) , (4.8) where we have introduced (4.9a) i = 1 , 2 . By differentiating in (4.2) we find with the aid of (2.9b) and (4.4d) that 1- u 4 ( q (4.9b) U(5)(0) = 0 . The coefficients in (4.8) are already computed for use in the final Newton iterate (4.5b). Thus only the additional system (4.9b) is solved to evaluate kl and i2 from (4.8). Then for initial estimates we use the first two terms in the Taylor expansion : (4.10) t y \u2019 ( P f A P ) = E j ( P ) & t j ( P ) A P , j = 1 , 2 . The derivatives l j ( P ) are of physical interest, especially when P is near a bifurcation point or near a local maximum or minimum point of P(5;). The corresponding continuation analysis and computation for variation of the geometric parameter k follow in an obvious manner. In fact, to replace P by k only the right-hand side in (4.8) need be changed by using the components of (4.11a) Proceeding the same way as in the derivation of (4.9b) we find that (4.llb) , U(S\u2019(0) = 0 . 540 L. BAUER, E. L. REISS AND H. B. KELLER 4.3. Parallel shooting for the full sphere. We treat the full sphere by employing the previous procedure for two hemisphere^.^ We integrate from each pole to the equator and adjust four parameters in order to satisfy four continuity conditions at the equator. Consider the two initial value problems, (4.12a) (4.12b) o S e j g T , Here the ti are the four initial parameters, two for each of the two initial value problems. The solutions of these problems are denoted by u(0; t1 , Ez) and v(0; E 3 , la). If we can find ti such that (4.13) U j ( h E l , t 2 ) = % ( B G 5 s , E , ) Y j = 1,2,3,4, then a solution of the full sphere problem is given by (4.14) For fixed P and k, the number of distinct solutions of Problem S is equal to the number of distinct real roots (tl , l2 , 5 , E4) of (4.13). The equations (4.13) are also solved by Newton's method. Now however there are two nonlinear systems (4.12) and four linear variational systems to be solved for each Newton iteration step. The numerical integration of the initial value problems is done in the same way as for the hemisphere. All convergence criteria are the same as in the hemisphere calculations. Corresponding continuity methods in both k and P are also used for obtaining initial iterates. It is inconvenient to treat the full sphere by integrating from 0 = 0 and adjusting El and t2 to satisfy the two boundary conditions at 8 = v. Some of the derivatives are indeterminate a t 0 = v, and the derivatives of some of the auxiliary variables U(') and U(2) are infinite there. Numerically, these singularities are handled more readily by the special starting procedure, (4.6) and (4.7), than by integrating up to v - E, and then using special formulas. AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 541 4.4. Parallel shooting for hemispheres. For some of the solution branches for the hemisphere problem boundary layers occur at 8 = 0 or 8 = BT; see the discussion in Section 5. When a boundary layer occurs at 8 = in, the solution varies rapidly in a small neighborhood of 8 = BT. Thus small variations in the parameters El and t2 produce large variations in the solution of (4.2) a t 0 = $T. When a boundary layer occurs at 8 = 0, u, and up essentially vanish in an interval a < 8 2 +T. Then relatively large changes in El and E2 produce small changes in the solution at 8 = QT. In both cases the simple shooting method of subsection 4.1 is unsatisfactory for an accurate determination of the roots of (4.3) and parallel shooting is employed. Thus we select a point 8 , in the interval 0 < 0, < $7 and integrate from 8 = 0 to 8 , and from 8 = $7 to 8,, . The corresponding four initial parameters are determined from continuity requirements anaIogous to (4.13). The procedure is completely analogous to the parallel shooting for the full sphere described in subsection 4.3. Appropriate values of 0 , are determined from numerical experiments. 5. Presentation of Results Extensive numerical solutions of Problem S have been obtained for shells with k = (the thin sphere) over a wide range of P values. For k = 1.2 x a less extensive P range has been covered. At the fixed pressure P = 6 x solutions have been obtained for various k in the range low5 k 2 2 x We shall describe the thick sphere results that seem most relevant to buckling and briefly mention significant differences for the thin sphere case. The implications of these results for axisymmetric buckling are discussed in Section 6. The thick sphere computations are summarized in Figures 1 and 2 where we plot P vs. A(P) and e ( P ) . The quantity (the thick sphere) and k = is a measure of the amplitude of the deviation of the deformation at load P from the uniformly compressed state, w = 0. Similarly e (P) , defined in (2.19), is proportional to the difference between the potential energies of the buckled and unbuckled states at the same load, P. The circles and crosses on the P-axis denote, respectively, the symmetric and unsymmetric eigenvalues of the linear theory (see Table IA in Section 3). Each point ( A ( P ) , P) with A(P) > 0 on the graphs in Figure 1 represents buckled states, i.e., nontrivial solutions of Problem S. If the point corresponds to a symmetric state, then it represents a single solution. If it corresponds to an unsymmetric state, then it represents a pair of solutions. The graphs show that for fixed values of P, Problem S may have many solutions. To describe and 542 L. BAUER, E. L. REISS AND H. B. KELLER Figure la. Graphs of P vs. the amplitude A , which is defined in equation (5.1), corresponding to the 7 lowest symmetric eigenvalues and the 4 lowest unsymmetric eigenvalues for the thick sphere k = 0.001. The circles on the P-axis indicate the symmetric eigenvalues and the crosses the unsymmetric eigenvalues. Several of the lower symmetric branches BaSj and the lower unsymmetric branches B , 2 j are explicitly labeled in the graph. Several of the upper P X j and lower P$,J critical loads are also shown. The branches B& , j = 1, 2, * . . , 7, and and B6,0 are not completely shown in the figure since the corresponding values of A are too large. They are shown in Figure 1 b. The circles on the graphs indicate the pressures a t which unsymmetric branches merge with symmetric branches. dicates the pressure at which Bsf, merge with BSel. 544 L. BAUER, E. L. REISS AND H. B. KELLER values of - (&e)lI3 are too large. They are shown in Figure 2b. discuss this multiplicity, we decompose the graphs of A(P) into single-valued segments of maximal extent and denote each such segment by Bn,, with integers n and j . The procedure for choosing appropriate values of n and j is described in subsection 5.1. This is equivalent to decomposing the graph of e(P) in Figure 2 into monotone segments of maximal extent. The P coordinates of the end points of the segments are denoted by Pt,, and PEj . We call them, respectively, the lower and upper critical points of the segment. If each point on Bn,i corresponds to a symmetric (unsymmetric) solution, then we denote the branch of solutions corresponding to Bn,j as Bn,j(P) (B;,j(P)). The P-axis corresponds to the unbuckled states. We shall not include this branch in our discussion of the multiplicity. Buckled solutions of Problem S are said to bifurcate from the unbuckled solution at or from a pressure Po if there is a solution branch, y(0 , P), depending AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 545 546 L. BAUER, E. L. REISS AND H. B. KELLER continuously on P such that y(0, Po) = 0 and y(0, P ) $ 0 for P # Po but IP - POI sufficiently small. This solution branch is called a bifurcation branch. The bifurcation branch need not exist for P in a full neighborhood of Po . If it exists, locally, for P > Po ( 0.05; compare Figures 3a and 4a with Figures 3c and 4c. However, for P near PL 6.1 = P t o = 0.0105 the shapes on both branches are quite similar. Thus there 548 L. BAUER, E. L. REISS AND H. B. KELLER ----- Graph 9 Number 1 2 3 4 5 6 7 8 Branch B, , l + * %.l B6v0 550 L. BAUER, E. L. REISS AND H. B. KELLER 4 AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 55 1 is no abrupt change in mode (see Figures 3b and 4b). As P increases the states on B,,, develop a boundary layer near 8 = $7~. For example, at P = 0.10, t ( 8 ) is almost constant over 0 s 0 s and then changes rapidly over in < 8 < $7 to satisfy the boundary conditions. The graph of w(0) is approximately a parabola with maximum at 8 = 0 so that the deformed sphere is essentially two pushed-in hemispheres joined at the equator. The development of the boundary layer and the simple pushed-in shape of the sphere on B6,, suggests that this mode and branch of solutions continue to exist as P + + 00. The rapid decay of energy e,,,(P) would seem to be consistent with this assumption. The results shown in Figures 3 and 4 and elsewhere indicate that the amplitudes of the solutions on B,,, and on parts of other branches may be so large that the shell theory is not applicable. Therefore, these results do not have significance for real shells. A real shell would deform plastically at these large stresses. These remarks also apply to corresponding branches for the thin sphere. I n Figures 5 and 6 we show four solutions on the branches B6,1, Be,, and B6,3 E B4,1 . One of these solutions is for P = 0.0712594, near the critical pressure PZl = P z 2 , and another is for P = 0.0678672 near the critical pressure P t 2 = P t l . The other solutions are for P near the bifurcation loads P, and P, . These solutions have distinct mode shapes and relatively small amplitudes since P is close to P, or P, . This behavior is typical for all even n since the solutions on different symmetric bifurcation branches Bn,l have distinctly different deformation and stress modes for P near P,, and as P varies the solutions continuously change on each branch and merge with the solutions on some other branch which is usually not a bifurcation branch.6 Thus all symmetric solutions are connected as P varies up and down on the appropriate symmetric branches. The energy variation on all branches is, as previously noted, monotone decreasing. However, for P < P, , the energy on most symmetric branches is mainly positive but, for P > P, , the opposite occurs (the notable exception is B 6 , , , see Figure 2a and Table 11) . merge continuously at the eigenlvalues P = P, for n odd. The branches B:l bifurcate down from the lowest eigenvalue P, = 0.0675 and merge, respectively, with BSfz at P f , = 0.0128. Similarly, BZ2 joins BC3 which joins BZ, which joins BL5 which joins BL6 which joins B17 which finally joins BL7 at P f 7 = 0.0124; see Figure 2b and Table IIB. The obvious mergers also occur for the B;, . Since BL7 and BL7 join at P f 7 i.e., The pairs of unsymmetric bifurcation branches B;, yf(e, \u2018 t 7 ) = y-(. - 8, \u2018 t 7 ) = y\u2019(. - e, \u2018 6 7 ) J B&(P) must be symmetric at P = P t 7 . Furthermore, the results show that The only symmetric bihrcation branches to merge directly with each other were B,,,, and B12,1 * 552 L. BAUER, E. L. REISS AND H. B. KELLER P near the critical loads PEl and Pg2. Graph Number P Branch l / 2 l 1 4 i 0.070 I 0.0712594 I 0.678672 1 0.074 I this symmetric state lies on the branch . The value Pk, is not a critical pressure for B6,1. see Table 11. Equal energy loads are found on the branches B t 2 and B& . Graphs of typical solutions on branch B21 are shown in Figures 7a and 8a. Solutions a t some of the upper and lower critical loads P z j and P k j are shown in Figures 7b and 8b. The transition from one branch to another is indicated by these graphs. We note that on BZ1 the \u201csouthern\u201d hemisphere is less distorted than the \u201cnorthern\u201d hemisphere which suffers a relatively large indentation, or dimple, around the pole. Similar features occur in all the B& branches. In fact, we find that P& < P t , < PCl ; AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 553 At each of the unsymmetric eigenvalues P, , for n = 7 , 3 and 9, the solutions B$,l bifurcate up and go through a series of mergers with intermediate branches. Finally, B:, joins BGi for some j at P = P x j or P = Again the symmetric state into which the unsymmetric pairs of solutions finally merge is found to lie on some symmetric branch of solutions. For example, B t 3 join B4,4 at PF3 = 0.0646. Thus we find the amazing result that all bifurcation branches, for both symmetric and unsymmetric modes, are connected to each other by means of intermediate branches. The energies on the bifurcation branches B2#l for n = 7, 3, 9 are negative for P > P , . They are also negative on BnS2 for a limited range of P values. 554 L. BAUER, E. L. REISS AND H. B. KELLER AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 555 is close to P t , & 0.0123971, this solution is nearly symmetric. 5.2. The thin spheres. The results for the thin sphere, k = 10-5, are summarized in Figures 9 and 10. For this value of k the lowest eigenvalue is also unsymmetric. The eigenvalues for k = low5 (see Table IB of Section 3) , are closely spaced. For example a 10% change in P from P = P,, spans seven additional eigenvalues. A 1 yo change includes two additional eigenvalues. The solutions for the thin sphere are qualitatively similar, in many respects, 556 L. BAUER, E. L. REISS AND H. B. KELLER to those previously discussed for the thick sphere.? All the branches bifurcating from symmetric eigenvalues are continuously connected in the same way as for the thick sphere. The solution branch bifurcates down from the lowest eigenvalue P I , . The solution branches bifurcate up from the next two unsymmetric eigenvalues P,, and P I , and have negative energy for P near the eigenvalues. We have not completely investigated the unsymmetric branches of the solution for the thin spheres. However, numerical results that are not shown in the graphs indicate that the unsymmetric solutions connect with the symmetric ones in the same way as for the thick sphere. The formation of boundary layers as P varies on B16,j is more pronounced for the thin sphere than for the corresponding branch of the thick sphere. A feature of the thin sphere that has not been observed for the thick sphere is the existence of isolated solution branches. They are branches that are not connected to any of the solutions which bifurcate from the eigenvalues. For example, one of these occurs for P in the interval 0.006005 < P < 0.010338. 7 Perhaps the most significant difference is the increase in the multiplicity of the solutions as k decreases. For example, for the thick sphere, 7 different symmetric solutions were determined at P = 0.07. For the thin sphere, 46 different symmetric solutions were determined at P = 0.007. AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 557 There are critical loads at P = 0.007760, 0.006095, 0.010338 and 0.006005. The energies on this branch are in the interval 0.119 < (se)ll3 < 0.232. Since the energy is large and positive this branch is not shown in Figure 9. We have not found any isolated branches with negative energy. 558 I (e l27 ( -.I( - .2 - .3' - .4 L. BAUER, E. L. REISS AND H. B. KELLER k = 10-5 Figure lob. Graphs of ( 4 ~ ) ~ ' ~ vs. P for the lower part of El,,, and for the branches B,,,, , BI6,- , and a part of E16 , -2 . 5.3. Boundary layers. We have observed in subsection 5.1 (see Figures 3 and 4) that for the bifurcation branch from the lowest symmetric eigenvalue, a boundary layer forms at 8 = &r. A second boundary layer was observed to develop at 8 = 0 as k -+ 0 ; the solution is small everywhere except at 8 = 0. In Figures 1 2 and 13 we show the formation of this boundary layer by presenting graphs of solutions for a sequence of decreasing values of k (compare with AXISYMMETRIC BUCKLING OF HOLLOW SPHERES AND HEMISPHERES 559 P,, &0.0073640, P I , t 0.007392. Figures 3 and 4). These results partially substantiate Friedrichs\u2019 conjectures in [4] about the formation of \u201cdimples\u201d as k -+ 0." + ] + }, + { + "image_filename": "designv10_3_0001850_978-3-319-31126-5-Figure5.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001850_978-3-319-31126-5-Figure5.3-1.png", + "caption": "Fig. 5.3 Example 5.3. Acceleration analysis of the Geneva wheel", + "texts": [ + "2 gives us an important clue to simplify the kinematic analysis of mechanisms when screw theory is used: the proper selection of the reference pole. Example 5.3. The Geneva wheel of Example 4.7, Chap. 4, is reconsidered here. We need to compute the angular acceleration of the driven wheel D while taking into account that the driver wheel A is rotating at the constant angular velocity !1 D 2 rad/s clockwise. To do this, consider the data and numerical results obtained from the corresponding velocity analysis. Solution. For clarity, the figure of the Geneva wheel as well as the results of the velocity analysis are reproduced in Fig. 5.3. 112 5 Acceleration Analysis One classical solution of the acceleration analysis of the Geneva wheel is as follows. Using elementary kinematics, since the angular velocity !1 of the driver wheel is constant, then the acceleration of pin P is given by aP D !1 .!1 rP=O1 /: (5.64) Furthermore, the acceleration vector aP may be obtained upon the driven wheel as aP D a0 P C a00 P C 2!2 v00 P; (5.65) where a0 P is the acceleration of the point of body D which is instantaneously coincident with point P" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001815_j.procir.2014.03.015-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001815_j.procir.2014.03.015-Figure1-1.png", + "caption": "Fig. 1. Schematic of a typical SLS set-up", + "texts": [ + " S lection and peer-review under responsibility of the International Scientifi c Committee of the 6th CIRP International Conference on High Performance Cutting beam typically has a nominal diameter on the order of 0.5 mm or less. The scan rate can vary between 2 and 200 cm/s. Once one layer of powder is sintered, the fabrication bed lowers and a new layer of powder is placed on top by the roller. This layer-by-layer, additive manufacturing process is repeated until the final part has been fabricated. Figure 1 illustrates the set-up of a typical SLS machine. To aid in the sintering process, frequently the sintering chamber is heated to minimize required laser energy and expedite the process. Additionally, an inert gas, such as nitrogen, is often present to avoid oxidation or burning of the powders. Upon completion of the sintering process, the final part is removed and often bead blasted to remove unsintered, adhering particles [1]. To increase the density of the final part, additional operations, such as hot isostatic pressing or infiltration, are also required depending on the application [9]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002235_lra.2018.2847405-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002235_lra.2018.2847405-Figure2-1.png", + "caption": "Fig. 2. The quad-rotor tail-sitter UAV coordinate system.", + "texts": [ + " Furthermore, it is applicable to non-minimum phase systems with measurement noise and returns the optimal, stable plant inverse andQ filter with guaranteed closed loop stability; Finally, the proposed method provides the ability to mitigate the effect of measurement noise, which commonly exists in actual UAVs. The remainder of this letter is organized as follows: Section II-A introduces the vehicle dynamic model and the baseline feedback controller. In Section III, we will present the proposed DOB design method and their application in a quadrotor tail-sitter VTOL UAV model. Experiments are supplied in Section IV. Section V draws conclusions and discusses future work. The coordinate frames of our tail-sitter UAV are shown in Fig. 2: the body frame xb , yb , zb , the inertial frame xi , yi , zi , and the intermediate frame xc , yc , zc . The origin ob of the body frame is set to coincide with the vehicle\u2019s center of gravity. The intermediate frame is defined through rotating along zi by \u03c8d , the desired yaw angle when the vehicle is hovering. Rotation along body axis xb , yb , and zb are respectively called roll, pitch, and yaw. The roll, pitch, and yaw angles are respectively denoted by \u03c6, \u03b8, and \u03c8. Z \u2212X \u2212 Y Tait-Bryan angles are used to represent the vehicle attitude to prevent the singularity point at pitch angles equal to \u00b190\u25e6, which are commonly experienced angles on tail-sitter vehicles [20]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000014_20.106375-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000014_20.106375-Figure1-1.png", + "caption": "Figure 1 A switched reluctance motor [3]", + "texts": [ + "ntroduction Many electrical devices include parts which can move relative to the others. Examples of this include rotating electrical machines and h e a r actuators. A representative machine is shown in Fig. 1. This class of device can be troublesome to model using ffite elements. Often a simulation of such a machine requires modelling many different rotor positions. Several different approaches are described in the literature, as follows: Several different models can be meshed and used in turn. This is not very satisfactory, it is expensive to produce many meshes and difficult to generalise the method. Local remeshing is also possible, the program could move the rotor, retaining the same mesh topology as long as is practical, and then re-mesh, joining 'nearest nodes' on the moving interface (Fig", + " All similar constraints on surface r1 can be written as: A r - f [ A s ] - O (7) This condition may be enforced by introducing a new set of variables which exist only on r l . Lagrange multipliers. A constrained variational principle may be obtained: 550 Switched reluctance motors (SRM) give a torque which varies considerably with rotor position, hence the performance of such a machine can only be evaluated using finite elements by solving for many different rotor positions. The new scheme was used to model an SRM which has been previous1 evaluated in some detail using conventional f i i t e elements [3f Fig. 1 shows the machine for the position in which a rotor and stator pole are 6 degrees away from alignment. Fig. 5 shows the airgap region (for a different machine) and illustrates how the interface nodes need not be coincident. Fig. 6 shows the flux linkage for one stator pole when the rotor is in several different positions. Good agreement with the previous results were obtained, considering that the B-H characteristics were inaccurately taken from a small diagram from reference [3]. Conclusions We have found in various trials that comparable results from this scheme and conventional meshes are obtained for similar discretisations" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002033_j.jsv.2016.01.041-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002033_j.jsv.2016.01.041-Figure3-1.png", + "caption": "Fig. 3. Load distribution in a bearing.", + "texts": [ + " The outer race spinning with the planet gear about the planet pin will cause effects of load zone passing and time-varying angle between gear pair mesh and impact force vector. Meanwhile, the outer race revolution with the rotating planet carrier around the sun and ring gear center will lead to time-varying vibration transfer path. We model the sensor perceived signal of outer race fault by incorporating these effects to the signal model of vibration generated at the bearing fault point. Planet bearing bears radial forces. Fig. 3 shows the load distribution in a rolling element bearing. According to the Stribeck equation [25,26], under a radial force, the circumferential load distribution around a rolling element bearing can be described as q\u00f0\u03b2\u00de \u00bc q0 1 1 2\u03b5 \u00f01 cos \u03b2\u00de n ; (5) where q0 is the maximum load intensity, \u03b5 is the load distribution factor, \u03b2max is the angular extent of the load zone, and n\u00bc1.5 for ball bearings. Assume that the fault point is on the outer race. When the spinning frequency of the planet bearing outer race is f \u00f0s\u00deo , the angel between the fault point and the radial force direction changes with time \u03b2\u00bc 2\u03c0f \u00f0s\u00deo t" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001697_tro.2011.2148250-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001697_tro.2011.2148250-Figure1-1.png", + "caption": "Fig. 1. (Left) Following the straight path f (x, y) = y = 0. (Right) Following a generic curve f (x, y) = 0.", + "texts": [ + " Results that are obtained with a real robot are presented in Section V followed by the conclusion. Assume a unicycle robot that moves in the plane, and let (x, y) \u2208 2 and \u03b8 \u2208 correspond to the vehicle position and orientation. The state equations are x\u0307 = u cos \u03b8 y\u0307 = u sin \u03b8 \u03b8\u0307 = r. (1) The inputs u and r correspond to the translational and rotational speed. To begin with, let the path be a straight line, d the signed distance to the line computed in the current robot position (x, y), and \u03c8 the difference between the robot orientation and the orientation of the line (in Fig. 1 on the left d = y and \u03c8 = \u03b8). According to [2], asymptotic stability (d = 0, \u03c8 = 0) is obtained by setting u = u(t), lim t\u2192\u221e u(t) = 0 r = \u2212K1ud sin(\u03c8) \u03c8 \u2212 K2 |u|\u03c8, K1 , K2 > 0. (2) In the case of a straight line, (2) guarantees global asymptotic convergence, since the distance to the path can be uniquely computed. However, this is not true in the case of a generic curve; the control law in (2) no more guarantees global convergence, since it is no longer possible to uniquely compute the normal projection of the robot position on the path, which is the basis to compute d and \u03c8, for every start configuration [2]. This paper develops a different approach. We express the curve through its implicit equation, i.e, f (x, y) = 0 [see Fig. 1 (right)], and\u2014 even if it does not represent the signed distance from the curve\u2014we use the value f (x, y) when the robot is in (x, y) as a distance value. Geometrically, z = f (x, y) is a surface that, when intersected with the plane z = 0, produces the desired path f (x, y) = 0 (see Fig. 6 as an example). The function f (x, y) (referred to in the following as the distance error) has some good properties that make it appropriate for our purpose: 1) f (x, y) is a scalar field; 2) f (x, y) = 0 when (x, y) lies on the curve (by definition); and 3) given that the gradient of f (x, y) is not 0 on the curve, f (x, y) is positive/negative, depending on which side of the plane (x, y) is located with respect to the curve. Let fx , fy , fxx , fxy , and fy y be the first- and second-order partial derivatives of f . In addition, let \u03c8 be the angle that is between the heading of the vehicle \u03b8 and the vector (fy ,\u2212fx ) that is tangent to the level curve [ see Fig. 1 (right)]. The following assumptions are in order. A.1) f is differentiable, and \u2016\u2207f\u20162 = f 2 x + f 2 y > 0 in 2 that is deprived of a neighborhood of points, where \u2016\u2207f\u2016 = 0. A.2) limt\u2192\u221e u = 0. A.3) f is twice differentiable, and fx , fy , fxx , fxy , and fy y are bounded in any bounded domain D \u2282 2 , where f is bounded. A.4) u and u\u0307 are bounded. To guarantee asymptotic convergence to the path, we require that A.1 to A4 hold and set u = u(t) r = K1 (\u2212\u2016\u2207f\u2016uS(f ) \u2212 fx |u| cos \u03b8 \u2212 fy |u| sin \u03b8) + \u03b8\u0307c (3) where K1 > 0 and S(f ) is the Cn sigmoid function S(f ) = K2f\u221a 1 + f 2 , 0 > K2 \u2264 1", + " The advantage of such a 1The analysis has been performed with the pplane MATLAB toolbox: http://math.rice.edu/\u02dcdfield function f is that (20) can be interpreted as the equation of the straight line, while f is the signed Euclidean distance from the line itself. As stated in Remark 1, the sign of f (x, y) determines the heading of the vehicle along the path. By (20), it follows that \u2016\u2207f\u2016 = 1 for all (x, y), and hence, (10) can be rewritten as f\u0307 = u sin \u03c8 \u03c8\u0307 = K1 (\u2212uS(f ) \u2212 |u| sin \u03c8). (21) Consider now Fig. 1 (left). In this case, without losing generality, we let f = y, and \u03c8 = \u03b8. The component of u along f is f\u0307 = u sin \u03c8, and is referred to as the approaching velocity. Now, f\u0307 can be increased (up to a maximum value u) or decreased (down to a minimum value \u2212u) by controlling \u03c8 that, in turn, requires that one operates on the rotational speed. In particular, if u > 0, (21) sets the rotational speed \u03c8\u0307 as proportional to the difference between a reference approaching velocity\u2212uS(f ) and the real approaching velocity u sin \u03c8" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001223_j.rcim.2014.07.004-Figure17-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001223_j.rcim.2014.07.004-Figure17-1.png", + "caption": "Fig. 17. A feature frame.", + "texts": [ + " The Engineering System is a high level programming interface implemented as a plugin to the programming and simulation IDE ABB RobotStudio,8 shown in Fig. 16. When creating a station, objects such as the robot, workpieces, sensors, trays and fixtures can be manually generated in the station or downloaded from KIF together with the corresponding ontologies. A physical object is characterized by its local coordinate frames, the object frame and a number of relative coordinate frames called the feature frames, see Fig. 17. Geometrical constraints are expressed as relations between feature frames, and may be visualized as in Fig. 18. Fig. 16. The Engineering System is a plug-in to the programming environment ABB RobotStudio. 8 http://new.abb.com/products/robotics/robotstudio Please cite this article as: Stenmark M, Malec J. Knowledge-based instruction of manipulation tasks for industrial robotics. Robotics and Computer Integrated Manufacturing (2014), http://dx.doi.org/10.1016/j.rcim.2014.07.004i An example program sequence is shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001587_9781118824603-Figure8.10-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001587_9781118824603-Figure8.10-1.png", + "caption": "Figure 8.10 Conductor distribution and winding functions.", + "texts": [ + "2A-1) The winding function is only given for the first 18 slots since the pattern is repetitive. In order to obtain the continuous winding function, let us apply (8.1-22) and (8.1-23) where the slot positions are given by (8.1-8). Truncating the series (8.1-19) after the first two nonzero harmonics yields nas =N 7:221 sin 2fsm \u2212 4:4106 sin 6fsm (8.2A-2) Comparing (8.2A-2) to (8.1-12), we see that Ns1 = 7:221N and Ns3 = 4:4106N. From (8.2-11) we obtain was =N 7:221 2 cos 2fsm \u2212 4:4106 6 cos 6fsm (8.2A-2) Figure 8.10 depicts the conductor distributions and winding function for the winding. The discrete description of the winding function is shown as a series of arrows suggesting a delta function representation. The corresponding continuous distribution (which is divided by 4) can be seen to have a relatively high-peak. It is somewhat difficult to compare the discrete winding description to the continuous winding description since it is difficult to compare a delta function to a continuous function. The discrete representation of the winding function is shown as a set of horizontal lines spanning one tooth and one slot, and centered on the tooth" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000882_j.rcim.2010.08.007-Figure7-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000882_j.rcim.2010.08.007-Figure7-1.png", + "caption": "Fig. 7. Category 3.1.", + "texts": [ + " 5, three LPs intersect at a line with noncolinear spherical centers, and two LPs are coincident and perpendicular to the other LP. Note that this architecture was disclosed by Carretero [20]. Substituting a\u00bc1801, b\u00bc01into (14), (16), and (17), we can obtain the three parasitic motion fuction as following: x\u00bc rscsy, y\u00bc 0, f\u00bc 0 Hence, the 3-PRS PM in subcategory 2.2 has only one parasitic motion and it is depicted in Fig. 6. The three LPs of the 3-PRS PMs in this category intersect at a line with collinear spherical centers. As shown in Fig. 7, three LPs intersect at a line with colinear spherical centers, and the angle between every two LPs is 1201. Without loss of generality, let r1\u00bcr2\u00bcr. We can obtain au1 \u00bc \u00bd r,0,0 T, au2 \u00bc \u00bdr,0,0 T, au3 \u00bc \u00bd0,0,0 T. Because the attachment point Ci can only move in the limb plane, we have the following Fig. 6. Parasitic motion (x) for r\u00bc0.1, c, yA( 60,60)deg. three constraint equations for each leg: l3x \u00bc 0, l1y \u00bc \u00f0l1x\u00fer\u00detan\u00f0a\u00de, l2y \u00bc \u00f0l2x r\u00detan\u00f0b\u00de \u00f021\u00de As shown in Fig. 7, we have li \u00bc ai\u00feP\u00bc Taui\u00feP and it can be rewritten as lix \u00bc x\u00feT11auix, liy \u00bc y\u00feT21auix, liz \u00bc z\u00feT11auix \u00f022\u00de Substituting aui into (22) yeilds l1x \u00bc x\u00feT11\u00f0 r\u00de, l2x \u00bc x\u00feT11\u00f0r\u00de l1y \u00bc y\u00feT21\u00f0 r\u00de, l2y \u00bc y\u00feT21\u00f0r\u00de \u00f023\u00de Substituting Eq. (23) into constraint equations in Eq. (21) yields x\u00bc 0 \u00f024\u00de As shown in Fig. 9, three LPs intersect at a line with three spherical joint centers being colinear, and two LPs are coincident and perpendicular to the other LP. Obviously, we havea\u00bc1801,b\u00bc01,r1\u00bcr2\u00bcr, r3\u00bc0. Substituting them into Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002397_1.4040264-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002397_1.4040264-Figure1-1.png", + "caption": "Fig. 1 The schematic diagram of the laser powder bed fusion (LPBF) process", + "texts": [ + " In comparison, conventional signal analysis techniques\u2014e.g., neural networks, support vector machines, linear discriminant analysis were evaluated with Fscore in the range of 40\u201360%. [DOI: 10.1115/1.4040264] Keywords: additive manufacturing (AM), laser powder bed fusion (LPBF), sensing, process monitoring, spectral graph theory 1.1 Motivation. 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]. A schematic of the PBF process is shown in Fig. 1. 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 schematic of the PBF process shown in Fig. 1 embodies a laser power source for melting the material, and accordingly, the convention is to refer to the process as laser powder bed fusion (LPBF). A mirror galvanometer scans the laser 1Corresponding author. Manuscript received January 9, 2018; final manuscript received May 3, 2018; published online June 4, 2018. Assoc. Editor: Zhijian J. Pei. Journal of Manufacturing Science and Engineering SEPTEMBER 2018, Vol. 140 / 091002-1 Copyright VC 2018 by ASME Downloaded From: http://manufacturingscience" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001098_tmech.2008.2008802-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001098_tmech.2008.2008802-Figure1-1.png", + "caption": "Fig. 1. NH-WMM. (a) CAD model. (b) Corresponding physical prototype.", + "texts": [ + " The challenges, however, arise from the manifestation (and need for resolution) of the redundancy\u2014both kinematic redundancy due to the surplus of articulated DOFs than required for the task, as well as actuation redundancy due to the surplus of actuation over the controlled outputs. The challenges come to the forefront especially during dynamic interactions of these mobile manipulators with the environment (e.g., during a painting task) making a dynamic-level redundancy resolution critical. Our focus is on a subclass of such mobile manipulators called nonholonomic wheeled mobile manipulators (NH-WMMs), as shown in Fig. 1. The NH-WMM consists of a wheeled mobile robot (WMR) base with one or more mounted manipulator arms. While robust physical construction makes wheeled bases popular, the kinematics of rolling contact of the various wheel assembly combinations with the terrain creates nonholonomic constraints [9]. The coupling of these nonholonomic constraints with the kinematic/actuation redundancy in a dynamic setting creates interesting control challenges. Our guiding vision is to create and evaluate an overall control framework for such NHWMM to realize a prioritized satisfaction of its own end-effector interactions", + " However, the utility of such virtual testing is limited by: 1) the ability to correctly model and simulate the various phenomena within the virtual environment; 2) the fidelity of the available simulation tools; and ultimately, 3) the ability of the designer to correctly model the desired system and suitably interpret the results. We employ an HIL methodology for rapid experimental verification of the real-time controllers on the electromechanical mobile manipulators prototypes. We opted to create a physical NH-WMM system [shown in Fig. 1(b)] from scratch due to the flexibility it offered over retrofitting an off-the-shelf WMR base with an off-the-shelf manipulator arm. The additional dynamic bandwidth obtained by use of high-performance components is especially pertinent to our anticipated use of the NH-WMMs for active force redistribution during cooperative payload manipulation tasks. The NH-WMM is constructed using two geared motor powered wheels and one passive Mecanum-type casters. A passive Mecanum-type front caster is preferred (over a conventional wheel caster) to eliminate any constraints on the maneuverability", + " The first joint can be placed anywhere along the midline on top frame of the platform at a distance Ld = d + La from the center of the wheel axle (see Fig. 2). The end-effector is a flat plate supported by a passive revolute joint that ensures that no moment can be transferred to the manipulator. Each of the two joints is instrumented with an optical encoder that can measure the joint rotations and has a dc motor attached. Independent lead\u2013acid batteries provide power supplies for the actuator systems and the electronic controllers. The complete assembled two-link mobile manipulator is shown in Fig. 1(b). A PC/104 system equipped with an xPC Target real-time operating system (RTOS) serves as the embedded controller. A PC104+ embedded computer (VersaLogic EPM-CPU-3 133 MHz 32-bit processor) is used to perform all the onboard highlevel processing, control, and communication. A custom Atmelbased encoder counter circuit board is constructed for the purpose of reading up to six quadrature encoders that can store the position of each encoder with a 32-bit integer variable and asynchronously sends such data to the PC104" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003058_1.4859375-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003058_1.4859375-Figure1-1.png", + "caption": "FIG. 1. Definition sketch of a spherical squirmer of radius a, swimming at a velocity U (R)ez in a viscous fluid. The thrust to sustain motion is provided by a tangential surface velocity vs , solely along e\u03b8 (1). The fluid motion is analyzed in a frame moving with the squirmer, for which the fluid at infinity translates at a uniform velocity \u2212U (R)ez that is dependent on the Reynolds number, R.", + "texts": [ + "14, 15 However, as noted by WA, fluid inertia is of importance to the locomotion of millimeter scale organisms, such as meso- and macro-plankton. In any case, the squirmer provides a mathematically tractable model to quantify the impact of fluid inertia on self-propulsion, a question of fundamental fluid-mechanical interest. WA considered a tangential surface velocity vs = (B1 sin \u03b8 + B2 sin \u03b8 cos \u03b8 )e\u03b8 , (1) where B1 and B2 are constants; \u03b8 is the polar angle measured from the direction of propulsion, which is taken as the z-axis of a Cartesian frame (Figure 1); and e\u03b8 is the unit vector in the polar direction. At zero Reynolds number the squirmer translates at a velocity U = 2 3 B1ez , where ez is a unit vector in the z direction.2, 3 The squirmer exerts a stresslet S = 4 3\u03c0\u03b7a2 B2(3ez ez \u2212 I) on the fluid, where \u03b7 is the viscosity of the fluid, a is the radius of the body, and I is the second rank isotropic tensor.8 The sign of the ratio \u03b2 = B2/B1 differentiates two types of squirmer: for \u03b2 > 0 the squirmer draws fluid from up- and down-stream and is termed a \u201cpuller\u201d; in contradistinction, a \u201cpusher\u201d (\u03b2 < 0) expels fluid at its front and rear", + " The paper does not attempt to determine inertial corrections to the particle velocity. In conclusion, the present work is distinct from Sennitskii\u2019s papers. The governing equations shall be rendered dimensionless by scaling distance with the squirmer radius a, velocity by 2B1/3, and pressure by 2B1\u03b7/3a (a viscous scaling). Henceforth all variables and equations are dimensionless. It is convenient to analyze the flow in a frame anchored at the centre of the squirmer, for which the fluid at infinity streams past it at a velocity \u2212U (R)ez (Figure 1). The strength of the free stream U(R) is unknown a priori; it is to be found at each order in R through the requirement that the net hydrodynamic force at that order vanishes. The flow is axisymmetric about the direction of swimming; a stream function \u03c8 is introduced such that vr = 1 r2 \u2202\u03c8 \u2202\u03bc and v\u03b8 = 1 r (1 \u2212 \u03bc2)1/2 \u2202\u03c8 \u2202r , (3) where vr and v\u03b8 are the radial and polar components of the fluid velocity vector v in a spherical coordinate system, respectively, and \u03bc = cos \u03b8 . Taking the curl of the Navier-Stokes equations and using (3) yields the familiar equation for the stream function16 1 r2 \u2202(\u03c8, E2 r \u03c8) \u2202(r, \u03bc) + 2 r2 E2 r \u03c8 Lr\u03c8 = \u2212 1 R E4 r \u03c8, (4) where the differential operators E2 r = \u22022 \u2202r2 + 1 \u2212 \u03bc2 r2 \u22022 \u2202\u03bc2 , (5) Lr = 1 r \u2202 \u2202\u03bc + \u03bc 1 \u2212 \u03bc2 \u2202 \u2202r " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002302_j.ymssp.2017.01.032-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002302_j.ymssp.2017.01.032-Figure3-1.png", + "caption": "Fig. 3. Lumped-parameter model.", + "texts": [ + " For instance, in this example it shows that vibration measured in the PG would produce a spectrum with a component at the gear mesh frequency (PG with other planet configurations and tooth number combinations can produce no component at the gear mesh frequency [1,2,4,5]). It is obtained that the spectrum only has components at frequencies f=f c \u00bc pN (p N0), as reported in [2,4,5,7]. Other planetary gear sets can be simulated using this model by changing the geometry parameters (number of planets, planet positions, and number of teeth). Lumped parameter model used in this work is shown in Fig. 3. It models a spur planetary gear for the in-plane case. It consists of a ring gear, a sun gear, a carrier and N planet gears. Each of these elements has three degrees of freedom (DOFs): two translational motions and one rotational motion. For all elements, the rotational DOFs are wk (k \u00bc r; s; c;1;2; . . . ;N), while the translational DOFs are xj and yj for the ring, sun and carrier (j \u00bc r; s; c), and gi and ni for the planet gears (i \u00bc 1;2; . . .N). The translational DOFs are fixed to and rotating with the carrier reference frame (X;Y) at an angular frequency Xc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure12.15-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure12.15-1.png", + "caption": "Figure 12.15.1 Strut-and-arm geometry for front-view two-dimensional numerical solution.", + "texts": [ + " Note that SYD\u00bc SYU SYLwill inevitably be negative in practice, so\u00abBC2will be positive.HBJD ismuch larger than for a conventional double-wishbone suspension. The longitudinal properties can be analysed in the sameway, with similar adaptations to Table 12.11.1, giving Table 12.14.2. 246 Suspension Geometry and Computation A computer numerical analysis can be made of the strut-and-arm suspension in two dimensions, using a geometrically correct solution, without approximations for the upper arm. The technique required is different from the double-arm suspension. Figure 12.15.1 shows the geometry. AB is the lower arm, with pivotA and outer ball joint B, ED is the slider axis, at front-view slider initial angle uYSL,with E the foot of the perpendicular from B. Point F is the wheel contact point. A preliminary analysis is made of some initial or unchanging lengths and angles, as in Table 12.15.1. Point B may be inboard or outboard of E, which must be accounted for, for example with a variable IBDE, effectively representing a sign of angle uBDE. The solution for a given lower arm angle proceeds as in Table 12" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000341_978-0-387-68964-7-Figure5.23-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000341_978-0-387-68964-7-Figure5.23-1.png", + "caption": "Figures 5.23 and 5.24 depict a better illustration of a robot hand's links and joints. 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 , 5 , 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 II 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.", + "texts": [ + " To check the correctness of the final transformation matrix to map the coordinates in tool fram e into the base frame, we may set the joint variables at a specific rest position. Let us substitut e the joint rotational angles of the spherical robot analyzed in Example 149 equal to zero. (5.116) 238 5. Forward Kinematics Therefore, the transformation matrix (5.101) would be \u00b0T6 = \u00bbr, lT2 2T33T44T55T6 [ ~ ~ ~ l~] (5.117)o 0 1 d3 o 0 0 1 that correctly indicates the origin of the tool frame in robot 's stretched-up configuration, at (5.118) Example 151 Assembling a wrist mechanism to a manipulator. Consider a robot made by mounting the hand shown in Figure 5.23, to the tip point of the articulated arm shown in Figure 5.25. The resulting robot would have six DOF to reach any point within the working space in a de sired orientation. The robot's forward kinematics can be found by combining the wrist transformation matrix (5.73) and the manipulator transformation matrix (5.80). \u00b0T7 = Tarm Twrist 6T7 \u00b0T3 3T6 6T7 (5.119) (5.120)~ ] The wrist transformation matrix 3T7 has been analyzed in Example 147, and the arm transformation matrix \u00b0T3 has been found in Example 148" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002696_s11071-014-1745-y-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002696_s11071-014-1745-y-Figure3-1.png", + "caption": "Fig. 3 Schematic of the contact type between a ball and the small surfaces at defect edges with different topographies: a case 1, b case 2, c case 3, and d case 4", + "texts": [ + " However, when the defect edge topographies are changed due to the impacts between the ball and the defect edges, as shown in Fig. 1a, the contact type between the ball and the defect edges become a ball\u2013plane contact type. It depends on three parameters as follows: (1) the ratio of the defect length to its width, which is defined as \u03bed = L/B, where L is the defect length, and B is the defect width; (2) the ratio of the ball size to the defect minimum size, which is defined as \u03bebd = d/ min(L , B), where d is the ball diameter; and (3) the elevation angle \u03b3 (0 < \u03b3 < \u03c0/2) of the small plane surface as shown in Fig. 2b, c. Figure 3 shows effects of the defect edge topographies on the contact types between the ball and the different defect cases. The elevation angle \u03b3 and the length l of the small surfaces at the defect edges are used to determine the contact types between the ball and the defects. It is assumed that l is larger than Hertzian contact radius in this paper. For case 1, \u03b3 \u2265 arcsin ( 0.5 min (L , B)/ \u221a R2 + l2 ) + arctan (l/R) and \u03bebd > 1, where R is the radius of the ball, as shown in Fig. 3a. The ball is only in contact with the line edges of the defect in considering a case of an early defect stage. For this case, the contact type between the ball and the defect is a ball\u2013line contact type when the ball passes over the defect. It is the early stage of the plastic deformations at the defect edges caused by the periodic impacts arising from the balls against the defect edges for a small localized surface defect. For case 2, min (L , B) / (2R) < \u03b3 \u2264 arcsin ( 0.5 min (L , B) / \u221a R2 + l2 ) + arctan (l/R) and \u03bebd > 1, as shown in Fig. 3b, the contact type between the ball and the defect depends on the defect parameters \u03bed and \u03bebd. The contact type between the ball and the beginning edge of the defect is the ball\u2013line contact type, as well as that between the ball and the ending edge of the defect. It is a ball\u2013plane contact type when the ball is in contact with the small surfaces between the points A and D. It is the middle stage of the plastic deformations at the defect edges caused by the periodic impacts arising from the balls against the defect edges for a small localized surface defect. For case 3, \u03b3 \u2264 arcsin(min(L , B)/(2R)) and \u03bebd > 1, as shown in Fig. 3c, the contact type between the ball and the defect is a ball\u2013plane contact type when the ball is in contact with the surfaces between points A and B, and between points C and D. It is a ball\u2013line contact type when the ball makes contact with the beginning edge, the edges at points B and C, and the ending edge of the defect. This case denotes the large plastic deformations at the defect edges. It is the late stage of the plastic deformation at the defect edge caused by the periodic impacts arising from the balls against the defect edges for a small localized surface defect", + " 1a and 3d, the contact type between the ball and the defect is a ball\u2013line contact type at the points A, B, C, and D; it is the ball\u2013plane contact type when the ball is in contact with the surface between the points A and B, the bottom surface, and the surface between the points C and D of the defect. It is used to describe the plastic deformations at the defect edges caused by the periodic impacts arising from the balls against the defect edges for a large localized surface defect. For cases 2 and 3, as shown in Fig. 3b, c, the numbers of the contact surfaces are determined by the defect sizes. Here, five different defect types are discussed according to the defect parameters \u03bed and \u03bebd. Figure 4a depicts the first defect type, which denotes a very small defect such as a point defect and a small crack. Thus, effects of the edge topographies of the first defect type can be ignored. Figure 4b plots the second defect type with the length of the defect smaller than its width. The ball only strikes the edges 1 and 4 when the ball passes over the defect, and the numbers of the contact surfaces are 1, 2, and 1, respectively", + "5d\u2212H)2 Di ) + l cos \u03b3 defect on inner race arcsin (\u221a (0.5d)2\u2212(0.5d\u2212H)2 Do ) + l cos \u03b3 defect on outer race (19) where d is the diameter of the ball, H is the defect depth, and \u03b8 f 2 is given by \u03b8 f 2 = \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u03b8d \u2212 arcsin (\u221a (0.5d)2\u2212(0.5d\u2212H)2 Di ) \u2212 l cos \u03b3 defect on inner race \u03b8d \u2212 arcsin (\u221a (0.5d)2\u2212(0.5d\u2212H)2 Do ) \u2212 l cos \u03b3 defect on outer race (20) On the other hand, there is an additional deflection due to effects of the presence of the defect with different edge topographies. As shown in Fig. 3, the additional deflection depends on the ratio of the defect length to its width, the ratio of the ball size to the defect minimum size, and the elevation angles of the small surfaces at the defect edges. According to the descriptions in Fig. 3, the maximum of the addition deflection can be obtained. For case 1 hmax 1 = 0.5d \u2212 ((0.5d)2 \u2212 (0.5 min (L , B) + l cos \u03b3 )2)0.5 (21) For case 2 hmax 2 = 0.5d \u2212 ((0.5d)2 \u2212 (0.5 min (L , B))2)0.5 + (0.5 min (L , B) + l cos \u03b3 \u2212 0.5d sin \u03b3 ) tan \u03b3 (22) For case 3 hmax 3 = 0.5d \u2212 ((0.5d)2 \u2212 (0.5 min (L , B))2)0.5 + l sin \u03b3 (23) For case 4 hmax 4 = H (24) Then, the time-varying deflection excitation H \u2032 is given by a piecewise response function, including both the half-sine and the rectangular functions [23], which is defined by H \u2032 = \u23a7 \u23aa\u23aa\u23a8 \u23aa\u23aa\u23a9 H1 \u03bebd >> 1 H2 \u03bebd > 1 and \u03bed \u2264 1 H3 \u03bebd > 1 and \u03bed > 1 H4 \u03bed \u2264 1 (25) where H1, H2, H3, and H4 are the time-varying deflection excitations caused by the first through fifth defect types, respectively, which have been given in Ref", + " In order to reduce the calculation time and obtain enough points to describe the impulse waveforms caused by the localized surface defects with different edge topographies, the time step for the numerical investigation in this paper is assumed as the time required for 0.0092 \u25e6 of rotation. For the shaft speed of 2,000 rpm, the time step utilized in this numerical solution is t = 2 \u00d7 10\u22126 s. The initial displacements used for the inner race and the shaft are x0 = 10\u22126 m and y0 = 10\u22126 m, and the initial velocities in the X - and Y -directions are zero. The sizes and depth of the three different defect cases of interest are listed in Table 2. According to the descriptions in Fig. 3 and the parameters of the ball bearing and the defects in Tables 1 and 2, the value of the elevation angle \u03b3 of the small plane surface at the defect edge can be from 0.001 rad to 1.571 rad, which is calculated by the method in Fig. 3. 4.1 Effects of the defect edge topographies on the contact stiffness between the ball and the defect Figure 7a, b shows the total contact stiffnesses between the healthy outer race and the defective inner race, and those between the healthy inner race and the defective outer race, respectively. As shown in Fig. 7, the total contact stiffnesses between the healthy race and the defective race of the ball bearing increase with the numbers of contact surfaces between a ball and the edges of the defect", + " These parameters of a discrete signal s are given by [8] RMS = \u221a\u221a\u221a\u221a 1 Nf Nf\u2211 i=1 s2 i (37) CF = max(s) \u2212 min(s) RMS (38) Kurtosis = \u2211Nf i=1 (si \u2212 mean(s))4 Nf RMS4 (39) where Nf is the number of samples, si is the i th data of the discrete signal s, max() is the maximum value of the discrete signal s, min() is the minimum value of the discrete signal s, and mean() is the mean value of the discrete signal s. Figures 16, 17, and 18 show the statistical measures of the acceleration response in the X -direction of the inner race of the ball bearing from 0.3 to 0.4 s for the defect cases 1, 2, and 3. According to the parameters in Table 2 and the descriptions in Fig. 3, the range of the elevation angle \u03b3 can be chosen to be from 0.4 to 0.5 rad in this section. The RMS of the X -direction acceleration response for cases 1, 2, and 3 are shown in Figs. 16a, d, g, j, m, 17a, d, g, j, m, and 18a, d, g, j, m, respectively. The RMS increases consistently with the length l and the elevation angle \u03b3 for the three different cases. This occurs because the amplitude of the acceleration response of the ball bearing increases with the elevation angle \u03b3 and the length l as shown in Figs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002979_978-1-4471-6747-1-Figure6.2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002979_978-1-4471-6747-1-Figure6.2-1.png", + "caption": "Fig. 6.2 Schematic description of inverse kinematics using a closed form analytical approach", + "texts": [ + " In this case the inverse kinematic problem can be phased as follows: Find a posture of the limb for which you know the location of the endpoint is on a particular trajectory of interest, preferably its start. This trajectory is of course already known to you, such as that of reaching from one point to another. This posture should be valid in the sense that the joint angles should be achievable by the robot or vertebrate limb. Then take steps away from that point along the trajectory to build a time history of joint angles that produce that trajectory. Figure 6.2 shows the limb at the starting posture that produces the endpoint location (x0, y0); call this q0. At that posture the Jacobian of the limb is J (q0). Given that Eq. 2.26, which is can be expressed in discrete form as \u0394q = J (q)\u22121 \u0394x (6.9) we can use the following equation to bootstrap across discrete postures from i = 0 to the end of the discretized trajectory. \u0394qi+1 = J (qi ) \u22121 \u0394xi (6.10) Note that this is not unlike an Euler integration method, or an initial value problem, where you know the gradient of a function at any point, and you use that gradient plus an initial condition to take steps forward in time or space" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003099_tro.2016.2633562-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003099_tro.2016.2633562-Figure2-1.png", + "caption": "Fig. 2. Rotor control volume along with the streamtube, generated forces, and the different air velocities. The vehicle velocity V and wind speed W have an apparent stream velocity into the rotor of vs = \u2212 V + W . The actual air velocity at the rotor va is the sum of the induced velocity vi plus the apparent stream velocity vs . The scalar thrust T and scalar drag H are shown in the two-dimensional plane associated with the longitudinal flight dynamics.", + "texts": [ + " The rotor hub/shaft and rotor blades of a rotor can be represented in three separate frames of reference [11]: the vehicle body-fixed frame {B}, the rotor reference frame {C} that rotates with the rotor but does not tilt with blade flapping, and the tip-path-plane (TPP) or {D}. The TPP rotates with the rotor and is also aligned with the tilt of the rotor due to blade flapping and, to first order, the rotor is stationary in this frame. Throughout the paper, e1 , e2 , e3 are used to denote unit vectors in the x, y, z directions, respectively. Consider the control volume shown in Fig. 2 associated with a slightly tilted actuator disc, a result of the rotor experiencing both translational and axial air motion with velocity V \u2208 R3 . This is the relative velocity between the vehicle\u2019s body-fixed frame {B} and inertial frame {A} expressed in {B} as shown in Fig. 3. The stream velocity is equal in magnitude but opposite in direction to the vehicle velocity V when there is no wind but is the sum when the wind velocity W \u2208 R3 expressed in {B} is present, i.e., vs = \u2212 V + W \u2208 R3 . The spinning rotor induces additional air velocity vi \u2208 R3 through the rotor so that the total air velocity through the rotor va is va = vi + vs ", + " The thrust T generated by the rotor is associated with the component of force F in the \u2212 e3 direction, that is, T = \u2212 e 3 F . This convention ensures that in normal flight, the thrust T is positive. Note that in most helicopter texts, for example, [12], the thrust is modeled as orthogonal to the TPP. However, we find that modeling the thrust in the body-fixed frame \u2212 e3 direction and introducing a horizontal thrust component Fhor due to the tilting of the thrust vector is a more effective modeling framework for small-scale fixedpitch rotor systems used in robotic applications. Fig. 2 shows the rotor tilting backward with respect to the rotor shaft as a result of blade flapping. The net effect of rotor flapping is to tilt the lift force generated by the rotor disc and contribute to the horizontal force Fhor. The horizontal force also comprises other aerodynamic effects such as induced and translational drag [11], [21] that in many cases are even more important than blade flapping for small fixed-pitch rotors used on quadrotor vehicles. Critically, these additional drag forces can be lumped into the same mathematical model used to model flapping [21] (cf", + " Moreover, when vsh = 0, then vix = viy = 0 and the horizontal force Fhor = 0, yielding H = 0 as expected. In the case where vsh \u2212 Wh = 0, the induced horizontal scalar velocity vih is nonnegative since the rotor tilt opposes the horizontal motion of the rotor hub and consequently the induced component of the velocity will be pushing air against the direction of motion of the rotor. Note that due to the motion of the rotor, the actual horizontal component of air through the rotor will be negative as expected (see Fig. 2). The aerodynamic rotor power Pa is defined to be the power supplied to the air streamtube by the rotor and is a key variable in the following development. It comprises a component due to the induced air velocity and a component due to the stream velocity, that is Pa = \u03ba\u3008 F , vi\u3009 + \u3008 F , vs\u3009 (2) where the scalar \u03ba \u2265 1 is the induced power factor [12, pg. 92] [18, pg. 105]. The constant \u03ba is an adjustment factor that models the additional power dissipated due to wake rotation, tip loss effects, and nonuniform inflow that are not modeled by classical momentum theory" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure4.3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure4.3-1.png", + "caption": "Fig. 4.3 Diagrams of a synchronous machine with many damper windings.", + "texts": [ + " There are also eddy current paths in the iron, whether solid or laminated, of the magnet system. All these circuits should be allowed for in a complete representation. Normally no external voltages are impressed on the damper circuits. The General Equations of A.C. Machines 75 Consider a cage type damper winding of the type represented in Fig. 4.4 in which there are six bars in the pole face (shown dotted) connected by complete end rings. All the circuits are symmetrical with respect to both the direct and quadrature axes and in the general case can be represented in Fig. 4.3 by m direct-axis coils and n quadrature axis coils. However for practical work only an approximate representation, using a small number of damper coils, is feasible. The winding in Fig. 4.4 requires three direct-axis coils and three quadrature-axis coils in the idealized machine. Fig. 4.4a shows the paths of the direct-axis currents and Fig. 4.4b those of quadrature axis currents. In the practical machine the currents id 1, id 2, id 3, iq 1, iq 2, iq 3, are superimposed in the bars and rings. Because of the symmetry about the axes there is no mutual action between the direct and quadrature-axis coils, but there is a mutual inductive coupling between the three coils of one axis", + " There is also a mutual resistance coupling because the current in any pair of bars flows through the end rings and introduces an ohmic drop in the circuit through any other pair of bars. The eddy current paths in the iron can be considered as a cage winding having an infinite number of bars, but there is the additional complication that the eddy currents cause the flux to be concentrated at the outer surface of the iron (the so-called skin effect) so that local saturation occurs. The problem of determining the effects of eddy currents is discussed in Chapter 10. The equations for a system of stationary mutually coupled coils comprising coils D, F and Dl to Dm of Fig. 4.3 can be written down in terms of their self- and mutual inductances. For the rotating machine, however, equation (4.15) for the armature coil vo ltage term w t/I q \u2022 The flux linkage t/I d depends only on the direct-axis currents and is given by: ( 4.17) where Lfd, Ld 1 d, etc., are the mutual inductances between coils F, Dl etc., and D; and Ld is the complete self-inductance of coil D. The equations for the field and direct-axis damper coils are as follows: The General Equations of A.C. Machines Uf = (R f + Lffp )if + L fd 1 pid 1 + L fd 2Pid 2 + " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003645_tie.2017.2698358-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003645_tie.2017.2698358-Figure2-1.png", + "caption": "Fig. 2. Schematic diagram of HAHC system", + "texts": [ + " 1, the towed payload is attached to a heavily armored cable which is driven by a storage winch and two auxiliary tension winches. The HAHC system is placed between the frame and the tension winches. The vessel motions are measured with a motion reference unit (MRU) which has three accelerometers for detecting surge, sway, and heave and three rotation rate sensors for measuring roll, pitch, and yaw. The acceleration signals are double integrated in order to obtain the desired relative position of the ship as the feedback signal of HAHC. Fig. 2 shows the schematic diagram of HAHC system. It consists of an electro-hydraulic system driving a single-rod actuator as main cylinder and two plunger cylinders as active cylinders. The rodless chamber of the main cylinder is connected to the hydraulic accumulator, constituting a passive heave compensator (PHC). The PHC system is used to accumulate the kinetic energy during movements before releasing the accumulated energy for compensating the payload\u2019s heave motion. The two chambers of the active cylinders can be treated as one compartment due to the direct connection", + " The forward chamber and return chamber are controlled by a servo valve, making up an active heave compensator (AHC). The AHC is to counteract the vertical movement of the payload actively, overcoming the passive compensator friction and the friction of the other elements of the load. The AHC system is generally more effective than PHC but needs more power. Therefore, this paper designs a hybrid heave compensation system which has two independent compensation systems parallel driving a moving sheave black. As shown in Fig. 2, the cable is guided across the sheave on top of the compensation cylinders by the lever with the ratio of 1:2. This ratio value comes from the fact that the cable is guided by the sheave where the cable achieves the double speed of the heave cylinders speed. As a result, the load forces and equivalent mass of the heave cylinders are also doubled. The goal is to make the active heave compensation cylinders track the predicted trajectory as closely as possible so as to counteract the payload\u2019s vertical movement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003068_tie.2014.2360070-Figure4-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003068_tie.2014.2360070-Figure4-1.png", + "caption": "Fig. 4. search coils locations. The search coils are mechanically spaced by 120\u00b0 and occupy the upper part of six slots.", + "texts": [ + " In other words, if the search coils are not distributed uniformly, then higher errors are to be expected especially for minimum air-gaps situated between two coils that are further apart as the resolution of the search coils is less in these parts. As a result, the angle between coils should be selected as follows: 0278-0046 (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. = (21) where n represents the number of the search coils and is the angle between them. According to (21) the three search coils C1, C2 and C3 are placed at = 0\u00b0,120\u00b0 and 240\u00b0 for fault diagnosis purposes (see Fig. 4). In this figure, is the angle measured from a reference point on the stator. The coils are displaced by =120\u00b0 and therefore they are located above the coils of three different phases. This happens for any slot per pole combination. In fact, the positions at 120\u00b0 and 240\u00b0 are electrically spaced by P\u00d7120\u00b0 and P\u00d7240\u00b0 respectively, P being the number of pole pairs. So the measured voltages of these coils will have three phase waveforms. Firstly, it should be noted that according to equation (20) the amplitude of the induced voltage of each search coil is affected only by the air-gap length above each coil which is covered in the last term of the equation", + " Secondly, three axes are assumed from the center of stator to the center of search coils which are shown in Fig. 5. It should be noted that these are not magnetic axes of search coils. Along each axis, a vector is assumed with the amplitude of search coil rms voltage and orientation of the axis. In a healthy condition, the resultant vector approaches zero, estimating SEF as zero. In an eccentric condition, the vectors close to the minimum air-gap become larger directing the resultant vector toward their own direction. For example, if the minimum air-gap is placed at = 0\u00b0 (see Fig. 4) then the vector becomes larger and vectors and will become smaller but with the same amplitude. Thus, the outcome vector has a direction of vector which is the minimum airgap position. As an overall result, in the following discussion it will be analytically confirmed that the result of these three vectors always has amplitude proportional to SEF and a direction toward the minimum air-gap position. This is also confirmed by the numerical analysis and experimental tests carried out in the course of this research", + " The simulations are based on a circuit-coupled model with a transient electromagnetic solver. Two layers of elements are constructed in the air-gap to achieve precise results. The total number of nodes is 460,000 in this simulation which is very high. The reason is that due to the asymmetric air-gap, the machine geometry is not periodic; therefore the entire geometry was modeled. In 3D-FEM simulations, three search coils C1, C2 and C3 made of eighteen coplanar turns are placed at = 0\u00b0,120\u00b0 and 240\u00b0 as shown in Fig. 4. As the first 3D-FEM results, Fig. 5 shows the induced voltages of three search coils in healthy condition at rated speed. As it can be seen these search coils have the same rms voltages of 6.6 V owing to the same value of air-gap length in healthy condition. Also the experimental measurement in the same condition has been provided which shows a very good agreement. The angular speed in the experiment is 1285rpm, corresponding to 300Hz frequency. The rms values of the voltages in experimental measurement differ by 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002966_j.jsv.2015.02.021-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002966_j.jsv.2015.02.021-Figure2-1.png", + "caption": "Fig. 2. Simplified model of the linear guide under vertical load (Fv40): (a) load\u2013displacement relationship and (b) centers' positions of grooves.", + "texts": [ + "1=3 ; (2) where E1, E2 and \u03bd1, \u03bd2 are the elastic moduli and Poisson ratios respectively of the material of ball, rail and carriage, \u03bc is named as Hertz coefficient related with the geometry of the ball bearing, and P \u03c1 is the main curvature of the ball bearing. The parameters \u03bc, E1, E2, \u03bd1, \u03bd2 and P \u03c1 are constant for a certain contact model, so Eq. (2) can be simplified as \u03b40 \u00bc 2\u03b7P2=3 0 ; (3) with \u03b7\u00bc 3\u03bc 2 1 12 1 \u03bd21 E1 \u00fe1 \u03bd22 E2 2 X \u03c1 !1=3 ; where \u03b7 is named as resemble flexibility coefficient used to describe the relation between the elastic deformation and the contact force. Under vertical load Fv, the altered model is shown in Fig. 2. Because of the symmetry of the structure, we only analyze the ball deformations in grooves 1 and 4. To simplify the processing of analysis, the rail is fixed. v is the relative displacement between carriage and rail, Q1 and Q4 are the nominal contact forces, \u03b41 and \u03b44 are the deformations of ball bearings, and \u03b81 and \u03b84 are the nominal contact angles of grooves 1 and 4, respectively. Because we presume carriage and rail as rigid, the curvature centers of grooves of rail do not change, but those of carriage transform to O0 c1 and O0 c4. From Fig. 2 (b), the distances s1 and s4 between centers of carriage and rail are satisfied as given below: s1 cos \u03b81 \u00bc s0 cos \u03b80; (4a) s1 sin \u03b81 \u00bc s0 sin \u03b80\u00fev; (4b) s4 cos \u03b84 \u00bc s0 cos \u03b80; (4c) s4 sin \u03b84 \u00bc s0 sin \u03b80 v: (4d) According to the relationship between the distances s1, s4 and the deformations \u03b41, \u03b44, we can obtain s1 \u00bc 2r d0\u00fe\u03b41; (5a) s4 \u00bc 2r d0\u00fe\u03b44: (5b) Based on the Hertz contact theory, the deformations \u03b41 and \u03b44 are obtained as \u03b41 \u00bc 2\u03b7Q2=3 1 ; (6a) \u03b44 \u00bc 2\u03b7Q2=3 4 : (6b) To obtain the relationship between Fv and v, we establish the mechanical balance equation of carriage, which can be expressed as XNb j \u00bc 1 Q1 sin \u03b81\u00feQ2 sin \u03b82 Q3 sin \u03b83 Q4 sin \u03b84 \u00bc Fv: (7) where Nb represents the number of balls in every groove" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000837_j.optlaseng.2009.06.010-Figure3-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000837_j.optlaseng.2009.06.010-Figure3-1.png", + "caption": "Fig. 3. An experimental buildup of a four-layer wall fabricated using the LSFF process.", + "texts": [ + " The powder used in the experiment was 98% pure on a metal basis. The laser beam had a spot diameter of 1.4 mm at the deposition zone, and the same gas used for the powder delivery was also used as shielding gas to protect the optics. Two XCIB hightemperature Inconel overbraided ceramic fiber insulated type K thermocouples were used to measure the temperature around the melt pool. For a 15 mm straight path, the deposition of four layers was carried out on a substrate of sandblasted SS304L plate with dimension of 25 20 5 mm3 as shown in Fig. 3. To verify the numerical model, the simulations and experiments were all performed with the same process parameters listed in Table 1. All descriptions regarding the accuracies of the numerical analyses in terms of the time-dependent temperature distributions and stress/strain fields as well as the geometry of the deposited material in a layer-by-layer time-dependent deposition fashion are provided in details by Alimardani et al. [2]. To address the verification process, a comparison between the average heights of each layer obtained from experimental and numerical results showed a maximum average relative error of 9" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003353_j.msea.2019.03.014-Figure1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003353_j.msea.2019.03.014-Figure1-1.png", + "caption": "Fig. 1. Rhombic dodecahedron unit cell and its geometrical characteristics.", + "texts": [ + " The obtained results allowed the application of the GibsonAsbhy model with the real parameters of the lattice (relative density, relative modulus and relative strength) instead of the designed one. The current study focused on the analysis of microlattice structures produced via EBM, from an Arcam Ti6Al4V ELI (Grade 23) fine powder. The used titanium alloy contains reduced levels of oxygen, nitrogen, carbon and iron and its particle size distribution is between 45 and 100 \u03bcm. The selected unit cell was the rhombic dodecahedron (RD), which is shown in Fig. 1. Three different configurations were obtained by varying the diameter (D) of the unit cell and the struts length (L). The designed geometrical parameters of the three investigated structures are reported in Table 1. Experimental investigations regarded both the parent material and the lattice structures. The base material characterisation was necessary to verify the conformity to ASTM F3001 of the chemical and mechanical properties of the structures produced by EBM. A XRF spectrometer was used to obtain the chemical composition of a bulk sample produced via EBM" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001587_9781118824603-Figure8.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001587_9781118824603-Figure8.1-1.png", + "caption": "Figure 8.1 Distributed winding stator.", + "texts": [ + "1-7) The reason for the introduction of these electrical angles is that it will allow our analysis to be expressed so that all machines mathematically appear to be 2-pole machines, thereby providing considerable simplification. Rotating machinery generally has multiple sets of windings known as phases. Commonly, in a three-phase machine, the three phase stator windings are referred to as the a-phase, b-phase, and c-phase, respectively, and denoted as, bs, and cs. In distributed winding machines, such as shown in Figure 8.1, these windings may be described using either a discrete or continuous formulation. The discrete description is Ns Ns Ns Ss Ss Ss P=6 Sr SrSr Nr Nr Nr based on the number of conductors in each slot; the continuous description is an abstraction based on an ideal distribution. A continuously distributed winding is desirable in order to achieve uniform torque. However, the conductors that make up the winding are not placed continuously around the stator, but are rather placed into slots in the machine\u2019s stator and rotor structures, thereby leaving room for the stator and rotor teeth that are needed to conduct magnetic flux", + " In general a ring mapped index may be expressed as mod i\u2212 1; Sy + 1, where i is the original index and where mod a; b returns a modulus b. Since Mx;i is the net number of conductors and Cx;i is the number of canceled conductors, the total number of (unsigned) end conductors between slots i\u2212 1 and i is Ex;i = Mx;i + 2Cx;i (8.1-28) The total number of end conductors is defined as Ex = XSy i= 1 Ex;i (8.1-29) Before proceeding, it is convenient to consider some common machine winding schemes. Consider the 4-pole, 3.7-kW, 1800-rpm induction machine shown in Figure 8.1. As can be seen, the stator has 36 slots, which corresponds to three slots per pole per phase. Figure 8.7 illustrates a common winding pattern for such a machine. Therein, each conductor symbol represents N conductors, going in or coming out as indicated. This is a double-layer winding, with each slot containing two groups of conductors. Both single- and double-layer winding arrangements are common in electric machinery. The number of a-phase conductors for the first 18 slots may be expressed as Nasj1\u221218 =N 0 0 0 1 2 2 1 0 0 0 0 0\u2212 1\u2212 2\u2212 2\u2212 1 0 0 (8" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0001793_tmech.2017.2748887-Figure2-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0001793_tmech.2017.2748887-Figure2-1.png", + "caption": "Fig. 2. Motor load test bench.", + "texts": [ + " From (14)\u2013(15) and the definition of \u03be(t) in (17), the information of x3(t) is reflected in the event-triggered output measurement \u03be(t); through the extended state observer in (16), x\u03023(t) tries to learn the determined but unknown behavior of x3(t) by exploring this information. In other words, taking advantage of the knowledge of \u03be(t), the dynamic behavior of x\u03023(t) mimics that of x3(t). In particular, (37) of Theorem 1 indicates that the difference between x\u03023(t) and x3(t) can be sufficiently small as t \u2192 \u221e for \u03b5 \u2208 (0, \u03b5\u2217). In this section, the introduced event-triggered control scheme is evaluated on a dc torque motor platform Fig. 2. The experimental platform mainly consists of a motor load test bench and an embedded measurement and control test bench. The motor load test bench contains a permanent-magnet dc torque motor (130LYX03), a magnetic brake, a speed reducer, an inertial loading mechanism, and a speed sensor (JN338). By regulating the input current, the magnetic brake can simulate the adjustable sliding friction load. The embedded measurement and control test bench is regarded as a controller, since it can generate signals to control the motor and process the received signals" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003857_j.engfailanal.2018.08.028-Figure13-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003857_j.engfailanal.2018.08.028-Figure13-1.png", + "caption": "Fig. 13. Nephograms of comprehensive deformation: (a) health; (b) l3= 9mm; (c) l3= 19mm; (d) l3= 29mm.", + "texts": [ + " The deformation caused by the end face penetrating crack is the largest among all crack types due to its minimum healthy part (see Fig. 11e), so the loss of the stiffness is largest under this crack type. It should be noted that the proposed method only costs 2min, while the FE method costs 2.5 h. The TVMS obtained from the proposed method and the FE method under different crack growth distances along face width l3= 9, 19, 29mm and constant q0= 2.5mm, qe= 0.5mm and l1= 3mm is shown in Fig. 12. The comprehensive deformation at moment E under different l3 is shown in Fig. 13. The mesh stiffness at moments D and E is listed in Table 5, and the maximum error is about 3.93%. The increase of l3 leads to the reduction of the healthy part, so the deformation increases (see Fig. 13), and the reduction of the TVMS becomes more significant (see Fig. 12). The TVMS obtained from the proposed method and the FE method under different crack growth distances along tooth depth l2= 0, 3, 6mm and constant q0= 2.5mm, qe= 0.5mm and l1= 2mm is shown in Fig. 14. The comprehensive deformation at moment E under different l2 is shown in Fig. 15. The mesh stiffness at moments D and E is listed in Table 6, and the maximum error is about 5.37%. With the increase of l2, the loss of stiffness decreases slightly (see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0003025_tie.2018.2877165-Figure20-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0003025_tie.2018.2877165-Figure20-1.png", + "caption": "Fig. 20. Test platforms. (a) Static test platform. (b) Dynamic test platform.", + "texts": [ + " 18 (c)-(f). Therefore, the magnetization of the mechanical components in the end of the proposed machines (CPM2, CPM3, HPM1 and HPM2) can be effectively eliminated. V. EXPERIMENTAL VERIFICATION AND DISCUSSION The proposed HPM1 is prototyped for the verification of previous analyses. Fig. 19 show the photos of the 9-slot stator and 10-pole HPM1 rotor. For the tested line-line back-EMF, a DC motor is used to drive the machine to the rated speed. The platform for testing the static torque is shown in Fig. 20 (a), and it is measured based on the reported method [30]. Fig. 20 (b) shows the dynamic test platform. A DC-motor-based dynamometer is adopted as a variable load. Moreover, an encoder is employed to detect the rotor position of the prototype, whilst a torque transducer is built in the experimental platform to measure the dynamic output torque. Moreover, a tesla meter with hall sensor is adopted to test the leakage flux density at the end shaft, as shown in Fig. 21 (a). Fig. 22 shows the FE predicted and experimental cogging torques with rotor position. It can be seen that the period of the measured result agrees with the FE predicted one" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000523_978-94-009-5802-9-Figure2.1-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000523_978-94-009-5802-9-Figure2.1-1.png", + "caption": "Fig. 2.1 Directions of the conductors in the armature circuits.", + "texts": [ + " The transfonner voltages can thus be expressed by using inductance coefficients as in Eqns. 0.5). Ifthe distribution of the flux density is assumed to be sinusoidal, certain relations hold between the inductance coefficients which are of importance in connection with the two-axis theory (see Eqns. (2.8)). The transformer voltage between the direct-axis brushes due to a direct-axis flux can be found by calculating the voltages induced in individual turns and integrating over half the circumference. In Fig. 2.1a the dots and crosses on the conductors indicate the directions in which the armature conductors are traversed as the circuit is followed through in the positive direction between the direct-axis brushes. A positive current in this circuit would set up a flux along the positive direct axis in accordance with the convention stated on p. 6. If the direct-axis flux density curve is sinusoidal, with maximum value Bm, then B =Bm cos (J (a) Direct axis. (b) Quadrature axis. and .rr/2 m d = j Blrd(J = 2Bm lr ", + "1), the flux linkage for a sinusoidal flux density wave is: I/!md = md Z\u2022 Similarly, if the quadrature-axis flux distribution is sinusoidal, the transformer voltage is: Uqt = pI/! m q where I/!mq = mq Z 2.1.2 Rotational voltages in the armature (2.2) The rotational voltage induced between the quadrature-axis brushes due to the armature rotation through a direct-axis flux, The Primitive Machine 31 can be found by calculating the voltages in the individual conductors and integrating over half the circumference. In Fig. 2.1 b the dots and crosses on the conductors indicate the directions in which the armature conductors are traversed as the circuit is followed through in the positive direction between the quadrature axis brushes. The voltage in the positive direction in the conductors of coil QQ' occupying a small part of the periphery subtending an angle de is, by the flux-cutting rule: The direct-axis flux is given by: n/2 it is equivalent to the rotation matrix G R B. Expanding eit = 1+ usin \u00a2 + u2 (1 - eos\u00a2) gzves (3.104) [ ui vers \u00a2 + c\u00a2 UlU2vers \u00a2 - U3S\u00a2 UlU3vers \u00a2 + U2S\u00a2 ] eit = UlU2vers \u00a2 + U3S\u00a2 u~ vers \u00a2 + c\u00a2 U2U3vers \u00a2 - Ul s\u00a2 UlU3vers \u00a2 - U2S\u00a2 U2U3vers \u00a2 + Ul s\u00a2 u5vers \u00a2 + c\u00a2 (3.105) which is equal to the axis-angle Equation (3.5), and therefore, Ru, GRB l eos \u00a2 +uuT vers \u00a2 + usin \u00a2 . Example 55 * New form of the Rodriguez rotation formula. Considering Figure 3.3 we may write (3.106) to find eos~ IMPI 1N:MIMPi sin ~ IN:MI IMPilu x N:M (3.107) (3.108) (3.109) 3. Orientation Kinematics 95 Now using the following equalities ---+ 2MP' --t 2NM --t --t N P' -NP it x (NP +FiP) --t --t = N P' - NP --t --t N P' +NP r' - r it x (r' + r) (3.110) (3.111) (3.112) (3.113) we can write an alterna tive form of the Rodriguez rotation formula cos~ (r' - r ) = sin ~ it x (r' + r) or (r ' - r ) = tan ~it x (r ' + r ) . Example 56 * Rodriguez vector. Th e vector (3.114) (3.115) (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0002912_1.4039092-Figure19-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0002912_1.4039092-Figure19-1.png", + "caption": "Fig. 19 The distribution of the residual stress component in the build direction, rzz, predicted by the simulation based on new framework for the large part", + "texts": [ + " The simulation time for the completion of each discretization step is shown in Fig. 18. The plot shows that the simulation time, consistent with the total DoF, also remained constant throughout the analysis. The variation of simulation time for the new framework is consistent with the variation of DoFs (the variation of DoF is not clearly visible in Fig. 17 due to rapid growth in DoFs for the conventional framework, but can be validated by changing the scale of the graph). The distribution of residual stress component along the build direction, rzz, is shown in Fig. 19 as an example result for the large part. According to the distribution, the variation of rzz along the length is not very significant, but a large variation from a compressive stress on the inside surface of a tensile stress on the outside surface can be seen. In this paper, the development of a new computationally efficient FE framework for problems involving a continuous change in the model geometry is reported. The new framework allows the introduction of updated discretized geometries with selectively coarsened mesh at regular intervals during the simulation process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_3_0000115_9780470682906-Figure12.14-1.png", + "original_path": "designv10-3/openalex_figure/designv10_3_0000115_9780470682906-Figure12.14-1.png", + "caption": "Figure 12.14.2 Basic strut-and-arm geometry for analysis of the effective upper arm length.", + "texts": [ + " The strut-and-arm suspension, commonly just called a strut suspension, typically uses a basically transverse lower arm, with the upper arm and wheel carrier (wheel upright) replaced by an integrated unit of wheel carrier, slider and spring\u2013damper unit, acting on an upper trunnion where it connects to the inner part of the bodywork. The upper joint is a really a combination of the sliderwith a ball joint, or rubber bush, the latter allowing various angular movements. The combination acts geometrically like a trunnion, which is a slider passing right through a swivel joint (in two dimensions) or ball joint (in three dimensions), as seen in Figure 12.14.1. The steering action normally acts about a steering axis passing through the lower ball joint and the trunnion point. However, a separate steering axis could be provided, as used to be done on some double-transverse-arm suspensions. The two-dimensional analytical methods applied to the double-transverse-arm suspension are easily adapted to the common strut suspension. The one issue to be resolved is how to find the equivalent upper arm. The plane of the equivalent upper arm is through the trunnion point and perpendicular to the strut slider centreline. Intersecting this with the transverse vertical plane gives the equivalent arm, as usual, but with length yet to be determined. Note that the strut slider is generally not alignedwith the ball joint on the lower arm, so not coinciding with the steering axis which passes through the two joints, Figure 12.14.1. The lower arm angle is uYL, positivewhen the outer ball joint is higher than the axis, but usually negative in the static position. The upper arm length can simply be taken effectively as infinite, that is, as having zero shortness. A slightly better equivalent is to take it to be equal to the swing arm length in front view and the pitch arm length in side view. In Figure 12.14.2, AB is the lower arm, E is the foot of the perpendicular from B onto the slider centreline, DE is the slider centreline, and BD is the steering axis through the lower ball joint B and trunnion centre D. Figure 12.14.2(b) shows the velocity diagram for a lower arm angular velocityW. The fixed points are A and C. The line ab has length value (units m/s) ab \u00bc VLAB at the angle c \u00bc uYL. The line cd is perpendicular to CD, and parallel to slider DE. Line bd is perpendicular to BD. Triangle cbd is similar to CBD. The radius of the movement arc of D, the velocity of D and the angular velocity of ED are related by VD \u00bc vEDRD The angular velocity is vED \u00bc ed LED The radius of the arc is therefore RD \u00bc VD vED \u00bc cd LED ed \u00bc LCD so the effective centre of the arc is at C, on the line BA, and the effective length of the upper arm is LYU RS Adapting Table 12" + ], + "surrounding_texts": [] + } +] \ No newline at end of file